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.
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