Ordering Phenomena in Undercooled Alloys

Abstract

Much of the work performed under this grant was devoted to using modern ideas in kinetics to understand atom movements in metallic alloys far from thermodynamic equilibrium. Kinetics arguments were based explicitly on the vacancy mechanism for atom movements. The emphasis was on how individual atom movements are influenced by the local chemical environment of the moving atom, and how atom movements cause changes in the local chemical environments. The author formulated a kinetic master equation method to treat atom movements on a crystal lattice with a vacancy mechanism. Some of these analyses [3,10,16] are as detailed as any treatment of the statistical kinetics of atom movements in crystalline alloys. Three results came from this work. Chronologically they were (1) A recognition that tracking time dependencies is not necessarily the best way to study kinetic phenomena. If multiple order parameters can be measured in a material, the ''kinetic path'' through the space spanned by these order parameters maybe just as informative about the chemical factors that affect atom movements [2,3,5-7,9-11,14-16,18,19,21,23,24,26,36,37]. (2) Kinetic paths need not follow the steepest gradient of the free energy function (this should be well-known), and for alloys far from equilibrium the free energy function can bemore » almost useless in describing kinetic behavior. This is why the third result surprised me. (3) In cluster approximations with multiple order parameters, saddle points are common features of free energy functions. Interestingly, kinetic processes stall or change time scale when the kinetic path approaches a state at a saddle point in the free energy function, even though these states exist far from thermodynamic equilibrium. The author calls such a state a ''pseudostable'' (falsely stable) state [6,21,26]. I have also studied these phenomena by more ''exact'' Monte Carlo simulations. The kinetic paths showed features similar to those found in analytical theories. The author found that a microstructure with interfaces arranged in space as a periodic minimal surface is a probably an alloy at a saddle point in its free energy function [21,26,37].« less