Second-order phase transitions of pure substances

Abstract

In this report we are dealing with the thermodynamic theory of second-order phase transitions or continuous transitions of unary systems. The first classification of these phase transitions is due to Ehrenfest (1933), based on chemical potentials. First-order transitions are changes in which the derivatives of the chemical potentials, with respect to temperature or pressure are discontinuous. Second-order phase transitions are continuous in the first derivatives of the chemical potentials, but exibits discontinuity for at least one second derivative. However, the modern classification is based on systems, with or without latent heat, during the transitions. Landau (1937) formulated the first theory, which is based on a power series of the Gibbs free energy, including a so-called scalar order parameter. It’s a simple and powerful theory, but fails for temperatures in the vicinity of the transition line. This is because there exists long-range fluctuations in the systems. The order parameter is zero for the high temperature, high symmetric, disordered phase, whereas it is non-zero for the low temperature, low symmetric, ordered phase. The classical Landau theory can be outlined with statistical thermodynamics and with symmetry considerations in crystals, which is in fact the group/representation theory. There are two Landau symmetry rules: the space group of the low symmetric phase should be a subgroup of the high symmetric phase. The second is that the continuous transitions leads to crystal changes which corresponds to a single irreducible representation of the initial space group. The last subject contains some remarks about the study of critical phenomena and exponents and the renormalization group theory (temperatures near the transition). However a thorough discussion of these subjects are beyond the scope of this report.