Catastrophe theory and thermodynamic instability to predict congruent melting temperature of crystals

Abstract

Melting temperature (T_m) is a crucial physical property of solids and plays an important role in the characterization of materials. Therefore, the capacity to predict T_m is a relevant issue for solid state sciences. This investigation aims i) to provide a theoretical basis for the link between catastrophe theory and thermodynamic instability; ii) to estimate T_m through the notion of “degenerate critical temperature” (T_d), related to (P_d,V_d,T_d), where K_T → 0 and the Gibbs function shows a non-Morse behaviour; iii) to compare predictions of (P_m,T_m) with observations for three crystalline pure substances that undergo congruent melting and exhibit different bonding and stability ranges: NaCl (halite), SiO_2,st (stishovite), and MgSiO₃ (perovskite). The P-T locus of K_T = 0 associated with melting is identified using the maximum values of T_d and ΔH/ΔV at a given pressure. We observed an average absolute discrepancy ranging between 0.2 % (halite) and 5.8 % (stishovite), and an agreement between theoretical and experimental T(P)_melting-points from better than 1 to approximately 14 %.