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The ELASTICITY task computes the second-order elastic tensor of a crystal by:
  1. Fully relaxing the structure with OPT.
  2. Applying a set of normal and shear strains to generate deformed structures via pymatgen.analysis.elasticity.DeformedStructureSet.
  3. Computing the stress tensor of each deformed structure.
  4. Fitting a linear stress-strain relationship to extract the 6×6 Voigt elastic tensor.
The implementation is adapted from MatCalc.

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Function signature

from mlip_arena.tasks import ELASTICITY

result = ELASTICITY(
    atoms=atoms,
    calculator=calc,
    optimizer="BFGSLineSearch",
    optimizer_kwargs=None,
    filter="FrechetCell",
    filter_kwargs=None,
    criterion=None,
    normal_strains=np.linspace(-0.01, 0.01, 4),
    shear_strains=np.linspace(-0.06, 0.06, 4),
    persist_opt=True,
    cache_opt=False,
)

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Parameters

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body.atoms
ase.Atoms
required
Input structure. A copy is made internally before relaxation.
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body.calculator
ase.calculators.calculator.BaseCalculator
required
Calculator for energy, force, and stress evaluations.
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body.optimizer
Optimizer | str
default:"BFGSLineSearch"
Optimizer passed to the initial OPT task. See structure optimization for valid values.
​
body.optimizer_kwargs
dict | None
default:"None"
Extra keyword arguments forwarded to the optimizer constructor.
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body.filter
Filter | str | None
default:"FrechetCell"
Cell filter for the initial full relaxation. Defaults to "FrechetCell" to allow both positions and cell to relax.
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body.filter_kwargs
dict | None
default:"None"
Extra keyword arguments forwarded to the filter constructor.
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body.criterion
dict | None
default:"None"
Convergence criterion dict forwarded to the OPT task (e.g. {"fmax": 0.001}).
​
body.normal_strains
list[float] | ndarray
default:"np.linspace(-0.01, 0.01, 4)"
Normal strain magnitudes applied along each of the three Cartesian directions. Default covers ±1% in 4 steps. More points improve the linear fit accuracy.
​
body.shear_strains
list[float] | ndarray
default:"np.linspace(-0.06, 0.06, 4)"
Shear strain magnitudes applied for the off-diagonal components of the strain tensor. Default covers ±6% in 4 steps. Larger range needed because MLIPs often show weaker shear stiffness.
​
body.persist_opt
boolean
default:"true"
If True, the OPT result is persisted to Prefect’s result store.
​
body.cache_opt
boolean
default:"false"
If True, the OPT result is cached and reused if the same structure and calculator are provided again.

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Return value

Returns a dict on success, or a Prefect State if the initial relaxation fails:
KeyTypeDescription
elastic_tensorpymatgen.analysis.elasticity.ElasticTensorFull 3×3×3×3 (Voigt 6×6) elastic tensor in GPa, zeroed below numerical tolerance
residuals_sumfloatSum of least-squares residuals from all stress-strain fits — a measure of fit quality
The ElasticTensor object provides derived moduli: 
et = result["elastic_tensor"]

print("K_Voigt (GPa):", et.k_voigt)
print("K_Reuss (GPa):", et.k_reuss)
print("G_Voigt (GPa):", et.g_voigt)
print("G_Reuss (GPa):", et.g_reuss)
print("Young's modulus (GPa):", et.y_mod / 1e9)   # convert Pa → GPa
print("Poisson ratio:", et.universal_anisotropy)

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Example

1

Import and set up

import numpy as np
from ase.build import bulk
from mlip_arena.tasks import ELASTICITY
from mlip_arena.tasks.utils import get_calculator
from mlip_arena.models import MLIPEnum

atoms = bulk("Cu", "fcc", a=3.6)
calc = get_calculator(MLIPEnum.MACE_MP)
2

Run ELASTICITY

result = ELASTICITY(
    atoms=atoms,
    calculator=calc,
    filter="FrechetCell",
    criterion={"fmax": 0.001},
    normal_strains=np.linspace(-0.01, 0.01, 5),
    shear_strains=np.linspace(-0.06, 0.06, 5),
)
3

Extract elastic moduli

et = result["elastic_tensor"]

print("Elastic tensor (GPa):")
print(et.voigt)

print(f"Bulk modulus (Voigt):  {et.k_voigt:.1f} GPa")
print(f"Bulk modulus (Reuss):  {et.k_reuss:.1f} GPa")
print(f"Shear modulus (Voigt): {et.g_voigt:.1f} GPa")
print(f"Shear modulus (Reuss): {et.g_reuss:.1f} GPa")
print(f"Fit residuals sum: {result['residuals_sum']:.4f}")
For accurate elastic constants, use a tight convergence criterion (e.g. fmax=0.001) for the initial relaxation. Poorly relaxed structures produce inconsistent stress-strain data.