diff --git a/phase_diagram/LiAl_poscar b/phase_diagram/LiAl_poscar
new file mode 100644
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--- /dev/null
+++ b/phase_diagram/LiAl_poscar
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diff --git a/phase_diagram/exercise_2.ipynb b/phase_diagram/exercise_2.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..3c4bd918f98889117a86907a639aff8f22810ef3
--- /dev/null
+++ b/phase_diagram/exercise_2.ipynb
@@ -0,0 +1,318 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "e9cdf324-526d-426f-82f3-4dea4112355e",
+ "metadata": {},
+ "source": [
+ "<table border=\"0\">\n",
+ " <tr>\n",
+ " <td style=\"width:30%\"><img src=\"img/potentials_logo.png\" width=\"100%\" align=\"justify\"></td>\n",
+ " <td style=\"width:70%\"> <p style=\"width:100%;color:#B71C1C;font-size:24px;text-align:justify\"> From electrons to phase diagrams </p> <p style=\"width:100%,font-size:16px\">Day 03 Hands-on session exercise (Part 2)</td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "026431fb-44fa-4b99-8fff-d0a1a9b642e2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from helpers import potential_list\n",
+ "from pyiron_atomistics import Project\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "08881280-a4a9-40c1-b8a5-38d176bb01da",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pr = Project('exe2') "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "78f75741-2f78-4e2a-8c07-470336383dfd",
+ "metadata": {
+ "tags": []
+ },
+ "source": [
+ "### Task 1: Calculate free energy of FCC Al at 500 K, 10000 bar"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5e7a9194-4eee-450b-b83a-9e5315ad4d00",
+ "metadata": {},
+ "source": [
+ "Use a lattice constant of 4.099 for the BCC structure"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a3bd0dee-2d28-44ca-a3c4-0f0ad7569246",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "46f74c25-174e-44a8-9803-75c9eeaf8ba7",
+ "metadata": {},
+ "source": [
+ "### Task 2: Does Al have a solid-solid phase tranformation?\n",
+ "\n",
+ "Calculate the free energy of Al in BCC and FCC structures in the temperature range of 500-1000 K. See if there is a solid-solid phase transformation. Use lattice constant of 3.264 for BCC, and 4.099 for FCC."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "db1aea00-abb6-434e-bb98-7d99cde10bb7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure_fcc = pr.create.structure.ase.bulk('Al', cubic=True, a=4.099).repeat(5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "db7ad739-0952-40aa-ad81-c72b275f8dff",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job al_fcc_600 was saved and received the ID: 162\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "al_fcc = pr.create.job.Calphy(\"al_fcc_600\", delete_aborted_job=True)\n",
+ "al_fcc.potential = potential_list[0]\n",
+ "al_fcc.structure = structure_fcc\n",
+ "al_fcc.server.cores = 4\n",
+ "al_fcc.calc_free_energy(temperature=[500, 1000], \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ "al_fcc.run()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "d8719e67-f884-4e01-9729-91d09275a919",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure_bcc = pr.create.structure.ase.bulk('Al', \n",
+ " crystalstructure='bcc',\n",
+ " cubic=True, a=3).repeat(5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "1b8775e0-8b9b-45bf-b0ad-829feb171eec",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job al_bcc_600 was saved and received the ID: 161\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "al_bcc = pr.create.job.Calphy(\"al_bcc_600\", delete_aborted_job=True)\n",
+ "al_bcc.potential = potential_list[0]\n",
+ "al_bcc.structure = structure_bcc\n",
+ "al_bcc.server.cores = 4\n",
+ "al_bcc.calc_free_energy(temperature=[500, 1000], \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ "al_bcc.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "eae4fe4d-a679-48bb-b706-0b9e14603f00",
+ "metadata": {},
+ "source": [
+ "Plot the solution"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "107c1a02-a2bf-47b4-a9fb-dff78d32ef74",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7f445de4b9a0>"
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(al_fcc.output.temperature, al_fcc.output.energy_free,\n",
+ " label=\"Al FCC\", color='#C62828')\n",
+ "plt.plot(al_bcc.output.temperature, al_bcc.output.energy_free,\n",
+ " label=\"Al BCC\", color='#006899')\n",
+ "plt.xlabel(\"Temperature (K)\")\n",
+ "plt.ylabel(\"Free energy (eV/K)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0be8c561-51d5-4335-b3cd-6538bd52894f",
+ "metadata": {},
+ "source": [
+ "As expected the free energy of the FCC lattice is lower than BCC:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a280a075-7f1e-4ec1-bd25-70b47c687b14",
+ "metadata": {},
+ "source": [
+ "### Task 3: Calculate melting temperature of Al at 10000 bar"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1df200ab-5785-4565-b05f-3d39bf050ef3",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9a812126-0cf4-4b08-9e11-00dbcb9585db",
+ "metadata": {},
+ "source": [
+ "### Task 4: Calculate the melting temperature of Li\n",
+ "\n",
+ "The potential for Li can be accessed as `potential_list[1]`. Use temperature range of 350-500. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "0b321950-f17e-43a7-b5f1-249e901ab36f",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "workshop",
+ "language": "python",
+ "name": "workshop"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/phase_diagram/exercise_3.ipynb b/phase_diagram/exercise_3.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..1d0377c10dd6d01713689b63307636025189700a
--- /dev/null
+++ b/phase_diagram/exercise_3.ipynb
@@ -0,0 +1,107 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "763c1b9b-9b87-4ab9-9092-a2b4d76fa4be",
+ "metadata": {},
+ "source": [
+ "<table border=\"0\">\n",
+ " <tr>\n",
+ " <td style=\"width:30%\"><img src=\"img/potentials_logo.png\" width=\"100%\" align=\"justify\"></td>\n",
+ " <td style=\"width:70%\"> <p style=\"width:100%;color:#B71C1C;font-size:24px;text-align:justify\"> From electrons to phase diagrams </p> <p style=\"width:100%,font-size:16px\">Day 03 Hands-on session exercise (Part 3)</td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "4c028a0d-d46b-4fbb-9b8e-1956a7d5215d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "from pyiron_atomistics import Project\n",
+ "from helpers import *\n",
+ "from calphy.integrators import kb"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "dbab0aaf-cdd5-48f7-b08e-c051e8e63d84",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pr = Project('exe2') "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a72ce933-f6c2-4da6-920b-937aea94a8cc",
+ "metadata": {},
+ "source": [
+ "### Calculate the melting temperature of the B32 structure"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "c3ecfde2-aaab-4c8d-ab4d-69d8ae8cf2f8",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b287e662-f040-4ffc-997a-64f4820da418",
+ "metadata": {},
+ "source": [
+ "### Calculate free energy as function of composition of Li"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1da9205a-bbe3-40d4-b198-e4fb049e17c0",
+ "metadata": {},
+ "source": [
+ "- Choose composition of Li from 0 to 0.25\n",
+ "- Choose a temperature from 700 to 1000\n",
+ "- Choose B32 and fcc structures\n",
+ "- Calculate and plot the free energy curves\n",
+ "- Perform common tangent construction\n",
+ "- Identify regions of stability of the two structures"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2c84e7b6-b9df-456a-9f9f-f03d54f59b28",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "workshop",
+ "language": "python",
+ "name": "workshop"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/phase_diagram/export.csv b/phase_diagram/export.csv
new file mode 100644
index 0000000000000000000000000000000000000000..1bed3b89e5ee485ab06691d5b0d38f0bb5e5c1c2
--- /dev/null
+++ b/phase_diagram/export.csv
@@ -0,0 +1,19 @@
+,id,status,chemicalformula,job,subjob,project,timestart,timestop,totalcputime,computer,hamilton,hamversion,parentid,masterid
+0,0,finished,,x0_sol,/x0_sol,lial/lial_thermodynamics_composition,2022-05-27 00:15:29.733653,2022-05-27 00:21:34.589072,364.0,pyiron@cmleo26#4,Calphy,0.4,,
+1,1,finished,,x0_lqd,/x0_lqd,lial/lial_thermodynamics_composition,2022-05-27 00:21:34.911022,2022-05-27 00:26:39.285689,304.0,pyiron@cmleo26#4,Calphy,0.4,,
+2,2,finished,,x0_alli,/x0_alli,lial/lial_thermodynamics_composition,2022-05-27 00:26:39.609501,2022-05-27 00:29:36.121032,176.0,pyiron@cmleo26#4,Calphy,0.4,,
+3,3,finished,,x1_sol,/x1_sol,lial/lial_thermodynamics_composition,2022-05-27 00:29:36.439161,2022-05-27 00:34:08.102581,271.0,pyiron@cmleo26#4,Calphy,0.4,,
+4,4,finished,,x1_lqd,/x1_lqd,lial/lial_thermodynamics_composition,2022-05-27 00:34:08.393575,2022-05-27 00:39:53.247222,344.0,pyiron@cmleo26#4,Calphy,0.4,,
+5,5,finished,,x1_alli,/x1_alli,lial/lial_thermodynamics_composition,2022-05-27 00:39:53.742922,2022-05-27 00:44:11.875476,258.0,pyiron@cmleo26#4,Calphy,0.4,,
+6,6,finished,,x2_sol,/x2_sol,lial/lial_thermodynamics_composition,2022-05-27 00:44:12.178900,2022-05-27 00:50:18.355354,366.0,pyiron@cmleo26#4,Calphy,0.4,,
+7,7,finished,,x2_lqd,/x2_lqd,lial/lial_thermodynamics_composition,2022-05-27 00:50:18.664603,2022-05-27 00:54:28.207543,249.0,pyiron@cmleo26#4,Calphy,0.4,,
+8,8,finished,,x2_alli,/x2_alli,lial/lial_thermodynamics_composition,2022-05-27 00:54:28.696677,2022-05-27 01:01:56.467409,447.0,pyiron@cmleo26#4,Calphy,0.4,,
+9,9,finished,,x3_sol,/x3_sol,lial/lial_thermodynamics_composition,2022-05-27 01:01:56.729048,2022-05-27 01:07:48.331324,351.0,pyiron@cmleo26#4,Calphy,0.4,,
+10,10,finished,,x3_lqd,/x3_lqd,lial/lial_thermodynamics_composition,2022-05-27 01:07:48.548404,2022-05-27 01:13:14.236686,325.0,pyiron@cmleo26#4,Calphy,0.4,,
+11,11,finished,,x3_alli,/x3_alli,lial/lial_thermodynamics_composition,2022-05-27 01:13:14.712876,2022-05-27 01:18:11.052385,296.0,pyiron@cmleo26#4,Calphy,0.4,,
+12,12,finished,,x4_sol,/x4_sol,lial/lial_thermodynamics_composition,2022-05-27 01:18:11.514232,2022-05-27 01:24:25.968831,374.0,pyiron@cmleo26#4,Calphy,0.4,,
+13,13,finished,,x4_lqd,/x4_lqd,lial/lial_thermodynamics_composition,2022-05-27 01:24:26.355495,2022-05-27 01:29:27.170347,300.0,pyiron@cmleo26#4,Calphy,0.4,,
+14,14,finished,,x4_alli,/x4_alli,lial/lial_thermodynamics_composition,2022-05-27 01:29:27.552810,2022-05-27 01:59:49.532453,1821.0,pyiron@cmleo26#4,Calphy,0.4,,
+15,15,finished,,xp_sol,/xp_sol,lial/lial_thermodynamics_composition,2022-05-27 06:49:08.217437,2022-05-27 06:51:56.469011,168.0,pyiron@cmleo26#4,Calphy,0.4,,
+16,16,finished,,xp_lqd,/xp_lqd,lial/lial_thermodynamics_composition,2022-05-27 06:51:56.705974,2022-05-27 06:54:42.587704,165.0,pyiron@cmleo26#4,Calphy,0.4,,
+17,17,finished,,xp_alli,/xp_alli,lial/lial_thermodynamics_composition,2022-05-27 07:20:21.591321,2022-05-27 07:22:29.775974,128.0,pyiron@cmleo26#4,Calphy,0.4,,
diff --git a/phase_diagram/helpers.py b/phase_diagram/helpers.py
index bcd67aadf80889e4ca46ee901c83346ae13edd96..0b9793538608380515764ccbb9b332ed34d9b700 100644
--- a/phase_diagram/helpers.py
+++ b/phase_diagram/helpers.py
@@ -1,5 +1,8 @@
import pandas as pd
import os
+import numpy as np
+from calphy.integrators import kb
+from scipy.optimize import fsolve
file_location = "../potentials/AlLi.eam.fs"
pot_al = pd.DataFrame({
@@ -23,5 +26,93 @@ pot_alli = pd.DataFrame({
'Species': [['Al', 'Li']],
'Config': [['pair_style eam/fs\n', 'pair_coeff * * AlLi.eam.fs Al Li\n']]
})
+pot_lial = pd.DataFrame({
+ 'Name': ['LiAl_eam'],
+ 'Filename': [[os.path.abspath(file_location)]],
+ 'Model': ["EAM"],
+ 'Species': [['Li', 'Al']],
+ 'Config': [['pair_style eam/fs\n', 'pair_coeff * * AlLi.eam.fs Li Al\n']]
+})
+potential_list = [pot_al, pot_li, pot_alli, pot_lial]
+
+def fe_at(p, temp, threshold=1E-1):
+ """
+ Get the free energy at a given temperature
+
+ Parameters
+ ----------
+ p: pyiron Job
+ Pyiron job with calculated free energy and temperature
+
+ temp: float
+ Required temperature
+
+ threshold: optional, default 1E-1
+ Minimum difference needed between required temperature and temperature found in pyiron job
+
+ Returns
+ -------
+ float: free energy value at required temperature
+ """
+ arg = np.argsort(np.abs(p.output.temperature-temp))[0]
+ th = np.abs(p.output.temperature-temp)[arg]
+ if th > threshold:
+ raise ValueError("not a close match, threshold %f"%th)
+ return p.output.energy_free[arg]
+
+def normalise_fe(fe_arr, conc_arr):
+ """
+ Get the enthalpy of mixing by fitting and subtracting a straight line connecting the end points.
+
+ Parameters
+ ----------
+ fe_arr: list of floats
+ array of free energy values as function of composition
+
+ conc_arr: list of floats
+ array of composition values
+
+ Returns
+ -------
+ norm: list of floats
+ normalised free energy
+
+ m: float
+ slope of the fitted line
+
+ c: float
+ intercept of the fitted line
+ """
+ m = (fe_arr[-1]-fe_arr[0])/(conc_arr[-1]-conc_arr[0])
+ c = fe_arr[-1]-m*(conc_arr[-1]-conc_arr[0])
+ norm = fe_arr-(m*conc_arr+c)
+ return norm, m, c
-potential_list = [pot_al, pot_li, pot_alli]
\ No newline at end of file
+def find_common_tangent(fe1, fe2, guess_range):
+ """
+ Do a common tangent construction between two free energy curves.
+
+ Parameters
+ ----------
+ fe1: numpy array
+ first free energy curve
+
+ fe2: numpy array
+ second free energy curve
+
+ guess_range: list of floats length 2
+ The guess range to find end points of the common tangent
+
+ Returns
+ -------
+ res: list of floats length 2
+ The end points of the common tangent
+ """
+ def _ct(x, p1, p2):
+ p1der = np.polyder(p1)
+ p2der = np.polyder(p2)
+ term1 = np.polyval(p1der, x[0])-np.polyval(p2der, x[1])
+ term2 = (np.polyval(p1, x[0]) - np.polyval(p2, x[1]))/(x[0]-x[1]) - np.polyval(p1der, x[0])
+ return [term1, term2]
+ res = fsolve(_ct, guess_range, args=(fe1, fe2))
+ return res
\ No newline at end of file
diff --git a/phase_diagram/img/Picture1.png b/phase_diagram/img/Picture1.png
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diff --git a/phase_diagram/img/Picture2.png b/phase_diagram/img/Picture2.png
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diff --git a/phase_diagram/img/alli_phase_diagram.jpg b/phase_diagram/img/alli_phase_diagram.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..f6d9b96a56080172298faf6f9dbf54fee413a255
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diff --git a/phase_diagram/img/calphy_logo.png b/phase_diagram/img/calphy_logo.png
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index 0000000000000000000000000000000000000000..04bfc422a1f333eb5ae495e43027be80c752b22d
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diff --git a/phase_diagram/img/cimg1.png b/phase_diagram/img/cimg1.png
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diff --git a/phase_diagram/img/cimg2.png b/phase_diagram/img/cimg2.png
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diff --git a/phase_diagram/img/cimg3.png b/phase_diagram/img/cimg3.png
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diff --git a/phase_diagram/img/cimg4.png b/phase_diagram/img/cimg4.png
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diff --git a/phase_diagram/img/cimg5.png b/phase_diagram/img/cimg5.png
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diff --git a/phase_diagram/img/cimg6.png b/phase_diagram/img/cimg6.png
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diff --git a/phase_diagram/img/fig1.png b/phase_diagram/img/fig1.png
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diff --git a/phase_diagram/img/logo.png b/phase_diagram/img/logo.png
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diff --git a/phase_diagram/img/phase_dia_1.png b/phase_diagram/img/phase_dia_1.png
new file mode 100644
index 0000000000000000000000000000000000000000..b8b289cb638b803f726137b1894339d6be7f1d72
Binary files /dev/null and b/phase_diagram/img/phase_dia_1.png differ
diff --git a/phase_diagram/img/potentials_logo.png b/phase_diagram/img/potentials_logo.png
new file mode 100644
index 0000000000000000000000000000000000000000..53566714c76d7a311bba76c33e94f8a1235cb738
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diff --git a/phase_diagram/lial.tar.gz b/phase_diagram/lial.tar.gz
new file mode 100644
index 0000000000000000000000000000000000000000..ed16e78f77aa40b99c3dc5b8dd9bb4b38a8135be
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diff --git a/phase_diagram/tutorial.ipynb b/phase_diagram/tutorial.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..95f87b443943547baebc90ac1968a77d0fad10c0
--- /dev/null
+++ b/phase_diagram/tutorial.ipynb
@@ -0,0 +1,188 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "10444b16-f852-48eb-ab46-b5ce43e962b3",
+ "metadata": {},
+ "source": [
+ "<table border=\"0\">\n",
+ " <tr>\n",
+ " <td style=\"width:30%\"><img src=\"img/potentials_logo.png\" width=\"100%\" align=\"justify\"></td>\n",
+ " <td style=\"width:70%\"> <p style=\"width:100%;color:#B71C1C;font-size:24px;text-align:justify\"> From electrons to phase diagrams </p> <p style=\"width:100%,font-size:16px\">Day 03 Tutorial</td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ad615a36-1703-4c42-822f-062109a99e3b",
+ "metadata": {},
+ "source": [
+ "In this notebook, we will use the potentials fitted in the previous days for the calculation of thermodynamic properties such as Helmholtz and Gibbs free energies, which in turn can be used for the calculation of phase diagrams. We will discuss calphy, the tool for automated calculation of free energies, and the methology involved.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9b8152d6-5edb-4be2-9d7b-2b80017f70bb",
+ "metadata": {},
+ "source": [
+ "---"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bfdfcbbf-cc13-4b43-8b6e-31bc25cd4212",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Phase diagrams and how to calculate them </font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c53d510c-cd30-4e38-9a42-1d84132c0e19",
+ "metadata": {},
+ "source": [
+ "<table border=\"0\">\n",
+ " <tr>\n",
+ " <td style=\"width:40%\"><img src=\"img/phase_dia_1.png\" width=\"100%\" align=\"justify\"></td>\n",
+ " <td style=\"width:60%\"> <p style=\"font-size:14px\">Phase diagrams provide a wealth of information such as: coexisting lines, melting temperature, phase stability, nucleation mechanism. </p></td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "61ecb35b-a285-45d8-a8e5-a6a1f62d6459",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Calculation of phase diagrams: the essential ingredients</font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7d819917-9a56-4589-9627-baff1e4296f3",
+ "metadata": {},
+ "source": [
+ "<table border=\"0\">\n",
+ " <tr>\n",
+ " <td style=\"width:50%\"><img src=\"img/cimg4.png\" width=\"100%\" align=\"justify\"></td>\n",
+ " <td style=\"width:50%\"> <p style=\"font-size:14px\">Phase diagrams can be evaluated from free energy diagrams. <br> <br>\n",
+ " The required input are: <br> <br>\n",
+ " ● $G(P, T)$ for unary systems <br>\n",
+ " ● $G(x, T)$ for binary systems </p></td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6198fc41-3bc2-4436-a272-1a168e44307a",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Calculation of free energies: Thermodynamic integration </font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "607f3c8d-4e49-4fb6-be8d-39999eba5f7b",
+ "metadata": {
+ "tags": []
+ },
+ "source": [
+ "<img src=\"img/fig1.png\" width=\"1000\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8bab199b-a1a0-42eb-a595-cd545d23873a",
+ "metadata": {},
+ "source": [
+ "- free energy of reference system are known: Einstein crystal, [Uhlenbeck-Ford model](https://doi.org/10.1063/1.4967775)\n",
+ "- the two systems are coupled by \n",
+ "$$\n",
+ "H(\\lambda) = \\lambda H_f + (1-\\lambda)\\lambda H_i\n",
+ "$$\n",
+ "- Run calculations for each $\\lambda$ and integrate \n",
+ "$$\n",
+ "G_f = G_i + \\int_{\\lambda=0}^1 d\\lambda \\bigg \\langle \\frac{\\partial H(\\lambda)}{\\partial \\lambda } \\bigg \\rangle\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4756bb61-6a01-48f8-98b1-9d076b7dccc0",
+ "metadata": {},
+ "source": [
+ "To calculate $F$,\n",
+ "\n",
+ "- for each phase\n",
+ " - for each pressure\n",
+ " - for each temperature\n",
+ " - for each $\\lambda$\n",
+ "\n",
+ "If we choose 100 different $\\lambda$ values; 100 calculations are needed for each temperature and pressure! \n",
+ "\n",
+ "**Dimensionality: (phase, $P$, $T$, $\\lambda$)**\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6ab61ee6-2273-408b-aad5-329601bf79a3",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Speeding things up: Non-equilibrium calculations </font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c4a61c05-3f8c-47ff-b01a-8ae2c3672998",
+ "metadata": {},
+ "source": [
+ "##### Non-Equilibrium Hamiltonian Interpolation\n",
+ "\n",
+ "<img src=\"img/cimg5.png\" width=\"600\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bb228e05-ae48-4150-a033-9e0004f09db6",
+ "metadata": {},
+ "source": [
+ "In this method:\n",
+ "\n",
+ "- Discrete $\\lambda$ parameter is replaced by a time dependent $\\lambda(t)$\n",
+ "- Instead of running calculations at each $\\lambda$, run a single, short, non-equilibrium calculation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7968c6d8-f410-499f-9341-5abb6243f0a2",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "pyiron-atom-dev",
+ "language": "python",
+ "name": "pyiron-atom-dev"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.4"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/phase_diagram/tutorial_2.ipynb b/phase_diagram/tutorial_2.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..05ac8b358033f861e1f515384d6aa6d5f6ab054c
--- /dev/null
+++ b/phase_diagram/tutorial_2.ipynb
@@ -0,0 +1,1795 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "26a98d00",
+ "metadata": {},
+ "source": [
+ "<table border=\"0\">\n",
+ " <tr>\n",
+ " <td style=\"width:30%\"><img src=\"img/potentials_logo.png\" width=\"100%\" align=\"justify\"></td>\n",
