Fourth-order invariants for the Landau free-energy expansions of elastic phase transitions

The fourth-order invariants in the irreducible strain space have been obtained for the Landau free-energy expansion for elastic phase transitions pertaining to each of the 32 crystallographic point groups. Investigation of these invariants yields information about: (i) those invariants which correspond to the order parameter, (ii) the condition which must be imposed on the fourth-order invariants for an elastic phase transition to be second order. Relations are given in terms of second-, third-and fourth-order elastic constants for the entropy difference between the two phases at the transition and for the latent heat of transformation. The results are examined with reference to experimental studies of the f.c.c.-f.c.t. transition in indium-thallium alloys.