# Determination of the lattice spacing of graphite

Using the electron diffraction tube, the lattice spacing in graphite crystals can be determined. For this, the de Broglie wavelength of the electron diffracted on the graphite layers must be known. From the resulting interfence maxima - which must fulfill the Bragg condition for n=1 (first order interference maximum) - and the tube geometry, the lattice spacing d can be calculated. With $$$$\lambda = 2\cdot d\cdot \sin(\theta)\quad\Rightarrow\quad d=\frac{\lambda}{2\cdot \sin(\theta)}$$$$ and $$$$\theta=\frac{1}{2}\cdot \tan^{-1}\left(\frac{r}{L-R+\sqrt{R^2-r^2}}\right)$$$$ follows $$$$d=\frac{\lambda}{2\cdot \sin\left(\frac{1}{2}\cdot \tan^{-1}\left(\frac{r}{L-R+\sqrt{R^2-r^2}}\right)\right)}$$$$ where$\lambda$ is the de Broglie wavelength $\lambda_\text{de Broglie}=\frac{h}{\sqrt{2\cdot m_\text e \cdot e\cdot V_\text a}}$. Thus the formula for the lattice spacing of graphite in our experimental setup is: $$$$d=\frac{\frac{h}{\sqrt{2\cdot m_\text e \cdot e\cdot V_\text a}}}{2\cdot \sin\left(\frac{1}{2}\cdot \tan^{-1}\left(\frac{r}{L-R+\sqrt{R^2-r^2}}\right)\right)}$$$$