# Interatomic Potentials

## 1st Edition

**Authors:**Iam Torrens

**eBook ISBN:**9780323158695

**Imprint:**Academic Press

**Published Date:**1st January 1972

**Page Count:**262

## Description

Interatomic Potentials provides information pertinent to the fundamental aspects of the interaction between atoms. This book discusses the theory of interatomic forces or potentials, which deals with the complicated problem of many-body interactions.

Organized into 10 chapters, this book begins with an overview of the physical principles behind a range of atomic interactions and show how they can be applied to some atomic problems. This text then examines some of the theories of the atom that employ various approximate methods to simplify the many-body problem and estimate it potential energy. Other chapters consider the application of computer techniques to atomic problems. This book discusses as well the general principles and the particular types of pair interactions based on the pseudopotential method. The final chapter deals with some applications of interatomic potentials.

This book is a valuable resource for graduate students, research workers, and teachers. Atomic and solid state physicists will also find this book useful.

## Table of Contents

Preface

ACknowledgments

Introduction

Chapter I. The Nature of Interatomic Forces

1.1 Atomic Interactions in Physical Phenomena

1.2 Concept of an Atomic Potential Energy: The Many-Body Problem

1.3 The Potential Energy of a Pair of Atoms or Ions

1.4 Types of Interatomic Force

1.5 The Chemical Bond

1.6 Cohesion in Crystals

1.7 The Relation of Physical Properties to the Interatomic Potential

1.8 Energetic Collisions of Atoms and Ions

1.9 The Validity of the Two-Body Approximation

1.10 Summary

References

Chapter II. Theoretical Models of the Atom

2.1 The Central Field Hypothesis

2.2 The Born-Oppenheimer Approximation

2.3 The Hartree Self-Consistent Field Method

2.4 The Thomas-Fermi Statistical Model of the Atom

2.5 Variational Derivation of the Thomas-Fermi Electron Density

2.6 Introduction of Exchange: The Thomas-Fermi-Dirac Equation

2.7 Solution of the Thomas-Fermi Equation for the Isolated Atom

2.8 Analytical Approximations to the Thomas-Fermi Screening Function

2.9 Conclusion

References

Chapter III. Interatomic Potentials Based on Thomas-Fermi Theory

3.1 Introduction

3.2 The Firsov Thomas-Fermi Pair Potential

3.3 The Firsov Variational Derivation of the Thomas-Fermi Potential

3.4 Solution of the Thomas-Fermi Equation for the Diatomic Molecule

3.5 Variational Derivation of the Thomas-Fermi-Dirac Interatomic Potential

3.6 Analytical Thomas-Fermi Two-Body Potentials

References

Chapter IV. Empirical Interatomic Potentials

4.1 Introduction

4.2 Simple Models

4.3 The Buckingham Potentials

4.4 The Lennard-Jones Potential

4.5 The Morse Potential

4.6 Analytical Potentials for Atomic Collisions

4.7 Screened Coulomb Potentials

4.8 The Born-Mayer Potential

4.9 Adjustment of the Born-Mayer Potential to Crystal Elastic Constants

4.10 Mixed Analytical Forms of Potential

4.11 The Moliere Potential

4.12 Composite Polynomial Potentials

4.13 Determination of Interatomic Potential Parameters from Experiment

4.14 The Virial Coefficients

4.15 Radiation Damage Interatomic Potentials

4.16 Shock Wave Experiments

4.17 Conclusion

References

Chapter V. Pseudopotential Theory

5.1 What Is a Pseudo-Atom?

5.2 Orthogonalized Plane Waves

5.3 The Pseudopotential for a System of Ions

5.4 The Structure Factor for a Periodic Lattice

5.5 The Single Ion Form Factor

5.6 Electron Screening of the Pseudopotential

5.7 Total Energy of an Ion-Electron System

5.8 The Energy-Wavenumber Characteristic

5.9 The Pair Interaction Potential

5.10 Application of Pseudopotential Theory to Noble and Transition Metals

5.11 Summary of the Pseudopotential Method

References

Chapter VI. Pair Potentials Based on Pseudopotential Theory

6.1 Introduction

6.2 First-Principle Derivations of the Interatomic Potential

6.3 The Heine-Abarenkov-Animalu (HAA) Model Potential

6.4 The Screening of Nonlocal Potentials

6.5 The Ashcroft Model Potential Applied to Simple Metal Pair Interactions

6.6 The Pair Potential of Ho for the Alkali Metals

6.7 Pair Potentials Determined from Pseudo-Atom Phase Shifts

6.8 Impurity Potentials and Alloys

6.9 Derivation of the Pair Interaction from Phonon Spectra

6.10 Sensitivity of the Potential to the Choice of wb(g) and e(q)

6.11 Some Observations Concerning Interatomic Potentials and Pseudopotential Theory

6.12 Conclusion

References

Chapter VII. Atomic Collision Theory and Interatomic Potentials

7.1 Atomic Collisions

7.2 Reduction of the Two-Body Scattering Problem

7.3 Transformation to the Laboratory System

7.4 The Impulse Approximations

7.5 Scattering Cross Sections

7.6 Large-Angle Scattering Using Matching Potentials

7.7 The Inversion Problem

7.8 Inelastic Collision Losses

References

Chapter VIII. Experiments on the Scattering of Atoms and Ions

8.1 Direct Experimental Determination of the Potential

8.2 Basic Features of Atom or Ion Beam Experiments

8.3 Experimental Equipment for Atom-Atom Scattering

8.4 Measurement of the Differential Scattering Cross Section

8.5 Ion-Atom Scattering Experiments

8.6 Deflected Beam Detection Experiments

8.7 Measurement of the Inelastic Energy Loss

8.8 Coincidence-Counting Techniques in Ion-Atom Collisions

8.9 Current and Possible Future Developments in Beam Scattering

References

Chapter IX. Liquid Metal Pair Interaction Potentials

9.1 Liquid Metals

9.2 Correlation Functions and Atomic Interactions

9.3 The Liquid Metal Structure Factor

9.4 Solutions for the Pair Potential

9.5 Interatomic Potentials Obtained from Liquid Metal Data

9.6 Sensitivity of the Pair Potential to Liquid Structure

9.7 The Computer Experiment Applied to Liquid Metals

9.8 Future Developments in Liquid Metal Potentials

References

Chapter X. The Application of Interatomic Potentials

10.1 Which Potential?

10.2 Why a Pair Interaction?

10.3 Radiation Damage and Atomic Collision Studies

10.4 Atomistic Computer Simulations

10.5 Crystal Defect Simulations

10.6 Molecular Dynamics

10.7 Low-Energy Damage Events

10.8 High-Energy Atomic Displacement Cascades

10.9 Interpretation of Computer Simulation Results

10.10 Interatomic Potential: The State of the Art

References

Appendix 1 The Thomas-Fermi Screening Function

Appendix 2 Hartree Dielectric Screening of the Pseudopotential

Appendix 3 The Cohesion of Ionic Crystals

Appendix 4 Interatomic Potentials Derived from Planar Channeling Data

Author Index

Subject Index

## Details

- No. of pages:
- 262

- Language:
- English

- Copyright:
- © Academic Press 1972

- Published:
- 1st January 1972

- Imprint:
- Academic Press

- eBook ISBN:
- 9780323158695