Recent progress in experimental triplet phase determination by the method of three-beam diffraction for 0108-7673/90/050393-10503.00 non-centrosymmetric light-atom structures is reported. The measurements were carried out with a special 0-circle diffractometer installed at the DORIS II storage ring in Hamburg. Experimental results O 1990 International Union of Crystallography 394 DIRECT MEASUREMENTS OF TRIPLET PHASE RELATIONSHIPS confirm the theoretical considerations. In general, the ~-scan profiles consist of a phase-independent Umweganregung or AuJhellung part superimposed on a phase-dependent part due to the three-beam interference, which contains the phase information.Experimentally, Umweganregung and Aufhellung effects can be evaluated by comparison of the two centrosymmetrically related three-beam cases. It is shown that with moderate phase-independent effects the triplet phase can be determined with an accuracy of about 45 ° . IntroductionIn a recent paper (Hiimmer, Weckert & Bondza, 1989) we reported the direct measurements of triplet phases by means of three-beam interference experiments for two non-centrosymmetric test structures with relatively small unit cells using Cu radiation from a rotating-anode generator. It was shown that the threebeam interference effect leads to typical 0-scan profiles for triplet phases near 0, 180, +90 or -90 °.On the other hand, the theoretical considerations in the preceding paper (Weckert & Hiimmer, 1990) show that it should be possible to achieve a higher precision in experimental triplet phase determination in spite of phase-independent Umweganregung and Aufhellung effects superimposed on the interference effect. The three-beam interference between the primary diffracted wave and the Umweg wave gives rise to the typical 'ideal' 0-scan profiles which carry the phase information. It should be possible to evaluate the troublesome Umweganregung and Aufhellung effects by comparing the 0-scan profiles of two centrosymmetrically related three-beam cases 0/h/g and O/-h/-g which involve equal triples of structurefactor magnitudes but triplet phases of opposite sign if anomalous-dispersion effects can be neglected. However, because of the experimental systematic uncertainties the Umweganregung and Aufhellung should be avoided. Thus, the basic requirement for this procedure is that the primary, secondary and the coupling reflections have nearly equal intensities.Our method of quantitative determination of triplet phases is in some important aspects different from that proposed by Shen & Colella (1988) and Tang & Chang (1988).In the experiments of Shen & Collella the intensity change of very weak primary reflections caused by strong multiple reflections is used. The phase information is obtained from the asymmetry in the wings of the multiple-reflection peaks which are dominated by strong Umweganregung. The asymmetry decreases with decreasing cosine of the triplet phase. So the authors stated that only cos ~b can be determined.In the paper of Tang & Chang (1988) the ...

Direct measurements of triplet phase relationships for non-centrosymmetric light-atom organic structures with medium-size unit cells are reported. The phase information can be extracted from the three- beam profiles of a Renningerψ-scan experiment. The measurements were carried out with a specialψ-circle diffractometer installed on a rotating Cu-anode generator. The incident-beam divergence is reduced to 0.02°. The experimental results confirm the theoretical considerations of paperIof this work [Hümmer & Billy (1986).Acta Cryst.A42, 127-133]. As triplet phases of +90° can be distinguished, the absolute structure can be determined unambiguously. The measurements show that the triplet-phase-dependent interference effects may be superposed on phase-independentUmweganregungorAufhellungeffects. By a comparison of theψ-scan profiles of two centrosymmetrically related three-beam cases, the triplet phases of which have opposite signs, it is possible to evaluate the phase-independent effects and to determine the value of the triplet phase with an accuracy of at least 90°.

The X-ray standing wave technique for the localization of surface atoms has been used so far with crystals in the Bragg-case geometry. Since the standing wave intensity is modulated along the diffracting vector h, the Laue-case geometry with h nearly parallel to the surface is more preferable for the studies of lateral structures of the surface.For this purpose total exter~al reflection at grazing incidence angles is used to create a standing wave extending on both sides of the boundary surface (P. L. Cowan, 1985, Phys. Rev., 32, 5437-5439). Dynamical X-ray diffraction in thisgeometry _ involves two angles that can be controlled independently: the angle of incidence ¢o and the deviation angle 68 from the exact Laue incidence. The geometry is best inspected using a three-dimensional dispersion surface. It can be sgown that the sectioned reciprocal space is divided into four regions, I to IV, where there are zero, one or two standing waves.For P 0 ' located in region I simple specular reflection occurs with no standing wave formed even when the Laue condition is exactly met.In region II the external diffracted wave is evanescent and the standing wave is confined in shallow depths of a few tens Angstrom on the both sides of the interface (P. L. Cowan, ibid.).Here the real part of the external wave vector ;em8ins parallel to the crystal surface. Calculations show that an abrupt change occurs in the specularly reflected beam intensity whenever P 0 ' traverses the sectioned dispersion surface.The ¢ 0 angles where the change occurs define critical angles of total reflection for the two wave fields associated with the two branches of the dispersion surface. A 100% specular reflectivity is expected from non-absorbing crystals only when P 0 ' is located in region I. Otherwise the incident energy is partly spent in exciting the crystal fields.We have confirmed some of the above predictions in experiments using a germanium or gallium arsenide crystal at a synchrotron radiation source, where secondary fluorescent X-rays were measured from the specimen together with the specular and diffracted beams.

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Potassium nitra-c.e {KN'0 3) exhibits complex polymorphism with seven polymorphs in the pressure range Q .• 0-4.0 GPa. We have studied this material at room temperature as a function of pressure up t:o 9.3 GPa usino enercrv dispersive pm-:der diffraction at the SERC Svnchr~'t.ron Radiation source (SRS). ~•le have confirm~d the structure of phas'2. IV r:eEined by neutron Uiffraction at o.JG GPa (Worlton et al., Physica l36B (1986) 503) t orthorhombic ?nma, z = 4. ?he compressibility measured in the range 0.3-9.3 GPa is found-co be anisotropic \•,rith the axial compression a-cios a:b:c = 1.00:0.64:0.50. The differing IT:erits o both X-!:ays and neutrons for high pressure studies are iscussed.