Rutgers Center for Emergent Materials and Department of Physics & Astronomy, Rutgers University , Piscataway, New Jersey 08854, United States.
J Am Chem Soc. 2014 Jun 11;136(23):8368-73. doi: 10.1021/ja5026134. Epub 2014 May 29.
Common mathematical theories can have profound applications in understanding real materials. The intrinsic connection between aperiodic orders observed in the Fibonacci sequence, Penrose tiling, and quasicrystals is a well-known example. Another example is the self-similarity in fractals and dendrites. From transmission electron microscopy experiments, we found that FexTaS2 crystals with x = 1/4 and 1/3 exhibit complicated antiphase and chiral domain structures related to ordering of intercalated Fe ions with 2a × 2a and √3a × √3a superstructures, respectively. These complex domain patterns are found to be deeply related with the four color theorem, stating that four colors are sufficient to identify the countries on a planar map with proper coloring and its variations for two-step proper coloring. Furthermore, the domain topology is closely relevant to their magnetic properties. Our discovery unveils the importance of understanding the global topology of domain configurations in functional materials.
常见的数学理论可以在理解真实材料方面产生深远的应用。在斐波那契数列、彭罗斯镶嵌和准晶体中观察到的非周期性顺序之间存在内在联系，这是一个众所周知的例子。另一个例子是分形和树枝状晶体中的自相似性。从透射电子显微镜实验中，我们发现 x = 1/4 和 1/3 的 FexTaS2 晶体表现出复杂的反相和手性畴结构，这与插层 Fe 离子的有序性有关，分别具有 2a×2a 和 √3a×√3a 超结构。这些复杂的畴图案与四色定理密切相关，四色定理表明，通过适当的着色及其两步适当着色的变体，可以用四种颜色来识别平面地图上的国家。此外，畴拓扑与它们的磁性密切相关。我们的发现揭示了理解功能材料中畴构型全局拓扑的重要性。
