key: cord-0010150-a4ld83jz
authors: Tsuchida, T.; Kaneko, R.
title: Temperature Dependence of Activation Energy in Stage II Recovery in Deformed Aluminium
date: 2006-02-15
journal: Physica Status Solidi A Appl Res
DOI: 10.1002/pssa.2211040213
sha: ab992e417152e8fdad2c4f1bed86a2a65362e479
doc_id: 10150
cord_uid: a4ld83jz

The activation energy of recovery in 99.999% aluminium deformed at 4.2 K is investigated at temperatures between 50 to 180 K by means of the change of slope method. The activation energy varies from 0.15 to 0.60 eV with raising temperature. This behaviour is simulated by considering an overlapping of several first order processes within stage II. It is supposed that the variation of activation energy in stage II is due to recovery of vacancies and their small clusters by pipe diffusion mechanism.

It is well known that point defects are produced in deformed metals together with dislocations. Several mechanisms have been proposed for the production of point defects: (a) non-conservative motion of jogs on moving screw dislocations, (b) mutual annihilation of dislocations with an edge component, (c) dislocations cutting through an attractive tree of a disloaation forest [l] . A problem, argued for years, is whether the point defects produced are vacancies or interstitials or both.

Recently, experimental techniques such as perturbed angular correlation (PAC') and Mossbauer spectroscopy, which can clearly discriminate between vacancies and interstitials, were applied to study point defects in deformed metals [2 t o 61. These works all indicated that no signal of interstitial-probe complexes were detected while several signals of vacancy-probe complexes were observed. From these experimental results, it appears that the majority of point defects produced in deformed metals are vacancies. Especially for the stage IT recovery in cold-worked aluminium, Sassa e t al. [6] analyzed the defect line of the Mossbauer spectrum and concluded that the defects annealed a t a temperature as low as 100 I ( were vacancies. I n our previous paper [ 7 ] , we have proposed that defects recovered a t stage T I were of vacancy type on the basis of the following reason: the suppressive effect of impurities on stage IT recovery was ordered as Ge > Si > Cu > Ag > Mg, consistent with the order of magnitude of the interaction between vacancies and impurities, in reactions leading to the formation of dislocation loops in quenched dilute aluminiiiin alloys [8] .

It is worthwhile to measure the activation energy to clarify the mechanism of stage I1 recovery. The activation energy of the recovery around 100 K was estimated t o be 0.2 to 0.3 eV by Sassa et al., according to the analysis of the temperature dependence of the defect line intensity [6] . Frois [9] obtained activation energies of 0.22 and 0.32 eV for the recovery peaks at about 80 and 125 K, respectively. As pointed out by this author, however, it seems that the activation energy increases gradually with increasing temperature and annealing should not be assigned to simple processes. For the separation of processes, the activation energy has to be measured with a temperature interval as small as possible, as described in the next section. Also, only an apparent activation energy is obtained experimentally, when some recovery processes occur simultaneously. We have examined the activation energy change in the region of 50 to 85 K (transition period between stages I and 11) in deformed pure aluminium and its dilute alloys [lo] . It was reported that the recovery in this temperature range can be interpreted by an overlapping of two processes consisting of dislocation rearrangement (below 6 0 K ) and the annihilation of vacancies due t o diffusion along dislocations.

Up to date, it has riot sufficiently been clarified how defects recover a t any temperature in stage 11. I n this paper, we examine the recovery of electrical resistivity in deformed aluminium and will try to simulate the temperature dependence of the activation energy. Then, stage I1 recovery will be discussed from the point of view of an overlapping of some recovery processes of vacancy-type defects.

Polycrystalline wires of pure aluminium with 99.999 yo in nominal purity were prepared for the electrical resistivity measurements. The specimens of 0.2 mm diameter were annealed a t 773 K for 30 min in vacuum and then extended by about 10% a t 4.2 K. The electrical resistivity measurements were executed after the release of the stress. The detailed description of the electrical resistivity measurement technique has been presented in our previous paper [7].

