ASE calculators

Any ASE calculator that returns the stress can be used directly from Python: EMT and other interatomic potentials, machine-learned potentials such as MACE, and DFT codes driven through ASE such as CP2K. The first tutorial uses EMT, and the CP2K tutorial a DFT code.

calculate

result = minelastic.calculate(atoms, calc, relax_ions=False, method="uncoupled", fmax=1e-4, steps=500,
                              optimizer=None, dipole=None, **setup_kwargs)

builds the strain set of atoms (ElasticSetup(atoms, **setup_kwargs)), computes every strained and displaced cell with the ASE calculator calc and returns the ElasticResult. For each cell it takes

• the stress, calc.get_stress() in eV/Å\(^3\), converted to GPa (tension positive, as in ASE);
• the forces, for the internal-strain tensor and, with ionic=True, the force constants;
• the dipole dipole(atoms) in e Å, if a function is given, for the Born charges and the piezoelectric tensors.

With relax_ions=True the atoms of each strained cell are first relaxed at fixed cell with optimizer (default BFGS) to fmax (eV/Å). setup_kwargs are the options of ElasticSetup: scheme, delta, stencil, symprec, frame, ionic and displacement (Python API).

The how-to pages show each quantity with an ASE calculator:

quantity	example	page
clamped- and relaxed-ion constants	fcc and hcp Cu, EMT	Your first elastic tensor
relaxed-ion constants, two routes	hcp Cu, EMT (examples/emt_ionic.py)	Relaxed-ion constants
internal-strain tensor, force constants	hcp Cu, EMT (examples/emt_internal_strain.py)	Internal strain
Born charges, piezoelectric e and d	alpha-quartz, BKS rigid-ion model (examples/bks_quartz_piezo.py)	Piezoelectricity
finite temperature	fcc Al, EMT molecular dynamics (examples/emt_finite_temperature.py)	Finite temperature

Tip

Relax the reference cell with the same calculator first: the textbook constants refer to a stress-free reference.

Machine-learned potentials

Any ASE calculator works.

Double precision

Run machine-learned potentials in double precision: the stresses of the strained cells differ by only about 1 GPa.

from ase.io import read
from ase.filters import FrechetCellFilter
from ase.optimize import BFGS
from mace.calculators import mace_mp
import minelastic

atoms = read("POSCAR")
calc = mace_mp(model="medium", default_dtype="float64")
atoms.calc = calc
BFGS(FrechetCellFilter(atoms)).run(fmax=1e-4)           # stress-free reference
result = minelastic.calculate(atoms, calc, relax_ions=True)
print(result.summary())

For wurtzite AlN with MACE-MPA-0, the minimal set and the six single strains agree to 0.1 GPa, and the two routes to the relaxed-ion constants to 0.3 GPa (Validation).