Michel Jacobs

A new equation of state based on Grover, Getting and Kennedy's empirical relation between volume and bulk modulus. The high-pressure thermodynamics of MgO

The empirical linear relation between volume and logarithm of bulk modulus, discovered by Grover, Getting and Kennedy, is taken as the basis for a new pressure–volume equation of state. This linear relation and the equation of state have the same two substance-dependent parameters, the values of which can be derived from low-pressure data. For MgO, in the temperature range 100–3100 K and the pressure range 0–225 GPa, it is shown that the new methodology allows the careful calculation of high-pressure thermodynamic properties: all available experimental data are reproduced with great precision.

The vapour pressure and enthalpy of sublimation of ferrocene

The vapour pressure of ferrocene was measured in the temperature range 277 to 360 K. A static method (diaphragm manometer) and dynamic methods (torsion and mass-loss effusion) were used. The results are represented by the equation: {R/(·K−1·mol−1}1n(p/p°) =-(4817±26)(K/θ)+(74.29±0.14)x103(K/θ-K/T)-(71±){(θ/T)-1+1n(T/θ)} , where R is the gas constant, po is a standard pressure of 1 Pa, and θ = 317.20 K (mean experimental temperature). The numerical values with their root-mean-square-error ranges represent the thermodynamic function changes on sublimation: ΔsgGmo, ΔsgHmo, and ΔsgCp, mo respectively at 317.20 K.

A critical thermodynamic evaluation of the system MG-NI

Abstract Within the framework of COST Action 507 a critical thermodynamic analysis has been carried out of the system Mg-Ni. All thermodynamic data obtained in this action and existing data reported in the literature are described by the thermodynamic analysis. This thermodynamic evaluation is valid between 300 K and 1728 K (the melting temperature of Ni) and for the complete composition range. The purpose of the evaluation is to establish a firm basis for the thermodynamic description of the ternary system Cu-Mg-Ni.

Vapour-pressure measurements on trans-diphenylethene and naphthalene using a spinning-rotor friction gauge

Abstract Vapour pressures of trans-diphenylethene and naphthalene were measured in the temperature ranges 297.5 to 316.5 K and 244 to 256 K respectively with a spinning-rotor friction gauge. Together with results obtained with a diaphragm manometer (and for trans-diphenylethene, also torsion mass-loss effusion results) these results were fitted to a vapour-pressure equation derived by Clarke and Glew. For the mean temperatures and reference pressure of 1 Pa the following thermodynamic function changes were evaluated: for trans-diphenylethene: ΔsgGmo(331.64 K) = (2065.1 ± 1.2) J · mol−1; ΔsgHmo(331.64 K) = (100.17 ± 0.11) kJ · mol−1; ΔsgCp,mo(331.64 K) = −(63 ± 13) J · K−1 · mol−1, and for naphthalene: ΔsgGmo(306.74 K) = −(8243.1 ± 3.8) J · mol−1; ΔsgHmo(306.74 K) = (72.146 ± 0.049) kJ · mol−1; ΔsgCp,mo(306.74 K) = −(57.3 ± 2.1) J · K−1 · mol−1; ( ∂Δ s g C p, m o ∂T ) p (306.74 K ) = −(1.17 ± 0.15) J · K −2 · mol −1 . From an intercomparison of the results obtained by the different techniques we conclude that the coefficient of tangential momentum exchange is unity within experimental error.

A realistic equation of state for solids. the high pressure and high temperature thermodynamic properties of MGO

As has been found for pure metals, there exists a linear relationship between molar volume and the logarithm of bulk modulus. This relation is also valid for oxide and silicate substances. From the relationship, an equation of state has been developed and applied to the substance MgO. With this equation of state and by using experimental thermodynamic data at 1 bar pressure only, it is possible to make accurate predictions of thermodynamic properties at very high pressures and temperatures. Thermodynamic anomalies encountered in using e.g. a Birch-Murnaghan equation of state do not occur and the number of adjustable parameters is reduced.

