Sine wave structure

Erbium. The easy direction in Er is the c-axis, and below the second-order Neel transition (Tn = 85 K), the moments order in a longitudinal sine-wave structure. As the temperature is lowered the sine squares up. Aroimd Tb = 52 K, a basal plane component begins to order, leading to a helical AFM structure. Finally, at 7c = 20K a first-order transition into a steep cone (opening angle 30 ) FM spin structure takes place. Several (first-order) spin-slip transitions occur in the helical AFM phase. 

A woven sine-wave structure is shown in Figure 9.40, and a complex woven preform is shown in Figure 9.41. The electronics can be placed into slots for various E-textiles applications. 

The structure of iodine at four different pressures. The outlined face-centered unit cell in the 30-Gpa figure corresponds to that of a (distorted) cubic closest-packing of spheres. At 24.6 GPa four unit cells of the face-centered approximant structure are shown the structure is incommensurately modulated, the atomic positions follow a sine wave with a wave length of 3.89 x c. The amplitude of the wave is exaggerated by a factor of two. Lower left Dependence of the twelve interatomic contact distances on pressure... 

This representation of a structure factor is equivalent to thinking of a wave as a complex vector spinning around its axis as it travels thorough space (Fig. 6.2b). If its line of travel is perpendicular to the tail of the vector, then a projection of the head of the vector along the line of travel is the familiar sine wave. The phase of a structure factor tells us the position of the vector at some arbitrary origin, and to know the phase of all reflections means to know all their phase angles with respect to a common origin. 

Fig. 7. Geometry of a helical structure (A) and the form of its diffraction pattern (B). In (A), the pitch (P) of the helix is like the wavelength of a sine wave. The radius (r) of the helix is like the amplitude of the sinewave. The subunit axial translation (h) is the rise along the helix axis from one monomer to the next. If there is not a whole number of monomers in one turn of the helix (said to be a non-integral helix), then there may be a longer repeat (C). In the case illustrated C = 2P. Dimensions in the helix in (A) have their counterparts in the diffraction pattern illustrated in (B), but dimensions in (B) are reciprocal to those in (A). Meridional reflections occur at positions m/h from the equator, where m is an integer. Each of these positions is the center of a so-called helix cross consisting of layer lines, which are n/P up or down from the meridional peaks, where n is another integer. All of the resulting layers of intensity can be related to orders of 1/C, where C is the repeat of the helix and l is the layer line number.

Figure 10 shows the amplitude-weighted phase difference (AWPD) and phase structure (AWPS) functions 1.37 measured using PALS for the aqueous CdS particles (144] discussed in Fig. 9. The conditions are identical (24 C and u = 24 ) with the experiment employing a moving real fringe setup [1.37] and a. 30 Hz, 1.37 V/mm sine wave electric field. The autotrack results utilize a feature of the experimental analysis software [140] that corrects for other convective effects such as sedimentation. The mobility of the particles can be determined by analyzing the data in Fig. 10 with appropriate models for AWPD and AWPS functions (137], Analysis of the data in Fig. 10 yielded AWPD and AWPS...

FIG. 10 Amplitude-weighted phase difference (AWPD) and phase structure (AWPS) functions measured using PALS with autotrack on and off for aqueous CdS particles 1144] at 24 C and 0 = 24 subject to 30 Hz, 1.37 V/mm sine wave electric field. 

In the rheological structure of most food systems there is a viscous element present, and the deformation curves are often highly influenced by the rate of the imposed strain. This is due to the fact that the material relaxes (or flows) while tested under compression and the resultant deformation of this flow is dependent on the nature of the viscous element (Szczesniak, 1963 Peleg and Bagley, 1983). In the viscoelastic food systems, where during processing it is caused to oscillate sinusoidally, the strain curve may or may not be a sine wave. In cases when a periodic oscillatory strain is applied on a food system like fluid material, oscillating stress can be observed. The ideal elastic solid produces a shear stress wave in phase with... 

Fig. 7.17. Arrangement of magnetic moments in more complex ordered materials (a) a helimagnetic structure (b) a sine wave modulated structure.

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