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E-raamat: Materials Modelling using Density Functional Theory: Properties and Predictions

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(, Associate Professor of Materials Modelling, Department of Materials, University of Oxford)
  • Formaat: 304 pages
  • Ilmumisaeg: 15-May-2014
  • Kirjastus: Oxford University Press
  • Keel: eng
  • ISBN-13: 9780191639432
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Materials Modelling using Density Functional Theory: Properties and PredictionsSuurem pilt
  • Formaat: 304 pages
  • Ilmumisaeg: 15-May-2014
  • Kirjastus: Oxford University Press
  • Keel: eng
  • ISBN-13: 9780191639432
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This book is an introduction to the quantum theory of materials and first-principles computational materials modelling. It explains how to use density functional theory as a practical tool for calculating the properties of materials without using any empirical parameters. The structural, mechanical, optical, electrical, and magnetic properties of materials are described within a single unified conceptual framework, rooted in the Schrödinger equation of quantum mechanics, and powered by density functional theory.

This book is intended for senior undergraduate and first-year graduate students in materials science, physics, chemistry, and engineering who are approaching for the first time the study of materials at the atomic scale. The inspiring principle of the book is borrowed from one of the slogans of the Perl programming language, 'Easy things should be easy and hard things should be possible'. Following this philosophy, emphasis is placed on the unifying concepts, and on the frequent use of simple heuristic arguments to build on one's own intuition. The presentation style is somewhat cross disciplinary; an attempt is made to seamlessly combine materials science, quantum mechanics, electrodynamics, and numerical analysis, without using a compartmentalized approach. Each chapter is accompanied by an extensive set of references to the original scientific literature and by exercises where all key steps and final results are indicated in order to facilitate learning. This book can be used either as a complement to the quantum theory of materials, or as a primer in modern techniques of computational materials modelling using density functional theory.

Arvustused

At last an undergraduate/graduate textbook that demonstrates the power of density functional theory not only to help interpret experimental data but also to predict the properties of new materials. Each chapter is lucidly presented with heuristic, intuitive arguments leading to the main ideas before numerous examples illustrate the often remarkable accuracy of density functional theory over a wide range of electronic, structural, mechanical, optical and magnetic properties. A book that should be on the shelves of every library in Materials Science and Engineering, Physics and Chemistry departments. * David Pettifor, University of Oxford * The density functional theory has finally brought quantum mechanics into materials science. Its proven ability to produce correct predictions of properties of real materials means that it has taken over as the premier method in solid state materials, ultimately because of its suitability as a numerical method. While traditional books still build from analytically tractable models, this book reflects more accurately current practice. The book will be ideal for a graduate-level student with a grounding in quantum mechanics, and could be tackled in an undergraduate course. * Graeme Ackland, University of Edinburgh *

