Quasicrystals: how and why do they form?

准晶体：它们如何以及为何形成？

• 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; Quasicrystals; how; why; do; they

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翻译对称性的原子的有序排列形成的，即通过某些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材料（QCS）在1982年被发现，后来在2011年吸引了诺贝尔化学奖。这些材料缺乏晶体的翻译对称性，但它们平均具有旋转对称性。准晶体通常是由至少两种原子制成的金属合金形成的，并且已经发现了数百种示例。晶状体不限于原子，最近发现了由胶束共聚物，树状聚合物或其他颗粒形成的准晶体。聚合物是弦状的分子，共聚物是由两种或更多化学上不同类型的聚合物组成的聚合物。胶束是由（例如）树枝状聚合物（例如）组成的（例如）疏水聚合物核心，该聚合物核心被一个由亲水性聚合物的电晕包围。树突聚合物是通过在树状结构中连续层连接的分支聚合物来制成的聚合物分子。调查软性物质准稳定的形成和稳定性的主要理论方法涉及最大程度地减少适当的自由能，但是其稳定性的基本原理才开始理解。该提议的一种核心思想是，从模式形成和非线性动态的数学中带来了这种思想和洞察力。在1990年代的法拉第波浪实验中发现了具有准晶体结构或准图形的模式。在这些实验中，液体托盘受到垂直振动。如果强迫足够强大，则液体的平坦表面变得不稳定，并形成静电波的图案或准图案。理解准图质的形成机制的最新进展证实了关键成分是波长的非线性相互作用。从树突聚体之间的有效相互作用潜力开始，以及许多相互作用的粒子的统计物理学，我们将通过两个中间的理论链接到模式形成，每个中间的理论都会链接到一个中间的框架，每个级别都会增加级别的细节。这些是动态密度功能理论和相位晶体部分微分方程。其中的第一个是颗粒平均密度的理论，可以从树枝状聚合物之间的相互作用势中得出。第二个是对第一个的简化，并且直接适合模式形成理论的技术。此过程中的每个步骤都涉及近似和简化，但是可以控制近似值并可以测试简化。从模式形成理论中制定了形成和稳定QC的成分，我们可以通过简化并将新的见解带入可能会产生QC的树状设计原理中的新见解。