A physically consistent method to implement volume properties in Calphad-type thermodynamic descriptions of alloys
Final Report Abstract
Knowledge of volume changes in alloys is indispensable in optimizing performance and density of materials, the development of joints and in the study of materials behavior during processing when phase transformations occur, such as casting and heat treatment. Knowledge of volume properties is also a mandatory requirement in other scientific fields, such as geophysics, mineral physics, and astrophysics. It is therefore not surprising that development of thermodynamic databases, enabling the computation of properties related to volume is an asset for scientists in multidisciplinary fields. Thermodynamic databases rely on formalisms or models to characterize the thermophysical behavior of materials. A mandatory requirement of these formalisms is that they are computationally efficient to derive thermophysical properties for phase assemblages in multicomponent systems. The development of thermodynamic databases in which volume properties are incorporated is hampered by the problem that formalisms commonly used in Calphad methodology are cumbersome to apply in the calculation of thermodynamic properties at pressure, and that the Mie-Grüneisen-Debye method increasingly popular in geophysics and mineral physics is cumbersome to use for substances such as silicates and oxides. To address this problem a general method was developed for solid materials that enables the use of microscopic properties predicted by ab initio methods, such as the phonon density of states and Grüneisen parameters of vibrational modes. Model parameters can, in principle, be measured via Raman and infrared spectroscopy, or predicted via ab initio techniques. This feature enables to arrive at more accurate results than the Mie-Grüneisen-Debye method. Additionally spurious results obtained with parameterizations commonly used in Calphad methodology, at pressures addressed to in mineral physics, are eliminated. To make the method generally effective, it allows description of intrinsic anharmonic effects, crystal field electronic and magnetic effects and electron-phonon coupling. Because of computational efficiency, the developed method is necessarily semi-empirical in nature and requires experimental data to constrain the model parameters. The method is similar in complexity and computational efficiency as the Mie-Grüneisen-Debye method and is therefore suitable as an extension of Calphad methodology. The method has been validated by testing it on materials for which sufficient experimental data are available, such as metallic elements, silicates and oxides. The method allows discrimination between the correctness of different experimental data sets, such as for heat capacity of the polymorphs of Mg2SiO4 and MgSiO3. Additionally it allows the calculation of thermodynamic properties at temperatures below room-temperature down to zero Kelvin in an accurate manner. The method has been tested to (1) develop pressure scales; (2) incorporate nontrivial effects such as spin transitions; (3) calculate phase diagrams in pressure-temperaturecomposition space. It has been shown in this project that phonon density of states and Grüneisen parameters resulting from present-day ab initio methods, for elements and magnesium silicates, are sufficiently accurate to serve as constraints in a thermodynamic analysis of experimental data using the developed method. Although not anticipated at the beginning of the project it appeared possible to incorporate mechanical properties in a physically consistent manner via finite strain theory. For the system MgO-SiO2-FeO and for elements Ag, Al, Au, Cu, Fe, Ni, Pt databases have been developed from which thermophysical and mechanical properties are derived superior to previous databases. Thermophysical and mechanical properties derived from the oxide database are reliable from zero Kelvin, zero pressure to conditions prevailing in planetary interiors. It has been demonstrated that the method can be applied successfully in multi-disciplinary fields of science, such as metallurgy, mineral physics, and high-pressure sciences. Open software code has been developed to facilitate implementation of the method in standard thermodynamic software nowadays applied in industrial applications, such as ThermoCalc, FactSage and Pandat. This enhances development of thermo-mechanical databases applicable in wide ranges of pressure and temperature. Presently, the developed database is applied in determining heterogeneity in Earth by coupling it to seismic experiments and determining geodynamic processes such as thermal evolution and slab movement behavior in terrestrial planets via mantle convection simulations.
Publications
- Geodynamic modelling and multi-scale seismic expression of thermo-chemical heterogeneity and phase transitions in the lowermost mantle, Phys. Earth and Planet. Inter, 180 (2010) 244-257
A.P. van den Berg, M.V. de Hoop, D.A. Yuen, A.D. Duchanov, R.D. van der Hilst, M.H.G. Jacobs
- Complex phase distribution and seismic velocity structure of the transition zone: Convection model predictions for a magnesium-endmember olivine-pyroxene mantle. Phys Earth Planet Inter, 186 (2011) 36-48
M.H.G. Jacobs and A.P. van den Berg
- Small-scale mineralogical heterogeneity from variations in phase assemblages in the transition zone and D’’ layer predicted by convection modelling, J. Earth Science (2011) 22 160-168
A.P. van den Berg, D.A. Yuen, M.H.G. Jacobs, M.V. de Hoop
- Equilibrium between Phases of Matter. Supplemental text for material science and high-pressure geophysics, Springer, Dordrecht Heidelberg London New York, ISBN 987-94-007-1947-7 (2012)
M.H.G. Jacobs and H.A.J. Oonk
- An alternative use of Kieffer’s lattice dynamics model using vibrational density of states for constructing thermodynamic databases, Phys Chem Minerals, 40 (2013) 207-27
M.H.G. Jacobs, R. Schmid-Fetzer, A.P. van den Berg
(See online at https://doi.org/10.1007/s00269-012-0562-4) - Models based on lattice vibrations, Geomaterials Genome Project, Miami, Florida, USA, March 19th-23rd, 2013
M.H.G. Jacobs
- Thermal equation of state of synthetic orthoferrosilite at lunar pressures and temperatures. Phys. Chem. Minerals, 40 (2013) 691-703
J. de Vries, M.H.G. Jacobs, A.P. van den Berg, M. Wehber, C. Lathe, C.A. McCammon, W. Van Westrenen
(See online at https://doi.org/10.1007/s00269-013-0605-5) - Including the effects of pressure and stress in thermodynamic functions, Physica Status Solidi B, 251 (2014) 81-96
T. Hammerschmidt, I.A. Abrikosov, D. Alfè D, S.G. Fries, L. Hoglund, M.H.G. Jacobs, J. Koßmann, X.-G. Lu, G. Paul
(See online at https://doi.org/10.1002/pssb.201350156) - Impact of compressibility on heat transport characteristics of large terrestrial planets. Phys Earth Planet Inter 268 (2017), 65-77
H. Čížkovă, A.P. van den Berg, M.H.G. Jacobs
(See online at https://doi.org/10.1016/j.pepi.2017.04.007) - Phase diagrams, thermodynamic properties and sound velocities derived from a multiple Einstein method using vibrational densities of states: an application to MgO-SiO2, Phys. Chem. Minerals, 44 (2017) 43-62
M.H.G. Jacobs, R. Schmid-Fetzer, A.P. van den Berg
(See online at https://doi.org/10.1007/s00269-016-0835-4)
