Ferromagnetic Spheres Research Articles

Magnetization and domain structure of cylinders and spheres in subsaturating fields

We explore the magnetization patterns and domain walls which may occur in ferromagnetic cylinders and spheres in a certain range of sizes, placed in a uniform external magnetic field below saturation. The solutions found are field-free inside the sample. The analysis is explicitly carried out for circular and elliptic cylinders and spheres, and may be extended to general ellipsoids.

Magnetic Methods for the Treatment of Minerals

Introduction. I. The Physical Principles of Magnetic Separation. Principles of magnetic beneficiation. Magnetic units. Magnetic properties of minerals. Generation of magnetic field in magnetic separator. Measurement of magnetic properties. II. Review of Magnetic Separation Techniques. Dry low-intensity magnetic separators. Wet low-intensity magnetic separators. High-intensity magnetic separators. Wet high-intensity high-gradient magnetic separators. Superconducting magnetic separators. Laboratory magnetic separators. III. Theory of High-Gradient Magnetic Separation. Theory of single-wire particle capture. Theory of capture in multi-wire matrices. Particle capture by ferromagnetic spheres. Particle capture in a real matrix. Magnetic flocculation. Open-gradient magnetic separation. IV. Practical Aspects of Magnetic Separation. Selection of magnetic separation technique. Dry magnetic separation. Wet magnetic separation. Magnetic field. Matrix. Flow velocity. Pulp density. Feed rate. Rinse and flush water. The effect of particle size. The speed of rotation. Pre-treatment of pulp. The selectivity of separation. Comparison of wet high-gradient magnetic separators. Magnetic flocculation. V. Industrial Applications of High-Gradient Magnetic Separation. Minerals treatment. The magnetic beneficiation of coal. The magnetic beneficiation of fly ash. The application of HGMS to waste water treatment. The application of HGMS in nuclear industry. Magnetic filtration of gases. VI. The Economics of Magnetic Separation. Energy costs. The cost of magnetic separators and their economic comparison. The economics of mineral treatment by magnetic separation. Appendices: List of symbols. List of abbreviations. Values of physical constants. Conversion of units. Definitions of derived units. List of selected companies manufacturing magnets, magnetic separators, magnetic measuring instruments and matrices. Bibliography. Subject Index.

Numerical micromagnetics: prolate spheroids

Magnetization patterns during reversal in a ferromagnetic prolate spheroid with a 2:1 aspect ratio were studied by a numerical micromagnetics scheme for a range of material parameters. Some of the results are quite analogous to those observed previously in the authors' (1988) study of a ferromagnetic sphere. Because of the shape anisotropy of the spheroid, certain switching mechanisms found for the sphere were not seen. However, new states, whose dominant features are most easily interpreted in terms of a complex domain wall structure, are found. The reversal process is governed by these states when they occur, and the process is quite complex. >

Nucleation in a ferromagnetic sphere with surface anisotropy

The whole eigenvalue spectrum is studied for the nucleation field in a sphere with a uniaxial surface anisotropy. Detailed calculation is given for the magnetization buckling mode in such a sphere, which is the only reversal mode for rather small radii before the onset of the magnetization curling mode.

New, Z-direction anisotropically conductive composites

This paper reports the development of a new class of anisotropically conductive materials based on magnetic alignment of conductive particles in nonconductive matrix materials such as elastomeric or adhesive polymers. These composites contain many vertically aligned but laterally isolated chains of ferromagnetic metal spheres, the ends of which protrude from the surfaces for better electrical contact. These novel composite structures exhibit Z-direction-only electrical conduction (>1012 to 1 anisotropy ratio), which, in combination with the compliant nature of the materials, can be exploited advantageously for a variety of electronic applications including fine-pitch, area-array, circuit interconnections, circuit-testing, heat sink interfacing, and sensor devices. The movement and alignment of magnetic particles in a viscous medium, and the stability of configurations in a magnetic field will be discussed. The properties of the composite materials as well as potential circuit and device applications will be discussed.

