Theory and application of quantum-based interatomic potentials in metals and alloys / John A. Moriarty.

Format:

Book

Author/Creator:

Moriarty, John A., author.

Series:

Oxford series on materials modelling ; 8.

Oxford scholarship online.

Oxford series on materials modelling ; 8

Oxford scholarship online

Language:

English

Subjects (All):

Metals--Properties.

Metals.

Alloys--Properties.

Alloys.

Quantum chemistry.

Density functionals.

Physical Description:

1 online resource (593 pages)

Place of Publication:

Oxford : Oxford University Press, 2023.

Summary:

This text spans the entire QBIP process from foundation in fundamental theory, to development and machine-learning optimization of accurate potentials for real materials, to the application of the potentials to materials modeling and simulation of structural, thermodynamic, defect and mechanical properties of important metals and alloys.

Contents:

Cover

Title page

Copyright

Contents

Preface

1 Introduction

1.1 Why quantum-based interatomic potentials

1.2 Basic concepts and nomenclature

1.2.1 Total-energy functional, multi-ion potentials and radial vs. angular forces

1.2.2 Environmental dependence, transferability and physical convergence

1.2.3 Extension to alloys and intermetallic compounds

1.2.4 Units, length scales and reference physical data

1.3 Failure of pure pair potentials in metals

1.4 Guiding principles in metals for quantum-based potentials

1.4.1 Linear embedding in a uniform electron gas: volume-dependent potentials for bulk simple metals

1.4.2 Extension of volume-dependent potentials to bulk transition metals

1.4.3 Nonlinear embedding and free surfaces: glue and bond-order potentials

1.4.4 Absence of bond charges in the electron density

1.4.5 Finite ion-ion interaction range and order-N scaling

1.4.6 Quantum-mechanical pillar of structural phase stability

1.4.7 Machine learning and statistical interatomic potentials

2 Fundamental Principles in Metals Physics

2.1 Born-Oppenheimer or adiabatic approximation

2.2 Density functional theory

2.2.1 Exchange and correlation functions in the local density approximation

2.2.2 Exchange and correlation beyond the LDA

2.3 Small-core approximation and the valence binding energy in metals

2.4 Guidance from the DFT electronic structure: simple metals vs. d-band metals

2.5 Weak pseudopotentials and perturbation theory for simple metals

2.5.1 Plane waves and nearly free-electron valence energy bands

2.5.2 First-order electron density and second-order valence band energies

2.6 Localized d-states for the narrow d bands in transition-series metals

2.6.1 Equivalence of resonance and tight-binding descriptions of the d bands.

2.6.2 Canonical d bands and their simplifying features

2.6.3 Density of states moments in a tight-binding representation

2.7 Generalized pseudopotential theory for d-band metals

2.7.1 Hybrid nearly free-electron tight-binding energy bands

2.7.2 Pseudo-Green's functions in a mixed plane-wave, d-state basis

2.7.3 Transition-metal ion with a d resonance in a free-electron gas

2.7.4 Valence band-structure energy for bulk transition-series metals

2.7.5 Valence electron density for bulk transition-series metals

3 Interatomic Potentials in Simple Metals

3.1 Simple-metal cohesive-energy functional in DFT

3.1.1 Reciprocal-space representation

3.1.2 Real-space representation

3.2 Self-consistent electron screening

3.3 Evaluation of the energy-wavenumber characteristic and volume term

3.4 First-principles pair potentials for simple metals

3.4.1 Impact of pseudopotential nonlocality and exchange and correlation

3.4.2 Energy dependence and the optimization of nonlocal pseudopotentials

3.4.3 Trends with valence, volume and atomic number

3.5 Long-range Friedel oscillations and materials application

3.5.1 Exact methods for static lattice properties

3.5.2 Damping and smooth truncation techniques for atomistic simulations

3.6 Higher-order corrections

4 Interatomic Potentials in Metals with Empty or Filled d Bands

4.1 Inclusion of sp-d hybridization and d-state overlap in the GPT cohesive-energy functional

4.1.1 Valence band-structure energy

4.1.2 Valence electron density and self-consistent screening

4.1.3 Volume term, energy-wavenumber characteristic and overlap potential

4.1.4 Evaluation of the real-space volume term and pair potential

4.2 Zero-order pseudoatoms and optimized d basis states

4.3 Modified FDB-GPT treatment for the special case of the noble metals.

4.4 Alternate resonant model potential approach

4.5 Trends in first-principles GPT pair potentials with atomic number and volume

5 Interatomic Potentials in Transition Metals

5.1 GPT multi-ion potentials for metals with partially filled d bands

5.1.1 Essential new elements of the valence band-structure energy

5.1.1.1 Formal multi-ion d-state potential series

5.1.1.2 Tight-binding moments and multi-ion series convergence

5.1.2 Valence electron density and self-consistent screening

5.1.2.1 Zero-order pseudoatoms for transition metals

5.1.2.2 Oscillatory screening and orthogonalization-hole components

