Solid State Physics for Metallurgists

Metal Physics and Physical Metallurgy, Volume 6: Solid State Physics for Metallurgists provides an introduction to the basic understanding of the properties that make materials useful to mankind. This book discusses the electronic structure of matter, which is the domain of solid state physics. Organized into 12 chapters, this volume begins with an overview of the electronic structure of free atoms and the electronic structure of solids. This text then examines the basis of the Bloch theorem, which is the exact periodicity of the potential. Other chapters consider the fundamental assumption in the solid whereby the bonding electrons between atoms act as nearly harmonic oscillator spring being somewhat stiffer in compression than expansion. This book discusses as well the various properties of the nucleus. The final chapter deals with the different experimental measurements on copper and iron. This book is a valuable resource for metallurgists, experimentalists, and solid state physicists.

List of Tables

Foreword

Theory

Chapter I. The Atom

Introduction to Quantum Mechanics

The Schrödinger Equation

The Hydrogen Atom

The Heisenberg uncertainty principle

Problems

The Helium Atom

Hartree Self-Consistent Field

Pauli Exclusion Principle

Building Up the Periodic Table

The Properties of the Elements in the Periodic Table

Problems

Chapter Summary

Chapter II. The Molecule and the Solid

The Hydrogen Molecule

Other Molecules

Theoretical Approach to More Complicated Molecules

Summary

Problems

Electron Theory of Solids, Lithium Metal

Various Methods for Solving the Schrödinger Equation for Crystals

Free Electron Theory

The Bonding Electrons in the Periodic Table

Crystal Field Theory; Liquids

The Bonding Electrons in Transition Metals and Rare Earth Metals

Electronic Origin of Magnetism

Problems

Chapter III. Temperature and Pressure

The Meaning of Temperature

The Harmonic Oscillator

The Anharmonic Oscillator

Coupled Harmonic Oscillators

How to Determine the Eigenvalues of a Crystal

One Dimensional Chain of Atoms

Normal Modes in Three Dimensions

Thermodynamics

Debye Theory

Frequency Spectrum for Vanadium

Phonons

Elastic Constants

Electronic Specific Heat

Fermi-Dirac Function

Magnetic Specific Heat, Spin Waves

Thermodynamics of Phase Changes

Effects of Pressure

Liquids

Problems

Chapter Summary

Chapter IV. The Nucleus

Static Properties of the Nucleus

Dynamical Properties of the Nucleus

Problems

Chapter Summary

Experiment

Chapter V. Experimental Techniques

Introduction

Sample Preparation

Analysis of Pure Metals

Analysis of Alloys

Problems

Chapter Summary

Chapter VI. Diffraction

What can be Learned from Diffraction

X-RAYS—X-ray Diffraction Equipment

Crystal Structure Determinations

Atomic Sizes in Alloys

Short Range Order

Long Range Order

Theory of Ordering

How to Determine the Electron Probability Distribution

Experimental Difficulties, in Determining Electron Probability Distributions

Converting the Structure Factor into an Electron Probability Distribution

Determination of Electron Probability Distributions from Compton Scattering

Thermal Scattering of X-rays

NEUTRONS—Introduction to Neutron Diffraction

Experimental Details

Determining the Arrangement of Magnetic Moments in a Crystal

The Magnetic Structure of the Transition Metals

The Magnetic Structure of the Rare Earth Metals

Ordered Alloys

Size Effects

Extinction Effects

Diffuse Scattering

Summary

Determination of the Unpaired Electron Probability Distribution

Neutron Diffraction of Nickel

Neutron Magnetic Scattering of Iron

Thermal Scattering of Neutrons

Experimental Techniques

Thermal Scattering from Silicon and Aluminum

ELECTRONS—Introduction

Electron Probability Distribution in Argon Gas

Electron Diffraction of Molecules, Surfaces, etc.

