Vacancy Annealing Research Articles

The kinetics of radiation point defect accumulation in metals during irradiation

The approximation method of analytical solution of a set of kinetic equations describing free point defect concentration evolution in metals during irradiation is presented. It is shown that at low temperatures, when the vacancies are frozen, the consideration of only the single channel of vacancies annealing related to their mutual recombination with mobile interstitials leads to physically senseless results: unlimited increase in the radiation vacancy concentration during irradiation. Vacancy concentration stabilization on a physically reasonable level requires taking into account some more channels of vacancy annealing. The athermal annihilation of radiation vacancies, with both the existing sinks and the radiation interstitials, is considered as a potential annealing mechanism. In addition, the mechanism of radiation-enhanced vacancy diffusion towards sinks is taken into account, too. The possible contributions of each of the annealing mechanisms are estimated.

Defect structures in cold worked and small grain pure and boron-doped Ni3Al alloys

Positron lifetime spectroscopy was used to study the isochronal annealing of cold worked Ni3Al samples. In pure Ni76Al24, Ni74Al26, and boron-doped Ni74Al26 three annealing stages were observed. Boron-doped Ni76Al24 showed only two annealing stages. Vacancy annealing (stage III) was identified in all cases to start at ∼250 °C, somewhat higher than previously reported. The discrepancy is suggested to be due to carbon-vacancy interactions, because carbon (impurities) was observed to diffuse out of all samples at or above ∼350 °C. The high-temperature annealing stage in boron-doped Ni76Al24 (which is ductile) starts at 700–750 °C and is complete at 1000 °C. This stage was attributed to migration of dislocations to various sinks. In pure Ni76Al24, Ni74Al26, and boron-doped Ni74Al26 (which are brittle) the intermediate and high-temperature annealing stages occur at ∼750–800 and 1000 °C, respectively. These stages were attributed to the migration of dislocations (750–800 °C) and recrystallization (∼1000 °C) with incomplete annealing of dislocations at 1000 °C. This being the case, it is clear that dislocations interact with grain boundaries far more strongly in brittle than in ductile Ni3Al alloys. Thus, these data strongly suggest that the ductilization of Ni76Al24 by boron is largely due to a change in grain boundary structure which inhibits the pinning of dislocations at grain boundaries that occurs in pure Ni76Al24 (i.e., boron increases the susceptibility of grain boundaries to slip). Similar results for small-grain samples support this interpretation.

Positron-lifetime study of vacancy annealing in neutron-irradiated GaAs

Positron-lifetime measurements have been used to study the annealing of vacancies in neutron-irradiated GaAs. The vacancies which are interpreted as defects in the Ga sublattice disappear in a single annealing stage (at 500°C in GaAs doped with Si or Zn, and at 600°C in Cr-doped GaAs).

A positron study on the effect of As, Sb, W, and Ti on the annealing of defects in cold‐rolled Ni

AbstractThe peak height of the 2γ‐angular correlation curve is measured as a function of the sample temperature during time linear heating of cold‐rolled Ni dilute alloyed with Sb, As, W or Ti (0.03 to 1.4 at.%). The effect of these foreign elements on the annealing of defects is very different. In Ni alloyed with As or Sb the formation of a large number of three‐dimensional vacancy clusters is observed indicated by a strong increase of the peak height. Obviously As and Sb atoms act as nucleation centres for the vacancy clustering. The addition of W to Ni leads to a shift of the vacancy annealing to higher temperatures. In Ni alloyed with Ti relative smooth peak height recovery curves are observed. Positron lifetime measurements show that no vacancy clusters are formed. The effect of the impurities on the vacancy annealing correlates with their binding enthalpy for vacancies in Ni.

Theory of pulsed irradiation microstructures

Flux pulsing is predicted to influence microstructures because of pulse annealing effects on aggregate annealing and on point defect annealing. Specifically void annealing and vacancy annealing are analyzed. A high dislocation density enhances the void annealing effect but inhibits the point defect annealing effect. Furthermore, pulsing effects are greater for higher damage rates and smaller defect aggregates. It is concluded that pulsed ion irradiations can simulate pulsed fusion irradiations if it is recognized that the ions exaggerate the expected neutron effect.

