DISCUSSION

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DISCUSSION

Dr Schiller

To cite this version:

Dr Schiller. DISCUSSION. Journal de Physique Colloques, 1971, 32 (C2), pp.C2-159-C2-162.

�10.1051/jphyscol:1971236�. �jpa-00214562�

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DISCUSSION

Rapporteur : Dr P. SCHILLER

The topic was introduced in the morning with an invited paper, by Prof. Lucke (Aachen). The introduction was followed by eighteen contributed papers which had to be given in two sessions. The time for the discussion allowed by the program was not sufficient so one decided to continue during the time scheduled for round table discussions on Friday after- noon.

The discussion was opened by some questions of more general character referring to the introduction by Prof. Lucke. Mr. BENOIT (Lausanne) asked how the different radiation effects can be separated.

Mr. Hillairet had observed a decrease in elastic modulus during irradiation and explained it by a bulk effect of the defects introduced while in the session on the interaction between point defects and dislocations all changes of elastic modulus were explained by pinning processes. Prof. LUCKE answered that, in fact, both effects are observed ; Mr. ROTH (Aachen) pointed out that since pinning effects occur at low doses while the bulk effects are considerable only at high doses, it is possible to separate the two different effects by this dose dependence.

Later on in the discussion Mr. MOSER (Grenoble) raised the question, why for measurements in the range of 1 c/s the background damping is generally of the order of 10-4 while for the kilocycle range one observes very often a background in the order of 10-6. This observation is clearly a contradiction to the Granato- Lucke Theory. Prof. LUCKE (Aachen) expressed the opinion that this is not generally true and there exist measurements in the kilocycle range which may schow background damping as high as I O - ~ . This may be due for example to thermoelastic damping. Further- more it is not correct to attribute all background damping in the 1 c/s range to the dislocation damping.

Mr. ROTH (Aachen) confirmed the opinion of Prof.

Lucke.

As far as Hasiguti peaks are concerned the only elaborate model was the one presented by Hasiguti and Koiwa, where the break away of a straight dislocation from one pinning point is considered. In this model there may be an error in calculation as no amplitude dependence occurs, while Prof. Licke is convinced that in all break-away processes a strong amplitude dependence must appear.

Prof. SEEGER (Stuttgart) gave in two parts, which for convenience have been put together, a prepared contribution on the problem how the interaction between dislocations and point defects must be understood. Prof. Lucke in his introduction stated that the idea of a point defect arriving at the dislocation and interacting only if it has reached the core of the dislocation is a rather crude one and neglects perfectly the long range interaction between dislocations and point defects. Prof. Seeger introduced an elaborate model for the interactions which have to be considered.

A crystal containing point defects and dislocations can be considered in three stages which are valid for different time or temperature ranges.

In the first stage dislocations and point defects d o interact only if a defect is casually placed in the core of the dislocation, no long range interaction takes place, the point defects are not acted on by the long range stress field of the dislocation (may be they are frozen in).

In the second stage one considers point defects with a symmetry lower than the symmetry of the crystal lattice. Examples of defects of this type are the carbon atom in a-iron or the dumbbell interstitial in fcc-metals.

These defects will interact with the stress field of the dislocation and reorientate themselves. This means that around the dislocations these defects are no longer statistically orientated. Consequently the dislocation finds itself in a potential well which becomes the deeper the more defects orientate in the stress field. This is Mr. FELTHAM (London) asked whether the motion practically a sort of pinning. The time dependence of of kinks has to be considered in treating the problems this orientation is clearly given by the orientation of and to what extent the proposed probability of the defects and therefore one observes by Hasiguti must be criticized, as was mentioned an exponential pinning law.

briefly in the introduction. The third stage does not reauire anisotro~ic defects.

Prof. L ~ ~ C K E answered that the string model and It is characterised by the diffusion of point defects the kink model for the motion of dislocations are for towards the dislocation. This, too, gives rise to a most purposes equivalent though he did not treat the lowering of the potential energy of the dislocation and kink model explicitly. is a sort of pinning, but not in the usual sense for the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971236

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C2- 1 60 P. SCHILLER potential energy will be lowered already before a

single defect has reached the dislocation, just due to the long range stress field. The motion of the dislocation will become more difficult and therefore one observes some sort of pinning. The time law in this case is more complicated and has been generally described by a Cottrell law. But Prof. Seeger showed that the Cottrell-Stokes-Law is without theoretical foundation. His calculations lead to a t1I2 law instead of a t1I3 law, for the diffusion of the point defects to the dislocation.

Measurements during electron irradiation on copper made by Keefer can be very satisfactorily explained by this model.

We can now try to align different measurements considering the model derived above. The mechanical aftereffect is one of the measurements we begin with.

