reciprocal lattice vector
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“Umklapp collisions and thermal conductivity” deals with heat conduction in a dielectric solid. Collisions of phonons are divided into Umklapp and normal according as a reciprocal lattice vector is or is not involved in the phonon momentum balance. A local temperature is defined by appeal to local thermodynamic equilibrium. An equilibrium phonon distribution can be off-centred, yet non-decaying, if the only collisions are “normal”, conserving the total phonon momentum. Then heat flow does not decay, even if a representative collision reverses the phonon group velocity. Conversely, in an Umklapp collision it is the non-conservation of phonon momentum that causes heat flow to decay.

The title compound, C16H9FN2S, crystallizes as a nonmerohedral twin with twin rotation about the reciprocal-lattice vector [10\overline{1}]*. The molecules are nearly planar and the dihedral angle between the planes of the two aryl rings is only 4.4 (2)°. The molecules are linked by pairs of C—H...N hydrogen bonds to form cyclic centrosymmetricR22(18) dimers, which are linked into chains by an aromatic π–π stacking interaction. Comparisons are made with some related 3-aryl-2-thienylacrylonitriles.

High-resolution multi-crystal X-ray diffraction was employed to characterize silicon-on-nothing samples made by a one-dimensional periodic planar array of buried empty channels. When the channels are normal to the scattering plane, under the constraint of lattice continuity from the perfect substrate to the surface, this periodic array gives rise to a well defined Fraunhofer diffraction in a scan crossing a selected reciprocal lattice point and normal to the reciprocal lattice vector (transverse or ω scan). In a longitudinal scan (ω/2θ scan crossing the reciprocal lattice point and parallel to the reciprocal lattice vector) interference fringes are observed. By analysis of the ω scan and numerical fit of the ω/2θ scan, the period of the buried empty channels and their shape, size and lateral gap were easily determined, thanks to the high-resolution optics used for the measurements.

A general procedure for angle calculations for a three-circle goniostat has been developed. This new approach is based on a vector description of the transformation of a reciprocal-lattice vector under the action of a rotation shaft. It does not invoke the use of rotation matrices and applies equally well to cases where the directions of the rotation axes do not conform with coordinate axes of the laboratory system adopted for the analysis.

The design for a large-area doubly focusing neutron monochromator consists of a large number of small square copper single crystals mounted onto thin aluminium blades that both buckle and rotate independently. This avoids the need for large individual alignment mechanisms for each crystal that introduce unacceptably high levels of background. However, it does require that the crystals be oriented such that the diffracting crystallographic planes are parallel to the crystal face. Cold pressing broadens the natural narrow mosaic of the virgin crystal discs to increase the diffracted intensity. This introduces anisotropy into the crystal that determines its orientation in the final monochromator. The alignment procedure used for each crystal before cutting out the square tile in the correct orientation is described. A few crystals are characterized in detail by neutron diffraction at various stages of the operation, revealing the variation in the mosaic width and the angular position of the reciprocal-lattice vector as a function of the azimuthal angle by rotating the crystal about the normal to its face. The twofold symmetry of the mosaic width of the pressed crystal is modulated by the 2π periodicity introduced by the precession of the reciprocal-lattice vector around the crystal face normal. Satisfactorily aligned crystals have a variation in the angular position for diffraction within the allowed tolerance.

By parametrizing the conic surfaces spanned by the reciprocal-lattice vector under the action of the rotation axes, a new procedure for angle calculations for a κ diffractometer is presented. It is applied to obtain angle settings in various modes for a newly developed six-circle diffractometer.

ABSTRACTThe width of double axis X-ray rocking curves of epitaxial GaN layers is shown to be critically dependent on the width of the detector aperture. We show that triple axis diffraction measurements using a crystal analyser before the detector enables the instrument function to be defined and the tilt and dilation distributions separated. All GaN samples examined showed a mosaic structure of misoriented sub-grains with little dilation within the mosaic blocks. In reciprocal space maps this was revealed as a wide distribution of intensity in a direction perpendicular to the reciprocal lattice vector.

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.