Direct Measurements of Densities of Nickel-rich Nickel-Manganese Alloys

The present short note reports the density data measured at room temperature on face-centered cubic nickel-rich Ni-Mn alloys. The specimens were cylindrical rods, about 2mm in diameter and about 140mm long, prepared from electrolytic nickel and electrolytic manganese. The nominal manganese compositions were 6.0, 11.0, 17.0, 22.0 and 27.0 weight percent. The density measurements were made, by using the weighing-in water method, at room temperature (13~14℃) after quenching from 600℃. The results of the measurements show that the density of nickel decreases linearly and rapidly with increasing addition of manganese. The density values calculated from the data of lattice constants of Ni-Mn specimens quenched from 1000℃, as measured by Koster and Rauscher, are in good agreement with the measured data within the limits of experimental error

The ΔE-Effect and Young\u27s Modulus in Nickel-Cobalt Alloys

Young\u27s modulus and its change by magnetization (the ΔE-effect) in annealed nickel-cobalt alloys covering the whole composition range have been measured at ordinary temperatures with the method of magnetostrictive vibration. Young\u27s moduli of γ-phase (face-centered cubic) alloys containing less than 20% Co and of two-phase and ε-phase (close-packed hexagonal) alloys containing 69 to 85% Co increase with magnetization throughout (the ΔE-effect of the first kind), while those of γ-phase alloys containing more than 21% Co decrease first at low magnetizations and then increase (the ΔE-effect of the third kind). This negative ΔE-effect at low magnetizations amounts to -5% at 50% Co, being far more conspicuous than those hitherto known. Young\u27s moduli of ε-phase alloys containing more than 85% Co increase at first, but soon decrease, and finally increase again (the ΔE-effect of the second kind). The saturation value of the ΔE-effect, (ΔE/E_0)_s, shows two conspicuous maxima of 28.0 and 23.7% at 3 and 18% Co, respectively. These values of the ΔE-effect are the highest ones ever found at ordinary temperatures. It is shown that the observed and computed values for (ΔE/E_0)_s are in good agreement with each other for γ-phase alloys. Young\u27s modulus at unmagnetized state, E_0, takes a course nearly opposite to that of (ΔE/E_0)_s in the γ-phase region, showing two minima at 3 and 18% Co. Young\u27s modulus at magnetically saturated state goes parallel to E_0, taking a complicated course even in the γ solid solution range

A new construction of the d-dimensional Buratti–Del Fra dual hyperoval

AbstractThe Buratti–Del Fra dual hyperoval Dd(F2) is one of the four known infinite families of simply connected d-dimensional dual hyperovals over F2 with ambient space of vector dimension (d+1)(d+2)/2 (Buratti and Del Fra (2003) [1]). A criterion (Proposition 1) is given for a d-dimensional dual hyperoval over F2 to be covered by Dd(F2) in terms of the addition formula. Using it, we provide a simpler model of Dd(F2) (Proposition 3). We also give conditions (Lemma 4) for a collection S[B] of (d+1)-dimensional subspaces of K⊕K constructed from a symmetric bilinear form B on K≅F2d+1 to be a quotient of Dd(F2). For when d is even, an explicit form B satisfying these conditions is given. We also provide a proof for the fact that the affine expansion of Dd(F2) is covered by the halved hypercube (Proposition 10)

Ferromagnetic Domain Structure as Affected by the Uniaxial Anisotropy Induced in a 40 Percent Co-Ni Single Crystal

We have found that the domain structure in the annealed state of a 40 percent cobalt-nickel single crystal is very fine and complicated as compared with those of ordinary ferromagnetic crystals but it becomes simpler and larger after quenching from above the Curie temperature. This can be explained as follows : Since the domain structure may in general be fine and complicated at temperatures just below the Curie temperature, domain walls must displace to establish a more stable domain configuration as the temperature lowers. But, this process is suppressed appreciably at relatively low temperatures, because, in solid solution, the ferromagnetic uniaxial anisotropy is induced, in compliance with the domain distribution, by the anisotropic distribution of atoms at high temperatures and the domain wall displacement can take place only by being accompanied by the redistribution of atoms which can not occur at low temperatures. While, in quenching, the specimen crystal is cooled down so rapid that the uniaxial anisotropy and hence the anisotropic distribution of atoms can not be induced, and thus the quenched specimen crystal behaves just as ordinary ferromagnetic crystals. It is shown that these findings together with the results of considerations reported previously lead us to the conclusion that the perminvar-type magnetic properties are due to the stabilization of domain walls by the induced uniaxial anisotropy in f. c. c. solid solutions with cubic anisotropy constants of any sign and b. c. c. solid solutions with negative cubic anisotropy constants

The Additional Magnetic Anisotropy Induced by Magnetic Anneal in Ferromagnetic Face-Centered Cubic Solid Solutions : Part I. Dependence of the Induced Magnetic Anisotropy on the Temperature and Duration of Magnetic Anneal, on the Measuring Temperature, and on the Alloy Composition in Face-Centered Cubic Nickel-Cobalt Alloys

