Dynamical Effective Field Model for Interacting Ferrofluids: I. Derivations for homogeneous, inhomogeneous, and polydisperse cases

Quite recently I have proposed a nonperturbative dynamical effective field model (DEFM) to quantitatively describe the dynamics of interacting ferrofluids. Its predictions compare very well with the results from Brownian dynamics simulations. In this paper I put the DEFM on firm theoretical ground by deriving it within the framework of dynamical density functional theory (DDFT), taking into account nonadiabatic effects. The DEFM is generalized to inhomogeneous finite-size samples for which the macroscopic and mesoscopic scale separation is nontrivial due to the presence of long-range dipole-dipole interactions. The demagnetizing field naturally emerges from microscopic considerations and is consistently accounted for. The resulting mesoscopic dynamics only involves macroscopically local quantities such as local magnetization and Maxwell field. Nevertheless, the local demagnetizing field essentially couples to magnetization at distant macroscopic locations. Thus, a two-scale parallel algorithm, involving information transfer between different macroscopic locations, can be applied to fully solve the dynamics in an inhomogeneous sample. I also derive the DEFM for polydisperse ferrofluids, in which different species can be strongly coupled to each other dynamically. I discuss the underlying assumptions in obtaining a thermodynamically consistent polydisperse magnetization relaxation equation, which is of the same generic form as that for monodisperse ferrofluids. The theoretical advances presented in this paper are important for both qualitative understanding and quantitative modeling of the dynamics of ferrofluids and other dipolar systems.

Study of the effect of the demagnetizing field in Epstein strips of grain-oriented electrical steels through 3D finite element analysis

Purpose The purpose of this study is to explore the effect of the demagnetizing field in the Epstein characterization of grain-oriented electrical steels through a finite element method (FEM) simulations. Design/methodology/approach A 3D finite element simulation has been realized to represent the parallel and X-stacking configurations in the Epstein frame. The numerical results have been compared with experimental measures. Findings In a parallel configuration, the measured induction is actually the one in the material, whereas the resulting magnetic field differs from the applied one (in magnitude and angle) due to the shape anisotropy (demagnetizing field). In X-stacking configuration, the resulting magnetic field is close to the applied magnetic field (and then the supposed excitation field in the Epstein frame), whereas the magnetic induction has deviated from the axis of the strips. Originality/value Both stacking configurations (parallel and cross) of the Epstein frame are analyzed by three-dimensional finite element simulation.

A peculiarity of the magnetization of a ferromagnet by an alternating field

It has been experimentally established that the demagnetizing field of the magnetic poles formed at the ends of an open ferromagnetic cylinder decreases with increasing frequency of the magnetizing field due to a decrease in their size under the influence of the surface effect. For this reason, as the frequency of the magnetizing external field increases, the internal field in a ferromagnetic cylinder near the surface approaches it in amplitude. In addition, it has been found that the field on the surface of a ferromagnetic rod magnetized by an alternating field significantly exceeds the latter in strength with increasing frequency of this field.

Magnetic Control over the Topology of Supramolecular Rod Networks

Understanding and controlling supramolecular polymerization are of fundamental importance to create advanced materials and devices. Many stimuli have been explored in the past decades, but magnetic fields and field gradients have received little attention. This is because magnets do not provide enough magnetic energy to overcome thermal noise at the single molecule level. Here we show that significant changes in network topology of Gd³⁺-decorated supramolecular polymer rods can nevertheless be observed using magnetic fields of order 1 T at room temperature. The structure of the rod networks is influenced during a slow diffusive process over a timescale of hours by the anisotropy of the demagnetizing field. Our approach opens opportunities to control and tune structure formation of many supramolecular and coordination polymers using a variety of rare earth or other paramagnetic ions.

Magnetic Control over the Topology of Supramolecular Rod Networks

Understanding and controlling supramolecular polymerization are of fundamental importance to create advanced materials and devices. Many stimuli have been explored in the past decades, but magnetic fields and field gradients have received little attention. This is because magnets do not provide enough magnetic energy to overcome thermal noise at the single molecule level. Here we show that significant changes in network topology of Gd³⁺-decorated supramolecular polymer rods can nevertheless be observed using magnetic fields of order 1 T at room temperature. The structure of the rod networks is influenced during a slow diffusive process over a timescale of hours by the anisotropy of the demagnetizing field. Our approach opens opportunities to control and tune structure formation of many supramolecular and coordination polymers using a variety of rare earth or other paramagnetic ions.

Micromagnetics of curved thin films

In this paper, we aim at a reduced 2d-model describing the observable states of the magnetization in curved thin films. Under some technical assumptions on the geometry of the thin-film, it is well-known that the demagnetizing field behaves like the projection of the magnetization on the normal to the thin film. We remove these assumptions and show that the result holds for a broader class of surfaces; in particular, for compact surfaces. We treat both the stationary case, governed by the micromagnetic energy functional, and the time-dependent case driven by the Landau–Lifshitz–Gilbert equation.

NON-DESTRUCTIVE MAGNETIC TESTING OF THE PHYSICAL AND MECHANICAL PROPERTIES OF MISSION-CRITICAL MOUNTING COMPONENTS MADE OF 30HGSA STEEL

The mounting products with mission-critical functions (bolts, studs, rods) used in aviation technology are subject to increased strength, hardness, and wear resistance requirements. They are made of specially developed medium-carbon steel 30KhGSA alloyed with chromium, manganese, and silicon. According to international classifications, the steel 30KhGSA is steel 42CrMo4-T (EN), 1.7225 (DIN, W.NR), 4140H (AISI). The balance between the strength and plastic properties of the products is achieved by the choice of the mode of their heat treatment – quenching and subsequent medium or high temperature tempering. Possible deviations in the chemical composition of the product materials and the modes of their heat treatment from the prescribed ones lead to unacceptable deviations of the properties of the products. This requires monitoring all products. The physical basis of magnetic structural analysis relies on the fact that mechanical and magnetic properties of steels are sensitive to the structural transformations occurring in them during thermal treatments. It has been proven that the coercive force Нc and the remanent magnetization Мr of many steels are related to their structure. When controlling mass batches of products, the best results in reliability and productivity are achieved by magnetization of products when they fall through a coil with the direct current and measuring the remanent magnetic flux Fd in the product. In this case, Fd in the product is not proportional to Mr, but to Hc of the product material. A characteristic feature of alloyed steels with a carbon content greater than 0.3 %, including steel 30KhGSA (steels 42CrMo4-T, 1.7225, 4140H, 37Cr4, 41Cr4, 46Cr2 and others), is a non-monotonic change in Hc with an increase in the tempering temperature Tо of products. Therefore, magnetic quality control of products from such steels requires a specific procedure. To test the tempering mode of such products, we have proposed to expose the magnetized products to a graded demagnetizing field with the strength Нp, before measuring Fd. The developed method allows us to choose the value of Hp, at which the optimum sensitivity to changes in Tо is achieved while monitoring products of specific sizes. In this report we show that such testing is based on the sensitivity of Fd in the product after its reverse magnetization in the field Hp to the remanent magnetization of the material Mr. We also article the technical means ensuring application of the developed methodology in industrial settings with a control output of up to 2 products per second. Examples of application of the method for controlling the hardness of small bolts made of steel 30HGSA, intended for use in aircraft construction, are given.