The Theory of Brillouin Zones and Electronic States in Crystals

Donald S. McClure. J. Am. Chem. Soc. , 1961, 83 (16), pp 3541–3542. DOI: 10.1021/ja01477a055. Publication Date: August 1961. ACS Legacy Archive...
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Aug. 20, 1961

BOOK REVIEWS Isotope Effects on Reaction Rates. By LARSMELANDER. thoughtfully provide a list of recommended experiments for Kobe1 Institute of Chemistry, Stockholm. The Ronald the purpose in the introduction. Even for the uon-polymer Press Company, 15 East 26th Street, New York 10, chemist, this book should make fascinating reading if he N. Y . 1960. vi 181 pp. 14 X 21 cm. Price, has any curiosity about how these things are actually done, which play such an important part in chemical technology 56.00. and which support so many of his friends and former stuThis little volume, written by an active worker in the dents. field, deals both with theoretical and experimental aspects DEPARTMENT OF CHEMISTRY of isotope effects on chemical rates. In the earlier chapters COLUMBIA UNIVERSITY CHEVESWALLING the theory of isotope effects based on transition state theory is presented and the evaluation of relative isotopic rate con- NEW YORK27, NEW YORK stants from experimental data is treated. It is somewhat unfortunate that some of the more recent theoretical methods for the treatment of isotope effects are not discussed. Sub- The Theory of Brillouin Zones and Electronic States in Crystals. By H. JONES, Professor of Mathematics, sequent chapters deal with isotope effects observed in Imperial College, University of London Interscience various systems. The emphasis is very heavily on hydroPublishers, Inc., 250 Fifth Avenue, New York 1, 1L’. Y. gen and carbon isotope effects in organic systems. First 1960. ix 268 pp. 16 X 23 cm. Price, $9.50. the experimental magnitudes of these isotope effects and the theoretical predictions of these magnitudes are discussed for The chemistry and physics of crystalline matter depend simple systems. Subsequently isotope effects are discussed heavily on the band theory of solids: the theory of the from the point of view of learning about reaction mech- electronic structure of perfect crystals. Professor Jones anisms in more complicated systems. In general the book has presented a carefully written introduction t o this subis well written, although there are one or two obscure pas- ject. sages. The book should form a valuable addition to the announced purpose of the book is t o give a n account libraries of those interested in the application of kinetic iso- of The the mathematical methods for the approximate solutions tope effectsto problems in organic chemistry. of the one-electron Schroedinger’s equation for crystals. CHEMISTRY DEPARTMEKT The emphasis is placed on the use of symmetry, or group BROOKHAVES NATIONAL LABORATORY MAXWOLFSBERG theory, for displaying the nature of the solutions independent UPTON,LOX ISLAND, NEWYORK of models for the potential. This policy is started in the first chapter on the one-dimensional periodic potential, where notation and symmetry theory applicable to the Preparative Methods of Polymer Chemistry. By WAYNE three-dimensional case are introduced. In chapter 2 the R . SORENSON, Research Chemist, and TODW. CAMPBELL, direct and reciprocal lattice and the translation group are Research Manager, Pioneering Research Division, Tex- introduced using a notation which is both clear and useful tile Fibers Department, E. I. du Pont de Nemours and in later chapters. Bloch functions and Brillouin zones are Co., Inc. Interscience Publishers, Inc., 250 Fifth Avenue, then introduced followed by a discussion of constant energy 337 pp. 16 X 23.5 surfaces and some examples of three-dimensional zones. S e w York 1, N. Y. 1961. viii The next two chapters, which take u p about half of the cm. Price, $10.50. book, are devoted to the development of group theory for If one decides actually to do some polymer chemistry (as the classification of electronic states. The division into distinguished from reading or talking about it) he quickly two chapters is based on the distinction between space groups finds that the information he needs for carrying out poly- having or not having glide planes and screw displacements. merization reactions is scattered through the original literaI n each chapter, examples of the symmetry properties of ture, patents and industrial lore which never appears in states within the Brillouin zone are worked through in print. Even when he has found what he wants, he finds it helpful detail. For instance, the ten pages devoted to the very difficult to evaluate the merits of different procedures. a-uranium structure begin with a detailed description of the Sorenson and Campbell’s book should go a long way toward direct and reciprocal lattices and the Brillouin zone. The resolving this dilemma, and, in these days of multiple- groups of the wave vectors a t several points in the zone are authored compendia, it is a pleasure to encounter a volume derived and the wave functions and energy bands for the which sets itself a specific goal and proceeds to reach it case of free electrons are developed in some detail. clearly, concisely, and with adequate but not unnecessary There follows a chapter on nearly free electrons and the detail. extended zone scheme. The value of band theory as an The authors start with a brief account of the general proper- approximation method is brought out in this chapter in the ties of polymers and equipment and techniques for poly- discussion of perturbation theory and in the applications t o merization and polymer handling, together with a very alloy phases. helpful definition and discussion of the terms used in polymer The chemist will be on familiar ground when reading chemistry. The main part of the book, however, consists chapter six in which specific models for the potentials are of some 275 specific sets of laboratory directions for poly- chosen; much space is given t o the LCAO method. Other merization reactions (including a number of preparations commonly used approximations and their strong and weak of commercially unavailable monomers). These proce- points are also discussed. This chapter is a concise and dures are divided into polycondensations (83 examples), valuable critique of these methods. vinyl polymerizations (106 examples, including radical, The final chapter is a short account of the modifications carbonium ion, carbanion and “Ziegler” processes), ring which must be made to include effects of spin-orbit coupling. opening polymerizations (41 examples ranging from cyclic The double groups are shown to follow from the invariance ethers to sulfur), “non-classical routes to polymers” (20 of the Schroedinger equation with spin, and examples of examples including some strange and wonderful reactions), spin-orbit splitting in crystals are worked out. and synthetic resins (25 examples). Each section begins This book is unique among all other books treating band with a clear and sensible discussion of the general principles theory because of its emphasis on the use of symmetry. involved, and ends with an extensive bibliography of the T o this reviewer’s mind the use of group theory is a great original literature. The individual directions appear to advantage; it enables one t o distinguish clearly between the contain just about the right amount of detail, and the parts of the subject which are indisputably correct such as authors state that most have been checked, either by themselection rules and those which depend on approximations. selves or their associates. Physical chemists on the average are more used to thinking I n addition to its utility for practicing polymer chemists, in terms of group theory than are physicists, and this book this book should provide a splendid basis for a laboratory should appeal especially to them for this reason. It is uncourse in polymer chemistry (or as a source of individual ex- fortunate that the unsystematic notation for representations perimcnts i l l a n organic chemistry cnurse) and the authors used b>*d i d s t a t e physiciqtq was used instead of the Mullia