+ " <td style=\"width:70%\"> <p style=\"width:100%;color:#B71C1C;font-size:24px;text-align:justify\"> From electrons to phase diagrams </p> <p style=\"width:100%,font-size:16px\">Day 03 Hands-on session (Part 2)</td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2764026b-7e3c-49c5-bd55-cd8c3483e622",
+ "metadata": {},
+ "source": [
+ "In this notebook, we will use the potentials fitted in the previous days for the calculation of thermodynamic properties such as Helmholtz and Gibbs free energies, which in turn can be used for the calculation of phase diagrams. We will discuss calphy, the tool for automated calculation of free energies, and the methology involved.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "07b882f8-7f51-4a52-a705-ace7e1ebeed3",
+ "metadata": {},
+ "source": [
+ "---"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d0179a03-9fb9-4df5-b3f1-71b3328d77c5",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Phase diagrams and how to calculate them </font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "edf671a7-a872-403d-9ee0-b64362898b8a",
+ "metadata": {},
+ "source": [
+ "<table border=\"0\">\n",
+ " <tr>\n",
+ " <td style=\"width:40%\"><img src=\"img/phase_dia_1.png\" width=\"100%\" align=\"justify\"></td>\n",
+ " <td style=\"width:60%\"> <p style=\"font-size:14px\">Phase diagrams provide a wealth of information such as: coexisting lines, melting temperature, phase stability, nucleation mechanism. </p></td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c49bf79a-fb01-4195-8c91-bd01e507edf5",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Calculation of phase diagrams: the essential ingredients</font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7a31d904-9d7f-49c4-ba7a-87f62d487533",
+ "metadata": {},
+ "source": [
+ "<table border=\"0\">\n",
+ " <tr>\n",
+ " <td style=\"width:50%\"><img src=\"img/cimg4.png\" width=\"100%\" align=\"justify\"></td>\n",
+ " <td style=\"width:50%\"> <p style=\"font-size:14px\">Phase diagrams can be evaluated from free energy diagrams. <br> <br>\n",
+ " The required input are: <br> <br>\n",
+ " ● $G(P, T)$ for unary systems <br>\n",
+ " ● $G(x, T)$ for binary systems </p></td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7b91a437-4e0f-466e-9655-88f1a3fdf55b",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Calculation of free energies: Thermodynamic integration </font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "137d7e14-d08d-4333-9509-d551d4f58ee2",
+ "metadata": {
+ "tags": []
+ },
+ "source": [
+ "<img src=\"img/fig1.png\" width=\"1000\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "04177e7c-c1fa-4d60-aa6e-48483534aa15",
+ "metadata": {},
+ "source": [
+ "- free energy of reference system are known: Einstein crystal, [Uhlenbeck-Ford model](https://doi.org/10.1063/1.4967775)\n",
+ "- the two systems are coupled by \n",
+ "$$\n",
+ "H(\\lambda) = \\lambda H_f + (1-\\lambda)\\lambda H_i\n",
+ "$$\n",
+ "- Run calculations for each $\\lambda$ and integrate \n",
+ "$$\n",
+ "G_f = G_i + \\int_{\\lambda=0}^1 d\\lambda \\bigg \\langle \\frac{\\partial H(\\lambda)}{\\partial \\lambda } \\bigg \\rangle\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6040fc8d-d177-43f0-adc0-78124d6675e1",
+ "metadata": {},
+ "source": [
+ "To calculate $F$,\n",
+ "\n",
+ "- for each phase\n",
+ " - for each pressure\n",
+ " - for each temperature\n",
+ " - for each $\\lambda$\n",
+ "\n",
+ "If we choose 100 different $\\lambda$ values; 100 calculations are needed for each temperature and pressure! \n",
+ "\n",
+ "**Dimensionality: (phase, $P$, $T$, $\\lambda$)**\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "491f35d6-bd71-45f1-bd8c-96994acc5d12",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Speeding things up: Non-equilibrium calculations </font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9beb73ad-4bf4-4e2b-95a5-ceaadbdb7631",
+ "metadata": {},
+ "source": [
+ "##### Non-Equilibrium Hamiltonian Interpolation\n",
+ "\n",
+ "<img src=\"img/cimg5.png\" width=\"600\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "772faf05-a45d-4a73-9fa9-6debe9c01b91",
+ "metadata": {},
+ "source": [
+ "In this method:\n",
+ "\n",
+ "- Discrete $\\lambda$ parameter is replaced by a time dependent $\\lambda(t)$\n",
+ "- Instead of running calculations at each $\\lambda$, run a single, short, non-equilibrium calculation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b8724300-dc2e-448f-9e73-5c94b5fd16e2",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "G_f = G_i + \\int_{t_i}^{t_f} dt \\frac{d\\lambda (t)}{dt} \\frac{ H(\\lambda)}{\\partial \\lambda }\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4e0c133b-9940-4210-96c2-8f011eec2359",
+ "metadata": {},
+ "source": [
+ "As discussed:\n",
+ "- the coupling parameter $\\lambda$ earlier is replaced by a time dependent parameter\n",
+ "- The equation also no longer has an ensemble average \n",
+ "\n",
+ "These aspects makes it quite easy and fast to estimate this integral."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c3d5ac19-d984-42b6-8681-2072225db24c",
+ "metadata": {},
+ "source": [
+ "However:\n",
+ "- this equation holds when the switching betwen the system of interest and reference system is carried out infinitely slowly\n",
+ "- Practically, this is not not possible. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ef6c1b6d-fceb-4027-a434-08a1e4ccdc0b",
+ "metadata": {},
+ "source": [
+ "Therefore we can write:\n",
+ "\n",
+ "$$\n",
+ "\\Delta G = W_{rev} = W_s - E_d\n",
+ "$$\n",
+ "\n",
+ "$$\n",
+ "W_s = \\int_{t_i}^{t_f} dt \\frac{d\\lambda (t)}{dt} \\frac{ H(\\lambda)}{\\partial \\lambda }\n",
+ "$$\n",
+ "\n",
+ "- $E_d$ is the energy dissipation\n",
+ "- $E_d \\to 0$ when $t_f-t_i \\to \\infty$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d886249a-1bae-495b-a330-37111f901328",
+ "metadata": {},
+ "source": [
+ "So far, so good, but how is this useful?\n",
+ "\n",
+ "- Instead of a single transformation from system of interest to reference, we switch back too\n",
+ "- These are called forward $(i \\to f)$ and backward $(f \\to i)$ switching\n",
+ "- $t_f - t_i = t_{sw}$ is the switching time in each direction\n",
+ "- If $t_{sw}$ is long enough, $E_d^{i \\to f} = E_d^{f \\to i}$\n",
+ "- and $\\Delta G = \\frac{1}{2} (W_s^{i \\to f} - W_s^{f \\to i})$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0b698a0b-9de7-42c3-8c07-18fad961c5b4",
+ "metadata": {},
+ "source": [
+ "Now, we have all the components required for actual calculations.\n",
+ "\n",
+ "We have also managed to successfully reduce the dimensionality\n",
+ "\n",
+ "- for each phase\n",
+ " - for each pressure\n",
+ " - for each temperature\n",
+ " - ~~for each $\\lambda$~~\n",
+ "\n",
+ "**Dimensionality: (phase, $P$, $T$)**\n",
+ "\n",
+ "\n",
+ "So, how do we calculate the free energy of a system modelled with a given interatomic potential?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3a155704-80bf-423a-9581-e3f262b06008",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Hands-on: Calculate free energy </font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f5615847-ca0b-4ca5-8e7f-6321bdf9040d",
+ "metadata": {},
+ "source": [
+ "Before we really do the calculations, let's convert our equations to a workflow."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "71d29847-1f0c-45d1-aeb6-6a90a8bbaa9e",
+ "metadata": {},
+ "source": [
+ "#### Task: Find free energy of Al in FCC lattice at 500 K and 0 pressure"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9d8f99a1-5523-4e5c-967d-cfe8a4150dc6",
+ "metadata": {},
+ "source": [
+ "1. Create an Al FCC lattice\n",
+ "2. Choose an interatomic potential\n",
+ "3. Run MD calculations at 500 K and 0 pressure to equilibrate the system\n",
+ "4. Introduce the reference system\n",
+ "5. Switch....\n",
+ "6. ....."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c6a413cf-6b7d-435f-b856-42108db12c86",
+ "metadata": {},
+ "source": [
+ "Steps 1-3 should be fairly easy, we saw this in the last days and also in the first session. But how do we introduce a reference system?\n",
+ "\n",
+ "- A reference system is simply one for which the free energy is analytically known ($G_i$)\n",
+ "- We calculate the free energy difference between this and the system of interest.\n",
+ "\n",
+ "In case of solids, a good choice of a reference system is the Einstein crystal. An Einstein crystal is a set of independent harmonic oscillators attached to the lattice positions. \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "62a6c58c-ceca-4440-bb6b-507fa0af306c",
+ "metadata": {},
+ "source": [
+ "The free energy of the Einstein crystal is:\n",
+ "\n",
+ "$$\n",
+ "F_E = 3 k_B T \\sum_{i} ln \\bigg ( \\frac{\\hbar \\omega_i}{k_B T} \\bigg )\n",
+ "$$\n",
+ "\n",
+ "We need to calculate:\n",
+ "\n",
+ "- $\\omega$\n",
+ "- A common way is $$ \\frac{1}{2} k_i \\langle (\\Delta \\pmb{r}_i)^2 \\rangle = \\frac{3}{2} k_\\mathrm{B} T $$\n",
+ "- $\\langle (\\Delta \\pmb{r}_i)^2 \\rangle$ is the mean squared displacement."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "99e90f66-4d61-4a32-9001-dbca3b757299",
+ "metadata": {},
+ "source": [
+ "Now that we know about the reference system, let's update our pseudo workflow:\n",
+ "\n",
+ "1. Create an Al FCC lattice\n",
+ "2. Choose an interatomic potential\n",
+ "3. Run MD calculations at 500 K and 0 pressure to equilibrate the system\n",
+ "4. Calculate the mean squared displacement, therefore spring constants\n",
+ "5. Switch system of interest to reference system\n",
+ "6. Equilibrate the system\n",
+ "7. Switch back to system of interest\n",
+ "8. Find the work done\n",
+ "9. Add to the free energy of the Einstein crystal"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5aa2903b-1da2-4a25-8bfc-f60dd570d7f5",
+ "metadata": {},
+ "source": [
+ "As you can see, there are a number of steps that need to be done. This is where **calphy** and **pyiron** come in. These tools automatise all of the above steps and makes it easy to perform these calculations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "eac7fc00-1896-4781-900d-bd7551f86faf",
+ "metadata": {},
+ "source": [
+ "#### Import modules"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "36610adb-6834-41f1-9de8-b95f322901af",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from helpers import potential_list\n",
+ "from pyiron_atomistics import Project\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1b32a5db-7c1c-4d4c-8af3-51ed4a9e7e02",
+ "metadata": {},
+ "source": [
+ "#### Create a project"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "29ab8d01-2777-4dde-b14c-3ac46e80b4f7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pr = Project('lial_thermodynamics_2') "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0e8bd0a3-dad4-473e-9a72-0809a56345a6",
+ "metadata": {},
+ "source": [
+ "Now we create a job within"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "a3cf44e3-5440-42ce-a687-d34610046c53",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "al_sol = pr.create.job.Calphy(\"al_fcc_500\", delete_aborted_job=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "944349e8-66a6-4456-a639-329fd05169b7",
+ "metadata": {},
+ "source": [
+ "There are a number of input the job can take. We can gain some information about the job from the docstrings."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "id": "639c9cdd-529c-42e7-a497-1f66b7cc2aba",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[0;31mType:\u001b[0m Calphy\n",
+ "\u001b[0;31mString form:\u001b[0m {'groups': [], 'nodes': []}\n",
+ "\u001b[0;31mFile:\u001b[0m ~/miniconda3/envs/workshop/lib/python3.9/site-packages/pyiron_atomistics/calphy/job.py\n",
+ "\u001b[0;31mDocstring:\u001b[0m \n",
+ "Class to set up and run calphy jobs for calculation of free energies using LAMMPS.\n",
+ "\n",
+ "An input structure (:attr:`structure`) and interatomic potential (:attr:`potential`) are necessary input options. The additional input options such as the temperature and pressure are specified in the :meth:`.calc_free_energy` method. Depending on the input parameters, a corresponding calculation mode is selected. Further input options can be accessed through :attr:`input.md` and :attr:`input.tolerance`.\n",
+ "\n",
+ "An example which calculates the free energy of Cu using an interatomic potential:\n",
+ "\n",
+ "```python\n",
+ "job.structure = pr.create.structure.ase.bulk('Cu', cubic=True).repeat(5)\n",
+ "job.potential = \"2001--Mishin-Y--Cu-1--LAMMPS--ipr1\"\n",
+ "job.calc_free_energy(temperature=1100, pressure=0, reference_phase=\"solid\")\n",
+ "job.run()\n",
+ "```\n",
+ "\n",
+ "In order to calculate the free energy of the liquid phase, the `reference_phase` should be set to `liquid`.\n",
+ "\n",
+ "The different modes can be selected as follows:\n",
+ "\n",
+ "For free energy at a given temperature and pressure:\n",
+ "\n",
+ "```python\n",
+ "job.calc_free_energy(temperature=1100, pressure=0, reference_phase=\"solid\")\n",
+ "```\n",
+ "\n",
+ "Alternatively, :func:`calc_mode_fe` can be used.\n",
+ "\n",
+ "To obtain the free energy between a given temperature range (temperature scaling):\n",
+ "\n",
+ "```python\n",
+ "job.calc_free_energy(temperature=[1100, 1400], pressure=0, reference_phase=\"solid\")\n",
+ "```\n",
+ "\n",
+ "Alternatively, :func:`calc_mode_ts` can be used.\n",
+ "\n",
+ "For free energy between a given pressure range (pressure scaling)\n",
+ "\n",
+ "```python\n",
+ "job.calc_free_energy(temperature=1000, pressure=[0, 100000], reference_phase=\"solid\")\n",
+ "```\n",
+ "\n",
+ "Alternatively, :func:`calc_mode_pscale` can be used.\n",
+ "\n",
+ "To obtain the free energy difference between two interatomic potentials (alchemy/upsampling)\n",
+ "\n",
+ "```python\n",
+ "job.potential = [\"2001--Mishin-Y--Cu-1--LAMMPS--ipr1\", \"1986--Foiles-S-M--Cu--LAMMPS--ipr1\"]\n",
+ "job.calc_free_energy(temperature=1100, pressure=0, reference_phase=\"solid\")\n",
+ "job.run()\n",
+ "```\n",
+ "\n",
+ "Alternatively, :func:`calc_mode_alchemy` can be used.\n",
+ "\n",
+ "The way `pressure` is specified determines how the barostat affects the system. For isotropic pressure control:\n",
+ "\n",
+ "```python\n",
+ "job.calc_free_energy(temperature=[1100, 1400], pressure=0, reference_phase=\"solid\")\n",
+ "```\n",
+ "\n",
+ "For anisotropic pressure control:\n",
+ "\n",
+ "```python\n",
+ "job.calc_free_energy(temperature=[1100, 1400], pressure=[0, 0, 0], reference_phase=\"solid\")\n",
+ "```\n",
+ "\n",
+ "To constrain the lattice:\n",
+ "\n",
+ "```python\n",
+ "job.calc_free_energy(temperature=[1100, 1400], pressure=None, reference_phase=\"solid\")\n",
+ "```\n",
+ "\n",
+ "In addition the boolean option :attr:`input.npt` can be used to determine the MD ensemble. If True, temperature integration and alchemy/upsampling are carried out in the NPT ensemble. If False, the NVT ensemble is employed.\n",
+ "\n",
+ "After the calculation is over, the various output options can be accessed through `job.output`.\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "al_sol?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2dc51399-994d-441e-a091-bc8e872904ea",
+ "metadata": {},
+ "source": [
+ "First the interatomic potential need to be set"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "bb07f393-4cd8-4151-a83f-a4b48c9270f9",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "al_sol.potential = potential_list[0]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0aac11a3-bef6-472c-b48d-0a7d49f321ed",
+ "metadata": {},
+ "source": [
+ "Now we create an FCC structure and assign it to the Job"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "id": "8e1196f2-f25a-473c-b760-8f9515db7954",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure = pr.create.structure.ase.bulk('Al', cubic=True, a=4.099).repeat(5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "id": "e3996191-1c90-4977-ba5a-858aff93716a",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "873c1c66a2a4400bafcd131e56ae263b",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "NGLWidget()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "structure.plot3d()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "id": "53bd6a33-1dd3-4ba7-9f61-060e81281151",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "al_sol.structure = structure"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f5d757dc-1c28-4d41-8a5b-c27e529710e9",
+ "metadata": {},
+ "source": [
+ "We run the job on four cores"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "e32b6251-fcb9-45b1-9a6d-449baa109c7c",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "al_sol.server.cores = 4"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "364a7381-91ca-4aec-a14f-9fc0028a65e3",
+ "metadata": {},
+ "source": [
+ "Now set up the calculation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "id": "b76b64c5-dd04-4f2c-bfd0-e6bb60fd7a5a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "al_sol.calc_free_energy(temperature=500, \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3932555c-45e7-4783-8737-9ef3ef843147",
+ "metadata": {},
+ "source": [
+ "Before we actually run the calculation, let us discuss the various parameters. `temperature` keyword gives the temperature range over which the free energy is to be calculated. Since we provide `500`, the free energy is calculated at this temperature. `pressure` denotes the pressure of the calculation, we chose 0 in this case. Since we are using a solid FCC lattice, we set `reference_phase` to `\"solid\"`. This means that the Einstein crystal will be used as the reference system. Finally, we have `n_equilibration_steps` and `n_switching_steps`. `n_equilibration_steps` denotes the number of MD steps over which the system is equilibrated to the required temperature and pressure. `n_switching_steps` are the number of MD steps over which the system is continuously transformed between the given interatomic potential, and the reference Einstein crystal."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b3c69ae1-f50e-414a-94ea-4080062411a2",
+ "metadata": {},
+ "source": [
+ "Now we can actually run the calculation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "id": "df679a80-f200-4c78-970f-dfd3f732c17b",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job al_fcc_500 was saved and received the ID: 155\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "al_sol.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9f71b947-dce2-4f34-ad7c-afee8bf67b69",
+ "metadata": {},
+ "source": [
+ "Let's take a look at the output, first the free energy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "id": "5d49cf4e-7508-47a6-8a1a-d4955fc604b9",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "-3.5648682956586852"
+ ]
+ },
+ "execution_count": 24,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "al_sol.output.energy_free"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "87c988b7-5d25-4f30-b746-d52987057c21",
+ "metadata": {},
+ "source": [
+ "The units are in eV/atom. We can also see the contributions from the reference system and the work."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "id": "634755ce-7145-4db4-bd30-f0f4d7ee4c8b",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(-0.14942931614249494, -3.4154389795161904)"
+ ]
+ },
+ "execution_count": 25,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "al_sol.output.energy_free_reference, al_sol.output.energy_work"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d5345566-291a-438f-86a8-3dac09564b9e",
+ "metadata": {},
+ "source": [
+ "The sum of which gives the energy."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6c3725e8-708d-45d3-a118-24d68c9104df",
+ "metadata": {},
+ "source": [
+ "We can plot and see the energy difference between the system of interest and reference system as a function of the coupling parameter."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "id": "44a697c1-cc57-438e-809f-1727980577b4",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 0, '$\\\\lambda$')"
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(al_sol.output.forward_lambda, al_sol.output.forward_energy_diff[0], \n",
+ " label=\"forward\", color='#C62828')\n",
+ "plt.plot(al_sol.output.backward_lambda, al_sol.output.backward_energy_diff[0], \n",
+ " label=\"backward\", color='#006899')\n",
+ "plt.legend()\n",
+ "plt.xlabel(r\"$\\lambda$\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0fee4e17-fa64-4c35-b9f7-1814696ae6fd",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Free energy variation with temperature </font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "917b1d54-c1e6-4d4a-b6b6-6e8627ee756f",
+ "metadata": {},
+ "source": [
+ "Now that we have calculated the free energy successfully, we can see how we get the variation of free energy with temperature. The easiest option is to run the calculations we saw above at multiple temperatures. We do at 600 K and 700 K."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "57058b90-d90f-482f-ba16-b7d10500dfa3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure = pr.create.structure.ase.bulk('Al', cubic=True, a=4.1118).repeat(5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "id": "81157bd3-cf1f-4507-8305-85f8c244cf9b",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job al_fcc_600 was saved and received the ID: 156\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "al_sol1 = pr.create.job.Calphy(\"al_fcc_600\", delete_aborted_job=True)\n",
+ "al_sol1.potential = potential_list[0]\n",
+ "al_sol1.structure = structure\n",
+ "al_sol1.server.cores = 4\n",
+ "al_sol1.calc_free_energy(temperature=600, \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ "al_sol1.run()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "72a8df4f-28ea-4953-b882-796e3ee0640d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure = pr.create.structure.ase.bulk('Al', cubic=True, a=4.123).repeat(5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "id": "78428b2d-766a-48c2-91d6-0bf8e12377cb",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job al_fcc_700 was saved and received the ID: 157\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "al_sol2 = pr.create.job.Calphy(\"al_fcc_700\", delete_aborted_job=True)\n",
