Crystals anisotropy

If there is a crystal anisotropy, with the easy axis parallel to the shape-anisotropy axis of the particle, the total anisotropy is = shape + crystal and the total switchHig field is = (A — Aj,)Af + 2Aj = crystal anisotropy constant). In the case of practical... 

In the following development we consider a plane wave of infinite lateral extent traveling in the positive Xj direction (the wave front itself lies in the Xj, Xj plane). When discussing anisotropic materials we restrict discussion to those propagation directions which produce longitudinal particle motion only i.e., if u is the particle velocity, then Uj = Uj = 0. The <100>, <110>, and <111 > direction in cubic crystals have this property, for example. The derivations presented here are heuristic with emphasis on the essential qualitative features of plastic flow. References are provided for those interested in proper quantitative features of crystal anisotropy and nonlinear thermoelasticity. 

This relation is only valid for a crystal with isotropic /-factor. The effect of crystal anisotropy will be treated in Sect. 4.6.2. The function h(6) describes the probability of finding an angle 6 between the direction of the z-axis and the y-ray propagation. In a powder sample, there is a random distribution of the principal axes system of the EFG, and with h 6) = 1, we expect the intensity ratio to be I2J li = I, that is, an asymmetric Mossbauer spectrum. In this case, it is not possible to determine the sign of the quadmpole coupling constant eQV. For a single crystal, where h ) = — 6o) 5 delta-function), the intensity ratio takes the form... 

Effect of Crystal Anisotropy on the Relative Intensities of Hyperfine Splitting Components... 

Mirzamaani et al. [74, 75] point out that the earlier studies of the interrelationships between structure and magnetics have examined films substantially thicker than those now being used in thin-film disks. These authors have examined very thin CoP films and have studied the relative roles of shape anisotropy, stress anisotropy, and crystal anisotropy in determining the magnetic properties. For their CoP-deposition system, shape anisotropy dominated the other factors in determining the film magnetic properties. The shape anisotropy of a particular deposit was determined by the surface condition of the substrate on which the CoP was deposited. 

Complete scattering patterns of samples with a complex single-crystal anisotropy can only be recorded in a texture setup (Chap. 9, Fig. 9.3). The samples must be rotated in order to scan the required fraction of reciprocal space. 

Equation (13) must be made more complicated whenever the crystal anisotropy is taken into account. The relation... 

The main difference from the alkaline dissolution scheme is the hole needed to initiate step 1 of the divalent reaction. The polarizing effect on the Si backbonds is the same for Si-F and Si-OH. From this similarity a certain crystal anisotropy is expected for the divalent reaction, too. Faceting along (111) planes in HF electrolytes is observed when the current density is close to JPS and micro PS formation becomes suppressed. This is the case for the electrode surface shown in Fig. 2.4 or at the tips of macropores as shown in Fig. 9.13b. 

Relaxation induced by super-paramagnetic crystals is moreover complicated by another feature the influence of the electron magnetic moment is modulated by Neel relaxation, which depends on the crystal anisotropy (see Fig. 4). 

The first type is the crystal anisotropy which is responsible for the dependence of the magnetization curves on the orientation of the crystal in the magnetic field. The energy E, which is necessary to deflect the magnetic moment in a single crystal from the easy direction into less easy ones is given for cubic crystals by ... 

For all three types of anisotropy the coercivity can be calculated (Tab. 7.7). For SD magnetite and maghemite, shape anisotropy, dominates over strain and crystal anisotropy, whereas for hematite and goethite, morphology has little influence on coer-civity. 

An alternative way of identifying the domain state of magnetite utilizes the dependence of both the crystal and strain anisotropy constants on temperature. Kj of eq. (7.2) is negative at RTand becomes positive at -118 K, which is the so-called Ver-wey transition at which the crystal anisotropy vanishes and any original remanence, which is controlled by this anisotropy, is lost. This provides an easy test for the do-... 

In frequency regions where absorption is small the two indices of refraction , and n2 give rise to the phenomenon of double refraction. One of the most common uses for this property is in making wave retarders such as quarter-wave plates incident light linearly polarized with equal x and y field components is phase shifted upon transmission because of the two different phase velocities c/w, and c/n2. An entire field, usually referred to as crystal optics, arises out of this and further applications of crystal anisotropy. 

The crystal field does, however, have a dramatic effect on the magnetic anisotropy of lanthanide complexes. For complexes of less than cubic symmetry the three principal values of the susceptibility tensor are unequal. For uniaxial symmetry, Xx — Xy Xz and for biaxial symmetry Xx Xy Xz- Very extensive studies632-640 have been carried out on the single crystal susceptibilities of the D3d lanthanide hexakis(antipyrene) triiodides over the temperature range 80-300 K, and crystal field parameters were obtained. This crystal field-induced anisotropy is responsible for the effectiveness of lanthanide complexes as NMR shift reagents, and single crystal anisotropies of lanthanide complexes have been determined in this connection also.563... 

Another effect of crystal anisotropy is that the diffusion coefficient D turns out to become the diffusion tensor D [73-75]. It results in the asymmetric escape probabilities of geminate pairs in different directions. 

With this background, we have proposed and developed a new purely electrical method for imaging the state of the polarizations in ferroelectric and piezoelectric material and their crystal anisotropy. It involves the measurement of point-to-point variations of the nonlinear dielectric constant of a specimen and is termed scanning nonlinear dielectric microscopy (sndm) [1-7]. This is the first successful purely electrical method for observing the ferroelectric polarization distribution without the influence of the screening effect from free charges. To date, the resolution of this microscope has been improved down to the subnanometer order. 

Therefore, we have concluded that the sndm is very useful for observing ferroelectric nano domain and local crystal anisotropy of dielectric material with sub-nano meter resolution and also has a quite high potential as a nano-domain engineering tool. 

The effect of the strong correlations combined with the restriction to large wavelengths is to give a very narrow spectral response for the bulk substance compared with its structural units. (This may be broadened out in polycrystal specimens as a result of crystal anisotropy.) The crystal situation is in contrast with that in amorphous material, where the response of the units is regarded as only moderately perturbed by correlations which are largely accounted for by an internal-reaction field. 

Today s angle sensors based on the AMR effect allow an accuracy of better than 1° to be obtained over the full measuring range and for temperatures up to +150°C. The main causes of errors are offset drifts (<2 pV V K-1 per bridge). Inaccuracies due to form and uniaxial or crystal anisotropy are only in the range of... 

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