Interplanar angles equations

X rays from a copper X-ray tube (A = 1.54 A) were diffracted at an angle of 14.22° by a crystal of silicon. Assuming first-order diffraction (n — 1 in the Bragg equation), what is the interplanar spacing in silicon ... 

We measure accurately the distances between the lines on the film. From these and the dimensions of the camera, the diffraction angle 29 can be calculated for each set of planes. From the Bragg angle 9 the interplanar spacings d are calculated from the Bragg equation. 

Diffraction is described by either Bragg or von Laue equations. The Bragg equation relates as a condition for constructive interference the wavelength of the electromagnetic radiation k to the interplanar distance a and the observation angle 0... 

It is clear that the XRD pattern of the modified cellulose exhibited diffraction peaks at the 20 angles of 17 and 22°. The position of the peak at 17° indicated an increase in interplanar distance of the treated fibres when compared to the pristine sugar cane leaves. The results indicated the formation of order in cofibres after chemical treatment. The crystalline content of the modified cellulose was calculated from Equation (13.1) " ... 

Solution Bragg s law should be used to solve this problem (refer to Section 6.3.5 and eq. (6.3.11), Figure 6.20). In the equation mentioned, 9 is the incident angle and (p is the deflection angle. The picture is repeated here to make the situation clearer (Figure E6.14 an atomic arrangement is not depicted substituted by two reflected planes with interplanar distance d ). It is seen in the picture that cp = 26. The crystallographic plane s index is (600), in fact there is no such plane in the crystal this should be understood as a 6th order of reflection from the plane (100) (i.e., at distance... 

Periods of lattices a, b, c together with angles a, y, plane indexes (/ , k, 1) and interplanar spacing d are bound by a so-called quadratic form. For the simplest case of a cubic crystal, the quadratic form is presented by the equation... 

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