Instability of the body-centered cubic lattice within the sticky hard sphere and Lennard-Jones model obtained from exact lattice summations,Physical Review E

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Instability of the body-centered cubic lattice within the sticky hard sphere and Lennard-Jones model obtained from exact lattice summations
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-22 , DOI: 10.1103/physreve.104.035306
Antony Burrows ₁ , Shaun Cooper ₂ , Peter Schwerdtfeger ₁

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A smooth path of rearrangement from the body-centered cubic (bcc) to the face-centered cubic (fcc) lattice is obtained by introducing a single parameter to lattice vectors of a cuboidal unit cell. As a result, we obtain analytical expressions in terms of lattice sums for the cohesive energy where the interaction is described by a Lennard-Jones (LJ) interaction potential or a sticky hard-sphere (SHS) model with a

r^{- n}

long-range attractive term. These lattice sums are evaluated to computer precision by expansions in terms of a fast converging Bessel function series. Applying the whole range of lattice parameters for the SHS and LJ potentials we prove that the bcc phase is unstable (or, at best, metastable) toward distortion into the fcc phase in the low temperature and pressure limit. Even if more accurate potentials are used, such as the extended LJ potential for argon or chromium, the bcc phase remains unstable. This strongly indicates that the appearance of a low temperature bcc phase for several elements in the periodic table is due to higher than two-body forces in atomic interactions.

中文翻译：

粘性硬球内体心立方晶格的不稳定性和从精确晶格求和获得的 Lennard-Jones 模型

通过将单个参数引入立方晶胞的晶格矢量，可以获得从体心立方 (bcc) 到面心立方 (fcc) 晶格的平滑重排路径。因此，我们获得了内聚能的晶格总和的解析表达式，其中相互作用由 Lennard-Jones (LJ) 相互作用势或粘性硬球 (SHS) 模型描述

r^{- n}

长期有吸引力的期限。这些晶格和通过快速收敛的 Bessel 函数级数的扩展被评估为计算机精度。将整个范围的晶格参数应用于 SHS 和 LJ 电位，我们证明 bcc 相在低温和压力极限下向 fcc 相变形是不稳定的（或者，最好是亚稳态）。即使使用更精确的电位，例如氩或铬的扩展 LJ 电位，bcc 相仍然不稳定。这有力地表明，元素周期表中几种元素的低温 bcc 相的出现是由于原子相互作用中高于二体力。

更新日期：2021-09-22

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