Use of High-Gradient Magnetic Fields for the Separation of Macromolecules

Abstract High gradient magnetic field separation (HGMS) has been used to separate several types of > 1 μm sized ferro- or paramagnetic particles from bulk streams. The majority of the studies have been carried out using a single ferromagnetic wire or wire mesh to produce the field gradients necessary for particle capture. The purpose of this paper is to examine the possibility of using HGMS on < 1 μm entities for the purpose of macromolecular separations. Preliminary experimental results demonstrate that HGMS techniques can be used to capture 0.1 μm diam latex beads from a paramagnetic salt solution passing through a columnar bed of ferro-magnetic spheres.

Cylindrical domains in small ferromagnetic spheres with cubic anisotropy

Magnetization configurations are computed for small ferromagnetic spheres with cubic anisotropy. A cylindrically symmetrical configuration is found, which has a lower energy than a single domain, for a sphere radius larger than about 27.7 nm, for cubic cobalt. In magnetite, the changeover from a single domain to the cylindrical configuration is at a radius of about 27.0 nm. This problem has been studied particularly for cubic iron oxides, used in magnetic recording. >

Cylindrical magnetic domains in small ferromagnetic spheres with uniaxial anisotropy

Abstract Magnetization configurations are computed for ferromagnetic spheres with a uniaxial anistropy, in zero applied field. The magnetization is constrained to be symmetrical about the central plane perpendicular to the easy axis, and to have a cylindrical symmetry about the easy axis, but no other constraint is introduced a priori. The resulting configuration is essentially that of two domains separated by a 180°, cylindrically symmetrical wail. For a sphere with the physical constants of cobalt, this configuration has a lower energy than that of two domains separated by a planar domain wall, calculated by Stapper (1969).

Magnetization distribution in an ideally soft sphere

The magnetization in a perfect, small ferromagnetic sphere with no anisotropy is calculated for a modified Ritz model that allows a central, spherical domain to remain completely saturated. Such a domain is found to be formed at a magnetic field which is about 1/2 of that which is required to saturate the sphere, but it causes only a small change in the total energy, and in the average magnetization. The latter is, thus, still saturating well below the rigorous nucleation field.

Rheological properties of living cytoplasm: a preliminary investigation of squid axoplasm (Loligo pealei).

A magnetic sphere viscoelastometer has been developed to perform rheological experiments in living axoplasm of Loligo pealei. The technique includes the use of a calibrated magnetic sphere viscoelastometer on surgically implanted ferro-magnetic spheres in intact squid giant axons. The axoplasm was discerned to be "living" by the biological criterion of tubulovesicular organelle motility, which was observed before and after experimentation. From these in vivo experiments, new structural characteristics of the axoplasm have been identified. First, analysis of magnetic sphere trajectories has shown the axoplasm to be a complex viscoelastic fluid. Directional experimentation showed that this material is structurally anisotropic, with a greater elastic modulus in the direction parallel to the axon long axis. Second, both magnetic sphere and in vivo capillary experiments suggested that the axoplasm is tenaciously anchored to the axolemma. Third, it was found that axoplasm could be modelled as a linear viscoelastic material in the low shear rate range of 0.0001 to 0.004 s-1. The simplest mechanical model incorporating the discovered properties of the material in this range is Burger's model.

NMR enhancement factor inCuMn(Fe) spin glasses

The spin glass magnetic enhancement factor\(\hat \eta \) has been measured at T=1.3 K with63/65Cu NMR spin echo technique. Alloying iron to CuMn,\(\hat \eta \)(Ho) shows a large range of constancy against an external field Ho, applied in and opposite to the direction of the freezing field Hc. It is supposed that the stiffness of the frozen spin glass is stabilized in this range by a subsystem of ferromagnetic iron clusters. Bound by its own crystalline anisotropy energy, the subsystem has its own stiffness. It probably behaves as a powder system consisting of ferromagnetic single domain particle spheres, having also an isotropic distribution of domain magnetization directions and giving rise to a mean ferromagnetic NMR enhancement factor.

The ball matrix magnetic separator

The ability of a single ferromagnetic ball, magnetized by a uniform magnetic field and surrounded by equisized nonmagnetic balls, to capture magnetizable particles, carried by a fluid through the ball structure, is examined theoretically. It is found that the ability of the ball to capture these particles increases rapidly with an applied field, until the magnetization of the ball is saturated, and then the ability decreases with increasing applied field. A ball matrix magnetic separator consists of a collection of randomly packed equisized ferromagnetic spheres magnetized by an externally applied magnetic field. It has been found that the ability to collect magnetizable particles by such a system improves with increasing applied field until the ferromagnetic balls are magnetically saturated after which the ability to retain capture particles is almost independent of the applied field. This is in contrast to the behavior of a single ferromagnetic ball in free fluid flow whose ability to capture magnetizable particles continues to increase with applied magnetic field after the magnetization of the ball is saturated, it is suggested that the behavior of the ball matrix magnetic separator is largely determined by the geometry of the fluid flow through the matrix rather than by the magnetic properties of the matrix.

