Stacking faults of hexagonal close-packed layers (HCPLs) often exist as kinetically trapped defects in the close-packed lattices of metallic atoms and spherical colloidal particles. Here, we show that the population of stacking faults in the hexagonal close-packed (HCP) lattice of the micelles formed by the blends of poly(ethylene oxide)-block-poly(1,4-butadiene) (PEO-b-PB) with PEO or PB homopolymer increased with decreasing temperature in a thermally reversible manner. We argue that, while HCP is the equilibrium lattice for a close-packed micellar phase with an infinitely large grain, introduction of stacking faults becomes thermodynamically favored when the lateral dimension of the HCPL and the difference in the bulk free energy between face-centered cubic (FCC) and HCP lattices are small. An optimal degree of stacking fault exists in the close-packed structure under the balance between the bulk lattice free energy and an entropic gain from the combinatorial mixing of FCC and HCP layers in the stacking direction. The higher extent of stacking faults at lower temperature found in the present system was attributed to the smaller difference in the bulk free energy between FCC and HCP lattices, which further signified that the micelles packed in the HCP lattice have higher entropy than those organized in the FCC phase.

中文翻译：

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嵌段共聚物胶束密堆积结构中由热力学引起的堆垛层错

六角密堆积层 (HCPL) 的堆垛层错通常作为金属原子和球形胶体颗粒的密堆积晶格中的动力学捕获缺陷而存在。在这里，我们表明，在密排六方（HCP）由聚共混物（氧化乙烯）形成的胶束的晶格堆垛层错的人口-嵌段-聚（1,4-丁二烯）（PEO- b-PB) 与 PEO 或 PB 均聚物以热可逆方式随温度降低而增加。我们认为，虽然 HCP 是具有无限大晶粒的密堆积胶束相的平衡晶格，但当 HCPL 的横向尺寸和面心立方之间的体积自由能差异时，堆垛层错的引入在热力学上是有利的。 (FCC) 和 HCP 晶格很小。在体晶格自由能和 FCC 层和 HCP 层在堆叠方向上的组合混合的熵增益之间的平衡下，密堆积结构中存在最佳的堆垛层错程度。在本系统中发现的较低温度下较高程度的堆垛层错归因于 FCC 和 HCP 晶格之间的体自由能差异较小，