论文标题
Lennard Jones的潜力重新审视 - 分析表达式在立方和六角形封闭式晶格中的振动效应
The Lennard Jones Potential Revisited -- Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices
论文作者
论文摘要
分析公式是针对内聚能的零点振动能和非谐波校正的，以及在爱因斯坦模型中用于立方晶格（SC，BCC和FCC）的模式Grüneisen参数，以及hexagonal封闭式结构。这扩展了Lennard Jones和Ingham在1924年，1939年的Corner和1965年的Wallace所做的工作。该公式基于对两体能量贡献的描述（扩展的Lennard-Jones潜力）。这些利用三维晶格总和可以将其转换为快速收敛的系列，并通过各种膨胀技术准确确定。我们将这些新的晶格总和表达式应用于稀有气体固体，并讨论相关的关键点。派生的公式给出了定性但深刻的洞察力，但仍对从最轻（氦）到最重的稀有气体元素（Oganesson）的固体振动作用，既呈现特殊情况，因为对前者的量子效应强，并且对后者具有强大的相对论效应。
Analytical formulae are derived for the zero-point vibrational energy and anharmonicity corrections of the cohesive energy and the mode Grüneisen parameter within the Einstein model for the cubic lattices (sc, bcc and fcc) and for the hexagonal close-packed structure. This extends the work done by Lennard Jones and Ingham in 1924, Corner in 1939 and Wallace in 1965. The formulae are based on the description of two-body energy contributions by an inverse power expansion (extended Lennard-Jones potential). These make use of three-dimensional lattice sums, which can be transformed to fast converging series and accurately determined by various expansion techniques. We apply these new lattice sum expressions to the rare gas solids and discuss associated critical points. The derived formulae give qualitative but nevertheless deep insight into vibrational effects in solids from the lightest (helium) to the heaviest rare gas element (oganesson), both presenting special cases because of strong quantum effects for the former and strong relativistic effects for the latter.