Problems

Chapter summary

Chapter VII. Spectroscopy of the Solid

Introduction

How Photons Interact with Solids

Absorption of X-rays in Argon

Emission of X-rays from Argon

X-ray Emission from Fe, Co, Ni, Cu, Zn, Ga, and Ge

Determination of the Density of States in Beryllium

Fluorescent Yield

Structure of X-ray Absorption Edge

Satellites

Experimental Techniques in X-ray Emission

Optical Absorption in Diamond

The Color and Band Structure of Copper and Silver

Experimental Techniques in the Optical Region

Problems

Chapter Summary

Chapter VIII. Transport Properties

Introduction

Types of Measurements

Resistivity

Magnetoresistance

De Haas Van Alphen Effect

Cyclotron Resonance

Anomalous Skin Effect

Hall Effect

Thermoelectric Power

Superconductivity

Problems

Chapter Summary

Chapter IX. Thermodynamics and Cohesion

Introduction

Experimental Details of Specific Heat and Heat Content Measurements

Analysis of the Specific Heat of Iron

Low Temperature Specific Heat of Cobalt

Nuclear Quadrupole Contribution to the Specific Heat

Information Gained from Specific Heat Measurements

Experimental Measurement of Thermal Conductivity

Thermal Conductivity of Copper and Nickel

Thermal Conductivity at Low Temperature

Ultrasonic Experimental Technique

Ultrasonic Attenuation in a Magnetic Field

Thermodynamics and Cohesion of Alloys

Hume-Rothery Rules

Thermodynamics of Copper-Gold and Platinum-Gold Alloys

Experimental Techniques

Platinum-Gold

Copper-Gold

Pressure Measurements

Problems

Chapter Summary

Chapter X. Magnetization

Introduction

Experimental Techniques

Results of Measurements

Orbital Diamagnetism

Ferromagnetic Metals

Antiferromagnetic Metals

Paramagnetism

Pauli Paramagnetism

Orbital Diamagnetism

Exchange Polarization of Electrons in Metallic Bands

Van Vleck Paramagnetism

Ferromagnetic Resonance

Antiferromagnetic Resonance

Paramagnetic Resonance of Transition Metal and Rare Earth Atoms

Paramagnetic Resonance of Electrons at Fermi Level

Einstein de Haas Effect

Problems

Chapter Summary

Chapter XI. Nuclear Measurements

Introduction

Theoretical Background for Nuclear Magnetic Resonance (NMR) and Nuclear Quadrupole Resonance (NQR)

How the Measurements are Made

The Knight Shift in Lithium, Sodium and Beryllium

The Knight Shift in Silver-Cadmium Alloys

The Ferromagnetic Shift in Iron

Pure Quadrupole Resonance in Gallium

Pressure and Temperature Dependence of Knight Shift

Intensity of Cold Worked Copper

Intensity of the Resonance in Dilute Copper Alloys

The Second Moment

Anisotropic Knight Shift in Tin, Thallium, Cadium and Mercury

Exchange Broadening in Silver

Nuclear Resonance in Manganese

Line Shape in Cold Worked Copper

Diffusion in Sodium

Theory of Diffusion

Relaxation Times in Aluminum and Copper

Overhauser Effect

Theory of the Mössbauer Effect

Mössbauer Effect in Iron

Diffusion Studies with Radioactive Tracers

Autoradiography

Radiation Damage in Copper

Elemental Analysis by Activation

Radioactivity and its Health Hazard

Van de Graaff Accelerators

Positron Annihilation in Solids

Problems

Chapter Summary

Chapter XII. Jig-Saw Puzzle; Problem in Synthesis

Introduction

Electronic Structure of Copper and Iron

Solutions of the Schrödinger Equation for an Imperfect Crystal

Problems

Chapter Summary

Appendix I. Thermodynamics Tables

Debye Entropy

Debye Energy

Debye Specific Heat

Appendix II. Nuclear Tables

Nuclear Magnetic Moments, Nuclear Quadrupole Moments, Nuclear Spins

Absorption Cross Sections, Coherent Scattering Cross Sections, Total Scattering Cross Sections for Thermal Neutrons

Appendix III.

Suggested References

Constants and Conversion Factors

General References

List of Symbols According to Chapters

Index