Electronic Basis of the Strength of Materials

Electronic Basis of the Strength of Materials , John Gilman  Cambridge U. Press, New York, 2003. $95.00 (280 pp.). ISBN 0-521-62005-8

What underlying effects lead to the inherent strength of a solid? Can a material’s response (elastic or plastic, for example, under applied stress) exhibit universal scaling behavior in terms of basic electronic quantities? Can such scaling behavior be explained from simple chemistry and physics principles?

Such questions have been under scrutiny for more than a century as cohesion and strength properties (really, a collection of properties) of materials have guided the development of several engineering disciplines and applications—whether structural (improved steels or turbine blades, for example) or microelectronic devices. Of course, the strength of a particular material, gleaned by science or alchemy, has been used for millennia without an understanding of its origin. Progress toward comprehending the strength of materials in terms of their microscopic mechanisms has been slow, in part, because the plastic deformation rate from small strains or shock loading varies by more than 30 orders of magnitude—just like electrical conductivity!

In Electronic Basis of the Strength of Materials , John Gilman addresses such issues by showing relationships between electronic structure of solids and ensuing mechanical properties. In most undergraduate textbooks on mechanical properties, the one example of a universal trend governed by bonding is, in fact, taken from Gilman’s Micromechanics of Flow in Solids (McGraw-Hill, 1969). A log–log plot of the bulk modulus B, which quantifies a material’s volume response to hydrostatic stress, versus the equilibrium atomic spacing r ₀ yields a universal slope of –4 for ionic solids. The universal slope arises from the Coulomb potential’s (U ∼ r ⁻¹) dominant effect on B (defined as −V ₀[∂² U/∂V ²]₀, with V ₀ ∼ r ₀ ³). Remarkably, the same universal slope is also found for alkali metals and many tetrahedral covalently bonded crystals, as originally shown by Gilman in Micromechanics of Flow in Solids.

Now, after 40-plus years of studying the response of materials to applied stress, Gilman, in his new book, offers his unique perspective to provide simple, unifying concepts that connect a variety of observations. Electronic properties of particular relevance to strength are valence-charge density and electronic polarizability. Gilman, via simple arguments, shows such inherently quantum properties provide broad trends for elastic moduli (chapter 12), shear moduli (chapter 13), and dislocation mobility (chapter 18). But he also discusses other macroscopic responses driven by electronic effects, including chemical hardness in molecular systems (related to molecular-orbital gaps), ionization energy in non-metals (related to band gaps), and plasmons in many other materials.

The plasmon picture is rarely discussed in Gilman’s book but leads to observed trends, such as the linear relation with slope –4 found when plotting ln(B) versus ln(r ₀); standard effective-mass arguments, in contrast, predict a slope of –5. There are other small jewels for the reader to explore, including the answer to the good preliminary-exam question, Why do simple metals form body-centered crystals instead of close-packed structures? Gilman provides brief historical perspectives and a plethora of important, original references—the kind of referencing often not done properly because of the use of internet search engines whose information reaches only to the predawn of the 1960s.

I would, however, be remiss not to discuss the book’s shortcomings. For one, the publisher should have provided a biographical overview of the author to intimate to readers Gilman’s professional qualifications. In addition, few recent references, except those of the author, are provided. Although typeset using LaTeX, the book’s many equations are difficult to read. Improved editing is needed in several instances; for example, in chapter 4, elastic coefficients and ratios are introduced with terse descriptions that would benefit from a figure, but the figure does not appear until chapter 13. Also, the variable δ is used multiple times for different things. Oddly enough, the book just ends: No summary exists to tie discussions together. Finally, electronic-structure methods have recently addressed the strength of materials, such as ideal shear strength, and researchers are using those methods to help relate strength to structure defects and electronic properties, including changes in bonding topology. Because such issues are addressed in the book, it would have been worthwhile for Gilman to have made some connection to electronic-structure methods—especially because those methods will eventually affect mechanical modeling.

Because solids are, by nature, complex, Gilman offers a view that it is better to make approximations first—sometimes drastic ones—and provide simple calculations that are consistent with the rules of quantum mechanics and still yield properties in agreement with observation. In fact, Gilman uses only basic stress–strain relations, elasticity theory, Coulomb’s law, the Heisenberg uncertainty principle, and simple quantum mechanics. All the concepts are presented in the initial eight chapters concisely (sometimes too much so) and with undergraduate-level mathematics. Hence the book should be accessible to advanced undergraduate students. Even so, I am dubious whether Gilman’s book would, as the publisher claims, serve well as a supplementary text for teaching solid mechanics—that is, unless students have a good background in quantum mechanics and solid-state physics.

Nonetheless, whether intended for students trying to understand the basic origin of trends in strength of materials or for veteran researchers searching for a broader perspective, Gilman’s book offers a one-of-a-kind contribution based on his lifetime of scholarship and his unique point of view. His contribution is our gain, and, for those interested in the field, Electronic Basis of the Strength of Materials is a worthy read.