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Electronic states and optical transitions in solids
Book Reviews riere is greater for this new material than in the rest of the book. Nevertheless, the authors succeed very well in conveying the significance of the recent developments which they describe. As regards black holes, they give more details about gravitational collapse, and they introduce the Kerr metric for rotating black holes. They mention the beautiful uniqueness theorems of Israel and of Carter, which state essentially that a static (non-rotating) black hole devoid of matter must be Schwarzschild and that a stationary rotating black hole devoid of matter must be Kerr. However, the proofs of these theorems are not given; presumably they are too long and difficult to be suitable for inclusion. The book has appeared just too early to contain an account of the quite remarkable developments in black hole theory which occurred in 1973 and 1974. I have in mind particularly the realization that black holes have thermodynamic properties, and Hawking’s discovery of the quantum radiance of a black hole. The spirit of these discoveries conforms closely to the Landau-Lifshitz style, and I hope that a fifth edition will appear soon to take account of them. I am sure that they would be well treated, but I am saddened at the thought that Landau himself could never know of them. D. W. SCIAMA Oxford University Oxford, U.K. ELECTRONIC TRANSITIONS
STATES
AND
OPTICAL
IN SOLIDS, by F. Bassani
and G. Pastori Parravicini. Vol. 8. 300+ xi PP., 79 illus, 7 X 10 in. Pergamon Press, Oxford, 197.5. Price $23.50. A number of books are already available which deal with the optical properites of solids such as the metals, semiconductors and insulators. In some the approach is essentially experimental in which the theory of dispersion is outlined, and the relation of the optical properties to the
Vol.303,No.1,January 1977
band structure is brought out to help in the interpretation of various features in the optical absorption spectra. In a sense the book being reviewed starts at the other end. Professor Bassani is of course well known throughout the world for his contributions to the calculation of the band structures of a wide variety of solids. It comes as no surprise to see a book by Bassani and Parravicini begin with a discussion of symmetry in solids and of those sections of group theory required for the treatment of electron energy bands. There follows an account of the different methods being used in band structure calculations. These include the tight bonding method, the orthogonalized plane wave method, the pseudo potential method, the cellular method, the augmented plane wave method, the Green’s function method, the quantum defect method, and the k.p. method. There is also a section on relativistic effects in crystals. I like this treatment, and although the discussion is not sufficiently detailed to allow a new arrival in the field to start his own calculations, it is beautifully clear and logically arranged. This leads to a chapter on the electronic band structure of many different types of solids. It includes diamond and silicon as representatives of good three dimensional systems, graphite which is a layer type material and which can be classed as a pseudo “two dimensional” solid, and selenium which has a chain like structure and is a pseudo “one dimensional” solid. This discussion is particularly appropriate at present when there is considerable interest in the unusual physical phenomena met in the layer solids such as the transition metal dichalcogenides and in the chain like solids such as TTF-TCNQ, KCP(Br) and the sulphur nitrogen polymer. After dealing with the band structures we find an analysis of interband transitions and optical properties, and of excitons in crystals including the Frenkel and the Mott-Wannier type of excitons. The treatment is naturally very
105
s
Book Reviews theoretical but there is a good sprinkling of experimental results in this chapter taken from a wide variety of solids. It was at first surprising to see a chapter on impurity states in insulators and semiconductors in a book of this kind, but what the authors mean by an impurity state is a localized electronic state in a crystal which can be due to (a) a foreign atom in the lattice, (b) a vacancy, (c) an interstitial or a dislocation and (d) a surface. This naturally makes sense. The final chapter deals with the effects of external perturbations of the kind treated in Cardona’s excellent book on modulation spectroscopy. Here we are concerned with the effects of hydrostatic pressure and alloying, uniaxial stress, and electric and magnetic fields. This book, written by two distinguished theoretical physicists, bears the stamp of
106
authority. It is the product of clear thinking and writing, and has hccn written after careful preparation and trial in a postgraduate course. There is a comprehensive theoretical account of band structure and optical properties, and there are numerous examples and illustrations of experimental results, mainly up to about 1973. Indeed it is known that the authors like to keep one foot in an experimental laboratory, and to many these are the most valuable kind of theoreticians. The book should be in every library dealing with solid state physics and will be used extensively by research students and by lecturers preparing graduate courses. It can be warmly recommended.
A. D. YOFFE University of Cambridge U.K.
Journal of The Franklin Institute
STATES
AND
OPTICAL
IN SOLIDS, by F. Bassani
and G. Pastori Parravicini. Vol. 8. 300+ xi PP., 79 illus, 7 X 10 in. Pergamon Press, Oxford, 197.5. Price $23.50. A number of books are already available which deal with the optical properites of solids such as the metals, semiconductors and insulators. In some the approach is essentially experimental in which the theory of dispersion is outlined, and the relation of the optical properties to the
Vol.303,No.1,January 1977
band structure is brought out to help in the interpretation of various features in the optical absorption spectra. In a sense the book being reviewed starts at the other end. Professor Bassani is of course well known throughout the world for his contributions to the calculation of the band structures of a wide variety of solids. It comes as no surprise to see a book by Bassani and Parravicini begin with a discussion of symmetry in solids and of those sections of group theory required for the treatment of electron energy bands. There follows an account of the different methods being used in band structure calculations. These include the tight bonding method, the orthogonalized plane wave method, the pseudo potential method, the cellular method, the augmented plane wave method, the Green’s function method, the quantum defect method, and the k.p. method. There is also a section on relativistic effects in crystals. I like this treatment, and although the discussion is not sufficiently detailed to allow a new arrival in the field to start his own calculations, it is beautifully clear and logically arranged. This leads to a chapter on the electronic band structure of many different types of solids. It includes diamond and silicon as representatives of good three dimensional systems, graphite which is a layer type material and which can be classed as a pseudo “two dimensional” solid, and selenium which has a chain like structure and is a pseudo “one dimensional” solid. This discussion is particularly appropriate at present when there is considerable interest in the unusual physical phenomena met in the layer solids such as the transition metal dichalcogenides and in the chain like solids such as TTF-TCNQ, KCP(Br) and the sulphur nitrogen polymer. After dealing with the band structures we find an analysis of interband transitions and optical properties, and of excitons in crystals including the Frenkel and the Mott-Wannier type of excitons. The treatment is naturally very
105
s
Book Reviews theoretical but there is a good sprinkling of experimental results in this chapter taken from a wide variety of solids. It was at first surprising to see a chapter on impurity states in insulators and semiconductors in a book of this kind, but what the authors mean by an impurity state is a localized electronic state in a crystal which can be due to (a) a foreign atom in the lattice, (b) a vacancy, (c) an interstitial or a dislocation and (d) a surface. This naturally makes sense. The final chapter deals with the effects of external perturbations of the kind treated in Cardona’s excellent book on modulation spectroscopy. Here we are concerned with the effects of hydrostatic pressure and alloying, uniaxial stress, and electric and magnetic fields. This book, written by two distinguished theoretical physicists, bears the stamp of
106
authority. It is the product of clear thinking and writing, and has hccn written after careful preparation and trial in a postgraduate course. There is a comprehensive theoretical account of band structure and optical properties, and there are numerous examples and illustrations of experimental results, mainly up to about 1973. Indeed it is known that the authors like to keep one foot in an experimental laboratory, and to many these are the most valuable kind of theoreticians. The book should be in every library dealing with solid state physics and will be used extensively by research students and by lecturers preparing graduate courses. It can be warmly recommended.
A. D. YOFFE University of Cambridge U.K.
Journal of The Franklin Institute