First-Principles Calculations of Heusler Phase Precursors in the Atomic Short-Range Order of Disordered BCC Ternary Allo
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ABSTRACT We apply our recently developed first-principles theory of atomic short-range order in disordered multicomponent alloys to CuAuZn 2 and AgAuZn 2, two alloys which display partially-ordered B2 phases as well as fully-ordered Heusler structures. The calculated Warren-Cowley pair correlation functions for both alloys peak at the special points (½11) and (100), with the peak at (100) dominant. This is indicative of a tendency to B2 order at high temperatures, and a subsequent tendency to Heusler-type order at lower temperatures. An analysis in terms of effective interactions shows that the Au Zn interaction drives the (100) ordering tendency, while the Ag Au and Cu Au interactions contribute more to the (11j) ordering tendency - this effect is larger in CuAuZn 2 and should lead to a slightly higher transition temperature for the B2 to Heusler transition in CuAuZn 2 as compared to AgAuZn 2. INTRODUCTION Many alloy systems display a disordered solid solution phase at high temperature. This phase is characterized by an absence of chemical long range order (LRO) but a presence of atomic short-range order (ASRO). This ASRO is directly measurable by diffuse scattering experiments and provides valuable information on both the atomic interactions in the disordered phase and the ordering tendencies toward possible ordered phases. Even if a particular alloy does not experimentally possess a solid solution phase, the properties of a hypothetical solid solution phase can still be calculated and provide similar information. The ASRO found in the solid solution is often a precursor to the transition from the disordered state to a lower temperature ordered state. In such cases, the ASRO provides a direct indication of the ordering tendencies which will be realized. In the present work we discuss two ternary alloys, AgAuZn 2 and CuAuZn 2 , for which the ASRO is a precursor to two ordering transitions. We calculate and discuss the ASRO. Multicomponent alloys often exhibit a series of ordering transitions, with one or more partially-ordered phases appearing as the temperature is lowered, ultimately reaching a fully-ordered state. The site occupations of the partially-ordered state may be obtained, at least approximately, from information on the interatomic interactions in the disordered state. Thus, the interactions determine not only the ordering wave vector and spinodal temperature, as in the binary case, but the occupations in the partially-ordered states as well. The present work utilizes our recently-developed first principles theory of ASRO in alloys 339 Mat. Res. Soc. Symp. Proc. Vol. 408 0 1996 Materials Research Society
of an arbitrary number of components. Because the present calculations are based on the homogeneously disordered phase, there is no bias to any particular ASRO: the system is "free" to find its own ASRO due to the underlying electronic interactions.
ATOMIC SHORT-RANGE ORDER IN ALLOYS The ASRO in a multicomponent alloy is described by the pair correlation function
q9Y (T) (crc;)
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(c)(c)
(1)
wher
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