Topic

# Anisotropy

About: Anisotropy is a research topic. Over the lifetime, 55875 publications have been published within this topic receiving 1076026 citations.

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04 May 1948-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences

TL;DR: In this paper, the effect of shape anisotropy on magnetization curves was studied for the case of ellipsoidal spheroids of revolution (e.g., ellipses of revolution).

Abstract: The Becker-Kersten treatment of domain boundary movements is widely applicable in the interpretation of magnetization curves, but it does not account satisfactorily for the higher coercivities obtained, for example, in permanent magnet alloys. It is suggested that in many ferromagnetic materials there may occur ‘particles’ (this term including atomic segregates or ‘islands’ in alloys), distinct in magnetic character from the general matrix, and below the critical size, depending on shape, for which domain boundary formation is energetically possible. For such single-domain particles, change of magnetization can take place only by rotation of the magnetization vector, I O . As the field changes continuously, the resolved magnetization, I H , may change discontinuously at critical values, H O , of the field. The character of the magnetization curves depends on the degree of magnetic anisotropy of the particle, and on the orientation of ‘easy axes’ with respect to the field. The magnetic anisotropy may arise from the shape of the particle, from magneto-crystalline effects, and from strain. A detailed quantitative treatment is given of the effect of shape anisotropy when the particles have the form of ellipsoids of revolution (§§ 2, 3, 4), and a less detailed treatment for the general ellipsoidal form (§ 5). For the first it is convenient to use the non-dimensional parameter such that h = H /(| N a - N b |) I O , N a and N b being the demagnetization coefficients along the polar and equatorial axes. The results are presented in tables and diagrams giving the variation with h of I H / I O . For the special limiting form of the oblate spheroid there is no hysteresis. For the prolate spheroid, as the orientation angle, θ , varies from 0 to 90°, the cyclic magnetization curves change from a rectangular form with | h O | = 1, to a linear non-hysteretic form, with an interesting sequence of intermediate forms. Exact expressions are obtained for the dependence of h θ on θ , and curves for random distribution are computed. All the numerical results are applicable when the anisotropy is due to longitudinal stress, when h = HI 0 /3λδ, where λ is the saturation magnetostriction coefficient, and δ the stress. The results also apply to magneto-crystalline anisotropy in the important and representative case in which there is a unique axis of easy magnetization as for hexagonal cobalt. Estimates are made of the magnitude of the effect of the various types of anisotropy. For iron the maximum coercivities, for the most favourable orientation, due to the magneto-crystalline and strain effects are about 400 and 600 respectively. These values are exceeded by those due to the shape effect in prolate spheroids if the dimensional ratio, m , is greater than 1·1; for m = 10, the corresponding value would be about 10,000 (§7). A fairly precise estimate is made of the lower limit for the equatorial diameter of a particle in the form of a prolate spheroid below which boundary formation cannot occur. As m varies from 1 (the sphere) to 10, this varies from 1·5 to 6·1 x 10 -6 for iron, and from 6·2 to 25 x 10 -6 for nickel (§ 6). A discussion is given (§ 7) of the application of these results to ( a ) non-ferromagnetic metals and alloys containing ferromagnetic ‘impurities’, ( b ) powder magnets, ( e ) high coeravity alloys of the dispersion hardening type. In connexion with ( c ) the possible bearing on the effects of cooling in a magnetic field is indicated.

4,108 citations

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TL;DR: In this paper, an efficient line-of-sight method was implemented to calculate the anisotropy and polarization of the cosmic microwave background for scalar and tensor modes in almost Friedmann-Robertson-Walker models with positive spatial curvature.

Abstract: We implement the efficient line-of-sight method to calculate the anisotropy and polarization of the cosmic microwave background for scalar and tensor modes in almost Friedmann-Robertson-Walker models with positive spatial curvature. We present new results for the polarization power spectra in such models.

3,851 citations

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TL;DR: The equations governing weak anisotropy are much simpler than those governing strong anisotropic, and they are much easier to grasp intuitively as discussed by the authors, which is why they are easier to understand intuitively.

Abstract: Most bulk elastic media are weakly anisotropic. -The equations governing weak anisotropy are much simpler than those governing strong anisotropy, and they are much easier to grasp intuitively. These equations indicate that a certain anisotropic parameter (denoted 6) controls most anisotropic phenomena of importance in exploration geophysics. some of which are nonnegligible even when the anisotropy is weak. The critical parameter 6 is an awkward combination of elastic parameters, a combination which is totally independent of horizontal velocity and which may be either positive or negative in natural contexts.

3,507 citations

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TL;DR: In this article, a theory is suggested which describes the yielding and plastic flow of an anisotropic metal on a macroscopic scale and associated relations are then found between the stress and strain-increment tensors.

Abstract: A theory is suggested which describes, on a macroscopic scale, the yielding and plastic flow of an anisotropic metal. The type of anisotropy considered is that resulting from preferred orientation. A yield criterion is postulated on general grounds which is similar in form to the Huber-Mises criterion for isotropic metals, but which contains six parameters specifying the state of anisotropy. By using von Mises' concept (1928) of a plastic potential, associated relations are then found between the stress and strain-increment tensors. The theory is applied to experiments of Korber & Hoff (1928) on the necking under uniaxial tension of thin strips cut from rolled sheet. It is shown, in full agreement with experimental data, that there are generally two, equally possible, necking directions whose orientation depends on the angle between the strip axis and the rolling direction. As a second example, pure torsion of a thin-walled cylinder is analyzed. With increasing twist anisotropy is developed. In accordance with recent observations by Swift (1947), the theory predicts changes in length of the cylinder. The theory is also applied to determine the earing positions in cups deep-drawn from rolled sheet.

3,097 citations

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TL;DR: A detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) is presented to predict its electrical and optical properties, finding that the mobilities are hole-dominated, rather high and highly anisotropic.

Abstract: Two-dimensional crystals are emerging materials for nanoelectronics. Development of the field requires candidate systems with both a high carrier mobility and, in contrast to graphene, a sufficiently large electronic bandgap. Here we present a detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) to predict its electrical and optical properties. This system has a direct bandgap, tunable from 1.51 eV for a monolayer to 0.59 eV for a five-layer sample. We predict that the mobilities are hole-dominated, rather high and highly anisotropic. The monolayer is exceptional in having an extremely high hole mobility (of order 10,000 cm(2) V(-1) s(-1)) and anomalous elastic properties which reverse the anisotropy. Light absorption spectra indicate linear dichroism between perpendicular in-plane directions, which allows optical determination of the crystalline orientation and optical activation of the anisotropic transport properties. These results make few-layer BP a promising candidate for future electronics.

3,004 citations