Lindemann developed the melting temperature theory over 100 years ago, known as the Lindemann criterion. Its main assumption is that melting occurs when the root-mean-square vibration amplitude of ions and atoms in crystals exceeds a critical fraction, h of the inter-atomic spacing in crystals. The Lindemann coefficient h is undefined and scientific papers report different h values for different elements. Here we present previously unobserved data trends pointing to the fact that the Lindemann coefficient could be linked to the periodic groups of the periodic table, having an exact value for each element belonging to a given periodic group. We report 12 distinctive Lindemann coefficient values corresponding to 12 groups of the periodic table containing solid elements with identifiable melting temperature. Using these vales, the recalculation of the melting temperatures indicates a good match to the experimental values for 39 elements, corresponding to 12 out of 15 periodic groups. This newly observed result opens up the possibility of further refining the Lindemann melting criterion by stimulating analytical studies of the Lindemann coefficient in the light of this newly discovered result.

中文翻译：

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广义林德曼熔化系数

林德曼在 100 多年前开发了熔化温度理论，称为林德曼准则。它的主要假设是当晶体中离子和原子的均方根振动幅度超过晶体中原子间距的临界分数 h 时，就会发生熔化。林德曼系数 h 未定义，科学论文报告不同元素的不同 h 值。在这里，我们展示了以前未观察到的数据趋势，指出林德曼系数可以与元素周期表的周期组相关联，对于属于给定周期组的每个元素都有一个精确的值。我们报告了 12 个独特的林德曼系数值，对应于周期表的 12 组，其中包含具有可识别熔化温度的固体元素。使用这些值，熔化温度的重新计算表明与 39 种元素的实验值非常匹配，对应于 15 个周期组中的 12 个。根据这一新发现的结果，通过刺激林德曼系数的分析研究，这一新观察到的结果开辟了进一步完善林德曼熔化标准的可能性。