Short-range Order Kinetics Research Articles

Kinetics of short-range order formation in the ternary alloy Au25Ag25Pd50

The kinetics of short-range order (SRO) formation was investigated in the alloy Au25Ag25Pd50by using the residual electrical resistometry. The resistivity was found to increase with the formation of SRO. The resistivity values varied linearly with respect to the inverse of temperature, characterizing the different states of SRO. The analysis of isothermal experiments obeying the fundamental laws showed that the SRO kinetics followed the two-exponentials law. The characteristic time constants for the SRO formation corresponding to various annealing temperatures in the isothermal annealing process and the activation enthalpies were determined with high accuracy. The time constants for the SRO formation and destruction were different, implying that the reaction paths in these processes are different. Further, the crossover experiments confirmed the existence of two-exponential kinetics and the variation of the time constants.

Kinetics of short-range order formation in the ternary Au–Ag–Pd alloys

The kinetics of formation and destruction of short-range order (SRO) were investigated in the ternary Au 40Ag 40Pd 20 alloy using the residual resistometry. The changes in residual electrical resistivity were measured during down-quenching (DQ) and up-quenching (UQ) 1 1 In up-quenching (UQ) experiments T q < T a and in down-quenching (DQ) experiments T q > T a. T q and T a are the quenching and annealing temperatures. cross-over annealing experiments. The quantitative analysis of the resistivity data showed that three kinetic processes are involved in the short-range ordering and disordering process. The results agree qualitatively with the Yu–Lucke model for the kinetics of SRO in the fcc ternary alloys. However, the kinetic parameters derived from the cross-over experiments during ordering and disordering was found to be complicated and different from the unidirectional isothermal kinetics. These differences suggest that the reaction paths during ordering and disordering are different.

DSC evaluations of short-range-order kinetics in Cu–10at.% Al solid solutions as influenced by bound vacancies

Abstract A modified first order kinetic law which describes the roles of bound and unbound vacancies is proposed in order to predict defect decay and short-range-order (SRO) kinetics of quenched binary alloys during linear heating experiments. The model has been applied to differential scanning calorimetry (DSC) thermograms of Cu–10at.% Al quenched from different temperatures. Transient effects at the end of de-freezing when heating after quenched were examined. Activation energy for migration of solute–vacancy complexes was also assessed from the kinetics of SRO using DSC traces. A value of 85.6 kJ mol −1 was obtained. The relative contribution of bound and unbound vacancies to the ordering process as influenced by quenching temperature was determined.

Equilibrium kinetics of short-range order formation in the ternary Au 40Ag 40Pd 20 alloy

The kinetics of short range order (SRO) were investigated in the ternary Au 40Ag 40Pd 20 alloy under equilibrium conditions using residual electrical resistivity measurements. The changes in electrical resistivity were measured during isothermal annealing experiments after producing small deviations from the SRO-equilibrium. The analysis of these measurements gives evidence of three kinetic processes involved in the evolution of SRO. The results obtained from the determined kinetic parameters were found to be in good agreement with the Yu–Lucke theory of kinetics of SRO-formation in multi-component alloys.

Short-range order kinetics during post-deformation annealing in different binary alloys

Alloys of Cu–15at.% Al, Ag–21at.% Zn and Au–14at.% Fe are compared with respect to short-range ordering in the recrystallized state and after high deformation by cold-rolling, respectively. Additional information on the defect annealing behaviour is gained from an investigation of microhardness and by microscopy.

Resistometric study of short-range order kinetics in α-AgZn

Short-range ordering (SRO) kinetics was investigated under temperature conditions of isochronal and isothermal annealing in completely recrystallized Ag-21, -23, -28 at.% Zn by residual resistometry. The SRO kinetics deviated considerably from a single exponential relaxation process and was therefore analysed using a log—normal spectrum of SRO relaxation times. This yields activation enthalpies for changes in the degree of SRO in good accordance with literature data. Isothermal SRO relaxation of undeformed samples was compared with that of cold-rolled and partially annealed samples.

Short-range order kinetics in α-AgZn for various states of post-deformation defect annealing after cold-rolling

Kinetics of short-range ordering (SRO) in Ag with 21, 23 and 28 at% Zn is investigated by residual resistometry during isochronal and isothermal heat treatment for different states of post-deformation defect annealing after cold-rolling to about 30 and 60% thickness reduction. Resistivity changes due to pure ordering can be separated from the as-measured total resistivity change which includes defect annealing. Although the initial state of SRO of the as-rolled material can be estimated to be comparably low, for as-rolled and partially annealed states by appropriate thermal treatment evolution of SRO is achieved which corresponds quite well to that of recrystallized samples. It is observed, however, that quenched-in surplus vacancies contribute considerably to the ordering process for the recrystallized state and that this contribution is still increased by the grain growth during the final stage of annealing. It therefore turns out that SRO-kinetics under equilibrium vacancy conditions can be better observed in a state of post-deformation annealing, for which deformation induced point defects are annealed-out, but a relatively high dislocation density is still present to act as a vacancy sink.

