HIGHER-ORDER ELASTIC-CONSTANTS AND GENERALIZED GRUNEISEN PARAMETERS OF ELASTIC-WAVES AND LOW-TEMPERATURE THERMAL-EXPANSION OF TITANIUM

The expressions for the 19 fourth order elastic constants, 10 third or der elastic constants, and 6 second order elastic constants of a solid are derived using the method of homogenous deformation with interacti ons extending up to second neighbors using the sublattice displacement s to the second degree in strains. These expressions are used to obtai n the higher order elastic constants and their pressure derivatives in titanium, Titanium belongs to the hexagonal class of crystals. The hi gher order elastic constants are used to find the generalized Gruneise n parameters of the elastic waves propagating in different directions in titanium. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared wit h the available reported values. (C) 1997 Academic Press.