Analysis of crystal structure using Bragg's X-ray spectrometer:

• Bragg's spectrometer was designed on the basis of Bragg's law. It is a modified form of ordinary spectrometer to suit the use the x-ays.
• A monochromatic x-ray beam obtained from x-ray tube is made to pass through slits S1 and S2 which are made of lead. The fine beam is made to fall on crystal C that is fixed on a crystal, mount exactly at the center of circular turn table.
• The x-rays reflected are collected by ionization chamber as it is sturdy, the turn table is rotated until there is a sharp increase in the intensity.
• The sudden increase in the intensity of x-ray suggests that Bragg's law is satisfied at given angle$\theta$ of the incident beam.
• The peak in ionisation current which represent the intensity occurs more than once as$\theta$ is varied since Bragg's law states$n\lambda=2d \sin \theta$ that is n=1, 2, 3, ... we have$\theta_1, \theta_2, \theta_3,...$
• If the intensity or ionisation current is plotted, we can find$\theta_1, \theta_2, \theta_3,...$using the graph where the peak occurs.
• The crystal face used for reflecting the x-rays can be cut so that it remains parallel to one set of planes, then to another and so on when placed at center of the turn table on Bragg's spectrometer with x-rays of known$\lambda$ incident upon it.
• For a given plane used as reflecting surface, find the corresponding d using,$n\lambda=2d \sin \theta \ (take \ n=1)$
• Similarly find value of d for other planes as well, for cubic structure we select three planes that is (100), (100), (111).
• As$\lambda$ is same through entire experiment we get,$\lambda=2d _{100}\sin \theta_1 =2d _{110}\sin \theta_2=2d _{111}\sin \theta_3$
  Hence,$d_{100}:d_{110}:d_{111}::\dfrac 1 {\sin \theta_1}:\dfrac 1 {\sin \theta_2}:\dfrac 1 {\sin \theta_3}$ where$\theta_1, \theta_2, \theta_3 $ obtained from graph intensity tends to$\theta$, where the peak occur.
• The reason for selection of planes (100), (110) and (111) is that these planes possess atoms. The ratios of$d_{100}, d_{110} and\ d_{111} $for SC, BCC and FCC are as follows:| SC | 1 | $: \ \dfrac 1 {\sqrt2}$ | $:\ \dfrac 1 {\sqrt3}$ | | --- | --- | --- | --- | | BCC | 1 | $:\ \dfrac 2 {\sqrt2}$ | $:\ \dfrac 1 {\sqrt3}$ | | FCC | 1 | $:\ \dfrac 1 {\sqrt2}$ | $:\ \dfrac 2 {\sqrt3}$ |
• The values obtained experimentally of$\theta_1, \theta_2, \ and \ \theta_3 $ will provide$d_{100}:d_{110}:d_{111}$. Comparing their ratio with above table one can determine crystal structure.