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Quasicrystals: how and why do they form?

准晶体：它们如何以及为何形成？

基本信息

批准号：
EP/P015689/1
负责人：
Andrew Archer
金额：
$ 37.4万
依托单位：
Loughborough University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2017
资助国家：
英国
起止时间：
2017 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FP015689%2F1
关键词：
Quasicrystals how why do they

项目摘要

Crystals are formed from ordered arrangements of atoms with rotation and translation symmetries, i.e. rotating or shifting the crystal by certain specific values leaves the crystal looking unchanged. However, some rather striking materials, named quasicrystals (QCs), were discovered in 1982, later attracting the Nobel Prize for Chemistry in 2011. These lack the translation symmetries of crystals and yet they have rotation symmetry on average. Quasicrystals are usually formed from metallic alloys made from at least two types of atoms and hundreds of examples have been discovered.Crystallisation is not limited to atoms, and quasicrystals formed from micellar copolymers, dendrimers or other particles have been discovered recently. Polymers are string-like molecules and copolymers are polymers that are made of two or more chemically different types of polymers that are bonded together. The micelles are formed from (for example) dendrimers which comprise a hydrophobic polymer core surrounded by a corona of hydrophilic polymer. Dendrimers are polymeric molecules made by joining branched polymers in successive layers, in a tree-like structure. The main theoretical approach to investigating the formation and stability of soft-matter quasicrystals involves minimising an appropriate free energy, but the principle(s) underlying their stability are only beginning to be understood.One central idea of this proposal is to bring ideas and insights from the mathematics of pattern formation and nonlinear dynamics to bear on this physical problem. Patterns with quasicrystalline structure, or quasipatterns, were discovered in Faraday wave experiments in the 1990s. In these experiments, a tray of liquid is subjected to vertical vibrations. If the forcing is strong enough, the flat surface of the liquid becomes unstable and a pattern or quasipattern of standing waves is formed. Recent progress in understanding the formation mechanism for quasipatterns has confirmed the key ingredient is the nonlinear interaction of waves with two different wavelengths.Starting from the effective interaction potential between dendrimers, and the statistical physics of many interacting particles, we will link to pattern formation via two intermediate theoretical frameworks, each representing an increase in degree of level of detail - i.e. in coarse graining. These are Dynamical Density Functional Theory and Phase Field Crystal Partial Differential Equations. The first of these is a theory for the average density of particles, and can be derived from the interaction potential between the dendrimers; the second is a simplification of the first, and is directly amenable to techniques from pattern formation theory. Each step in this process involves approximations and simplifications, but the approximations can be controlled and the simplifications can be tested.Having worked out from pattern formation theory the ingredients for forming and stabilising QCs, we can go back through the simplifications and bring the new insights into the design principles for dendrimers that are likely to produce QCs.

晶体是由具有旋转和平移对称性的原子的有序排列形成的，即按一定的特定值旋转或移动晶体使晶体看起来不变。然而，一些相当引人注目的物质，被称为准晶(QCs)，在1982年被发现，后来在2011年吸引了诺贝尔化学奖。它们缺乏晶体的平移对称性，但它们平均具有旋转对称性。准晶通常是由至少两种原子组成的金属合金形成的，已经发现了数百个例子。结晶化并不局限于原子，最近也发现了由胶束共聚物、树枝状大分子或其他粒子形成的准晶。聚合物是线状分子，而共聚物是由两种或两种以上化学上不同类型的聚合物粘合在一起制成的聚合物。所述胶束由(例如)树枝状大分子形成，所述树状大分子包括被亲水性聚合物的电晕包围的疏水聚合物核心。树枝状大分子是通过在连续的层中连接支化聚合物而形成的树状结构的聚合物分子。研究软物质准晶的形成和稳定性的主要理论方法包括使适当的自由能最小化，但其稳定性背后的原理(S)才刚刚开始被理解。这一提议的一个中心思想是将图案形成和非线性动力学的数学思想和见解引入这个物理问题。具有准晶结构的图案，或称准图案，是在20世纪90年代的法拉第波实验中发现的。在这些实验中，一盘液体受到垂直振动。如果作用力足够强，液体的平面就会变得不稳定，并形成驻波的图案或准图案。最近在理解准图案形成机制方面的进展已经证实，其关键因素是两个不同波长的波的非线性相互作用。从树枝状大分子之间的有效相互作用势和许多相互作用粒子的统计物理出发，我们将通过两个中间理论框架联系到图案形成，每个框架代表细节程度的增加-即粗粒化。它们是动力学密度泛函理论和相场晶体偏微分方程组。其中第一个是颗粒平均密度的理论，可以从树枝状大分子之间的相互作用势推导出来；第二个是第一个的简化，直接服从图案形成理论的技术。这个过程中的每一步都包括近似和简化，但近似是可以控制的，简化是可以测试的。从图案形成理论得出形成和稳定QC的成分后，我们可以回顾简化过程，并将新的见解带入可能产生QC的树枝状大分子的设计原则中。