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ken notation which has become well established in molecular physics and chemistry. However, anyone conversant with point groups can easily make the changes Although the book is mainly a mathematical text, physical facts are brought in t o illustrate important points and t o maintain interest in the mathematical results. The book does not give a discussion of the limits of validity of the oneelectron band theory nor of exciton levels. In the reviewer’s opinion, a student who has had no previous exposure t o the theory of point groups would have difficulty with this book; however, a relatively simple briefing on groups of symmetry operations and their iise in constructing symmetrized functions should be sufficient introduction. The book is highly recommended t o serious students of chemistry who wish t o gain a n appreciation of the electronic structure of crystalline solids.

This is a book of chemical data and analytical methods, largely without detailed prescriptions. Most of the methods are classical with a small admixture of recently reported reagents; one must not expect a compilation of the latest precipitants or color reagents. I n this Reviewer’s opinion the book is a useful contribution to analytical literature, an excellent classical test for qualitative courses a t the university level, and a distinct asset t o any chemical library. DIVISIONOF ANALYTICAL RESEARCH F. E. BEAMISTI UNIVERSITY OF TORONTO TORONTO 5, CANADA

Advances in Organic Chemistry. Methods and Results. Volume 11. Edited by RALPHA. RAPHAEL,The University, Glasgow, Scotland, EDWARD C. TAYLOR,Princeton DOSALDS XCCLL-RE University, Princeton, New Jersey, and HANS~VYNBERG, Kijksuniversiteit, Leiden, The Netherlands. Interscience Publishers, Inc., 250 Fifth Avenue, New York 1, N. Y. 504 pp. 16 X 23.5 cm. Price, $15.00. 1960. vii Physiko-chemische Grundlagen und Tabellen zur QualitaThis second volume of what promises t o be a most useful tiven Analyse (Mit Ausnahme der Gasanalyse). By W. D. and stimulating series on new developments in organic TREADWELL. Nach dem Tode des Verfassers herausge- chemistry continues the high standard of excellence set by geben von Prof. Dr. 0. Giibeli, Zurich, und Dr. W. Volume I. The objective of the editors is a series of volumes Prodinger, Wien. Verlag Franz Deuticke, Helferstorfer- containing articles providing a critical appraisal and evalu236 pp. 17.5 X strasse 4, Wien I, Austria. 1960. xi ation of new aspects of organic chemistry ripe for further 24.5 cm. Price, ost. S 168.-. development and of novel extensions t o well-established “By their fruits you shall know them” remairis an infal- methods, ideally by the originator of the method described lible standard by which one may measure accurately the or a practitioner expert in its use. This objective is very well realized in Volume 11. capacity and usefulness of an individual in any sphere of The topics covered and the authors are the following: activity. Against a background of multitudinous analytical Alkenylmagnesium Halides (65 pp.) by H. Normant (Paris); methods and much chemical triviata, the researches of W. D. Treadwell are a convincing reassurance that the Dialkoxydihydrofurans and Diacycloxydihydrofurans as analytical researcher need not be merely a sharpener of tools Synthetic Intermediates (49 pp.) by Niels Elming (Copenbut may possess inherently a distinct approach to chemical hagen); Ethynyl Ethers and Thioethers as Synthetic Intermediates (96 pp.) by J. F. Arens (Utrecht); Ketene in problems. Organic Synthesis (51 pp.) by R. N. Lacey (Hull, England); Unmistakably, Treadwell’s “Qualitative Analysis” indiNuclear Magnetic Resonance in Organic Structural Elucicates the direction which can be given to the solving of analytical problems by a n adequate accumulation and inte- dation (64 pp.) by Harold Conroy (New Haven, Conn.); Hydrogenation-Dehydrogenation Reactions (38 pp.) by gration of descriptive material. Perhaps a rearrangement of the title t o emphasize analytical aspects would more appro- L. M. Jackman (London); Ultraviolet Photochemistry of Simple Unsaturated Systems (59 pp.) by Paul de Mayo priately describe the content of the book. With a total of (London, Canada); The Chemistry of Muscarine (29 pp.) 231 pages, approximately 54 pages are concerned with explanations for some three dozen physical chemical terms by C. H. Eugster (Zurich). Alkenylmagnesium halides represent a most useful addias well as tables of such physical constants as activity coeffition t o synthetic methods involving the Grignard reagent; cients, solubility products, dissociation constants, and this brief review is timely. Dialkoxydihydrofurans and optimum acidities for precipitation, etc., of chemicals related Diacycloxydihydrofurans are of more limited value but to analytical procedures. The remainder of the book, in deserve the attention this review will focus on them. The five sections, deals with methods of approach and prelimichapter on ethynyl ethers and thioethers, the most exhausnary examinations of materials with a view to qualitative separations of the common elements extended to include tive review in this volume, is an important survey of all of such metals as uranium, gold, titanium, molybdenum, etc. the work on these compounds and admirably illustrates their general utility. Ketene is an old chemical but new aspects The procedure, preceded also by a detailed description of the physical and chemical properties of the elements in- of its chemistry make its inclusion here appropriate; the sections on isopropenyl acetate and 8-propiolactone are volved, is largely the classical chloride-sulfidecarbonate separation with the final methods of identification involving especially interesting. Nuclear magnetic resonance is probably the most impora few of the more effective recently developed reagents. il similarly complete qualitative scheme for anions is included. tant new development included in this volume. The theFor those metals not included in the qualitative schemes, oretical part is somewhat too condensed to be easily underthe author has supplied a supplement. I n this section the stood but the examples are well chosen to illustrate the scope the method. physical properties, precipitants, methods of dissolution and of Only a small portion of the field of hydrogenation-dehyseparation are listed for the alkali metals, lanthanide series, drogenation reactions is covered in the sixth chapter-that and the rarer metals of the sulfide group. Momentarily, with homogeneous hydrogen transfer between one’s enthusiasm for this book is tempered by the contents dealing of the final page. One cannot associate the proved compe- organic molecules without catalysis by inorganic derivatives. Short sections on catalytic, photochemical and tence and thoroughness of the author’s work, here and else- biochemical hydrogen transfer are barely illustrative. where, with the antiquated procedure for the separation of Probably the most provocative topic is ultraviolet photothe noble metals of column “111. Neither the author nor chemistry of simple unsaturated systems. Photolysis any one else has yet succeeded in separating ruthenium by promises to be of increasing importance in organic chemistry heating in oxygen at 700’. This small section of the volume and the examples reviewed suggest much further work. is of little value. The final chapter on the chemistry of muscarine presents Furthermore, the book may not be acceptable to those who, for either pedagogical or practical purposes, require a concise review of the application of modern and older methods to structure elucidation of a simple but intractable some integration of the empirical separational procedures molecule. A better choice might have been made to illustrate such as chromatography or ion exchange techniques. It application of modern techniques to such problems, h u t would seem that the author could profitably have made some the the chapter is well written and interesting. concession t o the more effective ion exchange methods, even at the expense of reduced instructional value. This would CHEMISTRYDEPARTMENT have improved the out-dated section dealing with the sepnruUNIVERSITY OF CALIFORNIA AT Los ANCELES TrrvhfAS L. JACOBS tion of the lanthanide metals. Los XXGELES21, CALIPORNIA RCA LABORATORIES RADIOCORPORATION OF AMERICA PRINCETON, NEW JERSEY

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