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

MATERIALS SCIENCE & ENGINEERING ELSEVIER

Materials Science and Engineering A214 (1996) 17-22

A

,

Resistometric study of short-range order kinetics in -AgZn M. Migschitz a, W. Garlipp b, W. Pfeiler a ~Institut far FestkSrperphysik, Universitiit Wien, Strudlhofgasse 4, A-I090 Vienna, Austria blnstituto de Qu#nica, Universidade Estachml Paulista "Julio de Mesquita Filho ", Rua Prof. Fra/zcisco Degni s/n, CEP 14800-900 Araraquara SP, Brazil Received 27 December 1995: revised 15 February i996

Abstract Short-range ordering (SRO) kinetics was investigated under temperature conditions of isochronal and isothermal annealing in completely recrystallized Ag-2I, -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. Keywords: Short-range ordering; AgZn

1. Introduction

Usually the two sorts of atom of a binary alloy are distributed over the points of the crystal lattice in a non-random way. Owing to differences in the atomic interaction energies between like and unlike atoms, short-range ordering (SRO) and short-range clustering (SRC) respectively result as a common property of alloys. AgZn solid solutions have been intensely investigated with respect to irradiation induced point defects. It was found that because of strong trapping effects, interstitial atoms were partially retained above 350 K [1,2]. Some of these investigations also included isochronal annealing treatments of unirradiated samples [3,4]. However, a detailed investigation of the evolution of SRO with temperature without particle irradiation is still lacking. It has been found recently that for direct determination of SRO parameters, e.g. by measuring diffuse scattering intensities, it is of great importance to know how to bring the samples into a state of thermodynamic equilibrium to which the values measured afterwards can be related [5-8]. In a very recent investigation, the SRO kinetics of ct-AgZn alloys were studied for different states of postdeformation annealing after heavy mechanical deforNOOI-gNO'4/Of;/~I~ (IN (~1 1QQ~ - - V:l¢~vi~r q r i ~ n r ~ q A

All ri~ht¢ r~¢~r~A

marion by cold-rolling [9]. It is the aim of the present paper to report the results for completely recrystallized, undeformed sample material, which were not included in the former publication.

2. Experimental and thermal treatment

Samples of 21, 23 and 28 at.% Zn in Ag were prepared by melting together 99.999% silver and 99.999% zinc in a graphite crucible by high frequency heating under purified argon atmosphere. Sheets of 0.2 mm thickness were rolled with several intermediate anneals in purified argon atmosphere. A final recrystallization treatment was carried out for 3 h at 843 K. For resistivity measurements, serpentine-shaped samples were cut out of the foils by spark erosion. Contact leads were spot welded to resistivity samples using copper wires of thickness 0.3 ram. For mechanical stabilization of the samples on the sample holder, these wires were fixed with Ceramabond 503 in small steel rolls, which then were fastened to the sample holder [10]. Resistivity changes were measured in a stirred bath of liquid nitrogen by the standard potentiometric method relative to a dummy specimen with an accuracy of about _+ 3 x 10 .5

I8

M, Migschitz et al. / Materials Science and Engineer#~g A214 (1996) 17-22

The isothermal and isochronal .annealing treatments were carried out in a bath of silicone oil (Baysilon PN200). After each annealing period the samples were quenched directly into liquid nitrogen. A typical resistance furnace was used for the 3 h recrystallization annealing at 843 K using a quartz tube filled with pure argon atmosphere to prevent oxidation and loss of zinc of the samples. To achieve a higher quenching rate the samples in this case were quenched into water of room temperature.

-,25

&

3. Results -.75 300

p ,.350

3. I. Isochronal annealing Fig. 1 is a sketch of the change in electrical resistivity during isochronal annealing treatment as a function of temperature for different sink concentrations (dislocation densities). After quenching from a temperature Tq, the resistivity during isochronaI annealing starts to change owing to a reincrease in SRO brought about by surplus vacancies in the case of low and medium dislocation densities (curve a and curw~ b). A second stage of resistivity decrease for medium dislocation density (curve b) is due to ordering or disordering by thermal vacancies generated with rising annealing temperatures. For very low dislocation densities (curve a) this second stage of resistivity decrease may overlap with the first, depending on the lifetime of surplus vacancies. For relatively high dislocation densities (curve c) quenchedin surplus vacancies do not contribute at all to SRO. Therefore curve c starts to decrease in a single stage at somewhat higher temperatures, where the thermal vacancies become mobile. At still higher temperatures, the resistivity increases owing to a recluction in the degree

