Setting up an elastic constants calculation

In most cases, the calculation of elastic constants proceeds by full geometry optimization, including cell optimization. This involves the generation of elastic constants for the theoretical lattice constants. However, you can skip this step and generate elastic constants for the experimental structure.

Elastic constants evaluation involves calculating the stress tensor for a number of distorted structures. Internal coordinates are optimized in each run, while keeping the lattice parameters fixed. The accuracy of the elastic constants depends largely on the accuracy of the SCF part and on the geometry optimization convergence level for each distorted structure.

Elastic Debye temperature and averaged sound velocity are not reported if the calculated elastic constants do not produce physically meaningful sound velocities in some directions (for example, if certain Cij values or their combinations are negative when they should be positive). This can happen for low quality calculations or for calculations that were not preceded by a geometry optimization (including optimization of the lattice parameters).

A CASTEP elastic constants calculation can also produce the piezoelectric strain tensor if you request polarization. The calculation uses the same set of optimized structures, with the applied strain tensor to differentiate numerically calculated polarization with respect to applied strain. This property is even more sensitive to the accuracy of the calculation than elastic coefficients. In particular, you can improve results by using extremely tight SCF convergence criteria and verifying convergence of the results with respect to k-point sampling of the Brillouin zone.

Setting up strain patterns

CASTEP generates the strain patterns automatically, based on the lattice type of the structure. The maximum number of patterns required is six for a monoclinic structure, while one pattern is sufficient for cubic cells. Certain symmetries allow you to modify the patterns so that, whenever possible, the calculation generates volume-conserving strains.

The quality of the calculated values depends strongly on the amplitude of the applied distortions and the number of points used for each strain pattern. Use at least four steps for each strain to obtain a statistically reliable linear fit of the stress-strain relationship. Choose the maximum strain amplitude so that:

To set up strain patterns

  1. Choose Modules | CASTEP | Calculation from the Materials Studio menu bar.
  2. Select the Setup tab.
  3. Choose the Elastic Constants task.
  4. Click More... to open the CASTEP Elastic Constants dialog.
  5. Select the Elastic Constants tab.
  6. Specify the Number of steps for each strain and Maximum strain amplitude in the appropriate text boxes.

Convergence criteria

The Quality setting on the Minimizer tab of the CASTEP Geometry Optimization dialog controls the accuracy of the calculation.

For a detailed description of the quality settings, see Setting the quality of a calculation.

To change the convergence tolerances

  1. Choose Modules | CASTEP | Calculation from the Materials Studio menu bar.
  2. Select the Setup tab.
  3. Choose the Elastic Constants task.
  4. Click More... to open the CASTEP Elastic Constants dialog.
  5. Select the Options tab.
  6. Specify the Quality using either the dropdown list or by providing individual convergence tolerances for the energy, maximum force, and maximum displacement in the corresponding text boxes.

For trigonal symmetry, you must use the orientation standard where C lies along the z-axis and A is in the xz plane. For further details on the lattice orientation standard and how its configuration, see Viewing or changing the lattice parameters.

See Also:

Elastic constants theory
CASTEP Elastic Constants task
CASTEP Geometry Optimization task
Calculating elastic constants