ElasticConstants¶

class ElasticConstants(configuration, optimizer=None, max_forces=None, max_steps=None, max_step_length=None, eta_max=None, n_eta=None, enable_symmetry=None, fit_order=None)¶

Class to calculate the elastic constants of a bulk material. Uses finite strain and calculates the elastic constants from the linear stress response.

Parameters:

configuration (BulkConfiguration.) – The BulkConfiguration for which the elastic constants should be calculated.
optimizer (FIRE | LBFGS | NoOptimization) – The optimizer method used for optimizing the internal coordinates after each strain. Set this to NoOptimization to disable optimization of the strained cell.
Default: LBFGS
max_forces (PhysicalQuantity of type force) – The force threshold for the geometry optimization.
Default: 0.005 * eV / Ang
max_steps (int) – The maximum number of steps used by the optimizer.
Default: 200
max_step_length (PhysicalQuantity of type length) – The maximum step length the optimizer may take.
Default: 0.2 * Ang
eta_max (float) – The maximum strain that can be be applied to the cell. Must be positive.
Default: 0.005
n_eta (int) – The total number of different strain magnitudes for each strain vector. Must be larger than 1.
Default: 3
enable_symmetry (bool) – Flag to select if only the independent elastic constants are calculated for each crystal system, or if all 21 constants are calculated.
Default: True if the configuration has standard orientation, False otherwise.
fit_order (int) – The order of the polynomial fit of the stress-strain dependency. Must be in the interval 1 to (n_eta - 1).
Default: 1

bulkModulusHill()¶

Returns:: The Hill type bulk modulus.
Return type:: PhysicalQuantity of type pressure

bulkModulusReuss()¶

Returns:: The Reuss type bulk modulus.
Return type:: PhysicalQuantity of type pressure

bulkModulusVoigt()¶

Returns:: The Voigt type bulk modulus.
Return type:: PhysicalQuantity of type pressure

enableSymmetry()¶

Returns:: True if only the independent elastic constants are calculated for each crystal system, and False if all 21 constants are calculated
Return type:: bool

etaMax()¶

Returns:: The maximum strain that can be be applied to the cell.
Return type:: float

evaluate()¶

Returns:: The elastic constants as a shape (6, 6) array.
Return type:: PhysicalQuantity of type pressure

fitOrder()¶

Returns:: The order of the polynomial fit of the stress-strain dependency.
Return type:: int

maxForces()¶

Returns:: The force threshold for the geometry optimization.
Return type:: PhysicalQuantity of type force

metatext()¶

Returns:: The metatext of the object or None if no metatext is present.
Return type:: str | None

nEta()¶

Returns:: The total number of different strain magnitudes for each strain vector.
Return type:: int

nlprint(stream=None)¶

Print a string containing an ASCII table useful for plotting the AnalysisSpin object.

Parameters:: stream (python stream) – The stream the table should be written to.
Default: NLPrintLogger()

poissonRatio()¶

Returns:: The Poisson ratios in various directions as a shape (3, 3) array.
Return type:: numpy.array

setMetatext(metatext)¶

Set a given metatext string on the object.

Parameters:: metatext (str | None) – The metatext string that should be set. A value of “None” can be given to remove the current metatext.

shearModulusHill()¶

Returns:: The Hill type shear modulus.
Return type:: PhysicalQuantity of type pressure

shearModulusReuss()¶

Returns:: The Reuss type shear modulus.
Return type:: PhysicalQuantity of type pressure

shearModulusVoigt()¶

Returns:: The Voigt type shear modulus.
Return type:: PhysicalQuantity of type pressure

uniqueString()¶: Return a unique string representing the state of the object.

youngsModulus()¶

Returns:: The Young’s moduli.
Return type:: PhysicalQuantity of type pressure

Usage Examples¶

Calculate the elastic constants of bulk silicon using the Stillinger-Weber potential [1], print the results, and save the object to an nc file:

# Set up bulk configuration
bulk_configuration = BulkConfiguration(
    bravais_lattice=FaceCenteredCubic(5.4306*Angstrom),
    elements=[Silicon, Silicon],
    fractional_coordinates=[[ 0.  ,  0.  ,  0.  ],
                            [ 0.25,  0.25,  0.25]])

# Define the calculator
calculator = TremoloXCalculator(parameters=StillingerWeber_Si_1985())
bulk_configuration.setCalculator(calculator)
bulk_configuration.update()

# Calculate the elastic constants
elastic = ElasticConstants(bulk_configuration,
                           optimizer=LBFGS(),
                           max_forces=0.001*eV/Angstrom,
                           eta_max=0.002,
                           n_eta=3,
                           enable_symmetry=True,
                           fit_order=1)
# Print the results
nlprint(elastic)
# Save the elastic constants analysis object
nlsave('elastic_constants.nc', elastic)

elastic_constants.py

Notes¶

Set optimizer=None if the atoms in the strained cell should not be optimized before calculating the Stress. If the cell only contians one atom, the optimization is automatically disabled.
Other properties, such as bulk modulus, shear modulus, Young’s modulus, or Poisson ratios can be calculated from the elastic constants. To view these results use the method nlprint.
An ElasticConstants calcualtion can be performed using any calculator that supports the calculation of Stress.
Before calculating the elastic constants of a given BulkConfiguration, the cell vectors should be optimized using the OptimizeGeometry function.