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Statistical mechanics
Book reviews
747
any of the impurities there listed. In the last decade, however, a quiet revolution has been taking place in the standards of purity of commercial chemicals, and many elements and compounds can now be obtained with a total impurity content of only a few parts per million. The demand for these, arising from industry, universities and gove~ment departments, has been met by means of new techniques of por&cation (zone mehing, ion exchange, etc.), with the help of new and extremely refined methods of purity control (such as vapour phase chromatography). This report describes what happened when attempts were made to prepare very pure metals by the decomposition of organometallic compounds. These were thought to offer some promise because their volatility allows them to be purified by physical methods not suitable for most of the inorganic compounds of the metals. The standard of purity aimed at was a content of less than OWl ppm of any impurity. Full success was achieved only with mercury, which was formed in a state of absolute spectroscopic purity by the photolysis of diethyl mercury. The pyrolysis of rhenium and nickel carbonyls gave metal samples of good purity, but not nearly approaching the O.Wl-ppm standard. Impure magnesium was obtained by the electrolysis of ethyl magnesium hydride. No results of any value were obtained with organocalcium and organogallium compounds. The whole report is of an exploratory character; none of the investigations described could be regarded as exhaustive or final; and much of its value lies in the guidance it will give to future experimenters. H.G. HEAL
Statistical Mechanics. NORMANDAVIDSON. McGraw-Hill Publishing Co. Ltd., London: Hill Book Company, Inc., New York, 1962. pp. ix + 540. E5.12.6. STATISTICALmechanics are concerned
McGraw-
with the derivation of the macroscopic properties of materials, such as pressure, heat capacity, entropy, magnetic susceptibihty, etc. from a knowledge of the quantum state accessible to the atoms or molecules making up the material. Often the calculation of the macroscopic property by the methods of statistical mechanics is easier than direct measurements: in all cases statistical mechanics provide the theoretical link between the two types of knowledge and thus indicates what are the important atomic or molecular factors that determine the macroscopic property. Applications of methods of statistical mechanics to problems in analytical chemistry are as yet few : one such is the appli~tion to the equilibria of isotope fractionation reactions. By their nature, statistical mechanics are mathemati~l and depend upon the logically prior subjects of classical mechanics and quantum mechanics. At the same time the subject has many and diverse applications in physics and chemistry. To write a successful book on statistical mechanics for chemists is, therefore, not easy. Professor Davidson, in his book, presents the fundamentals and main applications of the subject lucidly and thoroughly. The book will be valuable to the chemist who wishes to understand the mathematical and theoretical basis of the subject and who is prepared to read the text carefully and to work through at least those of the problems which are interspersed in the main text. Ma~emati~ of appro~mat~ly university summary standard is require. Professor Davidson devotes quite a large part of the book to concise accounts of subjects which are either logically prior to statistical mechanics, such as classical mechanics and quantum mechanics, or subjects like spectroscopy and the activity coefficients of ions in solution, of which a knowledge is needed for the application of statistical mechanics in the system considered. Generally these accounts are good, though the reviewer feels that many topics are discussed so concisely that the reader who is not previously acquainted with (to take a few examples) Lagrange’s and Hamilton’s equations of motion, quantum mechanical operators or the calculation of the vibration frequencies of polyatomic molecules, will find the going difhcult. In a few cases the presentation could be improved. The reader might well spend considerable time puzzling over equation (3-6d) without reading the further half page necessary to discover that the rule he or she had been trying to apply, given on the previous page, did not hold in this case. Omission of “. . .” made several equations (from a pedantic viewpoint) not true. In places it seemed to this reviewer that the treatment tended to be unnecessarily austere, and that the mathematical bare bones were not sr&iciently covered with chemical fact : perhaps an example of thii tendency is the single seventeen-year-old reference given on p. 194 to (pr~umably) data on characteristic vibration frequencies. These are, however, minor criticisms of a well-written, useful and thorough book: the fact that it is written as a standard classroom textbook for graduate students in America is food for thought for those who teach students elsewhere. A. D. E. PULLIN
