Short-range Order Kinetics Research Articles

Study of Vacancies and Vacancy Behaviour in Concentrated Au-Pd Alloys Using the Kinetics of Short Range Order

Study of Vacancies and Vacancy Behaviour in Concentrated Au-Pd Alloys Using the Kinetics of Short Range Order

Atomic short-range order in CuMn alloys

The establishment of atomic short-range order (SRO) has been investigated in CuMn alloys (5, 8,13,16,20 at. % Mn) by measurement of the electrical resistivity during isochronal and isothermal annealing. An increasing degree of SRO is accompanied by a reduction of resistivity; this effect increases with Mn concentration. For 8,13 and 16 at. % Mn SRO kinetics turn out to deviate significantly from single exponential behavior with a maximum at 13 at. % Mn, whereas at 5 and 20 at. % Mn SRO is adjusted in a single exponential process. For data analysis three methods are used: a sum of two and three exponentials as well as a log-normal spectrum of relaxation times. The strong interaction between second-nearest-neighbor atoms in CuMn seems to be essential for SRO kinetics but of minor importance for the value of SRO-induced resistivity change.

Annealing effects and short-range ordering in the non-magnetostrictive amorphous alloy Co58Ni10Fe5Si11B16

Effects of isothermal and isochronal annealing on the coercive field and the effective magnetic anisotropy in the as-quenched and the stress relieved amorphous alloy Co58Ni10Fe5Si11B16 were investigated. The mechanisms of the deterioration of soft magnetic properties in non-magnetostrictive amorphous alloys by annealing at low temperatures,T a <T c , are discussed. It turned out, that short-range ordering, i.e., topological short-range ordering (TSRO) and chemical short-range ordering (CSRO), caused by annealing lead to changes of the magnetostrictionλ s , and of the induced magnetic anisotropyK i . Both effects give rise to an increase of the coercive field. In addition, the kinetics of short-range ordering was studied and from these data, which are closely related to the stability of soft magnetic properties, the activation energy and a preexponential factor was derived:Q s.r=0.7eV,v 0=9.6×103s−1.

Acceleration of coarsening by temperature changes in CuMn

The establishment of atomic short-range order (SRO) has been investigated in CuMn alloys (5, 8,13,16,20 at. % Mn) by measurement of the electrical resistivity during isochronal and isothermal annealing. An increasing degree of SRO is accompanied by a reduction of resistivity; this effect increases with Mn concentration. For 8,13 and 16 at. % Mn SRO kinetics turn out to deviate significantly from single exponential behavior with a maximum at 13 at. % Mn, whereas at 5 and 20 at. % Mn SRO is adjusted in a single exponential process. For data analysis three methods are used: a sum of two and three exponentials as well as a log-normal spectrum of relaxation times. The strong interaction between second-nearest-neighbor atoms in CuMn seems to be essential for SRO kinetics but of minor importance for the value of SRO-induced resistivity change.

Kinetics of Short Range Ordering and Behavior of Vacancies in Binary Substitutional Alloys

Kinetics of Short Range Ordering and Behavior of Vacancies in Binary Substitutional Alloys