After the deformation, isothermal annealings were carried out a t intervals of about 10 K between 40 and 160 K. At every temperature, the time of annealing is fixed to 360 s and the electrical resistivity was measured every 120 s a t 4.2 K. By the use of a series of isothermal annealings, activation energies were obtained by the change of slope method. The experimental data of each isothermal annealing are fitted to simple exponential decay curves by means of the least square method and slopes a t the beginning and the end of each fitted curve are used for the calculation of the activation energy.

As was noted in a previous paper [7], an isochronal annealing at every 5 K was performed, while Takamura and Okuda [ll] and Swanson [12] adopted every 10 and 15 K, respectively. The former annealing a t every 5 K was suitable for the study of stage 11, recovery (between 60 and 100 K), because of the large recovery rate. I n the case of a small recovery rate in stage 11, (between 100 and 160 K), the latter annealing a t 10 or 15 K intervals will be successful, on account of the demand for an accurate calculation of slopes a t the beginning and the end of each isothermal annealing. If we liked to investigate the recovery stage I1 (between 60 and 160 K) all over, then the latter annealing was adopted.

A typical series of isothermal annealings of the electrical resistivity is given as a function of temperature in Fig. 1 , where Ap and AQ,, are the residual resistivity increment' and the total residual resistivity increment just after the deformation, respectively. The isochronal annealing curve together with the differential isochronal annealing curve are also given as shown in Fig. 2 . As is shown by the differential isochronal curve in Fig. 2 , two substages (a large recovery a t around 85 K (stage 11,) and a rather wide and small recovery stage from 100 to 160 K (stage 11,)) are obtained obviously. But subpeaks in stage 11, appearing a t 75 and 90 K, which are newly found in our previous work [7] and investigated in detail by Ohtaki [13] , are not observed. This comes from the difference in annealing treatment, 6 min pulse every 10 K, as mentioned in the preceding section. Though i t is clear that every 10 K is not close enough t o analyze stage II,, the temperature interval of the annealing is chosen as mentioned above, in an effort t o make accurate measurements of activation energies throughout stage 11, especially the small recovery stage 11,.

The temperature dependence of the activation energy is shown in Fig. 3 where temperatures are determined as an average temperature of two subsequent isothermal annealjngs. The activation energy proves to vary gradually with temperature all over Fig. 1 ( 0 ) and its differential curve ( 0 ) 1 Fig. 3 . Temperature dependence of activation energy between 40 and 180 K (present work: 0). Also shown are Frois's data ( 0 ) T ( K )stage 11. This is consistent with Frois's results [9] , which are also shown in Fig. 3 , makiiig an exception for a few data points in the temperature region of 150 t o 180 K.

It is considered that in this region the temperature was not sufficiently stabilized to determine the activation energy accurately in the present work. Excluding this region, the temperature dependence of the activation energy for the recovery of 15% deformed specimens shows no evident difference in comparison with 10% cold-worked specimen. At present, it will be considered that the amount of extension has no apparent effect on the activation energy in stage 11. As has been shown before, the activation energy certainly increases with increasing temperature.

As suggested in Section 1, the recovery stage I1 occurs as an overlapping of several recovery processes. I n these processes, we assume that N defect species are recovered. In such a case, the electrical resistivity increase contributing to stage 11, AeIl, which is caused by the production of defects during low-temperature deformation, will be described by with a summation of AeII,, due t o the recovery of a species n among N species. Since the mechanism of the recovery is not clear at present, we assume for simplicity that it obeys a first-order process, that is,

where AeIr,,(O) represents the initial electricd resistivity contribution of defects of the species n. The rate constant is given by

where En is the migration energy of the species n, and B, is the constant given as the product of geometrical factor gn, jump-attempt frequency vn, and sink concentration B,, and E, are not available at present. So we take 3, and En as adjustable parameters, arid try to simulate the series of isothermal annealing curves a t temperatures between 60 to 150 K in Pig. 1. From the simulated curves, we can calculate activation energies by meaiis of the change of slope method, which caii be compared with the experimental results in Fig. 3 directly. Also here the number A' of species is not known, so we carried oiit simulations for different N and compared calculated activation energies with experimental ones and estimated the required number of N .

