RELAXATION AND X-RAY DIFFRACTION LINE BROADENING PHENOMENA DURING GRAIN GROWTH OF METALS

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RELAXATION AND X-RAY DIFFRACTION LINE BROADENING PHENOMENA DURING GRAIN

GROWTH OF METALS

P. Gondi, R. Montanari, F. Veniali

To cite this version:

P. Gondi, R. Montanari, F. Veniali. RELAXATION AND X-RAY DIFFRACTION LINE BROAD-

ENING PHENOMENA DURING GRAIN GROWTH OF METALS. Journal de Physique Colloques,

1987, 48 (C8), pp.C8-429-C8-434. �10.1051/jphyscol:1987865�. �jpa-00227169�

RELAXATION AND X-RAY DIFFRACTION LINE BROADENING PHENOMENA DURING GRAIN GROWTH OF METALS

P. GONDI, R. MONTANARI and F. VENIAL1

Department of Mechanical Engineering, University of Rome "Tor Vergata", I-00173 Rome, Italy

RE IS^

On a observe des pics de frottement interieur et de ^defaut de module pendant la phase de recristallisation par croissance des grains des mbtaux.

Les resultats d'analyses avec les rayons X et les observations m6tallographi- ques sont conformes & l'attribution de ces pics 5 116mission des dislocations des

joints des grains.

ABSTRACT

Internal friction and modulus defect peaks have been observed during the recrystallization phase of grain growth of r t a l s .

X-ray diffraction analyses and metallographic observations are consistent with the attribution of these peaks to dislocation emission from non equilibrium grain boundaries.

INTRODUCTION

Previous observations (1,2) have shown that isothermal grain growth in A1 is accompanied a sequence of discrete peaks vs.time of the internal friction coefficient Q" and of concomitant peaks of the modulus defect Dm.

These peaks follow the one of primary recrystallization ,which occurs starting from conditions of work-hardening ,as observed with A1 by us(1,3), with Ag by Kame1 and Attia(4) and by Isore et al.(5) and with various other metals by many authors (6 for a review).

In this research the observations regarding these peaks appearing during grain growth have been extended to other metalslimpurity contents,etc.,to ascertain whether these phenomena occur only in particular conditions or they are of general validity.

For the explanation of these relaxation phenomena the Q-1 and Dm measurements have been accompanied by metallographic observations and by X-ray diffraction analyses regarding the broadening of the diffraction lines and the grain textures.

For the interpretation results of the bibliography (7,8,9,10) will be recalled,dealing with the attribution to dislocation damping of the internal friction peaks(vs.T)at intermediate temperatures.

EXPERIMENTAL

Metals taken into examination were A1 99.9%,Al 99.999%,Cu 99.90,Zn 99.99%.

The specimens for the various observations were cut from sheets 0.5 mm thick,obtained by cold rolling with reductions of "98%.

The grain sizes before recrystallization,measured by microscopy or from X-ray diffraction line broadening,were 0.2 pm for A1 99.9%, 5 pm for A1 99.9998, 8 pn for Cu, 7 pm for Zn.

At the various temperatures considered, recrystallization was followed isothermally.

The internal friction coefficient,Q-I ,and the modulus defect D were measured directly at the recrystallization temperatures; metallographic observations and X-ray diffraction analyses were made on specimens cooled at room temperature after each recrystallization treatment.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987865

JOURNAL DE PHYSIQUE

The Q" meas~rements~were carried out by detection,with frequency

modulation,of flexural vibrations;amplitudes

<

Grain textures were analysed by means of a Schultz camera

.

RESULTS

The behaviour with the different metals is considered first.

Fig.s 1-a-b-c) refer respectively to A1 99.9 8,Cu 99.9 8 and to Zn 99.99t.The internal friction coefficient Q-l is represented by the dashed line diagrams,the modulus defect Dm by the continuous 1ines;the dotted lines show the corresponding grain size evolution during isothermal heating at the temperatures

indicated;recrystallization temperatures are for comparable grain growth rates.

6 0 At the initial stages (primary

recrystallization P.R.)peaks of Q-' are observed for both

m

s 4 0 A1 and Cu;a corresponding peak

-

appears only with Al;with Cu

X E during pr imary

-

1 2 0

3

o defect presents a continuous

A trend.

cl

V After pr imary

B re~rysta1lization~i.e. during

0 1 2 3 4 grain growth (G.G. ), peaks of

T i m e ( s ) x 1 0 - ~ ^Q-1 are observed,all

accompanied by peaks of D m . 1 -100 For the temperature in

evidence the primary recrystallization of the high purity Zn occurs in small times and the data refer to grain growth,with good correspondence between 0-1

- 4 0 A and D m peaks.

a _{The Q-'} and D m increases leading to the above mentioned peaks, come about at the end of the step of <D> during grain growth

.

