The elastic anisotropy of permalloy sheet II. Texture of recrystallization

During the recrystallization of rolled permalloy an oriented growth of new grains is observed. The crystals are arranged so that a (100) face is set up parallel to the plane of the plate, and the edge of a [001] cube lies close to the direction of rolling. The formation of a new type of texture also adversely affects the elastic anisotropy of the sheet: the Fourier series which describes the anisotropy after recrystallization then contains a fourth harmonic.     

Magnetocrystalline anisotropy in permalloy revisited

Permalloy with a body-centered-cubic structure has been grown on GaAs(001) by molecular beam epitaxy. Its magnetism, Curie temperature, and magnetic anisotropy are determined experimentally and compared to those of conventional face-centered-cubic Permalloy. Unexpectedly the vanishing magnetic cubic anisotropy in Permalloy is found to be independent of its atomic structure but depends only upon the stoichiometry of Fe and Ni in the FexNi1-x alloy. This observation is further investigated and confirmed by first-principles electronic band calculations, which help to understand the long-standing issue of why Permalloy should be a soft magnet.     

The study of the shape anisotropy in patterned permalloy films

In this paper a systematic ferromagnetic resonance study shows that an in-plane magnetic anisotropy in the patterned micron octagon permalloy (Ni透磁合金;定型薄膜;形状各向异性;铁磁共振patterned film, shape anisotropy, ferromagnetic resonanceProject supported by the National Natural Science Foundation of China (Grant No~50171020) and the Foundation for youth of Liaocheng University (Grant No~X051050).1/5/2007 12:00:00 AMIn this paper a systematic ferromagnetic resonance study shows that an in-plane magnetic anisotropy in the patterned micron octagon permalloy （Ni80Fe20） elements is mainly determined by the element geometry. The easy-axis is along the edge of the elements, and the hard-axis is along the diagonal. The shape anisotropy of the octagon elements is determined by square and equilateral octagon, and the theoretical calculation was studied on the shape anisotropy. The shape anisotropy of rectangular was calculated by using the same theory.     

The elastic anisotropy of nematic elastomers

We examine the robustness of order in nematic elastomers under mechanical strains imposed along and perpendicularly to the director when director rotation is prohibited. In contrast to electric and magnetic fields applied to conventional nematics, mechanical fields are shown theoretically and experimentally to greatly affect the degree of nematic order and related quantities. Unlike in liquid nematics, one can impose fields perpendicular to the director, thereby inducing biaxial order which should be susceptible to experimental detection. Nematic elastomers with unchanging director and degree of order should theoretically have the same elastic moduli for longitudinal and transverse extensions. This is violated when nematic order is permitted to relax in response to strains. Near the transition we predict the longitudinal modulus to be smaller than the transverse modulus; at lower temperatures the converse is true, with a crossover a few degrees below the transition. The differences are ascribed to the different temperature dependence of the stiffness of uniaxial and biaxial order. We synthesised side chain single-crystal nematic polymer networks, performed DSC, X-ray, birefringence, and thermo-mechanical characterisations, and then obtained linear moduli from stress-strain measurements. Received 29 September 2000     

Macrospin limit and configurational anisotropy in nanoscale permalloy triangles

In permalloy submicron triangles, configurational anisotropy—a higher-order form of shape anisotropy—yields three equivalent easy axes, imposed by the structures’ symmetry order. Supported by micromagnetic simulations, an experimental method was devised to evaluate the nanostructure dimensions for which a Stoner-Wohlfarth type of reversal could be used to describe this particular magnetic anisotropy. In this regime, a straightforward procedure using an in-plane rotating field allowed us to quantify experimentally the six-fold anisotropy fields for triangles of different thicknesses and sizes.     

On the effective magnetization and uniaxial anisotropy of permalloy films

The values of the effective magnetization and uniaxial induced anisotropy were measured on permalloy films, vacuum deposited on unheated glass slides, by the method of local ferromagnetic resonance. The double resonance curves of these films indicate the existence of two magnetically different components; to both components there correspond different values of the effective magnetization and uniaxial anisotropy. These quantities have different local and time variations for each component. The results of measurement agree with the recently proposed model of the stratification of thin ferromagnetic films.The authors thank J. Kaczér and F. Kroupa for valuable discussions.     

