A Thermodynamical Model for Analysis of Isothermal Phase Transformations under High Pressure
In the present study we elaborated a thermodynamical model for analysis of isothermal phase transformations under high pressure. Our study was provoked by the necessity to characterise the behaviour of MTe2 chemical compounds (M = Pd, Pt) while subjected isothermally to high pressure. As known  MTe2 powders are representatives of the CdI2 structure type. This structure type is a bi-dimensional one and as such is atypical for the big family of lamellar MQ2-type dichalcogenides (M = Pd, Pt; Q = S, Se, Te). Specific of lamellar structure is the strong ionicity of the bonds. One of the most interesting points stands on the possibility for realising interactions between the layers of different types of ions. That could be done under high pressure by any of the following transformation processes: (i) phase transition to the typical pyrite structure; (ii) phase rearrangement changing the parameters of the crystal cell but keeping the 2D-type structure. In this framework our aim was to elaborate a thermodynamical model for analysis of such isothermal phase transformations under high pressure. Our analysis model is designed to answer the following questions: (i) if the treated compound undergoes a classical phase transition or a phase rearrangement; (ii) which is the order of the phase transition or the phase rearrangement, respectively; and (iii) what is the degree-of-stability of the treated compound under high pressure. To detect if the transformation process is a phase transition or a rearrangement, we compute both volumetric and longitudinal Gibbs free energies and their partial derivatives. We recognise the transformation to be: (i) a phase transition when it affects the volumetric Gibbs free energy and its partial derivatives; (ii) a phase rearrangement if it affects the longitudinal Gibbs free energy and its partial derivatives. The order of the transformation process (phase transition or rearrangement, respectively) is determined by the order of the partial derivative of the Gibbs free energy (volumetric or longitudinal, respectively), which is discontinuous in the transformation point. Hence, we compute the two first partial derivatives (i.e., the first one and the second one) of the Gibbs free energy (both volumetric and longitudinal). For characterising the degree of stability of the treated compound under high pressure we calculate its entropy generation (volumetric and longitudinal, respectively) during the treatment process. The established model was further applied to PdTe2 and to PtTe2 while subjected isothermally to high pressure.
Prof. Andreas Öchsner and José Grácio
V. Grigorova and D. Roussev, "A Thermodynamical Model for Analysis of Isothermal Phase Transformations under High Pressure", Materials Science Forum, Vol. 553, pp. 57-62, 2007