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The Borrmann effect (the anomalous transmission of x rays through thick perfect crystals) has been used as the primary diffraction in a study of simultaneous diffraction. The major part of the work is an analysis of multiple diffraction using the dynamical theory of x-ray diffraction. In the analysis we have utilized the concept of normal modes in describing the propagation of the x-ray wave field. We have determined these modes when the Bragg condition is exactly and simultaneously satisfied for all the diffracting planes. The particular configuration studied was one in which only three noncoplanar waves have appreciable amplitudes. We have shown that at least one of the proper modes of any three-field case of the type considered is a nonabsorbing mode of propagation (i.e., having nodes of the electric field at the atomic planes). This indicates that the primary anomalous transmission will persist with little or no change in intensity when a third reciprocal lattice point enters the Ewald sphere. In particular, when the third reciprocal lattice point is of the same family as the primary, simultaneous anomalous transmission is predicted. For this case, a relatively small change in the primary reflected beam and a twofold enhancement of the forward beam is calculated which are seen to be due to a superposition of two degenerate Borrmann effects having a common forward diffraction direction. Experimental results using polarized and unpolarized incident radiation are presented and discussed. 9 E. J. Saccocio and A. Zajac, Acta Cryst. 18, 478 (1965). 10 E. J. Saccocio, Ph.D. thesis, Polytechnic Institute of Brooklyn, 1964 (unpublished).

Changes with temperature of x-ray intensities of the 001 reflections in ice and heavy ice are investigated. Fr~m these the amp~itudes. of thermal motion of oxygen and hydrogen atoms are determined separately. This can be accomplished slllce only hydrogen atoms contribute to the 004 reflection. The thermal amplitudes of the oxygen atoms, which represent molecular amplitudes, can be expressed in terms of a constant Debye c~arac~eristic temperature; 224°K f~r ordinary ice and 237°K for heavy ice. The amplitudes of thermal vibratIOn of the hydrogen and deuterIum atoms as derived from absolute intensities of 004 at various temper~tures, cannot be expressed in terms of a characteristic temperature. They consist of superimposed stretching, bending and Iibrational motions. In addition to these a rotational motion of low zero point energy seems to be present.

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