Correlation functions are the basis for the understanding of many thermodynamic systems that can be directly observed by scattering experiments. In this manuscript, the correlation functions include the steric repulsion of atoms that also leads to distinct shells of neighbors. A free energy is derived on the basis of these assumptions, and in the following the temperature dependence of the density (or specific volume), the typical time scale of the α-relaxation, and the heat capacity. From this, I argue that the glass transition is dominated by the vicinity of a first-order phase transition. While the correlation length stays rather constant in the vicinity of the glass transition, the intensity of the fluctuations is considerably increasing. The scattering amplitude is connected to the cluster size, also introduced in the cooperativity argument. Additionally, correlations of loops are discussed. The additional correlations describe rather small structures. Applying this to scattering intensities, a correlation peak was described that may be connected to the “Boson Peak” or a “cooperativity length.” The new concept of correlation functions on sterically repulsive atoms may find more attention in the wider field of physics.

中文翻译：

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关于玻璃化转变和相关函数

相关函数是理解许多可以通过散射实验直接观察到的热力学系统的基础。在这份手稿中，相关函数包括原子的空间排斥，这也导致了不同的邻居壳。自由能是在这些假设的基础上推导出来的，下面是密度（或比体积）的温度依赖性、α-弛豫的典型时间尺度和热容。由此，我认为玻璃化转变由一级相变附近主导。虽然相关长度在玻璃化转变附近保持相当恒定，但波动的强度正在显着增加。散射幅度与集群大小有关，也在协同性论证中引入。此外，还讨论了循环的相关性。额外的相关性描述了相当小的结构。将此应用于散射强度，描述了可能与“玻色子峰”或“协同长度”相关联的相关峰。空间排斥原子的相关函数的新概念可能会在更广泛的物理学领域引起更多关注。