A DIFFUSE NEUTRON SCATTERING STUDY OF CLUSTERING KINETICS IN Cu-Ni ALLOYS

Diffuse scattering of thermal neutrons was used to investigate the kinetics of clustering in Cu-Ni alloys. In order to optimize the experimental conditions the isotopes 6SC~ and 62Ni were alloyed. The time evolution of the diffuse scattered intensity at 400 oC has been measured for eight Cu-Ni alloys, varying in composition between 30 and 80 at. % Ni. The relaxation of the so called null matrix. containing 56.5 at. O/, Ni, has also been investigated at 320, 340, 425 and 450 OC. Using Cook's model from all these measurements information has been deduced about diffusion at low temperatures and about thermodynamic properties of the Cu-Ni system. It turns out that Cook's model is not sufficiently detailed for an accurate description of the initial stages of these relaxations. Introduction. - The kinetics of clustering and short range order (s.r.0.) in stable solid solutions were discussed from a theoretical point of view by Cook (I). His model is based on the lattice diffusion theory for spinodal decomposition as developed by Cook, De Fontaine and Hilliard 123. The model gave good agreement with data on the kinetics of s.r.0. as measured by one of the authors (3,4). At that time no experimental data on clustering were available. One of the important results of Cook's theory was that he demonstrated the impossibility of describing cluster- ing kinetics, even approximately, by a single relaxation time in contrast to short-range order kinetics. Important theoretical contributions have been given by Khachaturyan (5) and Yamauchi (6), but in this paper we will mainly limit ourselves to a comparison with Cook's theory. For binary alloys he derived the following expres-

Two processes in the kinetics of short-range ordering and disordering in Cu-15 at% Al

Ordering and disordering to a short-range ordered (SRO) state was studied by suddenly changing the annealing temperature by 5 deg after establishment of equilibrium. The measurement of residual resistivity indicates the existence of two kinetic processes. This and an ordering rate, that is smaller than the disordering rate harmonize better with inhomogeneous SRO, than with homogeneous SRO, often assumed in α-CuAl. A quantitative comparison of experimental results with an inhomogeneous SRO-model is given. Die Ordnungseinstellung und Entordnung eines nahgeordneten Zustandes wurde studiert. Dabei wurde nach der Einstellung des Gleichgewichtes die Anlastemperatur plotzlich um 5 grad geandert. Die Messung des temperaturunabhangigen Anteiles des elektrischen Widerstandes weist auf die Existenz zweier kinetischer Vorgange hin. Diese Tatsache und eine Ordnungsgeschwindigkeit, die langsamer ist als die Entordnungsgeschwindigkeit, lassen sich leichter mit einer inhomogenen Nahordnung interpretieren, als mit der in α-CuAl oft angenommenen homogenen Nahordnung. Ein inhomogenes Nahordnungsmodell wird quantitativ mit den experimentellen Ergebnissen verglichen.

Relaxation of Diffused Zinc Atoms During Short-Range-Ordering in Cu-30% Zn Alloy

Abstract The internal friction which is a diffusion dependent physical property has been used as a means to determine the kinetics of short range order in (Cu-30% Zn) alloy. Curves of relative (Q~ l /Q0~ 1) against annealing time have been plotted for various annealing temperatures. An average activation energy of 1.7 eV was found for the ordering process, which is equal to the activation energy for zinc diffusion in coarse grained copper. When an alloy having short range order (SRO), is quenched from high temperatures, excess vacan-cies are liberated which will enhance diffusion, and hence the ordering rate during subsequent anneal-ing. Due to this enhanced ordering rate, the equi-librium degree of short range order canbe achieved in reasonable times even at rather low temperatures, provided that vacancies are mobile at these tempera-tures. For copper-zinc alloys in the alpha phase, the existence of SRO has been theoretically 1 establish-ed and experimentally demonstrated by many wor-kers (cf. CLAREBROUGH et al. 2). Evidence from diffuse X-ray and/or neutron scattering experiments is not available because of the small difference in scattering power of copper and zinc 3 atoms. Long range order in alpha brass above — 30 °C is im-probable 3 because of the rather low ordering en-ergy of the system.

Theory of the kinetics of short range order

The theory of kinetics of short range order for an AB alloy containing vacancies of Kidin and Shtremel is criticized and an alternative set of equations of motion for the probabilities of atom-atom pairs and atom-vacancy pairs is proposed. Formulae are derived for the equilibrium probabilities which are consistent with the quasi-chemical theory and it is shown that the equilibrium state of atom-atom pairs implies the equilibrium state of atom-vacancy pairs. The integration of the equations of motion for the case of a quenching experiment in which the degree of short range order increases with time shows that the approach to equilibrium cannot be described by a simple exponential, in qualitative agreement with experiment. The study of the initial relaxation times gives also results in qualitative agreement with experiment. It is proposed that restrictive conditions that relate the equilibrium energy parameters to the energy of motion parameters should apply if the system is ever going to reach the state of thermodynamic equilibrium.

