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Physical properties of crystals: Their representation by tensors and matrices
BOOK J. F. NYE: Physical Properties of Crystals: Their Representation by Tensors and Matrices, Clarendon Press, Oxford, 322 pp., %r8.00.
THERE is no other text in English with which to compare this book. The nearest text is W. VOIGT’S ~e~r~~ der ~y~t~l~hys~k, published in 1910. W. G. CADY’S book Piexoelectricity published in 1946 is, as the title indicates, primarily concerned with piezoelectricity and W. P. MASON’S book Piezoelectric Crystals and their Applications to Ultrasonics, published in 1950 is more concerned
with engineering uses of crystals. CADY’S book is rather an encyclopedia of piezoelectricity and related matters. Since crystal physics is now considered to be more important than it was in 1910, and nomenclature has matured since then, a text with the academic viewpoint and modern nomenclature should be well received, NYE’S book is a systematic exposition on anisotropy as it applies to crystals. This reviewer wishes that the thirty-two point groups (into which crystals are classified by symmetry) were discussed early in the book instead of being left to the appendix. This would make the book seem to be more about crystals than about tensors. The first forty-eight pages develop the ideas of Cartesian tensors, then these tensors are used to relate vector properties to other vector properties, the refations forming tensor properties. Tensor properties are then related to other tensor properties, these relations forming tensors of higher rank. In this way we find related to one another: magnetic field strength, magnetic induction, stress, strain, temperature, entropy, electric field and electric displacement. This entails the study of magnetic susceptibility, electric polarization, pyroelectricity, thermal expansion, piezoelectricity, the
REVIEW
converse piezoelectric effect, elasticity, thermoelectricity, conductivity the electro-optic effect, the photo-elastic effect and optical activity. About midway through the book matrices are introduced as a more compact representation that saves time in actual computation. A few sample calculations are presented. One gets the feeling that matrices are inferior to tensors since they are not necessarily tensors. This reviewer believes that tensors are an algebraic extension of geometry while matrices are pure algebra and not less powerful than tensors. Is this book physics or applied mathematics? The spirit is mathematical but the usefulness is to physicists. This book could serve as a limited introduction to tensors-limited because Cartesian tensors lack the beautiful generality of general tensors. They iack it just because they are conceived entirely on right angles. However, most physical properties are always best expressed in rectangular co-ordinates and general tensors are much more complicated than Cartesian tensors. Hence crystal physics problems play right into the “hands” of Cartesian tensors. Triclinic assymmetric crystals have no symmetry but such physical properties as elastic effects are not more clarif?ed by general tensors than by Cartesian tensors, Rowever, some crystal geometry problems are simplified by the more general approach. The problems of anisotropy in crystals are complex-such problems as the rotations of axes and what these rotations do to the numbers that represent, for example, the twenty-one independent elastic constants of a triclinic crystal. This book gives a systematic and useful treatment of these problems. W. L. BOND
338
THERE is no other text in English with which to compare this book. The nearest text is W. VOIGT’S ~e~r~~ der ~y~t~l~hys~k, published in 1910. W. G. CADY’S book Piexoelectricity published in 1946 is, as the title indicates, primarily concerned with piezoelectricity and W. P. MASON’S book Piezoelectric Crystals and their Applications to Ultrasonics, published in 1950 is more concerned
with engineering uses of crystals. CADY’S book is rather an encyclopedia of piezoelectricity and related matters. Since crystal physics is now considered to be more important than it was in 1910, and nomenclature has matured since then, a text with the academic viewpoint and modern nomenclature should be well received, NYE’S book is a systematic exposition on anisotropy as it applies to crystals. This reviewer wishes that the thirty-two point groups (into which crystals are classified by symmetry) were discussed early in the book instead of being left to the appendix. This would make the book seem to be more about crystals than about tensors. The first forty-eight pages develop the ideas of Cartesian tensors, then these tensors are used to relate vector properties to other vector properties, the refations forming tensor properties. Tensor properties are then related to other tensor properties, these relations forming tensors of higher rank. In this way we find related to one another: magnetic field strength, magnetic induction, stress, strain, temperature, entropy, electric field and electric displacement. This entails the study of magnetic susceptibility, electric polarization, pyroelectricity, thermal expansion, piezoelectricity, the
REVIEW
converse piezoelectric effect, elasticity, thermoelectricity, conductivity the electro-optic effect, the photo-elastic effect and optical activity. About midway through the book matrices are introduced as a more compact representation that saves time in actual computation. A few sample calculations are presented. One gets the feeling that matrices are inferior to tensors since they are not necessarily tensors. This reviewer believes that tensors are an algebraic extension of geometry while matrices are pure algebra and not less powerful than tensors. Is this book physics or applied mathematics? The spirit is mathematical but the usefulness is to physicists. This book could serve as a limited introduction to tensors-limited because Cartesian tensors lack the beautiful generality of general tensors. They iack it just because they are conceived entirely on right angles. However, most physical properties are always best expressed in rectangular co-ordinates and general tensors are much more complicated than Cartesian tensors. Hence crystal physics problems play right into the “hands” of Cartesian tensors. Triclinic assymmetric crystals have no symmetry but such physical properties as elastic effects are not more clarif?ed by general tensors than by Cartesian tensors, Rowever, some crystal geometry problems are simplified by the more general approach. The problems of anisotropy in crystals are complex-such problems as the rotations of axes and what these rotations do to the numbers that represent, for example, the twenty-one independent elastic constants of a triclinic crystal. This book gives a systematic and useful treatment of these problems. W. L. BOND
338