+ "al_sol2.potential = potential_list[0]\n",
+ "al_sol2.structure = structure\n",
+ "al_sol2.server.cores = 4\n",
+ "al_sol2.calc_free_energy(temperature=700, \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ "al_sol2.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e652ec3d-6208-486f-b94f-0c3a4fbb77db",
+ "metadata": {},
+ "source": [
+ "Compile the results and plot them"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "id": "773d99a7-1efa-4483-9691-ac6eab995f2f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "temp = [500, 600, 700]\n",
+ "fes = [al_sol.output.energy_free, al_sol1.output.energy_free, al_sol2.output.energy_free]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "id": "4e47ab3c-9abf-4e62-b74e-4faa8d43aad2",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, 'Free energy (eV/K)')"
+ ]
+ },
+ "execution_count": 36,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(temp, fes, 'o', label='fcc', color=\"#e58080\", markeredgecolor=\"#424242\")\n",
+ "plt.xlabel(\"Temperature (K)\")\n",
+ "plt.ylabel(\"Free energy (eV/K)\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "702b45e5-e9cd-4bc8-bedc-f4f4186faecf",
+ "metadata": {},
+ "source": [
+ "That works very well, but can we need three different calculations to arrive at the plot. Furthermore, in order to find the free energy at, for example, 650 K, we need to run another calculation. That is where, reversible scaling, the method discussed in the morning comes in."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "64237f43",
+ "metadata": {},
+ "source": [
+ "### Reversible scaling\n",
+ "\n",
+ "<img src=\"img/cimg6.png\" width=\"600\">\n",
+ "\n",
+ "As discussed in the morning lecture, Gibb's free energy via reversible scaling at a constant pressure is given by,\n",
+ "\n",
+ "$ G(N,P,T_f) = G(N,P,T_i) + \\dfrac{3}{3}Nk_BT_f\\ln{\\dfrac{T_f}{T_i}} + \\dfrac{T_f}{T_i}\\Delta G $,\n",
+ "\n",
+ "Therefore, $G(N,P,T_f)$ can be computed from $G(N,P,T_i)$ via the free energy difference $\\Delta G$. \n",
+ "\n",
+ "Here, $\\Delta G = \\dfrac{1}{2}[W_{if}-W_{fi}$] --- (2)\n",
+ "\n",
+ "The reversible work is related to the internal energy $U$ by,\n",
+ "$W = \\int_{1}^{\\lambda_f}<U> \\,d\\lambda$ --- (3)\n",
+ "\n",
+ "Using MD $W$ can be computed as:\n",
+ "- equilibrate for time $t_{eq}$ in NPT ensemble\n",
+ "- switch $\\lambda$ : $1->\\dfrac{T_f}{T_i}$ over time $t_{sw}$\n",
+ "- calculate work $W_{if}$ from (3)\n",
+ "- equilibrate for time $t_{eq}$ in NPT ensemble\n",
+ "- switch $\\lambda$ : $\\dfrac{T_f}{T_i}->1$ over time $t_{sw}$\n",
+ "- calculate work $W_{fi}$ from (3)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2ef94419-583c-4c73-8a59-82c9a75907b2",
+ "metadata": {},
+ "source": [
+ "In terms of actual calculation, nothing really changes. If a list of temperature is provided, pyiron realises that you want to perform a free energy calculation withing this range. Let's try this now."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "id": "f4737882-9b35-4f67-9084-d00544b3dbcc",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure = pr.create.structure.ase.bulk('Al', cubic=True, a=4.099).repeat(5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "id": "73831609-feb4-4ed4-8d26-f37d2807e5a7",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job al_fcc_ts was saved and received the ID: 158\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "al_sol3 = pr.create.job.Calphy(\"al_fcc_ts\", delete_aborted_job=True)\n",
+ "al_sol3.potential = potential_list[0]\n",
+ "al_sol3.structure = structure\n",
+ "al_sol3.server.cores = 4\n",
+ "al_sol3.calc_free_energy(temperature=[500, 700], \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ "al_sol3.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3669b919-ea6f-4acd-ab72-11d06963aac0",
+ "metadata": {},
+ "source": [
+ "Lets plot the results together with the free energy values we calculated earlier"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "id": "684a5d2d-70ec-4057-b2b2-87273aec50e8",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fa8866e4580>"
+ ]
+ },
+ "execution_count": 40,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(al_sol3.output.temperature, al_sol3.output.energy_free, label='RS', color=\"#e58080\", markeredgecolor=\"#424242\")\n",
+ "plt.plot(temp, fes, 'o', label='Direct', color=\"#e58080\", markeredgecolor=\"#424242\")\n",
+ "plt.xlabel(\"Temperature (K)\")\n",
+ "plt.ylabel(\"Free energy (eV/K)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "91598ee0-ccd9-4d0d-a0e1-79372e8f132e",
+ "metadata": {},
+ "source": [
+ "We can see that there is excellent agreement between the direct and reversible scaling calculations. However for reversible scaling calculations, we just need to run a single calculation instead of different ones."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c77a16e4-5d75-4d31-ad4e-028f966749cb",
+ "metadata": {},
+ "source": [
+ "### <font style=\"color:#B71C1C\" face=\"Helvetica\" > Melting temperature of Al</font>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a1af199c-208d-4023-985c-4edd620f67bc",
+ "metadata": {},
+ "source": [
+ "With the recipe we have, we can now go ahead and calculate the melting temperature of Al. This will actually give our first point on the phase diagram. First, the steps needed to find the melting temperature:\n",
+ "\n",
+ "- Since the $T_m$ is 933 K, we can choose the range of 800-1100 K to calculate free energy\n",
+ "- Calculate free energy of FCC structure in this range\n",
+ "- Calculate free energy of liquid in this range.\n",
+ "\n",
+ "By now, we have seen how to calculate the free energy of the FCC structure. This can be done rather quickly."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5bfa4845-2d2a-4de0-9ec2-c0112d12bcd2",
+ "metadata": {
+ "tags": []
+ },
+ "source": [
+ "#### Free energy of solid"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "id": "ef7113ad-24fb-4c79-99c6-8e3e6c658816",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure = pr.create.structure.ase.bulk('Al', cubic=True, a=4.1362).repeat(5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 41,
+ "id": "5f66dab9-8e06-49fc-a37b-f1a88d651650",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job al_fcc_tm was saved and received the ID: 159\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "al_fcc = pr.create.job.Calphy(\"al_fcc_tm\", delete_aborted_job=True)\n",
+ "al_fcc.potential = potential_list[0]\n",
+ "al_fcc.structure = structure\n",
+ "al_fcc.server.cores = 4\n",
+ "al_fcc.calc_free_energy(temperature=[800, 1100], \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ "al_fcc.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2f5d0015-2de7-4cf5-8e9a-fa9a0f5cbec6",
+ "metadata": {},
+ "source": [
+ "#### Free energy of liquid"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7ffc4750-e7dc-4252-94b6-3d7fbe6b27f4",
+ "metadata": {},
+ "source": [
+ "Calculation of the free energy of liquid is as easy as changing the option `reference_phase` to `\"liquid\"`. That is all the change that is needed. Run the calculation.."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "id": "fd197b78-fd21-4f95-9537-9e1e514e00c7",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job al_lqd_tm was saved and received the ID: 160\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "al_lqd = pr.create.job.Calphy(\"al_lqd_tm\", delete_aborted_job=True)\n",
+ "al_lqd.potential = potential_list[0]\n",
+ "al_lqd.structure = structure\n",
+ "al_lqd.server.cores = 4\n",
+ "al_lqd.calc_free_energy(temperature=[800, 1100], \n",
+ " pressure=0, \n",
+ " reference_phase=\"liquid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ "al_lqd.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "de5ac3e5-c6d7-4b78-80dc-70dfe35e9487",
+ "metadata": {},
+ "source": [
+ "Before we actually look at the results, there are a couple of points to be discussed:\n",
+ "\n",
+ "**How is the liquid prepared in this calculation?**\n",
+ "\n",
+ "- Start from the given structure\n",
+ "- This structure is heated until it melts.\n",
+ "- Melting of the structure is automatically detected by calphy\n",
+ "- Once melted, it is equilibrated to the required temperature and pressure."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b4bf190e-ef08-446a-a9d4-4592c9c4fbb4",
+ "metadata": {},
+ "source": [
+ "**What about the reference system for liquid?**\n",
+ "\n",
+ "The reference system for the Liquid structure is also different. In this case, the Uhlenbeck-Ford system is used as the reference system for liquid.\n",
+ "\n",
+ "The Uhlenbeck-Ford model is described by,\n",
+ "\n",
+ "$$\n",
+ "E = - \\epsilon \\log(1-\\exp(-r^2/\\sigma^2))\n",
+ "$$\n",
+ "\n",
+ "where,\n",
+ "\n",
+ "$$\n",
+ "\\epsilon = p k_B T\n",
+ "$$\n",
+ "\n",
+ "$\\epsilon$ and $\\sigma$ are energy and length scales, respectively.\n",
+ "\n",
+ "It is purely repulsive liquid model which does not undergo any phase transformations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f6206120-b7d6-4691-9030-13f7e69edccc",
+ "metadata": {},
+ "source": [
+ "Now that we have covered these details, we can go ahead a look at the results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "id": "30d5fef8-701a-41f9-9231-da4c31ae7b36",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fa8753e4d30>"
+ ]
+ },
+ "execution_count": 46,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(al_fcc.output.temperature, al_fcc.output.energy_free,\n",
+ " label=\"Al solid\", color='#C62828')\n",
+ "plt.plot(al_lqd.output.temperature, al_lqd.output.energy_free,\n",
+ " label=\"Al liquid\", color='#006899')\n",
+ "plt.xlabel(\"Temperature (K)\")\n",
+ "plt.ylabel(\"Free energy (eV/K)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "56173b36-3238-4d14-b187-bd5e5fe4dfbc",
+ "metadata": {},
+ "source": [
+ "The melting temperature is defined as the temperature at which the free energy difference between the solid and liquid phases is zero. We can also plot the free energy difference directly."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "id": "87d3a2fc-bffd-4173-9383-b80151462a3c",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fediff = al_fcc.output.energy_free - al_lqd.output.energy_free"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "10a4d907-ace2-456d-9dd9-c069a822c3a3",
+ "metadata": {},
+ "source": [
+ "Find where the value is zero and get the corresponding temperature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "id": "60d9834e-628f-4ae8-8b54-fddaa11fc956",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "977.1369936920375"
+ ]
+ },
+ "execution_count": 50,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "arg = np.argsort(np.abs(fediff))[0]\n",
+ "tm = al_fcc.output.temperature[arg]\n",
+ "tm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e5898a32-54e3-40ec-b8ed-2cfc81e95a10",
+ "metadata": {},
+ "source": [
+ "The calculated melting temperature is 977 K."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "id": "73fb6d4f-05e8-4285-b541-f518cb18d711",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fa8692099d0>"
+ ]
+ },
+ "execution_count": 54,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(al_fcc.output.temperature, fediff,\n",
+ " label=r\"$\\Delta F$\", color='#C62828')\n",
+ "plt.axhline(0, color=\"gray\")\n",
+ "plt.axvline(977, color=\"black\")\n",
+ "plt.xlabel(\"Temperature (K)\")\n",
+ "plt.ylabel(\"Free energy (eV/K)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "57112bc2",
+ "metadata": {},
+ "source": [
+ "# 2. Li\n",
+ "## 2a. Solid phase calculation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "id": "b6ad0c4a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "li_sol = pr.create.job.Calphy(\"tm_li_sol3\", delete_aborted_job=True, delete_existing_job=True) "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "id": "264ec23f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "li_sol.potential = potential_list[1] # read potential from fit the previous day\n",
+ "li_sol.structure = pr.create.structure.ase.bulk('Li', cubic=True).repeat(5) # set up structure\n",
+ "li_sol.server.cores = 4 # assign number of cores required for calculation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "id": "f999e336",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ }
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/omkar/Documents/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job tm_li_sol3 was saved and received the ID: 7\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/omkar/Documents/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "li_sol.calc_free_energy(temperature=[200, 500], \n",
+ " pressure=0, # Set up parameters for the free energy calculation\n",
+ " reference_phase=\"solid\")\n",
+ "li_sol.run() "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "973a45cd",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 0, 'Temperature (K)')"
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(li_sol.output.temperature, li_sol.output.forward_energy_diff[0], label=\"forward\")\n",
+ "plt.plot(li_sol.output.temperature, li_sol.output.backward_energy_diff[0], label=\"backward\")\n",
+ "plt.legend()\n",
+ "plt.ylabel(\"Reversible work (meV)\")\n",
+ "plt.xlabel(\"Temperature (K)\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7aa1cc3d",
+ "metadata": {},
+ "source": [
+ "## 2b. Liquid phase calculation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 47,
+ "id": "795050c1",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "li_lqd = pr.create.job.Calphy(\"tm_li_lqd3\", delete_aborted_job=True, delete_existing_job=True)\n",
+ "li_lqd.structure = li_sol.structure # set up structure\n",
+ "li_lqd.potential = potential_list[1] # read potential from fit the previous day\n",
+ "li_lqd.server.cores = 4 # assign number of cores required for calculation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "id": "240a108b",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ }
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/omkar/Documents/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job tm_li_lqd3 was saved and received the ID: 8\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/omkar/Documents/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "li_lqd.calc_free_energy(temperature=[350, 700], \n",
+ " pressure=0, # Set up parameters for the free energy calculation\n",
+ " reference_phase=\"liquid\")\n",
+ "li_lqd.run() "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "651b9661",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 0, 'Temperature (K)')"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(li_lqd.output.temperature, li_lqd.output.forward_energy_diff[0], label=\"forward\")\n",
+ "plt.plot(li_lqd.output.temperature, li_lqd.output.backward_energy_diff[0], label=\"backward\")\n",
+ "plt.legend()\n",
+ "plt.ylabel(\"Reversible work (meV)\")\n",
+ "plt.xlabel(\"Temperature (K)\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "458a6190",
+ "metadata": {},
+ "source": [
+ "## 2c. Li melting temperature"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "43331dec",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 0, 'Temperature (K)')"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(li_sol.output.temperature, li_sol.output.energy_free, label=\"solid\")\n",
+ "plt.plot(li_lqd.output.temperature, li_lqd.output.energy_free, label=\"liquid\")\n",
+ "plt.legend()\n",
+ "plt.title(\"Li\")\n",
+ "plt.ylabel(\"Free energy (eV/atom)\")\n",
+ "plt.xlabel(\"Temperature (K)\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "628b90a3",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/phase_diagram/tutorial_3.ipynb b/phase_diagram/tutorial_3.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..4f7e262f134db4cb55a2ff0382e0805958fad0b1
--- /dev/null
+++ b/phase_diagram/tutorial_3.ipynb
@@ -0,0 +1,1970 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "e6829c50-ea89-4b95-b76b-5d61dd4a122a",
+ "metadata": {},
+ "source": [
+ "<table border=\"0\">\n",
+ " <tr>\n",
+ " <td style=\"width:30%\"><img src=\"img/potentials_logo.png\" width=\"100%\" align=\"justify\"></td>\n",
+ " <td style=\"width:70%\"> <p style=\"width:100%;color:#B71C1C;font-size:24px;text-align:justify\"> From electrons to phase diagrams </p> <p style=\"width:100%,font-size:16px\">Day 03 Hands-on session (Part 3)</td>\n",
+ " </tr>\n",
+ "</table>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "abee24ee-55ed-4ad0-b4af-b53c59d398b9",
+ "metadata": {},
+ "source": [
+ "In this notebook, we will use the EAM potential fitted in the previous day and move towards the AlLi phase diagram. We will use many of the methods and tools we discussed in the last sessions and put them together for calculation of phase diagrams. We start with the phase diagram of AlLi from Ref. [[1]](https://doi.org/10.1002/adma.19910031215). "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4df3f86c-245c-4b80-bac9-4a73e5d321cb",
+ "metadata": {},
+ "source": [
+ "<img src=\"img/alli_phase_diagram.jpg\" width=\"50%\" align=\"justify\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "593a2179-b9d7-47d2-a56d-7bdfbad7b253",
+ "metadata": {},
+ "source": [
+ "In the last session, we calculated the melting temperatures of the pure phases Al and Li, thereby arriving at two points on the phase diagram. In this notebook, we will start with the left side of the phase diagram, until $X_{Li} < 0.5$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "719cf65b-4052-4858-9295-869d4340c9dc",
+ "metadata": {},
+ "source": [
+ "As always, we start by importing the necessary modules."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "2fdb55d8-d5f9-4b93-81ff-45116ee94e3a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "from pyiron_atomistics import Project\n",
+ "from helpers import *\n",
+ "from calphy.integrators import kb"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e2c2b8ac-418c-4d6d-b937-60f56710c491",
+ "metadata": {},
+ "source": [
+ "We unpack the project; this can be deleted later when the calculations are run directly"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "98c1e405-f9fe-42b1-87b9-99f95317d248",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pr = Project(\"phase_diagram_2\")\n",
+ "pr.unpack(\"lial\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7763e0b6-693e-42eb-89bf-e22f3e1e4001",
+ "metadata": {},
+ "source": [
+ "Most of the interesting features of the phase diagram at composition of $X_{Li} < 0.5$ lies between the temperature range of 700-1000 K. Therefore, we will calculate the free energy in this range. Similar to the previous session, we will use reversible scaling to obtain the free energy in this temperature range in a single calculation. We will recalculate the free energy of pure Al in FCC lattice and pure Al liquid first."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "97370438-9cb7-477d-888e-82a9b6545cc0",
+ "metadata": {},
+ "source": [
+ "## Pure Al"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "abc918e0-96b9-427c-9fb1-3f996d0f4193",
+ "metadata": {},
+ "source": [
+ "### Solid"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2d17f281-807d-4c0e-b449-3a3884cd4732",
+ "metadata": {},
+ "source": [
+ "We start by creating an FCC structure. The converged lattice constant has been provided so as to speed up the calculations (CHANGE). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "5f2e42f8-6f0f-4b4d-8463-c0fbd7536e02",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure = pr.create.structure.ase.bulk('Al', cubic=True).repeat(5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8468bcbe-f760-43ae-bdf3-d3d32c20453b",
+ "metadata": {},
+ "source": [
+ "We can visualise the structure."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "106b6736-9516-4846-b0ff-547f1b00ca29",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "1bccd060c2274c18ac29fc98af6a66cb",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": []
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "85cb2cfbddbc4c3f9094e26181005a34",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "NGLWidget()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "structure.plot3d()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "41df6862-5651-4346-8db0-05d07d62a192",
+ "metadata": {},
+ "source": [
+ "Our FCC lattice consists of a 5x5x5 supercell consisting of 500 atoms. Now we create a Calphy job in pyiron and assign a potential. The interatomic potentials have been prepared already. Let's take a look."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "f0fad1dd-9d47-4fe0-b9ec-46eb684099f2",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div>\n",
+ "<style scoped>\n",
+ " .dataframe tbody tr th:only-of-type {\n",
+ " vertical-align: middle;\n",
+ " }\n",
+ "\n",
+ " .dataframe tbody tr th {\n",
+ " vertical-align: top;\n",
+ " }\n",
+ "\n",
+ " .dataframe thead th {\n",
+ " text-align: right;\n",
+ " }\n",
+ "</style>\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>Name</th>\n",
+ " <th>Filename</th>\n",
+ " <th>Model</th>\n",
+ " <th>Species</th>\n",
+ " <th>Config</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>Al_eam</td>\n",
+ " <td>[/mnt/c/Users/menon/Documents/winrepos/worksho...</td>\n",
+ " <td>EAM</td>\n",
+ " <td>[Al]</td>\n",
+ " <td>[pair_style eam/fs\\n, pair_coeff * * AlLi.eam....</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " Name Filename Model Species \\\n",
+ "0 Al_eam [/mnt/c/Users/menon/Documents/winrepos/worksho... EAM [Al] \n",
+ "\n",
+ " Config \n",
+ "0 [pair_style eam/fs\\n, pair_coeff * * AlLi.eam.... "
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "potential_list[0]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8bcacb95-c984-434b-a2cc-970b8c513bfb",
+ "metadata": {},
+ "source": [
+ "The potential has been configured for pure Al."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "41f8d1e0-8f8c-4dfb-b3d9-805801cdb488",
