An Introduction to Aspects of Thermodynamics and Kinetics Relevant to Materials Science

Eugene Machlin

• Éditeur: Elsevier Science
• Année: 2010
• ISBN:
  9780080549682
• Édition: 3
• Sujet: Ciencias físicas
• Sous-sujet: Química física y teórica

This book is based on a set of notes developed over many years for an introductory course taught to seniors and entering graduate students in materials science. An Introduction to Aspects of Thermodynamics and Kinetics Relevant to Materials Science is about the application of thermodynamics and kinetics to solve problems within Materials Science. Emphasis is to provide a physical understanding of the phenomenon under discussion, with the mathematics presented as a guide.

The problems are used to provide practice in quantitative application of principles, and also to give examples of applications of the general subject matter to problems having current interest and to emphasize the important physical concepts.

End of chapter problems are included, as are references, and bibliography to reinforce the text. This book provides students with the theory and mathematics to understand the important physical understanding of phenomena.

• Based on a set of notes developed over many years for an introductory course taught to seniors and entering graduate students in materials science
• Provides students with the theory and mathematics to understand the important physical understanding of phenomena
• Includes end of chapter problems, references, and bibliography to reinforce the text

CHAPTER I

Thermodynamics of Phases having Constant Composition

Publisher Summary

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.

Introduction

Application of thermodynamics and kinetics to phenomena of interest in materials science is the theme of this book. Most materials in the phrase “materials science” consist of phases or mixtures of phases. By “phase” is meant the homogeneous configuration of atoms or molecules corresponding to a liquid; or to some crystalline solid, such as a solid having the body-centered-cubic (bcc) structure; or to an amorphous solid, such as glass; or to a vapor. A phase has a set of properties including thermodynamic potentials, such as entropy, enthalpy and Gibbs free energy. The phase may or may not be in an equilibrium state. In the equilibrium state the thermodynamic properties of a given phase are not functions of its past history, but are unique. A state of equilibrium is defined for a closed system by the condition that the entropy is at a maximum. Related to this condition it is also defined by the existence of a minimum in one of the thermodynamic potentials listed in Table 1.1 along with the corresponding variables that are constrained to be constant in the minimization procedure.

Table 1.1

Thermodynamic potentials corresponding to stable equilibrium.

Thermodynamic potential	Constrained variables
Gibbs free energy (G)	P,T,N
Helmholtz free energy (F)	V,T,N
Enthalpy (H)	P,S,N
Internal energy (E)	V,S,N
Grand (Ω)	V,T,μ

At equilibrium, there are a variety of variational properties of the thermodynamic potentials. For example, the bulk modulus is given by –V[∂²G/∂V²]_T. A listing of the relations between derivatives of thermodynamic parameters and physical properties of materials is given in Table 1.2. The symbols in the table are defined in the list of symbols at the end of this chapter. From examination of this table it is apparent that a knowledge of the dependence of a thermodynamic potential on pressure or temperature of a material will provide a basis for determining a number of material properties. However, there is a more important reason for wanting this knowledge which relates to the relative stability of competing allotropes or polymorphs of a given material.

Table 1.2

Summary of thermodynamic relations.^a

X	Y	Z	${\left[\frac{\partial \text{Y}}{\partial \text{X}}\right]}_{\text{Z}}$	X	Y	Z	${\left[\frac{\partial \text{Y}}{\partial \text{X}}\right]}_{\text{Z}}$
T	V	p	αV	T	p	V	α/β
T	S	p	Cp/T	T	S	V	Cp/T – α^2V/β
T	V	p	Cp – αpV	T	U	V	Cp – α^2VT/β
T	H	p	^CP	T	H	V	Cp – α^2VT/β + αV/β
T	F	p	− αpV – S	T	F	V	−S
T	G	p	−S	T	G	V	αV/β – S
p	V	T	−βV	T	p	S	Cp/αVT
p	S	T	−αV	T	V	S	−βCp/αT + αV
p	U	T	βpV – αVT	T	U	S	βpCp/αT – αpV
p	H	T	V – αVT	T	H	S	Cp/αT
p	F	T	β...