Single-Ion Heat Capacities, Cp(298)ion, of Solids: with a Novel Route to Heat-Capacity Estimation of Complex Anions

Abstract

Single-ion heat capacities, C(p)(298)(ion), are additive values for the estimation of room-temperature (298 K) heat capacities of ionic solids. They may be used for inferring the heat capacities of ionic solids for which values are unavailable and for checking reported values, thus complementing our independent method of estimation from formula unit volumes (termed volume-based thermodynamics, VBT). Analysis of the reported heat-capacity data presented here provides a new self-consistent set of heat capacities for both cations and anions that is compatible (and thus may be combined) with an extensive set developed by Spencer. The addition of a large range of silicate species permits the estimation of the heat capacities of many silicate minerals. The single-ion heat capacities of individual silicate anions are observed to be strictly proportional to the total number of atoms (Si plus O), n, contained within the silicate anion complex itself (e.g., for the anion Si(2)O(7)(2-), n = 9, for SiO(4)(2-), n = 5), C(p)(silicate anion)/J K(-1) mol(-1) = 13.8n, in a new rule that is an extension of the Neumann-Kopp relationship. The same linear relationship applies to other homologous anion series (for example, oxygenated heavy-metal anion complexes such as niobates, bismuthates, and tantalates), although with a different proportionality constant. A similar proportionality, C(p)(complex anion)/J K(-1) mol(-1) ≈ 17.5n, which may be regarded as a convenient "rule of thumb", also applies, although less strictly, to complex anions in general. The proportionality constants reflect the rigidity of the complex anion, being always less than the Dulong-Petit value of 25 J K(-1) mol(-1). An emergent feature of our VBT and single-ion approaches to an estimation of the thermodynamic properties is the identification of anomalies in measured values, as is illustrated in this paper.