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "2022-05-30 10:13:26,923 - pyiron_log - WARNING - Job aborted - please remove it and run again! xp_sol\n"
+ ]
+ }
+ ],
+ "source": [
+ "xd2_sol = pr.create.job.Calphy(\"xp_sol\")\n",
+ "xd2_sol.potential = potential_list[0]\n",
+ "xd2_sol.structure = structure"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1d2731f6-8c1c-484f-9161-e679cd253428",
+ "metadata": {},
+ "source": [
+ "We have assigned the potential and structure. To speed up the calculations, we will run it on 2 cores."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "dcd99a88-7a0d-49ef-b943-0c5ac1195224",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "xd2_sol.server.cores = 4"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "28e6d72d-3821-4f25-92e2-0b2827ad3c6e",
+ "metadata": {},
+ "source": [
+ "Now let's use the `calc_free_energy` method."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "1a9c5498-cf05-4f77-b78e-488076fa666d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "xd2_sol.calc_free_energy(temperature=[700, 1000], \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9979b8d5-2cd5-42ab-b48d-3d39022a6337",
+ "metadata": {},
+ "source": [
+ "Before we actually run the calculation, let us discuss the various parameters. `temperature` keyword gives the temperature range over which the free energy is to be calculated. Since we provide `[700, 1000]`, the free energy is calculated between this range. `pressure` denotes the pressure of the calculation, we chose 0 in this case. Since we are using a solid FCC lattice, we set `reference_phase` to `\"solid\"`. This means that the Einstein crystal will be used as the reference system. Finally, we have `n_equilibration_steps` and `n_switching_steps`. `n_equilibration_steps` denotes the number of MD steps over which the system is equilibrated to the required temperature and pressure. `n_switching_steps` are the number of MD steps over which the system is continuously transformed between the given interatomic potential, and the reference Einstein crystal."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0420ab48-1095-4f11-8061-6e04795f8b24",
+ "metadata": {},
+ "source": [
+ "Finally we run the calculation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "6d076f83-949a-44d7-8128-cf568dec5e07",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "xd2_sol.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b6b98c51-35a4-45c9-a2b6-27049378cd19",
+ "metadata": {},
+ "source": [
+ "### Liquid"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "201d5bd1-88e4-4de9-8a54-08ee6acebf66",
+ "metadata": {},
+ "source": [
+ "Before we look at the output of the previous calculation, we will also calculate the free energy of the liquid phase. For this we can use the same structure as the solid. The Calphy workflow will first superheat the structure, melt it, and then equilibrate to the required temperature and pressure. Therefore the input for the pyiron job looks fairly same."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "361de986-8a22-4df7-b91c-2c74d11e2ee3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "xd2_lqd = pr.create.job.Calphy(\"xp_lqd\")\n",
+ "xd2_lqd.potential = potential_list[0]\n",
+ "xd2_lqd.structure = structure\n",
+ "xd2_lqd.server.cores = 4\n",
+ "xd2_lqd.calc_free_energy(temperature=[700, 1000], \n",
+ " pressure=0, \n",
+ " reference_phase=\"liquid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9acd93d9-a5bc-4410-9db3-fb35cf925edc",
+ "metadata": {},
+ "source": [
+ "The major change in the input is that the `reference_phase` is `\"liquid\"`, instead of `\"solid\"`. In this case, the Uhlenbeck-Ford model is used as the reference system instead of the Einstein crystal. Now run the job,"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "1ba6b5cf-a275-4d05-a28c-8fb051bd7621",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job xp_lqd was saved and received the ID: 81\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "xd2_lqd.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "29e45736-f6ed-43a6-b5d5-7a595344dfc1",
+ "metadata": {},
+ "source": [
+ "Now we can look at the output; and plot the free energies of the two phases and calculate the melting temperature."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "a7831534-8932-4646-a714-81c30cb82968",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'groups': ['lial_thermodynamics_composition'], 'nodes': []}"
+ ]
+ },
+ "execution_count": 15,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "pr"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "7b67fdc6-2954-4af9-9b2a-9ae2df890c2a",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[<matplotlib.lines.Line2D at 0x7fcf3d789d90>]"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(pr['lial_thermodynamics_composition/xp_sol'].output.temperature, pr['lial_thermodynamics_composition/xp_sol'].output.energy_free,\n",
+ " label=\"Al solid\", color='#C62828')\n",
+ "plt.plot(pr['lial_thermodynamics_composition/xp_lqd'].output.temperature, pr['lial_thermodynamics_composition/xp_lqd'].output.energy_free,\n",
+ " label=\"Al liquid\", color='#006899')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "919abb78-a241-4c02-8bba-20d74fa1a587",
+ "metadata": {},
+ "source": [
+ "Great, finally, we will also calculate the free energy of the Al Li structure. Let's read in the structrue from the given file and plot it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "33bf1f2d-ba68-473c-809b-ad4ee81fa528",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "alli = pr.create.structure.ase.read('LiAl_poscar', format='vasp')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "0530321e-6292-4f35-a319-9a04f56ff9a3",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "bdbc8b6be86647fa91de5629e6b486a0",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "NGLWidget()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "alli.plot3d()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0df357e6-6f40-411f-b443-2c0f27af19b8",
+ "metadata": {},
+ "source": [
+ "We are calculating the free energy at zero percent Li, there will replace all the Li atoms with Al."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "a4724977-e552-434e-8543-2ebe54fd5d4b",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "alli[:] = 'Al'"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "47d97564-88d2-40ec-87c9-de6b70a16045",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "11a01396f3c24ea5b6d6183e32451c61",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "NGLWidget()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "alli.plot3d()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d7efef54-b256-4b79-939e-df6fedd5e808",
+ "metadata": {},
+ "source": [
+ "Now we run the calculation to calculate the free energy at the same temperature range."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "id": "c468175e-f485-47b9-b504-0ba8e02a8f1f",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The job xp_alli was saved and received the ID: 82\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/menon/miniconda3/envs/workshop/lib/python3.9/site-packages/h5io/_h5io.py:56: PerformanceWarning: \n",
+ "your performance may suffer as PyTables will pickle object types that it cannot\n",
+ "map directly to c-types [inferred_type->mixed,key->block0_values] [items->Index(['Name', 'Filename', 'Model', 'Species', 'Config'], dtype='object')]\n",
+ "\n",
+ " data.to_hdf(fname, rootpath)\n"
+ ]
+ }
+ ],
+ "source": [
+ "xd2_alli = pr.create.job.Calphy(\"xp_alli\")\n",
+ "xd2_alli.potential = potential_list[0]\n",
+ "xd2_alli.structure = alli\n",
+ "xd2_alli.server.cores = 4\n",
+ "xd2_alli.calc_free_energy(temperature=[700, 1000], \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ "xd2_alli.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8b9ee4b4-ecf1-4096-bfd0-1a1381970606",
+ "metadata": {},
+ "source": [
+ "## Free energy with composition"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5f1f69ce-2262-4612-b0f5-079f651698c6",
+ "metadata": {},
+ "source": [
+ "Now we will calculate the free energy of FCC solid, liquid and B32 phases with increasing Li compositions. We will use compositions from 0.1 to 0.5 Li. For the solid structure, we will first create an Al FCC structure, and replace randomly selected atoms with Li. Let's see how we do this."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "6c4cb706-98f6-4a33-a3dd-8b3f23f28e02",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure = pr.create.structure.ase.bulk('Al', cubic=True).repeat(5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "7c68c80e-5e78-4312-b341-fa1eb9a2fa43",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "d8a5683a9d1c4fd5b84c8baff7d5f953",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "NGLWidget()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "structure.plot3d()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "51033367-421a-44e9-b4cb-637a2edce59b",
+ "metadata": {},
+ "source": [
+ "Now we assume we need to create 0.1 composition of Li. Therefore, the number of Li atoms needed are:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "dfed2430-c0a9-4454-b8e5-8ce234bf3327",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "50"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "comp = 0.1\n",
+ "n_li = int(comp*len(structure))\n",
+ "n_li"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e57d7ab8-1813-4f33-b365-296261923a08",
+ "metadata": {},
+ "source": [
+ "Now we randomly replace 50 Al atoms with Li."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "6693b34e-53d3-42b2-a851-514969123a43",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure[np.random.permutation(len(structure))[:n_li]] = 'Li'"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "id": "30832772-cfba-41c5-927f-afb58c2055b3",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "ba179f7afd71483ebe5a7227c40c5cfd",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "NGLWidget()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "structure.plot3d()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8bbc1c83-207e-4025-a803-48b830fd09b5",
+ "metadata": {},
+ "source": [
+ "We can see that some Al atoms are now replaced with Li. We also need to create B32 structures of varying compositions. For that we start with the LiAl B32 structure, and replace randomly selected Li atoms with Al, therby reducing the amount of Li in the structure."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "d3d3bafa-b5f5-4c9e-8d76-38e2564d9bdb",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "structure = pr.create.structure.ase.read('LiAl_poscar', format='vasp')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "id": "a02da17c-666f-4703-aec4-439f04744d18",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "fd68e27d4dc248dd871d978493f1b6b3",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "NGLWidget()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "structure.plot3d()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0874a585-7ed2-47fc-9d6d-244c596ac252",
+ "metadata": {},
+ "source": [
+ "Once again, find the number of Li atoms that need to replaced."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "id": "d00ec755-8331-457b-866b-5ad0a93cdbab",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "172"
+ ]
+ },
+ "execution_count": 19,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "n_li = int((0.5-comp)*len(structure))\n",
+ "n_li"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "17b20f88-6588-402c-9999-1cd96bcff667",
+ "metadata": {},
+ "source": [
+ "Now replace random Li atoms with Al"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "id": "39799961-d2e7-4545-8f87-948e2ee1847b",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rinds = np.random.choice(range(len(structure)//2), n_li, replace=False)\n",
+ "structure[rinds] = 'Al'"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "393a96e9-6592-4a1c-bc90-7446124f3555",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "24172e887fd445abbfdae2466448f256",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "NGLWidget()"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "structure.plot3d()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0cd85ff7-2a54-45f3-9f97-3446f91bd0d6",
+ "metadata": {},
+ "source": [
+ "Now we have all the necessary components in place. We can simply create a loop over the compositions and run the calculations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1ac33e3e-e6bc-426b-a7d4-837643022670",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "for count, comp in enumerate([0.1, 0.2, 0.3, 0.4, 0.5]):\n",
+ " structure = pr.create.structure.ase.bulk('Al', cubic=True).repeat(5)\n",
+ " n_li = int(comp*len(structure))\n",
+ " structure[np.random.permutation(len(structure))[:n_li]] = 'Li'\n",
+ " xd2_sol = pr.create.job.Calphy(\"x%d_sol\"%count)\n",
+ " xd2_sol.potential = potential_list[3]\n",
+ " xd2_sol.structure = structure\n",
+ " xd2_sol.server.cores = 4\n",
+ " xd2_sol.calc_free_energy(temperature=[700, 1000], \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ " xd2_sol.run()\n",
+ " xd2_lqd = pr.create.job.Calphy(\"x%d_lqd\"%count)\n",
+ " xd2_lqd.potential = potential_list[3]\n",
+ " xd2_lqd.structure = structure\n",
+ " xd2_lqd.server.cores = 4\n",
+ " xd2_lqd.calc_free_energy(temperature=[700, 1000], \n",
+ " pressure=0, \n",
+ " reference_phase=\"liquid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ " xd2_lqd.run()\n",
+ " alli = pr.create.structure.ase.read('LiAl_poscar', format='vasp')\n",
+ " n_li = int((0.5-comp)*len(structure))\n",
+ " rinds = np.random.choice(range(len(alli)//2), n_li, replace=False)\n",
+ " alli[rinds] = 'Al'\n",
+ " xd2_alli = pr.create.job.Calphy(\"x%d_alli\"%count)\n",
+ " xd2_alli.potential = potential_list[3]\n",
+ " xd2_alli.structure = alli\n",
+ " xd2_alli.server.cores = 4\n",
+ " xd2_alli.calc_free_energy(temperature=[700, 1000], \n",
+ " pressure=0, \n",
+ " reference_phase=\"solid\",\n",
+ " n_equilibration_steps=10000,\n",
+ " n_switching_steps=10000)\n",
+ " xd2_alli.run()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "03f0bd9e-fb40-48da-94dc-8d57e54f8641",
+ "metadata": {},
+ "source": [
+ "## Analysing the results"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8a4fed77-59f8-41da-b4ae-4a6047f33685",
+ "metadata": {},
+ "source": [
+ "Now we can analyse the results of the above calculations. First we create an array of the composition values."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "id": "c3344c98-42d0-4ed7-9389-8a2a60ba9a5d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "comp = np.arange(0, 0.6, 0.1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2143e427-776b-4db4-b7d0-243296865a3d",
+ "metadata": {},
+ "source": [
+ "For the initial set of analysis, we will choose a temperature of 700 K. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 91,
+ "id": "d22070b3-0c72-49c5-bf69-cf792a39982c",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "temp = 700"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f7b14a89-34b5-4e99-964f-865c07a80d9f",
+ "metadata": {},
+ "source": [
+ "The calculations we ran already has the free energy at all temperatures from 700-1000 K. We need to extract the free energy at the correct temperature. The `helpers.py` file in the folder contains some helper functions for this notebook. We provide a `fe_at` method which can extract the free energy at the required temperature. Let's take a look at the method."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 92,
+ "id": "f27266d0-04e0-4525-8814-dd3e6959c98c",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[0;31mSignature:\u001b[0m \u001b[0mfe_at\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtemp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mthreshold\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+ "\u001b[0;31mDocstring:\u001b[0m\n",
+ "Get the free energy at a given temperature\n",
+ "\n",
+ "Parameters\n",
+ "----------\n",
+ "p: pyiron Job\n",
+ " Pyiron job with calculated free energy and temperature\n",
+ " \n",
+ "temp: float\n",
+ " Required temperature\n",
+ " \n",
+ "threshold: optional, default 1E-1\n",
+ " Minimum difference needed between required temperature and temperature found in pyiron job\n",
+ " \n",
+ "Returns\n",
+ "-------\n",
+ "float: free energy value at required temperature\n",
+ "\u001b[0;31mFile:\u001b[0m /mnt/c/Users/menon/Documents/winrepos/workshop_preparation/phase_diagram/helpers.py\n",
+ "\u001b[0;31mType:\u001b[0m function\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fe_at?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3ea1923f-43a9-42e5-8314-2025f34e3141",
+ "metadata": {},
+ "source": [
+ "For for pure Al calculations, and for each composition, we extract the free energy at 700 K of the FCC, liquid and B32 phases."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 93,
+ "id": "62e66d3a-c9c4-40c0-8df7-ae796d8f2d65",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fcc = []\n",
+ "b32 = []\n",
+ "lqd = []\n",
+ "\n",
+ "fcc.append(fe_at(pr[\"lial_thermodynamics_composition/xp_sol\"], temp))\n",
+ "lqd.append(fe_at(pr[\"lial_thermodynamics_composition/xp_lqd\"], temp))\n",
+ "b32.append(fe_at(pr[\"lial_thermodynamics_composition/xp_alli\"], temp))\n",
+ "\n",
+ "for i in range(5):\n",
+ " fcc.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_sol\"%i], temp))\n",
+ " lqd.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_lqd\"%i], temp))\n",
+ " b32.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_alli\"%i], temp))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "20231991-df18-4556-b217-0fe731699be5",
+ "metadata": {},
+ "source": [
+ "Plot the results"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 94,
+ "id": "f6eabcb1-7a02-4e34-9fef-ea584f3a547c",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fcf10b47610>"
+ ]
+ },
+ "execution_count": 94,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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4mE8//RQwSohPnTqVY8eMP1Vaa9566y1Gjhx5ru38+fNZu3YtmZmZlzcgIcRFcba0UPPKK9R/9BFhV1xB3MKF+IeHd9hea+M867+dgMEhRtI6VZXD/t+B9RRk/gAGfbfrBuBl3TL/UUr9GpgLOIEKYJHWurSddjOBJwF/4Fmt9W+7on9nE9bePqx81KhR/OMf/+DBBx9k+PDh/OAHP2DGjBlYLBa01owfP56//vWvAPzqV7+iqqqKH/7whwAEBASwa9euyxuYEKJTdrOZ6pdewl5RQdRNNxF+9dVu8xE2J7xwEr6ogStNcG8qBDUUwOGnAQWjfgqRGV3Wf19QWuuuv6lSUVpri+vrHwOjtdYPtWnjDxwBZgAlwJfA3VrrA519/qRJk3TbX6oHDx5kVCfPFnurvjw2IbpSc3ExNS+/jHY4iFmwgJBhw9y2t9iM8uCFjTB3ENycAKrmazj2LASajKR16OU9su4qSqndWutJ7b3XLTOKs0HCJRxoL1pdBRzTWhcAKKVewpiFdBoohBDiYjV89RW1mzbhbzIRf/fdBMS7PwPipBX+pwDq7fDgEJhoAk5vhxMvQngajPwRBHa8x6I36bbUu1LqN8C9QC0wrZ0mg4GTrb4vAa7ugq4JIfoR7XRiee89Gj7/nOCMDGIWLMAv1P3S1a/N8HwxhPrDo8MhNdQJxRuhdAuYsmD4A+DfcfXY3sZngUIptRVob4nA41rrjVrrx4HHlVKPAQ8DT7T9iHau7fA5mVJqGbAMIDU19dI6LYToV5xNTdS89hrNx48TfvXVRN14o9vKr1rDuxWwocw40/qH6RDtb4fj/4AzX8DA6yH9LlAdH3naG/ksUGitPc38/gvYxIWBogRIafV9MnBBwrvV/VYBq8DIUXTQxm1SqjfqjhyTEH2B/cwZql56CUdNDdG33kr4xIlu29uc8M+T8FkNTDLBfakQ5LTCob+C5TCkzIWkm3vl8tfOdNeqp+Fa66Oub+cA7R0S/SUwXCmVDpwC7gK+f6n3DAkJoaqqiri4uD4TLLTWVFVVERIS0t1dEaJXaTp+nJpXX0X5+xN3770Ep6W5bW+xGUtfjzfArYPglgRQLTVGzSZrGQxdBAOu7ZK+d4fuylH8Vik1AmN5bBHwEIBSKgljGewsrbVdKfUw8C7G8tjntdbfXOoNk5OTKSkpobKy0gvd7zlCQkJI7qRypRDCoLWm4fPPsbz3HgEDBhB7990EmExurylxJa3r7LBsCHzHBDSegkNPgcMKI5aDaXQX9L77dMvyWF9rb3msEKJ/0w4HtZs20bhnDyEjRmCaPx+/IPdnUu+theeKjKT1D9JhSBhQexiO/NU4z3rkcghPcfsZvUWPWx4rhBBdydHQQM0rr9BSXEzEddcROW2a20fQWsN7FfBGGaSGGkEiJggjYX38H0aJ8JE/huDYrhtEN5JAIYTo02ynTxvHlTY0YJo/n7CsLPftnbCuBD6tNh4zLUqFIKWh9D0ofh0ih8OIH0BAxyU9+hoJFEKIPiUvL491a9ZwsqyMwfHx3DpgAFPS043jSgcPdnttnR3+VgjHGmB2AsweBAonnHgZyj+E2O/AsMXgF9g1g+khJFAIIfqMvLw8nn3qKZamp5OZkcERi4Vnjx4lauZMZnQSJE5ZjTOtLTa4Pw2ujME4z/roc1DzNSROh9TbjeNL+5n+N2IhRJ+1bs0alqanM9pkIsDPj9EmE/cPH86LL73k9rr8WvjdUbA74WfDXUHCVg8H/gg1eyHtDuOffhgkQGYUQog+5GRZGZkZ51dqzYyK4mR+frvttYatlbC+FFJCjZ3WMUFAU6Wx/LW5yijHEfedLuh9zyWBQgjR62mnk/odO0gMDeWIxcLoVnsjjlgspCQmXnCN3Qn/KoGPq2FitJG0DvYH6k8YJcKdDhj1bxDlvoJsf9A/51FCiD7DYbFQ9cIL1G3fzoIpU3iuoIADZjN2p5MDZjPPFRaSu2jRedfU2+FPx40gcUsCPDDEFSRq9hsn0qkgGPuoBAkXmVEIIXqtpsOHqdm4Eex2TPPmMWf8eMLPrnrKzyclMZH7ly8nJyfn3DWlrqS12QZL0+CqGNcbFTuhYB2EDTY20gVFd8+geiAJFEKIXkfb7Vjef5+GL74gcNAgYhYsIMB1rnxOTs55gaG1/RZ45gQE+cHPhkF6OEaiouQtOLUJokdD5oPgL/XTWpNAIYToVexnzlD92mvYy8uN0uDTp6MC3P8q0xryKuG1Ukh2Ja1jgzDyEIX/hMpPYMBkSL8H/PpWiXBvkEAhhOgVtNZYv/6a2s2bUQEBxN59NyGZmZ1eZ3fCiyWwsxomRMPis0lrRxMc+TvUHoDBsyF5dp8sEe4NEiiEED2es7mZ2rffxrp/P0FDhhBz2234R7V/zOjWvG2sXruO8pJiBianMmhGLg1jsrk5AeYMAj8FtNQay18bT0HGQhg4tWsH1MtIoBBC9Ggtp05Rs349DrOZyGnTiJg6tcNT6LbmbePJVc9jumMFGelZWAvz+ebllcyPgHlXZBuNrKfh4J/BXgcjfggx7ms/CVkeK4ToobTW1H/yCWeefx4cDuIWLSLy+uvdHlW6eu06THesIGzYBJR/AGHDJjDwzhXseGOd0cByDPb/DnQLjF4hQcJDMqMQQvQ4jvp6zBs20Hz8OCEjR2KaMwe/0NBOrysvKSYj/fxf/qHpWRSUFEPVV3DsOaM0+MgfG6XChUckUAghepSm48cxv/EGzqYmomfNImzSJI+OLy5ogOCEVKyF+YQNm3DudWthPgmJA+HoKohIhxE/gsAIXw6hz5FAIYToEbTDQd0HH1D/8ccExMcTt3AhgQkJnV7n0PBOObxzGpJuzKXkn/+HoCA/GqprCI+NwdZs46ezwiFmPAxfapxMJy6KBAohRLez19RQs349tlOnCJs4kaiZM/EL7PzMh4pmeL4IChvh6hhISnLyj4AmHp0XS1ZaBvlFVn7/mgW/qO8YG+n6afXXyyWBQgjRraz792N++20AYhYsIHTMmE6v0dqo0/TKKfBX354fsfSJ1Tw6P5YJGWEATMgI49EFA3n63UNk3y1B4lJJoBBCdAunzYZl82Ya9+whcPBgYm6/nYCYmE6vq7PDP0/C17UwIsKo+hrreppUXFJOVtr5Zcaz0kIpLinwxRD6DQkUQoguZysvp+a117CfOUPElClETpuG8u+8dMZ+C/yjGBodsCAJcga4NtABaCepiVHkF1nPzSgA8ouspCZ3nusQHZNAIYToMlprGnftovbdd/ELDSX2nnsIGTq00+tanMbhQh+egaQQeGSoUbPp2wYWOP48uVNDWPnGGVbcFk9WWij5RVZWbjCz5MFHfDeofkAChRCiSzitVsxvvknToUMEDxuGad48/MPDO72uuNFIWJc1GzOI2xIhsHW6wXwAjq8Gu5XseT+Aoc08/c/VFJcUkJqcwJIHHyE7Z7rvBtYPSKAQQvhcc3Ex5vXrcdTXEzVjBuHXXtvp3ginhvcq4M3TEBkAPxkKoyJbN3BAyZtQ+i6EDoJRP4GwwWQnQPZ0CQzeJIFCCOEz2umk/qOPqNu+HX+TifglSwgaPLjT6840w+piONZgHFN6TwqEt/5t1VwFR5+F+gKjoF/aneAv+yN8pdNAoZRKBu4CrgOSACuwH9gEbNZaO33aQyFEr+SwWKh54w1aTpwgNCuL6FtuwS842O01WsPnNUZZcDBWNF0T06b6d/VXcHwt4IRh90P8lT4bgzC4DRRKqdXAYOBt4HdABRACZAIzgceVUv+htd7h644KIXqPpiNHMG/YgLbbMc2dS+j48Z0+amqww79KYJcZhobDklSIbx1XnDYoehXKt0N4Ggx/QOo1dZHOZhQrtdb723l9P/C6UioISPV+t4QQvVHrI0oDBg0i9vbbCYiP7/S6Q3WwphhqbTA3EWYObLXsFYzS4EefgcYSSJwBKfPAT56cdxW3/6U7CBKt328Bjnm1R0KIXsl+5gzV69djP32a8KuuImrGjE6PKLU5YWMZvF8JCcHw80wYEtamUeWnUPiiERhGPCylwbuBRyFZKTUb+DWQ5rpGAVpr3f4RU0KIfkNrjXXvXmrfeQcCAoi96y5CRozo9LpTVniuCE41wXfj4PYk1xGlZzmajABx5jOIzIThSyCo853bwvs8nbv9CZgP5Gutte+6I4ToTZzNzdRu2oQ1P5+gtDRi5s/v8IjSc9do2FYJb5RBqD88nA5Z0W0aNRQbj5qaKiH5Vhg8Swr6dSNPA8VJYL8ECSHEWS2lpdS89ppxROkNNxBx3XVuT58DqGkxSnAcrIdxUbAwBaJaF4nVGso/gKL1xpkRo38KUZm+HYjolKeB4lHgHaXUdqD57Ita6//nk14JIXosrTUNn32GZetW/CIiiLvvPoLT0jq9brfZKOZn15CbDNfFtVn2am+A4/+Amr1gyoKhi+SAoR7C00DxG6AeY2ms7GoRop9yNDQYR5QeO+bxEaVWB7xUAp/VGInqJamQENKmkeUYHHsWbBZIuwMG5bSJIqI7eRooYrXWN/q0J0KIHq25oICaN97AabUSffPNhF15Zad7I47Vw/PFUN0CtyTALYOM8yPO0U4o3QIn34LgOBjzKEQM8ek4xMXzNFBsVUrdqLV+z6e9EUL0ONrhoO7DD6nfudM4ojQ3l8BBg9xeY3fC2+WwpRziguDfhxub6M7TUgvHngfLIYi7EtJzIcD97ER0D08DxY+AR5VSLYDN9ZosjxWij7ObzcYRpSUlhE2YYBxRGuT+6fPpJmPZa7EVJsfCnYMhpO1RE+b9cGwNOJsg414YMFkeNfVgHgUKrXVk5608p5T6NTAXcGKUBVmktS5t0yYFeAEY5Gq3Smv9pDf7IYTomPWbbzC/9RZoTczttxM6dqzb9lrDjip49RQE+cGDQ2CiqU0jpwNOboCy9yA0CYb/FMKSfDQC4S0e74FXSs0Brnd9+6HW+u3LuO8ftNa/dH3uj4H/BB5q08YOrNBaf6WUigR2K6Xe11ofuIz7CiE64bTZsGzZQuNXX3l8RKnFBi+chHwLjI6E+1LBFNimUdMZI2FdXwgDr4chd4CfrI3pDTzdmf1b4EpgneulR5RSU7XW/3EpN9VaW1p9Gw5csD9Da10GlLm+rlNKHcQoUCiBQggfsVVUGEeUVlYSMXkykdnZnR5RurcW1p40VjfdORhuiG9TpwmgajcUrDW+Hr4M4r7jmwEIn/B0RjELuOJsSXGl1D+APcAlBQrXZ/wGuBeoBaZ10nYIMAH4/FLvJ4TomNaaxt27jSNKg4M9OqK02QGvlsJHVZAcAj8dCkltc9HOFjjxKlTsgIh0oyx4SOdFAkXPcjHlF01AtevrthvuL6CU2oqRX2jrca31Rq314xhlyh8DHgae6OBzIoD1wE/azETatlsGLANITZWCtkJ4ymm1Yn7rLZoOHiR46FDjiNII9xvdChuMZa+VzXDjQJgzqM3xpADWMlfF11OQeKOr4qv72YnomZQnVTmUUncDvwU+wCgIeD3wC631i5fdAaXSgE1a6wsyZUqpQIyzMN69mF3gkyZN0rt27brcrgnR5zUXF2N+/XUcdXVEZmcTMXmy270RDg2by2HTaYgOhMWpMKLtUhetofITOPES+AXDsEVgcp8IF91PKbVbaz2pvfc8XfX0olLqQ4w8hQJ+rrU+fRkdGq61Pur6dg5wqJ02CngOOCilQoTwLu10Ur9zJ3Uffoh/dDTxixcTlJzs9prKZmPZa2EjXBUDdw+GsLa/QexWKPwXVH0BUSNg2FII6vQBhOjhPE1m52mtc4A323ntUvxWKTUCY9lrEa4VT0qpJOBZrfUsYAqwEMhXSn3tuu4XWut3LvGeQgjAUVdHzeuvG0eUjh1rHFEa0ramxre0hk+q4eVT4AcsTTMCxQXqTxjnWDefgZS5kDRTKr72EZ0dhRoChAHxSqkYjNkEQBTG+dmXRGt9ewevl2IkztFa72x1PyHEJcjLy2PdmjWcLCsjJTGR7910E1eUlaFtNkxz5hB6xRVuHzXV241CfntqITMcFqdBbNsVrVrD6Twofh0Co2D0zyBqmG8HJrpUZzOKB4GfYASF3Xz7i9sC/I/vuiWEuFx5eXk8+9RTLE1PJzMjgyMWC8+++CJ3jhvH7J/+lMAB7s+b/sZilASvd8D8JJgxoJ1lr7Z6OL4GzPkQMx6G3gcBbWt1iN6us6NQnwSeVEot11o/1UV9EkJ4wbo1a1ians5okwmA0SYT92dmsu7kSW5zEyRanPB6KXxwBhJDYHkGpLQ9nhTAcgSOPWcEiyF3QsI0KcPRR3mazH5KKTUWGI1Ravzs6y/4qmNCiMtzsqyMzIyM817LjIqiJD+/w2uKG+H5Iihrhux4uC3JKMdxHu2EU+9AydsQMgDG/hzCZUl6X+ZpMvsJ4AaMQPEOcDOwE6MWkxCih7FXV5MUGckRi+XcjALgiMVCSmLiBe2dGt6vgI2nIcIfHsmA0e2V/GwxG7MIyxGIvxrSvw/+HSfCRd/g6Ya7BcB4YI/WerFSKgF41nfdEkJcCq01jV9+iWXrVuakpvLc8eMsHTqUzKgojlgsPFdYyP3Ll593TXULrC6CIw0wIRruSYGI9n4z1OQb+Qhni3H63IBru2JIogfwNFBYtdZOpZRdKRWFUfE1o7OLhBBdx242Y964kZYTJwgeOpR5Dz+M6csvjVVP+fmkJCZy//Ll5OR8u6r9ixr410ljnfq9KUZZ8AvSDE67q+Lr+xCWDMMfgFD351GIvsXTQLFLKWUCnsFY/VQPfOGrTgkhPKe1pvGrr7C8Z5wrFj17NmETJ6KUIicn57zAcFaDHV4sgS/NkBEGS9JgQHA7H95UaeyNaDgBCTdA2gLwa1sWVvR1ne2jCNBa27XWP3S99Del1BYgSmu9z/fdE0K447BYML/5Js3HjxOUno5pzhwCWuUk2nO4DlYXQ63NqNE0M6HN8aRnnfkSCv8J+EHmgxA70RdDEL1AZzOKz5RSJcAWYIvW+oTW+oTvuyWEcEdrjXXvXmq3bAGns8MzrLfmbWP12nWUlxSTkJzK2Nm5FA3LZkAwPDoc0tvb8uBogaKXoWInRGTA8PuN86xFv9XZPopJrqJ9NwN/UkoNxljttBnYrrVu7oI+CiFacdTVYX77bZqPHCEoNRXT3LkExMZe0G5r3jaeXPU8pjtWkJGehbUwnw9fXsmUO+Dnt2cT3F4h18ZTRsVX62mjBEfyHKn4KjyrHnuusVHN9TpgJsZy2Uqt9S2+6dqlk+qxoi/SWmPdv5/ad95B2+1EZWcTfvXVKL/26ynlLlqK3+yHCRs24dxrjcf24Hz7adatea7thxsziBMvQ0AIDF0CptG+HI7oYS65eqxS6mfAS1rrEgCttQ3Y5voH1wxDCOFjjoYGajdtoungQeN40nnzCIjv+AAgraG8pJiM9KzzXg9Nz6KgpPj8xnarkYuo2gXRo2DoYqn4Ks7TWY5iMPCpUqoQeBF4VWt95uybWutTvuycEAKsBw5Qu2kTzuZmInNyjDMjOphFgHGo0MunIDAhFWth/nkzCmthPgnJrXZR1xe6Kr5WQ8ptkHSjVHwVF3D7J0Jr/W9AKvBLYBywTym1WSl1r1Kq7XElQggvcjY2UrN+PTWvvop/dDQDli0jcurUDoNETYtRfuO3R6GqBeZ8LxfzqytpPLYH7bDTeGwP5ldXsnhhrlGGo/R9+Ob3xtdjfgaDpSy4aF+n+yi0kcTYDmxXSj0MTMc47e5vGCXIhRBe1nT4MOa338bZ2EjkDTcQMXUqyr/9pHKLE96rgHcrjFIcMwfCzQkQMjab4RGweu3TFLhWPT2ybAnTr78SDv8PmPdDzBUw9F6p+Crc8vjMbKVUFnAXcCdQBfzCV50Sor9yNjVRu2UL1r17CUhIIC43l8BB7e+C1trYMPd6KdTYYGI03J4E8a02zvnhJIQmFJoQmvBrLIV9vwZ7Awy5GxK+KxVfRac6S2YPxwgOdwMO4CXgRq11QRf0TYh+penYMcxvvomzvp6I664j8rvf7XAWcaIRXi6BgkZICTV2VmdGnN9mW95Wnv/7k6yYZyIrLYP8Iisr/7EWZqWTfefjEJ7SBaMSfUFnM4p3MZLYd2qtO65NLIS4ZM7mZizvvUfjV18REB9P7J13EjS4/QWFNS2woQw+q4GoAKM+07Wx7RwoBKxbu5oV80xMyDCeEE/ICGPF/IE8/Z6F7CUSJITnOttwd67wn2vj3XCt9ValVCgQoLWu83UHhejLmgsLMW/ciKO2lvDJk4maNg0VcOH/li1Oowz4Flce4iZXHiLUzV644pJystLOr92ZlRZKcYk8EBAXx9PzKB4AlgGxwFAgGSOZfWG1MSFEp5wtLVi2bqXxyy/xj40lfskSglIu/Fu+1rDLbOQhql15iPlJHRTwa81ylNSBIeQXWc/NKADyi6ykJid4dzCiz/M0mf0j4CrgcwCt9VGl1ECf9UqIPqy5uBjzhg04amoIv/pqInNy8Au8sCLriUZ45RQcb4DkEFiUCiM6W5Ruq4fi9VD5Cbk5SazcUMqKecZMIr/IysoNZpY8+IhPxiX6Lk8DRbPWuuVswTGlVADgee0PIQTaZsOybRsNn32Gv8lE3H33ETxkyAXtzDYjD/FpNUQGwELXORHt5SG+/XAnVH5qBAmHFZJmkn3lLTBkB0+vXU1xSQGpyQksefARsnOm+2yMom/yNFBsV0r9AghVSs0Afgi85btuCdG3tJSUYN6wAXtVFWGTJhE1YwZ+QUHnt3HCVlcewqHhxoEwq5M8BACNpVC4DuqOQeQwSM+FsCQAsnOmS2AQl83TQPEfwFIgH3gQ49xsOQpViE5ou526Dz+k/pNP8I+MJG7hQoIzzk8waw27zUYeosoGV0TDAk/yEI4WOLUJyt4D/1DIuNc4nlR2Vwsv8yhQaK2dGKfbPePb7gjRd7SUlhqziMpKwiZMIOrGG/ELCTmvTZErD3HMlYf4qSd5CDDOrz7xIjRXGcEhdQEERnR+nRCXoLMNd28BqzAOLbK1eS8DWASc0Fo/77MeCtHLaIeDuh07qP/oI/wiIoj9/vcJGT78vDa1rfIQEQFwTwpM6SwPAdBcA0WvQPVXEJoIo1dAVKbvBiMEnc8oHgB+inFoUTVQCYQA6cAx4Gmt9UbfdlGI3sNWXk7Nhg3YT58mdNw4omfOxC809Nv3nbC1EjaXg13DDE/zENoBpz+EkxuNxHXKPEicAX4eV+ER4pJ1tuHuNPAo8KhSagiQCFiBI1rrRt93T4jeQTud1O/cSd327fiFhhJz552Ejhz57fsavqqF9aVGZdfxUbBgMAzsLA8BRinwgnXQeBJMY2HIXRAywHeDEaINj/864jor+4TPeiJEL2WrrMS8YQO20lJCxowhetYs/MO+3eRW7MpDHG2AwSHwk6EwypM8hL0RTm6A8h0QGA3Dl0HsRCniJ7qczFuFuETa6aThs8+wbNuGX1AQMQsWEDpmzLn3a22wsQw+qYZwf8hNhqlxHuQhtDZOmyt6BWx1MGiacXZ1QGgnFwrhGxIohLgE9qoqajZuxHbyJCEjRxJ9yy34RxirjmxOyHPlIWwapg8w8hBhnvzf1lQBhf+C2oMQngYjHoaINN8ORohOdLbqKVVrXeyujRD9idaahi++oG7rVggIwHTbbYRmZaGUQmvY48pDnHHlIW4fDAme5CGcNih9F05tNhLUQ+5ynRUheyJE9+vs7zgbgIkASqn1Wuvbfd4jIXooe00N5o0baSkqInj4cEy33op/pJFsONkIr5TCkXpIupg8BEDtIWMW0VQOcZMg7Q4IMvlsHEJcrM4CReunqRkdthKiD9Na07h7N5b33gOlMM2ZQ+gVV6CUwuLKQ3xcDWH+8H1XHsLfk3yzzQJFr8GZzyE4Hkb+GExjOr9OiC7WWaDQHXwtRL/gqK3F/OabNBcUEJSRgWnOHAKio7E5YVsFvFNu1GjKGQC3eJqH0E6o2AnFb4CzGQbPgsE3g19Q59cK0Q06+2M9XillwZhZhLq+xvW91lpH+bR3QnQTrTXWr7+m9t13wekk+pZbCPvOdwDFHjO85spDjIsy6jIlhHT2iS4NJUYBv/oCY0d1ei6Etn8mthA9RWcb7jrbLypEn+Ooq8P81ls0Hz1KUFoaprlzCYiJ4aQVXj0Fh115iEcyYLSnf1VyNEHJ21CWBwFhMHQRxF8jeyJEryDLY4Vw0Vpjzc+ndvNmsNuJmjmT8Kuuos6uePMk7Kwy8hB3J8N1nuYhAKq/hhMvQUsNDJwKqfMhINyXQxHCqyRQCAE46uup3bSJpkOHCExOJmbePIiJ4/1K2HTayENku/IQ4R4f91UFJ16Gmr0QmgRj7jfOixCil+mWQKGU+jUwF3ACFcAirXVpB239gV3AKa317K7rpegvrN98Q+077+BsbiZqxgzCrr6GffV+rD8EFS2Q5cpDDPI0D+F0wOk8KHGd7ZU6HwZNBz95kit6p+6aUfxBa/1LAKXUj4H/BB7qoO0jwEFAEufisuXl5bFuzRpOlpWRnJDAvDFjuNJmIzApibh586iIGMAzhXCoHhKD4ccZMOZi/uTVHTeS1Y2nIGacsXEuOM5n4xGiK3RLoNBaW1p9G04HS2+VUsnALcBvMMqdC3HJ8vLyePapp1iank5mRgZHLBae/fhjAmbN4rr7lvJKuR8fnTLyEHcNhuvjLyIPYW8wlrtWfARBMZD5A4i9wpfDEaLLdFuOQin1G+BeoBaY1kGzP2GUOfd0j6sQHVq3Zg1L09MZbTIBMNpk4v7MTJ77+DPev+5HNDthWjzMHnQReQitjQ1zRa8ZwSJxBiTPBn9Pn1MJ0fP5LFAopbYC7S0Qf1xrvVFr/TjwuFLqMeBh4Ik2188GKrTWu5VSN3hwv2XAMoDU1NTL7L3oa5zNzRSXlVEVGclPv97Hmbpa4iOjuS0xgcqKMiZHGHmIxIv5/W49bZTesByGiHRIfwTCU3w2BiG6i9K6ezdcK6XSgE1a67FtXv8vYCFgxzhVLwp4XWt9T2efOWnSJL1r1y5fdFf0MtrhoHH3bup27ODhbduwBkcQm/sYoelZWAvzqV73X4QoJ+tff83zD3W2wKktRhE/vyBIvc1Y9ioF/EQvppTarbWe1N573bXqabjW+qjr2znAobZttNaPAY+52t8A/MyTICEEGHsimg4cwJKXh6OmhqAhQ3BERBP7vUcJGzYBwPh37mM0vvbfnn+w+YAxi2iuhPirIPUOCJJ1FqJv664cxW+VUiMwlscW4VrxpJRKAp7VWs/qpn6JPqC5sBDL1q3YSksJGDiQ2juXkBeUjGXtPxmQnnVe29D0LMrOVHT+oS21UPQqVH0JIQNh1E8gepRvBiBED9Ndq57aLVfu2ktxQZDQWn8IfOjbXonezlZejmXrVpqPHcMvKoryufewLTyDIw2KcBtEJ6ViLcw/N6MAsBbmk5DsJqelnVC+3TiS1GmH5Fsh6SbwC/T9gIToIWRntuj17GYzdR98gHXfPnRICMUz7+QD0wiKrApTC9yRZJTc+Oi+XJ5ctRLuWHEuR2F+dSWPLFvS/gc3FEPBOmg4YcwehtwNoQldOjYhegIJFKLXclqt1H30EQ1ffIFD+XF02u1sjx/N6RY/BjhgYQpcHQOBrhzz9JxsAFavfZqCkmISklN5ZNmSc6+fY7dCyZtw+gMIjIRhSyHuSingJ/qtbl/15Auy6qlv0zYb9Z9/Tv3OnbTYHHwzeTYfJWRRbfcjOQRmJsBE00Vsljv3wRqqv4ITr4CtFhKuh5R5RrVXIfq4HrfqSYhLoZ1OrHv3YvngA6zWZr6edDMfJ2ZR5/QnIwi+nwJjoy7xL/5NZ+DEi2DeD2EpkPkQRKZ7fQxC9EYSKESPp7Wm+cgRLHl5WGrr+XL8dD4fPB6r9md0ONycAMPDLzFAOO1Q9j6c2gT4GedVD5oGSgr4CXGWBArRo7WUlGB5/33OVNTw2dhp7B48nhb8mBBlPGIacpFPhbblbWXd2tUUl5STmhRH7g1xZI92QOwESPseBMf6ZiBC9GISKESPZD9zBsu2bZwqLueTUd9l7xVj0UpxdYzipoSLLLXhsi1vK8///UlWzDORlZZBfpGVla8XQPydZF+z2PuDEKKPkEAhehRHXR1127dTcOwUOzOv40DOHfj7wXVxihkDID740j973drVrJhnYkKGMQ2ZkBHGivkDePr1rWTPkUAhREckUIgewdncTP3HH3Pw0Ek+GnotR2+YTYif5sZ4Rc4AiL6c/W1aQ81eiktOk5U29Ly3stJCKS4puLzOC9HHSaAQ3Uo7HNTv2sXe/cXsSLuSosnZhPs5mTMQbohXnpf77kj9CaP0Rt0xUgeGkl9kPTejAMgvspKaLJvohHBHAoXoFlprGvd/wxf7itg+eAJl37kak5+D7yXC1Fg/gi930VHTGaPsRtWXEBAJ6d8nd0kzK1c9xYp5xkwiv8jKyg1mljz4iBdGJETfJYFCdLnG4wV8tLeIHQPGcmbMWOJVCwsHa66O9T+3i/qS2Rvh1GY4vQ1QMPhmSLwJAkLJTgCUH0+vXU1xSQGpyQksefARsnOme2FUQvRdsjNbdJmGstN8sKeYHaZMasNMJGFlVmoI34lR+F1udQynAyq2Q8nbRrCIvxpS5spyVyE8JDuzRbeqqzaz9etTfBSWRkPSVQxxWLgnzUGWKfTyyydpDTVfQ/Hr0FQBUSMgbQGEyymHQniLBArhM7WWRrbsK+Pj4ME0x44hs+UMs1MDyYyJ8k59vfpC46zqumMQmggjHgbTWCneJ4SXSaAQXnem0caW/RV86j8Qe3gGY61lzB4SRfqAeO/coHWiOjAS0nNh4BQpuyGEj0igEF5z2urknUPV7NIxOAMSmVBXxKxhUaQMTvLODVonqpWCwbOMQ4T8L2GbthDCYxIoxGUrbtS8c7yOr+0R+DujmVR1mJnDokia6KXqq047lO+AU2cT1de4EtUx3vl8IYRbEijEJTtWD5uKrBywhRJkC2bq6T3cODSSATNGobyRJ9AaavZA8RuuRPVIV6I65fI/WwjhMQkU4qJoDQfq4J0SG8daAglrdpJdspOcIRHE3TIB5Xe5GyFc6gqhuHWiejmYxkiiWohuIIFCeMSp4etaeKfUwckWfyKtVmYWfsh1yaHE3noVfkFB3rnReYnqKElUC9EDSKAQbjk0fF4NW8qdlLf4EVtv5tZjn3DtoCBMc6fiHx7unRvZG1yJ6g9ciepbIOlGSVQL0QNIoBDtanHCx1XwXoWm2qYYZKlkweEdTIzzJ3ruNAJivJRIdtqhfLtxwpy9EQZcCylzIEgS1UL0FBIoxHmsDvjwDORVaursipTaMmYe+IDREU6iZ08nKDHROzfSGqr3GDuqmyshehSk3i6JaiF6IAkU/djWvG2sXruO8pJiBianMv7WXEqHZ9PkhOHmEm7fv5WhgS1E3TidkKFDO/9AT9UVQvGrUHccQpNg5HKIlkS1ED2VBIp+amveNv7412eIvetRMtKzsBbms+1fv2d8diULbbWkKCuR2dmEjh3rnaWu4EpUvwFVu1yJ6ntg4GRJVAvRw0mg6IccGp5e9Ryxdz1K2LAJAIQNm8DAux/l6NpfMfKxnxM+aRIqwEt/PCRRLUSvJoGiH6lsho+r4dNqqDtTzsD0rPPeD03PorS+johrrvHODZ12KP8QSjaBwwoDJkPKrZKoFqKXkUDRx9mcxv6HnVVwqB4UMDqkhd3BIVgL88/NKACshfmoYC/8LV9rqP7K2FEtiWohej0JFH3UKasxe/isGhocEBcIt0TUk7V/B8H7drEDJ9Xr/gtyHyPUlaOoXvdfxIVeZqCoO26U/q4vcCWqf2zsqBZC9FoSKPqQJgfsMhuzh8JG8FdwRTRc46gg8Ys8bEeOoIKCCJ88mQe/8x3+8te/0rj2V5Q11BEdHkmQw8ayf/u3S7x5pTGDqN5tJKozFhqPmpSXSnoIIbqNBIpeTms40WgEhy/N0OyExGBYkKSZUFsIH+6gpagIR1gYkdOmEX7llfiFhjID8AsJYd2aNVga6oiOiiB30SJycnIurgP2Bjj1jitR7Q+DZ0PSDElUC9GHyJnZvVS9HT6vMQJEaRME+cGVJpgSq0ksOkjDxzuxlZXhFxVFxLXXEjZxovfqMQE4bcaO6vMS1XMgyOS9ewghuoycmd1HODUcrjdKa+ypBbuGIWGQmwyTohxwIJ/6N3dirqrCPzYW05w5hI4bh/L34j6Fc4nq16H5DESPdiWqk713DyFEjyKBohcw2+CTaiNAnGmBMH+4Lg6mxMHgABuNX31F3Sef4LBYCBg0iJgFCwgZNcp7Jb/Pap2oDhssiWoh+gkJFD2UQ8N+i/FoKd8CGhgRAXMTjQR1QEsTDV9+ScVnn+FsbCQoNZXo2bMJHjbMezupzzovUR0NGfcaxfskUS1EvyCBooepaDZmDp9WQ60dogLgpoHG7GFgMDjq62nY9hkNu3ahm5sJHjaMiKlTCU5L835n7A1GDqL8QyNRnTwbEiVRLUR/I4GiB7A5jZzDziojB6GArCiYGgdjo4xlrnazmdq8T2jYswfsdkLGjCFyyhQCvVXNtTWnzbWj+h0jUT1wCiTPgaBo799LCNHjdUugUEr9GpgLOIEKYJHWurSddibgWWAsxtOXJVrrT7uwqz5VYjWCw+c10OiA+CDj0dK1MRDjWqBkq6zE8vHHWPPzAQgbP56IKVMIiIvzfoe0Nh4vFb/hSlSPgbTbjXyEEKLf6q4ZxR+01r8EUEr9GPhP4KF22j0JbNFaL1BKBQFhXdhHn2hywBc1xq7pE40QoGBCtDF7yIwAP1d6oaW0lPqdO2k6eBAVGEj4lVcSMXky/lFRXuvLtrytrFu7muKSclKT4sjNHkT2yCYIS4aRj4BptNfuJYTovbolUGitLa2+DceYLZxHKRUFXA8scl3TArR0Rf+8TWsoaDRyD7vMxqa4pBD43mC4OgYiAs620zSfKKL+o49oLihAhYQQcf31hF99Nf5h3o2R2/K28vzfn2TFPBNZaRnkF1lZ+fphiJ5L9rwHJVEthDin23IUSqnfAPcCtcC0dppkAJXAaqXUeGA38IjWuqHrenl56u1GraWd1VDWBMGuTXFT44z9D2cXJ2mtaT5yhLqdO7GVlOAXHk7U9OmETZqEX3CwdzpjqwdrKTSWgbWUdc//ixXzTEzIMALQhIwwVswfwNMbd5J92w+8c08hRJ/gs0ChlNoKDGrnrce11hu11o8DjyulHgMeBp5op28TgeVa68+VUk8C/wH8soP7LQOWAaSmpnppFBfPqY0qrTurjKqtDg3pYbAwBSaZIKTV3jftdGL95hvqd+7EXlGBv8lE9KxZhE2YcOlnQdgbzgUDIzCUgrUMbK0mcf4hFJc3kpV2fiI8Ky2U4pKCS7uvEKLP8lmg0FpP97Dpv4BNXBgoSoASrfXnru9fwwgUHd1vFbAKjBIeF9fby1fT4toUVw1VLRDuDzfEw5RYGBzapq92O41ff039J5/gqKkhYMAATLfdZpwm5+kmObu1VSBwBYPGUrDVftvGLxhCE8E01qjkGpZo/DsohtTke8gvsp6bUQDkF1lJTU7wwn8NIURf0l2rnoZrrY+6vp0DHGrbRmt9Wil1Uik1Qmt9GMgBDnRlPzvj0LCv1ni09I1rU9yoCLjNtSkusM3vfGdzM427d1P/6ac46+sJHDyYqBtvJGTEiI43ydmtRhBoPTuwlkKL+ds2fkFGQIge/W0wCDMCQke5htyFi1n59ydZMc+YSeQXWVm5wcySBx/xxn8aIUQf0l05it8qpUZgLI8twrXiSSmVBDyrtZ7larccWOda8VQALO6OzrZV3mw8WvqsGix2MAXCzQkwORYGtJNScDY2Uv/FFzR8/jm6qYmg9HQi588naMiQbwOEo6nNI6OzAaHm2w/yCzQCQtRI499hSUZQCI696ORzdo4x4Xt67WqKSwpITU5gyYOPnHtdCCHOkuqxHmpxwldmY+XSkQbwA8ZFw9RYGO3aFNeWw2Kh/tNPady9G22zETJyJBGTryIoRl34yKil+tsLVSCEDvp2dnB2hhAcJ6uRhBA+IdVjPbA1bxur166jvKSYhORUFi/MZXpONicbjUdLn1eD1QkDgoxHS9fGQnRg+59lr66m/uMd2Aq+IiCshZirTAQNjMDPsRdObYNTroYqwAgIkUMh7DpXUEiEkAESEIQQPYYECowg8eSq5zHdsYIM17Ggf/z7SjaWQcvYbAIUTDQZs4fMiG+XtQLgbAHraWgsxXHmGI7Th/DT1UTHO1ADXG2UBRgEEekwYMq3M4WQAUYNJSGE6MEkUACr164j+Ipp1L3+35RVlBMxMIHQCdkUblnHipuyuSoGwv1sRkCoKjv/sVFTJWf3C/o5wekIRAcnohPGoKKHGI+MJCAIIXoxCRRAeUkRMfUVPDH/213K//f1DTSZG5lW/Vc4VQZNFXy7gdwPHTIQp9NE85kgmkoacNgjCBk3lfApV+MXGurudkII0atIoADCQwP4xfzzdyn/Yj787381G7OGsCSImwShieiQQTQVman/+FPjqNHISCImz/D+UaNCCNFDSKAAGqw2stLOnwVkpYXS0OSAK34FgHY4sO7bR/3HG7H78qhRIYToYSRQAGnJg9rdpZyWPAinzThqtKErjhoVQogeSAIFxi7l3//1jzw6/9tdyr9fX8U9ObdQ8ac/+f6oUSGE6MEkUAAaRZMV/vByFZUNzQwID6ap2UnTNwcInDzZd0eNCiFELyCBAli3Zg0/ysxktMl07rUDZjPrTp/m9tzc7uuYEEL0APKQHThZVkZmm5PjMqOiKKms7KYeCSFEzyGBAkhJTOSIxXLea0csFlISEzu4Qggh+g8JFEDuokU8V1jIAbMZu9PJAbOZ5woLyV20qLu7JoQQ3U5yFEBOTg5g5CpO5ueTkpjI/cuXn3tdCCH6MwkULjk5ORIYhBCiHfLoSQghhFsSKIQQQrglgUIIIYRbEiiEEEK4JYFCCCGEW0pr3XmrXkYpVQkUXeLl8cAZL3anN5Ax9339bbwgY75YaVrrAe290ScDxeVQSu3SWk/q7n50JRlz39ffxgsyZm+SR09CCCHckkAhhBDCLQkUF1rV3R3oBjLmvq+/jRdkzF4jOQohhBBuyYxCCCGEW/0yUCilZiqlDiuljiml/qOd95VS6s+u9/cppSZ2Rz+9yYMxj1RKfaqUalZK/aw7+uhtHow51/Xz3aeU+kQpNb47+ulNHox5rmu8XyuldimlpnZHP72pszG3anelUsqhlFrQlf3zBQ9+zjcopWpdP+evlVL/eVk31Fr3q38Af+A4kAEEAXuB0W3azAI2Awq4Bvi8u/vdBWMeCFwJ/Ab4WXf3uYvGPBmIcX19cz/5OUfw7SPnccCh7u63r8fcqt024B1gQXf3uwt+zjcAb3vrnv1xRnEVcExrXaC1bgFeAua2aTMXeEEbPgNMSqnefNxdp2PWWldorb8EbN3RQR/wZMyfaK1rXN9+BiR3cR+9zZMx12vXbxIgHOjtSUpP/n8GWA6sByq6snM+4umYvaY/BorBwMlW35e4XrvYNr1JXxuPJy52zEsxZpG9mUdjVkrdppQ6BGwClnRR33yl0zErpQYDtwF/68J++ZKnf7avVUrtVUptVkqNuZwb9sdAodp5re3fqjxp05v0tfF4wuMxK6WmYQSKn/u0R77n0Zi11m9orUcC84Bf+7pTPubJmP8E/Fxr7fB9d7qEJ2P+CqMkx3jgKWDD5dywPwaKEiCl1ffJQOkltOlN+tp4POHRmJVS44Bngbla66ou6puvXNTPWWu9AxiqlIr3dcd8yJMxTwJeUkqdABYAf1FKzeuS3vlGp2PWWlu01vWur98BAi/n59wfA8WXwHClVLpSKgi4C3izTZs3gXtdq5+uAWq11mVd3VEv8mTMfU2nY1ZKpQKvAwu11ke6oY/e5smYhymllOvriRjJ0N4cIDsds9Y6XWs9RGs9BHgN+KHWekOX99R7PPk5D2r1c74K43f9Jf+c+92Z2Vpru1LqYeBdjNUDz2utv1FKPeR6/28YKyNmAceARmBxd/XXGzwZs1JqELALiAKcSqmfYKyksHRXvy+Hhz/n/wTiMP6GCWDXvbiInIdjvh3jL0E2wArc2Sq53et4OOY+xcMxLwB+oJSyY/yc77qcn7PszBZCCOFWf3z0JIQQ4iJIoBBCCOGWBAohhBBuSaAQQgjhlgQKIYQQbkmgEEII4ZYECiGEEG5JoBDCR5RSHyilZri+/j9KqT93d5+EuBT9bme2EF3oCeBXSqmBwARgTjf3R4hLIjMKIXzEVXRPAT/FKKHgAFBKvdW6nVKqt1dwFX2cBAohfEQplQUkAs1a6zrXa0OAE63aDEJm9qKHk0AhhA+4TkRch3HyWINS6ibXWxMxzgo4awLwddf2ToiLI4FCCC9TSoVhlC9fobU+iHE40P92vf0dYHer5lcggUL0cFI9VogupJTaDBQBduBV4F7gAa21s1s7JoQbEiiEEEK4JY+ehBBCuCWBQgghhFsSKIQQQrglgUIIIYRbEiiEEEK4JYFCCCGEWxIohBBCuCWBQgghhFsSKIQQQrj1/wG1YCXcGpgdhAAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(comp, fcc, '-', color=\"#e58080\")\n",
+ "plt.plot(comp, lqd, '-', color=\"#66cfff\")\n",
+ "plt.plot(comp, b32, '-', color=\"#ffc766\")\n",
+ "plt.plot(comp, fcc, 'o', label='fcc', color=\"#e58080\", markeredgecolor=\"#424242\")\n",
+ "plt.plot(comp, lqd, 'o', label='lqd', color=\"#66cfff\", markeredgecolor=\"#424242\")\n",
+ "plt.plot(comp, b32, 'o', label='b32', color=\"#ffc766\", markeredgecolor=\"#424242\")\n",
+ "plt.xlabel(r\"$x_{Li}$\")\n",
+ "plt.ylabel(r\"F (eV/atom)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "123556d1-6b6e-4cdb-97b5-8711c1989d68",
+ "metadata": {},
+ "source": [
+ "### Configurational entropy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2b4c03ca-56c7-4830-a6e7-b01eff5c219e",
+ "metadata": {},
+ "source": [
+ "In the above example, we had off stoichiometric compositions, but we did not include configurational entropy for the solid structures. The easiest way to do this, which we will use here, is to employ the ideal mixing assumption. In the case of ideal mixing, the configuration entropy of mixing is given by,\n",
+ "\n",
+ "$$\n",
+ "S_{mix} = -k_B (x \\log(x) + (1-x) \\log(1-x))\n",
+ "$$\n",
+ "\n",
+ "We can add this directly to the free energy.\n",
+ "\n",
+ "For the liquid phase, addition of configurational entropy explicitely is not needed as is it included in the free energy calculations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "id": "6c011541-030a-4ac8-99b4-c6d07d5f0340",
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ },
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/tmp/ipykernel_81/1902816561.py:1: RuntimeWarning: divide by zero encountered in log\n",
+ " smix = -kb*(comp*np.log(comp) + (1-comp)*np.log(1-comp))\n",
+ "/tmp/ipykernel_81/1902816561.py:1: RuntimeWarning: invalid value encountered in multiply\n",
+ " smix = -kb*(comp*np.log(comp) + (1-comp)*np.log(1-comp))\n"
+ ]
+ }
+ ],
+ "source": [
+ "smix = -kb*(comp*np.log(comp) + (1-comp)*np.log(1-comp))\n",
+ "smix[0] = 0"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 97,
+ "id": "be276386-1148-482b-8364-4ee77a2d6831",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fcc_mix = np.array(fcc)-temp*smix\n",
+ "b32_mix = np.array(b32)-temp*(smix-smix[-1])\n",
+ "lqd_mix = np.array(lqd)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 98,
+ "id": "a44bb0b3-12ba-4e39-8c9c-b2760dd65ae4",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fcf10bbb2b0>"
+ ]
+ },
+ "execution_count": 98,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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/03U8JYMoDu3NjxMdXB3nbw1Y73nKKsUx7FcQ1OwM/27DI4PZItLcoyZE5BgwpdHrj4CPOiquk04OWD+3dAk5uZkkxPdhzv3zzmsgGyA1NZWXX36Z+++/n5SUFH784x9zzTXXUF5ejogwcuRInn/+eQD+8Ic/UFxczE9+8hMAfHx82LRp0/l1TCnlMkddHVs+WsvSuCvx8fFi/hBvBgQbKNoIh5ZAYBwM/Rn4hXo6VLczIi2OD3dZY8aMkTN/qe7Zs4fU1O75/LA7900pT7CXl7Pmk295O3k8UV71zBsWSLQ/cHwtHH4dQgbBkAfBJ7DNc3UVxpjNIjKmufe0hIdSSjVSl3ec977az2cpkxnoZePBYYEEewvkfgS570F4GgyeC15+ng61w2iiUEopp+oDB3ltdxkbB41jdEANcwYH4msckP0WHE+H6Esh+Ufg1bVLcpwtTRRKKQWUbNrCksJg9iVexOSwWm4ZEIAXdji0FIrWQ9+JkDjDmuXUw/SoRCEi35mi2tV1xzEmpTqSiHAsfS2LvQdxrG8ct/VtYGJff3DUwYFFULId4qdCvyndom7TuegxiSIgIIDi4mKioqK6TbIQEYqLiwkI6HoboSjVGUh9Pfs/XMWSmEupDAzj/gEwKsIHGmyw7x9QcQAG3AF9x3s6VI/qMYkiPj6e3NxcCgsLPR1KuwoICCA+Pt7TYSjV5dirqtj2/mqWJk3C28+XX6R4kdzLQH057HkGbEdh0ByIvsTToXpcj0kUvr6+JCV135WTSinX1RcV8eUnG3hr6HWE+wgPD/Ulxh+oLYY9T0PdCRj8IER8d2uAnqjHJAqllAKoPXyYj9Yf5JNhNzDAt46fDvWnlw9gy7OShL0WUh+21kooQBOFUqoHqdy2nTcP2diQOpmRQXXcO8gfPy+gMgv2PmvtRDdsPgTr49zGNFEopbo9EaFk7RcsrYpi98CxTIho4AcJfngZoGwP7HsefEOsO4mA89umoDvSRKGU6tbEbufohyt5KTiNI/0SuDXWwTV9nL/6TmyBA4shoDekzgO/cI/G2llpolBKdSvp6ekse+kljuTlEd+nD5OHDmfXhPsoC47kvkRhTIRzwVzBl5D5qlUefOhPwSfYs4F3Yj1viaFSqttKT0/nub/9jbLySgQor6zmjfVfcmz/Fn6e4sWYCOcaqmOfQOZSCBtmPW7SJNEqTRRKqW5j4T+ep843iKC7fk/yn1YSdNfvcfgHU/XhQgb1AkQgeznkvA1RY2DIT8Db39Nhd3qaKJRS3UaxrYbImY8SNGgUxtuHoEGjiJz5KCW2GhAHZL0KeZ9C73Ew6B7w0qfvrvDUVqhPGGN2GGO2GWM+NcY0uz2UMeZFY0yBMWZnR8eolOpaHNXVSG0NgUlpTY4HJqUhtTVw4AVrXKLfFEj6YY8s7neuPPVv6i8iMkJELgQ+AH7fQruXgOs6KiilVNdUl5vLt//+AN+I3tiyMpq8Z8vKIDwy1JrhlDgD+k/rscX9zpWntkItb/QyGGi2BKqIrDPGDOiQoJRSXY6IULFhAx9m17L2wltJNBFkv/IH/AN8qDpRQnBkBLW2On55YwgMnAUxl3k65C7JYw/ojDFPAncDZcCEdjjfXGAuQEJCwvmeTinVyTlsNnI++ITXw0dyeGgSl4Ta6dfP8LJfHY/c1Iu0xGQysm38+a1yvPpO0yRxHty2Z7YxZhXQt5m3HhORdxu1exQIEJHHWzjPAOADEXG5Oldze2YrpbqPuqNH+Tb9W5YPuZYGvwBuT/Di8kjDvbNn8tNrvRiVHHSq7dbMap771MHil5Z5MOLOzyN7ZovIZBebvgZ8CDSbKJRS6iQRofzbjbybU89XI24m1rue+1O8iXVuyZKTm09aYnKTz6QlBpKTm+mBaLsPjzx6MsakiMgB58upwF5PxKGU6jocNTVkfbSK18JHkpvSn6vCGvhBoq9V1A/AUU9C315kZNua3FFkZNtIiO/jmaC7CU/NevqjMWanMWYHcC0wD8AYE2eM+ehkI2PM68B6YIgxJtcYc49nwlVKeVJdXh7rlq/imfhJFEXEcm+icGeSz+kkUVMIu/7MzKuCWLCimK2Z1TTYha2Z1Sx4p5SZd832aPxdndvGKDxJxyiU6h5EhLJNm3krV9iYdDEJ3nXMHexnbTJ00omtcOhlwMDAWazeWsiypUvIyc0nIb4PM++azcRJrj4J77k8MkahlFLnw1Fby4GVa3gtbCTHk2KZFF7P9AQ/fE49arLDkbchbxUEJ0LKXAiIZuIkNDG0M00USqlOp/74cdZ8vp33B03Ax9uLnwwQRob7nm5Qe8JaaV2ZCX0nQMIt4OXb8gnVedFEoZTqNESEks1b+fcxL7YN/R7JPjXcN9iXSL9GjUp2wqEXQeyQcp9V3E+5lSYKpVSn4KirY98n63g1fCTF/aO5PrKO7/cPwPtktQ2xQ+77cPRjCIq3HjUF6mymjqCJQinlcXXH81n1xS4+TL6aQCPMGwipoY1uI+rK4OAiKN8PMVdA0u3g5dfyCVW70kShlPIYEeHE1u0sO+7LrpSJDPGxce+QQEIbDzeU7bOShN2m9Zo8RBOFUsojHHV17PrsK5aFj6QsNpxpUbVcFx+I16lHTQ44thKOvOfc0/phCOrnyZB7LE0USqkOV5dfwEdf7eOTAeMIpZ5fDIKUkEaLI+or4eCLULYLoi6G5DvBO8BzAfdwmiiUUh2qcFsGr+T7sz/5Kob7VDFnaDDBjX8TVRyypr7WV1gbDPUep/tHeFibicIYEw/cDlwFxAE2YCdWIb+PRcTh1giVUt2Co76e7ekbeC1sBFUxvZgRXcukfsGnc4AIHE+HnOXgFwnDfw3BumVAZ9BqojDGLAH6Ye1C9yegAAgABmPtPPeYMeY3IrLO3YEqpbqu2sIi3l1/iNXxVxApNTwy2DCgV6NHTQ3VVhmOkm0QcSEM/BH4BLV0OtXB2rqjWCAize1XvRN42xjjB2jKV0q16Pj23bxcGEhmwqWM9qng7tQQAr0bNajKgf3/groT1lalfSfpo6ZOptVE0UKSaPx+HXCwXSNSSnULUl/PxjWbeCM0jbrIAGZG27iqX0jTR00F6+Dwf8A3BIb9EkIGejRm1TyXBrONMTcCTwCJzs8YQEQk1I2xKaW6qNqiYt76Jpt1cWPpY6/i/qFe9AsKPN3AXgOZy6D4Wwi7AAbNAd9engtYtcrVWU9PAdOBDOmOdcmVUu3mWMY+XiwM4ki/0VzmU8YPR4ad3jcCoPoo7F8INfnQfxrEXQfGU1vjKFe4miiOADs1SSilWiINDaxfu5X/hFyAPcyX2THVjO0X1rRR4XrIWgbegZD6cwgb4plg1VlxNVE8AnxkjFkL1J48KCL/ey4XNcY8AUwDHFgzqWaJyLEz2vQHXgH6OtstFJGnz+V6Sin3shWf4N/fHmV97MX0qy/n/lR/+gQ1mrXkqIOsN6DwKwgdDIPuBb+wlk+oOhVXE8WTQCXW1Nj2qMT1FxH5HYAx5mfA74EHzmjTAMwXkS3GmBBgszHmMxHZ3Q7XV0q1k5xdB3ixKIS82DTGeZfwgxER+DZ+kmTLhwMLoToX+l0P8d8H493i+VTn42qiiBSRa9vroiJS3uhlMPCdR1oikgfkOb+vMMbswVrToYlCqU5AGhpY98VO3uqVinewMDemiov6RTRtVLwZMl+xEsOQhyBiuGeCVefF1USxyhhzrYh82l4XNsY8CdwNlAET2mg7ABgFfNNKm7nAXICEBF3aoZQ7VReX8OqWfDbHXEhiXQn3Dw8lKrBRLSZHPWS/BfmfQ68ka+8I/0iPxavOj3FlfNoYU4H1l38dUO883Or0WGPMKqzxhTM9JiLvNmr3KBAgIo+3cJ5ewFrgSRF5u81ggTFjxsimTZtcaaqUOktZuzNZXBxCYa9oJvsUM3149OnNhQBqiqxaTVWHrcVzCdPBS8vKdXbGmM0i0ux2gS799EQk5GwvKiKu7m7+GlbdqO8kCmOML7AcWOZqklBKuYejwc7qr/awIngI/gH1/LRPJWlx0U0blWyHgy8BAoMfgMhRnghVtTOX07wxZiowzvnycxH54FwvaoxJEZEDzpdTgb3NtDHAYmDPuc6uUkq1j8oTpby8tYgdUcMZVFvEfSPCCQ9s9OvDYYcj70DepxDUHwbfDwExHotXtS9XV2b/EbgYWOY8NM8Yc6WI/OYcr/tHY8wQrGmv2ThnPBlj4oBFIjIFuAK4C8gwxmxzfu63IvLROV5TKXUODuzN5sXiEEoik5niXcD3L+l9enMhgLoSOLAIKg5aJcEH/AC8fFs8n+p6XB2j2AFceLKkuDHGG9gqIiPcHN850TEKpc6fo8HOyvX7+SAohWB7DffEOxgad8awZOlua4MhR521uVD0JZ4JVp238x6jcAoHTji/15UySnVj5SfKeXFHCXvCU0m15XPPqChCAhr9uhAH5H4IRz+EwFjrUVNgc3NXVHfgaqL4f8BWY8warIKA44Dfui0qpZTH7Nl7hCUloVSExnOTVx7XjY1tWvW7vty5TekeiB5r7ULn7d/i+VTX5+qsp9eNMZ9jjVMY4NcictydgSmlOpbd7uD9DYdYGTiQcFPJL/tWMDAutmmj8gPW1NeGaki+G2Iu170jegBXB7PTRWQS8F4zx5RSXVzJiQoW7SznYGgKI6qPMnt0b4ICGg1IiwPyPoOcdyAgGoY+BMH9PRav6lhtbYUaAAQB0caYCKy7CYBQrP2zlVJd3I59x3i5NJSa4N7MMLlMuiy+6U1CQxUcXAKlGRB5ESTfBT6BLZ5PdT9t3VHcDzyMlRQ2czpRlAN/d19YSil3a7A7WPFtNqsCBhBtL+WhhHoGxMY3bVSZBftfgPpSGHA79Bmvj5p6oLa2Qn0aeNoY85CIPNtBMSml3KyopJIXdlVxuFcSF1Vmc9fFcQT6N37UJJC/xqrX5BsOFzwCvQZ4KlzlYa4OZj9rjBkODMMqNX7y+CvuCkwp5R5b9uWxtCyM+oAIZpLNuCsTmzZosEHmUjixGcLTYNBs8An2TLCqU3B1MPtxYDxWovgIuB74EmtjIaVUJ/X0M8/w8Wfp1FdX4RsYzMARl9Lwg9/St66Q+5K9iI87I0lUHbH2jqgpsor5xV6j25Qql9dR3AqMxFqNPdsY0wdY5L6wlFLn6+lnnuGj1evo/aP/JjApDVtWBgdefZKBbzzBb//71/gHNNqDTMTafS7rDevuYdgvIDTFc8GrTsXVPxVszvIdDcaYUKztS5PdF5ZS6nx9/Fk6ve98jKBBozDePgQNGkWfOx8ja+empknCXguHXrIeN4UOghGPaZJQTbh6R7HJGBMOvIA1+6kS+NZdQSmlzl99dRWBSWlNjgUmpVFvqzp9wJYH+xda/4y/EfrdoI+a1He0tY7CR0QaROQnzkP/NMasBEJFZIf7w1NKna3KBnj7QAXegcHYsjIIGnR6TwhbVga+Qc6B6aJvIfNV8PKD1HkQluqhiFVn19YdxQZjTC6wElgpIodF5LD7w1JKnS2HwNeFdpbn2rERzMCUNDJffZLedz52aoyi4NUnmTJ5AmQug4J1EDIIUu4Fv4i2L6B6rLbWUYwxxiRizXJ6yhjTD2u208fAWhGp7YAYlVJtyKmGZVl1HK73I6Ekl+n1WQz54+/49e/+iz0v/pq8WjsB/t6MGJbKvAmVULAH4r4H/aeB8fZ0+KqTa3OMQkSygX9iPXbyBa4CrgP+rzGmUERucHOMSqkWVDXAu3nCuiIIqqtj+sFVjLs4hcDB41mdvoq8w3t54s4+pCUGkpFtY8Hb+1i9oYyJM34BEZ1yOxnVCbU1RvFL4A0RyQUQkXpgtfML5x3GWTPGPAFMw9rhrgCYJSLHzmgTAKwD/J1xviUi39lXW6meyCGw4QQsP+qgyg4XZ27keq98+k6/Bq9Aqw7TsqVLmH9TOKOSgwAYlRzE/OkxPPdJLRPnapJQrmvrjqIfsN4YkwW8DrwpIkUn3xSRo+d43b+IyO8AjDE/A36PczvURmqBiSJS6byT+dIY87GIbDjHayrVLRyphtdyhcxqQ/8TR7lzXzpDx11M4AWXNmmXk5tPWmLTWexpiYHkHM3syHBVN9DWGMXPjTG/wNqo6Hbgd8aY7VhJY4WIVJzLRUWkvNHLYOA7+7GKtUdrpfOlr/Or7X1bleqmqhvgvePweZEQVF/DtIxPuDjQRuRdt+Ldq1fTxvWVJPTtRUa27dQdBUBGto2E+D4dHLnq6lwZoxBgLbDWGPNTYDLwR6xxi6DWPtsaY8yTwN1AGTChhTbeWOs2BgF/F5FvWjnfXGAuQEJCwrmGpVSnIwIbSmD5MaGyHsbkbGHi/nX0nTyewAsvxDSu5ioCRRsg+y1mXhXMghXFzL+Z02MU75Qy5/55nuuM6pKMlQdcaGhMGtZdxW1AMfC6iDzVSvtVQHOb6D4mIu82avcoENDa+INzsd8K4CER2dlWrGPGjJFNmza11UypTi/XBq/nwsEq6F9dxPXfLicxIoDwadPwCQ9v2th2HLKWQfl+6DUQkmeyev0eli1dQk5uPgnxfZh512wmTprskb6ozs0Ys1lExjT7XmuJwhiTgpUc7gDswBtYCaLdHnI6p99+KCLD22j3OFAlIn9t65yaKFRXZ7PD+8dhTaEQiJ1JOz/jwuwthE2eTPAllzS9i3DUw9GVcGyltXgu4WbofaWusFZnpbVE0dajp0+wxiNuE5GMdgwoRUQOOF9OBfY20yYGqBeRUmNMINYjrz+1VwxKdUYi8G0JvHUMKhqES0ozufrrtwjtHUXEAw/gExXV9ANle627iJoCiLoEEmeAX6hnglfdVluD2aemTDj/8k8RkVXOX9w+5zqYDfzRGDMEa3psNs4ZT8aYOGCRiEwBYoGXneMUXsB/ROSDc7yeUp3eUedjpgNVkGBs3P7NW8QWHCZk/Hh6XXEFxqvRHUJ9hbWpUNEG8I+BofMgfJjnglfdmqv7UdyHNVAcCQwE4rEGsyedy0VF5JYWjh8Dpji/3wGMaq6dUt1JjR0+OA7phRDoLUwv3s7wL9/Ft08fIubOxbdPo1lK4oDCryF7OThqod/10G+K9chJKTdxtXrsg8AlwDcAInLAGNPbbVEp1QOIwKZS6zFTWT1c5lvOVZ+/RkBxAb2uvJKQ8eMx3o3Ka1Qfsx4zVRy0ajQlzYSgOI/Fr3oOVxNFrYjUnRxAM8b4oGsalDpnx2rgjVzYVwkJAQ7uzNtA1Fef4R0VRcScOfjFx59u7KiDox/BsU/BOwCS74aYy3SwWnUYVxPFWmPMb4FAY8w1wE+A990XllLdU40dPsyHVQUQ4A23BZeQ+slrSHERwZdcQsjkyXj5+p7+QOluyHoNagsheiwk3gq+IZ7rgOqRXE0UvwHuATKA+7H2zdatUJVykQhsLoU3j0FpPVwe4eCaQ1/Cl5/jFRpK+N1345+UdPoDdWWQ/SYUb4SAPpD6cwgb6rH4Vc/mUqJwboP6gvNLKXUWjjsfM+2phP6BMCf0BBEf/oeG/HwCL7yQsO99D6+AAKuxOKDgS8hZYT1y6ncj9LsOvHxbv4hSbtRW9dj3gYVYmxbVn/FeMjALOCwiL7otQqW6qFo7fJQPnxWCn4Hb4xyM3vcVVZ9/jiMwkMjbbydgyJDTH6g+au04V5kJoYOtwerA5oobKNWx2rqjuA/4BdamRSeAQiAASAIOAs81LsehlLIeM20tg/8chZJ6uCwCpgaewP7+CqpycwkYNoywG27AO8hZKs1eC7kfwPFV4B0IA2dZ4xGNV18r5UFtLbg7DjwCPGKMGYC1CM4G7BeRaveHp1TXkl9rPWbaXQHxAXBPghC7+1sqVq0CHx/Cp08ncPjw0yU4SjLg8OtQWwwxV0DCdPDt1fpFlOpgrg5m49wr+7DbIlGqC6tzOB8zFYCPgdv6wRW+ZVSseJfyrCz8Bw0ifOpUvEOcM5bqSuHwf+DEZgjoC8PmW4+blOqEXE4USqnvEoHtZfDvo3CiHsZGwM2xgt/u7ZxYuRJECLvxRoJGj7buIsQB+WvhyDvgaID4qRB3rQ5Wq05NE4VS56igFv6dCzsrIC4A5ifCQCope/sDSvftwy8x0SoHHhFhfaDqiDVYXXUYwlIh6YcQoAUOVOfX1qynBBHJ6ahglOoK6hywMh8+cT5mmhEHE2Kgbs9uCj/4AEddHaHXXkvw2LHWXYS9xhqszksH32AYdA9EXayD1arLaOuO4h1gNIAxZnlLxfyU6ilOPmYqroNLIuCWOAhtsFG24mNsGRn4xsURddNN+MbEWB8o2Q5Zr0NdCfS+ytorwifYs51Q6iy1lSga/8mT3GIrpbq5wlorQWSUQ2wA/GIgDAmBmgMHKHj/fRxVVVY58CuvtAr51ZbA4TegZBsExsEF91qF/JTqgtpKFNLC90r1CPUO6xHTynzwMtYdxKQYMHW1lL7/KdVbtuATE0PkHXfgFxtrDVbnpcORdwEH9L8ZYieDlw4Hqq6rrf96RxpjyrHuLAKd3+N8LSKiW2mpbiujDN44CkV1MCYcbo2DCD+ozc6m9J13sJeWEnz55YROmIDx8YHKbMh6FapyIOwCSLoDAmI83Q2lzltbC+68W3v/XBljngCmYe1wVwDMcm5a1Fxbb2ATcFREbnRHPEo1VlRrrareXg59/eHhgZAaAtLQQNkn6VRt2IB3RARRs2fjn5AADTY4vByOr7Equ6bcB5EX6WC16jY8dT/8FxH5HYAx5mfA73Fuh9qMecAeQO9elFvVO+DTAvg43/odf3MsTI4BHy+oO3aM0hUraCgqImjMGEKvucYqB35iCxz+t1Xttc846H8T+AR5uitKtSuPJAoRKW/0MpgWxj+MMfHADcCTWDWnlHKLneXWmoiCOhgdBjP6QaQfiN1O+Zp1VH7xBV69ehF5550EDBxoldzY/waU7ICgeEh5AEKS2r6QUl2Qx0bYjDFPAncDZcCEFpo9hVVrqs2dWowxc7H29SYhIaF9glTd3ok66zHT1jLo4w/zkmGY8961vqCA0hUrqD9+nMARIwi77jq8Avzg2GeQ+57VKOEW6DsJvNzylFapTsGIuGcykzFmFdBcjeTHGlecNcY8CgSIyONnfP5GYIqI/MQYMx74patjFGPGjJFNmzadc+yq+1qVvpolS5eRn5tDaFwCweNnEnbRRG7oaz1m8vUCcTioWr+e8jVr8PL3J+zGGwlMTYWKLGuwujoXwtOswWr/KE93Sal2YYzZLCJjmnvPbXcUIjLZxaavAR8Cj59x/ApgqjFmClZp81BjzKsicmc7hql6kFXpq3l64YuEz5hPclIatqwMiv6zgFv6wfUjJwLQcOIEpe++S11ODgFDhxJ24414+3tZ25HmrwPfMEi5HyJH6WC16jE88ujJGJMiIgecL6cCe89sIyKPAo8624/HuqPQJKHO2QuvLCN8xnyCBo0CIGjQKKJ/MJ83X3+OaddOoHrTJso/+wy8vAi/6SYC09IwJVth77+hvhz6jof4aeAT6NmOKNXBPDVG8UdjzBCs6bHZOGc8GWPigEUiMsVDcalu6GAlvH8cio7mMDAprcl7gUlpZObmcGLZMmoPHcI/OdkqB+5fD/v/DqU7ITgBhvwEeg3wTAeU8jBPzXpqtmaUcy3Fd5KEiHwOfO7eqFR3c7ASPjhu7VUd4gPhcQnYsjJO3VEA2LIyiA4Noy4nh7ApUwgaPQpzfBXs+wDwgsQZ0HcCGB2sVj2X1hVQ3c6ZCeLWOBgXBV/8aCZ/e/7PcPsjBDrHKIqX/Q/3pQ0j5oEH8PEtgZ1Pgu0YRFwIA24D/0hPd0cpj9NEobqNQ1XWI6Y9FU0ThL/zZsAg+NVUUL30D+RVVRAWHIJ/fS0hV1yKT+lHUPAF+EXA4B9D5IUe7YtSnYkmCtXlnZkgbomDqxsliJNeXbSI8dHRbC0rohwhxKueUb1789rifzD5F/2t4n3x3wfvAM90RKlOShOF6rIOVVmPmHa3kSDqCwupWL2aIwUF1Ib68qsZMaQlxpGRbeMvbx6noKIe0n5rDVorpb5DE4XqchoniF7eMD0OxjeTIBpKS6n4/HNsO3ZgfH0JDvDmVzNiGJVs1WIalRzEr2bE8H9eK9AkoVQrNFGoLsPVBGGvrKRy3TqqNm8GYwgeO5ZeV1xOVfoq0hKbroFISwyksqahA3uhVNejiUJ1epnOMYjGCeLqKAg4I0E4amqo/Oorqr75BmloIGjUKELGjcPbkQOH/pfEGD8ysm2n7igAMrJtJMY3V2lGKXWSJgrVaWU67yB2nUwQsXB1dDMJoq6Oqm+/pfKrr5CaGgKHDydk/Hh8/MohZxFU7Af/GGbedjMLXnuf+TdZdxIZ2TYWvFPKnPvneaR/SnUVmihUp5PlvINoK0GI3U715s1UfPEFjspK/FNSCJ04Ed8wA0fesvaK8AmBAbdD76uYOMoHQpJ5bukScnIzSYjvw5z75zFxkqtlyZTqmdxWPdaTtHps15TlvIPYWQHB3nBtbxjfXIJwOLBlZFDx+efYS0vxS0wkZOJE/PuGwdEPIf8L8PKF2Gsg7hqd7qqUCzxSPVYpV52ZIG6ObSFBiFCzbx8Vq1fTUFiIb9++hM2cif+Afpi8z2DbZyAN0Ocq6Hcj+OmmiEq1B00UymNcTRAAtZmZlK9eTf3Ro/hERRFx660EDB2MKfwCtv0TGiqsfar7T4PAPh3fGaW6MU0UqsNlVcEH+db2o20liLqjRylPT6cuKwvv0FDCp04lcISz/PeO/4baIggdDAkPQi/dilQpd9BEoTrMmQnipliY0EKCqC8ooGLNGmr27sUrKIjQ732P4DFjMFUHYPefoCoHgvrBkIcg/ALdREgpN9JEodzucLX1iCnDhQTRUFJCxdq12LZvx/j7EzJ+PMFjx+LVUAAH/g5lu8EvEgbOguhLwXh1eH+U6mk0USi3OZsEYa+spGLdOqo3bwYvL4Ivu4yQK6/Ey6sajrwKRd+CdxAk3GrtNOfl2+H9Uaqn8tRWqE8A07B2uCsAZjk3LTqz3WGgArADDS1N3VKdy5kJYpozQQQ2kyAcNhuVX399ejX16NHWaupALzj6AeSvBQzEXQdx3wOfoO+eRCnlVp66o/iLiPwOwBjzM+D3OLdDbcYEESnqsMjUOWucIILaShB1dVR98w2VX39traZOS7NWU4cFw/F02PcJ2Gsh5nKr9Ld/RMd3SCkFeG4r1PJGL4OB7rfqrwfJdiaIHScTRF+YENN8gji1mnrdOhxVVfgPHmytpu4dDQVfw7b3ob4MIkZC/5sgKK7D+6OUaspjYxTGmCeBu4EyYEILzQT41BgjwL9EZGEr55sLzAVISNCS0R3hrBJEM6upQ2+7Db/4eCjZBtv/DjX50CsZUuZC6KAO749SqnluK+FhjFkFNFeW8zERebdRu0eBABF5vJlzxInIMWNMb+Az4CERWdfWtbWEh3vlOBPEdmeCmBwDE1tKECLU7N1LxZo11mrq2Fir3MbAgZiKQ5CzHCozIaAvJNxs3UnoVFelOpxHSniIiKuV1l4DPgS+kyhODnCLSIExZgVwCdBmolDucWaCmNq35QQBztXU6enUHztmraaeMYOA1FSMLQ/2Pw8l28E3DJLuhN6Xg2nhREopj/LUrKcUETngfDkV2NtMm2DAS0QqnN9fC/yhA8NUTmebIOpycylfvbrpauqRIzH1ZZC5FAq/Bm9/q9xG38ng7dexHVJKnRVPjVH80RgzBGt6bDbOGU/GmDhgkYhMAfoAK4z1GMIHeE1EVnoo3h7pbBNEi6upqYPcdyBvNSDQdyL0mwK+vTqyO0qpc+SpWU+3tHD8GDDF+X0mMLIj41KWs00QDSUlp/em9vcnZMIEgi+9FC9fLzi+Bo5+BHYbRF8C8VMhILpjO6SUOi+6MrsHW5W+miVLl5Gfm0Of+ASm/WAmxakT2VYGgV7w/b4wMRqCWvivxF5RYa2m3rLFWk19+eWEXHEFXoEBUPQNHHkP6k5A2DBImA7B/Tu2g0qpdqGJoodalb6apxe+SPiM+SQnpWHLymDxkgX0nQIzrp/YaoJw2Gyn96Z2OKy9qa++Gu9evaB0Fxx8G6qPQnACDLwbwlI7tnNKqXaliaKHWrJ0GeEz5hM0aBQAQYNG0fu2+dR/8Bw3zp7Y7GdOrab+6iuktvb0aurISKg8DHsWQvl+8I+GQfdC1EVatE+pbkATRQ9T3QDrS+B4bg4Dk9KavBeYlEZmbs53PiMNDVRt3kzlF180XU3dpw/Y8mH/Qjixucn+1Hjpf1pKdRf6f3MPkV0Na4vg2xKoFwjqm4AtK+PUHQWALSuDPvGnV7WLw4Ftxw5rNXVZ2enV1P37Q105ZL0GBV+A8YV+N0Dctbo/tVLdkCaKbqzOARtLYF2xVbDPzwsujYSro2D/7Jk8vXABzJhPoHOMovTNBcybO+f0aurVq2koKsI3Npaw738f/+RkjKPWGqTOWwWOeuf+1DeAX5inu6uUchNNFN1Qfg2sLYb1J6DaDrH+cHs/GBt5eoprwiRrHGLJ0ufIdM56mjd3DlclDaBo0SJrNXV09OnV1GKH/M8h90Pdn1qpHkYTRTdhF9heZj1e2lsJXsDocLg6GlKCmy+fZBD87XUYBL/aaiq/WEfxl1/gHRZ2ejW1AYo3wZF3obYQQgZDou5PrVRPoomiiyupgy+L4csTUFoPEb5WFdcroiCslU3g0tPTWfTss9yTlMTg5GT2l5ezaONGfKdOZco992B8fKBsL+S8DVXZzv2pfwrhw7Von1I9jCaKLsghsK8SPi+CHWVWLfZhIfDDeEgLBa82fo+Lw8HSF17gnqQkhoWHAzAsPJx7Bw/mtS+/5IY7p8CBt3V/aqUUoImiS6lqgK9PWIPTBbXWNqOTe8O4KIjxb/vz9qoqqrdupXrTJnILCzkRGcFvt23kaIWNfiGBTIntz5G8Y5DxJHgH6v7USilAE0WnJ2LNWFpbDJucU1sHBsMNfeCicPB14Y/8uqNHqfr2W2y7doHdjt+AAUSGhLAiL4tHZsSQlhhHRraNP7+ZRWSwrzXNNe463Z9aKQVooui0au2wsdQanM6xgb8XXBYJ46Khf2Dbn5f6emy7dlG1cSP1x45h/PwIGj2K4NFp+Ib54vvRCn45LYZRyVYyGJUcxCMzYvjru1VWXSallHLSRNHJHK+xksP6E2BzQFwA3BEPl0a0XL0VsUN9BdSVYS89Rt3BDBqOZ+HlVUNIvA++aQF4+dVg6j+Gw+8BUFBcQVpi7yanSUsMpKA4z809VEp1NZooOgG7wDbn1NZ9leBtYHQYjI+oYaBfubXhT2k51JVBvfOrrgzqy6G+DKmvxGBtaesNBAYAA0BMAAT0wviGWgviTv0zjIS4v5KRbTt1RwGQkW0jIV7XRSilmtJE0dHEAQ2VUFdOha2MgyVl5FWU428vY7IpY5Z3GWFSjndBGRyv/e7njZe1fahvGOITTkN1ELVHS2gorUNMEH7JFxCQdgneEXGYVgahZ/5oLgv+9TTzb7LuJDKybSx4p5Q5989zX9+VUl2Sp7ZCfQKYhrXDXQEw6+T+2Ge0CwcWAcOxZoHOEZH17ohpdfoqli1dQk5uPgnxfZh512wmTnJ122+schan/uIvb/IX/6njdeVIfTkGBwAhwCjnl90rAC/fMIxvGPglNvrrP9RKDM47AXyCqM8voGrjRmwZGUh9Pb79kwm+5GICU1Ot9Q8uONm355YuISc3k4T4Psy5f97Z9Vkp1SMYEen4ixoTKiLlzu9/BgwTkQeaafcy8IWILDLG+AFBIlLa1vnHjBkjmzZtcjme1emrePFfTzP/pvCmf13PncfE8Zc1kwCsX/pNjtmrm+sp+IaAbxgNPmEclzAO1oaS5wij3ieUxLAw0qLCiAwOa3PfaLHbqdmzh6qNG6nLycH4+BCYlkbwxRfjGxvrcl+VUqo5xpjNIjKmufc8tRVqeaOXwcB3spUxJhQYB8xyfqYOqHNHPMuWLmH+TeFNZgDNvwmeW7yAib0SvvsBL9/Tf+UHxkLokNN/8fuGgV+o89FQCFk2L9YWwaZSaBAYFGKV1RgV5trUVnt5OVWbN1O9ZQuOykq8IyIIvfZagi68EK9AF6Y/KaXUefLYGIUx5kngbqAMmNBMk2SgEFhijBkJbAbmiUhVC+ebC8wFSEho5pd7K3Jy80lLTG5yLC0xkJzCOkic0ejRj/MxkHdAq2UsauxWOe91xXDEObX1iiirams/V6a2ilCXnU3Vxo3U7NkDIvinpBB88cX4DxqE0RIaSqkO5LZEYYxZBfRt5q3HRORdEXkMeMwY8yjwU+DxZmIbDTwkIt8YY54GfgP8rrnrichCYCFYj57OJtaE+D4tzADqC7GuP7M/5pzauuEE1DggPsAqq3FpBAS0NLW1EUddHbbt26nauJGGwkJMQADBY8cSfPHF+EREnE2XlFKq3bgtUYiIq79hXwM+5LuJIhfIFZFvnK/fwkoU7W7mXbPPeQZQgwO2Oqe2HqgCH+Os2hplraB25Y//+qIiqjdupHrbNqSuDt/YWKt66/DhGF8tn6GU8ixPzXpKEZEDzpdTgb1nthGR48aYI8aYISKyD5gE7HZHPOcyA6i4Dr4ohq+KobwBov1geixcHgUhLvxbFYeDmv37qfr2W+qyssDbm8ALLrAGp/v108dLSqlOw1OznpYDQ7Cmx2YDD4jIUWNMHLBIRKY4212INT3WD8gEZotISVvnP9tZT65yCOyusO4eMpzD8Wmh1uD0sJC2q7aCszDfli1Ub9qEvbwc79BQgsaMIWj0aLyDg9s9ZqWUckVnnPV0SwvHjwFTGr3eBjQbeEeqaICvi63B6aI6647huj5wVRREtT6rFbAGp+uPHrXWPpwszJeUROj11xMweDDGS8t3K6U6L12Z7bQqfTVLli4j37kt6Ow7Z5J02UQ+L4ItpdbU1sHBcFOsNbXVx4Xf7VJfj23nTqswX14exs+P4NGjCbr4YnxjYtzeJ6WUag+aKLCSxNMLXyR8xnySk9KwZWXw138tIDIHYsZM5Ern1NY4F5ctNJSUUHVycNpmwycmhrApUwgcMQIvfxc2jlBKqU5EEwWwZOkywmfMJ2jQKACCBo0i5rb52N57jj/9aKJLU1tFhNqDB6nauJHaAwfAGAJSUwm++GL8EhN1cFop1WVpogDyc3NITkprciwwKY28YzltJgmHzUb1tm1UbdqE/cQJvIKD6TVuHMEXXYR3aKgbo1ZKqY6hiQLoE5+ALSvj1B0FgC0rgz7xLa/wrj9+3No1LiMDaWjAr39/QidMICA1FePtwi2IUkp1EZoogNl3zeTphQtgxnwCnWMUpW8uYN7cOU3aid2Obfdua3D6yBGMry+BI0ZYax/6NrcIXSmluj5NFMDkSRMBWLL0OTKds57mzZ1z6ri9vJyqTZuswnxVVXhHRmphPqVUj6GJwskg+NvrTv0TcVCblWUV5tu71yrMN3iwVZhv4EAdnFZK9RiaKID09HQWPfss9yQlMTg5mf3l5Sx66inKEhO5PDGRXpddRtCYMVqYTynVI2miAJa99BL3JCUxLDwcgGHh4dybksKrx44x/amntDCfUqpH09oRwJG8PAafMZV1cGgoR4uLNUkopXo8TRRA/9hY9peXNzm2v7yc/rrFqFJKaaIAmDlrFouzsthdWkqDw8Hu0lIWZ2Uxc9YsT4emlFIep2MUwKRJkwBrrOJIRgb9Y2O596GHTh1XSqmeTBOF06RJkzQxKKVUM/TRk1JKqVZ5JFEYY54wxuwwxmwzxnzq3NnuzDZDnO+f/Co3xjzsgXCVUqpH89QdxV9EZISIXAh8APz+zAYisk9ELnS2uQioBlZ0aJRKKaU8kyhEpPFc1GCgrY27JwGHRCTbfVEppZRqjscGs40xTwJ3A2XAhDaa3w683sb55gJzARISWi4PrpRS6uwYkbb+mD/HExuzCmiu9vZjIvJuo3aPAgEi8ngL5/EDjgEXiEi+i9cuBM717iMaKDrHz3ZV2ufur6f1F7TPZytRRGKae8NticJVxphE4EMRGd7C+9OAB0Xk2g6KZ5OIjOmIa3UW2ufur6f1F7TP7clTs55SGr2cCuxtpfkdtPHYSSmllPt4atbTH40xO40xO4BrgXkAxpg4Y8xHJxsZY4KAa4C3PROmUkopjwxmi8gtLRw/Bkxp9LoaiOqouJwWdvD1OgPtc/fX0/oL2ud24/ExCqWUUp2blvBQSinVKk0USimlWtUjE4Ux5jpjzD5jzEFjzG+aed8YY55xvr/DGDPaE3G2Jxf6PNQYs94YU2uM+aUnYmxvLvR5pvPnu8MY87UxZqQn4mxPLvR5WqM6a5uMMVd6Is721FafG7W72BhjN8bc2pHxuYMLP+fxxpiyRrXyvlMm6ayISI/6AryBQ0Ay4AdsB4ad0WYK8DFggLHAN56OuwP63Bu4GHgS+KWnY+6gPl8ORDi/v76H/Jx7cXpscgSw19Nxu7vPjdqtBj4CbvV03B3wcx4PfNBe1+yJdxSXAAdFJFNE6oA3gGlntJkGvCKWDUC4MaYr74vaZp9FpEBENgL1ngjQDVzp89ciUuJ8uQGI7+AY25srfa4U528SXKuz1tm58v8zwEPAcqCgI4NzE1f73G56YqLoBxxp9DrXeexs23Ql3a0/rjjbPt+DdRfZlbnUZ2PMzcaYvcCHwJwOis1d2uyzMaYfcDPwzw6My51c/W/7MmPMdmPMx8aYC87ngj0xUZhmjp35V5UrbbqS7tYfV7jcZ2PMBKxE8Wu3RuR+LvVZRFaIyFDgJuAJdwflZq70+Sng1yJid384HcKVPm/Bqt00EngWeOd8LtgTE0Uu0L/R63isooNn26Yr6W79cYVLfTbGjAAWAdNEpLiDYnOXs/o5i8g6YKAxJtrdgbmRK30eA7xhjDkM3Ar8wxhzU4dE5x5t9llEykWk0vn9R4Dv+fyce2Ki2AikGGOSnJVpbwfeO6PNe8DdztlPY4EyEcnr6EDbkSt97m7a7LMxJgGrPMxdIrLfAzG2N1f6PMgYY5zfj8YaDO3KCbLNPotIkogMEJEBwFvAT0TknQ6PtP248nPu2+jnfAnW7/pz/jl7bD8KTxGRBmPMT4FPsGYPvCgiu4wxDzjf/yfWzIgpwEGsnfVmeyre9uBKn40xfYFNQCjgcG47O0yabjLVZbj4c/49VomYfzj/n2qQLlxt1MU+34L1R1A9YANuazS43eW42OduxcU+3wr82BjTgPVzvv18fs5awkMppVSreuKjJ6WUUmdBE4VSSqlWaaJQSinVKk0USimlWqWJQimlVKs0USillGqVJgql3MQYs8YYc43z+/9rjHnG0zEpdS563II7pTrQ48AfjDG9gVHAVA/Ho9Q50TsKpdzEWUvJAL/AWhlrBzDGvN+4nTGmqxfmU92cJgql3MQYkwbEArUiUuE8NgA43KhNX/TOXnVymiiUcgPnRlfLsDaUqTLGfM/51misEtAnjQK2dWx0Sp0dTRRKtTNjTBBWVdr5IrIHa8+H/3a+fRGwuVHzC9FEoTo5LQqoVAcyxnwMZAMNwJvA3cB9IuLwaGBKtUIThVJKqVbpoyellFKt0kShlFKqVZoolFJKtUoThVJKqVZpolBKKdUqTRRKKaVapYlCKaVUqzRRKKWUapUmCqWUUq36/8rFKYe8Lb4HAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(comp, fcc_mix, '-', color=\"#e58080\")\n",
+ "plt.plot(comp, lqd_mix, '-', color=\"#66cfff\")\n",
+ "plt.plot(comp, b32_mix, '-', color=\"#ffc766\")\n",
+ "plt.plot(comp, fcc_mix, 'o', label='fcc', color=\"#e58080\", markeredgecolor=\"#424242\")\n",
+ "plt.plot(comp, lqd_mix, 'o', label='lqd', color=\"#66cfff\", markeredgecolor=\"#424242\")\n",
+ "plt.plot(comp, b32_mix, 'o', label='b32', color=\"#ffc766\", markeredgecolor=\"#424242\")\n",
+ "plt.xlabel(r\"$x_{Li}$\")\n",
+ "plt.ylabel(r\"F (eV/atom)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "af6a293e-ccae-470e-b2f3-073c8354ad5f",
+ "metadata": {},
+ "source": [
+ "To obtain the results in a computationally efficient way, we used composition along every 0.1 Li. We can fit a 3rd order polynomial to these points to get a finer grid. We will use `numpy.polyfit` for this purpose."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2115a0d2-5553-4618-a85a-4a07bd24a0cb",
+ "metadata": {},
+ "source": [
+ "Let's first define a finer composition grid"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 99,
+ "id": "fa99fe26-a476-487a-8b55-582268321cff",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "comp_grid = np.linspace(0, 0.5, 1000)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "72988a94-4824-4d6f-9985-196595575065",
+ "metadata": {},
+ "source": [
+ "Now we fit the free energy values and use this fit to revaluate the free energy on the finer grid."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 100,
+ "id": "6c8627e1-3532-41e3-8bf4-3b2cd947bd5f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fcc_fit = np.polyfit(comp, fcc_mix, 3)\n",
+ "fcc_fe = np.polyval(fcc_fit, comp_grid)\n",
+ "\n",
+ "lqd_fit = np.polyfit(comp, lqd_mix, 3)\n",
+ "lqd_fe = np.polyval(lqd_fit, comp_grid)\n",
+ "\n",
+ "b32_fit = np.polyfit(comp, b32_mix, 3)\n",
+ "b32_fe = np.polyval(b32_fit, comp_grid)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1d974ab9-2920-464e-9944-9097a2f8b683",
+ "metadata": {},
+ "source": [
+ "Plot the fits"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 101,
+ "id": "d55cdaba-ba66-4c51-a6ae-650176ffe8c7",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fcf105cddc0>"
+ ]
+ },
+ "execution_count": 101,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(comp_grid, fcc_fe, '-', color=\"#e58080\")\n",
+ "plt.plot(comp_grid, lqd_fe, '-', color=\"#66cfff\")\n",
+ "plt.plot(comp_grid, b32_fe, '-', color=\"#ffc766\")\n",
+ "plt.plot(comp, fcc_mix, 'o', label='fcc', color=\"#e58080\", markeredgecolor=\"#424242\")\n",
+ "plt.plot(comp, lqd_mix, 'o', label='lqd', color=\"#66cfff\", markeredgecolor=\"#424242\")\n",
+ "plt.plot(comp, b32_mix, 'o', label='b32', color=\"#ffc766\", markeredgecolor=\"#424242\")\n",
+ "plt.xlabel(r\"$x_{Li}$\")\n",
+ "plt.ylabel(r\"F (eV/atom)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9b5cfc0b-9b8b-403a-8ec9-8c7b284c67d1",
+ "metadata": {},
+ "source": [
+ "Now in order to identify regions we need to construct common tangents to free energy curves. To make this easier, we convert to free energy of mixing relative to the liquid. For this purpose, we subtract a straight line connecting the free energy of the pure Al liquid to the 0.5 Li liquid, from the calculated free energy. This same line will then be subtracted from the fcc and b32 curves. Our `helpers.py` module previously introduced includes helper methods to do this."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 102,
+ "id": "1ac5a0ff-6f0d-4e69-a928-70821d7dbe7d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "lqd_fe_norm, slope, intercept = normalise_fe(lqd_fe, comp_grid)\n",
+ "fcc_fe_norm = fcc_fe-(slope*comp_grid + intercept)\n",
+ "b32_fe_norm = b32_fe-(slope*comp_grid + intercept)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 103,
+ "id": "0a9dd6eb-dd70-42fe-a72e-8fe091557c54",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fcf1048d070>"
+ ]
+ },
+ "execution_count": 103,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(comp_grid, fcc_fe_norm, '-', color=\"#e58080\", label='fcc')\n",
+ "plt.plot(comp_grid, lqd_fe_norm, '-', color=\"#66cfff\", label='lqd')\n",
+ "plt.plot(comp_grid, b32_fe_norm, '-', color=\"#ffc766\", label='b32')\n",
+ "plt.xlabel(r\"$x_{Li}$\")\n",
+ "plt.ylabel(r\"F (eV/atom)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cfd5ebae-3d31-434a-b5cf-20d0661bc5f8",
+ "metadata": {},
+ "source": [
+ "### Common tangent constructions\n",
+ "\n",
+ "With the above curves, we can move on to common tangent constructions to identify regions where the two phases coexist. In order to calculate the common tangent for two curves $f$ and $g$, we can solve the following set of equationns:\n",
+ "\n",
+ "$$\n",
+ "f^\\prime (x_1) = g^\\prime (x_1)\n",
+ "$$\n",
+ "\n",
+ "$$\n",
+ "\\frac{f(x_1) - g(x_2)}{(x_1 - x_2)} = f^\\prime (x_1)\n",
+ "$$\n",
+ "\n",
+ "$x_1$ and $x_2$ are the endpoints of the common tangent."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b191d6a8-4331-46bf-9e97-70bd231026ee",
+ "metadata": {},
+ "source": [
+ "The fitting is done using the `fsolve` method from `scipy`. Once again, `helpers.py` module offers a function to do this fitting."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 45,
+ "id": "99710428-1540-4b90-801c-e5f19267faa4",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[0;31mSignature:\u001b[0m \u001b[0mfind_common_tangent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfe1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfe2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mguess_range\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+ "\u001b[0;31mDocstring:\u001b[0m\n",
+ "Do a common tangent construction between two free energy curves.\n",
+ "\n",
+ "Parameters\n",
+ "----------\n",
+ "fe1: numpy array\n",
+ " first free energy curve\n",
+ "\n",
+ "fe2: numpy array\n",
+ " second free energy curve\n",
+ "\n",
+ "guess_range: list of floats length 2\n",
+ " The guess range to find end points of the common tangent\n",
+ "\n",
+ "Returns\n",
+ "-------\n",
+ "res: list of floats length 2\n",
+ " The end points of the common tangent\n",
+ "\u001b[0;31mFile:\u001b[0m /mnt/c/Users/menon/Documents/winrepos/workshop_preparation/phase_diagram/helpers.py\n",
+ "\u001b[0;31mType:\u001b[0m function\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "find_common_tangent?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f347c46d-c575-4a04-880d-408a4a4ae4fd",
+ "metadata": {},
+ "source": [
+ "We will use this method to find the common tangent between the fcc and b32 curves"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 104,
+ "id": "6f660266-9c7e-411b-886f-4c5ced59a2c5",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([0.04690301, 0.13432104])"
+ ]
+ },
+ "execution_count": 104,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "ct = find_common_tangent(fcc_fit, b32_fit, [0.0, 0.25])\n",
+ "ct"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7a11a4b0-2108-4a8e-9bd5-29cd9195395e",
+ "metadata": {},
+ "source": [
+ "Note that we provided the polynomials that describe the free energy curves, obtained from fitting to the function. We have obtained $x_1$ and $x_2$. We can plot the common tangent now."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 105,
+ "id": "aa60a42a-5d80-41b4-88ee-aa9d7f49b7ed",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fcf06aa9670>"
+ ]
+ },
+ "execution_count": 105,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(comp_grid, fcc_fe_norm, '-', color=\"#e58080\", label='fcc')\n",
+ "plt.plot(comp_grid, lqd_fe_norm, '-', color=\"#66cfff\", label='lqd')\n",
+ "plt.plot(comp_grid, b32_fe_norm, '-', color=\"#ffc766\", label='b32')\n",
+ "plt.plot(ct, [np.polyval(fcc_fit, ct[0])-(slope*ct[0] + intercept),\n",
+ " np.polyval(b32_fit, ct[1])-(slope*ct[1] + intercept)], color=\"#424242\")\n",
+ "plt.xlabel(r\"$x_{Li}$\")\n",
+ "plt.ylabel(r\"F (eV/atom)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2c97c878-34c6-4c36-ae63-c47547f3f22a",
+ "metadata": {},
+ "source": [
+ "Lets take a moment to analyse this plot. We obtained 0.047 and 0.134 as the end points of the common tangent. From the figure, this means that FCC is the most stable structure until $x_{Li} = 0.047$. Between $0.047 \\leq x_{Li} \\leq 0.134$, both fcc and b32 phases coexist. Finally, for $x_{Li} > 0.134$, b32 is the most stable phase. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5a875317-34fe-4985-8853-bab1e7a88521",
+ "metadata": {},
+ "source": [
+ "Therefore we have obtained already a slice of the phase diagram at 700 K. We can now put all of this methods together and easily calculate for different temperatures."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 108,
+ "id": "bb751ac8-0cea-4cc2-a903-5c1ede163ea6",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0.05998764 0.13910747]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fcf07a06a30>"
+ ]
+ },
+ "execution_count": 108,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "temp = 800\n",
+ "\n",
+ "fcc = []\n",
+ "b32 = []\n",
+ "lqd = []\n",
+ "fcc.append(fe_at(pr[\"lial_thermodynamics_composition/xp_sol\"], temp))\n",
+ "lqd.append(fe_at(pr[\"lial_thermodynamics_composition/xp_lqd\"], temp))\n",
+ "b32.append(fe_at(pr[\"lial_thermodynamics_composition/xp_alli\"], temp))\n",
