A relationship to estimate the excess entropy of mixing: Application in silicate solid solutions and binary alloys

AbstractThe paper presents new calorimetric data on the excess heat capacity and vibrational entropy of mixing of Pt–Rh and Ag–Pd alloys. The results of the latter alloy are compared to those obtained by calculations using the density functional theory. The extent of the excess vibrational entropy of mixing of these binaries and of some already investigated binary mixtures is related to the differences of the end-member volumes and the end-member bulk moduli. These quantities are used to roughly represent the changes of the bond length and stiffness in the substituted and substituent polyhedra due to compositional changes, which are assumed to be the important factors for the non-ideal vibrational behaviour in solid solutions

The Specific Heat of Astro-materials: Review of Theoretical Concepts, Materials, and Techniques

We provide detailed background, theoretical and practical, on the specific heat of minerals and mixtures thereof, ‘astro-materials,’ as well as background information on common minerals and other relevant solid substances found on the surfaces of solar system bodies. Furthermore, we demonstrate how to use specific heat and composition data for lunar samples and meteorites as well as a new database of endmember mineral heat capacities (the result of an extensive literature review) to construct reference models for the isobaric specific heat cP as a function of temperature for common solar system materials. Using a (generally linear) mixing model for the specific heat of minerals allows extrapolation of the available data to very low and very high temperatures, such that models cover the temperature range between 10 K and 1000 K at least (and pressures from zero up to several kbars). We describe a procedure to estimate cP(T) for virtually any solid solar system material with a known mineral composition, e.g., model specific heat as a function of temperature for a number of typical meteorite classes with known mineralogical compositions. We present, as examples, the cP(T) curves of a number of well-described laboratory regolith analogs, as well as for planetary ices and ‘tholins’ in the outer solar system. Part II will review and present the heat capacity database for minerals and compounds and part III is going to cover applications, standard reference compositions, cP(T) curves, and a comparison with new and literature experimental dat

A new activity model for Mg-Al biotites determined through an integrated approach

A new activity model for MgAl biotites was formulated through an integrated approach combining various experimental results (calorimetry, line-broadening in infrared (IR) spectra, analysis of existing phase-equilibrium data) with density functional theory (DFT) calculations. The resulting model has a sound physical-experimental basis. It considers the three end-members phlogopite (Phl, KMg3[(OH)2AlSi3O10]), ordered eastonite (Eas, KMg2Al[(OH)2Al2Si2O10]), and disordered eastonite (dEas) and, thus, includes MgAl orderdisorder. The DFT-derived disordering enthalpy, Hdis, associated with the disordering of Mg and Al on the M sites of Eas amounts to 34.5 3 kJ/mol. Various biotite compositions along the PhlEas join were synthesised hydrothermally at 700 C and 4 kbar. The most Al-rich biotite synthesized had the composition XEas = 0.77. The samples were characterised by X-ray diffraction (XRD), microprobe analysis and IR spectroscopy. The samples were studied further using relaxation calorimetry to measure their heat capacities (Cp) at temperatures from 2 to 300 K and by differential scanning calorimetry between 282 and 760 K. The calorimetric (vibrational) entropy of Phl at 298.15 K, determined from the low-T Cp measurements on a pure synthetic sample, is Scal = 319.4 2.2 J/(mol K). The standard entropy, So, for Phl is 330.9 2.2 J/(mol K), which is obtained by adding a configurational entropy term, Scfg, of 11.53 J/(mol K) due to tetrahedral Al-Si disorder. This value is 1% larger than those in different data bases, which rely on older calorimetrical data measured on a natural near-Phl mica. Re-analysing phase-equilibrium data on Phl + quartz (Qz) stability with this new So, gives a standard enthalpy of formation of Phl, Hof,Phl = 6209.83 1.10 kJ/mol, which is 78 kJ/mol less negative than published values. The superambient Cp of Phl is given by the polynomial [J/(mol K)] as follows: Cp=667.37(7)3914.50(258)T0.51.52396(0.15)107T2+2.17269(0.25)109T3. Calorimetric entropies at 298.15 K vary linearly with composition along the PhlEas join, indicating ideal vibrational entropies of mixing in this binary. The linear extrapolation of these results to Eas composition gives So = 294.5 3.0 J/(mol K) for this end-member. This value is in excellent agreement with its DFT-derived So, but 8% smaller than values as appearing in thermodynamic data bases. The DFT-computed superambient Cp of Eas is given by the polynomial [in J/(mol K)] as follows: Cp=656.91(14)3622.01(503)T0.51.70983(0.33)107T2+2.31802(0.59)109T3. A maximum excess enthalpy of mixing, Hex, of 6 kJ/mol was derived for the PhlEas binary using line-broadening from IR spectra (wavenumber region 400600 cm1), which is in accordance with Hex determined from published solution-calorimetry data. The mixing behaviour can be described by a symmetric interaction parameter WHPhl,Eas = 25.4 kJ/mol. Applying this value to published phase-equilibrium data that were undertaken to experimentally determine the Al-saturation level of biotite in the assemblage (MgAl)-biotite-sillimanite-sanidine-Qz, gives a Hof,Eas = 6358.5 1.4 kJ/mol in good agreement with the independently DFT-derived value of Hof,EasDFT = 6360.5 kJ/mol. Application examples demonstrate the effect of the new activity model and thermodynamic standard state data, among others, on the stability of MgAl biotite + Qz.(VLID)439383

