Mg/Ca Worked Example

In practice, you will calculate the free energies for each phase from some method (e.g. calphy) and then use landau for the plotting. This data was obtained from Atomic Cluster Expansion models run by calphy.

Load Free Energies into Landau

Here, we read the free energies as a function of temperature from a dataframe.

Prelude

import pandas as pd
import landau as ld

Load Free Energies

df = pd.read_pickle("MgCaFreeEnergies.pckl.gz")

def build(row):
    return ld.phases.TemperatureDependentLinePhase(row.phase, row.composition, row.temperature, row.free_energy, interpolator=ld.interpolate.SGTE(4))

df['phaseobj'] = df.apply(build, axis=1)

df

	phase	composition	temperature	free_energy	state	phaseobj
0	hcp Mg	0.000000	[300.0, 300.0042000588008, 300.0084002352066, ...	[-1.5225154593605692, -1.5225168694102966, -1....	solid	TemperatureDependentLinePhase("hcp Mg")
1	bcc Ca	1.000000	[300.0, 300.00461545700705, 300.0092310560326,...	[-1.9342844504225414, -1.9342865724018383, -1....	solid	TemperatureDependentLinePhase("bcc Ca")
2	Mg$_2$Ca	0.333333	[300.0, 300.0042000588008, 300.0084002352066, ...	[-1.781469669607899, -1.7814711895104098, -1.7...	solid	TemperatureDependentLinePhase("Mg$_2$Ca")
4	fcc Ca	1.000000	[300.0, 300.0042000588008, 300.0084002352066, ...	[-1.9365957848456883, -1.9365976398227, -1.936...	solid	TemperatureDependentLinePhase("fcc Ca")
14	liquid	0.333273	[800.0, 800.0053333635558, 800.0106667982238, ...	[-2.020797043491122, -2.020801126471374, -2.02...	liquid	TemperatureDependentLinePhase("liquid")
15	liquid	0.666636	[800.0, 800.0053333635558, 800.0106667982238, ...	[-2.161913993730873, -2.1619183103650097, -2.1...	liquid	TemperatureDependentLinePhase("liquid")
18	liquid	0.000000	[600.0, 600.0060000600006, 600.0120002400048, ...	[-1.632069098400621, -1.6320727216435675, -1.6...	liquid	TemperatureDependentLinePhase("liquid")
19	liquid	1.000000	[1000.0, 1000.0057143126531, 1000.011428690613...	[-2.3851575945277173, -2.3851625203296583, -2....	liquid	TemperatureDependentLinePhase("liquid")
22	liquid	0.166636	[800.0, 800.0053333635558, 800.0106667982238, ...	[-1.9109840875275999, -1.9109880541330522, -1....	liquid	TemperatureDependentLinePhase("liquid")
23	liquid	0.500000	[800.0, 800.0053333635558, 800.0106667982238, ...	[-2.1026342137400933, -2.102638434385509, -2.1...	liquid	TemperatureDependentLinePhase("liquid")
24	liquid	0.833273	[800.0, 800.0053333635558, 800.0106667982238, ...	[-2.2026799550501632, -2.2026842763304164, -2....	liquid	TemperatureDependentLinePhase("liquid")

def combine(dd):
    if len(dd) == 1:
        return dd.phaseobj.iloc[0]
    else:
        return ld.phases.InterpolatingPhase(dd.phase.iloc[0], dd.phaseobj.tolist(), num_coeffs=3)

phases = df.groupby('phase')[df.columns].apply(combine).tolist()

Check Interpolation

import matplotlib.pyplot as plt

for p in df.phaseobj:
    p.check_interpolation(Tl=.1)
plt.legend()

<matplotlib.legend.Legend at 0x7f33b23897f0>

Save to Pickle

import pickle

with open("MgCaPhases.pckl", 'wb') as f:
    pickle.dump(phases, f)

Plotting Diagrams

With the phase objects created landau can calculate and plot the phase diagram for us.

Prelude

import pandas as pd
import landau as ld
import numpy as np
import seaborn as sns

Load

Read existing phase objects from file.

phases = pd.read_pickle("MgCaPhases.pckl")

Calculate Diagram

%%time
df = ld.calculate.calc_phase_diagram(
    phases,
    Ts=np.linspace(100, 1500, 50),
    mu=150,
    keep_unstable=True
)

CPU times: user 6.69 s, sys: 17.2 ms, total: 6.71 s
Wall time: 6.78 s

df

	T	phase	phi	mu	c	stable	border	refined	f	f_excess
0	100.000000	Mg$_2$Ca	-1.480066	-0.757406	0.333333	True	True	no	-1.732535	-0.123050
1	100.000000	Mg$_2$Ca	-1.482567	-0.749905	0.333333	True	True	no	-1.732535	-0.123050
2	100.000000	Mg$_2$Ca	-1.485065	-0.742411	0.333333	True	True	no	-1.732535	-0.123050
3	100.000000	Mg$_2$Ca	-1.487513	-0.735066	0.333333	True	True	no	-1.732535	-0.123050
4	100.000000	Mg$_2$Ca	-1.489922	-0.727839	0.333333	True	True	no	-1.732535	-0.123050
...	...	...	...	...	...	...	...	...	...	...
38576	549.789157	Mg$_2$Ca	-1.805706	-0.265398	0.333333	True	True	delaunay-triple	-1.894172	0.058977
38577	549.789157	bcc Ca	-1.805706	-0.265398	1.000000	True	True	delaunay-triple	-2.071104	0.000000
38578	736.553962	liquid	-1.730833	-0.808065	0.083914	True	True	delaunay-triple	-1.798641	-0.045205
38579	736.553962	hcp Mg	-1.730833	-0.808065	0.000000	True	True	delaunay-triple	-1.730833	0.000000
38580	736.553962	Mg$_2$Ca	-1.730833	-0.808065	0.333333	True	True	delaunay-triple	-2.000188	-0.179570

38581 rows × 10 columns

Plot

Raw

sns.scatterplot(
    data=df.query('stable'),
    x='c', y='T',
    hue='phase',
)

<Axes: xlabel='c', ylabel='T'>

Colorful

ld.plot.plot_mu_phase_diagram(df)

/home/pmrv/.mamba/envs/landau/lib/python3.13/site-packages/landau/poly.py:37: FutureWarning: DataFrameGroupBy.apply operated on the grouping columns. This behavior is deprecated, and in a future version of pandas the grouping columns will be excluded from the operation. Either pass `include_groups=False` to exclude the groupings or explicitly select the grouping columns after groupby to silence this warning.
  return self.prepare(df).groupby(['phase', 'phase_unit']).apply(

ld.plot.plot_phase_diagram(df, tielines=True)

/home/pmrv/.mamba/envs/landau/lib/python3.13/site-packages/landau/poly.py:37: FutureWarning: DataFrameGroupBy.apply operated on the grouping columns. This behavior is deprecated, and in a future version of pandas the grouping columns will be excluded from the operation. Either pass `include_groups=False` to exclude the groupings or explicitly select the grouping columns after groupby to silence this warning.
  return self.prepare(df).groupby(['phase', 'phase_unit']).apply(
/home/pmrv/.mamba/envs/landau/lib/python3.13/site-packages/landau/plot.py:96: FutureWarning: DataFrameGroupBy.apply operated on the grouping columns. This behavior is deprecated, and in a future version of pandas the grouping columns will be excluded from the operation. Either pass `include_groups=False` to exclude the groupings or explicitly select the grouping columns after groupby to silence this warning.
  tdf.groupby("border_segment").apply(plot_tie)