Structure and Thermodynamics of Quasicrystals

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

0111198 Widom Aluminum-rich alloys containing transition metals form intricate crystal structures and quasicrystals. These alloys display unusual and useful mechanical properties such as low coefficients of friction, great hardness at low temperatures, and ductility at high temperatures. Quasicrystals already strengthen surgical alloys and coat surfaces of frying pans. Further applications such as coatings for ball bearings have been proposed. The greatest interest in quasicrystals lies in the fundamental scientific issues they raise. Coexistence of sharp diffraction peaks with crystallographically forbidden decagonal and icosahedral symmetry posed the paradox that initially drew researchers to the field. After recognizing that quasiperiodicity allows such symmetries, interest turned to explaining the origin and nature of quasiperiodic order. This problem, which remains unsolved today, is the focus of this theoretical research. Prior research applied methods of total energy calculations using interatomic potentials and full ab-initio calculations to intermetallic alloys. Total energy calculations were incorporated into sophisticated Monte Carlo computer techniques known as quasilattice gas simulations. These methods were developed to predict structures of AlCuCo and AlNiCo decagonal quasicrystal phases, achieving excellent qualitative agreement with experimental structural data. These methods reveal fundamental excitations in addition to optimal, energy minimizing, structures. In principle, the entire thermodynamic evolution with temperature and composition can be obtained. The current grant builds on this success by studying ternary decagonal phases. Accurate atomistic models and reliable energy calculations will be used to examine matching rule energetics and the coupling of adjacent decagonal layers. Detailed quantitative comparisons will be made of models with experimental data. The basic techniques used for decagonal phases will be adapted to stable icosahedral phases. Development of abstract random tiling models continues with study of high codimension tilings as model amorphous structures and study of codimension-1 tilings as models of stacked membranes. %%% Aluminum-rich alloys containing transition metals form intricate crystal structures and quasicrystals. These alloys display unusual and useful mechanical properties such as low coefficients of friction, great hardness at low temperatures, and ductility at high temperatures. Quasicrystals already strengthen surgical alloys and coat surfaces of frying pans. Further applications such as coatings for ball bearings have been proposed. The greatest interest in quasicrystals lies in the fundamental scientific issues they raise. Coexistence of sharp diffraction peaks with crystallographically forbidden decagonal and icosahedral symmetry posed the paradox that initially drew researchers to the field. After recognizing that quasiperiodicity allows such symmetries, interest turned to explaining the origin and nature of quasiperiodic order. This problem, which remains unsolved today, is the focus of this theoretical research. The current grant continues the study of ternary decagonal phases. Accurate atomistic models and reliable energy calculations will be used to examine matching rule energetics and the coupling of adjacent decagonal layers. Detailed quantitative comparisons will be made of models with experimental data. The basic techniques used for decagonal phases will be adapted to stable icosahedral phases. ***