The mixing term is
Note that without crystal field phonon interaction the mixing term is zero, because
the expectation values
are zero in this case. The last term reflects
the fact, that the energy is not invariant under rotations in case of transversal springs.
In (95) we made use of the phonon-strain interaction constants
defined writing explicitely the Voigt notation
by
Note a symmetry property:
in case of inversion symmetry at the position of an ion, the
phonon-strain interaction constants
will be zero.