Universal elastic anisotropy index

Practically all elastic single crystals are anisotropic, which calls for an appropriate universal measure to quantify the extent of anisotropy. A review of the existing anisotropy measures in the literature leads to a conclusion that they lack universality in the sense that they are non-unique and ignore contributions from the bulk part of the elastic stiffness (or compliance) tensor. Proceeding from extremal principles of elasticity, we introduce a new universal anisotropy index that overcomes the above limitations. Furthermore, we establish special relationships between the proposed anisotropy index and the existing anisotropy measures for special cases. A new elastic anisotropy diagram is constructed for over 100 different crystals (from cubic through triclinic), demonstrating that the proposed anisotropy measure is applicable to all types of elastic single crystals, and thus fills an important void in the existing literature.     

The anisotropy of elastic waves in a tellurium crystal

For acoustic waves propagating in an acoustooptic tellurium crystal, the dependence of their polarization on the propagation direction with respect to the crystal axes is discussed. The characteristic features of waves propagating in the crystal are considered; these features manifest themselves in an excess of the phase velocity of shear acoustic modes over the velocity of longitudinal modes. The change in the wave type from quasi-longitudinal to quasi-transverse as a result of the variation in the propagation direction of ultrasound is investigated. It is shown that such a behavior of bulk acoustic waves is caused by the specific relation between the elastic moduli, which differs from the corresponding relations observed in other acoustooptic materials.     

The Eshelby factor for cubic crystals with arbitrary elastic anisotropy

The Eshelby factor for cubic crystals has been calculated for arbitrary anisotropy. One of the two integrations needed could be performed analytically. An expansion up to 4th order in the anisotropy and exact results for special cases are also given.     

金属薄板弹性各向异性检测

当平面声波入射到液体中的金属薄板上时，透射系数将随声波入射角变化，根据这一规律，能够准确地测定声波入射面与金属薄板交线方向上金属板材料的弹性常数，测得金属薄板面内不同方向的弹性常数，对金属薄板弹性各向异性情况将有一清蜥的认识，由于测试过程采用微机控制、数据采集和处理，实现了各向异性测量的全自动化，该方法测试时间短、所需样品小且加工方便，并可测试金属薄板弹性各向异性的均匀度。     

Correlation between elastic anisotropy and magnetic susceptibility anisotropy of sedimentary and metamorphic rock

A correlation has been revealed between the types of acoustic anisotropy and magnetic susceptibility anisotropy for specimens from noncrystalline metamorphic and sedimentary rock has been revealed. This correlation makes it possible to assume that the anisotropy of magnetic and acoustic characteristics has the same origin, namely, the rock texture. The pronounced triaxial acoustic anisotropy for specimens of polycrystalline rock in the absence of external forces makes it possible to judge the fracturing caused by tectonic loads and the degree of this fracturing. The large body of available experimental data allows the expectation that it will be possible to obtain empirical dependences suitable for estimating the intensity of geological processes based on the values of the magnetic susceptibility anisotropy and elasticity tensor anisotropy.     

Influence of elastic anisotropy on structural nanoscale textures

We study the influence of elastic anisotropy on nanoscale precursor textures that exist in some shape-memory alloys and show that tweed occurs in the limit of high elastic anisotropy while a nanocluster phase-separated state occurs for values of anisotropy inhibiting the formation of martensite. These results are consistent with specific heat data, elastic constant measurements, and zero-field cooling or field cooling experiments in nonstoichiometric NiTi alloys.     

Dynamic anisotropy and localization in elastic lattice systems

This paper presents an analytical study and numerical simulations concerning the dynamic anisotropy of lattice systems in vector problems of elasticity. Connections are made with models of optics involving interaction of light with a small aperture and aberration effects. Special attention is given to standing waves possessing directional localization of different kinds. We analyze a special class of waveforms corresponding to saddle points on the dispersion surfaces. Furthermore, a modeling algorithm is developed to design a structured slab of finite thickness, which possesses focusing properties for waves within a certain frequency range.     

The electrical properties of thin permalloy films

The magnetic properties of thin Permalloy films have been the subject of many investigations, but the work on their electrical properties is very limited [1]. By observing the change in electrical resistance with temperature the structural transformations taking place during the annealing of the condensates can be inferred.The authors of [1] did not undertake a detailed study of the electrical properties of Permalloy. They used Permalloy 79NMA in their investigation, and the dependence of the change in electrical resistance on the temperature of annealing in a magnetic field enabled them to reach conclusions about the nature of the uniaxial anisotropy of thin films.In the present work a detailed study has been made of the electrical resistance of Permalloy films in relation to the temperature of the substrate during evaporation and annealing; the temperature coefficient of resistance (TCR) has also been studied.     

