ANISOTROPIC ELASTICITY CORRECTIONS FOR REFLECTION EFFICIENCY AND X-RAY STANDING-WAVE PATTERNS USING BENT CRYSTALS

Anisotropic elasticity corrections are taken into account to evaluate the reflection efficiency I-int and the X-ray standing-wave patterns ( XSWP) P(Delta theta, Phi) for bent crystals, where Delta theta is the angular coordinate associated with the conventional rocking curve and the phase Phi=hr(P) is related to the position with respect to the cry stalline lattice of the adsorbed atoms on the crystal surface, contrib uting to the XSWP. Analytical expressions are derived for the uniform strain-gradient parameter B = 1/4 (partial derivative(2)/ partial deri vative(so) partial derivative(sh)) [hu(r)] governing the peculiarities of the Bragg diffraction within elastically bent crystals, where h is the reflecting vector, u(r) is the displacement vector and so and s(h ) are the dimensionless coordinates along the incident and diffracted waves, respectively. The cases of the so-called free and forced bendin g in the Johann and von Hamos geometries are considered. The results o f the anisotropic elasticity corrections depending on the crystal-surf ace orientation are presented for bent silicon (111) and quartz (10.0) and(10.(1) over bar) orientations.