CASTEP results for the Elastic Constants task are returned as a set of `.castep`

output files. Each of
them represents a geometry optimization run with a fixed cell, for a given strain pattern and strain amplitude. The naming convention for these
files is:

seedname_cij__m__n

Where *m* is the current strain pattern and *n* is the current strain amplitude for the given pattern.

CASTEP can then be used to analyze the calculated stress tensors for each of these runs and generate a file with information about elastic
properties. The information in this file includes a summary of the input strains and calculated stresses; results of linear fitting for each
strain pattern, including quality of the fit; the correspondence between calculated stresses and elastic constants for a given symmetry; a table
of elastic constants, C_{ij}, and elastic compliances, S_{ij}; and finally, the derived properties such as bulk modulus and its
inverse, compressibility, Young modulus and Poisson ratios for three directions and the Lame constants that are needed for modeling the material
as an isotropic medium.

To calculate elastic constants

- Choose Modules | CASTEP | Analysis from the Materials Studio menu bar.
- Select Elastic constants from the list of properties.
- Use the Results file selector to pick the appropriate results file.
- Click the Calculate button.
- A new text document,
`seedname Elastic Constants.txt`

, is created in the results folder.

Below, the example of a hexagonal crystal, BeO, is used to explain the contents of the `Elastic Constants.txt`

output file
produced by CASTEP.

Two strain patterns are required for this lattice type. For each strain pattern there is a summary of calculated stresses as extracted from
the respective `.castep`

files:

Summary of the calculated stresses ********************************** Strain pattern: 1 ====================== Current amplitude: 1 Transformed stress tensor (GPa) : -1.249661 0.000000 0.000000 0.000000 -1.227407 0.001706 0.000000 0.001706 0.990234 Current amplitude: 2 Transformed stress tensor (GPa) : -1.423318 0.000000 0.000000 0.000000 -1.400907 0.001555 0.000000 0.001555 0.089948 ....

Any information about the connection between components of the stress, strain and elastic constants tensors is provided. At this stage each
elastic constant is represented by a single compact index rather than by a pair of *ij* indices. The correspondence between the compact
notation and the conventional indexing is provided later in the file:

Stress corresponds to elastic coefficients (compact notation): 8 8 3 0 0 0 as induced by the strain components: 3 3 3 0 0 0

A linear fit of the stress-strain relationship for each component of the stress is given in the following format:

Stress Cij value of value of index index stress strain 1 8 -1.249661 -0.003000 1 8 -1.423318 -0.001000 1 8 -1.592620 0.001000 1 8 -1.757343 0.003000 C (gradient) : 84.617400 Error on C : 0.706339 Correlation coeff: 0.999930 Stress intercept : -1.505736

The gradient provides the value of the elastic constant (or a linear combination of elastic constants), the quality of the fit, indicated by the correlation coefficient, provides the statistical uncertainty of that value. The stress intercept value is not used in further analysis, it is simply an indication of how far the converged ground state was from the initial structure.

The results for all the strain patterns are then summarized:

============================ Summary of elastic constants ============================ id i j Cij (GPa) 1 1 1 408.16095 +/- 0.601 3 3 3 447.05940 +/- 1.117 4 4 4 129.43210 +/- 0.094 7 1 2 114.84665 +/- 0.889 8 1 3 84.91535 +/- 0.392

The errors are only provided when more than two values for the strain amplitude were used, since there is no statistical uncertainty associated with fitting a straight line to only two points.

Elastic constants are then presented in a conventional 6×6 tensor form, followed by a similar 6×6 representation of the compliances:

===================================== Elastic Stiffness Constants Cij (GPa) ===================================== 408.16095 114.84665 84.91535 0.00000 0.00000 0.00000 114.84665 408.16095 84.91535 0.00000 0.00000 0.00000 84.91535 84.91535 447.05940 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 129.43210 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 129.43210 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 146.65715 ======================================== Elastic Compliance Constants Sij (1/GPa) ======================================== 0.0027235 -0.0006858 -0.0003870 0.0000000 0.0000000 0.0000000 -0.0006858 0.0027235 -0.0003870 0.0000000 0.0000000 0.0000000 -0.0003870 -0.0003870 0.0023839 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0077261 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0077261 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0068186

The final part of the file contains the derived properties:

Bulk modulus = 203.62075 +/- 0.321 (GPa) Compressibility = 0.00491 (1/GPa) Axis Young Modulus Poisson Ratios (GPa) X 367.17384 Exy= 0.2518 Exz= 0.1421 Y 367.17384 Eyx= 0.2518 Eyz= 0.1421 Z 419.48574 Ezx= 0.1624 Ezy= 0.1624

The last section of the file contains average properties that describe the elastic response of a polycrystal, for example:

==================================================== Elastic constants for polycrystalline material (GPa) ==================================================== Voigt Reuss Hill Bulk modulus : 235.70320 235.70320 235.70320 Shear modulus (Lame Mu) : 75.75417 64.59893 70.17655 Lame lambda : 185.20042 192.63725 188.91883 Universal anisotropy index: 0.86342

This output contains the bulk modulus and shear modulus averaged according to Voigt, Reuss, and Hill schemes (Nye 1957).

In addition an universal anisotropy index suggested by Ranganathan and Ostoja-Starzewski (2008) is evaluated.

Analyzing CASTEP results

Updating structure

Visualizing volumetric data

Displaying band structure charts

Displaying density of states charts

Displaying trajectory and chart data

Displaying optical properties

Accelrys Materials Studio 8.0 Help: Wednesday, December 17, 2014