Contributions to Mineralogy and Petrology / The accuracy of standard enthalpies and entropies for phases of petrological interest derived from density-functional calculations

The internal energies and entropies of 21 well-known minerals were calculated using the density functional theory (DFT), viz. kyanite, sillimanite, andalusite, albite, microcline, forsterite, fayalite, diopside, jadeite, hedenbergite, pyrope, grossular, talc, pyrophyllite, phlogopite, annite, muscovite, brucite, portlandite, tremolite, and CaTiO3perovskite. These thermodynamic quantities were then transformed into standard enthalpies of formation from the elements and standard entropies enabling a direct comparison with tabulated values. The deviations from reference enthalpy and entropy values are in the order of several kJ/mol and several J/mol/K, respectively, from which the former is more relevant. In the case of phase transitions, the DFT-computed thermodynamic data of involved phases turned out to be accurate and using them in phase diagram calculations yields reasonable results. This is shown for the Al2SiO5 polymorphs. The DFT-based phase boundaries are comparable to those derived from internally consistent thermodynamic data sets. They even suggest an improvement, because they agree with petrological observations concerning the coexistence of kyanite+quartz+corundum in high-grade metamorphic rocks, which are not reproduced correctly using internally consistent data sets. The DFT-derived thermodynamic data are also accurate enough for computing the PT positions of reactions that are characterized by relatively large reaction enthalpies (>100 kJ/mol), i.e., dehydration reactions. For reactions with small reaction enthalpies (a few kJ/mol), the DFT errors are too large. They, however, are still far better than enthalpy and entropy values obtained from estimation methods.(VLID)310451

Physics and Chemistry of Minerals / Excess enthalpy of mixing of mineral solid solutions derived from density-functional calculations

