Cubic Elastic Constants¶

CubicElasticConstantsAnalyzer ¶

CubicElasticConstantsAnalyzer(
    eos_name: Literal[
        "murnaghan",
        "birch",
        "birch_murnaghan",
        "pourier_tarantola",
        "vinet",
        "deltafactor",
        "numerical_eos",
    ] = "birch_murnaghan",
    delta_max: float = 0.05,
    step_size: float = 0.01,
    calculator: BaseCalculator | None = None,
    cubic_transformation: CubicElasticConstantsDeformationTransformation
    | None = None,
)

A class used to calculate cubic elastic constants for a given structure.

Computes the elastic constants (C11, C12, C44) for a cubic crystal structure from deformation and energy-volume data, along with derived mechanical properties such as bulk modulus, shear modulus, Young's modulus, and Poisson's ratio.

Initializes the CubicElasticConstantsAnalyzer object.

Parameters:

Name	Type	Description	Default
`eos_name`	`str`	The name of the equation of state (EOS) used for fitting energy-volume data. Defaults to "birch_murnaghan".	`'birch_murnaghan'`
`delta_max`	`float`	The maximum deformation magnitude. Defaults to 0.05.	`0.05`
`step_size`	`float`	The step size for deformations. Defaults to 0.01.	`0.01`
`calculator`	`BaseCalculator \| None`	The calculator object used for energy calculations.	`None`
`cubic_transformation`	`CubicElasticConstantsDeformationTransformation \| None`	The transformation object used to apply cubic distortions.	`None`

calculate ¶

calculate(
    structure: Structure | Atoms, is_relaxed: bool = False
) -> dict[str, float]

Calculates the cubic elastic constants for a given structure.

Applies cubic distortions to the input structure, computes the potential energies of the deformed structures, and derives the elastic constants (C11, C12, C44) and additional mechanical properties from the resulting energy differences.

Parameters:

Name	Type	Description	Default
`structure`	`Structure \| Atoms`	The input structure.	required
`is_relaxed`	`bool`	Whether the structure is already relaxed. Defaults to False.	`False`

Returns:

Type Description

dict[str, float]

dict[str, float]: Dictionary with keys: - C11: Elastic constant C11 in GPa. - C12: Elastic constant C12 in GPa. - C44: Elastic constant C44 in GPa. - youngs_modulus: Young's modulus in GPa. - voigt_bulk_modulus: Voigt bulk modulus in GPa. - voigt_shear_modulus: Voigt shear modulus in GPa. - reuss_bulk_modulus: Reuss bulk modulus in GPa. - reuss_shear_modulus: Reuss shear modulus in GPa. - voigt_reuss_hill_bulk_modulus: Voigt-Reuss-Hill bulk modulus in GPa. - voigt_reuss_hill_shear_modulus: Voigt-Reuss-Hill shear modulus in GPa. - poisson_ratio: Poisson ratio. - pugh_ratio: Pugh ratio (G_VRH / K_VRH). - chen_vickers_hardness: Chen-Vickers hardness in GPa.

Raises:

Type	Description
`ValueError`	If the calculator object does not have the 'energy' property implemented.

cubic_transformation ¶

cubic_transformation() -> (
    CubicElasticConstantsDeformationTransformation
)

Returns the cubic transformation object used to generate deformed structures.

Returns:

Name	Type	Description
`CubicElasticConstantsDeformationTransformation`	`CubicElasticConstantsDeformationTransformation`	The transformation object used for cubic distortions.