Estimated parameters are given in Table 1 , where Aerr,,(0) are calculated with parameters E , arid B, so as to minimize the difference between experimental data and calculated ones and the quantity Aeo is the total residual resistivity increase due to the deformation. The species are characterized by these three parameters. The activation energy calculated with these parameters is shown in Fig. 4 together with experimental results. They show very good mutual agreement between about 80 and 140 K.

Here we used N = 8, which is the number of defect species contributing t o stage 11. I t is difficult to reproduce the temperature dependence of activation energy with N <8. So eight species of defects are considered as a minimum for the simulation of isothermal curves in this temperature range. The origin is discussed in the following.

It is found from Table 1 that the recovery processes are divided into two different groups by values of parameters E,L arid B,. Group 1 (n = 1 to 3) have a relatively low activation energy E , and low-rate constant 3, compared to those of group2 (n = = 4 to 8). At first we discuss the parameters E , of the species in group 1, recovered a t stage 11, (between 60 and 100 K). T(N J --As discussed in our previous papers [7, lo], stage TI, is caused by the annihilation of vacancies due to enhanced diffusion along dislocation and the activation energy associated with the main recovery peak around 85 K is 0.21 eV. But three parameters (see Table 1 ) obtained here for species n = 1 to 3 give an impression that not only single vacancies but also small vacancy clusters such as di-and trivacancies contribute to stage IIA recovery. Collins [3] performed a PAC study of heavily deformed Au a t 77 K and resolved the recovery stage 111 into three different processes due to tri-, di-, and single vacancies. He found that in stage I11 of deformed Au trivacancies recovered a t the lowest temperature, then divacancies and finally single vacancies were annealed out in stage 111. So he concluded that tri-and divacancies were created during deformation without a reaction of single vacancies. Muller [4] also pointed out that lorig-range migration of divacancies occurred around 200 K in A1 elongated by 5 to 20% a t 77 K. Moreover, it is well known that the activation energy of stage I11

in deformed A1 is 0.57 eV [l] , which is different from a migration energy of 0.65 eV for single vacancies in quenched A1 [14] . From the experimental results stated before and considering the production mechanisms of point defects by low-temperature deformation (b) and (c) mentioned in Section 1, it is likely that small clusters of vacancies, which have smaller migration energies, are created simultaneously with deformation. So the species in group 1, which mainly recover at about 85 K, will be assigned to vacancies and their small clusters. We suppose that tri-, di-, and single vacancies move by diffusion along dislocations [7] with activation energies of about 0.16, 0.18, and 0.22 eV (Table l) , respectively, and are finally annihilated a t jogs.

Recovery of defects in group 2 is considered to correspond to the recovery stage 11, (between 100 and 160 K). As is mentioned in our previous paper 171, the recovery in this temperature region is strongly affected by impurities. Though the differential isochronal recovery curve of 5N A1 is almost flat throughout the stage 11, except for a small peak at about 140 K, the addition of each impurity up t o an amount of about 60 ppm produces small peaks a t subsequent temperatures. So the recovery in this substage is thought to be related to vacancy-impurity complexes. As shown in Table 1 , they have activation energies of 0.3 t o 0.42 eV, which are smaller than the migration energies of 0.47 to 0.65 eV for vacancy-type defects in the lattice [14] . So the recovery may occur by enhanced diffusion along dislocations, in the same way as in stage 11,. The difference between the activation energy of stage 11, (group.1) and that of stage 11, (group 2) can be explained by binding energies between vacancles and impurities. The binding energy between single vacancies and impurities in the lattice is smaller than 0.1 eV [15] , while that for small clusters is not known. When the vacancies are trapped at impurities, a summation of migration energy and binding energy between them is required for detrapping and annihilation of the vacancies.