A study of the mechanisms of particle buildup on single ferromagnetic wires and spheres

Particle buildup processes for paramagnetic, diamagnetic and ferromagnetic particles in HGMS are reviewed, and new data are presented. Previously published data are discussed using the local flow velocity in the vicinity of a collection wire instead of the average flow velocity.

Magnetization of small amorphous particles

Amorphous ferromagnetic particles are approximated by a theory which assigns, at random, exchange interactions between various parts of a ferromagnetic sphere. These interactions are randomly selected from a gaussian distribution with a standard deviation of 0.3, and include negative exchange values for the lower end of the distribution. The magnetization versus applied field curve is calculated with a specific Ritz model for such a sphere which has a radius of 200 Å and no anisotropy. The result is that the magnetization curve for such a sphere is essentially the same as that of a regular ferromagnet, with a somewhat smaller but constant exchange interaction.

Magnetization curve of zero-anisotropy sphere

A specific Ritz model is suggested, in which magnetization curls around the outer part of a sphere, while an inner core is saturated. This model is used to calculate the magnetic field dependence of the magnetization in perfect ferromagnetic spheres, with no anisotropy. For sufficiently small radii, the results indicate an infinite permeability at zero applied field, which brings the average magnetization to an appreciable part of its saturation value. This is then followed by an almost linear dependence of the average magnetization on the applied field, practically up to saturation.

Electromagnetic excitations of a small gyromagnetic sphere

The interaction of an electromagnetic wave with a small gyromagnetic sphere is formulated in analogy with the perturbation approach applied by Ford, Furdyna, and Werner to gyroelectric spheres. The results predict a new resonance in a magnetic sphere, excited by a uniform rf electric field, with the resonance intensity varying as the fifth power of the sphere radius. The possibility of observing this resonance in a saturated ferromagnetic sphere is suggested.

Magnetic Transfer Devices for Use in Solid-Phase Radioimmunoassays and Enzyme-Linked Immunosorbent Assays

A method was developed for the simultaneous transfer of large numbers of solid-phase adsorbents in radioimmunoassay (RIA) and enzyme-linked immunosorbent assay (ELISA). Specially coated ferromagnetic spheres (beads) were used as the solid phase. These beads were transferred from a reaction mixture through a rinse bath to another reaction mixture by magnetic probes. The quality of results obtained with this new methodology compared favorably with that obtained when solid-phase adsorbents were handled individually. The magnetic transfer system provided a high degree of mechanization, thus permitting many more tests to be performed at one time, under almost identical conditions. Certain mechanical features of the test and the micro scale of the reactions provided substantial economy in time and consumption of valuable reagents. The sensitivities of the RIA and ELISA for detection of viral antibody were about the same. An important advantage in using magnetic devices for transfer of beads is that the immune and enzyme-substrate reactions can be started and stopped instantly in either system.

Magnetic separators: Traction force between ferromagnetic and paramagnetic spheres

The magnetic force which attracts a paramagnetic sphere towards a magnetized ferromagnetic sphere is calculated analytically. The force is maximized with respect to the ratio between the radii of the spheres for different values of the ratio: (external field)/ (magnetization).

Measuring the rotational hysteresis for any orientation of magnetic field relative to the rotational axis of a ferromagnetic sphere

Measuring the rotational hysteresis for any orientation of magnetic field relative to the rotational axis of a ferromagnetic sphere

Magnetization curling in a sphere

Using simplifying assumptions, solutions for the magnetization distribution in the curling mode are obtained for a ferromagnetic sphere with a uniaxial anisotropy. These are used to obtain a magnetization curve for a vanishing anisotropy constant and the remanent domain configuration in a cobalt sphere. In the latter case it is shown that as the radius of the sphere increases, two cylindrically symmetric coaxial domains are being formed. Some features of this configuration are discussed and a comparison is made with previous literature.