Including the effects of pressure and stress in thermodynamic functions

Abstract

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.Most 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.

Theoretical description of pressure-induced phase transitions: a case study of Ti–V alloys

“…3. The left panel confirms that our calculations are in good agreement with earlier calculations [12]. BCC V is mechanically stable at ambient pressure, but it becomes unstable according to Eq.…”

“…(3) around 125 GPa in our calculations. The transition is well described in the literature [12]. Going beyond the known facts, we analyse it in more details.…”

“…In the right panel of Fig. 3 we show variation of the total energy E of bcc V as a function of square of distortion, δ 2 , used for calculations of the elastic moduli [12] (in case of C44 a monoclinic distortion is used). Usually, the dependence is linear for δ within the elastic limit.…”

The development of phase-based property data using the CALPHAD method and infrastructure needs

“…Vřešt'ál et al [24] developed an extension of the Dinsdale [4] Gibbs energy functions of the pure elements to 0 K employing an extended Einstein model. New model descriptions for the temperature and pressure dependence of the pure elements have been discussed at a recent workshop [25][26][27][28][29]. For solution phases with short-range and long-range ordering additional orderparameters are needed to fully define the state of the phase.…”

“…Brosh et al [91] proposed another EOS which attempts to address some of these capability issues; however, an EOS which satisfactorily accounts for the compatibility issues with CALPHAD has yet to be identified. Hammerschmidt et al [28] give a summary of the calculation of the elastic constants and point out that the magnetic properties of a phase also need to be taken into account for their treatment.…”