Theory and Practice in the Prediction of New Materials
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MRS BULLETIN/FEBRUARY 1993
satisfy these rules are the most likely to reward experimental investigation. In this article, I discuss the development of simple rules for the prediction of new materials. The emphasis is on rules derived from the quantum diagram method, briefly summarized in the next section. Construction of these diagrams for stable quasicrystals, high Tc ferroelectrics, and high Tc superconductors are then reviewed. Next, I discuss general considerations governing the prediction of new materials and the role of diagram-based rules. In the section following that is a more thorough examination and interpretation of the diagrammatic regularities exhibited by stable quasicrystals. The prediction of new quasicrystals is considered next, and prediction strategies for other classes of materials are covered in the following three sections.
|X,4 - XB|, AR = \RA - RB\, and 2N,, = NvA + NvB, where X is the MartynovBatsanov electronegativity,6 R is the pseudopotential core radius,7 and Nv is the valence electron number. These atomic parameters scales R, X, and Nv, although chosen from a large number of scales solely for their separation efficacy, have clear relevance to bonding. For ternary compounds, structure type is not a useful diagrammatic classification principle because most ternary structure types have only a few representatives. Instead, we use the "generalized structure type," which labels a crystal structure by the number and type of local coordination environments.1 With a generalization of the binary coordinate definitions and separate diagrams for one-, two-, three-, and fourenvironment structure types, excellent separation is achieved. 2,483 one-environment binary, ternary, and quaternary compounds have been separated to the 97% level1 and 4,721 one-, two-, three-, and four-environment binaries to 96%.2 Different combinations of atomic parameters are used as coordinates in the construction of the "quantum formation diagrams" (QFD), which systematize the relationship between composition and compound formation. Each ternary alloy system is represented by a point with coordinates
\ - -L | Ik + Ik + Ik I •J \ ' mA
1mA
\RB-RC
Review of the Quantum Diagram Technique The complexity of the systems under consideration dictates the use of the quantum diagram technique,1'23 which is a procedure for displaying data graphically and identifying trends in the full database of 22,000 intermetallic compounds.4 This global organization of structure and stability data involves three-dimensional diagrams in which each system is represented by a point whose coordinates are determined by its composition. Closely related systems have similar values of diagrammatic coordinates and, in general, simple surfaces can be drawn to separate different classes of systems. The goal of the "quantum structural diagrams" (QSD) is to systematize the relationship between composition and structure. It has been shown that binary compounds can be effectively classified according to their structure type5 with diagrammatic coordinate
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