Example 02: Phase transformation in Fe

In this example, we will make use of the temperature sweep algorithm in calphy to calculate the transformation temperature for BCC to FCC transition in Fe.

The EAM potential that will be used: Meyer, R, and P Entel. “Martensite-austenite transition and phonon dispersion curves of Fe1−xNix studied by molecular-dynamics simulations.” Phys. Rev. B 57, 5140.

The reference data is from: Freitas, Rodrigo, Mark Asta, and Maurice de Koning. “Nonequilibrium Free-Energy Calculation of Solids Using LAMMPS.” Computational Materials Science 112 (February 2016): 333–41.

The input file a is provided in the folder. The calculation can be started from the terminal using:

calphy -i input.yaml

In the input file, the calculations block is as shown below:

calculations:
- element: Fe
  lattice: BCC
  lattice_constant: 0.0
  mass: 55.845
  md:
    barostat_damping: 0.1
    equilibration_control: nose_hoover
    thermostat_damping: 0.1
    timestep: 0.001
  mode: ts
  n_equilibration_steps: 10000
  n_iterations: 1
  n_switching_steps: 25000
  pair_coeff: '* * ../potentials/Fe.eam'
  pair_style: eam
  pressure: 0.0
  queue:
    commands:
    - conda activate calphy
    cores: 4
    scheduler: local
  reference_phase: solid
  repeat:
  - 5
  - 5
  - 5
  temperature:
  - 100.0
  - 1400.0
- element: Fe
  lattice: FCC
  lattice_constant: 6.0
  mass: 55.845
  md:
    barostat_damping: 0.1
    equilibration_control: nose_hoover
    thermostat_damping: 0.1
    timestep: 0.001
  mode: ts
  n_equilibration_steps: 10000
  n_iterations: 1
  n_switching_steps: 25000
  pair_coeff: '* * ../potentials/Fe.eam'
  pair_style: eam
  pressure: 0.0
  queue:
    commands:
    - conda activate calphy
    cores: 4
    scheduler: local
  reference_phase: solid
  repeat:
  - 5
  - 5
  - 5
  temperature:
  - 100.0
  - 1400.0

The mode is listed as ts, which stands for temperature sweep. The sweep starts from the first value in the temperature option, which is 100 K. The free energy is integrated until 1400 K, which is the second value listed. Furthermore, there are also two calculation blocks. You can see that the lattice mentioned is different; one set is for BCC structure, while the other is FCC.

Once the calculation is over, there will a file called temperature_sweep.dat in each of the folders. This file indicates the variation of free energy with the temperature. We can read in the files and calculate the transition temperature as follows:

import numpy as np
import matplotlib.pyplot as plt

bt, bfe, bferr = np.loadtxt("ts-bcc-solid-100-0/temperature_sweep.dat", unpack=True)
ft, ffe, fferr = np.loadtxt("ts-fcc-solid-100-0/temperature_sweep.dat", unpack=True)

args = np.argsort(np.abs(bfe-ffe))
print(bt[args[0]], "K")

---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
Cell In[9], line 2
      1 bt, bfe, bferr = np.loadtxt("ts-bcc-solid-100-0/temperature_sweep.dat", unpack=True)
----> 2 ft, ffe, fferr = np.loadtxt("ts-fcc-solid-100-0/temperature_sweep.dat", unpack=True)
      4 args = np.argsort(np.abs(bfe-ffe))
      5 print(bt[args[0]], "K")

File ~/miniforge3/envs/calphy/lib/python3.12/site-packages/numpy/lib/_npyio_impl.py:1397, in loadtxt(fname, dtype, comments, delimiter, converters, skiprows, usecols, unpack, ndmin, encoding, max_rows, quotechar, like)
   1394 if isinstance(delimiter, bytes):
   1395     delimiter = delimiter.decode('latin1')
-> 1397 arr = _read(fname, dtype=dtype, comment=comment, delimiter=delimiter,
   1398             converters=converters, skiplines=skiprows, usecols=usecols,
   1399             unpack=unpack, ndmin=ndmin, encoding=encoding,
   1400             max_rows=max_rows, quote=quotechar)
   1402 return arr

File ~/miniforge3/envs/calphy/lib/python3.12/site-packages/numpy/lib/_npyio_impl.py:1024, in _read(fname, delimiter, comment, quote, imaginary_unit, usecols, skiplines, max_rows, converters, ndmin, unpack, dtype, encoding)
   1022     fname = os.fspath(fname)
   1023 if isinstance(fname, str):
-> 1024     fh = np.lib._datasource.open(fname, 'rt', encoding=encoding)
   1025     if encoding is None:
   1026         encoding = getattr(fh, 'encoding', 'latin1')

File ~/miniforge3/envs/calphy/lib/python3.12/site-packages/numpy/lib/_datasource.py:192, in open(path, mode, destpath, encoding, newline)
    155 """
    156 Open `path` with `mode` and return the file object.
    157
   (...)    188
    189 """
    191 ds = DataSource(destpath)
--> 192 return ds.open(path, mode, encoding=encoding, newline=newline)

File ~/miniforge3/envs/calphy/lib/python3.12/site-packages/numpy/lib/_datasource.py:529, in DataSource.open(self, path, mode, encoding, newline)
    526     return _file_openers[ext](found, mode=mode,
    527                               encoding=encoding, newline=newline)
    528 else:
--> 529     raise FileNotFoundError(f"{path} not found.")

FileNotFoundError: ts-fcc-solid-100-0/temperature_sweep.dat not found.

plt.plot(bt, bfe, color="#E53935", label="bcc")
plt.plot(ft, ffe, color="#0097A7", label="fcc")
plt.xlabel("Temperature (K)", fontsize=12)
plt.ylabel("F (ev/atom)", fontsize=12)
plt.legend()
plt.savefig("fe_transition.png", dpi=300, bbox_inches="tight")