A crystalline solid has a given energy level that is capable of taking or using a given number of electrons. The system is referred to as the density of states (herein referred to as DOS). Normally, molecules and atoms are isolated from other forms of matter. However, in a DOS system, the process is continuous. It is at this point that a system referred to as Van Hove singularity is realised. In this case, since the DOS occurs as a continuous process, a non-smooth point occurs on a crystallised solid. The point singularises the process, leading to Van Hove singularity.
Van Hove singularity occurs on specific points, normally known as critical points. There are different critical points, among them those seen in phase diagrams as separate scenarios. There are also those points seen in a three-dimensional view. Such points acquire a DOS that is quite differentiable. An example of Van Hove singularity is explained using properties of optical absorption. Optical absorption is a process through which energy is used by the electrons using the properties of spectra.
Bibliography
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Kittel, C, Thermal physics, Freeman and Company, New York, 2012.
Sze, S, Physics of semiconductor devices, John Wiley and Sons, New York, 2012.