W. L. Bragg considered the diffraction as the consequence of contemporaneous reflections of the Xray beam by various lattice planes belonging to the same family (physically, from the atoms lying on these planes). Let θ be the angle between the primary beam and the family of lattice planes with indices h, k, l. The difference in ’path’ between the waves scattered in D and B is equal to AB + BC = 2dsinθ. Consider the triangles ABD and CBD, and notice how DB=d:
AB = DB sin θ = d sin θ and
BC = DB sin θ = d sin θ Therefore, the total path difference between the tow rays (AB+BC) is equal to:
2 d sin θ For successive rays to reinforce, this difference must be a whole number of wavelengths. In other words, maximum positive interference will occur when: nλ =2 d sin θ Since the Xrays penetrate deeply in the crystal a large number of lattice planes will reflect the primary beam: the reflected waves will interfere destructively if the Bragg equation is not verified. The angle for which the Bragg equation is verified is the Bragg angle: for n=1,2,... we obtain reflections (or diffraction effects) of first order, second order, ..., relative to the same family of lattice planes H.

Crystallography > Diffraction >