XCVII. <i>The intensity of reflexion of X rays by crystals</i>

Abstract

W EEN a pencil of homogeneous X rays is incident upon a crystal face it is reflected when, and only when, the angle 0 between the pencil and the face satisfies the equation n~=2d sin Or, where X is the wave-length of the rays, n is an integer, and d is the distance between any plane and the nearest which is similar and similarly placed.In the simplest kind of arrangement, all the planes are similar and equally spaced, and d is then the distance between two neighbouring planes.If X and d are given, if, that is to say, a certain X-ray pencil falls on a certain crystal face, several values of 8 may be found to satisfy the equation, corresponding to consecutive values of the integer.The reflexions occurring at the angles 9 1 ~ 9 a 2k 3x sin-~d' sin-2d' sin-12d ' .... may be called the reflexions or spectra of the first, second, third order, and so on.When the planes are equal and squally spaced the intensities of the reflexions decrease rapidly and continuously as n increases ; reflexions of an order higher than the fifth or perhaps the sixth have not been observed.When the arrangement of planes is more complicated this regular diminution in intensity may be greatly modified.Complication may arise in either or both of two ways.The planes may be unequally spaced, or they may be dissimilar.An example of the former effect is to be found in the reflexion from the cleavage face (111) of the diamond.In this cas~ the planes are arranged at distances apart which are alternately as ] to 3 :~.In consequence the second order reflexion d,sappears entirely (lee.cir.).The intensity of the third and fifth are normal in comparison with the first, but the fourth is twice as strong as it should be.An example of the effect of want of similarity in the planes may be illustrated by reference to the (111) planes of rocksalt w In this case the spacing is uniform but the planes 9 Communicated by the Author.