A new, nonlinear X-ray diffraction technique is described which permits the direct experimental det~m~atio~ of the valence electron charge density in a wide variety of covalently bonded materials.
We describe here the theory of a new, nor&near X-ray diffraction technique which permits a direct experimental measurement of the valence eIectron charge d~st~bution in many covalently bonded crystals. Determination of this quantity is a long sought goal of chemical crystallography since its knowledge may be expected to significantly enhance OUT present understanding of chemical bonding. Conventional linear X-ray diffraction methods are capable of measuring only the total electron charge density. From this valence electron charge den&y may be obtained by subtraction of cafculated inner shell electron distributions. Two important limitations of such an approach are the uncertainties of the calculated inner sheIl electron densities -especially that of the'shell immediately below the valence shell, and the necessity of performing very highly accurate measurements throughout a large region of reciprocal space, since the valence electrons gene&y make only a comparatively small contribution to measurable structure factors. In contrast, the method described here permits a determination of diffracted intensities which, ic favorable circumstances, are governed almost completely by the valence electron charge density.
This new technique is based on the spontaneous parametric down conversion of a source of X-rays interacting with a suitabiy oriented crystal. In this nonlinear process an input quantum, called the pump, at the irequenw up, decays into two output quanta, called the signal and idler, at the frequencies os and wil respectively, such that the photon energies are conserved, i.e.,