Lattice strain anisotropy

PRE-TRANSFORMATION LATTICE STRAIN ANISOTROPY AND CENTRAL PEAK SCATTERING... 

Lattice gas Lattice parameter Lattice strain anisotropy Lic[uid alloys... 

Fig. 10. Applied field dependence of the = 0 magnon energy gap in Tb—10%Ho demonstrating the validity of the frozen-lattice strain approximation as manifested by the minimum, but non-vanishing, of the gap energy at a held corresponding to the basal plane anisotropy held. Data taken with the field along the hard basal plane direction, except for the curves marked easy (axis) which show a linear increase of gap energy with field. The lines are theoretical curves. Different symbols are used to distinguish data taken at different temperatures. (After Nielsen et al. 1970b.)...

There is a variety of methods available to coating, substrate and interface stresses. For metallic films. X-ray diffraction, in which the diffraction angle of X-rays is correlated to the internal strain in the crystalline structure of the coating, can be used to characterize the residual stress state. A common method is the so-called sin method, normally used when anisotropy is expected in the residual stress. The elastic lattice strain is measured via X-ray diffraction with respect to Euler angles, (p and xj/ as related to the Cartesian strain tensor, and finally to the residual stress tensor (see, for example, [69,70]). 

Oriented In-Plane Texture. In this kind of film the properties (H and in the various in-plane directions (texture and nontexture directions) are different. The texture of the film can be supported by the texture of the substrate and the crystal lattice can be smaller in the texture direction than in the transverse direction. This can be the source for strain-induced magnetic anisotropy (magnetostriction). It is also found that the crystal is aligned in the texture direction (92). 

The stored strain energy can also be determined for the general case of multiaxial stresses [1] and lattices of varying crystal structure and anisotropy. The latter could be important at interfaces where mode mixing can occur, or for fracture of rubber, where f/ is a function of the three stretch rations 1], A2 and A3, for example, via the Mooney-Rivlin equation, or suitable finite deformation strain energy functional. 

In metalloproteins, the paramagnet is an inseparable part of the native biomacromolecule, and so anisotropy in the metal EPR is not averaged away in aqueous solution at ambient temperatures. This opens the way to study metalloprotein EPR under conditions that would seem to approach those of the physiology of the cell more closely than when using frozen aqueous solutions. Still the number of papers describing metalloprotein bioEPR studies in the frozen state by far outnumbers studies in the liquid state. Several additional theoretical and practical problems are related to the latter (1) increased spin-lattice relaxation rate, (2) (bio)chemical reactivity, (3) unfavorable Boltzmann distributions, (4) limited tumbling rates, and (5) undefined g-strain. 

At variance with the evaporated samples, Am and did not change much for the sol-gel ones, in spite of the difference between AE cation radii size (Fig. lb, c). It can be suggested that the sol-gel method succeeded in better introduction of Nd into a solid solution (supported by the TPD results) which also depended to a lower extent on the cation radii size match. The increase of the lattice anisotropy AO (Fig. Id) and the trend of the local strain values to decrease or remain about constant (Fig. lc) indicated that there was competition between disorder sources of different nature dispersed lattice defects and Nd3+ agglomerates. 

A contribution caused by spin-orbit coupling and closely related to magnetocrystalline anisotropy is magnetoelastic anisotropy. Mechanical stress creates a strain which amounts to a lattice distortion and yields a correction to the magnetocrystalline anisotropy. Surface anisotropy is a manifestation of magnetocrystalline anisotropy, too (sections below and Ch. 3). 

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