A magnetization study of the development of short-range order in a concentrated - Mn spin glass

The kinetics of short-range order (SRO) growth in a Cu - 16.4 at.% Mn alloy have been studied by measuring the evolution with time of the low-temperature magnetic properties while aging at temperatures around 100 . This new approach was possible because atomic SRO leads to magnetic clustering at this Mn concentration. Several models, all based on the diffusion of vacancies and their annihilation in fixed sinks, implied that the sink density was higher at 115 than at 100 for identical quenching conditions. It was concluded that the quenched-in vacancies condense in clusters. These act as sinks, halting the growth of SRO when the excess quenched-in vacancies have been absorbed. Quenching faster or aging at a higher temperature nucleates more vacancy clusters, causing earlier vacancy exhaustion. Neutron irradiation was used to continuously supply vacancies, thereby driving the SRO process to equilibrium at about 100 . A much higher magnetic susceptibility was attained than previously reported, some 20 times the as-quenched value at the spin freezing temperature.

Atomic short-range ordering in AuFe alloys: a resistometric study

Kinetics and equilibrium of atomic short-range order (SRO) in Au 1− x − Fe x ( x=0.05, 0.10, 0.14, 0.20) have been investigated by measurement of residual electrical resistivity for a cold-rolled and a well-annealed state. Activation enthalpies of SRO relaxation correspond well to the sum of formation and migration enthalpies of vacancies, both determined separately In contrast to Mössbauer measurements a strong temperature dependence of SRO-induced electrical resistivity was observed. It was found that, because of the high density of vacancy sinks, SRO kinetics in the cold-rolled state in considerably slower than in the well-annealed state. Surprisingly, the as-rolled state for the alloys with 5, 10 and 14 at.% Fe has a high degree of SRO, whereas for Au-0.2.%Fe the initial state is disordered.No indications for precipitation of α-Fe were found for the samples with 5,10 and 14 at.% Fe, for both the cold-rolled and the recrystallized state. For 20 at.% Fe, however, a resistivity drift in the cold-rolled state was observed, which may be caused by precipitation of α-Fe.

Influence of Al concentration on the kinetics of short-range ordering in α-CuAl

The formation of short-range order (SRO) in a concentration series of α-CuAl is investigated by measurement of the electrical resistivity during isochronal and isothermal annealing. An important part of the paper deals with the problem of heterogeneity versus homogeneity of SRO. It turns out that the SRO relaxation kinetics can be described as a sum of at least two independent processes, each obeying an exponential law. As an interesting fact, one of the processes reverses its sign at about 15 at% Al, so that for this concentration a single exponential behaviour results. Our interpretation is that the expansion coefficients of electrical resistivity with respect to SRO parameters of various coordination spheres change with concentration. In einer Konzentrationsreihe von α-CuAl-Legierungen wird die Entwicklung der Nahordnung (NO) mit Hilfe von Restwiderstandsmessungen während isochroner und isothermer Auslagerung untersucht. Ein wesentlicher Teil der Arbeit geht auf die Problematik der heterogenen bzw. homogenen Interpretation der NO ein. Die NO-Kinetik kann als Summe wenigstens zweier unabhängiger Exponentialprozesse beschrieben werden. Bei 15 at% Al kehrt einer der Prozesse sein Vorzeichen um, so daß für diese Konzentration ein einfaches Exponentialverhalten beobachtet wird. Dies ist unserer Ansicht nach darauf zurückzuführen, daß sich die Koeffizienten der Entwicklung des elektrischen Widerstandes nach den NO-Parametern der verschiedenen Koordinationsschalen mit der Legierungskonzentration ändern.

The effects of Ti or Ta on the kinetics of short range ordering and self-diffusion in Ni(Al)-based solid solutions

The isothermal relaxation of short range order (SRO) was investigated in Ni-based ternary solid solutions containing 4 at.% Al + 2 at.% Ta, 4 at.% Al + 2 at.% Ti and 1 at.% Al + 3 at.% Ti by means of residual electrical resistivity measurements at 4.2 K. Short range ordering resulted in an increase of electrical resistivity and equilibrium values of this property, characterizing the SRO-equilibrium states, varied linearly as a function of reciprocal temperature. The analysis of the experimental results using phenomenological laws leads to the determination of characteristic time constants and thence of activation enthalpiesi of self-diffusions. The parameters deduced from different types of analysis are generally in good agreement. The comparison of our results with those obtained in bainary solid solutions shows that the presence of Ta or Ti (with 4 at.% Al) significantly reduces the atomic mobility in these alloys.

