Relation between the Chemical Short-Range Order in Liquid and Amorphous Alloys
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RAPIDLY SOLIDIFIED AMORPHOUS ANDCRYSTALLINE ALLOYS B.H. Kear, B.C. Giessen, and M. Cohen, editors
91
RELATION BETWEEN THE CHEMICAL SHORT-RANGE ORDER IN LIQUID AND AMORPHOUS ALLOYS 2
C.N.J. WAGNERI and H. RUPPERSBERG 1 Department of Materials Science and Engineering, University of California, Los Angeles, CA 90024, USA Fachbereich Angewandte Physik, Universitat des Saarlandes, 6600 Saarbricken, West-Germany.
ABSTRACT Recent advances in both diffraction theory and experiment have led to the determination of the topological and chemical short-range order in liquid alloys and metallic glasses. In binary alloys, three partial interference functions (or partial structure factors) must be determined to evaluate the Warren chemical short-range order parameter a. Examples of recent attempts to determine a in binary liquid and glassy alloys are given. In most glasses, studied so far, evidence exists for the occurrence of unlike nearest neighbor ordering which must be present in the liquid state. INTRODUCTION The distribution of two kinds of atoms A and B is completely random in an ideal gas. If a gas is condensed to a liquid or solid, a departure from randomness will be observed in most cases, because the atoms A and B usually have different sizes, and they interact chemically with each other. Only if all atoms in the condensed matter are isotopes of the same element can the distribution be assumed to be random. Departures from randomness have been studied extensively in substitutional solid structures. At higher temperatures, a disordered alloy, consisting of A and B atoms, may be regarded as an ideal crystal consisting of "average" atoms with a superimposed "inhomogeneity" represented by variations in the atomic scattering amplitudes and the static displacements due to the difference in sizes between the real atoms of the solid solution and the average atom on each lattice site. It is often advantageous to consider the diffraction pattern of such disordered solutions to consist of regular diffraction peaks (Bragg reflections) produced by the average lattice, and of a diffuse scattering produced by the fluctuations of composition and distortions (Laue diffuse scattering) [1,2]. The chemical short-range order, produced by the fluctuations in composition, can be readily characterized with the Warren(-Cowley) short-range order parameter Op defined as [2]
a = 1 - Zp/(c Zp) p
AB
(1)
Bp
where Z is the coordination number of the pth shell at the distance rp from any origin atom, z R2 is the partial coordination number, i.e., the number of j-type atoms in the pt1 shell at the distance rp from an i-type atom, and ci is the atomic concentration, i.e. ci = Ni/N where Ni is the number of i-type atoms, and N is the total number of atoms in the alloy of volume V. With this definition of the Warren parameter ap, we can express the Laue diffuse scattering ILDS( 20 ) for a polycrystalline sample as [2] SLDS(20) = N cACB(fA-fB)2 [1 +
I Z a sinKrp/(Krp)] p p=l P p
(2)
where fi is the co
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