Electronic Structure Of Metals – Brandt, Chudinov

In this post, we will see the book Electronic Structure Of Metals by N. B. Brandt and S. M. Chudinov.

About the book

“ Electronic Structure of Metals” is a textbook on the physics of metals. It opens with an exposition of the connection between the various properties of metals and the energy spectrum of their electrons. Employs the method of the structure of the Fermi surface. Devotes much space to describing the behaviour of the electron system in metals in the presence of a quantizing magnetic field, and gives a detailed exposition of various quasi-classical and quantum methods of investigating the Fermi sur­face. This textbook is for university students. Suitable also for col­leges of education and other higher teacher-training courses.

About the Authors

 Nikolai Brandt, Dr. Sc. (Phys.-math.), Professor, heads the department of solid-state physics and is the chair of low-temperature physics at the Moscow State University. The field of his scientific interests is solid-state physics. His scientific activities are mainly directed to the study of matter under the com­bined action of super-strong magnetic and electric fields, super-high pressures, strong anisotropic deformations, and strong alloying at low and ultra-low temperatures.
The most important results of Brandt’s scientific research are the discovery and study of phase electron transitions of 2.5 kind under the action of pressure which have been predicted by Acad. Lifshits; the discovery of electron phase transitions of the type metal-dielectric and dielectric-metal in strong magne­tic fields; the discovery and study of new types of gapless state of substances appearing under the action of pressure and magnetic field; the discovery and study of the stationary phase-exciton insulator; the dis­covery of superconductivity at high pressures for a number of new modifications cf phosphorus, antimony, arsenic, bismuth, and indium antimonide.
Nikolai Brandt is the author of more than 50 published Works.
Sergei Chudinov, Cand. Sc. (Phys,-math.), is an assistant professor at the chair of low- temperature physics at the Moscow State University.
The main direction of his scientific activities is the study of electron energy spectra of sub­stances.
The most important results of Chudinov’s scientific research are the establishment of zonal structure of bismuth-antimony alloys in the region of antimony concentrations up to 20 at. per cent and determination of the nature of its variation under the action of pressure and a strong magnetic field; the discovery of new types of gapless state of substances appearing under the action of pressure and magnetic field. Sergei Chudinov is the author of about 40 published Works.

The book was translated from Russian by V. Afanasyev was published in 1975 by Mir Publishers.

You can get the book here.

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Introduction 7


1-1. Metal Formation through Condensation of “Neutral Atoms. The Metallic Bond 13
1-2. The Metallic Bond and Crystal Lattice 17
1-3. The Nature of Oscillations of Atoms in a Crystal Lattice 18
1-4. The Natural-frequency Spectrum of a One-dimensional Lattice 23
1-5. Phonons. Thermal Oscillations in a One-dimensional Lattice 34
1-6. Specific Heat of a Lattice. Einstein’s Model 39
1-7. Specific Heat of a Lattice at Temperatures below 𝛩_{D} 41
1-8. The Spectral Density of Phonons 50
1-9. Interaction of Phonons 57


2-1. The Behaviour of the Electron System in a Metal 61
2-2. The Concept of Fermi Surface 62
2-3. The Effect of Crystal Lattice on the Motion of an Electron 67
2-4. The Dynamics of an Electron in the Crystal Lattice 79
2-5. Dependence of the Energy of an Electron in the Lattice on Quasi-momentum 89
2-6. Construction of Brillouin Zones 97
2-7. The Reciprocal Lattice. The Wigner-Seitz Method for Constructing the First Brillouin Zone 106
2-8. Filling the Brillouin Zone with Electrons 111
2-9. Fermi Surfaces of the Elements of Group I of the Periodic Table 115
2-10. Harrison’s Method for Constructing Fermi Surfaces 120
2-11. The Modern Scheme of Constructing Fermi Surfaces. Topological Classification of Fermi Surfaces 138
2-12. Motion of Quasi-particles in a Constant Magnetic Field 148
2-13. The Density of States 165
2-14. Quantization of the Energy of an Electron in a Magnetic Field. 169
2-15. Distribution of Electrons in p-space in the Presence of a Quantizing Magnetic Field 177
2-16. The Density of States in a Magnetic Field 183
2-17. A Two-zone Metal in a Magnetic Field 197


3-1. Phenomenological Description of Electric Conductivity 219
3-2. Electric Conductivity and Energy Spectrum of Electrons in a Metal 220
3-3. Temperature Dependence of Electric Conductivity 282
3-4. Electric Conductivity of Metals in a Magnetic Field. General Considerations 240
3-5. Weak Magnetic Fields 241
3-6. Weak Magnetic Fields. Hole-type Fermi Surfaces 248
3-7. Strong Magnetic Fields 250


4-1. General Remarks 268
4-2. Galvano-magnetic Methods for Studying the Energy Spectrum 269
4-3. The Azbel-Kaner Cyclotron Resonance 276
4-4. Gantmacher’s Radio-frequency Size Effect 289
4-5. Pippard’s Magneto-acoustic Resonance 300
4-6. Quantum-mechanical Magneto-acoustic Resonance 307
4-7. Oscillational Quantum Effects 314

Bibliography 331
Index 334

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