Short-range ordering of hydrogen isotopes in lutetium

The kinetics of short-range ordering of the hydrogen isotopes protium, deuterium and tritium in lutetium was studied by electrical resistivity measurements during isothermal annealing. The reaction order parameter decreased from above 2 to about 1 for temperatures from 160 to 190 K. The rate constant showed an apparent activation enthalpy of about 0.52 eV for tritium and slightly smaller values for the lighter isotopes. The data could be described by a model for clustering of hydrogen atoms with a binding energy per atom of about 0.5 eV, a migration enthalpy of about 0.45 eV and a reduction in the resistivity contribution per clustered atom by about 12%, compared with non-clustered atoms.

Kinetics of short-range ordering in αCu-Al alloys

The ordering behaviour in quenched αCu-Al was investigated by differential scanning calorimetry (DSC) under rising temperature conditions and by electron diffraction. It was found that the ordering processes can be better explained in terms of a homogeneous short-range order (SRO) model rather than a heterogeneous disperse order (DO) model as previously interpreted for the same type of experiments. The DSC traces indicate that the ordering takes place in two stages: the stage 1 ordering at lower temperatures is associated with the migration of excess vacancies and the stage 2 ordering at higher temperatures is associated with the migration of equilibrium vacancies. At higher temperatures, a marked surge of energy absorption occurs (stage 3) which is attributed to the destruction of order. For furnace-cooled alloys, only stage 3 appears. The relative dominance of stages 1 and 2 is influenced by the quenching temperature, the quench rate, the density of vacancy sinks and the sample shape before quenching. A relationship describing the overall SRO kinetics for both stages together, in terms of either the reacted fraction or the first SRO parameter, is proposed. A method for evaluating boundary values for this parameter is developed, making use of the features displayed by the DSC thermograms. The mobility of the vacancies, which controls their life-time and the short-range ordering rate, was evaluated by computing frequency factors and activation energies. Values for activation energies controlling the short-range ordering rate are somewhat smaller than the effective values obtained for stage 1 from the DSC traces, suggesting that the presence of solute-vacancy complexes may be important mainly as the aluminium concentration increases. From estimations of solute-vacancy and divacancy binding energies, it is inferred that divacancy formation is unlikely in the alloys under study. Process frequency factor values are in very good agreement with those calculated for a short-range order state developed during two-stage ordering by a vacancy mechanism. A flow diagram of the factors controlling the fractional increase of short-range order during anisothermal experiments is proposed.

Resistometric investigation of short-range order kinetics in gold–silver alloys

The formation of short-range order (SRO) is investigated in the AuAg alloy system by means of electrical resistivity measurements during isochronal and isothermal annealing. The kinetics of the adjustment of equilibrium values of resistivity indicating stable states of microstructure are carefully examined. In contrast to previous investigations reported in the literature, it is found that the SRO relaxation kinetics do not obey exactly a pure exponential law. The concentration dependence of SRO-induced resistivity shows a good correspondence with calculations based on nearest neighbour models. Die Entwicklung der Nahordnung im Legierungssystem AuAg wird mit Hilfe von Restwiderstandsmessungen während isochronen und isothermen Anlassens untersucht. Dabei wird besonders die Kinetik der Einstellung von Gleichgewichtswerten des Widerstandes als Hinweis auf stabile Zustände der Mikrostruktur untersucht. Entgegen früheren Untersuchungen gehorcht die Nahordnungskinetik nicht exakt einem reinen Exponentialgesetz. Die Konzentrationsabhängigkeit des nahordnungsinduzierten Widerstandes stimmt gut mit Modellrechnungen überein, bei denen nur nächste Nachbarn Berücksichtigung finden.

