(i) Rotating crystal method: In this method crystal is mounted on a rod & kept inside a cylindrical drum. A photographic film is wrapped over the drum & when X-rays are allowed to pass through a narrow aperture & when it reaches the crystal diffracted pattern will get recorded on the photographic film. The main advantage here is as crystal rotates all the 3 axes are taken into consideration & hence 3d diffracted pattern is obtained.
This principle is used in Bragg’s spectrometer. Thus variation in glancing angle is achieved here-
Bragg’s spectrometer is a modified version of ordinary spectrometer to satisfy the use of X-rays.
Bragg's X-Ray Spectrometer
Notations:-
C - Crystal
Co - Collimator
T - Turn Table
Ic - Ionization Chamber
θ - Glancing Angle
Here we focus on 3 planes $d_{100}, d_{110}, d_{111}$, so as the crystal keeps on rotating-
A peak in the intensity shows that Bragg’s law is satisfied.
By looking into the graph drawn between the intensity and the glancing angle we can find out $θ_1, θ_2, θ_3$ and so on.
By looking into the ratios of $d_{100}, d_{110}, d_{111}$, we can find the structure of the crystal.
For simple cubic- $d_{100}, d_{110}, d_{111} = 1:\frac{1}{\sqrt{2}} :\frac{1}{\sqrt{3}}$
For BCC - $d_{100}, d_{110}, d_{111} = 1:\frac{2}{\sqrt{2}}:\frac{1}{\sqrt{3}}$
For FCC - $d_{100}, d_{110}, d_{111} = 1:\frac{1}{\sqrt{2}}:\frac{2}{\sqrt{3}}$
(ii) Powder crystal method: In rotating crystal method the crystal has to be in single form but in general attaining single crystal form is very difficult task hence, powder crystal method is preferred. Here, we crush the crystal into a fine powder,which is taken into the capillary tube & when X-rays are passed through it diffracted pattern is obtained.(When Bragg’s pattern is satisfied)
$\frac{L}{πD} = \frac{4θ}{360}$
From the diffracted pattern value of θ is as follows-
$θ = \frac{90L}{πD}$
L- length of arc
D- diameter of the cylindrical drum.
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