Wrapping an adhesive sphere with an elastic sheet

We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss's Theorema Egregium shows that this operation necessarily generates metric distortions (i.e., stretching) as well as bending. As a result, a large variety of contact patterns ranging from simple disks to complex branched shapes are observed as a function of both geometrical and material properties. We describe these different morphologies as a function of two nondimensional parameters comparing, respectively, bending and stretching energies to adhesion. A complete configuration diagram is finally proposed.     

Torsional elastic deformations of microtubules within continuous sheet model

This paper develops a rigorous analysis of the microtubule elastic deformations in terms of the torsional degrees of freedom using the helix-based cylindrical structure of this biopolymer. Methods of differential geometry and the theory of elasticity are employed in our analysis. We find equilibrium conditions and constitutive equations in the linear regime. We estimate the value of torsional rigidity for microtubules based on their structure and some experimentally known elastic properties. The paper concludes with the derivation of a bulk modulus formula for a microtubule in solution. Both the entropy change and the fluctuation of the twist angle are obtained.     

Probing elastic anisotropy from defect dynamics in Langmuir monolayers

We study the dynamics of annihilation of point defects in Langmuir monolayers. The absence of hydrodynamic effects allows us to quantitatively relate the asymmetry in defect mobility to the elastic anisotropy of the material, which in turn can be varied through the control of the surface pressure applied to the monolayer. Using the proposed theoretical analysis, we are able to obtain rather elusive equilibrium properties out of relatively simple dynamical measurements. In particular, we measure the elastic constants and their pressure dependence.     

Relationship between elastic anisotropy and texture in metal-matrix composites

The relationship between elastic anisotropy and texture in two-phase metal-matrix composites has been developed under certain conditions. Using measurements of the six independent ultrasonic velocities V_ij in samples of the aluminium alloys 8091 and 7064 containing up to 20% SiC particles and the formulation given by Bunge, the fourt-order expansion coefficients of the orientation distribution function are determined. The Young's moduli in different directions are also obtained from ultrasonic velocity measurements. Linear correlations between anisotropy described by Young's moduli and texture determined by orientation distribution function expansion coefficients are obtained, and confirm developed relationships for two-phase metal-matrix composites. This result shows that ultrasonic measurements provide a technique for the characterization of texture and elastic anisotropy in these materials.     

First-principles characterisation of the pressure-dependent elastic anisotropy of SnO2 polymorphs

Using DFT calculations, this study investigates the pressure-dependent variations of elastic anisotropy in the following SnO₂ phases: rutile-type (tetragonal; P4₂/mnm), CaCl₂-type (orthorhombic; Pnnm)-, α-PbO₂-type (orthorhombic; Pbcn)- and fluorite-type (cubic; Fm-3m). Experimentally, these polymorphs undergo sequential structural transitions from rutile-type → CaCl₂-type → α-PbO₂-type → fluorite-type with increasing pressure at 11.35, 14.69 and 58.22 GPa, respectively. We estimate the shear anisotropy (A₁ and A₃) on {1?0?0} and {0?0?1} crystallographic planes of the tetragonal phase and (A₁, A₂ and A₃) on {1?0?0}, {0?1?0} and {0?0?1} crystallographic planes of the orthorhombic phases. The rutile-type phase shows strongest shear anisotropy on the {0?0?1} planes (A₂ > 4.8), and the degree of anisotropy increases nonlinearly with pressure. In contrast, the anisotropy is almost absent on the {1?0?0} planes (ie A₁ ~ 1) irrespective of the pressure. The CaCl₂-type phase exhibits similar shear anisotropy behaviour preferentially on {0?0?1} (A₃ > 5), while A₁ and A₂ remain close to 1. The α-PbO₂-type phase shows strikingly different elastic anisotropy characterised by a reversal in anisotropy (A₃ > 1 to < 1) with increasing pressure at a threshold value of 38 GPa. We provide electronic density of states and atomic configuration to account for this pressure-dependent reversal in shear anisotropy. Our study also analyses the directional Young’s moduli for the tetragonal and orthorhombic phases as a function of pressure. Finally, we estimate the band gaps of these four SnO₂ phases as a function of pressure which are in agreement with the previous results.     

High-pressure elastic anisotropy and superconductivity of hafnium:A first-principles calculation

The elastic anisotropy and superconductivity upon hydrostatic compression of α, ω, and β Hf are investigated using first-principle methods. The results of elastic anisotropies show that they increase with increasing pressure for α andω phases, while decrease upon compression for β phase. The calculated superconducting transition temperatures are in excellent agreement with experiments. Electron–phonon coupling constants(λ) are increasing with pressure for α and ωphases, while decreasing for β phase. For β phase, the large values of λ are mainly due to the obvious TA1 soft mode.Under further compression, the TA1 soft vibrational mode will disappear gradually.