Crystal axis

Austenitic Steel weld has a well defined transcrystalline (oriented) macrostructure with continuously changing orientation of the crystal axis - from the periphery towards the centre the angle between the axis of the crystal and the axis of the weld is changed from 90 to 0 degrees. Weld metal eould be possible to approximate in the form of a discrete combination of crystals with parallel axes of the crystallites. 

The examples in Figure 3 illustrate these possibilities. Figure 3a shows a diffraction pattern from a single crystal Fe thin film, oriented with the [001] crystal axis... 

Kristall. m. crystal, -abscheidung, /. separation of crystals, -achse, /. crystal axis, crystallographic axis. 

Figure 6-4. Qualitative energy level diagram of the 1 Bu excinm band structure of T<, at A =0 derived by the Ewald dipole-dipole sums for excitation light propagating along the a crystal axis.

Important ferroelectric materials are those with piezoelectric characteristics. They are crystalline ceramics that exhibit expansion along one crystal axis and contraction along another when subjected to an electrical field. Conversely, compression generates an electrical voltage across the material. These materials have a large number of industrial applications. 

SHG has been used to study electrode surface symmetry and order using an approach known as SH rotational anisotropy. A single-crystal electrode is rotated about its surface normal and the modulation of the SH intensity is measured as the angle (9) between the plane of incidence and a given crystal axis or direction. Figure 27.34 shows in situ SHG results for an Au(ll 1) electrode in 0.1 M NaC104 + 0.002 M NaBr, using a p-polarized beam. The results indicate the presence of two distinct onefold... 

Fig. 32. Packing relations and steric fit of the 26 acetic acid (1 1) clathrate (isomorphous with the corresponding propionic acid clathrate of 26)1U- (a) Stereoscopic packing illustration acetic acid (shown in stick style) forms dimers in the tunnel running along the c crystal axis of the 26 host matrix (space filling representation, O atoms shaded), (b) Electron density contours in the plane of the acetic acid dimer sa First contour (solid line) is at 0.4 eA" while subsequent ones are with arbitrary spacings of either 0.5 and 1 eA 3. Density of the enclosing walls comes from C and H atoms of host molecules.

Spectra of radicals in a dilute single crystal are obtained for various orientations, usually with the field perpendicular to one of the crystal axes. Each spectrum usually can be analyzed as if they were isotropic to obtain an effective g-value and hyperfine coupling constants for that orientation. Since the g- and hyperfine-matrix principal axes are not necessarily the same as the crystal axes, the matrices, written in the crystal axis system, usually will have off-diagonal elements. Thus, for example, if spectra are obtained for various orientations in the crystal vy-plane, the effective g-value is ... 

For, SHG it is desirable to fabricate fibres which allow single mode operation at the fundamental wavelength so that all the launched power is available for conversion. The frequencies for which single mode operation is possible in a step-index uniaxial crystal cored fibre with crystal axis along the fibre axis are given by (30.)... 

Solvates and hydrates can be unstable when removed from solution, and are not usually desired as the solid form of the final API. The water or solvent molecules often lie along a crystal axis and can diffuse out of the crystal along these channels to achieve equilibrium with the surrounding vapour phase. In some instances this weakens the crystal structure and may cause fragmentation. 

Figure 1.18 shows fluorescence microscopy images of a bipolar three-dye antenna material with POPOP in the middle, followed by Py+ and then by Ox+. The different color regions that can be observed in this simple experiment are impressive. The red color of the luminescence (1) disappears, when the crystal is observed trough a polarizer parallel to the crystal axis while the blue emission disappears when turning the polarizer by 90°. This material is very stable and is easy to handle. 

We consider a zeolite L crystal that contains alike dye molecules, large enough so that orbital overlap is not possible. This imposes restrictions on the angles between the electronic transition moments we must consider (see Figure 1.20). The two important situations where the electronic transition moments of the molecules are strictly oriented parallel to the channel axis and random orientation have been studied quantitatively in [75]. Here, we consider the angles 0 — ay and 7t — 0 + ay, which are equally probable. The parameter 0 is the angle between the transition moments and the crystal axis, which means that k . can be expressed as follows ... 

Since then this method has been used to solve numerous other complex crystal structures [6-13]. Because solving a stmcture from a single projection requires a short (3 to 5 A) crystal axis, the method was later extended to combine the information from several orientations which allows also to uncover stmctures with pronounced overlap of the atom columns in projection. This technique was applied in 1990 to solve the 3D stmcture of the mineral staurolithe HFe2Al9Si404 [14, 15] and more recently to determine the stmcture of the huge quasicrystal approximant v-AlCrFe [16] which contains 129 atoms per as5mimetric unit. How CIP works to solve a crystal stmcture from projected data is shown in figure 10 (for further details see [17]). 

Ketonate complexes of Ru are reported in a number of papers. The parent complex [Ru(acac)3] has been subject to a polarized neutron diffraction study at 4.18 K, to powder neutron diffraction studies and to single-crystal structure determinations at 293 K, 92 K, and 10.5 K. The structure is disordered at all temperatures. Measurements of the magnetic susceptibilities (at 2.5 K and 300 K) have been made along different crystal axis directions, and the results analyzed. An investigation of the relationships between ionization potentials and half-wave potentials of a series of tris(/3-ketonate)Ru complexes has been reported, and the electrochemical properties of [Ru(acac)3] in chloroaluminate molten salt media have been reported. The reduced species [Ru(acac)3] can react with AICI4 reduction by bulk electrolysis of a small amount of [Ru-(acac)3] in the melt yields [RuClg]. ... 

Equation (1) expresses the crystal polarization (P, C/iiF). as a function of the dipole moment (p, Cm) and the unit cell volume (V, iif). In PVDF, it suffices to express Eq. (1) in scalar form, where it is miderstood that P and p represent the components of the polarization and dipole moment vectors parallel to the ( -crystal axis. This arrangement of dipoles produces a significant local electric field in the... 

In drawn metal wires the fibre axis is usually not a crystal axis. The problem of the determination of crystal orientation in such specimens (and in rolled metal sheets), though closely related to those dealt with here, is outside the scope of this book. (The unit cell dimensions, and indeed the complete structures of such crystals, are usually known, and the problems that arise are questions of correlation of physical properties with orientation.) See Schmid and Boas, 1935 Orowan, 1942. 

A one-dimensional Fourier synthesis can be used for the direct determination of atomic parameters along any crystal axis, provided that the phase angles ct for the various orders of reflection are known. For an example, consider the structure of sodium nitrite, already described in Chapter IX. It is body-centred, hence only even orders of 00/ appear their structure amplitudes are 8, 15, 10, 2, and 7 for 002, 004, etc., respectively. 

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