Stress

	Stress
Forces	Eigenstate

Name

Stress — Class for calculating the stress of a configuration.

Synopsis

Namespace: NanoLanguage

Stress(
configuration,
fix_strain
)

Description

Constructor for the Stress object.

Stress Arguments

configuration

Configuration with a calculator that supports stress calculations.

Type: BulkConfiguration or DeviceConfiguration.

Default:


          None

fix_strain

Additional constraint parameter.

Type: FixStrain | None

Default:


          None

Stress Methods

A Stress object provides the following methods:

evaluate(): Return the stress as a physical quantity.
nlprint(stream): Print a formatted string with the stress.

stream

The stream the stress should be written to.
Type: A stream that supports strings being written to using 'write'.
Default: sys.stdout

Usage Examples

Calculate and print the stress tensor of a compressed GaAs crystal

# Set up configuration
bulk_configuration = BulkConfiguration(
    bravais_lattice=FaceCenteredCubic(5.4*Angstrom),
    elements=[Gallium, Arsenic],
    cartesian_coordinates=[[ 0.      ,  0.      ,  0.      ],
                         [ 1.413425,  1.413425,  1.413425]]*Angstrom
    )

calculator = LCAOCalculator(
    numerical_accuracy_parameters=NumericalAccuracyParameters(
    k_point_sampling=(4, 4, 4))
    )

bulk_configuration.setCalculator(calculator)

#calculate the stress
stress = Stress(bulk_configuration)
nlprint(stress)

stress.py

Notes

Stress is given by the derivative of the total energy, $E$ , with respect to a strain $\epsilon_{\alpha \beta}$ ,

$\displaystyle \sigma_{\alpha \beta} = \frac{1}{V}\frac{dE}{d\epsilon_{\alpha \beta}}.$

In this equation, $V$ , is the volume of the system and the strain tensor displaces positions by

$\displaystyle R^\epsilon_\alpha = \sum_\beta(\delta_{\alpha \beta} + \epsilon_{\alpha \beta}) R_\beta.$

Stress has unit energy per volume element, i.e. eV/Ang**3.


Forces		Eigenstate