The thermal expansion of gold: point defect concentrations and pre-melting in a face-centred cubic metal

摘要

On the basis of ab initio computer simulations, pre-melting phenomena have been suggested to occur in the elastic properties of hexagonal close-packed iron under the conditions of the Earth’s inner core just before melting. The extent to which these pre-melting effects might also occur in the physical properties of face-centred cubic metals has been investigated here under more experimentally accessible conditions for gold, allowing for comparison with future computer simulations of this material. The thermal expansion of gold has been determined by X-ray powder diffraction from 40 K up to the melting point (1337 K). For the entire temperature range investigated, the unit-cell volume can be represented in the following way: a second-order Grüneisen approximation to the zero-pressure volumetric equation of state, with the internal energy calculated via a Debye model, is used to represent the thermal expansion of the ‘perfect crystal’. Gold shows a nonlinear increase in thermal expansion that departs from this Grüneisen–Debye model prior to melting, which is probably a result of the generation of point defects over a large range of temperatures, beginning at T/T m > 0.75 (a similar homologous T to where softening has been observed in the elastic moduli of Au). Therefore, the thermodynamic theory of point defects was used to include the additional volume of the vacancies at high temperatures (‘real crystal’), resulting in the following fitted parameters: Q = (V 0 K 0)/γ = 4.04 (1) × 10⁻¹⁸ J, V 0 = 67.1671 (3) ų, b = (K 0′ − 1)/2 = 3.84 (9), θD = 182 (2) K, (v ^f/Ω)exp(s ^f/k B) = 1.8 (23) and h ^f = 0.9 (2) eV, where V 0 is the unit-cell volume at 0 K, K 0 and K 0′ are the isothermal incompressibility and its first derivative with respect to pressure (evaluated at zero pressure), γ is a Grüneisen parameter, θ D is the Debye temperature, v ^f, h ^f and s^f are the vacancy formation volume, enthalpy and entropy, respectively, Ω is the average volume per atom, and kB is Boltzmann’s constant.