The Gibbs energy formulation of α, γ, and liquid Fe2SiO4 using Grover, Getting, and Kennedy’s empirical relation between volume and bulk modulus

Abstract The empirical linear relation between the volume and logarithm of bulk modulus of metals, discovered by Grover, Getting, and Kennedy is taken as the basis for our equation of state. Recently, we have shown that we can use this equation of state to make accurate predictions of thermochemical and thermophysical properties at high pressure and high temperatures for MgO and the polymorphs of Mg 2 SiO 4 . Using the available experimental information, the equation of state is applied to the two polymorphs and the liquid form of Fe 2 SiO 4 to develop a consistent dataset of their thermodynamic properties in the temperature range between 150 and 2500 K and pressure range between 1 bar 13 GPa. Using thermodynamic methods we are able to discriminate experimental data from different sources. The results presented here are compared with results obtained with modern databases. For (Mg 1 − x ,Fe x ) 2 SiO 4 solid solutions around a pyrolitic composition, we conclude that bulk sound velocity is not a strong discriminator in selecting Gibbs energy formulations for Fe 2 SiO 4 using one database versus another. This is in contrast to what we found for Mg 2 SiO 4 .

The RI-liquid equilibrium in the ternary system n-pentadecane + n-hexadecane + n-heptadecane. Calculation of liquidus surface and thermal windows comparison with experimental data

Abstract The liquidus surface and thermal windows of the ternary system n-pentadecane + n-hexadecane + n-heptadecane were calculated from pure component data and excess Gibbs energies of binary subsystems. Calculations were made with temperature independent as well as temperature dependent excess Gibbs energies; the results were about the same. Comparison of calculated melting points of some ternary compositions with experimental values showed that the average temperature difference was within the uncertainty of the latter.

The high-temperature and high-pressure behavior of MgO derived from lattice vibration calculations. Kieffer's model revisited

The model of Kieffer has been extended and applied to derive thermodynamic properties from the lattice vibrational behavior of pure substances. The model for MgO has been validated in the pressure range between 0 and 300 GPa and temperature range between 100 and 4000 K. The model is constrained by thermodynamic data, lattice vibrational frequencies and data on transverse and longitudinal sound velocities. It is shown that intrinsic anharmonicity is present in the different modes of vibration. It is concluded that the accuracy of the results is not significantly affected by using different equations of state for the principal isotherm. It is shown that all thermodynamic data and sound wave velocity data are accurately described except for shock-wave data. The model of Kieffer is contrasted with the Mie–Gruneisen–Debye model and it is shown that the former represents more accurately experimental thermodynamic and longitudinal and transverse sound wave velocity data.

Measurement of the evaporation coefficient and saturated vapour pressure of trans-diphenylethene using a temperature-controlled vacuum quartz-crystal microbalance

Abstract At a temperature of 307.80 K the net evaporation coefficient αψ of trans -diphenylethene is measured in vacuum and at 0 to 4 per cent relative undersaturation using a temperature-controlled vacuum quartz-crystal microbalance. The net evaporation coefficient appears to be pressure independent and is found to be (0.99 ± 0.07). The saturated vapour pressure is p sat = (0.0274 ± 0.0012) Pa.

Equilibrium Between Phases of Matter: Supplemental Text for Materials Science and High-Pressure Geophysics

The Second Volume of Equilibrium between Phases of Matter, when compared with the First Volume, by H.A.J. Oonk and M.T. Calvet, published in 2008, amounts to an extension of subjects, and a deepening of understanding. In the first three sections of the text an extension is given of the theory on isobaric binary systems. The fourth section gives an account of the thermodynamic analyses of four isobaric binary key systems, highlighting the power of empirical, (exo)thermodynamic correlations. The fifth section is devoted to the thermodynamic description of ternary systems. The last three sections concentrate on the properties of materials, and the phase behaviour of systems under the conditions of high temperature and high pressure – conditions that prevail in the interior of the Earth. A new equation of state is the subject of the sixth section. In the seventh section a move is made to statistical thermodynamics and vibrational models; the description of the systems has changed from mathematical to physical. The last section is on the system MgO – SiO2, looked upon from a geophysical point of view.Throughout the work high priority is given to the thermodynamic assessment of experimental data; numerous end-of-section exercises and their solutions are included. Along with the First Volume, the work is useful for materials scientists and geophysicists as a reference text.AudienceVolume II is a lecture book for postgraduate students in chemistry, chemical engineering, geology and metallurgy. It is highly useful as a recommended text for teachers and researchers in all fields of materials science.