随机堆叠的固体中的相关性
Amna Khairi Nasr1,2, R Ganesh2
1Sir Winston Churchill Secondary School, St Catharines, Ontario, Canada, L2T 2N1.
Physical review. E
|October 18, 2023
概括
像巴洛堆叠和托尔卡托-斯蒂林格堆叠这样的球体包装结构在层相关性中表现出指数式衰变,即使偏差有利于特定的安排. 这一发现影响了对固体排序和合成方法的理解.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 材料科学 材料科学 材料科学
- 统计力学 统计力学
背景情况:
- 球体包装是一个具有历史根源的基本问题,导致像面中心立方体 (FCC) 和六角密集包装 (HCP) 这样的密集结构.
- 巴洛堆叠表示最大密度结构,而托尔卡托-斯蒂林格堆叠则建议在保持稳定性时保持最小密度.
- 了解层相关性对于预测堆叠固体的特性和形成至关重要.
研究的目的:
- 在随机的Barlow和Torquato-Stillinger堆叠家族中描述层相关性.
- 为了研究拉性偏差对巴洛堆叠中的层相关性的影响.
- 将堆叠结构与统计力学模型联系起来,以获得分析洞察力.
主要方法:
- 使用哈格代码将巴洛堆映射到一个单维的伊辛磁铁模型.
- 关联层的相关函数与伊辛模型的动量生成函数.
- 分析Torquato-Stillinger堆叠,将它们映射到一个结合的伊辛和三态波茨模型中.
主要成果:
- 随机的巴洛堆叠显示出呈指数级衰变的层相关性.
- 引入一种奇拉性偏差,有利于FCC排序,仍然会导致指数式衰变,表明没有长距离的顺序.
- 随机的Torquato-Stillinger堆叠也显示了指数级衰变的相关性,其形式类似于Barlow堆叠.
结论:
- 在最大 (Barlow) 和最小 (Torquato-Stillinger) 密度堆叠家族中的层相关性在随机条件下呈指数级衰减.
- 即使偏向于像FCC这样的特定结构,在这些堆叠模型中也无法实现远程顺序.
- 这些发现对堆叠固体中的集群的排序和层沉积合成技术有意义.
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