Higher order elastic constants and generalised gruneisen parameters of elastic waves and low temperature thermal expansion of dysprosium

The expressions for the 19 fourth order elastic constants, 10 third order elastic constants and six second order elastic constants are derived using the method of homogenous deformation with interactions extending up to second neighbours using the sublattice displacements to the second degree in strains. These expressions are used to obtain the higher order elastic constants and their pressure derivatives in dysprosium. Dysprosium belongs to the hexagonal class of crystals. The higher order elastic constants are used to find out the generalised Gruneisen parameters of the elastic waves propagating in different directions in dysprosium. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with the available reported values.