Notation xv
1 Computational materials modelling from first principles
1(18)
1.1 Density functional theory
2(1)
1.2 Examples of materials modelling from first principles
3(10)
1.3 Timeline of DFT calculations in materials modelling
13(3)
1.4 Reasons behind the popularity of density functional theory
16(1)
1.5 Atomistic materials modelling and emergent properties
17(2)
2 Many-body Schrodinger equation
19(17)
2.1 The Coulomb interaction
19(1)
2.2 Many-body Schrodinger equation
20(3)
2.3 Atomic units
23(2)
2.4 Clamped nuclei approximation
25(2)
2.5 Independent electrons approximation
27(2)
2.6 Exclusion principle
29(1)
2.7 Mean-field approximation
30(2)
2.8 Hartree-Fock equations
32(3)
2.9 Kohn-Sham equations
35(1)
3 Density functional theory
36(15)
3.1 Total energy of the electronic ground state
36(3)
3.2 Kohn-Sham equations
39(1)
3.3 The local density approximation
40(6)
3.4 Self-consistent calculations
46(3)
3.5 Remit of density functional theory and limitations
49(2)
4 Equilibrium structures of materials: fundamentals
51(15)
4.1 The adiabatic approximation
51(3)
4.2 Atomic forces
54(5)
4.3 Calculating atomic forces using classical electrostatics
59(3)
4.4 How to find the equilibrium configuration using calculated forces
62(4)
5 Equilibrium structures of materials: calculations vs. experiment
66(21)
5.1 Structure of molecules
66(3)
5.2 Structure of crystals
69(3)
5.3 Comparison of DFT structures with X-ray crystallography
72(4)
5.4 Structure of surfaces
76(4)
5.5 Comparison of DFT surface reconstructions with STM
80(7)
6 Elastic properties of materials
87(15)
6.1 Elastic deformations
87(1)
6.2 Intuitive notions of stress and strain using computer experiments
88(3)
6.3 General formalism for the elastic properties of solids
91(3)
6.4 Calculating elastic constants using the DFT total energy
94(2)
6.5 Examples of calculations of elastic constants
96(2)
6.6 The stress theorem
98(1)
6.7 DFT predictions for materials under extreme conditions
99(3)
7 Vibrations of molecules and solids
102(21)
7.1 Heuristic notion of atomic vibrations
102(4)
7.2 Formal theory of vibrations for classical nuclei
106(5)
7.3 Calculations of vibrational eigenmodes and eigenfrequencies
111(4)
7.4 Vibrations of crystalline solids
115(8)
8 Phonons, vibrational spectroscopy and thermodynamics
123(29)
8.1 Basics of Raman and neutron scattering spectroscopy
123(8)
8.2 Going beyond the classical approximation for nuclei
131(6)
8.3 Vibrons and phonons
137(3)
8.4 Phonon density of states
140(2)
8.5 Phonon DOS and pressure--temperature phase diagrams
142(10)
9 Band structures and photoelectron spectroscopy
152(25)
9.1 Kohn-Sham energies and wavefunctions
152(3)
9.2 Calculation of band structures using DFT
155(7)
9.3 Basics of angle-resolved photoelectron spectroscopy
162(6)
9.4 Metals, insulators and semiconductors
168(5)
9.5 The band gap problem
173(4)
10 Dielectric function and optical spectra
177(30)
10.1 The dielectric function of a model solid
177(12)
10.2 General properties of the dielectric function
189(4)
10.3 Using DFT to calculate dielectric functions
193(11)
10.4 Advanced concepts in the theory of the dielectric function
204(3)
11 Density functional theory and magnetic materials
207(32)
11.1 The Dirac equation and the concept of spin
207(7)
11.2 Charge density and spin density
214(6)
11.3 Spin in a system with many electrons
220(2)
11.4 Spin and exchange energy
222(5)
11.5 Spin in density functional theory
227(3)
11.6 Examples of spin-DFT calculations
230(9)
Appendix A Derivation of the Hartree--Fock equations 239(4)
Appendix B Derivation of the Kohn--Sham equations 243(3)
Appendix C Numerical solution of the Kohn--Sham equations 246(8)
Appendix D Reciprocal lattice and Brillouin zone 254(4)
Appendix E Pseudopotentials 258(6)
References 264(20)
Index 284
Feliciano Giustino is an Associate Professor of Materials Modelling in the Department of Materials at the University of Oxford, the co-Director of the Materials Modelling Laboratory, and Associate Editor of the European Physical Journal B. He holds an MSc in Nuclear Engineering from the Politecnico di Torino, a PhD in Physics from the Ecole Polytechnique Fédérale de Lausanne, and before joining the Department of Materials at Oxford he was a researcher in the Department of Physics at the University of California at Berkeley. His research team specializes in the computational modelling of nanomaterials and the development of methods for electronic structure calculations. He has been recipient of the European Research Council Starting Grant and of the Leverhulme Research Leadership Award. Besides his research work, he teaches two undergraduate courses on the quantum theory of materials at the University of Oxford.
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