Microstructure-property relationships in materials
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the development of the s c i e n c e of interrelation between the microstructure and physical properties of materials it is necessary to be able t o m e a s u r e and t o express the essential features of the geometry of microstructure in mathematically e x a c t t e r m s . Much progress has been made in the statistically precise definition and measurement of certain geom e t r i c p a r a m e t e r s of microstructure, which methods presently constitute the field of "quantitative m i c r o scopy". I The utilization of such parameters in the association of microstructure with physical propert i e s , however, involves some r a t h e r abstruse factors. It is the p u r p o s e of this paper t o d i r e c t attention t o this topic. UNBOUNDED IRREGULAR STRUCTURES It is important, at the outset, t o observe that m i c r o structures of materials differ fundamentally from the structures of isolated objects, in that objects normally possess specific form and size, whereas microstructure has a geometry of its own that goes on and on as a continuum, n e v e r appearing quite the same in any two places and having no beginning or ending. Microstructures may be said t o be " u n bounded i r r e g u l a r structures". Nevertheless, they have a constancy of character which distinguishes one microstructure from another and which r e l a t e s t o the physical properties of the material. Our language is rich in vocabulary for the description of isolated objects. We have qualitative adjectives such as: oval, tall, branched, squat, spongy, as well as more specific geometric t e r m s like: spherical, cubic, toroidal and polyhedral. By the use of such words and the ideas that they convey, w e a r e accustomed t o expressing ourselves r a t h e r effectively with respect to the geometric characteristics of individual objects. FREDERICK N. RHINES is Distinguished Service Professor, Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611. Manuscript submittedJune 22, 1976. METALLURGICAL TRANSACTIONS A
It is natural, therefore, for us t o attempt t o employ these same i d e a s in describing microstructure, but the r e s u l t must inevitably i n c u r fundamental e r r o r that will vitiate any structure-property relationship which w e may try to develop by its use. Such t e r m s are not adapted t o the description of unbounded i r r e g u lar structures, because they a r e all concerned with shape, which can have no specific meaning with respect t o microstructure. As will b e c o m e c l e a r presently, it is impossible, in principle, t o identify any shape which can be used as a building block to reproduce a m i c r o structure. It is necessary, instead, t o adopt a different kind of approach to the characterization of microstructure. In o r d e r t o perceive more c l e a r l y the nature of this problem, it may be helpful t o contemplate an analogy from common experience. Consider the m a n n e r in which w e are accustomed t o going about the description of a road system. A highway h
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