Abstract
AbstractMost applications of thermodynamic databases to materials design are limited to ambient pressure. The consideration of elastic contributions to thermodynamic stability is highly desirable but not straight‐forward to realise. We present examples of existing physical models for pressure‐dependent thermodynamic functions and discuss the requirements for future implementations given the existing results of experiments and first‐principles calculations. We briefly summarize the calculation of elastic constants and point out examples of nonlinear variation with pressure, temperature and chemical composition that would need to be accounted for in thermodynamic databases. This is particularly the case if a system melts from different phases at different pressures. Similar relations exist between pressure and magnetism and hence set the need to also include magnetic effects in thermodynamic databases for finite pressure. We present examples to illustrate that the effect of magnetism on stability is strongly coupled to pressure, temperature, and external fields. As a further complication we discuss dynamical instabilities that may appear at finite pressure. While imaginary phonon frequencies may render a structure unstable and destroy a crystal lattice, the anharmonic effects may stabilize it again at finite temperature. Finally, we also outline a possible implementation scheme for strain effects in thermodynamic databases.
Highlights
1.1 Motivation The CALPHAD method [1] is an established technique in alloy design
Reaching out for the simulation of pressure-driven effects in technical applications calls for an incorporation of strain effects in thermodynamic databases
Even in the low-pressure elastic regime, the often non-linear variation of elastic constants with pressure, temperature, and chemical compositions requires a sophisticated treatment of stress contributions to the free energy
Summary
1.1 Motivation The CALPHAD method [1] is an established technique in alloy design. Commercial software packages like Thermo-Calc [2] and FactSage [3] are applied to calculate phase diagrams and to determine precipitation and dissolution temperatures [4,5]. Databases of mineral systems developed by, e.g., Fei et al [6], Saxena [7], Holland and Powell [8] and Fabrichnaya [9] are based on the classical CALPHAD approach extended such that the pressure variable is included in the expression for the Gibbs energy It has been demonstrated in the literature that thermodynamic properties calculated with this approach often show physically unrealistic behaviour in specific regions of the pressure-temperature space. Successful attempts have been made by Stixrude and Bertelloni [14], Piazonni et al [15] and Jacobs and de Jong [16,17] to develop thermodynamic databases for mineral systems based on lattice vibrational methods, meeting this requirement These methods allow the calculation of thermodynamic properties free from physically unrealistic behaviour and include the calculation of the shear modulus in a self-consistent way. Because experimental data at ambient pressure are represented with high precision it is anticipated that these methods are generally suitable to develop databases in materials sciences, for silicate and oxide materials, and for metallic substances
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