Crystal anisotropic

M-type ferrites are mainly used as permanent magnet material. They have largely replaced the alnicos as preferred permanent magnet material, as a result of the lower material and processing costs. These ferrites were first introduced under the trade name Ferroxdure, the isotropic form in 1952 (22) and the anisotropic (crystal oriented) form in 1954 (23), and are widely available commercially under various trade names such as Oxid and Koerox. They cover about 55% of the world market of permanent magnet materials, corresponding to 1100 million U.S. doUars (1991), as weU as 55% of the U.S. market, at 300 million. 

Acousto-optic Filters. The newest type of spectrometer to become commercially available is the acousto-optic tunable filter (AOTF). An AOTF is a sohd-state, electronically tunable bandpass filter based on the diffraction of optical waves by acoustic waves in an optically anisotropic crystal. 

Other interference-produced colors falling into this section include doubly refracting materials such as anisotropic crystals and strained isotropic media between polarizers, as in photoelastic stress analysis and in the petrological microscope. 

The measurement of mechanical properties is a major part of the domain of characterisation. The tensile test is the key procedure, and this in turn is linked with the various tests to measure fracture toughness... crudely speaking, the capacity to withstand the weakening effects of defects. Elaborate test procedures have been developed to examine resistance to high-speed impact of projectiles, a property of civil (birdstrike on aircraft) as well as military importance. Another kind of lest is needed to measure the elastic moduli in different directions of an anisotropic crystal this is, for instance, vital for the proper exploitation of quartz crystal slices in quartz watches. 

In anisotropic crystals, the amplitudes of the atomic vibrations are essentially a function of the vibrational direction. As has been shown theoretically by Karyagin [72] and proved experimentally by Goldanskii et al. [48], this is accompanied by an anisotropic Lamb-Mossbauer factor/which in turn causes an asymmetry in quadra-pole split Mossbauer spectra, for example, in the case of 4 = 3/2, f = 1/2 nuclear transitions in polycrystalline absorbers. A detailed description of this phenomenon, called the Goldanskii-Karyagin effect, is given in [73]. The Lamb-Mossbauer factor is given by... 

Under the polarizing microscope, both polymorphs of (ii)-penicillamine were seen as anisotropic crystals, with Form I existing as needles and Form II as plates. 

Thermotropic phases are those that occur in a certain temperature range. If the temperature is raised too high, thermal motion will destroy the delicate cooperative ordering of the LC phase, pushing the material into a conventional isotropic liquid phase. At too low a temperature, most LC materials will form a conventional (though anisotropic) crystal. Many thermotropic LCs exhibit a variety of phases as the temperature is changed. For instance, a particular mesogen may exhibit various smectic and nematic (and finally isotropic) phases as temperature is increased. 

For an anisotropic crystal, jumping frequencies in different directions may not be the same, and, hence, D along each crystallographic direction may be different. The relation between D and jumping frequency may be written as follows ... 

From the very beginning of their experiments, the Curie brothers realized that the linear piezoelectric effect only exists in anisotropic crystals, such as quartz, tourmaline, and Rochelle salt (Curie and Curie, 1880). In fact, as seen from Fig. 9.3, if the +z and -z directions of the plate are equivalent, by reversing the direction of the electric field E-s, the strain should be the same. In such cases, the strain should be proportional to Es 1 instead of E3. In other words, there should be no linear piezoelectric effect. 

Kharlamov A1,K Kirillova NV, Zaytseva ZA (2007) Novel state of carbon transparent threadlike anisotropic crystals. Proc Ukr Acad Sci 5 101-106 Pul Ch, Owens F (2005) Nanotechnology. Tekhnosfera, Moscow, Russia Hoet P, Bruske-Holfeld 1, Salata O (2004) Nanoparticles - known and unknown health risks. J Nanobiotech 2 12-18... 

E. 1. Givargizov, Highly Anisotropic Crystals, Dordrecht, D. Reidel, 1986 1. Sunagawa (ed.j. Morphology of Crystals, Parts A and B, Dordrecht, D. Reidel, 1987 1. Sunagawa (ed.). Morphology of Crystals, Part C, Dordrecht, D. Reidel, 1994 1. Rostov and R. 1. Rostov, Crystal Habits of Minerals, Sofia, Professor Martin Drinov Academic Publishing House and Pensoft... 

The refractive index is the most important optical property and its effect in determining the appearance of the polymer composite has already been referred to above. Amorphous fillers such as glass fibres and beads have only one refractive index, but most mineral fillers are crystalline and have anisotropic crystal structures resulting in a number of different indices, and this can cause complex and undesirable interference effects [27]. 

Molecular type and arrangement deduced from anisotropic properties of crystals. It is evident that, in dealing with crystals of unknown structure, the anisotropic properties may often be used to give direct information about the general shajJe of the molecules or polyatomic ions in the crystals and the way in which the molecules or ions are packed. A strongly anisotropic crystal must contain strongly anisotropic molecules or polyatomic ions packed in such a way that the anisotropies of the different molecules or ions do not neutralize each other, and a consideration of the properties of the crystal in all direc-... 

Using relations (2.5) and (2.6) we can determine the elasticity tensor which describes the linear relation between components of the stress and strain tensors. 2 slr.ss = CEstta n is therefore an expression of Hooke s law for anisotropic crystals... 

Anisotropic crystals have a light absorption coefficient depending on the direction of the light wave and its polarization (IT). This again can be demonstrated in electrochemical experiments with layered crystals ( 1 8). Some results obtained with gallium selenide crystals are shown in the following Figures. 

Im SH, Huang R (2008) Wrinkle patterns of anisotropic crystal films on viscoelastic substrates. J Mech Phys Solids 56 3315-3330... 

The XY model is characterized by a = 0 and b = 1, and all spins are oriented perpendicular to the z-axis. The anisotropy interaction can originate from singleion anisotropy, magnetic dipole-dipole interactions, and anisotropic crystal morphologies. 

Introduction Light propagation within anisotropic crystals... 

The surfaces seen on these photographs are known as ray velocity surfaces. For all uniaxial anisotropic crystals, we have a double surface when the crystal has a positive optic sign (like quartz), the ellipsoid of revolution is enclosed by the sphere, but if the crystal is optically negative (like calcite), the ellipsoid encloses the sphere. The assumption that the form of the variation of velocity for the extraordinary disturbance in uniaxial crystals is ellipsoidal was... 

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