Structure and Thermodynamics of Quasicrystals

含有过渡金属的宽富铝合金形成错综复杂的晶体结构和准晶。这些合金表现出不同寻常和有用的机械性能，如低摩擦系数、低温下的高硬度和高温下的延展性。准晶已经强化了外科合金和煎锅的涂层表面。对准晶材料的最大兴趣在于它们所引起的基本科学问题。尖锐的衍射峰与结晶学上禁止的十角形和二十面体对称性共存，构成了最初吸引研究人员进入该领域的悖论。在认识到准周期性允许这种对称性之后，人们的兴趣转向解释准周期秩序的起源和性质。这一至今仍未解决的问题是本理论研究的重点。以前的研究将原子间相互作用势计算总能量的方法和全从头计算方法应用于金属间化合物合金。总能量计算被纳入复杂的蒙特卡罗计算机技术，称为准晶格气体模拟。这些方法被用来预测AlCuCo和AlNiCo十方准晶相的结构，与实验结构数据取得了很好的定性一致。这些方法除了揭示最优的、能量最小化的结构外，还揭示了基本的激励。原则上，可以获得随温度和组成的整个热力学演化。目前的拨款是通过研究三元十方相来建立在这一成功的基础上的。精确的原子模型和可靠的能量计算将被用来检验匹配规则、能量学和相邻十角形层的耦合。模型将与实验数据进行详细的定量比较。用于十方相的基本技术将适用于稳定的二十面体相。抽象随机瓦片模型的发展继续研究高协维瓦片作为模型非晶态结构，并研究协维-1瓦片作为堆积膜的模型。%含过渡金属的富铝合金形成复杂的晶体结构和准晶。这些合金表现出不同寻常和有用的机械性能，如低摩擦系数、低温下的高硬度和高温下的延展性。准晶已经强化了外科合金和煎锅的涂层表面。对准晶材料的最大兴趣在于它们所引起的基本科学问题。尖锐的衍射峰与结晶学上禁止的十角形和二十面体对称性共存，构成了最初吸引研究人员进入该领域的悖论。在认识到准周期性允许这种对称性之后，人们的兴趣转向解释准周期秩序的起源和性质。这一至今仍未解决的问题，是本次理论研究的重点。精确的原子模型和可靠的能量计算将被用来检验匹配规则、能量学和相邻十角形层的耦合。模型将与实验数据进行详细的定量比较。用于十方相的基本技术将适用于稳定的二十面体相。*

0111198WidomAluminum-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.***