QUANTITATIVE ANALYSIS OF SPATIAL DISTRIBUTION OF NUCLEATION SITES: MICROSTRUCTURAL IMPLICATIONS W. S. TONG, J. M. RICKMAN{ and K. BARMAK Department of Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015, U.S.A. (Received 28 July 1998; accepted 20 October 1998) AbstractÐVarious computational schemes for the determination of nucleation conditions from fully coa- lesced product microstructures are examined. In particular, a variety of types of nucleation sites, including those on the edges and corners of an underlying structure, are considered. The analysis is facilitated by simulating idealized cases wherein the nucleation conditions are known. In cases where only one type of site is active, the spatial distribution of nucleation sites is quanti®ed in terms of neighbor distributions and correlation functions. In cases of multiple types of site potency, maps revealing important microstructural behavior and trends are constructed. It is found that the dimensionality of the subspace of sites on which nucleation occurs can be described and thereby the unique signatures of bulk, edge and corner nucleation in the calculated quantities can be identi®ed. The results of the simulations allow possible nucleation con- ditions to be identi®ed which give rise to a given experimental microstructure. # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION Materials scientists have traditionally been inter- ested in characterizing complex polycrystalline sys- tems and have therefore recognized the importance of quantitative stereological analysis of microstruc- tures involving an assessment of size and shape of the constituent grains as well as the geometry of the associated grain boundaries [1±4]. Depending on the length scale of the system under consideration, various experimental techniques, including both optical (mm to mm) and electron microscopy (nm to mm), can be employed in microstructural interrog- ation. In systems of limited spatial dimensionality, having characteristic lengths of from 1 nm to 1 mm, microstructural quanti®cation is particularly im- portant as reliability and performance are greatly in¯uenced by speci®c microstructural features rather than by average, bulk properties [5]. This is particu- larly true, for example, in thin ®lms wherein domi- nant microstructural features are determined by deposition or reactive phase formation. Indeed, the functionalities of many important electronic devices and information storage media depend critically on the properties of thin metallic ®lm systems. A complete picture of microstructural develop- ment following a phase transformation often necessitates a detailed consideration of nucleation and growth issues. A classic metallurgical example of the interdependence of such phenomena is the catalytic nucleation of a solid phase in castings employing innoculants designed to promote uni- form, equiaxed grain structures. More recently, nu- merous experimental probes, including calorimetry and electron microscopy, have underlined the im- portance of both nucleation and growth in thin ®lm reactions, evolving our views of such processes beyond simpler one-dimensional growth models [6]. Unfortunately, given that nucleation often occurs catastrophically over a rather narrow temperature range, it is generally quite dicult to isolate spatially and temporally a signi®cant fraction of nucleation events and to deduce, for example, the relative potency of various catalysts (e.g. grain boundaries) in a solid-state transformation. In such circumstances one is faced with the problem of inferring nucleation information from a complex, transformed structure. This paper will examine various computational schemes for the a posteriori determination of nucleation conditions in a solid-solid transform- ation. These schemes employ useful relationships from stochastic geometry to extract this information from two-dimensional computer simulations of nucleation and growth to impingement. Our analy- sis will be based on the observation that the micro- structures obtained during these simulations can be viewed in terms of point processes with a particular distribution of generators. The statistical properties of these point processes, as embodied in multi-point correlation functions, re¯ect the spatial distribution of the associated generators and can therefore pro- vide considerable information as to the dimension- ality of the nucleation subspace. In this work we Acta mater. Vol. 47, No. 2, pp. 435±445, 1999 # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/99 $19.00 + 0.00 PII: S1359-6454(98)00382-6 {To whom all correspondence should be addressed. 435