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Double-crystal rocking Curves from a highly perfect silicon crystal were taken in extremely asymmetric schemes, in which the glancing angles of the incident X-rays were very close to the critical angle of total external reflection. The experimental rocking curves were compared with theoretical calculations based both on an ordinary dynamical theory of diffraction and also on an extended dynamical theory, which uses a more exact solution of the fundamental equation of the dynamical theory and takes the effect of specular reflection into account. It is demonstrated from such a comparison that, in the case of extremely asymmetric diffraction, the ordinary treatment of the dynamical theory of diffraction is not valid; in contrast, the extended theory explains the rocking curve very well.

The relationship between the intensity distributions of the crystal truncation rod (CTR) scattering and the surface roughness of a crystal is discussed by developing a kinematic theory for the CTR scattering so as to reflect the two-dimensional aspect of the surface. The intensity of the CTR scattering elongated from a Bragg point is shown to be reduced by a factor |Γ(q)|2 for a surface possessing some roughness, where Γ(q) is defined by a simple Fourier summation of γp, the relative area with the same step height p on a surface, i.e. Γ(q) = p = 0∞ γp exp (2πipq), with Σp γp = 1, q being the distance in reciprocal space from the Bragg point along the CTR scattering. A pair-correlation function between the steps can, therefore, be obtained by a simple Fourier integral of the roughness damping factor |Γ(q)|2. For the case where γp has a Gaussian distribution around the average step height, |Γ(q)|2 is approximated by the well known Debye–Waller-like factor, exp (−4π2〈Δp2〉q2), where 〈Δp2〉 is the mean square deviation of step height in units of the lattice spacing. The intensity formulae proposed so far by several authors are also discussed on the basis of the above factor.

Triple-crystal diffraction studies are capable of cleanly separating the various experimental components of the scattering in the vicinity of a Brags peak. The two-dimensional intensity distributions obtained in such an experiment consist of various components which extend in distinct directions in (Atos, A2Os) space, where Atos and A20s are the offset angles of the sample and analyzer/detector from the Bragg condition. One-dimensional 'slice' scans can be used in studying specific details, given a known disposition of the components, be they dynamical, kinematical or aspects of the instrumental arrangement. In this paper triple-crystal diffraction results obtained for given ion-implanted and other Si crystals using both a conventional X-ray tube and a synchrotron source are presented and compared.

In the paper by Stevenson & Harada [Acta Cryst. (1983), A39, 202-207] the calculated values of Δ' (and consequently δ{\bar B}) in Table 1 are in error. For KCl and BaF2 the conventional (rather than primitive) unit-cell volumes were mistakenly used when calculating qzB. For CdS and CdSe the factor used to get q'zB from qzB was incorrect. The new (corrected) Table 1 is given below. The agreement between δ{\bar B} and δ{\bar B}obs is, with the new δ{\bar B} values, generally better; with δ{\bar B} for KCl closer to the δ{\bar B}obs value given by Cooper & Rouse [Acta Cryst. (1968), A24, 405-410], namely 0.16 A2. The calculated value of the "overall" temperature parameter for CdS becomes 1.29 A2. It should also be noted that there is a factor of 2 missing from the denominator of equation (15).