Pig.s 1-a-b-c = Internal friction coeff icient(Q-',---I ,I4odulus defect(Dm, - ),and average grain size(<D>,

...

G r a i n s i z e (,urn) G r a i n s i z e ( w m )

8 course both these parameters

-10

X influence the grain growth

i

a

.a25

-

-

I modulus defect present always

0 5 corresponding peaks,analogous

to those considered previously. Microscopic observations have been made

0 with particular attention to

, 0 1 2 3 4 5 the metallographic behaviour

T l m e ( s ) x 1 8 - ~ in correspondence with peaks

and recrystallization steps.

Statistical observations of the grain sizes were made,

after various

recrystallization times;the histograms of fig.3-a-b are representative for the conditions before (-a) and ,$ after(-b) a Q-1 and D m

peak.

The grain sizes appear concentrated around some subsequent va1ues;grain growth is not characterized by a progressive maximum displacement but by decreases of the lower grain size maximum (1) in fig.3-a) with corresponding increases of the larger grain size one(maximum 2);before the lower grain size maximum disappears a new maximum at higher dimension (31 appears in general. These observations are consistent with grovth acts consisting in the inclusion of neighbour grains by the growing ones(see

0 1 2 3 5 also (11)).

T i m e x l J - 3

Fig.s 2-a-b-c = Temperature and impurity effects. & l , D ,<D> vs. time during heating of A1 99.9 9 at 538 K(-a1,Al 99.9 % at 723 K(-b),A1 99.9999 at 538 K(-c).

25

r-

lig.3 3-a-b = Histograms of the grain volumes after recrystallization of A1 99.9%

at 723 K for 1500 sec. -al,before the P3 peak of fig.2-bl and for 2400 sec.

-b),after the P 3 peak of fig.2-b).

1

S 2 8

I

5:zw)

2 s 9

@0 100 200 30-460 00 100 200 300 400

-

_{b 1}

- -

-

-

s f i 1

-

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Possible explanations of these grain growth relaxation phenomena can be found in terms of dislocation damping or of grain boundary sliding.

13 6 0

m B

'1 0 - 4 0

-

b

0 0

0 1 2 3 4 5 0 1 2 3 4 5

T i m e ( s ) T i m e (sl X I B - ~

Fig.s 4-a-b = Width of the X-ray dlffraction lines during isothermal recrystallization of A1 9 9 . 9 8 at 538 K(-a) and of Cu 9 9 . 9 % at 873 K(-b).

For A1 I2201 linerfor Cu I4001 1ine.For comparison the corresponding Q-1

diagrams are also drawn by dashed lines.

Trying to solve this question X-ray diffraction analyses have been carried out.

First observations refer to changes of the diffraction line width during grain growth. in fig.4-a-b) the widths are plotted as a function of the heating time;transient broadening of the widths occur,corresponding to the Q-I peaks.This favours the dislocation damping hypothesis since simple grain boundary sliding should not give rise to line broadening.

Further, grain growth has been followed by texture analyses.

Data for Cu,reported herefshow also peculiar features in correspondence of the peaks.Fig.5-a) is representative for the recrystallization texture;in fig.5-c)the average pole width is plotted as a function of the timefin comparison with the Q-I behaviour ;even if for limited amounts these widths also present maxima corresponding to the Q-'peaks.

F1g.s 5-a-b-c = Illl1t-a) and I2001 I-b) textures of Cu after recrystallization for 3600 sec. at 873 K. In -c) the average widths of the (1111 texture poles are plotted vs. timefin comparison with the Q-1 diagrams.

disappearing with time;the occurrence of the concomitant peaks of modulus defect Dm, corresponds to the second case, i.e. unrelaxed conditions before and after peak, since in the first case only a Dm increase should have been observed.

An indication on the processes responsible for these relaxation phenomena can be obtained from the X-ray diffraction results,in particular from the width variations of the diffraction lines with maxima in correspondence of the Q-1 and D m peaks. These maxima can be related to increases of the density of the dislocations inside the grains;thus the relaxation phenomena during grain growth are considered as depending on dislocation damping.

