Exercise 3: Visualizing Training Data

You’ll need to run the Unpack.ipynb notebook before this one!

Setup

from pyiron import Project
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns

plt.rc('figure', figsize=(16,8))
plt.rc('font', size=18)

pr = Project('training')

pr.job_table()

	id	status	chemicalformula	job	subjob	projectpath	project	timestart	timestop	totalcputime	computer	hamilton	hamversion	parentid	masterid
2	17168587	finished	None	full	/full	/cmmc/u/	zora/pyiron/projects/2022/POTENTIALS/TutorialNotebooks/workshop_preparation/introduction/training/	2022-06-03 00:02:34.816533	None	None	zora@cmti001#1	TrainingContainer	0.4	None	None
0	17168588	finished	None	basic	/basic	/cmmc/u/	zora/pyiron/projects/2022/POTENTIALS/TutorialNotebooks/workshop_preparation/introduction/training/	2022-06-03 00:02:47.281055	None	None	zora@cmti001#1	TrainingContainer	0.4	None	None
1	17168589	finished	None	Al_basic_atomicrex	/Al_basic_atomicrex	/cmmc/u/	zora/pyiron/projects/2022/POTENTIALS/TutorialNotebooks/workshop_preparation/introduction/training/	2022-06-03 00:02:48.226369	None	None	zora@cmti001#1	TrainingContainer	0.4	None	None

Loading Container

container = pr.load('basic')

Some Predefined Plots

Cell Information

container.plot.cell();

Cell Symmetries

container.plot.spacegroups();

E-V Curves

container.plot.energy_volume();

Custom Plots from Data

df = container.to_pandas()

E-V by Concentration

df['concentration'] = df.atoms.map(lambda s: (s.get_chemical_symbols()=='Li').mean())

df['energy_atom'] = (df.energy / df.number_of_atoms)

df['volume_atom'] = df.atoms.map(lambda s: s.get_volume(per_atom=True))

sns.scatterplot(
    data=df,
    x='volume_atom',
    y='energy_atom',
    hue='concentration'
)
plt.xlabel(r'Atomic Volume [$\mathrm{\AA}^3$/atom')
plt.ylabel(r'Atomic Energy [eV/atom]')
plt.legend(title='Li')

<matplotlib.legend.Legend at 0x1502c1833a60>

Convex Hull

First find the equilibrium energy at the terminal concentrations.

e_min_al = df.query('concentration == 0').energy_atom.min()
e_min_li = df.query('concentration == 1').energy_atom.min()
print(e_min_al, e_min_li)

-3.4827513025 -1.757035875

Next calculate the deviation to the “ideal” mixing enthalpy

\[ e(c_\mathrm{Li}) = e_\mathrm{Al} + c_\mathrm{Li} (e_\mathrm{Li} - e_\mathrm{Al}) \]

and call that the energy excess, where \(e\) are the per atom equilibrium energies of the pure phases.

df['energy_atom_excess'] = df.energy_atom - df.concentration * (e_min_li - e_min_al) - e_min_al

sns.lineplot(data=df,
             marker='o',
             x='concentration', y='energy_atom_excess',
             estimator=np.min)
plt.scatter(df.concentration, df.energy_atom_excess, marker='.')
plt.ylim(df.energy_atom_excess.min() * 1.2, .4)
plt.xlabel('Li concentration')
plt.ylabel('Excess Energy [eV/atom]')

Text(0, 0.5, 'Excess Energy [eV/atom]')

Extra Credit

1. Plot the energy against smallest nearest neighbor distance in a structure. You can get the neighbor information with the get_neighbor method on a structure.