I - 2 1-

& &

-8

(c) high -10 500

~ 400 T (K)

i 450

500

Fig. 2. Resistivity change during isochronal annealing of completely recrystallized AgZn solid solutions vs. temperature: Ag21Zn (A), Ag23Zn ([]), Ag28Zn (V),

of SRO. The short SRO relaxation times after the minimum of the isochronal curve enable equilibrium values of order to be established within the time intervals of isochronal annealing (equilibrium line). Fig. 2 shows the result of isochronat annealing (Air= t0 K, A t = 15 min) for all samples investigated after 1/2 h pre-annealing at 463 K and quenching into liquid nitrogen to establish a definite state of SRO. The increasing temperature during isochronal annealing first leads to a reduction in resistivity which is attributed to an increase in the degree of SRO. Owing to the low dislocation density and the long lifetime of quenched-in surplus vacancies, the resistivity decreases already after the first isochronal annealing period (15 min at 323 K). For Ag21Zn and Ag23Zn a second stage of resistivity decrease can be detected at about 360 K. At this temperature the thermal vacancies become mobile. In Ag28Zn the second stage overlaps with the first stage because of the very long lifetime of the quenched-in surplus vacancies. With increasing temperature, the resistivity for all samples reaches a minimum. At this temperature for some processes involved in SRO kinetics (see discussion) the isochronal time interval is long enough to enable equilibrium states of SRO to be achieved. The minimum temperature decreases with increasing zinc content. A continued increase in temperature leading to an increase in resistivity (equilibrium line) can be attributed to a decrease in degree of SRO [6].

[

r

i

q

__

350

400

4-50

500

3.2. Isothermal annealing

_ 550 T~

600

T (K) Fig. 1. Sketch of the variation in electrical resistivity vs. isochronal annealing temperature for three different dislocation densities: (a) low, (b) medium, and (c) high dislocation density.

To obtain more detailed information about the kinetics of SRO as well as the thermodynamic stability of the SRO microstructure, the method of isothermal annealing at neighbouring temperatures (small step an-

M. Migschitz et al./ Materials Science and Engineering A214 (1996) 17-22

healing [6]) was used in the temperature range between 383 K and 453 K. Fig. 3 shows a series of such isothermal anneals for all the samples investigated. The following features are observed. (1) Certain resistivity values correspond to specific annealing temperatures as plateau values. These are interpreted as temperature dependent equilibrium values of SRO demonstrating thermodynamic stability. (2) An increase in the degree of SRO reduces the electrical resistivity. (3) The atomic mobility increases with zinc concentration. (4) There is almost no influence of zinc content and temperature on the SRO-induced plateau values of resistivity (step height). As a consequence, equilibrium curves for all concentrations are equal and linear. (5) SRO relaxation consists of more than one exponential process. For better comparison of the SRO relaxation kinetics, Fig. 4 shows the normalized isothermal variation of electrical resistivity at 423 K as a function of annealing time after a sudden temperature change from 433 K, for all three concentrations. A tendency to shorter SRO relaxation with higher zinc content is observed.

4. Discussion

The results of isochronal measurements of the present investigation are in excellent correspondence with previous results [3,4] with respect to (i) the equilibrium line and (ii) the onset of vacancy mobility.

19

T,- 423 K

.8

.6

& \

.2

L

0 0

\ 80

40

120

160

200

t (min) Fig. 4. Normalized change in resistivity vs. time for isothermal annealing at 423 K: Ag2IZn (&), Ag23Zn (7q), Ag28Zn (V).

In Fig. 4 the normalized resistivity change is plotted vs. annealing time for isothermal annealings at 423 K. From this plot of SRO relaxation kinetics, the major influence of zinc concentration can be detected. The SRO relaxation process consists of more than one exponential process, at least for the samples with 23 and 28 at.% Zn. This can be seen better from a logarithmic plot of the resistivity change vs. linear annealing time, not shown here. For an analysis of the isothermal SRO relaxation kinetics, it was assumed therefore that a logarithmic distribution of relaxation times is involved in the ordering process:

['l

Ap(t)_Ap

(x)exp -~--~x) dx

(1)

with 41a

403

o i L-~_~_

393

i

393

383

403

423

413

Ta (K)

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I

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i

I

l

-06 I

I ]

-09 L. 0

2000

4000

6000

8000

=

I 10000

II

I

12000

14000

t (rain) Fig. 3. Isothermal annealing at falling and rising temperatures as a function of annealing time (small step annealing treatment): Ag21Zn (A), Ag23Zn (D), Ag28Zn (V). The curves are shifted along the ),-axis for clarity. Annealing temperatures are as indicated.

r(x) = r,,exp(x) This method accounts for small deviations from single exponential kinetics [11-13], which are attributed to small local fluctuations of concentration in the material (model of distributed SRO [14]). Table 1 gives the mean relaxation times f and the width of the distribution p determined by a least mean square fit procedure for all the samples. From this analysis Arrhenius plots can be derived, which are shown in Fig. 5. The resulting activation enthalpies of SRO relaxation are shown in Fig. 6. Very good correspondence with values from the literature is observed. The present results are given in Table 2 together with literature values.