Vacancy recovery in irradiated niobium

Positron lifetime and annihilation lineshape measurements are used to study defect recovery in pure and H-doped Nb after low-temperature electron and neutron irradiation. In neutron-irradiated specimens correlated vacancy migration and the concomitant vacancy clustering within the collision cascades are observed around 160K. However, in electron-irradiated Nb, no sign of vacancy annealing is seen until above 380K where the vacancies agglomerate strongly. According to earlier ideas this is interpreted as being due to hydrogen impurities bound at vacancies. Vacancy migration and clustering are possible only after the dissociation of the vacancy-hydrogen pairs at 380K. The results also indicate that hydrogen impurities play an important role in the stability of small three-dimensional vacancy clusters in Nb.

Measurement of the monovacancy formation enthalpy in copper

The monovacancy formation enthalpy in copper, H1vF=(1.30+or-0.05) eV, has been measured using precision electrical resistometry on samples quenched from temperatures in the range 525-650 degrees C. Comparison of this value for H1vF with the activation enthalpy for self-diffusion via a monovacancy mechanism in copper, previously measured over the same temperature range, yields H1vM=0.77 eV for the enthalpy for monovacancy migration. This value compares well with the activation enthalpy for post-quench vacancy annealing, (0.76+or-0.04) eV, measured in the present work. The results are compared with those of previous investigations.

Vacancy-scandium interaction in quenched copper

The effects of the addition of trace amounts (12-96 at PPM) of Sc upon the annealing of otherwise high-purity Cu quenched from 600-700 degrees C has been investigated. The Sc solute was observed to suppress the normal post-quench vacancy annealing in Cu, apparently by the formation of highly stable vacancy-Sc complexes which subsequently annealed only at temperatures in excess of approximately 300 degrees C.

Search for the vacancy annealing stage in heavy ion implanted BCC metals

Search for the vacancy annealing stage in heavy ion implanted BCC metals

Amorphization of silicon by ion implantation: Homogeneous or heterogeneous nucleation?

Abstract The importance of homogeneous and heterogeneous nucleation in the amorphization of silicon by ion implantation is considered. Previously a homogeneous model involving dose rate had been used to identify neutral vacancy and divacancy annealing as important mechanisms in the amorphization process. In an attempt to verify this dose rate model, experiments which detect the electron spin resonance signal from the amorphous regions have been performed. Both a light ion (N+) and a heavy ion (Kr+) at low (20 keV) and high (180 keV) energy were implanted into silicon at low (80°K) and higher (∼350°K) temperatures. No dose rate dependence was found, and the temperature dependence is not as predicted by the model. In addition, the production rate is not proportional to the dose to the one-half power-a power dependence which has previously been attributed to homogeneous nucleation. Furthermore, since the data agrees with the predictions of a heterogeneous model, it is concluded that homogeneous nucleation is not an important process in the amorphization of silicon by ion implantation.

A resistometric study of excess vacancies in AlCuMg alloys

Zone formation in Al - 3 wt.% Cu - 1 wt.% Mg alloys has been studied by resistivity technique, with a view to investigating the nature of excess vacancies in these alloys. Excess vacancies in these alloys are very strongly bound. The zones forming in these alloys are likely to be rich in vacancy concentration. When quenching of a solution treated alloy is interrupted for a minute above zone solvus temperature, the mode of vacancy annealing during interruption above 380°C is probably different from that below 300°C. In certain cases of interruption of the quench a diffusional barrier to zone formation has been observed and a mechanism for this has been proposed.

