Redetermination and new description of the crystal structure of vanthoffite, Na6Mg(SO4)4.

The crystal structure of vanthoffite {hexa-sodium magnesium tetra-kis[sulfate-(VI)]}, Na6Mg(SO4)4, was solved in the year 1964 on a synthetic sample [Fischer & Hellner (1964 ▸). Acta Cryst. 17, 1613]. Here we report a redetermination of its crystal structure on a mineral sample with improved precision. It was refined in the space group P21/c from a crystal originating from Surtsey, Iceland. The unique Mg (site symmetry ) and the two S atoms are in usual, only slightly distorted octa-hedral and tetra-hedral coordinations, respectively. The three independent Na atoms are in a distorted octa-hedral coordination (1×) and distorted 7-coordinations inter-mediate between a 'split octa-hedron' and a penta-gonal bipyramid (2×). [MgO6] coordination polyhedra inter-change with one half of the sulfate tetra-hedra in <011> chains forming a (100) meshed layer, with dimers formed by edge-sharing [NaO7] polyhedra filling the inter-chain spaces. The other [NaO7] polyhedra are organized in a parallel layer formed by [010] and [001] chains united through edge sharing and bonds to the remaining half of sulfate groups and to [NaO6] octa-hedra. The two types of layers inter-connect through tight bonding, which explains the lack of morphological characteristics typical of layered structures.

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

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/Tm > 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 = (V0K0)/γ = 4.04 (1) × 10-18 J, V0 = 67.1671 (3) Å3, b = (K0' - 1)/2 = 3.84 (9), θD = 182 (2) K, (vf/Ω)exp(sf/kB) = 1.8 (23) and hf = 0.9 (2) eV, where V0 is the unit-cell volume at 0 K, K0 and K0' are the isothermal incompressibility and its first derivative with respect to pressure (evaluated at zero pressure), γ is a Grüneisen parameter, θD is the Debye temperature, vf, hf and sf are the vacancy formation volume, enthalpy and entropy, respectively, Ω is the average volume per atom, and kB is Boltzmann's constant.