International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. C, ch. 5.2, p. 495

The symmetrical Bragg–Brentano (Parrish) and the Seemann–Bohlin angledispersive diffractometers are fully described in Chapter 2.3 . The centroid and peak displacements and the variances of the aberrations of the symmetrical diffractometer have been collected by Wilson (1961, 1963, 1965c, 1970a, 1974). For the Seemann–Bohlin type, they are collected in Table 5.2.4.1, mainly from Wilson (1974). They are expressed in inverse powers of the source–specimen distance S and the specimen–detector distance R, and tend to be larger for the Seemann–Bohlin arrangement than for the symmetrical arrangement. For the latter, S and R are constant and equal to the radius, say , of the diffractometer, whereas, for the former, and where is the constant angle that the incident Xrays make with the specimen surface. In the Seemann–Bohlin case, S will be constant at a value depending on the choice of angle , but usually less than , and R will vary with , approaching zero as θ approaches . There will thus be a range of for which the Seemann–Bohlin aberrations containing R become very large. Mack & Parrish (1967) have confirmed experimentally the expected differences in favour of the symmetrical arrangement for general use, even though the effective equatorial divergence (`flatspecimen error') can be greatly reduced by curving the specimen appropriately in the Seemann–Bohlin arrangement. The aberrations for the symmetrical arrangement are found by putting , in the expression in Table 5.2.4.1; they are given explicitly by Wilson (1963, 1965c, 1970a).
Notation: 2A = illuminated length of specimen; β = angle of equatorial missetting of specimen; γ = angle of inclination of plane of specimen to axis of rotation; Δ = angular aperture of Soller slits; μ = linear absorption coefficient of specimen; r_{1} = width of receiving slit (varies with θ in some designs of diffractometer); s = specimensurface displacement; f_{1} = projected width of focal line; h = half height of focal line, specimen, and receiving slit, taken as equal; 1 − δ = index of refraction; p = effective particle size.

References
Mack, M. & Parrish, W. (1967). Seemann–Bohlin Xray diffractometry. II. Comparison of aberrations and intensity with conventional diffractometer. Acta Cryst. 23, 693–700.Wilson, A. J. C. (1961). A note on peak displacements in Xray diffractometry. Proc. Phys. Soc. London, 78, 249–255.
Wilson, A. J. C. (1963). Mathematical theory of Xray powder diffractometry. Eindhoven: Centrex.
Wilson, A. J. C. (1965c). Röntgenstrahlpulverdiffractometrie. Mathematische Theorie. Eindhoven: Centrex.
Wilson, A. J. C. (1970a). Elements of Xray crystallography. Reading, MA: AddisonWesley.
Wilson, A. J. C. (1974). Powder diffractometry. Xray diffraction, by L. V. Azaroff, R. Kaplow, N. Kato, R. Weiss, A. J. C. Wilson & R. A. Young, Chap. 6. New York: McGrawHill.