On the efficiency of vacancy annihilation at an anodized gold surface

The efficiency of a thin, continuous and adherent anodic layer as a sink for supersaturated vacancies was measured using an electron metallographic technique. A 99.999 wt.% purity gold specimen was water quenched from 930°C, and subsequently a uniform distribution of completely nucleated and partially grown stacking fault tetrahedra was established adjacent to a free surface. The specimen was then anodized at 22°C for 400 sec to produce an anodic surface layer. Vacancy annealing was then completed at 60°C. Tetrahedron growth near the anodized surface was studied. These data, in conjunction with the solution of the appropriate diffusion problem evaluated under the boundary conditions at the interface, allowed a determination of the average vacancy sink efficiency of the anodized surface, \\ ̄ g3 s , relative to the tetrahedron sink efficiency, \\ ̄ g3 T . Using a value of \\ ̄ g3 T − 0.7 previously determined at 60°C under similar conditions, a value of \\ ̄ g3 s− 0.5 at 60°C was obtained. These results indicate that the anodized surface was a relatively efficient vacancy sink under the present experimental conditions, but less efficient than a free surface. The results are discussed in relation to the analysis of kinetic studies of vacancy precipitates in thin metal foils.

An Analytical Discrete Lattice Calculation of Vacancy Decay in Dilute Alloys

AbstractA discrete lattice calculation of vacancy annealing in dilute alloys has been performed, and the results are compared with the Damask and Dienes chemical reaction rate formulation. It is shown that the reaction rate scheme overestimates the initial transient vacancy decay rate. However, at long times, after the attainment of chemical equilibrium between solute‐vacancy complexes and f pee vacancies, the discrete lattice and rate theory formulations become identical. The rate of solute‐vacancy complex formation has been calculated using the theory of stochastic processes to determine the expected time required for a vacancy to migrate from a given position in the lattice to a first nearest neighbour position of a solute atom. Good agreement is found with the transient rate constants found from the discrete lattice annealing calculations.

Some aspects of serrated yielding in substitutional solid solutions of iron

Serrated yielding was observed between 500 and 775°K in alloys of iron which exhibited marked solid-solution hardening. The serrations result from the formation of bands of localized deformation. In a soft machine where the applied load remains constant, the band spreads immediately over the entire gauge length. In a hard machine the burst of strain associated with the formation of the band causes the load to drop, so that the spreading of the band front stops when the applied stress falls below a critical level. During reloading, aging of the dislocations in the band front occurs. At low temperatures where little aging occurs during reloading, the band front propagates along the gauge length with only small undulations in load. At higher temperatures, where aging is more rapid, the band front becomes pinned during reloading and can move only by breaking away. Alternate aging and breakaway recurs as the band front propagates along the gauge length, producing regular serrations on the load-extension curve, and surface markings on the specimen. The serration height Δθ increases with increase in reloading time, t, and temperature, T, according to Δθ = A + B log Z, where A and B are constants and Z = t exp ( −Q RT ) . The apparent activation energy for appearance and growth of serrations, Q, is about half the activation energy for diffusion of a substitutional atom in iron. The negative results of vacancy annealing experiments, and failure of the critical strain criterion indicate that the apparent high diffusivity is not due to deformation-induced vacancies. Rather, the results suggest that pinning of dislocations is due to a redistribution or reorientation of solutes or solute clusters in dislocation cores. At the upper critical temperature, which is dependent on strain rate, the growing serrations abruptly disappear. The critical rate appears to be that which just allows one lattice jump of the solute between serrations. The apparent activation energy associated with disappearance is near that for lattice diffusion of solutes in iron.

An analysis of vacancy annealing in dilute aluminium-indium alloys on quenching

Abstract The annealing of quenched dilute aluminium-indium alloys has been interpreted in the literature to give both high and low values for the indium atom-vacancy binding energy. The present work attempts to distinguish between the two proposals by comparing the predictions of a model system with the experimental observations. The results support the lower binding energy interpretation.

