Thermodynamic Procedures for Treating the Monoclinic/Triclinic Inversion as a High-Order Phase Transition in Equations of State for Binary Analbite-Sanidine Feldspars

Abstract

Many solid-state phase transitions (transformations) can be classified thermo-dynamically according to their order (Ehrenfest, 1933): an wth-order phase transition is characterized by discontinuities in the nth and all higher-order derivatives of G with respect to an intensive variable—e.g., pressure, temperature, or composition—while lower-order derivatives are continuous.¹ Therefore, a first-order phase transition produces discontinuities in V, H, and μ _i , because these properties are related to the first derivatives ∂G/∂P, ∂G/∂T, and ∂G/∂X _i , respectively, and properties related to higher-order derivatives of G—e.g., C _p=-T(∂² G/∂T ²), α= (1/V)(∂² G/∂P ∂T), and β=-(1/V) (∂² G/∂P ²)—also exhibit discontinuities. On the other hand, for a second-order phase transition, V, H, and μ _i , are all continuous at the point of phase change, so Δ V and ΔH of transition are zero, but, C _p α, and β are discontinuous. Finally, at a third-order phase transition all properties related to the first and second derivatives of G are continuous, and only third- and higher-order derivatives of G are discontinuous. In this chapter, transitions that fit into this classification scheme and whose order is greater than one will be referred to as high-order transitions.