As is mentioned before, migration energies of tri-, di-, and single vacancies are estimated to be 0.16, 0.18, and 0.22 eV, respectively. Assuming that binding energies between impurities and tri-, di-, or single vacancies in the dislocation pipe are about 0.1 eV, i.e. the same as in the lattice, the activation energy is estimated to be 0.26 to 0.32 eV. Another possibility of distributing the activation energy is the emission of vacancies from the small clusters and their annihilation a t sinks. The formation of small vacancy clusters during deformation are likely as mentioned before. In the lattice, binding energies of vacancies with their small clusters are estimated to be 0.22 to 0.25 eV [9] , and the activation energy for the annihilation of single vacancies detrapping from small clusters containing 4 to 10 vacancies is estimated to be 0.44 to 0.47 eV. Thus, if we assume pipe diffusion of vacancies detrapped from vacancyimpurity complexes and from small vacancy clusters, activation energies for stage 11, recovery may be distributed between 0.26 and 0.47 eV. Here we use binding energies of vacancy-impurity complexes and of vacancy clusters in the lattice, but they may have almost the same values as those in the dislocation pipe. So the estimated value of En in Table 1 , 0 . 3 to 0.42 eV, may be reasonable for the mechanisms mentioned above.

Another point of discussion is the parameter B, given in Table 1 . The values B, of the species in group 1 are of the order of los to lo9 s-l, while those in group 2 are 1011 to lOl3s-l. These values are understandable within the scope of the abovepresented discussion. Parameter B, consists of frequency factor v,, geometrical factor g,, and sink concentration C,. The values of vn and gn are estimated to be of the order of 10l2 s-l and 10, respectively. These values for groups 1 and 2 will not be different from each other, only the values of C, can change. The recovery of defects in group 1, corresponding stage II,, may be controlled by their diffusion processes. Then the value of C, estimated from B, in Table 1 with the value of vn and gn shown above is of the order of 10-5 to This is coincident with the jog concentration 011 dislocations in metals deformed by about 10% [16] . O n the other hand, by the same estimation as above, C, has a value of the order of lo-' to 1 for the species in group 2. Assuming pipe diffusion of vacancies for stage 11, recovery, i t will be natural that it has the same sink concentration as stage IIA. B u t the estimated value is different by an order of three to five. This is understood from the fact that the recovery processes of species in group 2 are controlled by the emission process of vacancies from vacancy-impurity complexes or small vacancy clusters. Then the emitted vacancies diffuse quickly along dislocations and are annihilated a t jogs, so that vacancies can reach sinks with only one jump process.

The last problem is the contribntion of each species to the electrical resistivity change AeII,,(O). The change isexpressed by the product of concentration C, of species n and electrical resistivity change due to the annihilation of 1 atyo of that species.

From the value of AeII,,(O)/Ap, in Table 1 have suggested that 20 to 50% of probe l l l i r i atoms in their PAC study captured vacancies. This enhancement of trapping of vacancies is not made clear a t present, but it may be necessary t o consider the peculiarity of recovery in deformed metals such as an inhomogeneous distribution of impurities according to impurity-dislocation interactions and/or the peculiarity of one-dimensional diffusion of vacancies along dislocations. It is not sufficient, however, to explain the amount of group 2 only by enhanced trapping of vacancies with impurities, so it is required to assume the existence of small vacancy clusters created during deformation.

(1) The measured activation energies of stage I1 recovery in deformed A1 varies from 0.15 to 0.50 eV with rising temperature, and it has been explained by the overlapping of eight first-order processes.

(2) According to the simulation, stage 11, is considered to be due to the annihilation of single, di-, and trivacancies along dislocation pipes associated with activation energies of 0.22, 0.18, and 0.16 eV, respectively.

(3) Stage 11, consists of five processes whose activation energies are between 0.3 and 0.42 eV. Each species of defects could not been assigned to these recovery processes one by one, but they are considered to be due to detrapping of vacancies from both vacancy-impurity complexes and small vacancy clusters and successive vacancy annihilation at sinks.

Varancies and Tnterstitials in Metals

Point Defect and Defect Interaction in Metals

The authors would like to sincerely thank Prof. H. Yamaguchi for his guidance and encouragement throughout this work. They also acknowledge Dr. I. Hashimoto and Dr. T. Yamauchi for their suggestions and for helpful discussions.