The annealing of deformed potassium

The stage B (15 K) recovery process in cold-worked potassium (which accounts for about 40% of the total recovery) is described by a new microscopic model of point-defect annealing. The extreme width and complex strain dependence of this stage are explained by a model in which vacancies and di-vacancies anneal to dislocation sinks. The point defects are considered to be originally deposited at random inside narrow ‘pipe-like” regions which are slightly diffused versions of the strings in which point-defects are usually thought to be deposited by cold-work. The dense initial vacancy distribution in these pipes gives rise to a high probability of vacancy combination and hence enhances the initial rate of vacancy annealing.

Short-Term Annealing in Electron-Irradiated p-Type Silicon

Studies of short-term annealing of minority carrier lifetime in bulk p-type silicon following ~1.4 MeV pulsed electron irradiation are reported. Investigations were performed on vacuum-float-zone boron-doped material in the temperature range 235-3860K and the maximum fluence employed was ~5 x 1012 electrons/cm . Simple exponential recovery under isothermal conditions, a characteristic of first order reaction kinetics, was observed. The amount of unstable damage varied as exp (-t/τR), where τR is the characteristic recovery time. The temperature dependence of τR yielded an activation energy of 0. 32 ± 0. 03 eV for the recovery process. The current results, when extrapolated to lower temperatures, compare quite closely with Watkins' EPR data for similar material. It is concluded that the present data is consistent with the observation of neutral vacancy annealing.

Kinetic Study of Vacancy and Interstitial Annealing in Metals

The rate equations governing the annealing of vacancies and interstitials in irradiated and prequenched irradiated metals for stage-III recovery have been studied. Vacancies were considered to be the mobile defect for this recovery, and the effects of the formation and migration of small vacancy clusters were investigated. Interstitials, either in the form of single trapped interstitials or small interstitial clusters, were assumed to be immobile. This system gives rise to two annealing stages, one of which involves annihilation of vacancies and interstitials, and the other, at higher temperatures, arises from vacancy migration to permanent sinks such as dislocations or grain boundaries. The form of the interstitial, trapped or clustered, has little effect on the calculated results. Peak temperatures and calculated effective migration energies, however, are sensitive to the vacancy clustering parameters (migration and binding energies). The presence of small concentrations of mobile vacancy clusters can shift the low-temperature peak to lower temperatures without changing its magnitude, and give rise to low and variable measured activation energies. The recovery model suggested by these calculations ascribes stage III to interstitial-vacancy annihilation and stage IV to vacancy migration to sinks. Depending on the clustering parameters, the kinetics for stage III may be primarily related to single-vacancy migration or may be complicated by vacancy clusters. This latter case does not require any initial cluster concentration and does not require high cluster concentrations during the recovery process.

Vacancy annealing kinetics during quenching

Abstract The differential equations which describe the annealing of vacancies in pure metals have been solved to study the loss of vecancies during a quenching operation. Using a wide range of paremeters for the chosen metal, aluminium, it is shown that divacancies can account for a substantial fraction of the vacancy loss. The extent of decay depends on the ratio of sink density to quenching speed which is the result of a state of dynamic equilibrium existing during that part of the quench where decay is significant. Extrapolation methods given in the literature and used to derive values of formation energy are briefly discussed.

Evidence for vacancy motion in low temperature ion-planted Si

Abstract Recent results have reported a strong implantation-temperature dependence between 125°K and room temperature for lattice disorder produced by 200-keV B implantation into Si. Using our previous annealing model incorporating implant temperature and dose rate, we have calculated a characteristic defect annealing time at the threshold of the crystalline to amorphous transition at 173°K for 1 μA/cm2 and find that it agrees very closely with that for neutral vacancy annealing. In addition, we have made measurements of the 1.8μ infrared absorption band, characteristic of the Si divacancy, following room temperature and 85°K implants of 400-keV B11 or Sb121 ions. Very few divacancies are observed immediately after 85°K implants, but annealing growth of divacancies occurs between 150 and 300°K yielding a density almost equal to that for the same ion Ruence at 300°K. These results strongly suggest that below 300°K neutral vacancy motion and trapping control both the implantation-temperature dependence of lattice damage production for B implantations and the divacancy formation upon annealing for B and Sb implants.