Quantitative principles of silicate glass chemistry R. Kerner a , J.C. Phillips b, * a Lab. Grav. and Cosmol. Relat., Univ. P. and M. CurieÐCNRS ESA 7065, 75005 Paris, France b Bell Laboratories, Lucent Technologies, 700 Mountain Avenue, Murray Hill, NJ 07974-0636, USA Received 1 August 2000; received in revised form 11 September 2000; accepted 15 September 2000 by S.G. Louie Abstract The optimal compositions of many commercial glasses (such as window glass) are close to the ternary 74SiO 2 ±16Na 2 O± 10CaO. Constraint theory determines the contributions of the modi®ers Na 2 O and CaO to network formation. Unexpectedly, the mechanical aspects of ionic oxide glasses are found to be quite similar to those of covalent chalcogenide glasses, which consist of network formers alone. The theory identi®es old critical experiments and predicts new ones. It correctly determines the composition of window glass, one of nature's most remarkable materials, without adjustable parameters. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Disordered materials; D. Melting; D. Phase transitions; D. Thermal expansion PACS: 61.43.Fs; 64.70.Pf; 81.05.Je It is dif®cult to imagine civilization without the various disciplines of materials science, from metallurgy to semi- conductor microelectronics and microphotonics. The chemistry of metallic alloys is described well by quantum structural diagrams [1] and that of semiconductors by the dielectric theory of chemical bonding and the covalent± ionic transition [2] as well as by pseudopotential theory [3], which is the basis of band-structure engineering. A similar quantitative theory of the chemistry of silicate (window) glass, which is central to ceramics, has yet to be developed, although excellent qualitative descriptions of the subject [4] are widely used. Here we will show that the constraint theory of network glasses [5±9], hitherto largely applied to covalent chalcogenide alloy glasses [10], is quantitatively successful in describing the compositions of ionic silicate glasses of technological importance. Although an apparently very large data base exists for the properties of these multinary glasses [11±13], the data base is frag- mentary and has been formed haphazardly over many decades in the absence of quantitative theoretical guidance. The present theory suggests a number of systematic research directions, and many others should emerge if the initial successes reported here are con®rmed. The quantitative successes of constraint theory for the chalcogenide glasses have depended primarily on its abstract nature. Instead of constructing ball-and-stick models of the glassy network, and then attempting to relate these models to observed properties, the theory focuses on the forces that determine the metastable equilibrium posi- tions of N atoms in the quenched glass. One further assumes that the interatomic forces of the network are of two kinds, ionic and covalent, and can be hierarchically arranged in the order of decreasing strength. For a given composition, ionic forces may favor a higher degree of chemical ordering (alternating cations and anions) and larger average bond angles. Usually, this ordering and the increased bond angles have little effect on the counting of con®gurations and in the absence of nanoscale phase separation, both are usually incidental to chemical trends. The relevant short-range covalent forces are of two kinds, bond-stretching and bond bending. If we construct the line- arized rectangular Lagrangian matrix for N locally unstrained atomic coordinates, it will have Nd (with d  3 columns, and Nn s 1 n b  rows, where n s (n b ) is the number of stretching (bending) forces (or constraints)/ atom. Matrix theory tells us that when the network is under- constrained, there will be Nd±n s ±n b  cyclical (or ¯oppy) Solid State Communications 117 (2001) 47±51 0038-1098/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S0038-1098(00)00403-8 PERGAMON www.elsevier.com/locate/ssc * Corresponding author. Tel.: 11-908-582-2528; fax: 11-908- 582-4702. E-mail address: jcphillips@bell-labs.com (J.C. Phillips).