+ "for i in range(5):\n",
+ " fcc.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_sol\"%i], temp))\n",
+ " lqd.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_lqd\"%i], temp))\n",
+ " b32.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_alli\"%i], temp))\n",
+ "fcc_mix = np.array(fcc)-temp*smix\n",
+ "b32_mix = np.array(b32)-temp*(smix-smix[-1])\n",
+ "lqd_mix = np.array(lqd)\n",
+ "fcc_fit = np.polyfit(comp, fcc_mix, 3)\n",
+ "fcc_fe = np.polyval(fcc_fit, comp_grid)\n",
+ "lqd_fit = np.polyfit(comp, lqd_mix, 3)\n",
+ "lqd_fe = np.polyval(lqd_fit, comp_grid)\n",
+ "b32_fit = np.polyfit(comp, b32_mix, 3)\n",
+ "b32_fe = np.polyval(b32_fit, comp_grid)\n",
+ "lqd_fe_norm, slope, intercept = normalise_fe(lqd_fe, comp_grid)\n",
+ "fcc_fe_norm = fcc_fe-(slope*comp_grid + intercept)\n",
+ "b32_fe_norm = b32_fe-(slope*comp_grid + intercept)\n",
+ "ct = find_common_tangent(fcc_fit, b32_fit, [0.0, 0.25])\n",
+ "print(ct)\n",
+ "plt.plot(comp_grid, fcc_fe_norm, '-', color=\"#e58080\", label='fcc')\n",
+ "plt.plot(comp_grid, lqd_fe_norm, '-', color=\"#66cfff\", label='lqd')\n",
+ "plt.plot(comp_grid, b32_fe_norm, '-', color=\"#ffc766\", label='b32')\n",
+ "plt.plot(ct, [np.polyval(fcc_fit, ct[0])-(slope*ct[0] + intercept),\n",
+ " np.polyval(b32_fit, ct[1])-(slope*ct[1] + intercept)], color=\"#424242\")\n",
+ "plt.xlabel(r\"$x_{Li}$\")\n",
+ "plt.ylabel(r\"F (eV/atom)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "21811466-885d-46fd-9fbd-e1fa8e450089",
+ "metadata": {},
+ "source": [
+ "Note that in this case we need a second common tangent construction to obtain coexistence between the b32 and liquid phases."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "id": "02615409-578b-4263-b37e-a3ff21c0ae2a",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0.3779039 0.42604146]\n"
+ ]
+ }
+ ],
+ "source": [
+ "ct1 = find_common_tangent(b32_fit, lqd_fit, [0.3, 0.5])\n",
+ "print(ct1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 53,
+ "id": "0f44c454-056b-4cd3-ba88-e2fbe966842c",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fcf103aa040>"
+ ]
+ },
+ "execution_count": 53,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(comp_grid, fcc_fe_norm, '-', color=\"#e58080\", label='fcc')\n",
+ "plt.plot(comp_grid, lqd_fe_norm, '-', color=\"#66cfff\", label='lqd')\n",
+ "plt.plot(comp_grid, b32_fe_norm, '-', color=\"#ffc766\", label='b32')\n",
+ "plt.plot(ct, [np.polyval(fcc_fit, ct[0])-(slope*ct[0] + intercept),\n",
+ " np.polyval(b32_fit, ct[1])-(slope*ct[1] + intercept)], color=\"#424242\")\n",
+ "plt.plot(ct1, [np.polyval(b32_fit, ct1[0])-(slope*ct1[0] + intercept),\n",
+ " np.polyval(lqd_fit, ct1[1])-(slope*ct1[1] + intercept)], color=\"#424242\")\n",
+ "plt.xlabel(r\"$x_{Li}$\")\n",
+ "plt.ylabel(r\"F (eV/atom)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9d51fdc8-4c00-4eff-a561-efa75da15052",
+ "metadata": {},
+ "source": [
+ "Now we continue this process for temperatures of 900 and 1000 K."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 110,
+ "id": "1c086539-7a4b-4b71-82db-744227af5d5f",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0.07370822 0.1439208 ]\n",
+ "[0.30479083 0.3709898 ]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fcf04791160>"
+ ]
+ },
+ "execution_count": 110,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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LqFu7lrjTTsM1cmTQi6HBpbtyOCFtks1c2lAW6tIopXqCugLY9izEDoMhFx3Y3BUd+AcLaXARkSkisklEtorInS18LiLyL9/na0TkyLaOFZFkEVkoIlt8z0lddT8B1+9EwGi+MaVU2zz1NiGlI8LOZ3GEAV3XgX+wkAUXEXECDwJTgdHAZSIy+qDdpgLZvscs4GE/jr0TeM8Ykw2853vfM7nS7LyXwo+1Y18p1TpjYPt/oW4vZF9nBwUB3sbGLuvAP1goay7HAFuNMduNMY3AHGD6QftMB5411jIgUUQGtHHsdOAZ3+tngBnBugGPgYWF0BTM1Yn7n2JXqQzSanFKqV5g3wdQshwGT7c/SPl6Br573z6SLrywxQ78leWQH6QlpEIZXDKA3c3e5/m2+bPPoY7tb4wpAPA992vp4iIyS0RWiMiKoqKOTVbcWg0v5cN/d9sfDkGRNB4iEmHfR0G6gFKqR6vaBjv/Z78rBp799eYPP6R+wwbiJ0/GlZ39rcOKGuDpXfBqkJKwtxlcRGSQiNwmIq+JyHIRWSwiD4nIOSLSmeDUUsPfwV/Rre3jz7GHZIx51Bgz0RgzMS0trT2HHnBYHJyXDsvK4O3CDp2ibeKEfidDxVdQty9IF1FK9UhNlXY+S0QyDL/aZvgA6tato3rxYqIOP5yY44771mFeA8/utgFg5qDgFO2QwUFEngKeBBqBPwOXATcBi4ApwCcicnIHr50HDG72fhCQ7+c+hzp2n6/pDN9zsL72AZjWH45JstF/VXmQLtLvRF8q/sVBuoBSqscxHtjyODTV2ImSYTEANObnU/baa0QMHkziOee02IH/cQlsroaLMyA5OAtREtbG5/cZY1qaxbcOeEVEIoAhHbz2ciBbRLKAPcBM4ODFnOcDt4jIHOBYoMIYUyAiRYc4dj5wFXCv7/m1DpbPLyLwvcG2ivnULkiNgCHRAb5IRAIkHQGFn8Kg6UFbllQp1YPsng+Vm2DY9yDG/tb2VFVROmcOzpgYki69FAn79ld8cQO8nA85cXBCcvCKd8iaSyuBpfnnjcaYrR25sDHGDdwCvANsAOYaY9aLyA0icoNvtwXAdmAr8Bi21tTqsb5j7gUmi8gWYLLvfVCFO+DGLIhxwoO5UB6MpVjSTwVPre20U0r1baWrIf9t26rR7wQAzP7ULvX1JM+ciTMm5luHGV9zmGB/FAdzVLL4s1iMiJwL/B4Yiq3tCGCMMfHBK1rXmThxolmxYkWnz7O7Dv66BdIj4bZsiAjkcAljYM3vwBEO434ZwBMrpXqU+iJY+0c7VWHM7eAItyPD5s2jbu1aki69lKhRo1o8dHExPJ8Hlw+Ck1M7XxQRWWmMmdjSZ/5+/f0D28SUYoyJN8bE9ZbAEkiDo+C6obCrzo7C8AZyBJmIHZZcsxOqdwTwxEqpHsPbCJsfAQSyf2B/bALVS5bY1C6nn95qYClptKNbc2LhpOCmFQP8Dy67gXUmmGti9hITEuD8gXb8+Jt7A3zy1GPBEQn7PgzwiZVS3Z4xkPsC1ObBiGvBZasedRs3UvXee0SNG0fsiSe2euhzvskbVwS5OWy/tjr097sdWCAiHwEN+zcaY/4elFL1II179hA+cOA3RmSclQZ76+GNfdDfZUeTBURYFKQdZzv2h1wE4bEBOrFSqtsr/BiKlkLGOZA0DrAjw8pfeYXwjAwSv/OdVlO7fFwCG6rgu4MgtYsm6ftbc/kjUAu4gLhmjz6tYft2ih9/nNovvvjGdhHbpjkiBp7ZZSdbBkz/U8A06TLISvUlVbmwYw4kjIZB5wI2Z1jp7Nk4YmJInjkTCQ9v8dDCBvifb3RYVzSH7edvzSXZGHNWUEvSA0VkZRGRmUnlO+8QmZVFWNLXVZQw3wiyP2+Bh3Lhjmxbi+m06AyIH2WbxgZMttmTlVK9V2MlbHnEZurI/j6IA299PaUvvIBpaiLle9/DGdtyK4bHwJM7IUzgqsHg6JqclYD/NZdFIqLB5SAiQuKMGSBC+bx5GO83k4zFhsGPhtk/6L+2Q5U7QBcecIbNN1a6KkAnVEp1S8ZjlypuNlHSeDyU/e9/uEtKSL70UsIPkWHk7X2QW2ubw5K6eHqcv8HlZuBtEakXkSrfozKYBespwhISSJg2jcbdu6n+9Nup8dMi4aYsqGiCB7dDYyCSXCaOteti730vACdTSnVbu+ZB5WYYdjnEDLGrSb75Jg3bt5N47rlEZmW1eujOWnhjLxydCEeHYOERv4KLb+ixwxjj8r3WocjNRI0bh2v0aKo++ICmvd8eIjYsxg5R3lFrq6idHqIsDrvKXHUuVG3v5MmUUt1S8XIoWAj9T4W04wE75Lj2iy+IPekkoo84otVDG732uyY+HC4LUu6wtvg9zU9EzhORv/ke5wazUD2NiJB4zjk4oqMpe+UVjPvb7V9HJMJFA+GLCjvWvNPSJoHTBXvfD8DJlFLdSu0e2P4cxA6HoRcDULd+vR1yPHYscaeddsjD5+XD3ga4egjE+NuzHmB+BRcRuRf4MfCV7/Fj3zbl44iOJnH6dNxFRVS+13Jz1Zn94PRUeK8I3u9Ylv+vOV029UPJSl0GWanexF1nJ0o6I2GkXVGycfduyubNs8kop08/5GqSX1XB+8X2uyYnhGN6/a25TAMmG2OeNMY8ic2IPC14xeqZXCNGEH300dQsW0ZDbm6L+1ycAYcnwNw98GV5Jy/Y/zTA6KRKpXoL44VtT0FDsV2qOCIRd0kJpbNn44yPJ2nmzBaTUe5X47bTH9Ij7WTuUGpP9qvEZq8TAlyOXiN+8mScKSmUv/oq3rpvL/HmENv/khkNj++E3JpOXMyVCkkT7OQqT2MnTqSU6hb2vAVlq21TWHw2nupqSv77XxAh5YorcEa3nnLdGBtYqtxw7dAA5zbsAH8v/3/AFyLytIg8A6z0bVMHcYSHk3T++Xiqqyl//XVaypgT4bAjyBLC4YHtdjZ/hw04A9w1ULysEydRSoVc+TrIex1Sj4H+p+FtaKD0+efx1tSQ/N3vEpZ86Pz4H5XA6ko4fwAMDfSyHx3g72ix2cBxwCu+x/G+baoFERkZxJ9+OvUbNlC7quW5KPHh8JPhtibzz21Q1tGKR1w2RA+GgvdslVop1fPUF8GWJ+wk6awrMV4vpS++SFNhIUmXXEJExsErwH9TXh38bw+MjYMzOrawbsD526H/njGmwBgz3xjzmjFmr4joJItDiJk0icjhw6l4+22aClteDDMt0k6yrPXYSZY1HZlkKQIDJ0P9Xihf27lCK6W6nqcRNv/Hvh55A8YRTvlrr9GYm0vid76Da8SIQx7e6IXHd0C0E64a0rWz8A+lrWWOXSKSDKSKSJKIJPsemUCIu4u6t/2z9x2RkZS99BKmqeUVxIZE2zQxhQ12obEOTbJMnggRKZD/bucKrZTqWsZA7vO+TMfXgSuNyoULD6TPjz788DZP8eIeO+z42qG2RaS7aKvm8gNs/8oo3/P+x2vAg8EtWs/njI0lccYM3EVFVLzzTqv7jYqz/zC218BjO2w+oHZxOGHAmVC1Faq2darMSqkutO9D21866DuQNJbqpUupWbqUmKOPbjV9fnMry+GTEji7X2iHHbekrWWO/2mMyQJuM8YMM8Zk+R4TjDH/7qIy9miuESOIOf54aleupG7Dhlb3OyoRZg6CNZXw/G77g6Zd+p0AYTFae1Gqp6jaCjvnQtJ4yJhK3bp1VL77Lq7Ro4mfMuWQc1kAihvguV2QFQ3nDeiiMreDX3M3jTEPiMhYYDQ27f7+7c8Gq2C9SfwZZ9C4cyfl8+cTPnAgYQktj+Q+NRUqm+DNfRAX1s5x6s5ImyZizwKo2wtR6QEpu1IqCBrKbD9LZCoMv4b67bl2kuTQoSSdfz7iOHSjkttrpzIY4PtDwdlN+lma87dD/x7gAd/jNOAvwHlBLFevIk4nSRdeCF6v7X/xeFrd9zvpds2FtwvtTP52ST8VJMzmI1JKdU/eJjsD39MAI2+ksaCEshdfJCwtza7LcohJkvu9lG+zHV81pOsW/2ovf+e5XAScAew1xlwDTAC66S11T2HJySSedx5NeXlULmz9y1/Epsc+wjeLf0lJOy4SHg/9JkHRMmis6HyhlVKBZQxs/y/U7IAR19JU5aTkhRdwxMWRcsUVOFxtL/q0vAw+KIYz0+DIxKCXuMP8DS51xhgv4BaReKAQGNbRi/pGnC0UkS2+5xYTQovIFBHZJCJbReTOZtv/KiIbRWSNiMwTkUTf9kwRqRORL32PRzpaxmCIGjOGmGOOoeazz6j76qtW99s/i390nF33emV5Oy4y4Ey7BoQmtFSq+9n7vq8D/1zcZjAlzz2HhIeTcuWVrS749Y3D6+13wvAYuKCbj9f1N7is8H2BP4YdLbYK+LwT170TeM8Ykw2853v/DSLixI5Im4rt67lMREb7Pl4IjDXGjAc2A79odug2Y8zhvscNnShjUMSfdRbhGRmUv/Ya7pLWqyXhDrgh0/4jenwHrPV39RxXP0g+EvZ9ZBPgKaW6h4oNsPMlSDocT9xJlDz3HBhDypVXEpaY2ObhDR74zw4IF7i+m/azNNfWPJcwAGPMTcaYcmPMI8Bk4Cpf81hHTQee8b1+BpjRwj7HAFuNMduNMY3AHN9xGGPeNcbsn3K4DAjRigXtJ04nSRdfjDidlM6di7eV+S8AkU64ZRgMioL/5MKmKj8vMvAs8NRB4eLAFFop1Tn1xbDlMYjqj2fgpZT893m8dXUkX375IVeS3M8YeD4PCurhusyuX1WyI9qquSwTkVdF5AbfxEmMMTuMMWs6ed3+xpgC3/kKgH4t7JMB7G72Ps+37WDXAm81e58lIl+IyEciclInyxkUYQkJJF5wAe7CQirefLPF/GP7RTnhx8Ntp92DuX4muozNhIQc27GvCS2VCi1PA2x+GIzBm/V9Sme/hLu8nOTLLiNioH9tWx+XwGdlcG66bS7vCdqa5zIRu44LwD9EZLmI3C8iZ4nIITv0RWSRiKxr4THdz7K1VOn7xrewiNwFuIHnfZsKgCHGmCOAnwEv+PqIWirfLBFZISIrioo6u7hK+7lGjCD2lFOoW72a2i++OOS+sWHw0+EQH2bTxOT509qVcQ40VWntRalQMga2PQO1e/BmXU3pK4to2reP5IsvJjIz069T5NbYWfij42Ba/+AWN5Da7HMxxuw0xjxijJkBTAJeB84EPhaRNw9x3JnGmLEtPF4D9onIAADfc0vJt/KAwc3eDwIOrOEoIlcB5wKXG99Pf2NMgzGmxPd6JbANGNlK+R41xkw0xkxM86NaGgxxJ59M5LBhVCxYQOOePYfcN8GX6DLSAf/Y5kcm5fhsiBsJ+Qvt0EelVNfLfxtKV2IyplP29load+4kccYMXCNb/Fr6loomeGSH/f//uqHdJ2+YP9rqc7lNRA70Zxhjmowx7xtjbjfGHAPM6uB15wNX+V5fhU0nc7DlQLaIZIlIBDDTdxwiMgW4AzjPGFPbrLxpvoEAiMgwIBvotovMi8NB4oUX4oyNpfTFF/FUVx9y/9RIG2DABpiihjYuMGgaNJVD4acBKa9Sqh3K1sLu1zDJEyn9uJSGbdtIPO88oseN8+twt9d24Ne4bf7B2BAtV9xRbdVcMoClIrJYRG4UkdTmHxpjDv1zu3X3ApNFZAt2gMC9ACIyUEQW+M7tBm4B3gE2AHONMet9x/8biAMWHjTk+GRgjYisBl4CbjDGlHawjF3CGR1N8syZmLo6yubOPeQES4B0l+2DafTC37faFBCtih8FscPsrydvR1IuK6U6pG4fbH0CE51B2ZcxNGzZSsI55xB9xBF+n+LFPbCtxk6UHBwVxLIGiRyqMxlAbIKbk7E1h+nAamA2MM8Y4+/4pW5t4sSJZsWKFSEtQ926dZS9/DLRRx1F4rnntrn/rlq4fxtEOeDWbEhpbfRI2TrY9AAMuxL6tZ0ITynVSe46WHcvxl1Nxa4J1K7NJX7KFGKPPdbvUywutqPDpvQL/XLFhyIiK31989/iT5+LMcZ8ZIy5EdsH8g/gp8C+gJayj4saO5bYE06gduVKalaubHP/IdG2iazOC/dthdLWBoUljoGYoXb5VHPoWpFSqpOM19ZY6gup3ptjA8vkye0KLFurYc4eGBMH07thQkp/+b3KsoiMA36HndjYCPwyWIXqq+JOP53IESOoWLCAhl272tx/aLRtIqt1HyLAiEDGNGgohuLlgS+0Uupru16B8rXUVeZQtXIPcaefTuykSX4fXtZo+1lSemAH/sHa6tDPFpFfichXwAtALXCWMeZYY8w/uqKAfYk4HCRdcAHOxETK5s7FU9n2tPzMaPjJCKj2BZgWl0tOmgDRg2zGZF0KWangKPwUChbSUDeU8qVlxJ1yCnEn+T/VrsEDD+VCg9d24Mf0sA78g7VVc3kHm2L/UmPMOGPMH40x3Xb0VW/giIqyHfxNTZTOno23se1JkJm+JrJWA4yInfdSvw+KO5O1RynVoqqtmNznaWpMoeTjRmJPPJHYU07x+3CvgSd3we46m9plYA/swD9YW5Mohxlj7jLGrBWRoSJyJoCIRIlID5kn2vOEp6WRdOGFNO3bR/krr2C8bdc2smJsE1mVG/6+rYUAk3w4RA+GvNfBq30vSgVMfTFm08N4myIo/iSc2BNPJu7009tc7Ku5eQXwZQVcnAHjWl7uqcfxdz2X67FDe//j2zQIeDVIZVKAa+RI4s8+m/pNm6hctMivY4bFwI+G2wXH/nbwMGVxwODptu+laElwCq1UX+Opx2x6CNNYT8myGGJPOJ34dgaWT0rg3UI4JRVOT217/57C3w79m4ETgEoAY8wWWs4HpgIo9thjiTn6aGqWLvVrBBnYLMo/HQG1Hhtg9jUPMIlj7byXPQt01r5SnWW8mC1PQO0eylbFE3Xs2cS1oykMYEOVXdZ8TBxcmmFbsHsLf4NLgy8zMXAgW3J7V3lXHRA/ZYodQfbmmzRs96+7KzMafjYC3Ab+tgXy9+ciE4HBM6CxDPZpzjGlOsPsnIeUr6FyYzyRR5zbrs57sCmcHt1hJ0Zfn9n9U+i3l7/B5SMR+SUQJSKTgf9hc4ypIBOHg6SLLiIsLY3SuXNp8jPJ5uAouHWEzf5531Y76RKAhMMg/jDIf8tma1VKtZvZtwTZ+y41u6Nx5lxA7AkntOv4yiZ4YLsNKDdn2eznvY2/weVOoAhYC/wAWADcHaxCqW9yREaS/N3vImFhlL7wQps5yPYb4ILbsiHCYWfzH0jXP3i6zZi894PgFVqpXspbthm2P0dDaQQMuZTY445v1/H1Hvj3dpuU8uYsmzOwN/IruBhjvMaYx4wxFxtjLvK91maxLhSWkEDyZZfhramh5Pnn8Tb4V+voF2kDTIzTJrvcUg3EDYfEcZD/jq5WqVQ7eCvzYf2/8NQ5cPebScyxx7XreI+xkyR318GsTDvKs7dqaxLl6yLyHREJb+GzYSLyOxG5NnjFU81FZGSQdMkluAsLKX3xRYzbv2SUKRG2iSwxHP65DdZWAIPPA08tFLwb3EIr1Ut4KkvwrvwLGDfu1JnETGxfU5gx8Owu+KoKrhgM43vJkOPWtFVzuR44CdjoWyhsgYi8LyK52GHJK40xTwa9lOoA14gRJJ53Ho25uZS9+uohV7FsLinC1mAGuOws4GUNQyBlIhQsgsby4BZaqR7OU16Ke+mfcEbW4U6+ENf4k9t9jnkFsKwMzkuHE1KCUMhu5pAJBowxe4Hbgdt9yxwPAOqAzc3XUVFdK3rCBDzV1VQtWkRlbCzxZ5/t17j6uDBbg3koF57aBZ60GZxQ+oWdWDnsyi4ouVI9j7u4mMYlfyW6fzVNCVOJyJnc7nO8XwTvFMIpKT1rNcnO8DtxpTFmhzFmqTHmSw0soRc7aRIxxx5LzWefUf2p/4uBuZzww2FwZAI8W5TG1thTMYVLoDa/7YOV6mOa9u6lduH9RPcvxxN/AuE5M9p9juVlMHcPHJ4AMwf1rrksh+J3cFHdi4gQf/bZuMaMoWrRImq//NLvY8Mddlz9SSnwUOM0msSF2fVK0MqqVE/UsGsXVW88SFxmMd6YsThzrmj3OdZUwJM77eTmnp7luL00uPRgIkLSjBlEDBtG+fz51K1f3/ZBPg6BywfByemxvO6cipSvxV2+KYilVarnqNuwgcpXHyMppwiihuAY8wObQqkdNlbZkWGDo+CWYXZKQF/S1mixIV1VENUxEhZG8qWXEjFoEGWvvEL95s3+HyswYwAkDTqNUpIo3vIyNU2akl/1bTWff07l/BdIOaIMXEnImB+Co7WlXlu2rcb2bfaLtPn+euMkyba0FUtf3f9CRF4OblFURzkiIkj+7ncJ79+f0rlzacjNbdfxp6dHUJY+g3TPTt76asU3E14q1UcYY6hcuJDKhW+ScnwN4gpDcn4I4fHtOs+uWnhgGySE26UwYnv4uiwd1VZwad5COCyYBVGd43C5SLniCsJSUiidPZvG3bvbdfzwocdQ7xrM6fWvct/mRnbokA3VhxiPh/J586heuoTUkzw4I+uQkT+A6PYtYF9Qb+eSRTnhp8NtgOmr2gouppXXqhtyREeTcuWVOOLiKHn+eRoLCvw/WBy4hl1CsinhDPe73LfVdkYq1dt56+spef556tauIe3MaMIjipCsKyAhp13n2VsPf99q+zN/MgKS29eS1uu0FVwmiEiliFQB432vK0WkSkTaXoO3FSKSLCILRWSL7zmplf2miMgmEdkqInc22/4bEdkjIl/6HtOaffYL3/6bROTsjpaxp3LGxpLyve/hcLkoefbZ9gWY+JGQfBRnNL7NyPBSHsqFD4uDV1alQs1dUUHx00/TuHMnadMGEu7YBhnnQr/2zb4vqLcJYsEuedG/l+YLa4+2VqJ0GmPijTFxxpgw3+v979vXEPlNdwLvGWOygfd8779BRJzAg8BUYDRwmYiMbrbL/caYw32PBb5jRgMzgTHAFOAh33n6lLCEBFKuugpHZKQNMPntmMMy9EIEuMn5MmPjYXYevLTHLsOqVG/SmJdH8WOP4SkvJ+38HMI9KyHtBBh0brvOk++rsYCdpDzQFYTC9kChGhw3HXjG9/oZYEYL+xwDbDXGbPetJTPHd1xb551jjGkwxuQCW33n6XPCkpJIufrqr2swe/b4d2BkCgw8G2fpCm5M2cwpqbCwCB7OtdlcleoN6tavp/iZZ5DwcNJmTiK8epFdTG/Y5e2a5Zhf983Akq6B5YBQBZf+xpgCAN9zS6taZgDNe6XzfNv2u0VE1ojIk82a1do6pk8JS0y0NZioKEqee47GvDz/Dhx4NkQk4dz5IpcN9DIzA9ZVwp+3oCPJVI9mjKHqo48oe+klIgYMIPWyMwnbNxdihkL2LGhHQ8eeOvj7NvslqoHl24IWXERkkYisa+HRVu3jwCla2La/ceZhYDhwOFAA3OfHMQeXb5aIrBCRFUV+LsDVE4UlJpJ69dU4oqNtgPFnFJkzAoZeBLV5SNEnnJZmx+qXN8GfNsNm/5aTUapbMW435fPmUfXhh0SNH0/KJWfj3PUERCbBqFvA6X9Hyc5aW2NxigaW1gQtuBhjzjTGjG3h8RqwT0QGAPieC1s4RR4wuNn7QUC+79z7jDEeY4wXeIyvm75aPaaF8j1qjJlojJmYlpbWmVvt9pwJCTbAxMZS8txz7Fm5su2Dko+CuJGw+1VoqiYnDu4cacfs378VPi4JerGVChhPdTXFzzxD3dq1xJ1+OonTTkO2PGhn3Y/6EYTH+X2uzdU2sEQ6bGDpr4GlRaFqFpsPXOV7fRXwWgv7LAeyRSRLRCKwHfXz4UBA2u98YF2z884UkUgRyQKygc+DUP4exxkfT+rVV7Osqorv33kni1966dAHiEDWTLuYmC/vWP9IuDMbcuLgv7vhxTy7+JFS3VljXh5Fjz6Ke+9eki6+mLjjJyKb/g1N1XDYLeDy/8fl2kr41za7NtLPs+0MfNWyUAWXe4HJIrIFmOx7j4gMFJEFAMYYN3AL8A6wAZhrjNmfPOsvIrJWRNYApwE/9R2zHpgLfAW8DdxsjNFuaB9nXByn/vjHZCQk8IdHHuHdZ5459AHRGTDgTChaApW21zI6zOZJOjMN3i+2q1tWNnVB4ZXqgJpVqyh++mnE6ST1uuuIGpUNmx+G2j0wchbEZvp9ruVl8ND2r5cPT+rj81jaIrpaMUycONGsWLEi1MXoMlVlZdx5001sKizklvPPZ8Ytt7S+s6cBVv8GnC4Ydxc4vs5lsbQUnt8NMWHwg0wY1ouXbFU9i/F4qHj7bWpXrCBi2DCSL7wQR1QkbH4Uyr6E4ddAmv9LFC8uhhfyYEQM3Dysb+YKa4mIrDTGTGzpsz6Wp1MBxCUl8bfHHmP8oEE8MG8ez997b+srWjojbfNYXb5dtbKZ45PhjmwIE/jbVjvhUn+rqFDzVFdT8swz1K5YQcykSaRcfjmOqCjY/l8bWIZe6ndgMQZeL4Dn82BMfN9NQtkRGlz6qKjYWP7vP//h2OHDeXLhQh6/+268bnfLOydNgKTDYc8bUP/NKfuDo+GXI2F0nJ1w+fQuaNTEyipEGnfvpujRR2nau5ekCy8kYfJku0rrrpeh6FPIOAcGnO7XuTwGnt0Nb+yzP6Ruyup7afM7Q/9T9WGRLhe/e+ghThs/njnLlvGvn/0MT11dyztnXgo4YMfsb1VPYsLs/3jfSYfPyuDPm6FI58OoLmSMoXrJEoqfegoJC7P9K2PH2g/z34aChdD/VBj0Hb/OV+eBf2+HT0vh3P5w1WA77Fj5T4NLHxcWFsYv77uPc044gdfXr+fPP/oRjaWl394xMhkGnwfl66Dk2/1TDoFz021nf2kT/GETrCwPfvmV8tbVUTpnDpWLFuEaNYq0WbMI7+9bqH7fR3Y4feox9geSH7Pvy5vgb1vsYl/fGwzfGdB3liYOJA0uCofDwU9/+1sumTqV97Zv5/c//jF1Lc3mTz/NzmTeMQeaqlo819h4uGukHVHz6A47ZFmbyVSwNOblUfSf/9CwdSvxU6aQdPHFOFy+iSfFyyF3NiSOg2FX+7WSZF4d3LsZihrhh8PghJTglr830+CiALtk8g9uu41rZs7k0/x8fn3rrVSuW3fQTk4YfhV46myAaUVqpJ0DcHY/O9ny/zbb5H5KBYoxhuqlSyl+6ikQIfXaa4k99ljbvwK2hr3tKYgbbtO6ONruhV9VDn/ZYlN6/HwEjO5Mal6lwUV90xXXX88t11/PquJi7r7nHgoXLfrmSLLoDNspWrICSr9o9TxOgQsGwo+HQZUb/rQJPinR0WSq8zzV1ZTOnk3lu+/iGjmStFmziMholkKwYiNsegSiBtpJks5DT0jxGnhjr13vfqDLDlAZHB3ce+gLdJ4LfW+eiz/eWbCAv/397wyLi+PuCy8k45JLcET4/if1emDd/0FTBYy/B8JjD3muiiZ4aidsqIaJifDdQXYQgFLtVb95M+Xz5+Otryd+8mRijjnm69oKQOUW2PgviEyF0be2+W+zwWNHOK6qgOOT4PLBEK4/uf2m81xUu509bRp3/+pX7Kip4Z65c9n20EO4y8vthw5f85i7GnbObfNcCeF2fsCMAbbp4Xeb4KsOLzWn+iJvUxPlb75J6ezZOGJjSZs165vNYABV22HjAxCRBDk/bTOwFDfYZrAvKuCigXDVEA0sgaS/H1WrTjnlFKKjo7nnV7/it++9xy+qqhhx+eVEDhsGMYNh4FTY86ZNcpk84ZDncghM7Q9j4uDJXfDP7XBqKlw4UOcOqENrKiig7JVXcBcXE3PcccSfcQYSdtBXV/VOW2MJj4fRP4WIQ3eYrK2w/w6NsSMcx2r/SsBpsxjaLNaWNWvWcNcvf0m0CHeOGcOIqVOJPekkBG+z5rFf2/+x/dDkhXkF8F6RTYZ5zRDI0tQx6iDG66V6yRKqPvwQR0wMSTNm2B82B6vJgw1/B4cLxtxmh823wmNgfgG8XQiDo2zaojRNPtlhh2oW0+CCBhd/bN68mTvuuAOn283tOTkMHzeOxAsuwCkVsPaPkJADh93crgkBm6pse3d5E0zpD9P6a7OEspoKCyl/7TWa8vNxjR5N4jnn4IhuoZe9rgDW32ebakffdsgMxxVN8PhOmzL/xBS4NENrzZ2lwaUNGlz8s2PHDm6//XYa6+q4LSeHEenpJF10EZHhW2Hni5D5XUg/pV3nrPPY1P1Ly+zcmCsHw3CtxfRZxuOh+pNPqFq8GIfLRcK0aUSNGdPyznX74Kv7AGMDS1T/Vs+7qcoGljqP7bQ/vvXKjWoHDS5t0ODiv/z8fH7+859TWV7OrRMnMtLpJO60U4lN/QKp2gLj7oao9Hafd12lnXBZ3gSnpcL0AeDSBIF9StPevba2sncvUWPHEj9lCs6YVn5p1BXAV3+3nSajfwbRA1vcze2F1/fCO4V27ZUfZEJGVPDuoa/R4NIGDS7tU1RUxO23387evXu5bfJkcqqqiByWTvKoTUhkMoy98xup+f1V77F9MR8VQ3K4/YU5Rjtaez1vUxPVixdT/emnOKKiSDjnHKJyclo/oDbf9rEgdlRYK4Flbz08sRN21dlmsEsGQqT+YAkoDS5t0ODSfuXl5dxxxx3s2LGD2y6/nLF79hCZWkvyuELMgLOQoRd2+Nxbq+G53bC3AY5JssNEE8IDWHjVbdRv2ULFggV4ysuJmjCBhLPOarlvZb+aPNhwv80WMfpnLdaSjbGZIf6XD+Fim1qPSAzePfRlGlzaoMGlY6qrq7nrrrv46quv+OmNN3JMRQVRsWuIGVyLN2sWjv5HdfjcTV54a59tzggTOG+AHbqsmWl7B09lJRXvvEP9V18RlppKwjnnEJmZeeiDanbBhn+AIxxyftZiH0tZo117ZW0l5MTC1UPtksQqODS4tEGDS8fV1dVxzz33sHLlSm6++WYm90vGVfcSTpeHxqSriRxz0AzqdtpXD3P2wFdVMMgFlw2CEYeeG6e6MeP1UvP551R98AHG6yXu5JOJnTQJcbbRXlW90wYWp8vWWA4aFWYMLCmF/+2xw43PH2j77hz6YySoNLi0QYNL5zQ2NvKHP/yBJUuWcO2113LxSeMJ2/0Q7ion1RUnkDDtXJxxcR0+vzF2FvXcPVDWBMcl2bxl2lTWs9Rv3Urlu+/iLioicsQIEqZNIywpqe0Dq7bbCZJh0bbG4kr9xscb8wq5f/Z8zBnXclicg+8N0bkrXUWDSxs0uHSex+PhL3/5C4sWLWLmzJlcN30Cju1PUL0rjqrcNBLOOouoww/vVC2mwQML9sHCIttUdnY/mNxP5yp0d03FxVS++y4NW7bgTEoi/qyzcB12mH//Fio2wKaHfTPvf/aNCZJNHi9/n/06i154HGO8zPrDv7joyOFaW+lChwoumv5FBYTT6eSOO+4gOjqaOXPmUFtbyw/PPYVYPsLrGED5/PnUfvklCdOmfb2QUztFOm1zx6QUmJcP8/fC4hKYng7HJWsTSHfjrauj6sMPqVmxAgkP/zrR5MGpW1pT+gVsedz2rYz6MUQkHPjok427uO+++6jcvo60nKO45/afkjNkQJDuRHVESGouIpIMvAhkAjuAS4wxZS3sNwX4J+AEHjfG3Ovb/iJwmG+3RKDcGHO4iGQCG4BNvs+WGWNuaKs8WnMJHGMMjz/+OHPmzGHymWfw86kGR2Mhdc7zqHxvJd76emKOPpq40077elGnDtpSDS/lw45a2x9zUQbkdLz1TQWIt6mJms8+o3rJEkxDA9FHHkncaae1PmelJYWfwvZnITYLRt0CYfbY0rom/vDEi6ye/1+ckS4uuu4mvn/eZBz6yyIkul2zmIj8BSg1xtwrIncCScaYOw7axwlsBiYDecBy4DJjzFcH7XcfUGGM+Z0vuLxhjBnbnvJocAm8F154gSeeeIITJx3DXec2EBEZg3f4T6hcvIzaFStwxMQQf+aZRE2Y0KmmMq+xyynPy4eSJhgVa0eW6Sz/rmc8HmpXraJq8WK81dVEZmcTf8YZ7a+pFrxns20n5MDIG8EZidsLzy/bwNyH7qO+IJfs407jNz+9ifRUnWofSt0xuGwCTjXGFIjIAOBDY8xhB+1zPPAbY8zZvve/ADDG/F+zfQTYBZxujNmiwaV7efXVV3nggQc4akIOvz3fTVRqDoz6IY1791GxYAFNeXmEp6cTP3lyywkJ26HJCx8W26HLVW4YG2fXPs/URZ+Czni91K1bR9WHH+IpKyNiyBDiTj+dyKFD23kiA3vegLw3IPkIGHEdRsJZtq+OBx97ioKPXsGVmMrNP/ox004+Pjg3o9qlO/a59DfGFAD4Aky/FvbJAHY3e58HHHvQPicB+4wxW5ptyxKRL4BK4G5jzMcBLLdqhxkzZhAVFcXf/vY37qzL4I+XrCU2eh4RQy8k9dprqVu7lqr336fkueeIHD6c+DPPJDy9/aljwCa8nNwPTkqxQebdQru88oR4+E66riwYDMbjoW7tWqo/+QR3SQlh6ekkf/e7RI4Y0f7aqPFA7hwoXAxpx8OwK9le6+SRhctZ/fw/cJfu5cQp53H7Td8npj3NaypkghZcRGQR0NI3xV3+nqKFbQdXsy4DZjd7XwAMMcaUiMhRwKsiMsYY862lqURkFjALYMiQIX4WSbXX2Wefjcvl4k9/+hO3PpvAn694i8ToDCTtOKLHjydq9Ghqli+navFiiv7zH6ImTCDu5JMJS+5Yc4fLaTMsn5IK7xfBwkL4w2a7jsyU/pAd067EzaoFxu2m9ssvqV6yBE95OWH9+5N00UW4Ro/uWBOnpwG2Pg5la2DgFHamTOeltVV8/N+HqVq5kNSBg7nr/n8wfvy4wN+MCpoe2ywmImHAHuAoY0xeK9f5ELjNGHPINi9tFgu+zz77jN/85jekJ4Xzl6vTSTvuNogfeeBzb10dVZ98Qs3nn4PHQ9T48cSddBJhKSmdum6tGz4ssYGmyg1Z0TClH4xP0NFl7eWtr6f2iy+oXroUb1UV4RkZxJ18MpHZ2R3vN2uqhI0PQs1OSgfOZHbTKSxZ/AHFrz6Iqavikksv46orLydi/xLbqlvpjn0ufwVKmnXoJxtjbj9onzBsh/4Z2CCyHPiuMWa97/MpwC+MMac0OyYNO1DAIyLDgI+BccaY0kOVR4NL11izZg133fVLElxe/nJdJgNP+RVEfXP4qKeqiupPP6V2xQqMx0PU2LHEnnQS4Wmtr9Phj0YvLC21zWXFjZAeCaenwbFJmn25Le7SUmo++4zaL7/ENDYSkZlJ3EknEZGV1anBGNTtg40P4G0s5+347/PS3oGUzvsnVeuXMfKwUfz8tlsZ1sm+OBVc3TG4pABzgSHYDvmLjTGlIjIQO+R4mm+/acA/sEORnzTG/LHZOZ7GDjV+pNm2C4HfAW7AA9xjjHm9rfJocOk6mzZt4o47bieCev7ygxwyz/jtN+Yv7OeprqZ66VJqly/HNDURmZ1N7PHHE5GZ2akvNI+BVeU2yOyqA5cDJiXbvGX9OzcyulcxxtC4YwfVy5bRsHkzOBxEjR1LzLHHEjGw5SzE7eGt3I5n04M0eeGfzhv56vN1FL35OA5juO66a5kxYwbOtlLCqJDrdsGlu9Hg0rVyc3O5/ee34m6o5s83HsHIs39rc0a1wFNTQ+3y5dQsX463tpaw/v2JPe44osaO9X8yXguMgdxa+KDYDmX2GBgdZ/tqxsX33QSZnpoa6lavpnbVKtwlJTiio4meOJGYiRM7lcJnvzoPbN+1nJH7nqFMEnm48gK2v/I0eZvXM3HiRH7yk58wYIBOhuwpNLi0QYNL19uzZw8/v/XHVFdW8IcbJzH+nF8dcg0Y43bbkUlLl+IuKsIRHU3UhAnEHHkkYamprR7nj8omm6J9cYldrCwuzDaXTUruGwtLGa+Xhu3bqV21ivpNm8DrJWLwYKKPPLLTQXy/XbXwUbGXtMI3mOJ+k1yG8dKXKbz36ku4XC5uuukmJk+e3LlmNtXlNLi0QYNLaBQVFfHzn91CYVEJv73hJI6efrddp+MQjDH2i3DFCuo3b7ZfhEOH2i/CnBwkvOPZLD0G1lfavpnVlfb9kCi7JO5Rib0rUaYxhqb8fOrWraNu3Tq81dU4oqKImjCB6COP7HQfF0CNG1ZVwCclkF/TwLVNT3OEdxUry7N56H8b2LFjB6eddho333wzSf4ksFTdjgaXNmhwCZ2ysjLuvPUmduQVcvf1p3DSRXeD+JeJ0lNdTe2XX1L7xRd4SkuRiAhco0YRNWYMkcOHt53G/RCq3fB5GXxaCrvr7Lj47FgbZI5I6JmBxhiDu6iIuvXrqVu3Dk9pKTiduEaMIGrcOJtMspO1lEavXUvls1JYV2UD9GERpVxf/xDOql089VkS895dSWpqKj/+8Y85/nidDNmTaXBpgwaX0KquruYXt97Axu0F3H7NqUy+7O52TUYxxtC4cyd1a9ZQt2EDpr4ecbmIysnBlZNDZFZWp74099TZfplV5VDQ4As0MTAhAcbGQ//I7jt3xng8NO7cSf2mTdRv3oynvBxEiMjMJHrcOFyjRuGI6lzbX70H1lfB6gr7qPdCfBgcnQQnRWwjfdcjrNhYwv2vV7KvqIzp06dz3XXX6WTIXkCDSxs0uIReXW0tv779BlZt2MOPrjyZ6Vf9ukPf2MbjoWHbNurWr6d+40ZMYyMSHk5EVhaukSNxZWfjjI/vcDnz9weaCsivt9tSI2yQGRsHI2NDu067MQZPaSkNubn2sW0bpqEBwsKIHDbM/jc47DCcsZ1bca244euAsqka3AZinHb+0LFJcFiMwVH4IRUb5vDwW+UsXFnMkCFDuPXWWxk7tl3ZmVQ3psGlDRpcuofGhgZ+/8sb+PTLXXz/wmO57MY/dqpKYNxuGnbsoGHzZuq3bLG/2oGw1FQihg4lYuhQIjMzOzwKqqQR1lXax8Zq2yTkAIZG2ya0kTE2gWZ0EJMsGWPwlJTQmJdHw44dNObm4qm0CSkccXG4hg8n8rDDiBw2DEcnJiJWNNkgsrHKPhc32u1pEbYGNyHB3qtTAE8DZvtzfPD++zy4oIyqOg+XXXYZl1+ukyF7Gw0ubdDg0n24m5r4yz03895n27hs2gSu++lfEUfnqwLGGNzFxTRs3kzDzp007tplf9EDzuRkIjIyCE9PJ3zgQMLT09u9HECT1y4BsKkattTYZQA8xjahDXDB0CgYEm0Dz+Coji1wZozBU1GBe98+GvfsoWnPHhrz8zH1tgrliIoiIiuLyMxMIocNw5mc3KHRV41eO7prh++RW/t1MIl22trZYbEwKg4GHNwkWLePws/+wT/mruOzTbWMGjWKW2/VyZC9lQaXNmhw6V68Hg///NNPeOPDr5h+2ihu+cU/cTgD+/PfeL007d1Loy/QNObn4638OgWdMymJsLQ0wpKTCUtNJSwlhbDkZByxsYij7cjQ6IXcGthcbb+cd9XZ9DNgA056pJ202T/SPtJ9r6MdBhrqcZeX4ykvx1NWRlNREW7fwzT6vuVFCOvXzwbFjAwiBg0iLC3N72BiDNR4bO1rb73tSyqot4+iBvD69ksOt5mls2JsQBkc1XraHG/xSua/cD+Pv7UPI2Fce933dTJkL6fBpQ0aXLof4/Xy6N/vYO269fzt59Nx5Vx3yHkwgeCpqaGpoMA+9u7FXVKCu6QE3O6vdxLBERuLMy4OZ1wcjpgYxOXCERmJREbicLns4AGHA0Tsl73DgfF4KW8y7PJEkOeJJJ8oComkxBGFp9nouDBPE/F1lcTVVxFfV0lsQzVReIhxhRMb4yImPoaYxHgiUpIJjwjHKV9/2bu9tu/DbezrOq8dDlzrsaPfajx2Hk9pI5Q22QC4nwMb3Aa4fDWtaBtU/BoV52lk57LHuO/xBazfVc/EIyfw01tvJ72DGa5Vz6HBpQ0aXLonm4LkDSL3vQHxo2DkDRDWtbMajTF4KitxFxfjKSvDU1WFt7IST3U1nspKvDU1eBsavhmA2nP+mBgqk9IpSexPaVwqVdEJVLriqQyPpsIRQaXXSZPp/FC0MIHYMEgIg5QISIqwtZLkCFuL6hcJYR1oqmuq2Mns//yGFxbtwuWK5Oabf8SZZ52tkyH7iO64notSbRIRIrO+A7Gpdsnbr/5ml7yN6LoJdyJCWEICYQnfzn/WnPF48DY0YOrrMW43eL1gDMYY+9rhQMLDkbAw+wgPRyIiEIeDjDbK0OS1aVNqfY8Gr+3Paf4ACBcbIMLEPlxOO4IrJqxjfTyHvmHDV5/8l/seeoEdhY2cfuJR3PSTX+hkSHWABhfV/aUdD+EJsPkRWPdnGPUjiO588sRAEqcTZ3Q0RAd+VbJwh33Ed5OJm3UVe3nygV8z78NtpCZE8Yff/pLjTzwj1MVS3Uygf88oFRyJo2HMbXbFwnX3QumXoS5R32MMyxc9x3XXXs28D7dx3plH8sQzszWwqBZpzUX1HDFDYOwvYfPD9jHoO5Axze90MarjKoryePjvv2Lh57sY0j+Gf/z5F4w96pS2D1R9lgYX1bNEJtkazPb/Qt7rUJsHw67q8o7+PsMY3p//GA8+8TJVdW6umDGJy2fdRUSkLn6jDk2Di+p5HBEw/BqIGQw7X4aaPMj+PsRmhrpkvUvdXsh9gS8+/Zj01Gj++vNfMCznmFCXSvUQOhQZHYrco1Vuga1P2LXYh1wA6Wd03yySPYW3Cfa8BfnvgCOc+n7nEp5xCs6wbjKiQHUbOhRZ9V7x2TDubjtUeef/oGIjDLsCIhJDXbKexxgoWwO7XoL6Qkg5BoZehKuFZaiVaosGF9XzhcfCyBth3wew8xVY/VvIvARSj9NajL9qdsHOl6ByE7jSIecnkJAT6lKpHkyDi+odRCD9dEgYA9ufgW1PQ8lKyLrcDgJQLWssh92vQdFSCIuGzMug30kQgGShqm/T4KJ6l6j+MPo22PsB7J4Hq++BjKkw4ExwaJ/BAY2VkP827FsMGBgw2f53Cgv8JFDVN2lwUb2POGDAGZA0wfbD7H4Vij6FoZdA4ti+3VTWVGU76vd9CF43pB0HGeeAKy3UJVO9TEiCi4gkAy8CmcAO4BJjTFkL+z0JnAsUGmPG+nO8iPwCuA7wAD8yxrwTxFtR3ZkrFQ67EcrXw44XYdO/IX4kDJ4BccNDXbquVV8Me9+DwiXgbYTUY2xQieof6pKpXiokQ5FF5C9AqTHmXhG5E0gyxtzRwn4nA9XAswcFlxaPF5HRwGzgGGAgsAgYaYzxHKo8OhS5D/C6Yd9HkP+W/fWeOA4Gn2dn/fdm1bmQvxBKV9kaW8rRNqtBlKbDV53X7VLui8gm4FRjTIGIDAA+NMYc1sq+mcAbBwWXFo/31Vowxvyfb793gN8YY5YeqjwaXPoQT73tj8l/Fzy1dkTUgLPsc29pLvM0QMkKKPzYBhenC/qdbAc86OAGFUDdcZ5Lf2NMAYAvQPQL0PEZwLJm++X5tn2LiMwCZgEMGdLLf72qrzldtuO6/ym2M3vv+7DxnxCdAf1Ptb/se2IqGWOgZgcUfgoln9sg6kqHoRdD2gk9855Ujxa04CIii4CW6t53Beua2BVkD9Zi1cwY8yjwKNiaSxDLpLqjsGjImGI7/ktWQMFCyH3eDgBIPgr6TYK4Ed07KaYxULvbDrkuWQENxXZEXPJRdjhx3PDeUxtTPU7Qgosx5szWPhORfSIyoFmzVmE7T9/a8XnA4Gb7DQLy23lu1Zc4wu16ManH+X75L4GS5VC81K4hkzQBko+A+MO6x9wPT6Od6Fi+zg5UaCgCHJAwyvalJB+hw4lVtxCqZrH5wFXAvb7n1wJ0/HzgBRH5O7ZDPxv4PBAFVr2cCMRm2cfQi6FsNZR+AcXLoHCxbU6LG2GDTPxhEDMIpAuCjbsGqnKhehtU+R7GbZN3xh8GA8+C5CNtlgKlupFQBZd7gbkich2wC7gYQEQGAo8bY6b53s8GTgVSRSQPuMcY80Rrxxtj1ovIXOArwA3c3NZIMaW+xRlph+qmHmOH7ZZ/ZWsJ+2sMABJu+2liBkP0YDtPJDLFPhzt/N/KeO0ItsYym9OrNh/qCqAu374HwGEDWv9T7Fyd+GydFKq6Nc2KjI4WU+3QWA6Vm6FmJ9Tstg9PbbMdBMLjICwGnNG2icoRBjhs7cgYG7A89fbhrobGCsDb7BwOcPWzSzlHD7I1ptihtvakVDfSHUeLKdUzRSR+XasBGyway23fR0OJnazYVA7uWtuk1Vhul2bG2BoK2JqRw2XPFZ0BEUn2dUSSnfjp6qe1EtXjaXBRqjNE7NwRnT+i1Dd043GWSimleioNLkoppQJOg4tSSqmA0+CilFIq4DS4KKWUCjgNLkoppQJOg4tSSqmA0+CilFIq4DT9CyAiRcDOTpwiFSgOUHF6gr52v6D33FfoPbfPUGNMWksfaHAJABFZ0Vp+nd6or90v6D33FXrPgaPNYkoppQJOg4tSSqmA0+ASGI+GugBdrK/dL+g99xV6zwGifS5KKaUCTmsuSimlAk6Di1JKqYDT4OInEZkiIptEZKuI3NnC5yIi//J9vkZEjgxFOQPJj3seJSJLRaRBRG4LRRkDzY97vtz3910jIp+KyIRQlDOQ/Ljn6b77/VJEVojIiaEoZyC1dc/N9jtaRDwiclFXli8Y/Pg7nyoiFb6/85ci8utOXdAYo482HoAT2AYMAyKA1cDog/aZBrwFCHAc8Fmoy90F99wPOBr4I3BbqMvcRfc8CUjyvZ7aR/7OsXzdPzse2Bjqcgf7npvt9z6wALgo1OXugr/zqcAbgbqm1lz8cwyw1Riz3RjTCMwBph+0z3TgWWMtAxJFZEBXFzSA2rxnY0yhMWY50BSKAgaBP/f8qTGmzPd2GTCoi8sYaP7cc7XxffsAMUBPHwXkz//PAD8EXgYKu7JwQeLvPQeMBhf/ZAC7m73P821r7z49SW+7H3+0956vw9ZWezK/7llEzheRjcCbwLVdVLZgafOeRSQDOB94pAvLFUz+/ts+XkRWi8hbIjKmMxfU4OIfaWHbwb/e/NmnJ+lt9+MPv+9ZRE7DBpc7glqi4PPrno0x84wxo4AZwO+DXagg8+ee/wHcYYzxBL84XcKfe16FzRU2AXgAeLUzF9Tg4p88YHCz94OA/A7s05P0tvvxh1/3LCLjgceB6caYki4qW7C06+9sjFkMDBeR1GAXLIj8ueeJwBwR2QFcBDwkIjO6pHTB0eY9G2MqjTHVvtcLgPDO/J01uPhnOZAtIlkiEgHMBOYftM984Hu+UWPHARXGmIKuLmgA+XPPvU2b9ywiQ4BXgCuNMZtDUMZA8+eeR4iI+F4fie0Q7slBtc17NsZkGWMyjTGZwEvATcaYV7u8pIHjz985vdnf+RhsfOjw3zmsE4XtM4wxbhG5BXgHO+riSWPMehG5wff5I9gRJdOArUAtcE2oyhsI/tyziKQDK4B4wCsiP8GOQKkMVbk7w8+/86+BFOwvWQC36cFZdP285wuxP5yagDrg0mYd/D2On/fcq/h5zxcBN4qIG/t3ntmZv7Omf1FKKRVw2iymlFIq4DS4KKWUCjgNLkoppQJOg4tSSqmA0+CilFIq4DS4KKWUCjgNLkp1IyLygYhM9r3+g4j8K9RlUqojdBKlUt3LPcDvRKQfcARwXojLo1SHaM1FqW7El7tLgJ9hZ0h7AETk9eb7iUhPTx6pejkNLkp1IyIyDhgANBhjqnzbMoEdzfZJR1sdVDenwUWpbsK3uNzz2EWcakTkbN9HR2LToe93BPBl15ZOqfbR4KJUNyAi0dhsy7caYzZg10z5je/jo4CVzXY/HA0uqpvTxJVKdXMi8hawE3AD/wO+B1xvjPGGtGBKHYIGF6WUUgGnzWJKKaUCToOLUkqpgNPgopRSKuA0uCillAo4DS5KKaUCToOLUkqpgNPgopRSKuA0uCillAo4DS5KKaUC7v8BJ9DIiBs+gJ4AAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "temp = 900\n",
