Experimental method of determining Crystal structure
X-ray diffraction and Bragg’s Equation : Crystal structure has been obtained by studying on the diffraction of X-rays by solids. A crystal, having constituents particles arranged in planes at very small distances in three dimension array, acts as diffraction grating for X– rays which have wavelengths of the same order as the spacing in crystal.
When a beam of X-rays passes through a crystalline solid, each atom in the beam scatters some of the radiations. If waves are on same phase means if their peak and trough coincides they add together to give a wave of greater amplitude. This enhancement of intensity is called constructive interference. If waves are out of phase, they cancel. This cancellation is called destructive interference.
Thus X– ray diffraction results from the scattering of X-rays by a regular arrangement of atoms or ions.
Bragg’s equation : Study of internal structure of crystal can be done with the help of X-rays. The distance of the constituent particles can be determined from diffraction value by Bragg’s equation, nλ = 2d sinθ where, l = Wave length of X-rays, n = order of diffraction,
θ = Angle of reflection, d = Distance between two parallel surfaces
The above equation is known as Bragg’s equation or Bragg’s law. The reflection corresponding to n = 1 (for a given family of planes) is called first order reflection; the reflection corresponding to n = 2 is the second order reflection and so on. Thus by measuring n (the order of reflection of the X-rays) and the incidence angle q, we can know d/λ.
From this, d can be calculated if l is known and vice versa. In X-ray reflections, n is generally set as equal to 1. Thus Bragg’s equation may alternatively be written as
λ = 2 d sinθ = 2 dhkl sinθ
Where dhkl denotes the perpendicular distance between adjacent planes with the indices hkl.
