Hiroshi Sato

Temperature dependent magnetic contributions to the high field elastic constants of nickel and an Fe-Ni alloy

Abstract Since the fundamental interaction between magnetic moments in a ferromagnet makes a contribution to the total energy, there should also be a corresponding contribution to the elastic constants. In order to observe this effect, the elastic constants C 44 , 1 2 (C 11 −C 12 ) and 1 2 (C 11 +C 12 +2C 44 ) have been measured in nickel and an Fe-30% Ni alloy through their respective Curie temperatures at high enough applied magnetic fields to eliminate the ordinary “Δ E effect” associated with domain wall motion. The intrinsic magnetic interaction which should produce changes in the elastic constants upon passing through the Curie temperature was clearly observed in both materials. The first and the second derivatives of the exchange energy are estimated from these results. Such an interpretation is relatively straightforward for nickel, but the large volume magnetostriction of the Fe-Ni alloy makes the analysis of the data difficult. The measurements on nickel were extended down to 4.2°K while those on the alloy do not go below room temperature because of a possible martensitic transformation of this alloy.

Cation Diffusion and Conductivity in Solid Electrolytes. I

The characteristics of cation diffusion and ionic conductivity in solid electrolytes are discussed using β‐ and β″‐alumina as examples. The problem is characterized by a cation migration by the vacancy mechanism in a “cation‐disordered phase,” a system in which the number of available vacant sites is of the same order of magnitude as the number of diffusing cations. The path probability method is used to derive both the tracer diffusion and the ionic conductivity; this method avoids the difficulties connected with the application of the ordinary random walk approach to such systems. β″‐Alumina is regarded as an example of the “cation‐disordered phases” in which all available cation sites are equivalent, while β‐alumina represents those in which available cation sites are divided into several nonequivalent sublattice sites. When the derived diffusion coefficient is interpreted using the language of the conventional random walk approach, the jump frequency of cations is found to include two factors, the vac...

Substitutional Diffusion in an Ordered System

A general treatment of the atomic diffusion in alloys is given using the path probability method with an approximation taking a pair of lattice points as the basic cluster. Diffusion coefficients for ternary alloys for any degree of order by vacancy mechanism are given. The equations are then simplified by regarding the third atomic species as the isotope of the second atomic species. The theory then gives the isotope diffusion coefficient in binary alloys as functions of the degree of order and of the composition; this diffusion coefficient corresponds directly to the experimental results, and they are compared. The specific importance of the correlation effect in the multicomponent system is emphasized. The calculation of the required physical quantities, the degree of long‐range order, short‐range order, the distribution of the vacancies, etc., in the equilibrium state in ternary alloys with vacancies are also given in the Appendices.

Long period stacking order in close packed structures of metals

Abstract The origin of the stabilization of close packed structures with periodic stacking order in relation to the specific shape of the Fermi surface is investigated. For this purpose, the crystal structures of Au-Mn alloys between 20 and 28% Mn have been analyzed systematically. The structures in these alloys are quite sensitive to a change in composition and each specimen invariably includes several structures which make usage of electron microscopes indispensible for the analysis. The application of electron microscopes to a systematic analysis of crystallographic structures is thus explored and a systematic method of identifying close packed structures and their relations is then established. This allows us to identify all the structures existing in this composition range unambiguously. The structures thus identified are: Au 4 Mn at and around 20% Mn; ∝″(the two-dimensional long period superlattice Au 3 Mn, first identified in single crystal thin films) at around 21–22% Mn, and a series of structures with long period stacking order between 23 and 28% Mn which are of direct interest here. These latter structures have periodic modulations of the stacking order of the M = 1 superlattice (a one-dimensional long period superlattice with antiphase boundaries at each Cu 3 Au type unit cell, often referred to as DO2 2 ), and can be specified as 1 R (the original M = 1 structure with 6 layers in a unit structural period), 5 H (10 layers), 3 R (18 layers) and 6 H 1 and 6 H 2 (both 6 layers). Although varying amounts of these structures coexist in specimens over this composition range, the statistical order of appearance with increasing Mn content is 5 H → 3 R → 6 H (6 H 1 and 6 H 2 ), with coexisting unmodulated M > = 1(1 R ) most noticeably in the composition range of 5 H and 3 R structures. The relation between the size of the Fermi surface and the order of appearance of these modulated structures indicates that these modulations are created in order to shift the Brillouin zone boundaries of the M > = 1 structure to proper places of the Fermi surface when the size of the Fermi surface (or the electron-atom ratio) deviates from the exact value which stabilizes the M = 1 structure. In other words, the modulation in stacking order is an effort of the alloys to create Brillouin zone boundaries at proper places of the Fermi surface in order to reduce the energy of electrons. It can thus be concluded that with respect to their origin, structures with long period stacking order belong to the same category as the long period superlattice, and that “stacking fault boundaries” are, like “antiphase boundaries” a form of low energy boundary which enables the modulated close packed structures to become more stable than the unmodulated structure. In the case of the M = 1 structure, the symmetry of the basal plane allows for the modulation boundary by a unit slip of amount l 6a〈112〉 without destroying the degree of order. Thus the energy to create the boundaries is low and this makes the modulation of the M = 1 structure more favorable. Remarks are made concerning the applicability of these explanations to other metallic systems.

