Quantum X-ray reflection in diamond

Abstract

It has been shown that, corresponding to the usual formula, equation for the classical or unmodified reflection of X-rays, the general geometric law of modified or quantum reflection by crystals is θ and ψ are here the glancing angles of incidence on the static and dynamic stratifications measured in the respective planes of incidence, &epsiv is the angle between these stratifications, and I the inclination of the phase-waves of the lattice vibration to the static crystal planes. The two planes of incidence would coincide when the equations are simultaneously satisfied, and more generally also when the observations are made in a plane of the symmetry of the crystal. We may then write 2 ψ = (φ + θ) and 2 &epsiv = (φ + θ ), where θ and φ are the glancing angles of incidence and of quantum reflection measured with reference to the static crystal planes. The angle I in equation (2) is thus capable of being evaluated directly from observations of the Laue and the quantum reflections over a sufficient range of incidences. If I is φ/2, equation (2) reduces to as a close approximation.