On Cyclical Phase Transformations in Driven Alloy Systems
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INTRODUCTION
MATERIAL synthesis via external dynamic forcing is called a ‘‘driven process.’’ Perhaps, the best known driven process is mechanical alloying—a high-energy ball-milling process—but other examples include severe plastic deformation and irradiation. An interesting feature observed in several driven processes is temporal oscillations in phase fractions. For example, during mechanical alloying, the microstructure of a binary alloy of elemental Al50Zr50 powders is shown to vary cyclically between a crystalline and an amorphous state,[1] while Co powders are shown to display changes between a fcc and a hcp structure.[2] In order to shed some light on the mechanism(s) of such cyclical phase transformations, we present a few findings obtained with both thermodynamic and atomic modeling approaches. Mechanical alloying is a nonequilibrium thermodynamic process used to synthesize a variety of both equilibrium and nonequilibrium materials; examples include nanocrystalline solids, intermetallics, and glassy alloys. From a thermodynamic viewpoint, a system under external dynamic forcing experiences continuous energy input, and neither the formation of nonequilibrium structures nor the recovery of equilibrium structures through the decomposition of nonequilibrium structures is unexpected. Temporal oscillations in phase structure (or in any other property) under driven conditions are phenomena that occur far from equilibJONG K. LEE, Professor, is with the Department of Materials Science and Engineering, Michigan Technological University, Houghton, MI 49931, USA. Contact e-mail: [email protected] This article is based on a presentation given in the symposium entitled ‘‘Solid-State Nucleation and Critical Nuclei during First Order Diffusional Phase Transformations,’’ which occurred October 15–19, 2006 during the MS&T meeting in Cincinnati, Ohio under the auspices of the TMS/ASMI Phase Transformations Committee. Article published online December 8, 2007 964—VOLUME 39A, MAY 2008
rium. Consequently, the term ‘‘equilibrium,’’ used frequently to describe the microstructure, is incorrect, as the system would continue to evolve even if the external driving force were removed. Whether a driven system undergoes sustained oscillations or reaches a steadystate microstructure, the total free energy, including that of the loading system, tends toward a minimum. A survey of some observed temporal oscillations in property under driven conditions[3,4] is provided in Table I. The first four alloy systems show cyclical phase transformations between a crystalline and a glass phase at high milling intensity. At low milling intensity, however, alloy Nos. 1 and 4 show a stable glass phase upon milling crystalline powders. Cyclical variations in hardness for elemental Zn (No. 7) and in stored enthalpy for Cu and austenitic steels (Nos. 8 through 10) suggest that a ductile crystalline phase could oscillate in its free energy under a given driven condition. This is the hypothesis on which this work is prescribed, and through which all the phenomena l
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