Tetsuo Eguchi

Process of Order-Disorder Transformation in Iron-Aluminum Alloys

The process of order-disorder transformation during slow cooling and isothermal annealing in Fe–Al alloys has been investigated by means of X-ray diffraction. During slow cooling the ordering takes place through the two-phase state at a certain composition. while at other compositions it occurs as a single-phase transformation. The isothermal ordering proceeds by a nucleation and growth of the ordered phase, and under certain circumstances the precipitation of disordered phase takes place gradually in the course of annealing. The disordering into the two-phase state from an ordered single phase proceeds in two steps. The most plausible phase diagram of the Fe–Al system containing the two-phase regions, α+B2 and α+DO3, is proposed. The size of ordered domains is estimated from the widths of superlattice reflections, and its change during the order-disorder transformation is discussed.

Electron Microscopic Study of Domain Structure in Iron-Aluminum Alloys

The change in the micro-domain structure of Fe-Al alloys during the isothermal annealing has been investigated by means of transmission electron microscopy. The domain structure shows very complicated features in each transition, but the results of the observation are consistent with those of our previous work using X-ray diffraction. In the transitions B2→α+B2 and α+B2→α+DO3 the decomposition of the ordered phase into a mixture of the ordered and disordered phases takes place. The transition α+DO3→DO3 is dominated by the nucleation of DO3 domains in the disordered phase. In the reverse process, from DO3 to α+DO3, the disordered phase precipitates in two steps from the DO3 phase.

VACANCY CONCENTRATION AND ARRANGEMENT OF ATOMS AND VACANCIES IN METALS AND ALLOYS

Abstract With a method of statistical thermodynamics fundamental equations are derived which describe the arrangement of atoms and vacancies in the alloys in the state of thermal equilibrium, where an ordering or a clustering can take place. The solutions of these equations give, among other things, a more precise description on the concentration of vacancies than the classical ones. The vacancy concentration in pure metals may almost precisely be expressed by the usual approximate expression, but in dilute alloys it is not always expressed by Lomers expression. The fraction of vacant sites in the alloys, furthermore, is very unlikely to be expressed by an Arrhenius type of equation, but it decreases or increases, according as a result of ordering or clustering. In binary alloys with short range orders or clusters the probability that one of the nearest neighbor sites of a vacancy is occupied by an atom of any particular kind does not always vary monotonically with temperature but in some alloys it increases after decreasing or decreases after increasing. A possibility for an interpretation of the anomalous behaviors of αCu-Al alloys is pointed out.

Ferromagnetism and ordering in Fe-Co alloys

Results of our experimental investigation on the magnetization, specific heat, and neutron diffraction in Fe-Co alloys are reported and interpreted by a statistical theory in B-W approximation. The exchange interactions between neighboring atoms in bcc are determined so that the theory reproduces the experimental magnetization versus temperature curves. The ordering energy is fixed so that the theory predicts the order-disorder transformation at 730°C as observed experimentally in the alloy with 50 atomic percent Co. The theory implies also that the nonmagnetic state, should it exist, would undergo the order-disorder transformation at about 550°C. An attempt is made to interpret the observed anomalies in terms of a coexistence of magnetic and nonmagnetic states in these alloys and to relate the specific heat with the neutron diffraction data.

Kinetic behaviour of vacancies and atoms in binary alloys

Abstract With the introduction of the two-particle distribution function a set of simultaneous rate equations is derived which describes the time dependence of the vacancy concentration as well as the arrangement of atoms and vacancies in binary alloys. The model takes into account the exchange of sites between atoms and vacancies with a jump rate that depends only on their immediate environment. The general theory thus developed, which includes as a special case tho state of thermal equilibrium, is applied to α Cu‒Al alloys with various compositions, and can reproduce satisfactorily the temperature dependence of the self-diffusion coefficient of Cu and Al atoms in these alloys. Furthermore, these equations account for the observed kinetic behaviour of their physical properties, such as the specific heat and electrical resistivity.

Precipitation Behavior in a Cu-4.5 wt%Co Alloy

Precipitation behavior during aging at 873 K in a Cu-4.5 wt%Co alloy was investigated by means of electron microscopy. The sets of satellites along directions flanking the matrix reflections were observed in the electron diffraction patterns of samples in the early stage of aging. With the progress of aging, the satellite reflections moved towards the matrix spots. The arrays of precipitates aligning along directions were locally observed in images.

Long Range Order Theory of Ferromagnetic Superlattices with Application to FeCo and FeNi3

A statistical theory of ferromagnetic superlattices is developed in the Bragg-Williams approximation with long range order for alloys of types AB and AB3 with bcc and fcc lattices, respectively. Five parameters are introduced to describe the distribution of the two kinds of atoms with magnetic moments. These parameters are obtained as functions of temperature under the equilibrium condition, and the critical temperatures are determined in terms of the interaction energies. The general results thus developed are then applied to the analysis of experimental data so far available in FeCo and FeNi3. In the case of FeCo, where the interaction energies have not yet been measured, the agreement between the prediction of our theory and the experimental data is not satisfactory, but in the case of FeNi3, where the data for the interaction energies are available, the agreement is very satisfactory.

Configuration of periodic antiphase boundaries in α2 phase of Cu‐Al alloys

The α2 phase of Cu‐Al alloys forms a one‐dimensional long period superstructure in a lattice of DO22. In order to clarify the details of antiphase domain structure of the alloy with a non‐integral period, the configuration of periodic antiphase boundaries was investigated by means of electron diffraction and high resolution electron microscopy. The lattice images reveal that the non‐integral value of the long period estimated from the separation of split order‐spots, or 4 to 5 in the present case, means a mixture of the integral periods 4 and 5. The mixing mode of these periods was examined on the electron micrographs and the following results were obtained. The fractional amount of the period 5 varies from part to part in a coherent crystal. However, the local mixing mode of the periods seems almost uniform. The domains of period 5 join together always by a set of eight in a matrix of period 4, and similarly, those of period 4 by a set of ten in a matrix of period 5.

Critical Voltage Effect in Ni3Fe and FeCo Ordering Alloys

The critical voltages in ordered and disordered states of Ni3Fe and FeCo alloys were measured for the systematic reflections without superlattice reflections. A small increase in the critical voltage was observed on ordering for the 111 systematic reflections of L12 type Ni3Fe. The temperature factors and the Debye temperatures were evaluated from the measured critical voltages. The changes on ordering in the temperature factors and Debye temperatures were in reasonably good agreement with those derived by X-ray investigation and elastic constants. It is shown that the change in the critical voltage of Ni3Fe is mainly due to the change in the thermal mean-square displacement of atoms. No obvious change in the critical voltage on ordering was detected for 110 systematic reflections of B2 type FeCo.

Nuclear Radiation from Solids

An operator identity concerning the Hamiltonian of a harmonic oscillator enables calculations of the distribution of the energy of nuclear radiation from solids, which includes the effect of multiple phonon processes exactly. The moments of the recoil energy or of the energy of radiation are obtained to any order in terms of the moments of the frequency of lattice vibration. These relations suggest a method of experimental determination of the frequency distribution of lattice vibration.