Kinetics of Ordering in Cu 3 Au: An Atomistic Approach
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KINETICS OF ORDERING IN Cu 3 Au: AN ATOMISTIC APPROACH Zhigang Xi and Bulbul Chakraborty * *Physics Department, Brandeis University, Waltham, MA 02254 ABSTRACT We study the kinetics of ordering in Cu 3 Au using a model Hamiltonian derived from the effective medium theory of chemical bonding. Monte Carlo simulations are used to investigate universal and non-universal features of the growth kinetics. Anisotropic scaling of the structure factor is observed in late-stage growth of ordered domains. The anisotropy is a non-universal feature determined by the details of the microscopic model, and we find that the anisotropy observed in the simulations is in excellent agreement with experiments on Cu 3Au. The simulations are discussed in the context of theories of unstable growth. To our knowledge, this is the first study of kinetics in a realistic model Hamiltonian describing the material-specific properties of Cu 3 Au. INTRODUCTION Kinetics of ordering is a fundamental problem in the statistical mechanics of nonlinear phenomena occurring far from equilibrium [1]. Binary alloys, such as Cu 3 Au, when quenched from a high temperature disordered state to a temperature below the order-disorder transition temperature, evolve from an initially metastable or unstable state [2] towards the stable ordered state. During the early stages of growth, the free energy difference between the disordered and ordered phases and the nucleation barriers between these phases determine the transformation into ordered regions. This stage of the growth process is expected to be system specific. In contrast, the late stages of growth, where the system consists of ordered domains separated by domain walls, are expected to have a more universal character and there have been various indications that there are universal scaling laws determining this late stage growth [1, 3]. From a practical viewpoint, a knowledge of the morphology and growth of metastable and unstable states is crucial to metallurgy. The theoretical study of growth kinetics in alloys have been based upon simulations of kinetic Ising models or simple Langevin dynamics defined by the Time-dependent Ginzburg-Landau (TI)GL) model [3]. There are fascinating experimental results in Cu 3 Au. The experiments probing late stage growth are in agreement with general ideas of scaling and universality but exhibit large anisotropy of the structure factor [4]. Experiments probing the early stages of growth [5] can distinguish between nucleated and continuous ordering and are more sensitive to the characteristics of a specific alloy through features like the activation barriers to nucleation and the approach to the classical spinodal. These experiments have have shown some unusual growth features that axe not completely well understood [5]. A question that intrigued us was whether a realistic model of cohesion and stability in intermetallic alloys such as Cu 3 Au would lead to a description of growth kinetics which were in essential agreement with the ideas of universality and the classification of
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