Remarks on magnetically dilute systems

Abstract Because of the inadequacies of previous treatments of the magnetic properties of magnetically dilute systems when used to interpret experimental results, a re-examination of the problem starting from a simple model is made. The treatments of the problem discussed here, using an Ising model, show that a Curie or a Neel temperature does not appear until a finite concentration of magnetic atoms is obtained if the atomic distribution is random. This concentration depends on the co-ordination number of the lattice and on the range of interaction, but not on the strength of the interaction. The results given here for nearest-neighbor interactions describe the general behavior observed in magnetically dilute solutions. Such things as anomalously high values of “effective magnetic moments” per magnetic atom and its concentration-dependence, curvature in inverse susceptibility against temperature plots, and parasitic paramagnetism in the weakly ferromagnetic alloys, &c., are reasonably well explained. When the system has antiferromagnetic interactions, it is found that the inverse susceptibility shows a complicated temperature-dependence varying with concentration and that the existence of a maximum in the susceptibility does not necessarily mean the onset of antiferromagnetism. Special references are made to iron in gold and chromium and to manganese in copper.

Characteristics of superlattice formation in alloys of face centered cubic structure

The order-disorder transition in the face centered cubic (f.c.c.) lattice and that in the body centered cubic (b.c.c.) lattice, both calculated based on the tetrahedron approximation of the cluster-variation method, are compared. Although in the b.c.c. lattice the mathematics for the Ising model ferromagnets and for the AB-type alloys are completely equivalent, the transition point Tc of superlattice formation in the f.c.c. lattice is of the first order and is much lower than Tc of the Ising model ferromagnetism. Reflecting this characteristic, an appreciable degree of short-range order is extended over a wide temperature range above Tc in f.c.c. alloys, while the short-range order is appreciable only near Tc in b.c.c. alloys and decreases rapidly as the temperature rises. If only the nearest neighbor interaction is taken into account, both the A3B- and the AB-type superlattices are not deterministic with respect to the one-dimensional disorder created by the antiphase boundaries of the first kind. The degeneracy is removed by the inclusion of long-distance interactions. The relation of this charactersitic to the longperiod superlattice is discussed. It is shown that the stability of the long-period superlattice at higher temperatures than the normal superlattice cannot simply be derived from the entropy effect within a single antiphase boundary using the nearest-neighbor interaction, as it was sometimes suggested. All the results on the stoichiometric AB-type ordered structure can readily be applicable to Ising model antiferromagnets. Conclusions drawn for the f.c.c. structure are also applicable to any type of ideal, close-packed structure.

Cation Diffusion and Conductivity in Solid Electrolytes. II. Mathematical Analyses

This paper constitutes Paper II of the series and presents theoretical analysis and supplements the results shown in Paper I. Equilibrium properties of the layer in which Na ions exist in β‐ and β″‐alumina are analyzed using the cluster variation method. Diffusion coefficients and ionic conductivities of Na ions in these two substances are derived using the path probability method.

Structure of martensites in β Au-Cd alloys

Abstract The crystal structures and metallographic features of martensites in the β phase region of Au-Cd alloys have been investigated by electron microscopy, the main emphasis being to investigate the origin of the stability of stacking variants of close packed structures which appear in martensites as compared to that of similar structures in equilibrium phases. Five types of martensite structures are found in the range of 45 at. % to 51 at. % Cd, and are designated with increasing Cd content as α′, β 2 ′, β 2 ′, γ 2 ′ and ζ 2 ′ among which the existence of two, γ 2 ′ and ζ 2 ′, had been known and been designated as β′ and β′ respectively. In addition, two structures, designated here as α 2 and α 20 are found to exist in the 45 % alloy as equilibrium phases, α′ has a disordered f.c.c. structure while β 2 ′ and γ 2 ′ are stacking variants, 3 R and 2 H respectively, of a CuAu type ordered structure. The β 2 ′ martensite is a distinct martensite phase but with a fine, regular lamellar mixture of β 2 ′ and γ 2 ′. The ζ 2 ′ martensite has an ordered hexagonal structure similar to ζ-AgZn. The composition dependence of the appearance of the crystal structures and their relative stability along with their metallographic characteristics are discussed in comparison with those in martensites in other noble metal base alloys as well as those structures found in noble metal alloys as stable states.

Correlation Factor in Substitutional Diffusion in Binary Alloys

The correlation factor is defined and derived by the path probability method of substitutional atomic diffusion (the vacancy mechanism) in binary alloys. The correlation factor thus defined is shown to be the same as that derived by the traditional random‐walk approach in all cases where the latter approach is capable of calculating the factor, namely in self‐diffusion, in impurity diffusion, and in randomly disordered alloys (excluding the nonpercolating limit in the last case). The calculation of the correlation factor is further extended by the path probability method to disordered and ordered alloys of arbitrary composition and arbitrary temperature. The relation of the present problem with the percolation problem is also discussed.

Diffusion Coefficient in an Ordered Binary Alloy

The isotope diffusion coefficient of one of the components in a binary ordered alloy is derived for the vacancy mechanism by the path probability method. By introducing the concept of the transposed lattice and making full use of the symmetry of the system, the derivation is made transparent and simpler than the treatment reported previously. The new derivation leads quite naturally to decomposition of the correlation factor into two components related to the two sublattices; the decomposition leads to a detailed interpretation of the correlation factor. The vacancy availability factor and the effective jump frequency factor are defined and their importance in the diffusion in the ordered phase is pointed out.