If, for example, copper is deformed at - 93 OC for about 10

%

and then the time dependence of the modulus is measured, a change which is exponential in time is observed in this particular case with a time constant of 400 min, and which is attributed to the orientation process. The experiments of the Snoek-peak of the dumbbell interstitials in copper, made by Wagner, can be added and fall together with the foregoing results on a straight line in an Arrheniusplot, with an activation energy of 0.69 eV and a time constant of z, = lO-" S-'. One can extend these considera- tions to the pinning experiments by Thompson and Buck, which observed the diffusion of interstitials created by y-irradiation over about 106 lattice dis- tances. Their jump time falls once more on the same Arrheniusplot giving rise to a plot which describes the motion of one defect (the interstitial in copper) over a range of jump frequencies which covers 11 powers of ten. This pl6t uses quite different techniques and measurements.

A similar summing up of different measurements with the help of the above developed pinning model can be made for Nickel. Nickel offers another interest- ing point as in this case the probability of reorientation and migration are clearly different. This gives rise to two exponential processes, the mere orientation process without shift of the mass center and the migration jump which combines reorientation and mass shift of the dumbbell interstitial. Prof. Seeger emphasized that without actual pinning in the crude sense this model gives all the effects of pinning which are well supported experimentally. On the other hand the discussion can be turned around and these effects used in order to study the motion of a defect under conditions where it would otherwise be difficult to do measurements.

All this is possible, due to the presence of dislocations which act as a sort of amplifier.

Prof. LUCKE (Aachen) asked whether it is necessary to have dumbbells or whether for example vacancies would be sufficient and how large the calculated effects are. Prof. SEEGER (Stuttgart) answered that for the reorientation process anisotropic defects are necessary,

they give an exponential time law, while for the migration to the dislocations the defects may have cubic symmetry. This part of the pinning process obeys a t1I2 law.

Mr. SOKOLOWSK~ (Aachen) wanted to know whether the peak-height of the relaxation process in copper which Prof. Seeger referred to, corresponds with the values of the theoretical calculations and what was the annealing treatment of the specimen between deformation and measurements.

Prof. SEEGER (Stuttgart) replied that one does not know the exact density of interstitials and therefore can only make approximations. Assuming an interstitial concentration of 10-4 after deformation the agreement between theoretical values and measured data is fairly good. As to the annealing treatment he mentioned that the material was heated up to temperatures slightly above the peak-temperature in order to get rid of the amplitude dependent part of the internal friction.

Mr. MOSER (Grenoble) pointed out that the experiments by Fourrer seem to give evidence that in stage 3 in nickel migrate divacancies which annihilate the interstitial clusters. Further he wanted to know whether divacancies may have the same effect as dumbbell interstitialas.

Prof. SEEGER (Stuttgart) replied that he is not sure that the measurements of Fourrer which were available one and a half year ago, do really warrant the conclu- sion which Mr. Moser drew from them, he thinks that these experiments can be explained much easier by interstitials migration.

That divacancies will migrate in the temperature range of stage 3 there is no doubt. But divacancies will not give rise to effects as in the model described above. For

i) The observed relaxation strength would give rise to an extremely high density of divacancies, while the numbers are reasonable for interstitials.

ii) The orientation dependence is not right for divacancies. One would have to make very special assumptions about the dipolar strength of divacancies in order to explain that they do not give an effect in (100) direction but give one in (1 11).

iii) With divacancies the fact that one gets two different relaxations with two sorts of exponentials could not be explained. For divacancies the reorientation and migration step would coincide, as they do in copper but not in nickel to which Mr. Moser's question was referring.

The discussion then shifted to topics introduced by the contributed papers. Prof. LUCKE did not agree with the assumption made by Perez Peguin and Gobin in their paper, that the activation energy for break away of a dislocation from n pinning point is n times the break away energy from one pinning point.

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proposed was not introduced in order to describe exactly the internal friction resulting from an unpinning process but simply made it possible to describe the results of a number of experiments which showed a peak of internal friction dependent on temperature or amplitude. He agrees with Prof. Lucke that one has to consider the line tension and then gets a value for N which is 30 to 40

%

higher. He stated that nevertheless the value for the interaction energy is exact, as can be seen from his calculations.

Mr. STOLL (Wurenlingen) observed that the value of the attempt frequency (vo = 1 0 ' ~ ~ ~ ) in the contribution of Mr. Perez and coworkers agrees rather well with the maximum frequency of the phonons which is well known for most metals.

Mr. PEREZ agreed with this observation but pointed out that the limited range of frequencies for which the measurements have been carried out introduces a rather large uncertainty in the extrapolated values of v,. The calculations made for the model gave a value which is right in the range of error of the measurements and in the proximity of the maximum frequency of the phonons.

Mr. FELTHAM (London) asked whether an activation energy depending linearly on stress does not give too strong a dependence of the unpinning frequency on stress.

Mr. PEREZ said that the model has been elaborated to interpret experimental results in the amplitude range between 2 ^X 10-6 and 20 ^X 10-6 and no evidence for the difficulties mentioned by Mr. Feltham exists.

