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The spectral density of the Barkhausen noise has been measured and a theoretical interpretation of the results is given. It is assumed that the single pulse is exponential with a time constant of the order of 10−4 second. Then the computed spectral density is constant up to 1 kcps, and then decreases exponentially. This behavior is only slightly dependent on the shape of the pulse. The theoretical conclusions are in good agreement with experimental data taken on iron, nickel, and ferroxcube specimens.The usual model introduced to explain the mechanism giving rise to the noise leads to the conclusion that the intensity of the spectrum is proportional to the frequency of the magnetizing current. This conclusion is not experimentally verified because of the extreme simplifications involved in the model itself.

A new approach to the problem of the synthesis of resistive n -port networks with (n + 1) nodes is given. First it is shown that, given a conductance matrix G of order n , the signs of its elements define the complete tree of the n port uniquely (if it exists). The case of two (or more) ports in "series" is exceptional: the order of such ports in the complete tree can be found by comparing the absolute values of a couple (or more couples) of elements of G . Once the complete tree has been determined, the synthesis becomes very simple, since the G matrix can be transformed into another matrix Go referred to a set of node-to-datum independent voltages, whose conditions of realizability are well known.

It is shown that every transformation in theJ-H plane of a ferromagnetic specimen can be computed from the magnetization curve and saturation loop of the material. This is based on the assumption that each volume element is characterized by a rectangular loop of sidesa andb (Preisach model). Also, it must be assumed that a distribution function φ(a, b), related to the probability density of finding a loop with given (a, b), exists and is unique. Then, given an arbitrary path ofH, φ(a, b) permits the computation of the corresponding path ofJ. The function φ(a, b) can be computed numerically by manipulation of the magnetization curve and saturation loop. Experiments have been carried out on two materials, magnetically quite different. The theoretical curves fit the experimental data quite well.

The theory of magnetic viscosity due to solute atom pairs has been verified on several bcc alloys. The results on Fe‐Si alloys with Si content up to 6% wt show that solute atom pairs give magnetic viscosity. If the strong effect of the temperature is taken into account, the induced anisotropy energy deduced from the viscosity field can be considered in agreement with the value measured directly from the magnetization curves. The results on a series of Fe‐Al alloys up to 25 at. % Al, where order occurs, further confirm the theory. The viscosity field is, with reasonable agreement, proportional to the number of solute atom pairs, as deduced from studies on ordering of the alloy and from the internal friction resulting from corresponding stress‐induced ordering.

The effects of fast neutron irradiation with doses of 1018 nvt on permeability, coercive force and approach to saturation of very high permeability pure iron and nickel were studied. No significant changes were noted on nickel (maximum permeability 5000). On iron (maximum permeability about 150 000,Hc 2.5 A/m) coercive force increased by about 0.8 A/m, maximum permeability decreased by about 30%, and no change was noted in the curve of approach to saturation and hence in the anisotropy energy. After annealing the irradiated iron specimens at 100 °C, a further increase of coercive force was observed, and after annealing at 200 °C, on one of the specimens a loop with strong waspwaisted form was noted. Finally most of the changes in magnetic properties due to irradiation were almost completely recovered below 250 °C. The possible theoretical interpretations of the results are discussed. The kinetics of the annealing leads to exclude that the effects are due to free iron interstitials and probably also to dislocations loops. Hence it shall be thought of some type of anisotropic point defects which interact with the magnetization vector and move with and activation energy of about 1.2 eV at temperatures of (100÷200) °C.

A specimen of iron containing 0.01% of C in solid solution has been cold worked by 7% and aged at room temperature. After this treatment it shows a new peak of magnetic viscosity at 180°C. The diffusion process giving rise to the peak is controlled by an activation energy of about 32 000 cal/g atom and a time constant at infinite temperature of about 10−14 sec. These figures agree with those of a peak of internal friction observed in similar specimens by Ke and by Koster, and interpreted as due to diffusion of C atoms in the surroundings of the dislocations. Hence the peak of magnetic viscosity can be related to the same mechanism.

In the present work we show that a sufficient, but not necessary condition, such as a magnetic material exibits magnetic annealing is that it presents also, in a proper temperature range, diffusion magnetic viscosity. Besides, ifH t is the maximum value of the viscosity field, the energyH tJs is nearly equal to the anisotropy energyK u induced by annealing in a magnetic field, at least for measurements performed at the same temperature. It is also shown that the anomalies of specific heat, associated to the process of annealing, are so small that they cannot be observed experimentally. The experimental verifications are made on iron containing interstitial carbon. The values of the energyH tJs, obtained from the measure of the maximum value of the viscosity field, are lower than, but of the same order of magnitude as those of the induced anisotropy constant, measured directly. If one considers the poor accuracy with whichK u could be determined one can consider the agreement obtained to be satisfactory.

It is shown that solute atom pairs in ferromagnetic alloys, as well as the interstitial atoms in iron, can give magnetic viscosity.The viscosity field of the alloys vs wall displacement is determined for various crystal structures. The maximum value of the viscosity field is related to the anisotropy energy induced in the same materials by heat treating in a magnetic field.

It is shown that the analytical theory of hysteresis, which determines the value of J at the end of an arbitrary path of H if the magnetization curve and the saturation loop are known, can be extended to compute the energy losses due to hysteresis along an arbitrary transformation, open or closed, in the (J, H) plane. The theoretical data have been computed for a soft iron specimen and for an Alnico type material. The latter have been compared with experimental data taken by Bates and Simpson on a similar material. The quantitative agreement between theoretical and experimental curves is quite satisfactory.

It is shown that it is possible to determine whether a given conductance matrix of order n is realizable by a network with n + 1 nodes without going through the actual realization of the tree. This realizability criterion requires only a proper arrangement of the rows and columns of the sign matrix, corresponding to the assigned conductance matrix.

The possibility of using the Preisach model for hysteresis in the high field region is beeing investigated. A similar research being in progress at the T. H. of Stuttgart (1), it seems useful to report some of our preliminary results. The detailed theory of the model, and more experimental data will be available shortly. PREISACH (3) has shown that magnetic hysteresis can be formally explained assuming that the ferromagnetic behavior of a volume element in the material is simply a rectangular loop, in general not symmetric with respect to the /-axes; so that the four sides of the loop are represented by

Among the various ways of representing the pores of a porous substance, we consider the “ink-bottles” model, according to which each pore is a cavity of radius r1 with a neck of radius r2. The size distribution of the pores is the function f(r1,r2) such that f(r1,r2)dr1, dr2 is the volume of pores having radii in the ranges dr1 and dr2 around r1 and r2. A method of determining f(r1,r2) from both the adsorption and desorption curves is given. It is very similar to a technique used in treating magnetic hysteresis since in both cases the whole specimen can be considered as composed of elementary parts having rectangular hysteresis loops. The distribution of pores thus obtained can be compared with the distributions obtained from other techniques.

Rings of iron with permeability of about 150 000, after neutron bombardment (1×1018 nvt), show lower permeability and higher coercive force. This effect can be interpreted as due to large defects giving long range internal stresses, or as due to anisotropic defects interacting with the magnetization vector at each point of the specimen.

Given a conductance matrix G of order n, the problem of realizing it by a network with n + 1 nodes can be split in two parts: to find the tree of the ports corresponding to the given matrix G; and to determine the actual resistances of the branches of the network. A procedure to solve the first (topological) problem is proposed, which is simply concerned with the signs of the elements of the given matrix G. The successful development of the procedure can be considered as a necessary and sufficient condition for the existence of a tree corresponding to G.