American Ceramic Society Bulletin

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Save the Date! Materials Science & Technology 2011 Conference & Exhibition OCTOBER 16–20 COLUMBUS, OHIO, USA www.matscitech.org Plenary Session Announced! Dr. Subra Suresh, Director of the U.S. National Science Foundation, will discuss the importance of the U.S.’s science & technology work force, followed by several prominent speakers on related topics. More information coming soon! ®The leading forum addressing structure, properties, processing and performance across the materials community. Organized by: ACerS | AIST | ASM | TMS Co-sponsor: NACE
Topological constraint theory of glass Topological constraint theory describes how microscopic physics governs the thermal, mechanical and rheological properties of glass and has proved to be a powerful tool for predicting the composition and temperature dependence of glass properties. John C. Mauro A microscopic physical description of the glassy state long has eluded even the top scientists in condensed matter physics because of the complicated noncrystalline nature of glass structure. Currently, many theorists turn to molecular dynamics or other atomistic simulations to determine the structure of various glass compositions. However, although available computing power has increased exponentially during the past several decades, it will be at least another 20 to 30 years before enough computing power is available for direct molecular dynamics simulations of glass on a realistic laboratory time scale. Fortunately, topological constraint theory provides another path forward. It focuses on the important microscopic physics governing the thermal, mechanical and rheological properties of glass, while filtering out unnecessary details that ultimately do not affect its macroscopic properties. Topological constraint theory has been successful in predicting the composition dependence of glass properties and can be used as a tool to enable the quantitative design of new glass compositions. American Ceramic Society Bulletin, Vol. 90, No. 4 Introduction Although perhaps better known, in general, for his later work on X-ray diffraction in crystals, Zachariasen’s only paper on the structure of glass 1 established him, at 26 years of age, as the father of theoretical glass science for the century to come. Zachariasen began his famous 1932 paper on the structure of glass with the humble remark, “It must be frankly admitted that we know practically nothing about the atomic arrangement in glasses.” What followed was a brilliantly insightful analysis of glass structure as a disordered network of polyhedral units. The polyhedra themselves define the short-range order of the atomic arrangement in glass, whereas the random connectivity of the polyhedra gives rise to long-range disorder. Based on this picture, Zachariasen postulated four rules of glass formation for an arbitrary oxide compound A m O n : • An oxygen atom is linked to no more than two A atoms; • The oxygen coordination around A is small; • The cation polyhedra share corners, not edges or faces; and • At least three corners are shared (for a three-dimensional network). Zachariasen’s theory essentially amounts to a list of topological conditions for formation of a macroscopic disordered network. These conditions were analyzed in detail by Cooper, 2,3 who determined that Zachariasen’s first two rules are sufficient to enable formation of a glassy network. The third and fourth rules are unneces- 31
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