Intensity of X-ray Diffraction by a One-dimensionally Disordered Crystal
(1) General Derivation
1951 Volume 6 Issue 3-4 Pages 95-104
Details
1951 Volume 6 Issue 3-4 Pages 95-104
The intensity formula for the X-ray diffraction by a one-dimensionally disordered crystal was obtained using the matrix-method of Hendricks and Teller for the case of a finite number N of layers (eqs. (15), (16) ) . Deviding (15) by N and putting N→∞, the agreement is obtained between (15) and eq. [29] in their paper, their ∅ (s) and V(s) being correlated with our ∅sand Vs by (20) .The general formula for S=0 (S is the degree of influence of the preceding layers on Pst) is (25) or (26) . Using the relation (27), the term with N in (26) is equal to [20] of Hendricks & Teller. For the special value of ∅s, of (28) the denominators in (26) become 0, in which case (25) becomes (29) and, while only the first term with N in (26) becomes (30) in the limiting value of γ→Γ and is generally very weak, the limiting value of the whole (26) becomes equal to (29) . In case S=0 and ∅s=∅ (26) becomes (32) . In case S=0 and Vs=V, we obtain (36) and (37) . The general formula for S=1 is (15) or (16) itself, which can be, if wanted, separated into two parts, one due to S=0 and the other to S=1, by using (42) or (43) . In case S=1 and ∅s=∅ (15) becomes (49), which turns out (53) for R=2. For a one-dimensional AB-alloy (53) becomes (56) which is equal to (57) in the complete disorder and to (58) or (59) in the perfect order. The agreement can be obtained between (15) and (38) used by Wilson 2) and Jagodzinski 3) by introducing (40) . SjS∗j+ngiven by them for S=1, (60), can be obtained from (40) by taking the special value of (61) for P, which is available only for the close-packed structure. The difference equations for Pn for, S=2 and 3 used by the mwill be obtained from a set of 2s-2simultaneous difference equations for S=S, which will be described in the third report. In conclusion, in order to examine only the general feature of the diffuse scattering we are satisfied only with the term with N in (16) but we should consider the higher term when we examine for example, the relation between the diffuse and Laue scatterings, the crystal with slight irregularities, the intensity near the special point ( (28) ), or specially the crystal with small N (Fig.1.) .
