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Elastic Tensor Axescposs logo
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Notes on definition of elastic tensor axes

The convention for defining elastic axes (See here for details) is that z should be along the highest order axis and x along a lower order axis if there is one normal to it. Neighbours uses the convention

x is parallel to reciprocal a, z is parallel to c, y is orthogonal to x and z and forms a right handed set

for most cases. This will give the conventional definition for the elastic constants except for a few special cases. These are

  1. Monoclinic crystals in non-standard settings.
  2. Triclinic crystals defined using rhombohedral axes
    a=b=c, alpha=beta=gamma
  3. Triclinic R centred crystals using hexagonal axes and hexagonal crystals, for which there is a two fold axis normal to the 3 (6) fold axis. In this case using x parallel to reciprocal a will put the x axis normal to the 2 fold axis rather than along it.

Neighbours does not attempt to use the correct transformation to get the elastic axes in the conventional definition in cases (1) and (2). However in these cases the elastic constants calculated by DMAREL are correct for the axis system used; it is just not a conventional axis system. So the normal message is correct for these cases including the rhombohedral axis case.

In case 3) Neighbours does move the x axis so that it lies along the 2 fold axis (if there is one) rather than being normal to it. This is the only case for which the normal definition does not apply.

What I would suggest doing is either

  1. using the message

    x is parallel to reciprocal a, z is parallel to c, y is orthogonal to x and z and forms a right handed set, unless beta =120 degrees

  2. Testing in the perl script whether $cell_param_beta is equal to 120 degrees and using the message

    x is parallel to a, z is parallel to c, y is orthogonal to x and z and forms a right handed set

    if it is.

Eventually we should modify neighbours to allow for cases 1) and 2) and at this point we may need to modify what is
written into the database.

Maurice Leslie, 17 October 2005

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