Predicting quasicrystals with quantum structural diagrams
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Binary and ternary quasicrystals have been successfully separated by means of quantum structural diagrams in the light of new experimental data, and new potential candidates for the quasicrystalline state are presented. A general and simple classification of alloy systems, consistent with the experimental data, is proposed, which allows predictions of any type of binary and ternary quasicrystals. Quantum coordinates are analyzed and interpreted, and suggestions are given for an improvement of the present method.
I. INTRODUCTION In the description of the ordering of a solid, quasicrystals are intermediate between the amorphous and crystalline states. They are now considered as a genuine, distinct thermodynamic state and can be found with various symmetries (icosahedral, octagonal, decagonal, dodecagonal) forbidden by classical crystallography and in stable or metastable forms. The quasicrystalline state is usually obtained from the melt, and apart from other experimental factors, its occurrence depends critically on the quenching rate, which can vary greatly with the method used. Nevertheless, a problem of considerable interest is the prediction of which alloy system can potentially give (disregarding quenching constraints) a quasicrystal, within given temperature and composition ranges. This interest is more than academic, since rapid solidification techniques are commonly used today to produce (mostly metastable) alloys with superior properties by providing a higher flexibility in alloy composition through extension of solid solubility limits in nonequilibrium processes. To predict quasicrystals or to understand where they come from, many theoretical approaches or simple empirical observations have been applied, to date, with a limited success. For instance, although Landau mean field theories (that have been given much attention in the literature) support the existence of quasicrystalline symmetry, they are unable to determine likely candidates for a quasicrystal. Moreover, the interpretation depends on the precision of calculations in the Landau expansion of the system free energy, which has given different and conflicting results.1 Also, we should mention the potential predictive ability of the often-encountered structural analogies between the quasicrystalline state and its crystalline counterpart, the Frank-Kasper phase.2 This well-known experimental fact is not a universal rule and suffers from many departures. Although an approach based on first principles calculations would be warranted, in this paper, it is not our intention to discuss or compare the theories advanced so far to justify the existence of quasicrystals. Instead, J. Mater. Res., Vol. 6, No. 6, Jun 1991
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we present a general analysis of binary and ternary quasicrystals based on the very simple but powerful technique of Quantum Structural Diagrams (QSD) introduced several years ago3 and applied successfully to high T c superconductors4 and quantum defect structures.5 At that time, there w
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