Geometrical Consieration of Lattice Spacings in Graphite

Graphite crystals from hexagonal structures. The inner angle $\alpha$ between two bonds in a graphite molecule is 120°. The length of a bond, or the distance between two neighboring graphite atoms, $a=1{.}42\cdot 10^{-10}\,\text m$.

From this, the two lattice spacings can be calculated by geometrical considerations. $d_{1}$ is:$$d_{1}=a+a\cdot \cos\left(\frac{\alpha}{2}\right)$$ $$\Rightarrow d_{1}=1.42\cdot 10^{-10}\,\text m+1.42\cdot 10^{-10}\,\text m \cdot \cos(60°)=2.13\cdot 10^{-10}\,\text m$$For \(d_2\) applies:$$d_{2}=a\cdot \sin\left(\frac{\alpha}{2}\right)$$ $$\Rightarrow d_{2}=1.42\cdot 10^{-10}\,\text m \cdot \sin(60°)=1.23\cdot 10^{-10}\,\text m$$

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