Grazing-incidence Bragg–Laue X-ray diffraction

Abstract

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.

Dynamical x-ray diffraction of multilayers and superlattices: Recursion matrix extension to grazing angles

“…[5][6][7][8][9][10][11][12] ͑ii͒ Surface or ''grazing-incidence'' diffraction 13 ͑GID͒ is the geometry where the Bragg planes are perpendicular to the surface and both the x-ray waves are grazing. [14][15][16][17][18][19][20][21][22][23] ͑iii͒ Finally, grazing Bragg-Laue diffraction ͑GBL͒ is a combination of the EAD and GID. It involves the diffraction from atomic planes inclined at a small angle to the crystal surface normal, so that the reciprocal lattice vector points outside the crystal at few degrees to the surface.…”

Phase effects in three-beam grazing-incidence X-ray diffraction

“…Kambe & Miyake, 1954;Hart & Lang, 1961;Colella, 1974;Post, 1977;Chapman, Yoder & Colella, 1981;H~ier & Aanestad, 1981;Chang, 1982;Juretschke, 1982;Hiimmer & Billy, 1986;Shen & Colella, 1988;Mo, Haubach & Thorkildsen, 1988;Chang & Tang, 1988;Hiimmer, Weckert & Bondza, 1989). In the case of grazing-incidence X-ray diffraction, abbreviated as GIXD (Marra, Eisenberger & Cho, 1979;Vineyard, 1982;Afanas'ev & Melkonyan, 1983;Cowan, 1985;Hoche, Briimmer & Nieber, 1986;Sakata & Hashizume, 1988;Fuoss, Liang & Eisenberger, 1989;Durbin & Gog, 1989;Hung & Chang, 1989), X-ray reflection phases should, in principle, also be involved in multi-beam diffraction processes. However, reports on this particular phase problem have not been found in the literature.…”

Theoretical considerations on two-beam and multi-beam grazing-incidence X-ray diffraction: nonabsorbing cases

“…Use of synchrotron radiation is indispensable for carrying out the GIXD experiments (e.g. Cowan, Brennan, Jach, Bedzyk & Materlik, 1986;Sakata & Hashizume, 1988;Durbin & Gog, 1989).…”