Short-range ordering by excess and thermal vacancies during linear heating experiments in α-CuAl alloys

The ordering behaviour in quenched α-CuAl was investigated by differential scanning calorimetry (DSC) under increasing temperature conditions. It was found that the ordering processes can be better explained in terms of an homogeneous short-range order (SRO) model rather than a heterogeneous disperse order model as previously interpreted for the same types of experiment. The DSC traces indicate that the ordering takes place in two stages; stage 1 ordering at low temperatures is associated with the migration of excess vacancies and stage 2 ordering at high temperatures is by the migration of equilibrium vacancies. The relative dominance of each stage is influenced by the quenching temperature, the quench rate, the density of vacancy sinks and the sample shape before quenching. A relationship describing the overall SRO kinetics for both stages together in terms of either the reacted fraction, or the first SRO parameter was proposed. A method for evaluating boundary values for this parameter was developed, making use of the features displayed by the DSC thermograms. The mobility of vacancies, which controls their lifetime and short-range ordering rate, was evaluated by computing frequency factors and activation energies. The resulting values for activation energies controlling the short-range ordering rate were somewhat smaller than the effective values obtained for stage 1 from the DSC traces, suggesting that the presence of vacancy-solute complexes may be important especially as the aluminium concentration increases. From estimations of vacancy-solute and divacancy binding energies, it was inferred that divacancy formation is unlikely in the alloys under study. The process frequency factor values were in very good agreement with those calculated for an SRO state developed during two-stage ordering by a vacancy mechanism.

Short Range Order Kinetics and Vacancy Behaviour in Au25 at.%Ag

Short Range Order Kinetics and Vacancy Behaviour in Au25 at.%Ag

A Mössbauer spectrometry study of the kinetics of short-range ordering in FeCo

Abstract Making use of the systematics of 57Fe hyperfine magnetic fields (HMFs) in b.c.c. Fe-Co alloys, we have performed a Mossbauer spectrometry study of the disorder→order transformation in FeCo. Features of the 57Fe HMF distribution were used to identify: (1) the numbers of 57Fe atoms near antiphase domain boundaries, and (2) the numbers of 57Fe atoms situated on Co sites. To produce an initial state of disorder, the alloys were rapidly quenched, mostly by the piston-anvil technique. Low-temperature annealings were then used to prepare different degrees of short-range order in these materials. The number of 57Fe atoms near antiphase domain boundaries decreases more quickly with ordering than the number of 57Fe atoms situated on Co sites. This is consistent with a picture in which a dense formation of small moderately ordered domains develops very quickly, and the domains grow quickly. This is followed by an increase of order within the domains.

SRO relaxation in dilute [formula omitted]Al solid solution through 4 K resistometry

Results of a detailed investigation of the short range order kinetics in the Ni 94Al 6 solid solution using 4 K resistometry are reported. The respective role played by equilibrium- and supersaturated vacancies is clearly differentiated. The overall data related to equilibrium vacancies are well described in a model which assumes a first order kinetics, a log-normal distribution of the relaxation times of half-width β ≈ 1, and an Arrhenius law: \\ ̄ gt(s) = 1.3 · 10 −13 exp 2.3(eV)/kT . The role played by the underlying equilibrium phase diagram is outlined. The whole result is qualitatively discussed in the frame of current ordering kinetics models. The relatively small value obtained for E A is compared with diffusion data in the solid solution phase and with those of ordering kinetics in the Ni 3Al compound. Previous data of SRO measurements are discussed in the light of the present study.

Wave vector dependent kinetics of short-range ordering in 62Ni 0.765Fe 0.235, studied by neutron diffuse scattering

In situ measurements of the diffuse elastic neutrons scattering from a short-range ordered 62Ni 0.765Fe 0.235 single crystal were carried out during annealing, along three high symmetrical lines of the reciprocal space. Transient as well as equilibrium measurements were done in order to elucidate the kinetic behaviour of the short range order in this alloy as the disorder to order transition is approached. The relaxation time of intensity variation was measured at several points of the reciprocal space near 001. as a function of temperature. The kinetic behaviour is correctly described by the linear theory of continuous transformation provided that more than one interaction potential is used. The values of the interdiffusion coefficient obtained in this way, and its activation energy, suggest a modification of the interdiffusion mechanism due to the proximity of the annealing temperature to the transition temperature. The Warren-Cowley short-range order parameters α lmn were approximated by a least square fit using a Lorenzian and corrective terms to describe the intensity halo. During the kinetic evolution, the smaller is the distance r lmn , the more rapid is the variation of α lmn . The correlation length for short-range order varies with the same relaxation time as the intensity at the maximum. I(001).

An effect of antiphase boundaries on the kinetics of short-range ordering by a vacancy mechanism

In Monte Carlo simulations of chemical short-range ordering on a square lattice, the number of single-atom domains was found to depend on the presence of antiphase boundaries and on the mechanism by which ordering occurred. When antiphase boundaries were present and the ordering occurred by a vacancy mechanism, the number of single-atom domains was found to increase with decreasing temperature, in contrast to thermodynamic predictions. This is understood as a consequence of highly correlated vacancy motions in those regions of the lattice away from antiphase boundaries.