747
any of the impurities there listed. In the last decade, however, a quiet revolution has been taking place in the standards of purity of commercial chemicals, and many elements and compounds can now be obtained with a total impurity content of only a few parts per million. The demand for these, arising from industry, universities and gove~ment departments, has been met by means of new techniques of por&cation (zone mehing, ion exchange, etc.), with the help of new and extremely refined methods of purity control (such as vapour phase chromatography). This report describes what happened when attempts were made to prepare very pure metals by the decomposition of organometallic compounds. These were thought to offer some promise because their volatility allows them to be purified by physical methods not suitable for most of the inorganic compounds of the metals. The standard of purity aimed at was a content of less than OWl ppm of any impurity. Full success was achieved only with mercury, which was formed in a state of absolute spectroscopic purity by the photolysis of diethyl mercury. The pyrolysis of rhenium and nickel carbonyls gave metal samples of good purity, but not nearly approaching the O.Wl-ppm standard. Impure magnesium was obtained by the electrolysis of ethyl magnesium hydride. No results of any value were obtained with organocalcium and organogallium compounds. The whole report is of an exploratory character; none of the investigations described could be regarded as exhaustive or final; and much of its value lies in the guidance it will give to future experimenters. H.G. HEAL
Statistical Mechanics. NORMANDAVIDSON. McGraw-Hill Publishing Co. Ltd., London: Hill Book Company, Inc., New York, 1962. pp. ix + 540. E5.12.6. STATISTICALmechanics are concerned
McGraw-
with the derivation of the macroscopic properties of materials, such as pressure, heat capacity, entropy, magnetic susceptibihty, etc. from a knowledge of the quantum state accessible to the atoms or molecules making up the material. Often the calculation of the macroscopic property by the methods of statistical mechanics is easier than direct measurements: in all cases statistical mechanics provide the theoretical link between the two types of knowledge and thus indicates what are the important atomic or molecular factors that determine the macroscopic property. Applications of methods of statistical mechanics to problems in analytical chemistry are as yet few : one such is the appli~tion to the equilibria of isotope fractionation reactions. By their nature, statistical mechanics are mathemati~l and depend upon the logically prior subjects of classical mechanics and quantum mechanics. At the same time the subject has many and diverse applications in physics and chemistry. To write a successful book on statistical mechanics for chemists is, therefore, not easy. Professor Davidson, in his book, presents the fundamentals and main applications of the subject lucidly and thoroughly. The book will be valuable to the chemist who wishes to understand the mathematical and theoretical basis of the subject and who is prepared to read the text carefully and to work through at least those of the problems which are interspersed in the main text. Ma~emati~ of appro~mat~ly university summary standard is require. Professor Davidson devotes quite a large part of the book to concise accounts of subjects which are either logically prior to statistical mechanics, such as classical mechanics and quantum mechanics, or subjects like spectroscopy and the activity coefficients of ions in solution, of which a knowledge is needed for the application of statistical mechanics in the system considered. Generally these accounts are good, though the reviewer feels that many topics are discussed so concisely that the reader who is not previously acquainted with (to take a few examples) Lagrange’s and Hamilton’s equations of motion, quantum mechanical operators or the calculation of the vibration frequencies of polyatomic molecules, will find the going difhcult. In a few cases the presentation could be improved. The reader might well spend considerable time puzzling over equation (3-6d) without reading the further half page necessary to discover that the rule he or she had been trying to apply, given on the previous page, did not hold in this case. Omission of “. . .” made several equations (from a pedantic viewpoint) not true. In places it seemed to this reviewer that the treatment tended to be unnecessarily austere, and that the mathematical bare bones were not sr&iciently covered with chemical fact : perhaps an example of thii tendency is the single seventeen-year-old reference given on p. 194 to (pr~umably) data on characteristic vibration frequencies. These are, however, minor criticisms of a well-written, useful and thorough book: the fact that it is written as a standard classroom textbook for graduate students in America is food for thought for those who teach students elsewhere. A. D. E. PULLIN