Calculations using the density-functional theory (DFT) in combination with the single defect method were carried out to determine the heat of mixing behaviour of mineral solid solution phases. The accuracy of this method was tested on the halitesylvite (NaClKCl) binary, pyropegrossular garnets (Mg3Al2Si3O12Ca3Al2Si3O12), MgOCaO (halite structure) binary, and on Al/Si ordered alkali feldspars (NaAlSi3O8KAlSi3O8); as members for coupled substitutions, the diopsidejadeite pyroxenes (CaMgSi2O6NaAlSi2O6) and diopsideCaTs pyroxenes (CaMgSi2O6CaAlAlSiO6) were chosen for testing and, as an application, the heat of mixing of the tremoliteglaucophane amphiboles (Ca2Mg5Si8O22(OH)2Na2Mg3Al2Si8O22(OH)2) was computed. Six of these binaries were selected because of their experimentally well-known thermodynamic mixing behaviours. The comparison of the calculated heat of mixing data with calorimetric data showed good agreement for halitesylvite, pyropegrossular, and diopsidejadeite binaries and small differences for the Al/Si ordered alkali feldspar solid solution. In the case of the diopsideCaTs binary, the situation is more complex because CaTs is an endmember with disordered cation distributions. Good agreement with the experimental data could be, however, achieved assuming a reasonable disordered state. The calculated data for the Al/Si ordered alkali feldspars were applied to phase equilibrium calculations, i.e. calculating the Al/Si ordered alkali feldspar solvus. This solvus was then compared to the experimentally determined solvus finding good agreement. The solvus of the MgOCaO binary was also constructed from DFT-based data and compared to the experimentally determined solvus, and the two were also in good agreement. Another application was the determination of the solvus in tremoliteglaucophane amphiboles (Ca2Mg5Si8O22(OH)2Na2Mg3Al2Si8O22(OH)2). It was compared to solvi based on coexisting amphiboles found in eclogites and phase equilibrium experiments.(VLID)480004

Heat capacity measurements of CaAlSiO4F from 5 to 850 K and its standard entropy

Heat capacity (CP) data of Al-F-bearing titanite are presented that yield the standard entropy S°298.15 of F-Al-titanite CaAlFSiO4 (FAT). CP of synthetic FAT was measured with relaxation calorimetry and differential scanning calorimetry between 5 and 764 K. The results constrain S°298.15 to be 115.4 ± 2.0 J/(mol.K) and subsequently the standard Gibbs free energy of formation from the elements, ΔfG°, of CaAlSiO4F to be between –2583 ± 3.0 and –2588 ± 3.0 kJ/mol, and the standard enthalpy of formation from the elements, ΔfH°, to lie between –2728 ± 3.0 and –2733 ± 3.0 kJ/mol depending on the thermodynamic data retrieval approach. These data, in turn, can be used to quantitatively model high-grade and UHP fluid-rock interaction. The calculation of future petrogenetic grids involving F-bearing minerals and titanite solid solutions in the system CaTiSiO4O–CaAlSiO4F will only be possible by expanding existing internally consistent thermodynamic databases to the F-system.This work was financed by the Austrian Science Fund (FWF) project P28724 (E.D.), which is gratefully acknowledge

The specific heat of regolith material

Specific heat cP(T) is one of the pa- rameters which determine a surface’s temperature re- sponse to heating. Remote sensing in the mid-infrared is often used to estimate a parameter termed the ther- mal inertia of the surface material, which is defined as = k(T )cp (T ) , where T is absolute temperature in K, k is thermal conductivity in W m-1 K-1, ρ is bulk density in kg m-3, and cP is specific heat at constant pressure in units of J kg-1 K-1. Knowledge or an esti- mate of cP(T) is required to extract information on, e.g. thermal conductivity k from the data, which in turn allows for an estimation of important surface properties like grain size [1-4] and porosity [5] . Furthermore knowledge of thermophysical surface properties is es- sential to model the Yarkovsky [6-8] and YORP [8, 9] effects as well as the response of planetary surfaces to impact cratering. Only a handful of meteorite heat capacities have been published, virtually all of them measured at tem- peratures at or above 300 K or at a ~175 K (Consol- magno et al., 2013). The only other extraterrestrial material with known cP over a limited temperature range is lunar samples from the Apollo missions, and many studies have used these values as a “standard” cP(T) curve. Heat capacity, however, strongly depends not only on temperature but also on composition, thus the use of lunar data for, e.g., C- or M-class asteroids or objects containing frozen volatiles may give rise to large systematic errors. Missing cP(T) data for rocks (in general, “regolith material”, any solid material found on the surface of solar system bodies) can be calculat- ed from the contributions of the constituent minerals (and mineraloids, i.e. amorphous substances): linear mixing model, neglecting (except for olivine Fo-Fa) the non-ideal “excess heat capacity”. Except at very low temperatures, the model specific heat is accurate to ~1% in general