Acta metall, mater. Vol. 39, No. 7, pp. 1657-1665, 1991 0956-7151/91 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright © 1991 Pergamon Press plc ALTERNATIVE LENGTH SCALES FOR POLYCRYSTALLINE MATERIALS--I. MICROSTRUCTURE EVOLUTION C. S. NICHOLSI', R. F. COOK, D. R. CLARKE and D. A. SMITH IBM Research Division, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A. (Received 7 September 1990) Abstract--It is a well-documented experimental observation that properties of grain boundaries depend on the atomic structure of the boundary. Yet constitutive relations for properties of polycrystalline materials containing a variety of grain boundaries currently do not take account of this boundary-to- boundary variability. Instead, a single-length scale---the average grain diameter is utilized with the underlying assumption that all grain boundaries are the same. In this (I) and the following paper (II), we extend the accepted veiwpoint to encompass a binary classification of grain boundaries based on their misorientation angle. The resultant new length scale is that associated with clusters of grains linked by grain boundaries sharing misorientations in the same category. This first paper focuses on how a model polycrystal is generated, the energetics of the model, and its evolution under various external influences. Rrsumr---I1 est prouv6 exprrimentalement que les proprirtrs des joints de grains drpendent de la structure atomique du joint. Cependant les relations constitutives relatives aux proprirtrs des matrriaux poly- cristallins contenant un grand nombre de joints de grains ne tiennent grnrralement pas compte de la variabilit6 de joint a joint. A la place, on utilise une seule 6,chelle de longueur--le diamrtre moyen des grains--avec l'hypothrse sous-jacente que tousles joints de grains sont identiques. Dans les parties Iet II de cet article, nous 6tendons ce point de vue pour proposer une classification binaire des joints de grains basee sur leur angle de drsorientation. La nouvelle 6chelle de longueur rrsultante est associre aux amas de grains lirs par des joints partageant des drsorientations de mrme catrgorie. Le premier article prrsente un polycristal modele, les aspects 6nergrtiques du modrle et son 6volution sous diverses influences exterieures. Zusammenfassnng--Eine wohlbekannte experimentell Beobachtung ist, dab die Eigenschaften der Korngrenzen von der atomaren Struktur abh/ingen. Allerdings beriicksichtigen bisher die Grundbeziehungen zur Beschreibung der Eigenschaften polykristalliner Materialien, die eine Vielfalt von Korngrenzen enthalten, diese Zusammenh/inge nicht. Stattdessen wird einfacher L/ingenmaBstab, n/imlich der mittlere Korndurchmesser, benutzt; dahinter steht die Annahme, dab alle Komgrenzen gleich sind. In dieser (I) und der nachfolgenden (II) Arbeit erweitern wir den akzeptierten Standpunkt, um eine bin/ire Klassifikation der Korngrenzen auf der Basis ihrer Fehlorientierungswinkel einzuarbeiten. Der sich ergebende neue L/ingenmaBstab h/ingt zusammen mit Kornhaufen, die fiber Korngrenzen mit Fehlorientierungen derselben Kategorie zusammenh/ingen. 1. INTRODUCTION It is well established that the physical, mechanical and chemical properties of a polycrystalline material differ markedly from those of the same material in single-crystal form. Yet, historically, the relationship between the properties of a polycrystal and its con- situent grains and grain boundaries has been some- what obscure. There are two general divergent lines of research. One approach is to formulate scaling laws for how properties depend on a length scale linearly related to the average grain size and, often, assumed to be the average grain size, d, which implies that all grain boundaries are the same. Specific tPresent address: Cornell University, Department of Materials Science and Engineering, Ithaca, NY 14853, U.S,A. examples of such relationships include the Hall-Petch relationship for plastic yield stress, a ocd-l/2; the Coble relationship for the strain rate in grain- boundary-diffusion-controlled creep, ~ocd-3; the Herring-Nabarro relationship for the strain rate in lattice-diffusion-controlled creep, ~ ocd-2; and the Fuchs' expression for resistivity, p oc d-l. There exist, however, many failings of these expressions. In par- ticular, there is ample experimental evidence that boundaries have distinctly different properties that depend on one or more interface degrees of freedom [1-14]. The second approach is to focus on "proto- typar' boundaries with the expectation that their properties are somehow generalizable to an arbitrary interface. The necessity remains, of course, to syn- thesize the information about individual boundaries and grains into a description of the polycrystal. 1657