+ "\n",
+ "fcc = []\n",
+ "b32 = []\n",
+ "lqd = []\n",
+ "fcc.append(fe_at(pr[\"lial_thermodynamics_composition/xp_sol\"], temp))\n",
+ "lqd.append(fe_at(pr[\"lial_thermodynamics_composition/xp_lqd\"], temp))\n",
+ "b32.append(fe_at(pr[\"lial_thermodynamics_composition/xp_alli\"], temp))\n",
+ "for i in range(5):\n",
+ " fcc.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_sol\"%i], temp))\n",
+ " lqd.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_lqd\"%i], temp))\n",
+ " b32.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_alli\"%i], temp))\n",
+ "fcc_mix = np.array(fcc)-temp*smix\n",
+ "b32_mix = np.array(b32)-temp*(smix-smix[-1])\n",
+ "lqd_mix = np.array(lqd)\n",
+ "fcc_fit = np.polyfit(comp, fcc_mix, 3)\n",
+ "fcc_fe = np.polyval(fcc_fit, comp_grid)\n",
+ "lqd_fit = np.polyfit(comp, lqd_mix, 3)\n",
+ "lqd_fe = np.polyval(lqd_fit, comp_grid)\n",
+ "b32_fit = np.polyfit(comp, b32_mix, 3)\n",
+ "b32_fe = np.polyval(b32_fit, comp_grid)\n",
+ "lqd_fe_norm, slope, intercept = normalise_fe(lqd_fe, comp_grid)\n",
+ "fcc_fe_norm = fcc_fe-(slope*comp_grid + intercept)\n",
+ "b32_fe_norm = b32_fe-(slope*comp_grid + intercept)\n",
+ "ct = find_common_tangent(fcc_fit, b32_fit, [0.0, 0.25])\n",
+ "print(ct)\n",
+ "ct1 = find_common_tangent(b32_fit, lqd_fit, [0.3, 0.5])\n",
+ "print(ct1)\n",
+ "plt.plot(comp_grid, fcc_fe_norm, '-', color=\"#e58080\", label='fcc')\n",
+ "plt.plot(comp_grid, lqd_fe_norm, '-', color=\"#66cfff\", label='lqd')\n",
+ "plt.plot(comp_grid, b32_fe_norm, '-', color=\"#ffc766\", label='b32')\n",
+ "plt.plot(ct, [np.polyval(fcc_fit, ct[0])-(slope*ct[0] + intercept),\n",
+ " np.polyval(b32_fit, ct[1])-(slope*ct[1] + intercept)], color=\"#424242\")\n",
+ "plt.plot(ct1, [np.polyval(b32_fit, ct1[0])-(slope*ct1[0] + intercept),\n",
+ " np.polyval(lqd_fit, ct1[1])-(slope*ct1[1] + intercept)], color=\"#424242\")\n",
+ "\n",
+ "plt.xlabel(r\"$x_{Li}$\")\n",
+ "plt.ylabel(r\"F (eV/atom)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 55,
+ "id": "3fe993bc-6253-46f5-9a4d-ce2de718cf90",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0.0890832 0.14978333]\n",
+ "[0.25995278 0.31921327]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x7fcf104a5ee0>"
+ ]
+ },
+ "execution_count": 55,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "temp = 1000\n",
+ "\n",
+ "fcc = []\n",
+ "b32 = []\n",
+ "lqd = []\n",
+ "fcc.append(fe_at(pr[\"lial_thermodynamics_composition/xp_sol\"], temp))\n",
+ "lqd.append(fe_at(pr[\"lial_thermodynamics_composition/xp_lqd\"], temp))\n",
+ "b32.append(fe_at(pr[\"lial_thermodynamics_composition/xp_alli\"], temp))\n",
+ "for i in range(5):\n",
+ " fcc.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_sol\"%i], temp))\n",
+ " lqd.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_lqd\"%i], temp))\n",
+ " b32.append(fe_at(pr[\"lial_thermodynamics_composition/x%d_alli\"%i], temp))\n",
+ "fcc_mix = np.array(fcc)-temp*smix\n",
+ "b32_mix = np.array(b32)-temp*(smix-smix[-1])\n",
+ "lqd_mix = np.array(lqd)\n",
+ "fcc_fit = np.polyfit(comp, fcc_mix, 3)\n",
+ "fcc_fe = np.polyval(fcc_fit, comp_grid)\n",
+ "lqd_fit = np.polyfit(comp, lqd_mix, 3)\n",
+ "lqd_fe = np.polyval(lqd_fit, comp_grid)\n",
+ "b32_fit = np.polyfit(comp, b32_mix, 3)\n",
+ "b32_fe = np.polyval(b32_fit, comp_grid)\n",
+ "lqd_fe_norm, slope, intercept = normalise_fe(lqd_fe, comp_grid)\n",
+ "fcc_fe_norm = fcc_fe-(slope*comp_grid + intercept)\n",
+ "b32_fe_norm = b32_fe-(slope*comp_grid + intercept)\n",
+ "ct = find_common_tangent(fcc_fit, b32_fit, [0.0, 0.25])\n",
+ "print(ct)\n",
+ "ct1 = find_common_tangent(b32_fit, lqd_fit, [0.3, 0.5])\n",
+ "print(ct1)\n",
+ "plt.plot(comp_grid, fcc_fe_norm, '-', color=\"#e58080\", label='fcc')\n",
+ "plt.plot(comp_grid, lqd_fe_norm, '-', color=\"#66cfff\", label='lqd')\n",
+ "plt.plot(comp_grid, b32_fe_norm, '-', color=\"#ffc766\", label='b32')\n",
+ "plt.plot(ct, [np.polyval(fcc_fit, ct[0])-(slope*ct[0] + intercept),\n",
+ " np.polyval(b32_fit, ct[1])-(slope*ct[1] + intercept)], color=\"#424242\")\n",
+ "plt.plot(ct1, [np.polyval(b32_fit, ct1[0])-(slope*ct1[0] + intercept),\n",
+ " np.polyval(lqd_fit, ct1[1])-(slope*ct1[1] + intercept)], color=\"#424242\")\n",
+ "\n",
+ "plt.xlabel(r\"$x_{Li}$\")\n",
+ "plt.ylabel(r\"F (eV/atom)\")\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3c820b12-db96-4c8b-89e0-5b8d93d9b21e",
+ "metadata": {},
+ "source": [
+ "The free energy curves at 1000 K are interesting. We are above the melting temperature. Therefore, we would expect to see a region where liquid is the most stable structure. We see at the very left such a region exists. One more common tangent construction is needed to obtain this region."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 58,
+ "id": "7bbb2fa6-0331-4f23-8c3d-51d2f1787d01",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[-0.01145623 0.03518758]\n"
+ ]
+ }
+ ],
+ "source": [
+ "ct0 = find_common_tangent(lqd_fit, fcc_fit, [0.01, 0.1])\n",
+ "print(ct0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4380aa40-d8af-4bb3-9865-6baad8b4263e",
+ "metadata": {},
+ "source": [
+ "Now let's put together all the common tangent constructions to arrive at the phase diagram."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 114,
+ "id": "0b0b1f9c-8409-4278-9bb0-777254e1f8aa",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fcc_temp = [700, 750, 800, 850, 900, 950, 975, ]\n",
+ "fcc_comp = [0.047, 0.052, 0.06, 0.066, 0.074, 0.081, 0.085]\n",
+ "fcc_lqd_temp = [975, ]\n",
+ "fcc_lqd_comp = [0.0]\n",
+ "fcc_b32_temp = [700, 750, 800, 850, 900, 950, 975]\n",
+ "fcc_b32_comp = [0.134, 0.136, 0.14, 0.141, 0.144, 0.147, 0.148]\n",
+ "b32_lqd_temp = [800, 850, 900, 950, 975, ]\n",
+ "b32_lqd_comp = [0.38, 0.335, 0.305, 0.28, 0.27, ]\n",
+ "lqd_temp = [800, 850, 900, 950, 975, ]\n",
+ "lqd_comp = [0.43, 0.397, 0.371, 0.34, 0.33, ]\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5600084e-5085-472c-bf90-ec6a9844e164",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "[0.08497226 0.1481879 ]\n",
+ "[0.27012884 0.33272737]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 115,
+ "id": "7fb9ec4d-319b-4ff2-a3f1-2097725b668e",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[<matplotlib.lines.Line2D at 0x7fcf10220730>]"
+ ]
+ },
+ "execution_count": 115,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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7NgFxhruIlInIuyLynojcHhvLFZEXRGRn7GNOr9cvE5FKEdkuIvOGqXbXWb21hrtWvQPATY+/weqtzus8U1FdweI1iwH4+ds/p6K6wuKK1GClnXsuydOn0/DQw3xw1gx2fvIKWtets7qsAaWkJ3Hx586gfvdhfvXtv/HIzS/y+F1/Z8cm+59ZPxwGDHcROQf4OnAB8BHgMyIyFfgesMEYMxXYEPscEZkBLAHOBq4EHhUR7/CU7x6rt9awbNU7HA5EbwjVtQZYtuodRwV8RXUF5RvLqe+MHiHbGmylfGO5BrzDtK5bR2jXLujuBmMI19ZS98O7HRHwYBCBYEf075G/KchLT36YkAEfz8z9LOA1Y0yHMSYMvAxcAywEHo+95nFgUeznC4GnjTFBY8wuoJLoPwzqJJav305nqO9j1J2hCMvXb7eoosFbsWUFgUigz1ggEmDFlhUWVaRORf1DD2O6+razM4EA9Q89bE1Bg/DammqO3e4e7urm1TVV1hRkoXjC/V3gEyKSJyLpwNXAeGCsMaYOIPaxIPb6EqD3Ycv7Y2N9iMhSEdksIpsbHHLc6HCqben/+NITjdvRgfb+Z0cnGlf2FK6rG9S4nfibgoMad7MBw90Y8wHwb8ALwHPAW8DJNpP2113iuLsbxpjHjDGzjTGz8/Pz4yzXvYqz0wY1bkeFGYWDGlf25CsqGtS4nYzKTRnUuJvFdUPVGPOfxphZxphPAE3ATuCgiBQBxD729OraT3Rm32McUDt0JbvTnfOmk3LMcQNpSV7unDfdoooGr2xWGanevm0BU72plM0qs6gidSoK7rgdST2mvaPHQ8Edt1tSz2BctLAUX3Lfv0den4eLFpZaVJF14t0tUxD7OAFYDDwFrAVujL3kRmBN7OdrgSUikiIik4GpwOtDWbQbLTq/hM/Niq5eCVCSncb9i2ey6PzjVrRsa/6U+ZTPLT+yv70oo4jyueXMnzLf4srUYGQtWEDRvffgKy4GETyZmdDdjTc7Z+A3W2zanEIuv/7MozN1gZzCNKbNSbzvHn1xvu5ZEckDQsAtxphmEXkAWCkiNwF7gc8DGGPeE5GVwPtEl29uMcbogctxyE5PxucRPrj3SpK8znwEYf6U+Wxv2s7vPvwdz1/7vNXlqFOUtWABWQsWANDd1cWuBZ/l4H33kbF2DZJs7wYs0+YUHgnzN5/bzWurqzlQ3UrhlCyLKxtZ8S7LfNwYM8MY8xFjzIbYWKMx5gpjzNTYx6Zer7/PGFNqjJlujPnTcBXvNpX1fibmpTs22HvouTLu4klOZuz376Jr926annjC6nIGZeZl40jLTOL1dYl3LIGzU8Rlqhr8nFHg/FBs62rTRh0uM+oTn2DU5Zdz6JFHCR2sH/gNNpGc6uP8T09k3wfN1O5ssbqcEaXhbhOhSDd7GjsozXd+uPu7/Dpzd6Gxy76HCYepf/BBq0sZlHMuLSF9dDKb1lYn1JnvGu42saexg3C3cUW4t4V05u5GyRMmkPu1r3J43To63nzT6nLilpTs5aNXTaR2Zwv7tzujjeBQ0HC3iaqG6GFbbliW0eN+3WvM0qX4ioo4cO+/YCLO2Scx45JiRuWk8HoCzd413G2iJ9yn5Dv3NMge2hzbvTzp6Yz97ncIfvghzb//vdXlxM2X5OWjV03iQPVh9r7XNPAbXEDD3SYq6/2MHZ1CZmqS1aWcNt0t426Z8+aRPmcODSv+nXCzc5Y5zppbRGZeKq+vS4zZu4a7TVQ1tLtiSSbcHaYz3KnLMi4mIhT+4Pt0+/00POycQ+G8Pg8fmz+J+j1t7HrrkNXlDDsNdxswxlBd73fFzVR/V3R5SbswuVvK1Knkful6WlaupPO996wuJ27T5xSSVZDG6+t2YVze0EPD3Qbq24K0BcOuCPe2ULTFmc7c3W/Mrbfizc3l4L3/gunutrqcuHi8Hi74zGQaa/xUbXX3abQa7jZQVe+unTKgM/dE4M3MpOCf/5nObdtoXbvW6nLidsbsseQUZfD6umpXt+PTcLeBnp0ybpi5a//UxJJ1zSJSP3Iu9Q/+hIjfb3U5cfF4hAs+M5nmAx3sfOOg1eUMGw13G6is9zMqxcfY0c4/c7qtK7oso1shE4N4PBT+4AdEGhs59MijVpcTt9Lz88kbN4o3/mcX3RFnLCkNloa7DVQ1tFOan4FIf31OnKVn5q7LMokjbeZMsq/9HE1PPEGwyhnt7MQjzFkwmdaGTj58zZ2dwjTcbaCqwR07ZeDozF2XZRJL/h134ElP5+B99zlmD/mkc8dQMDGTzRW7iYTdN3vXcLeYPximrjVAqQtupsLRG6oa7onFl5tL/m230b7xVdpeeMHqcuIiIlzw2Sm0NQX4YKP9+8MOloa7xapddDMVojP3VG8qSR7nP2mrBidnyRdImTaN+gf+je5OZzR2nzAjl8IpWWz+427CIeeclRMPDXeLHT0wzPlnykB0zV1n7YlJfD7G/uD7hGprafzFL60uJy4iwpzPTqa9Jch7f3NXq2cNd4tV1vvxeoQJue4I97YuPVcmkWVccAGjr76axl/+kq79+60uJy7jzsylZFo2bz63h1CXe2bvGu4Wq6pvZ2JeOsk+d/yv8If0RMhEV/CdO8Hn4+ADD1hdStwu+OwUOg938e5faqwuZci4I1EczE07ZUC7MClIKixkzM034//zBvx/e8XqcuJSfEY242fksuX5PXQFwlaXMyQ03C0UjnSzu7HdVeGuXZgUQO5XbiR54sTo1siuLqvLicucBVMI+EO8/ZIzlpMGouFuob1NHYQixhVnyvTQRh0KwJOczNi7ltG1ezdNTzxhdTlxGTt5NJPOHcO2F/YS7AhZXc5p03C3UFVDOwClLui+1MMf0mUZFTXq0ksZdfnlHHrkUUIH660uJy4XLJhMsCPMtg37rC7ltGm4W6gydhqkWx5gCnWHtFGH6mPssu9hwmHqf/Kg1aXEJX98JqXn5/PWhn0E/M6evWu4W6iqwU9BZgqjXdBaD3od96vLMiomecIEcr/2VQ6vXUfHm29aXU5cPrZgMqFghK0v7LW6lNOi4W4hN+6UAXRZRvUxZulSfEVFHPiX+zAR++8jzysexdTZY3n7pX10HHbGzeD+aLhbxBhDZb2fUpc8mQrahUn1z5OeztjvfofgBx/QsnKl1eXE5WPzJxEJdbPl+T1Wl3LK4gp3EblDRN4TkXdF5CkRSRWRchGpEZFtsR9X93r9MhGpFJHtIjJv+Mp3ptVba7jo/hdpC4RZ91Ytq7c6/8GJiuoKvvXnbwFw76v3UlFdYXFFyk4y580jfc4cDv6f5ey87DI+OGsGOz95Ba3r1lldWr9yCjOYPqeQt1/cx2++93ceuflFHr/r7+zY5JzjgQcMdxEpAW4DZhtjzgG8wJLYlx8yxpwX+/HH2OtnxL5+NnAl8KiIeIelegdavbWGZave4cDhAACtnWGWrXrH0QFfUV1B+cZyGgONADQGGinfWK4Br44QETIuuRjT2Un4wEEwhnBtLXU/vNu2AZ83bhSmG9pbggD4m4K89OSHjgn4eJdlfECaiPiAdOBkJ+wsBJ42xgSNMbuASuCC0yvTPZav307nMafPdYYiLF+/3aKKTt+KLSsIRAJ9xgKRACu2rLCoImVHzU89fdyYCQSof+jhkS8mDm+9ePx2yHBXN6+ucUZDkgHD3RhTAzwI7AXqgFZjzPOxL98qIm+LyK9EJCc2VgL0vir7Y2N9iMhSEdksIpsbGtzdhby32pb+j0I90bgTHGjvfyZzonGVmMJ1/Z+ZfqJxq/mbgoMat5t4lmVyiM7GJwPFQIaIfAn4KVAKnEc09H/S85Z+fpnjWrMYYx4zxsw2xszOz88/teodqDg7bVDjTlCYUTiocZWYfEVFgxq32qjc/nsan2jcbuJZlvkUsMsY02CMCQGrgLnGmIPGmIgxphv4BUeXXvYD43u9fxwnX8ZJKHfOm05aUt9bEGlJXu6cN92iik5f2awyUr2pfcZSvamUzSqzqCJlRwV33I6k9v1zgghjbr3FmoIGcNHCUnzJfSPSm+ThooWlFlU0OPGE+17gQhFJl2gH5yuAD0Sk9z+31wDvxn6+FlgiIikiMhmYCrw+lEU72aLzS7h/8Uw8se9vSrLTuH/xTBadf9zKlWPMnzKf8rnlR5piF2YUUj63nPlT5ltcmbKTrAULKLr3HnzFxSCCNycHjKH9pb/Ycv/7tDmFXH79mX1m6nnjMpg2xxnfkUo8zWxF5MfAF4AwsBX4R+CXRJdkDLAb+IYxpi72+u8DX4u9/nZjzJ9O9uvPnj3bbN68+ZR/E04TDEeY/oPnuONT0yj71FSryxkyP33rpzy67VG23bANr0c3SKmBNf7mN9Q/8G/kfOlLjP3+XUTnj/b0RsUuXl+3i6tunsmU8+yxlCwibxpjZvf3NV88v4Ax5kfAj44ZvuEkr78PuC/uChPMgdbozpLi7NQBXuks4e4wgmiwq7jlfeUrhOsO0PT44yQVFZJ3001Wl3RCs+ZNpGpLAy8/tZ2SadmkpNv72BB9QtUCNbGdMSUOvonan3B3GJ8nrvmCUkcUfPc7ZF51JfXLH6R13f9YXc4JeX0ePvnlM+k83MXGZyutLmdAGu4WqGmOhruTd8j0R8NdnQrxeCh+4AHSZ8+m9q67aH9tk9UlnVDBxNGc96kJvP/3OvZ92GR1OSel4W6B2pboskyRC5dlNNzVqfCkpDDukf8gZdJE9t96K4HtO6wu6YQuWDCZrPw0/vJfHxIK2u9GcA8NdwvUtnSSn5lCis9da9Ph7jBJHnuvQyr78mZlMf6xx/Ckp7Nv6VJCNn24yZfs5ZNfPpPDhwJsWlttdTknpOFugdrWTtctyUC0WYfO3NXpSCoqYvwvHqO7vZ19S5cSOXzY6pL6VTw1h3M+UcJbL+7jQHWr1eX0S8PdAjXNnZS4bEkGdOauhkbq9OmM+4//R3D3HvbfcivdNm2wfdE1pYzKTuHFJz4kEuq2upzjaLiPMGMMNS2drtspA7rmroZOxoUXUvyv/0rHG29Q973vYbrtF57JaT4u/eJ0muva2fzcbqvLOY6G+whrau8iGO525bJM2ITxiYa7GhpZCz5Dwbf/N4f/+Cfql9uzB+ukmWOYNmcsW/60h0P7/VaX04eG+wjr2SnjxnDXNXc11HJvuomcL36Rpl//mqbf/tbqcvp1yeenkpLh46UnPqA7Yp/vMDTcR1hNSwfgvgeYQJdl1NATEcZ+/y4y/9enOHj/Axx+br3VJR0nbVQyH//CNOr3tPHWhv1Wl3OEhvsIq4nN3DXclYqPeL0UL19O2nnnUfud79Bhw3OozvhoAZM/MoZN66ppOdhhdTmAhvuIq23pJC3JS7bNz6U4FRruarh4UlMZ9+gjJJWUsO+WWwlW2asbkohw6T9Mx+vz8NJ/fYjpHvhAxuGm4T7Cals6Kc5OtfXpd6dKw10NJ19ODuN/8RiSlMTer3+d0MF6q0vqIyM7hYuvPYPanS2894r1LSw03EdYTUsnJTnpVpcxLDTc1XBLHjeO8T//Gd0trez7xjeI+O21Q+WsuUWUTM9h46pK2poCA79hGGm4j7DaFnc+wATRrZBJ4r7lJmUvaWefTcmKFQQrK6m57TaMjR5yEhEu/9KZmG7Dy09tJ55+GcNFw30EBUIRDvm7KM5y381U0Jm7GjmjPn4JRffcQ/vGV6n74Q8tDdFjZeWnceHCUva808iO1w9aVoeG+wiqizXpKMnRcFfqdGUvvob8sttoXbOWhocetrqcPmZePo6xk0fzysqddBy25jsLDfcR5NZz3HvoQ0xqpOXdfDPZ111H42OP0fzUU1aXc4THI3zyhrPoCob520prji/WcB9BtS7twNRDZ+5qpIkIhXf/kFGXXcaBe/+Ftg0brC7piNziDGZfNYnKzfVUb2sY8f++hvsIqmnpRATGjnbpDVU9FVJZQHw+Sv7vT0g95xxq/vl/07F1q9UlHTFr3kTySjL461PbCXaERvS/reE+gmpbOhmbmUqyz52XPWx05q6s4UlPZ/xPH8U3diz7v/ktgrt2WV0S0NN39Sw6LOi76s6Usama2ANMbqXLMspKvrw8JvziMfB42Pf1pYQPHbK6JMC6vqsa7iMo+nSqO9fbQcNdWS954kTG/+ynhBsb2feNm+lub7e6JMCavqsa7iOku9tQ2xpw7c1UiIW7nueuLJZ27rmU/N+fEPjgA/bfcQcmNLJr3f3xJXu5/IaR7buq4T5CGtu76Ap3u3aPuzGGiInoDVVlC5mXX05h+Y9o/+vfqCsvt8VDTiXTcjh7BPuuariPkJrYNkg3P50K6LKMso2c665jzLe+Seuzqzj0H49YXQ4Ac0ew76qG+wjp2ePu1jX3UHf0W18Nd2UnY/7pn8havJhDjzxC8x/+YHU5I9p3VeL5dkVE7gD+ETDAO8BXgXTg98AkYDdwnTGmOfb6ZcBNQAS4zRhz0vYps2fPNptteAD/UFm9tYYfrX2X1s4wRVmpfPfKM1l0fonVZQ2pZ3Y8w49f/TEARRlFlM0qY/6U+RZXpRSYUIh937qF9o0byb3xyxx+bj3hujp8RUUU3HE7WQsWjHhNL/z6PXZsOkh6VjIdrV2Myk3hooWlTJtTOKhfR0TeNMbM7u9rA87cRaQEuA2YbYw5B/ACS4DvARuMMVOBDbHPEZEZsa+fDVwJPCoi3kFV7CKrt9awbNU7tHZGly3qWgMsW/UOq7fWWFzZ0KmoruCB1x848nldex3lG8upqK6wsCqloiQpiXEPP4Rv7FiafvVrwrW1YAzh2lrqfng3revWjXhNRVOyAOhojZ47428K8tKTH7Jj04Eh+2/EuyzjA9JExEd0xl4LLAQej339cWBR7OcLgaeNMUFjzC6gErhgyCp2mOXrt9MZ6rv1qTMUYfn67RZVNPRWbFlBMBLsMxaIBFixZYVFFSnVlycjAyLHb0E0gQD1Fhw69ub6PceNhbu6eXXN0HWYGjDcjTE1wIPAXqAOaDXGPA+MNcbUxV5TBxTE3lIC7Ov1S+yPjfUhIktFZLOIbG5oGPlzF0ZKz1p7vONOdKC9/9nGicaVskK4vv/OTeG6uhGuJDpTH8z4qYhnWSaH6Gx8MlAMZIjIl072ln7GjlvYN8Y8ZoyZbYyZnZ+fH2+9jnOiG6huurFamNH/OuGJxpWygq+oaFDjw2lUbsqgxk9FPMsynwJ2GWMajDEhYBUwFzgoIkUAsY89/yzuB8b3ev84oss4CenOedNJOeYsmbQkL3fOm25RRUOvbFbZcfvbU72plM0qs6gipY5XcMftSGrf4z8kNZWCO24f8VouWliKL7lvLviSPVy0sHTI/hvxhPte4EIRSZdoV+crgA+AtcCNsdfcCKyJ/XwtsEREUkRkMjAVeH3IKnaYReeXcMNFE4HotzQl2Wncv3imq3bLzJ8ynwWl0R0HglCUUUT53HLdLaNsJWvBAoruvQdfcTGI4CsupujeeyzZLTNtTiGXX3/mkZn6qNwULr/+zEHvljmZATclG2M2icgzwBYgDGwFHgNGAStF5Cai/wB8Pvb690RkJfB+7PW3GGNG5jAFmyrIjP4P3Hb3p8lKd+cTnBMyJwCw6fpNpPncs+Sk3CVrwQJLwrw/0+YUDmmYHyuuJ06MMT8CfnTMcJDoLL6/198H3Hd6pblHVX07Y0aluDbYAZoDzaT50jTYlbIJfUJ1BFQ2+CnNz7C6jGHVHGwmOyXb6jKUUjEa7sPMGENlvZ/SglFWlzKsWoItGu5K2YiG+zBrau+itTPEGfkuD/dACzmpOVaXoZSK0XAfZpX1fgDXz9ybg80a7krZiIb7MKtqiHaCcfuae0ughZwUDXel7ELDfZhVNfhJS/K69hx3gFAkRFuoTdfclbIRDfdhVlnvZ0p+Bh5Pf6cyuENLsAVAl2WUshEN92FW1eCn1OU3U5uDzQA6c1fKRjTch1FnV4Salk7OcPnN1JZAC6Azd6XsRMN9GFUf8mMMCTNz1xuqStmHhvswOrJTpsD9O2UAslOzLa1DKXWUhvswqqr34xGYlOfucG8KNgGQlZJlcSVKqR4a7sOossHP+Nx0UpPc3UK2JdBCZnLmcWe6K6Wso+E+jKrq3b9TBmJPp+p6u1K2ouE+TCLdhl2H2l3/ZCpEZ+663q6UvWi4D5Oa5k6C4W7Xb4OE6ENMuSm5VpehlOpFw32YVDXEDgxLgGWZpkCTztyVshkN92GSKOFujKElqIeGKWU3Gu7DpLLeT15GMjkZyVaXMqw6w50EI0GduStlMxruwyQRzpSBXoeG6cxdKVvRcB8mVQ3trn8yFfTQMKXsSsN9GDS1d9HU3pUYM3c9NEwpW9JwHwZHbqYmwDbIpkD06AENd6XsRcN9GFTF+qa6vSk2HF1z12UZpexFw30YVNb7SfF5KMl2b2u9Hs2BZrziJTM50+pSlFK9aLgPg6oGP1PyR7m6tV6PlmALWSlZeET/KCllJ/o3chhUNSTGmTKAPsCklE0NGO4iMl1EtvX6cVhEbheRchGp6TV+da/3LBORShHZLiLzhve3YB+rt9Yw9/4N7G3q4OUdDazeWmN1ScOqorqCl/e9TFVrFZ9+5tNUVFdYXZJSKsY30AuMMduB8wBExAvUAP8NfBV4yBjzYO/Xi8gMYAlwNlAM/FlEphljIkNbur2s3lrDslXv0BmK/jbbAmGWrXoHgEXnl1hZ2rCoqK6gfGM5Xd1dANS111G+sRyA+VPmW1iZUgoGvyxzBVBljNlzktcsBJ42xgSNMbuASuCCUy3QKZav334k2Ht0hiIsX7/dooqG14otKwhEAn3GApEAK7assKgipVRvgw33JcBTvT6/VUTeFpFfiUjPwmsJsK/Xa/bHxvoQkaUisllENjc0NAyyDPupbekc1LjTHWg/MKhxpdTIijvcRSQZ+Czwh9jQT4FSoks2dcBPel7az9vNcQPGPGaMmW2MmZ2fnz+Ymm2p+ATbHk807nSFGYWDGldKjazBzNyvArYYYw4CGGMOGmMixphu4BccXXrZD4zv9b5xQO1QFGtnd86bTtoxvVLTkrzcOW+6RRUNr7JZZaR6U/uMpXpTKZtVZlFFSqneBhPu/0CvJRkRKer1tWuAd2M/XwssEZEUEZkMTAVeP91C7W7R+SXcv3gmyd7oJS3JTuP+xTNdeTMVojdNv/2xbx/5vCijiPK55XozVSmbGHC3DICIpAP/C/hGr+H/IyLnEV1y2d3zNWPMeyKyEngfCAO3uH2nTI9F55ewYsNOzi4ezX98cZbV5Qy7S0ouAeDei+9l0RmLrC1GKdVHXOFujOkA8o4Zu+Ekr78PuO/0SnOmg4cDXD69wOoyRkQgHN0tk+pLHeCVSqmRpk+oDiF/MExHV4SC0SlWlzIiesI9zevOm8ZKOZmG+xCqPxwNu4LMxAj3znB0m6fO3JWyHw33IVTfFgRg7OjECLueh5g03JWyHw33IdQT7okycz+y5u7VcFfKbjTch9DRZZnECLueZZk0n665K2U3Gu5DqL4tSLLPw+i0uDYhOZ4uyyhlXxruQ6j+cICCzBRE3N+kA3QrpFJ2puE+hOrbgglzMxV0K6RSdqbhPoTq24IJczMVomvuPvGR5E2yuhSl1DE03IfQwdiyTKIIRAK6JKOUTWm4D5FAKEJbIExBAi3LdIY7NdyVsikN9yFSfzi6xz0/kWbu4YDucVfKpjTch0h9W/TmYqLdUNWZu1L2pOE+RBLt6VSAzkinPsCklE1puA+RRDs0DHTmrpSdabgPkYNtQXweISc92epSRoyuuStlXxruQ6T+cJD8zBQ8nsR4OhV05q6UnWm4D5H6tkBCbYOE6D53XXNXyp403IdIQ4I9nQqxfe66LKOULWm4D5FEO3oAossyOnNXyp403IdAV7ibpvauhDnHHcAYo8cPKGVjGu5DoMEf2+OeII2xAULdIbpNt4a7Ujal4T4Eeva4j02gcNcuTErZm4b7EDj6dGrizGJ7wl1vqCplTxruQyARjx7QLkxK2ZuG+xCoPxzAI5A3KoHCXfunKmVrGu5DoP5wkLxRKXgT7OlU0BZ7StnVgOEuItNFZFuvH4dF5HYRyRWRF0RkZ+xjTq/3LBORShHZLiLzhve3YK3VW2tYva2GhrYgFz/wIqu31lhd0rCrqK6g7KUyAO565S4qqissrkgpdawBw90Ys90Yc54x5jzgo0AH8N/A94ANxpipwIbY54jIDGAJcDZwJfCoiHiHp3xrrd5aw7JV7xAMdwNQ09LJslXvuDrgK6orKN9YTlOgCYDGQCPlG8s14JWymcEuy1wBVBlj9gALgcdj448Di2I/Xwg8bYwJGmN2AZXABUNQq+0sX7+dzlCkz1hnKMLy9dstqmj4rdiy4sh6e49AJMCKLSssqkgp1Z/BhvsS4KnYz8caY+oAYh8LYuMlwL5e79kfG+tDRJaKyGYR2dzQ0DDIMuyhtqVzUONucKD9wKDGlVLWiDvcRSQZ+Czwh4Fe2s+YOW7AmMeMMbONMbPz8/PjLcNWirP7v5l4onE3KMwoHNS4Usoag5m5XwVsMcYcjH1+UESKAGIf62Pj+4Hxvd43Dqg93ULt6M5500lL6ns7IS3Jy53zpltU0fArm1V23INLqd5UymaVWVSRUqo/gwn3f+DokgzAWuDG2M9vBNb0Gl8iIikiMhmYCrx+uoXa0aLzS7h/8UxKstMQoCQ7jfsXz2TR+cetQrnG/CnzKZ9bTlFGEYJQlFFE+dxy5k+Zb3VpSqlexJjjVkyOf5FIOtF19CnGmNbYWB6wEpgA7AU+b4xpin3t+8DXgDBwuzHmTyf79WfPnm02b958Or8PpZRKOCLypjFmdn9f88XzCxhjOoC8Y8Yaie6e6e/19wH3DbJOpZRSQ0SfUFVKKRfScFdKKRfScFdKKRfScFdKKReKa7fMsBch0gDsOY1fYgxwaIjKcRO9Liem1+bE9NqcmN2uzURjTL9Pgdoi3E+XiGw+0XagRKbX5cT02pyYXpsTc9K10WUZpZRyIQ13pZRyIbeE+2NWF2BTel1OTK/Niem1OTHHXBtXrLkrpZTqyy0zd6WUUr1ouCullAs5JtxF5MpYw+1KEfleP18XEfn32NffFpFZVtRphTiuzZki8qqIBEXk21bUaJU4rs31sT8vb4vIRhH5iBV1WiGOa7Mwdl22xbqmXWJFnSNtoOvS63UfE5GIiFw7kvXFzRhj+x+AF6gCpgDJwFvAjGNeczXwJ6KdoC4ENlldt42uTQHwMaIndX7b6pptdm3mAjmxn1+lf276vGYUR+/LnQt8aHXddrguvV73IvBH4Fqr6+7vh1Nm7hcAlcaYamNMF/A00UbcvS0EfmuiXgOyezpFudyA18YYU2+MeQMIWVGgheK5NhuNMc2xT18j2jksEcRzbfwmlmRABv20y3SheLIG4J+AZznagc52nBLu8TTdjqsxtwsl6u87HoO9NjcR/e4vEcTbyP4aEfkQqCDagMftBrwuIlICXAP8bATrGjSnhHs8TbfjasztQon6+45H3NdGRC4nGu7fHdaK7CPeRvb/bYw5E1gE3DvcRdlAPNflYeC7xpjI8Jdz6uLqxGQD8TTdTpjG3MdI1N93POK6NiJyLvBL4CoT7TCWCAb158YY81cRKRWRMcYYOx2cNdTiuS6zgadFBKIHiV0tImFjzOoRqTBOTpm5vwFMFZHJIpIMLCHaiLu3tcCXY7tmLgRajTF1I12oBeK5NolqwGsjIhOAVcANxpgdFtRolXiuzRkSS7DY7rNkwO3/+A14XYwxk40xk4wxk4BngG/ZLdjBITN3Y0xYRG4F1hO9S/0rY8x7InJz7Os/I3rX+mqgEugAvmpVvSMpnmsjIoXAZmA00C0itxPdAXDYqrpHQpx/bu4m2h/40ViOhY1DTv07HXFem88RnTCFgE7gC71usLpSnNfFEfT4AaWUciGnLMsopZQaBA13pZRyIQ13pZRyIQ13pZRyIQ13pZRyIQ13pZRyIQ13pZRyof8PxBdvY3aGvSEAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(fcc_comp, fcc_temp, 'o-')\n",
+ "plt.plot(fcc_lqd_comp, fcc_lqd_temp, 'o-')\n",
+ "\n",
+ "plt.plot(fcc_b32_comp, fcc_b32_temp, 'o-')\n",
+ "plt.plot(b32_lqd_comp, b32_lqd_temp, 'o-')\n",
+ "plt.plot(lqd_comp, lqd_temp, 'o-')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "11375903-8291-4baf-a9ff-68681b8f010e",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}