Structure and Thermodynamics of Quasicrystals

0111198 Widom含有过渡金属的富铝合金形成复杂的晶体结构和准晶体。 这些合金显示出不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。 准晶已经可以强化外科手术用合金，并覆盖在煎锅的表面。 人们对准晶最大的兴趣在于它们所引起的基础科学问题。 尖锐的衍射峰与晶体学上禁止的十角体和二十面体对称性共存，形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样的对称性之后，兴趣转向解释准周期性秩序的起源和性质。 这一问题至今仍未得到解决，也是理论研究的重点。以往的研究主要采用基于原子间相互作用势的总能量计算方法和从头算方法来计算金属间化合物合金。 总能量的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。 这些方法被开发来预测AlCuCo和AlNiCo十次准晶相的结构，实现与实验结构数据的良好的定性协议。 这些方法揭示了基本的激励，除了最佳的，能量最小化，结构。 原则上，我们可以获得整个热力学随温度和成分的演化，目前的资助是建立在研究三元十次对称相的成功基础上。 精确的原子模型和可靠的能量计算将被用来检查匹配规则的能量和相邻的十边形层的耦合。 详细的定量比较模型与实验数据。 用于十面体相的基本技术将适用于稳定的二十面体相。抽象随机镶嵌模型的开发继续进行高余维镶嵌作为模型无定形结构的研究和余维1镶嵌作为堆叠膜模型的研究。含有过渡金属的富铝合金形成复杂的晶体结构和准晶。 这些合金显示出不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。 准晶已经可以强化外科手术用合金，并覆盖在煎锅的表面。 人们对准晶最大的兴趣在于它们所引起的基础科学问题。 尖锐的衍射峰与晶体学上禁止的十角体和二十面体对称性共存，形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样的对称性之后，兴趣转向解释准周期性秩序的起源和性质。 这一问题至今仍未得到解决，是这一理论研究的重点。 精确的原子模型和可靠的能量计算将被用来检查匹配规则的能量和相邻的十边形层的耦合。 详细的定量比较模型与实验数据。 用于十面体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.***