5.1.3 Completion of the cohesive-energy functional

5.1.4 First-principles pair and multi-ion potentials

5.1.5 Multi-ion screening of sp-d hybridization

5.2 Simplified MGPT potentials for robust atomistic simulations

5.2.1 Baseline analytic MGPT for canonical d bands

5.2.2 Matrix MGPT for large-scale MD, noncanonical d bands and more

5.2.3 Optimized canonical d-band MGPT potentials for central bcc metals

5.2.4 Re-inclusion of sp-d hybridization and extension to late-series metals

5.2.5 Development of five- and six-ion potentials for mid-period metals

5.3 Bond-order potentials for transition metals

5.3.1 Localized d-state moments expansion for the bond energy

5.3.2 Simplified analytic bond-order potentials

5.3.3 Parameterization of bond integrals and the repulsive energy

5.4 Inclusion of magnetism in bond-order and MGPT potentials

6 Structural Phase Stability and High-Pressure Phase Transitions

6.1 Useful basic concepts and computational tools

6.1.1 Separation of cohesion and structure

6.1.2 Transformation paths connecting multiple structures

6.1.3 Simplified calculation of the total enthalpy difference between two structures at finite pressure.

6.2 QBIP-predicted structures and structural energies of the elements

6.2.1 Nontransition metals

6.2.2 Transition metals

6.3 High-pressure phase stability and pressure-induced phase transitions

6.3.1 sp-d electron transfer across the Periodic Table and systematic trends

6.3.2 Successful GPT and MGPT predictions of new high-pressure phases

7 Elastic Moduli and Phonons

7.1 Quasiharmonic lattice dynamics for QBIP applications

7.1.1 Dynamical matrix and the calculation of normal-mode phonon frequencies

7.1.2 Tangential and radial force-constant functions for pair potentials

7.1.3 Tangential and radial force-constant functions for multi-ion potentials

7.1.4 Important caveats and alternate approaches

7.2 Calculated quasiharmonic phonon spectra for elemental metals

7.2.1 Nontransition metals

7.2.2 Transition metals

7.3 Elastic moduli for QBIP applications

7.3.1 Elastic constants from stress-strain in linear elasticity

7.3.2 Elastic constants and the long-wavelength limit of QHLD

7.3.3 EOS calculation of the bulk modulus and local environment corrections

7.4 Thermodynamic properties in the QHLD limit

7.5 Temperature-induced solid-solid phase transitions

8 High-Temperature Properties, Melting and Phase Diagrams

8.1 Important QBIP computational tools at high temperature

8.1.1 Molecular dynamics simulation with fast algorithms

8.1.2 Reversible-scaling MD for ion-thermal free energies

8.1.2.1 RSMD applied to a stable solid phase

8.1.2.2 RSMD applied to the liquid

8.1.2.3 RSMD applied to a metastable solid phase

8.1.3 Variational perturbation theory for liquid metals

8.1.4 Two-phase melting simulations and other dynamic methods

8.2 Equation of state and high-temperature thermodynamic properties

8.2.1 Electron-thermal free energy in metals.

8.2.2 Shock physics and the Hugoniot

8.2.3 Thermodynamic derivatives

8.2.4 Thermoelasticity and sound velocity

8.3 Melting and the pressure-temperature phase diagram

8.4 Rapid solidification and polymorphism in transition metals

9 Defects and Mechanical Properties

9.1 Point defect formation and migration energies

9.2 Salient elastic and deformation properties of bcc transition metals

9.2.1 Shear elastic moduli and their pressure dependence

9.2.2 Ideal shear strength

9.2.3 Generalized stacking-fault energy surfaces

9.3 Screw dislocation atomic structure and mobility in bcc transition metals

9.3.1 Green's function simulation method for dislocation calculations

9.3.2 Equilibrium dislocation core structures

9.3.3 Movement under shear stress: kink-pair formation and the Peierls stress

9.3.4 Kink-pair activation enthalpy and high-temperature mobility

9.4 Multiscale modeling of single-crystal plasticity in bcc transition metals

9.5 Grain-boundary atomic structure in bcc transition metals

9.6 Defect properties in fcc transition metals

10 Alloys and Intermetallic Compounds

10.1 General constrains with composition as an independent environmental variable

10.2 Nontransition-metal binary alloys and compounds

10.3 Transition-metal aluminides and their phase diagrams

10.3.1 First-principles GPT interatomic potentials

10.3.2 Basic trends in cohesion and structure

10.3.3 Al-Co and Al-Ni binary phase diagrams

10.3.4 Extension to ternary phase diagrams and quasicrystals

10.4 The special case of Ca-Mg

10.5 BOP treatment of transition-metal aluminides: TiAl

10.6 Treating pure transition-metal alloys with the MGPT

11 Local Volume Effects on Defects and Free Surfaces

11.1 Local-density representations of the GPT and their application

11.1.1 Electron-density modulation.

11.1.2 Local density-of-states modulation.

Notes:

Also issued in print: 2023.

Includes bibliographical references and index.

Description based on online resource; title from home page (viewed on August 30, 2023).

Other Format:

Print version: Moriarty, John A. Theory and Application of Quantum-Based Interatomic Potentials in Metals and Alloys

ISBN:

1-5231-5613-9

0-19-186122-7

0-19-255535-9