Diffuse Reflexion of X-Rays

Abstract

PROF. G. E. M. JAUNCEY¹ derives the formula: for the relative position of a Bragg reflexion and the so-called “modified reflexion”. The symbols are defined as follows: i is the glancing angle of incidence on the crystal plane for which 8_B = i_B is the Bragg angle: θ_mB is the angle between the incident ray and the direction of scattering of the modified reflexion: i—i_B is supposed to be small. The disposition of the incident ray I, the scattered ray S, and the crystal plane are shown in Fig. 1. Prof. Jauncey deduces (1) from a formula of Sir William Bragg's, and it is obtained from quite different assumptions by Raman and Nath and by Zachariasen. In fact (1) is only an approximation to a formula due to Faxén which may be put in the form: where d is the spacing of the plane for which the Bragg angle is 8: θ(= θ_mB) and i are as shown in Fig. 1. Using Bragg's Law to eliminate d and λ from (2), That (3) is an exact form of (1) may be proved by varying i and θ for constant θ, giving When the angle of incidence changes from θ to i, δi = i—θ, and at the same time the angle of scattering changes from 2θ to θ, so that δθ = θ—2θ: if i is nearly equal to θ, θ = 2θ and θ—i = θ approximately, so that (4) gives which is identical with (1) when the suffixes are introduced.