The discussion on the paper given by Mr. Gelli (Novara) was opened by Mr. GRYNSZPAN (Vitry) who asked whether Mr. Gelli could observe interactions between different types of impurities, as he himself did and what the purity of the original material was.

Mr. GELLI found that the temperature range in his measurements was quite different from the range Mr. Gryuszpan had used. But in none of this measurements did he observe an interaction between impurities.

The most salient feature, it seemed to him, was that for relatively high impurity contents the amplitude dependence could be completely described by the Granato- Lucke theory.

Mr. PEGUIN (Lyon) remarked that in well-annealed aluminium one gets plastic deformation even at very low stresses. He wondered whether part of the amplitude dependence observed by Mr. Gelli could be attributed to this effect. Mr. Gelli said he believed that in general the impurity content is high enough to give real pinning and that therefore this is the right way to describe the phenomena.

some results concerning the pinning of dislocations in nickel by hydrogen. By deforming a nickel-specimen at - 200 OC and measuring the internal friction up to room temperature he observed that in the case of charge with hydrogen a strong pinning is observed between

-

^{1600 and}- 120OC.

This pinning remains until

-

60 OC where the hydrogen returns to the lattice. This experiments can be verified by the discontinuity of the elastic limit due to the pinning of dislocations by hydrogen. The activation energy for migration of hydrogen determined by aging turned out to be 0.2 eV in the range between - 160 to - 120 O C and 0.4 eV at temperatures above - 60 OC.

Mr. de Buurman (Delft) presented a paper which described the isochronal annealing of the Youngs modulus of copper after cyclic straining at low temperature.

Mr. FANTOZZI (Villeurbanne) asked him whether he could give any interpretation of the three recovery stages observed in these experiments ; Mr. DEN BUUR-

MAN answered that he was mainly interested in the differences in the recovery spectrum for ciclically deformed material and unidirectionally deformed copper. Therefore he did not determine the migration energy and accepted the existing explanation for the three stages.

Mr. LENZ (Aachen) referred to the fact that their work on pinning in irradiated and plastically deformed copper shows a large pinning stage from about 80 to 100 OC which they tend to attribute t o the arrival of vacancies coming from clusters. He said he would like to know whether this had been considered.

Mr. DEN BUURMAN thought that his interpretation was not affected by the presence of clusters of defects which become mobile at higher temperatures. He observed a defect which is mobile at room temperature and not mobile at low temperatures.

Referring to the paper presented by Miss Lomer, Mr. BENOIT (Lausanne) asked how unpinning could be understood. There exist two possibilities :

i) the defects responsible for the pinning leave the dislocation and go back to the lattice or,

ii) the defects on the dislocations are annihilated by other defects arriving, i. e. interstitials annihilated by vacancies.

Mr. Benoit asked which of the two models is the right one or whether both of them have to be considered.

Miss LOMER (Reading University) said she considers the depinning she observed to be due to defects leaving the dislocations, since a second pinning stage which is ascribed to vacancies is observed at much higher temperatures and this could not be explained if the annihilation of interstitials and vacancies was responsible for the depinning.

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C2- 1 62 P. SCHILLER

Mr. BENOIT (Lausanne) then asked the same ques- Miss LOMER (Reading University) admitted this tion about the low temperature depinning stages. necessity but said that she found that these experi-

~i~~ LoMER ( ~ ~university) said that she ~ d i ~ ~ ments were not detailed enough to answer this ques- thinks that most depinning is due to defects leaving tion, she took measurements only after one hour and the dislocations. The binding energy may depend on therefore short time effects may have escaped the the character of the dislocation and in this way several

stages or one very wide stage is obtained. In gold there may even exist one superposition of depinning of dislocations of different character and interstitials and pinning by interstitials released from impurities. This may be the explanation for the difference between her results and those of Sosin.

Mr. LENZ (Aachen) commenting on the question by Mr. Benoit, said that the possibility of annihilation of interstitial pinning points by vacancies is very fascinating, but in this case depinning in isothermal experiments should also be observed but at low temperatures this is not observed. Therefore his conclu- sion is, that low temperature depinning stages are due to some kind of rearrangement of pinning points on the dislocations.

Prof. LUCKE (Aachen) insisted that, for any explanation of depinning by a thermally activated process depinning in isothermal experiments too should also be considered.

Prof. LUCKE (Aachen) said that they had done experiments and could not observe isothermal depinning, but this question may be left open. But there is no doubt that if isothermal depinning cannot be observed the depinning process is not thermally activated.

Miss LOMER (Reading University) asked for a possible explanation of the << immediate H depinning.

Prof. LUCKE (Aachen) answered that in experiments under irradiation the radiation can be switched off and isothermal depinning then observed.

There were some questions on the thermal treatment of the specimens used by Mr. SOKOLOWSKI (Aachen).

He explained that an annealing temperature of 400 OC was chosen in order to still obtain complete annealing but not graingrowth which is not desirable as it alters the uniformity of the specimen.