Frequency Estimate for Multicomponent Crystalline Compounds
- 193 Downloads
Among crystal structures of N-component metal alloys, far fewer examples are known with \(N\ge 4\) than with \(N=2\) or 3, in apparent contradiction to the exponentially growing number of possible combinations of elements. Two effects contribute to this shortfall. Since the N-component composition space resides within a d-dimensional simplex with \(d=N-1\), the vanishing volume in high dimensions reduces the distinct N-component compositions. Additionally, the increasing surface area makes it more probable that stable structures reside on the surface of the simplex (containing fewer than N components) as opposed to its interior. Specific estimates are developed through application of the empirical Miedema enthalpy model. Despite their rarity, we propose that the actual number of \(N=4\)- and 5-component alloys greatly exceeds the number that are currently known.
KeywordsMulticomponent alloy Enthalpy Crystal structures Convex hull High entropy alloy
I thank Alan Frieze and Wesley Pegden for a discussion on generalized triangle numbers. This paper is dedicated to the memory of Prof. Leo P. Kadanoff, my Ph.D. thesis advisor. Supported by the Department of Energy under Grant DE-SC0014506.
- 22.ThermoCalc: TCHEA1 - TCS High entropy alloy database, Version 1.0 (2015). URL http://www.thermocalc.com/media/35873/tchea10_extended_info_bh.pdf
- 26.Widom, M.: Prediction of structure and phase transformations. In: Gao, M.C., Yeh, J.-W., Liaw, P.K., Zhong, Y. (eds.) High entropy alloys: fundamentals and applications, chap. 8, pp. 267–298. Springer, New York (2016)Google Scholar