Third-Order Elastic Constants and Thermal Expansion of Scandium

Abstract

The third-order elastic (T.O.E.) constants, the pressure derivatives of the second-order elastic (S.O.E.) constants and the temperature variation of the volume Gruneisen function of scandium have been calculated using the nearest-neighbour central force model for hcp metals proposed by Srinivasan and Ramji Rao. The T.O.E. constants have been employed to calculate the low-temperature limit Ȳ_L of the lattice thermal expansion. The theoretical value of Ȳ_L for scandium is 0.94. The high temperature limit of the lattice thermal expansion, Ȳ_H has the value 1.22 which agrees well with the experimental value 1.17 obtained from the thermal expansion and lattice specific heat data of scandium. The variation of the lattice parameters of scandium with hydrostatic pressure has been calculated using its T.O.E. constant data and the extrapolation formula of Thurston. The agreement with the compression data of Stephens is good.