A five‐parameter temperature‐corrected Murnaghan equation for P‐V‐T surfaces

Abstract

We have derived an explicit, empirical V(T,P) equation based on an exponential temperature correction of the isothermal Murnaghan equation. The equation is symmetrical with respect to the first-and second-order derivatives of volume and is consistent with the thermodynamic relationship between (•)KT/•)T)p and (•)ctp/•)P)T. The only input data required are the five room temperature, room pressure parameters: Koo, K'oo, Ctoo, Ct'oo, and (3KT/3T)oo. We have successfully tested our equation against literature pressurevolume-temperature (P-V-T) data for two materials which exhibit quite different isochore behavior: NaC1 and S iO2 (o• quartz). For NaC1 our equation predicts isochores which are very nearly straight and parallel, reflecting the fact that the product ctpK T is approximately constant for this substance. For SiO2 our equation reproduces the strong negative curvature [(•2T/•PZ)v << 0] of the experimentally determinedisochores. These results suggest that our five-parameter equation can be used to accurately predict the P-V-T behavior of a wide variety of solids, including those for which isochore curvature is pronounced.

Thermoelastic stability of multiple growth twins in quartz and general geobarothermometric implications

“…Nothing analogous to the work done in [54]- [56] for V(p, 0), could be found in the literature about the ratios a and • + p of interest to us. Here, we follow the lead of Fernandez Guillermet and Gustafson [55] and modify the Thurston equations by considering the temperature dependence of the parameters A~, A3, Bin, B3, Bo, B~ appearing in (6.13-14).…”

“…Attempts to fully describe the function V = V(p, O) for solids are made in very recent papers by Hosieni et al [54], Fernandez Guillermet and Gustafson [55] and Plymate and Stout [56]. By a careful analysis of the available experimental data, the authors give in [54] the coefficients of a 35-term polynomial expansion of V(p, O) for SiO2 in its various phases, whereas in [55] a non-polynomial expression of V(p, O) is given for Iron.…”

“…According to the authors, the equation obtained in this way accounts satisfactorily for the properties of the various phases of condensed iron, although the lack of experimental data was in some cases considerable, and forced the use of systematic linear approximation to most of the functions involved. For a discussion of the results in [55], the reader is referred to [56], in which another temperature-correction of the isothermal Murnaghan equation is presented.…”

Pressure-volume-temperature behavior of fayalite based on static compression measurements at 400� C

“…at room temperature and room pressure. This equation is derived by integrating the identity dV/V= c~ e d T-dP/K r after assuming that e and K each vary linearly with both Tand P. Details of the derivation of (2) are discussed by Plymate and Stout (1989); applications of the equation to the P-V-Tbehavior of the polymorphs of metallic tin are discussed by Cavaleri et al (1988) and Plymate et al (1988).…”

Pressure-volume-temperature behavior of ?-Fe2SiO4 (spinel) based on static compression measurements at 400� C

“…(3) implicitly incorporates the assumption that ap is a linear function of T. This assumption is adequate for modeling the Vpo(T ) behavior of many crystalline solids of geological interest (Plymate 1986;Plymate and Stout 1989). However, as the room-P expansivity curve of Suzuki et al (1979) indicates, this assumption does not become appropriate for y-FeaSiO4 until temperature exceeds approximately 400 ~ C. Therefore, to model the V(P, T) behavior of ~-Fe2SiO 4 we used Eq.…”