Third†order elastic constants, thermal expansion, and bulk modulus of body†centered cubic crystals

The method of homogeneous deformation is used to derive the expressions for the second‐order elastic and third‐order elastic (TOE) constants of a body‐centered cubic crystal. Two‐ and threebody interactions are taken into account. The TOE constants of the four alkali metals Li, Na, K, and Rb and of the two transition metals Ta and Nb, are then evaluated, and these, in turn, are employed to calculate the low‐temperature limit of thermal expansion for these metals following Thurston and Brugger's equation for the elastic waves propagating in a homogeneously strained crystal. The Anderson‐Grüneisen parameter δ is calculated for each of the metals from its TOE constants, and used to investigate the temperature dependence of the bulk modulus via Anderson's theory. Copyright © 1979 WILEY‐VCH Verlag GmbH & Co. KGaA