Under certain conditions, the elastic constant (Cij) of a single crystal calculated based on Materials Studio is negative, and the inspection structure is also the optimal configuration. Is the calculated elastic constant value reliable in this case?
Optimum configuration and "negative elastic constants" (at least one of the eigenvalues of the elastic 6x6 Cij matrix) is negative can only coincide if you determine the optimum configuration upon some symmetry constraints (e.g. cubic crystal lattice). Eg. bcc-Co has a negative C11-C12 in spite of the fact that you can determine a lattice constant corresponding to a minimum energy. In such a case you have to explore the path along the strain associated with the C11-C12 to find a true minimum. Note that there is also the possiblity of dynamic instability, which implies that some phonon not corresponding to the gamma point is associated with a negative energy. Also such a crystal is instable, although even the Cij matrix has all-positive eigenvalues.
Negative elastic constants of some crystal sometime carry information about weather its brittle of ductile in nature. Negative constant reveal instability and brittle nature of a crystal.
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"Negative elastic constants of some crystal sometime carry information about weather its brittle of ductile in nature." I regard this statement as a exaggeration from what can be reliably obtained from DFT based elastic constants. Personally, I do not highly regard Pugh's modulo ratio. It is, primarily, a desparate attempt to derive conclusions from elastic constants on plasticity....
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