The kinetics of clustering and short-range order in stable solid solutions

The kinetics of clustering and short-range order in stable solid solutions are examined from the viewpoint of a recent lattice diffusion theory. It is found that short-range order kinetics can be approximated by a single relaxation time but that clustering kinetics display a wide spectrum of relaxation times. For a regular solution, the short-range order relaxation time is ▪ is the lattice parameter, D is the chemical or interdiffusion coefficient, T is the temperature, T c is the critical temperature, and ▪ Consequently, if the interdiffusion coefficient shows Arrhenius type behavior when T ⪢ T c , the relaxation time will also show this behavior and have the same activation energy. As T → T c , the interdiffusion coefficient generally deviates somewhat from Arrhenius type behavior; the relaxation time, however, will show a much stronger deviation due to the singularity at T = T c .

Theory of the kinetics of short range order

Theory of the kinetics of short range order

Lattice theory of alkali halide solid solutions - II. Entropy of mixing and solid solubility

The theory of kinetics of short range order for an AB alloy containing vacancies of Kidin and Shtremel is criticized and an alternative set of equations of motion for the probabilities of atom-atom pairs and atom-vacancy pairs is proposed. Formulae are derived for the equilibrium probabilities which are consistent with the quasi-chemical theory and it is shown that the equilibrium state of atom-atom pairs implies the equilibrium state of atom-vacancy pairs. The integration of the equations of motion for the case of a quenching experiment in which the degree of short range order increases with time shows that the approach to equilibrium cannot be described by a simple exponential, in qualitative agreement with experiment. The study of the initial relaxation times gives also results in qualitative agreement with experiment. It is proposed that restrictive conditions that relate the equilibrium energy parameters to the energy of motion parameters should apply if the system is ever going to reach the state of thermodynamic equilibrium.

Kinetics of short-range order and Zener relaxation in substitutional solid solutions

A theoretical model of the relaxation time for changes in short-range order and for Zener relaxation in substitutional solid solutions has been developed using a kinetic approach. The resulting expressions are developed in a form which permits examination of the differences between activation energies for relaxation times and those for diffusion of the alloy components. These differences arise from two sources: correlation effects, and the differences in weight assigned in each of the processes to atom-vacancy exchanges in various environments. Experimental data for diffusion and for Zener relaxation in silver-gold and silver-zinc alloys are discussed within the framework of the present interpretation and contrasted with previous interpretations of Zener relaxation times.

The Kinetics of Short‐Range Order in Some Ag‐Au Alloys

The Kinetics of Short‐Range Order in Some Ag‐Au Alloys

ON THE KINETICS OF ORDERING IN AB ALLOY

According to the theory of the rate process of diffusion of atoms in lattice, the kinetics of long-range ordering and short-range ordering under the condition of zero long-range order in the nearest neighbour approximation has been investigated. The results obtained agree qualitatively with and quantitatively similar to the conclusions derived from the past experiments and calculations. The results obtained from the calculations of the kinetics of long-range ordering show that the process of ordering requires an induction period, the transformation curves have the form of C-curves and the degree of longe-range order depends upon time in the form of exp {-αt2} -approximately. The equilibrium values of the degree of long-range order obtained are very similar to those of the past workers. The results obtained from the calculations of the kinetics of short-range ordering in the condition of zero long-range order depends upon time in the form of exp {-βt} approximately, and the rate of ordering is so quick, that even with the fastest quenching a certain degree of short-range order exists in the specimen. The equilibrium values of the degree of short-range order also agree with the results obtained in the past.