NSF/DMR-BSF: Growth Induced Crystal Curvature

伟大的晶体学家舒布尼科夫说过：“晶体会闪现出它们的对称性。”他在这句精辟的评论中强调了晶体的特征，即它们引人注目的多面体形状、锋利的边缘和平坦的表面；水晶，顾名思义，是直的。见证刻面宝石，或自然生长的石英。然而，近一个世纪以前人们就认识到，可以使各种各样的晶体以扭曲的、螺旋状的形态生长——这种形态显然不是直的。值得注意的是，晶体王国的这一普遍特征在很大程度上被遗忘了，尽管它是阿司匹林等普通物质的特征。在固态和材料化学项目的支持下，研究小组的目标是了解晶体在生长过程中如何扭曲自己。这些过程是研究分子晶体机械特性的窗口，这些过程是重要工业操作的基础，如药物的片剂。扭曲晶体在其光学对比的节奏带中生动，有望在微观和宏观的手状形态之间架起一座桥梁。该研究团队与布朗克斯的几所公立高中合作，以提供科学身份建设的研究经验。【技术摘要】生长引起的形状变形的原因可能在于混合晶体的超分子化学性质，以及这些力在固体力学性能中的表现方式。该团队已经证明，添加剂会在生长的晶体界面上产生立体扭曲。添加剂可能通过产生具有不同度量属性的混合域来扭曲晶体。分子水平上的不匹配会产生应变，进而产生应力和扭转力矩。这个策略有三个方面：1。建立取代苯的扭曲混合或无序晶体的条件，我们已经从长期的单晶研究中了解了生长诱导应变的起源。2. 使用先进的显微镜精确地描述晶体的形状与生长诱导曲率——这项工作正在与Weizmann科学研究所的E. Efrati教授合作，由材料研究部和美以两国科学基金会建立的合作安排下进行。扭曲带的微分几何Weizmann专家在局部微分生长编码的几何挫折框架内分析了生长变形。这些研究将与原子力场和分子动力学模拟相匹配。

Non-Technical AbstractThe great crystallographer Shubnikov said that "crystals flash forth their symmetry." He was emphasizing in this pithy remark the characteristic feature of crystals, their striking polyhedral shapes with sharp edges and flat faces; crystals, by definition, are straight. Witness facetted gemstones, or naturally grown quartz. However, it was recognized almost a century ago that a wide variety of crystals can be made to grow with twisted, helix-like morphologies -- forms that are decidedly not straight. Remarkably, this general feature of the crystal kingdom was largely forgotten, even though it is characteristic of common substances such as aspirin. With support from the Solid State and Materials Chemistry program, the research team aims to understand how crystals twist themselves as they grow. These processes are windows into the mechanical properties of crystals built from molecules, processes that underlie important industrial operations such as the tableting of pharmaceuticals. Twisted crystals are vivid in their rhythmic bands of optical contrast, promising a bridge between microscopic and macroscopic handed forms. The research team is partnered with several Bronx public high schools in order to provide science identity-building research experiences. Technical AbstractThe origin of growth induced deformations of form presumably lie in the supramolecular chemistry of mixed crystals and in the manner in which these forces are manifest in the mechanical properties of solid bodies. The team has shown that additives induce twisting stereospecifically at growing crystal interfaces. Additives likely twist crystals by creating mixed domains with distinct metric properies. Mismatches at the molecular level produce strain that in turn can generate stress and twist moments. The strategy is threefold: 1. Establishing the conditions for twisting mixed or disordered crystals of substituted benzenes about which we already understand the origin of growth induced strain from long-standing studies of single crystals. 2. Using advanced microscopies to accurately describe the shapes of crystals with growth induced curvature -- this work is proceeding in collaboration with Professor E. Efrati at the Weizmann Institute of Science under the collaborative arrangement established by the Division of Materials Research and the US-Israel Binational Science Foundation. 3. Weizmann experts in differential geometry of twisted ribbons are analyzing growth deformation within the framework of geometric frustration encoded in local differential growth. These studies will be matched with atomistic force-field and molecular dynamics simulations.