Thermodynamic Modeling of Solid Phases

By Michel Soustelle

This book offers advanced students, in 7 volumes, successively characterization tools phases, the study of all types of phase, liquid, gas and solid, pure or multi-component, process engineering, chemical and electrochemical equilibria, 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 is given to the rigor of mathematical developments.  This book focuses on solid phases.

• Language: English
• Publisher: Wiley
• Release date: Aug 26, 2015
• ISBN: 9781119178538

Book preview

1

Pure Crystalline Solids

Crystalline solids are characterized by the regular and periodic spatial arrangement of entities at the nodes of a lattice. The nature of the entities thus arranged defines the nature of the solid. There are four distinct classes:

– atomic solids, comprising a lattice of atoms, such as solid argon, for example;

– molecular solids, where the entities arranged at the nodes of the lattice are molecules, as is the case in solid benzene;

– ionic crystals. In this case, the entities are ions, and they are arranged into two sublattices: one of cations and the other of anions. The proportions of sites occupied by these two sublattices are obviously such that the whole solid is electrically neutral, overall. The ions thus arranged could either be simple ions, as is the case with sodium chloride, or complex ions such as in ammonium carbonate;

– metals, in which ions are arranged at the nodes of the lattice. To ensure electrical neutrality, more-or-less mobile electrons are distributed around these ions.

1.1. Characteristic values of a solid

Solids are incompressible, which means that their derivative (∂V/∂P)T is practically zero, so they do not have an equation of state such as F(P,V,T) = 0.

However, solids do experience changes in volume, under the influence of temperature, which is characterized by its cubic expansion coefficient or its linear expansion coefficient.

Similarly, when heat is applied to it, solids heat up. The extent of that rise in temperature is characterized by the solid’s specific heat capacity.

When a solid is subjected to a stress (or load) – i.e. a certain amount of force per unit surface area or a moment per unit length, such as axial traction (Figure 1.1(a)) or axial compression (Figure 1.1(b)), for example – it normally deforms. This deformation is also known as strain.

Other values pertaining to the dielectric and magnetic properties are also available.

In the next section, we will examine the first three effects, starting with the effect of a stress. Then we will develop models of solids which we can go on to use in dealing with the questions of specific heat capacities and thermal expansion.

1.2. Effect of stress and Young’s modulus

When a solid is subjected to a stress, it generally experiences a strain which, if pursued, could cause the material to fracture. The applied stress is measured in newtons per square meter.

Figure 1.1. Cylindrical test tube a) under traction; b) under compression

Take the example of traction applied to a cylinder whose initial length is l0 and cross-section area is s (Figure 1.1(a)). If we begin with zero stress, and very gradually increase the stress (i.e. the traction force) at a constant temperature, the relative strain Δl/l0 increases, obeying a law which is often identical to its tangent to the origin – that is, a practically linear law (the part OA of the curve shown in Figure 1.2) – which is known as Hooke’s law, and is written as follows for a given temperature:

[1.1]

Figure 1.2. Strain/stress curve under