[1] | Bychkov D. A., Koptev-Dvornikov E. V. A technique for calculating the enthalpy of silicate melt of any composition // Petrology. — 2019. — Vol. 27, no. 2. — P. 109–123. Reasonably accurate quantitative analysis of the evolution of magmatic systems in melting–crystallization processes requires estimates of the changes in the enthalpy of the heterogeneous (melt + crystals) systems with regard for the latent heat of fusion of minerals within broad composition and temperature ranges. Thermodynamic reference books and summaries provide extensive information on the properties of some mineral phases that are the end members of solid solutions (see, for example, Naumov et al., 1971; Robie and Hemingway, 1995), but there are still no published equation for the temperature and composition functions of the enthalpy of melt. Nowadays only two program packages, those of the MELTS family and COMAGMAT, that take into account the latent heat of fusion. Of these two, only MELTS yields the enthalpies of all the phases. A generalized equation for calculation the ΔG is presented in (Ghiorso and Sack, 1995), which describes the thermodynamic model assumed in MELTS. Regretfully, this paper does not report any explicit expression for calculating the enthalpy of melts. It follows from the context that the enthalpy of the liquid phase is calculated using data on the enthalpies of fusion of melt components, with regard for the mixing energy of the melt components. At the same time, the authors demonstrate that the lack of experimental data on the thermodynamic properties of geologically important materials leaves the only possibility of assuming certain values, which are nothing else than expert estimates and may led to uncertainties of about 20% of the utilized values. Although coefficients in the equations for the thermodynamic model of MELTS were several times recalibrated (Asimow and Ghiorso, 1998; Ghiorso et al., 2002; Ghiorso and Gualda, 2015; Gualda et al., 2012), the equations themselves have not been modified. The program packages of the COMAGMAT-3.n family (Frenkel et al., 1988; Frenkel, 1995; Ariskin and Barmina, 2000) are employed in calculating data on the enthalpy of fusion of minerals but not the enthalpy of melts. Herein we suggest a method for calculating the enthalpy of a system with implicit regard for the latent heat of fusion of the phases. This method is underlain by approximating measured enthalpy of heterogeneous system with the Kirchhoff equation. However, it is fairly difficult to experimentally determine the enthalpy of a system (Navrotsky et al., 1989), and nowadays such experimental data are available only for a limited composition ranges and narrow temperature intervals, at atmospheric pressure, and this makes it impossible to calculate the coefficients of the Kirchhoff equation in its expanded form (3) for the whole range of the compositions and temperatures of naturally occurring melts. At the same time, most of the coefficients of Eq. (3) coincide with the coefficients of Maier–Kelly equation (2) (Maier and Kelley, 1932; Haas and Fisher, 1976) for the heat capacity of the system. This allows one to determine the coefficients of the Kirchhoff equation based on extensive experimental data on the heat capacity of silicate melts, which cover the whole composition and temperature ranges of natural melts. [ DOI ] |