Thermodynamics of Phases having Constant Composition

This chapter illustrates thermodynamics of invariant composition phases, such as elements, molecules, line intermetallic compounds, monodisperse colloidal assemblies of hard spheres, and Langmuir monolayers. The chapter emphasizes on relative stability of allotropes and polymorphs of these materials. The set of constraints that apply to the Gibbs free energy and are applicable to most of the phenomena are also examined. Materials exist in either solid, liquid or vapor states. When in the vapor state, a monatomic gas consists of atoms that do not interact and that move freely throughout the container that defines the volume of the gas. Thus, in this state the gas has no potential energy. Its energy is in the form of kinetic energy of the atoms. The potential energy is the sum over the interaction energies between atoms or molecules situated at the minima in their potential wells. The kinetic energy is the sum over the motional energy in vibrations, rotations, and translation of the atoms or molecules. Electrons also contribute to both forms of energy since as temperature increases; there are empty quantum states available for the outer electrons to occupy with a net increase in energy of each atom. These aspects of the states of materials affect their thermodynamic properties in that the configurational and thermal contributions differ in type in the different states and materials.