We have studied systematically the character of the induced magnetic anisotropy in face-centered cubic Ni-Co alloys, using a torque magnetometer designed specially for high-temperature measurements. Specimens used are polycrystalline disks of 10.57, 20.78, 30.84, 40.67, 50.17, and 60.20 %Co-Ni alloys and (110) disk single crystal of 12 %Co-Ni alloy. The results and conclusions obtained are as follows : -The magnetic anisotropy energy, E_u, induced by magnetic anneal is uniaxial. Generally, as the duration of magnetic anneal increases, E_u increases nearly exponentially and, as the temperature of magnetic anneal becomes higher, the rate of development of E_u increases but its saturation value decreases. The development of E_u can not be described in terms of single relaxation time and the associated relaxation times become longer as the duration of magnetic anneal increases. The dependence of E_u\u27 on the temperature, Θ, of magnetic anneal and on the measuring temperature, T, can be expressed well by an expression E_u=const. ×{ (I_Θ/I_0)^2/Θ} (I_T/I_0)^2 where I_Θ, I_T, and I_0 are the values of saturation magnetization at Θ(°K), T(°K), and 0°K, respectively, which was derived by Taniguchi and Yamamoto from the so-called directional order theory. The comparison of the measured data on the alloy composition dependence of E_u as corrected for the composition dependence of the Curie temperature with Neel\u27s theoretical formula indicates that the ordering energy of Ni-Co alloys is negative and hence the alloys may be of the precipitation type. In connection with this study, the temperature dependence of the cubic magnetocrystalline anisotropy constants, K_1 and K_2, was measured with 12 %Co-Ni alloy and pure nickel, and it has been found that, as the temperature rises, K_1 of 12 %Co-Ni alloy changes from positive to negative at about 150℃, while K_1 of nickel takes small positive values above 200℃ and that K_2 of 12% Co-Ni alloy is always positive, while K_2 of nickel changes from positive to negative at about 100℃

Magnetic Hysteresis in Annealed Nickel-Cobalt Alloys

The magnetic hysteresis loops have been determined ballistically on annealed nickel-cobalt alloys covering the whole composition range, and their shape, remanence (I_R), and coercive force (H_C) have been studied. Generally, the hysteresis loops of γ-phase (face-centred cubic) alloys are narrow (low H_C) and steep (high I_R), those of ε-phase (close-packed hexagonal) alloys are wide (high H_C) and flat (low I_R), and those of γ+ε-phase alloys are intermediate between the two former. The hysteresis loops of γ-phase alloys containing more than about 25 percent cobalt usually take an abnormal shape like those of perminvars and permalloys. It is pointed out that such abnormal hysteresis loops may be explained by the occurence of an additional uniaxial anisotropy along the direction of magnetization vectors during annealing, which may also be responsible for the effect of magnetic annealing on ferromagnetic solid solutions, as noted recently by us^. The observed I_R values for γ-phase alloys are shown to lie between the two extreme theoretical values derived assuming either that all of the directions of easy magnetization in every crystal grains are energetically isotropic or that only one of them is preferred. H_C as a function of the composition is discussed in terms of the magnetocrystalline anisotropy, magnetoelastic energy and induced uniaxial anisotropy. It is also pointed out that both I_R and H_C in ε-phase alloys may be influenced by the presence of free magnetic poles at grain boundaries

A Theory of the Uniaxial Anisotropy Induced by Magnetic Annealing in Ferrites

In order to explain the magnetic annealing effect in ferrites, we have extended our theory of the ferromagnetic uniaxial anisotropy induced by magnetic annealing in metallic cubic solid solutions to cases of ferrites and derived a general expression for the uniaxial anisotropy induced in ferrites. It is shown that our theory of the magnetic annealing effect in ferrites can explain almost all of the available experimental results on the induced uniaxial anisotropy as dependent on the concentration, on the orientation of the magnetic field during annealing, and on the temperature of magnetic anneal. Thus, we conclude that the uniaxial anisotropy induced by magnetic annealing in ferrite is caused by an anisotropic distribution among cations and cation vacancies, namely, by a mechanism similar to that in ferromagnetic metallic solid solutions. In connection with the present study, a criticism has been made on the explanation of the effect proposed recently by Williams et al., and the concentration dependence of the magnetocrystalline anisotropy constant in binary ferrites composed of cobalt ferrite and other inverse ferrite has also been discussed briefly, based on the model given by Van Vleck and extended by Sugihara

A Theory of the Uniaxial Ferromagnetic Anisotropy Induced by Magnetic Annealing in Cubic Solid Solutions

According to Van Vleck, the cubic ferromagnetic anisotropy may originate from the interplay between the orbital valence and spin-orbit interaction, which results an apparent existence of the dipole-dipole coupling between spins. In a solid solution, the dipole-dipole coupling energy depends not only on the kind of an atom pair but also on the direction of spontaneous magnetization relative to the axis of the atom pair, and consequently it may yield an anisotropic equilibrium distribution of solute atom pairs at temperatures below the Curie temperature, which, in turn, may induce an additional ferromagnetic anisotropy having symmetry lower than cubic. Basing on this idea and using the same model as in Van Vleck\u27s theory of cubic ferromagnetic anisotropy, we have calculated the uniaxial ferromagnetic anisotropy induced by magnetic annealing and obtained results, which agree well with available experimental data, especially as to its magnitude as dependent on the concentration of solute atoms and on the direction of magnetic field applied during annealing and its temperature dependence. Brief decussions in terms of the same idea are also given of the ferromagnetic behaviors of various alloys