X-ray diffraction in the range of two diffracted beams for extremely asymmetric case

Internal waves excited by the dynamical diffraction of X-rays from a single set of crystal planes perpendicular to the incidence surface can produce both Bragg diffracted and reflected beams and Laue diffracted and transmitted beams for crystal slabs of finite thickness. The excitation of Bragg and Laue beams for grazing-incidence diffraction geometries is investigated experimentally and theoretically. The traditional dispersion surface picture for describing allowed internal and external wave vectors is developed to illustrate how the Bragg and Laue beams arise. Experiments performed on a thin silicon wafer demonstrate the evolution of the Laue beams from the back surface into Bragg beams at the front surface of the crystal. The results are in good agreement with calculated curves obtained from the 'n-beam' diffraction theory of Colella [Acta Cryst. (1974), A30, 413-423]. This theory is shown to be very useful for grazing-incidence excitations because of its completely general treatment of Bragg and Laue beams, and the exact numerical nature eliminates the need for approximations. Experiments also reveal how the presence of a 40 ~ AuPd layer on the incidence surface suppresses the Bragg-diffracted beam but not the specular and Laue beams.

Section: Dynamical Diffraction Theorysupporting

confidence: 80%

Grazing-incidence Bragg–Laue X-ray diffraction

Durbin¹,

Gog²

1989

“…Starting with the work of Marra, Eisenberger & Cho (1979) a new technique was developed, the so-called X-ray surface diffraction. The dynamical treatment of these diffraction experiments was given by Afanas'ev & Melkonyan (1983) by means of the extended dynamical theory of X-ray diffraction given by Bedynska (1973Bedynska ( , 1974, Briimmer, Hibche & Nieber (1976a, b, 1979 0108-7673/86/060585-03501.50 and H/irtwig (1976,1977). The aim of this paper is the geometrical interpretation of the phenomena of X-ray surface diffraction on the basis of the three-dimensional dispersion surface.…”

Section: Introductionmentioning

confidence: 99%

Extremely skew X-ray diffraction

Höche¹,

Brümmer²,

Nieber³

1986

Skew reflections are becoming more and more important in X-ray surface diffraction. A geometrical discussion of the whole dispersion surface in extremely skew cases gives the angular ranges of incidence and emergence in which the condition of X-ray diffraction is fulfilled. The main intensity comes from the incidence range given by IX0 --)(hi l/2 • 0i < [,](0"~Xh[ 1/2, where go and gh are the Fourier coefficients of dielectric susceptibility of the crystal. Furthermore, the exit angle of the diffracted beam is of the order of the critical angle of specular total reflection.

“…The requirement of the conservation of total energy is hence fulfilled. For extremely asymmetric reflection, for which the angle between the incident (or diffracted) beam and the crystal surface is less than 2 ° , more than two modes are permitted (Kishino & Kohra, 1971;Bedynska, 1974). For N-beam (N > 2) Borrmann diffraction, there are 2N permitted modes since only transmissions are involved and the characteristics of two-beam (Laue) transmission can be applied.…”

Section: Introductionmentioning

confidence: 99%

The number of permitted modes of propagation inN-beam dynamical diffraction of X-rays

Chang¹

1979

It is shown that the real part of the root of the dispersion equation for the permitted modes of propagation is always positive for two-beam Laue and Bragg reflections at the exact diffraction position. Based on this, a general rule is proposed to determine the number, Np, of permitted modes of propagation for N-beam dynamical diffraction, where no extremely asymmetric reflections are involved. In other words, for both a-and n-polarized wavefields, Np= 2(N-Naragg), where NBrag$ is the number of Bragg reflections involved. This conclusion is supported by calculations for three-, four-, six-and eight-beam cases.