Abstract
In this paper we introduce Borrmann Spectroscopy as a method for measuring X-ray absorption spectra under conditions of an exotic wave field, namely, a coherent superposition of two plane waves. The essential features of the Borrmann Effect (also known as anomalous transmission) are outlined. We show that the Borrmann Effect can lead to a very strong relative enhancement of quadrupole absorption. After describing some early results in this field, and some general considerations of multiple-wave absorption, we contrast recent results on anisotropy in Borrmann spectroscopy with normal absorption. Despite the qualitative success of a simple model for quadrupole enhancement, temperature dependence and anisotropy, a general theory of the Borrmann Effect is required which includes anisotropic and non-dipolar scattering. We outline some first steps towards such a theory.
Highlights
Introduction and previous work1.1 The Borrmann effectThe Borrmann Effect, discovered over 70 years ago, is one of the most remarkable manifestations of the dynamical diffraction of X-rays [1, 2]
We have previous shown [3,4,5] that while the Borrmann effect leads to a dramatic reduction in dipole absorption, which is driven by the electric field strength, quadrupole absorption, which depends on the field gradient is not diminished, and is effectively enhanced by a very large factor (∼20 or so) relative to dipole absorption
In the absence of magnetism, has a very simple orientation dependence. It is described by a symmetric second-rank tensor i.e. its anisotropy takes the form of an ellipsoid, which is in turn constructed from a scalar plus atomic quadrupoles. (Note that atomic multipoles describe the angular dependence of the atomic or sample properties, whereas multipole absorption or scattering describes the angular dependence of the interaction between the photon and sample)
Summary
The Borrmann Effect, discovered over 70 years ago, is one of the most remarkable manifestations of the dynamical diffraction of X-rays [1, 2]. If the crystal orientation is manipulated so that a strong diffraction condition is excited, there is a dramatic increase in the transmission of the beam (reduction in absorption) for that precise setting This phenomenon is known as anomalous transmission or the Borrmann Effect. There follows a pendellosung oscillation of the relative intensity between the two waves, which eventually dies away and a steady state is reached whereby the two waves have identical intensity and any information about the initial beam direction is lost Such a coherent superposition of the two waves has two possible solutions for each of two linear polarization states: the β-branch, where the standingwave field formed perpendicular to the diffracting crystal planes has the strongest interaction with the lattice, and the α-branch, where the interaction is minimum.
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