Condensed Matter


"Impossibility of the Simple Cubic Metal in Nature"

Authors: Gokaran Shukla

In nature, metal only exist in $bcc$, $fcc$ and $hcp$ crystal structure. Question arises that why we do not have simple cubic metal in nature. In this paper we will discuss about the impossibility of the existence of the simple cubic metal by using the Brillouin zones and Bragg's plane diffraction condition and will show that the ``impossibility'' arises due to pure quantum mechanical effect rather than the packing fraction. We will also show that $why$ certain material have the band-gap while others are not. We will develop a general rule applicable to all crystal structures to decide whether it will be insulator, semi-metal or metal in nature. For a test case we will use our developed rule and will explain the long lasting mysterious question in condense matter physics that $why$ boron is insulator while aluminum is metal although they belong to the same group in periodic table; why carbon is insulator in diamond cubic crystal structure while metal in graphite form; why antimony and bismuth are such a poor conductor (semi-metal); why $hcp$ crystal structure $\frac{c}{a}$ ratio must be distorted in-order to behaves like a metal.

Comments: 12 Pages.

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Submission history

[v1] 2018-03-19 06:42:39

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