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M. Migsehitz et al. / Materials Science and Engineering A214 (1996) 17-22

e¢)

v=

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2

~d

~9

~

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M. Migschitz et al./ 3,Iaterials Scietzce and Engineering A214 (i996) 17-22

21

Table 2 Dependence of the activation enthalpies of SRO relaxation on the zinc concentration (accuracy _+0.I eV); values from the literature are given for comparison

1000

Zn concentration

This work (eV)

100

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[] .2

©

&

/

P

1o

F

1

2.15

2.25

l

2.35 2.45 IO00/T (i/K)

2.55

2.65

Fig. 5. Arrhenius plot of SRO relaxation times: Ag21Zn (4), Ag23Zn (r~), Ag28Zn (V).

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1.4

r

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g

1.2

;> &

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©

:ff .8 .6 .4 .2 0 0

10

20 cz~ (at%)

30

40

Fig. 6. Activation enthalpies of SRO relaxation as determined from Fig. 6 (V). Values as-measured in a partially annealed state after cold-rolling (state C [9]) are included (A). Values from the literature for several AgZn alloys ([]) as well as for pure Ag ([]) are given for comparison.

A similar investigation of SRO relaxation by small step annealing treatment was done [9] on samples deformed by cold-rolling to about 30% and 60% thickness reduction and subsequent isochronal annealing (AT= 10 K, At = 15 min) to 553 K, where deformation induced point defects are completely annealed but a high dislocation density is still present [15]. Whereas for the present fully recrystallized state a marked acceleration for down-steps at the beginning of the isothermal relaxation is observed, this effect is not found for the partially defected state (state C in [9]).

8 21 23 24 27 28 30 30 30 30 30 31 33 34

Cold-roiled

Recrystallized

1.4 1.3

1.3 1.3

1.3

Literature [eV]

1.6

[lV]

1.46 1.41

[18] [I8]

1.38

[171

1.3 1.4

[19]

1.38

[18]

1.36 1.32 1.31

[20] [21] [22]

1.35 1.30

[18] [23]

This can be interpreted as the vacancies quenched-in by the small temperature decrease of 10 K in the recrystallized samples taking part in the ordering process, whereas they do not contribute to ordering in the defected state. In agreement with results on AuFe solid solutions [14,16], this means that for certain concentrations of deformation induced defects, the SRO relaxation kinetics is investigated under equilibrium vacancy conditions. Relaxation times and activation enthalpies as obtained from analysis of SRO kinetics in the post-deformation annealed state after two amounts of cold-rolling are given in Tables 1 and 2 for comparison.

5. Conclusions

(1) Equilibrium changes of the degree of SRO as observed by resistivity measurements of the investigated AgZn alloys are found to be independent of the zinc concentration and temperature range. (2) The equilibrium line and the onset of vacancy mobility are in excellent correspondence with earlier results in the literature. (3) Analysing isothermal SRO kinetics by a log-normal distribution of relaxation times gives SRO activation enthalpies which are in good accordance with literature data. (4) Once more it is found that conditions of equilibrium vacancy concentration are met in the partially defected material rather than in the fully recrystallized material.

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M. Migschitz et al. / Materials Science and Engineering A214 (I996) I7-22

Acknowledgements This work was financially supported by the Austrian 'Fonds zur F6rderung der wissenschaftlichen Forschung', grant N R . 9585. We thank Professor A. K o r n e r for a critical reading of the manuscript.

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[8] H. Roelofs, B. Sch6nfeld, G. Kostorz and W. Biihrer, Plo,s. Status Solidi B, 187 (1995) 31. [9] M. Migschitz, W. Garlipp and W,Pfeiler, Aeta Metall. Mater., in press. [10] M. Migschitz, F. Langmayr and W. Pfeiler, Mater. Sol. Eng., A177 (1994) 217. '[11] B.S. Berry and J.L. Orehotsky, Acta Metalt,, 16 (1968) 697. [12] E. Balanzat and J. Hillairet, J. Phys, F, 1I (1981) 1977. [13] R. Reihsner and W. Pfeiler, J. Phys. Chem. Solids, 46 (1985) 31. [14] J. Hillairet, Defect Diffilsion Forum, 66-69 (1989) I015. [15] M. Migschitz, A,Korner, W.Garlipp and W.Pfeiler, Acta Metall. Mater., in press. [16] M. Migschitz and W. Pfeiler, Mater. Sci, Eng,, in press. [17] W. Schtile, J. Phys. F, I0 (1980) 2345. [18] B.S. Berry and J.L. Orehotsky, Aeta Metall,, 16 (1968) 683. [19] S. Radelaar, J. Phys. Chem. Solids, 31 (1970) 219. [20] A.S. Nowick and R.K. Sladek, Acta Metall,, 1 (1953) 131, [2I] A.E. Roswell and A.S. Nowick, J. Met., 5 (1953) 1259. [22] J.Th. Chardon and S. Radelaar, Phys. Status Solidi, 33 (1969) 439. [23] J.R. Cost, Acta Metall., 11 (1963) 1313.