In terms of dislocation damping modulus defect and internal friction can be expressed by

where dm is the relaxation strength, 1 is average length of the dislocation segments in density N. The factors R m and R q depend on the amount of relaxation; they correspond respectively to

1/(1t n a for R m and to ar/(l+ 9' for R q with some distribution of the relaxation times T

.

On account for the relevant levels of the Q-I peaks these damping processes should be characterized by values of o r not far from 1;observations of Woirgard et al(7-8) as well as of us (9-10) have shown indeed that in the range of these recrystallization temperatures peaks of Q1 vs T occur,i.e. damping phenomena with fir "1,which have been related to the diffusive motion of the dislocations.

On the other hand grain growth follows primary recrystallizati~n~thus involving freshly recrystallized grains which should contain dislocations in limited number. It seems thus reasonable to assume that the dislocation density increases responsible for the Q-I and Dm peaks during grain growth,depend on processes of dislocation emission from the grain boundaries.

The separate appearance of the peaks indicates, further,that dislocation emission does not occur continuosly during grain growth;moreover the evolution of the grain size histograms, before and after each peak,is consistent with dislocation emission beginning at the end of each growth stepfat the disappearance of the lower size grains.

On account of all these aspects the following explanation is considered

,

that dislocation emission is connected with non equilibrium conditions occurring when two boundaries collapse together.

Fig.s 6-a-b-c-d = Scheme for grain boundary migration and collapse with non equilibrium(-c) and final equilibrium(-d) conditions.

JOURNAL DE PHYSIQUE

As an example reference is made to the simplified case illustrated in the fig.s 6-a-b-c-d);due to the large misfit between grains 1 and 2 or 2 and 3 large densities of dislocations are present in the walls 1/2 and 2/3;the misfit between grains 1 and 3 is instead small and so only few dislocations are necessary at equilibrium in the boundary between 1 and 3 coming about when grain 2 disappears as a consequence of grain growth.However,when boundaries 1/2 and 2/3 collapse together the number of dislocations in the new boundary will be large,corresponding approximately to those present before col1apsing;the dislocations in excess above those of equilibrium m y disappear either by annihilation governed by climb in the grain boundary or because they are emitted

from the non equilibrium grain boundary.

The results presented here indicate that the second processlo£ dislocation emission,should be present with appreciable contribution.

With large misfit angle boundaries non equilibrium ledge structures will result;further, for stable equilibrium conditions reference has to be made to the deep minima present in the plots of g.b. energy vs. misfit angles.

After emission the dislocations will tend to rearrange themselves in grooves around cells or subboundaries thus leading to the decreasing part of the peaks of Q 1 and D m .Due to subgrain appearance misorientations will result within the grains ,consistently with the broadening,of limited amount,of the pole width in the recrystallization texture,observed in concomitance with the other peaks.

CONCLUSIONS

The recrystallization stage of grain growth in metals is characterized by the appearance of discrete peaks ,vs.time,of the internal friction coefficient Q-1

,following those which accompany primary recrystal1ization.For this recrystallization stage the modulus defect D m presents peaks,in concomitance with those of Q - l .

The phenomenon occurs in genera1,with different metals and for various impurity levels.

In correspondence of the Q 1 and Dm peaks effects of transient broadening of the X-ray diffraction lines and of the texture pole widths have been observed,which are consistent with the assumption that these peaks are connected with processes of dislocation emission from new boundaries.

BIBLIOGRAPHY

E.Bonetti,P.Gondi and R.Montanari;J.de Phys.C10,46(1985)363 P.Gondi and R.Montanari,Il Nuovo Cimento D,8(1986)647

E.Bonetti,E.Evangelista,P.Gondi,R.Tognato;phys.stat.s0l.a~~39~1977~661 R.Kame1 and A.Attia;Acta Meta11.,9(1961)1047

A.Isor6,W.Benoit and P.Stadelman;Phil.Mag.,34(1976)811 R.Schaller and W.Benoit;J.de Phys.C9,44(1983)17

J.Woirgard,J.P.Amirault and J. de Fouquet; Proc. 5th ICIFUAS, Aachen-Springer V.(1973)

J.Woirgard and J. de Fouquet;Scripta Ueta11.,8(1974)253 P.Gondi,R.Tognato,E.Evangelista;phys.stat.sol.a),33~1976)579

E.Bonetti,E.Evangelista,P.Gondi,R.Tognato;Il Nuovo Cimento B,33(1976)409 P.Gondi;La Met,Italiana,51(1959)185/221