Phase Transformations

Michel Soustelle

• Publisher: Wiley-ISTE
• Year: 2016
• ISBN:
  9781119178590
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Thermodynamics

This book is part of a set of books which offers advanced students successive characterization tool phases, the study of all types of phase (liquid, gas and solid, pure or multi-component), process engineering, chemical and electrochemical equilibria, and the properties of surfaces and phases of small sizes. Macroscopic and microscopic models are in turn covered with a constant correlation between the two scales. Particular attention has been given to the rigor of mathematical developments.

This fifth volume is devoted to the study of transformations and equilibria between phases. First- and second-order pure phase transformations are presented in detail, just as with the macroscopic and microscopic approaches of phase equilibria.

In the presentation of binary systems, the thermodynamics of azeotropy and demixing are discussed in detail and applied to strictly-regular solutions. Eutectic and peritectic points are examined, as well as the reactions that go with them. The study of ternary systems then introduces the concepts of ternary azeotropes and eutectics. For each type of solid-liquid system, the interventions of definite compounds with or without congruent melting are taken into account. The particular properties of the different notable points of a diagram are also demonstrated.

1
Phase Transformations of Pure Substances

In this chapter we shall examine the transformations undergone by a definite pure compound, with no chemical alteration. These transformations belong to the category of phase transitions, or phase transformations. Hence, this chapter excludes the transformations of isomerization and decompositions which are accompanied by a chemical alteration – i.e. a modification of the molecule.

1.1. Standard state: standard conditions of a transformation

The “standard state” of a substance at temperature T is defined as the state of the pure substance at that temperature, at a pressure of 1 bar and as its stable state of aggregation in these conditions (solid, liquid or gas). If the substance is a gas, its behavior is perfect. If the pure substance is a crystalline solid, its stable state of aggregation determines the crystalline system. A transformation takes place in standard conditions if it occurs with the components in their standard state in the final state. This means that at the start of the reaction, the substance is in a non-standard state, which is unstable, and that it returns to its stable standard state at the end. Thus, only the state of aggregation may possibly have been modified by the transformation. This is indeed a phase transformation, in that the state of aggregation defines a phase.

1.2. Classification and general properties of phase transformations

Phase transitions are classified into different types. The advantage of classifying definite compound transformations depending on their order lies in the fact that a series of relations characterizes each order.

The first classification of these transitions is attributable to Ehrenfest, in which we say that a transformation is of order n when at least an n^th derivative of the characteristic function in relation to its canonical variables undergoes a discontinuity for certain values of those variables, when the derivatives of order less than n are continuous. The most important are the first- and second-order derivatives which, by their discontinuities, respectively give us the first- and second-order transformations.

This classification has been abandoned, because it does not allow for the possibility of divergences other than discontinuities of derivatives of the Gibbs energy. However, numerous models allow for such divergences within the thermodynamic limit – i.e. when the system’s dimensions increase indefinitely. For example, a derivative such as the specific heat capacity (second derivative of the Gibbs energy in relation to temperature) is thought to be divergent during the ferromagnetic transition.

The ...