SHORT-RANGE-ORDER FORMATION AND VACANCY ANNIHILATION IN AN Au 15 at % Ag ALLOY AFTER QUENCHING

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SHORT-RANGE-ORDER FORMATION AND

VACANCY ANNIHILATION IN AN Au 15 at % Ag

ALLOY AFTER QUENCHING

R. Scheffel, H. Heidsiek, K. Lücke

To cite this version:

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JOURNAL. DE PHYSIQUE Colloclue C7. supplhment rru no 12. Tome 38. dhcemhre 1977. pfige C7-35 1

SHORT-RANGE-ORDER FORMATION

AND

VACANCY ANNIHILATION

IN

AN

Au 15

at

%

Ag

ALLOY AFTER QUENCHING

R. SCHEFFEL, H. HEIDSIEK and K. LUCKE

Institut fiir Allgemeine Metallkunde und Metallphysik der RWTH Aachen, West-Germany

Rbume. - Les variations de rksistivitt tlectrique au cours du recuit isochrone et isotherme d'un alliage trempk Au 15 % at Ag ont ete mesurtes a differentes temperatures de trempe et de recuit. D ' a p r b d'autres auteurs les variations de resistivitt observtes ont Ctt attribuees a des variations d'ordre a courte distance.

La formation d'ordre

a

courte distance est rCgie par I'excCdent de lacunes de trempe. A p r b dis- parition de celles-ci, les lacunes thermiques restantes determinent la formation nouvelle d'ordre a courte distance jusqu'a ce que I'kquilibre de I'ordre a courte distance soit ttabii.

L'analyse numkrique conduit a des donntes pour l'tnergie d'activation de migration et d e formation des lacunes aussi bien que pour I'autodiffusion dans cet alliage. Les valeurs autoconsistantes trouvtes correspondent bien aux valeurs d t j i publiees.

Abstract. - The changes of the electrical resistivity during isochronal and isothermal annealing of a quenched Au 15 a t % Ag alloy have been measured for different quenching temperatures and annealing temperatures. Following other authors the observed resistivity changes have been attri- buted t o changes in short-range-order (s.r.0.).

The formation of s.r.0. is governed by the quenched-in surplus vacancies. After these have disap- peared the remaining thermal vacancies determine the further s.r.0.-formation until the equilibrium of s.r.0. has been established.

A numerical analysis leads t o values for the activation energies of vacancy formation and migration as well as for selfdiffusion in this alloy. Selfconsistent values are found which are also in good agreement with those in literature.

1. Introduction. - By means of resistometric stu- dies of short-range-order (s.r.0.) formation in Au-Ag alloys with different quenching and annealing treat- ments, Schulze and Liicke [I, 21 were able to show :

First, s.r.0.-formation leads to an increase in electrical resistivity (see also [3-51). Second, this is considerably accelerated by high surplus vacancy concentrations frozen in during the initial quench from high temperatures (compare [4]).

These experiments were continued with an Au 15 at

%

Ag alloy after quenching from medium and low temperatures. This was done in order to study the transition of the s.r.0.-formation established by diffusion of annihilating surplus vacancies to the s.r.0.-formation due to selfdiffusion (e.g. by thermal vacancies). Quantitative investigations of these mea- surements lead to independent determinations for the activation enthalpies of formation and migration of vacancies, as well as for the sum of these quantities.

quenched in 0 OC water. Subsequently it was placed in a - 40 OC methanol bath where the initial resistivity p,, as well as the actual resistivity after each annealing step was measured. The annealing treatment (either isochronal or isothermal) was performed in silicon oil.

3. Experimental results.

-

Figure 1 shows the results for three isochronal experiments. The specimen was quenched from different temperatures

( T , = 700 oC, 300 O C and 250 OC), and then stepwise

annealed for specific time periods (t, = 15 min or 3 h) at each level of increased temperature as indicated. The following common features can be observed :

1) At the beginning of each isochronal heat treatment the resistivity increases.

2) The resistivity runs through a maximum value into a decreasing curve as the annealing temperatures increase.

2. Experimental methods. - Specimens and expe- 3) Above T, = 200 OC the isochronal curves

rimental methods were the same as described in [2]. combine. (This is an indication that the annealing A specimen cut out of a foil (0.1 mm thick) was curves' common decreasing part should be considered annealed at different quenching temperatures T, by the equilibrium curve of the s.r.0.-induced resistivity applying electrical current. It was then immediately (compare [3-51.)

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C7-352 R. SCHEFFEL, H. HEIDSIEK A N D K . L ~ J C K E

Annealing Temperature T, 1 . ~ 1

FIG. 1 . - Resistivity p (measured at TM = - 40 OC) versus anneal- ing temperature T, during isochronal annealing after quenching

from different temperatures T,.

Apart from these coincidences, considerable differences in the increasing parts of the isochronal curves can be noted (i.e. until the equilibrium curve of the resistivity is reached). It will be shown that these differences can be explained by regarding not only the s.r.0.-formation, but also the simultaneous annihila- tion of the quenched-in surplus vacancies (see [4]).

After quenching from Tq = 700 OC, the sample is rather disordered and contains a large supersaturation of vacancies. During subsequent annealing, these vacancies become mobile. They migrate to sinks and annihilate. Since increasing annealing temperature causes an accelerated increase in vacancy mobility, a steep rise of s.r.0.-formation and resistivity occurs. At Ta = 40 OC the equilibrium curve is reached. Further increase of the annealing temperature leads to destruction of s.r.o., and thus a decrease of resistivity follows.

Not only ordering below Ta = 40 OC, but also a certain amount of disordering above Ta = 40 0C

has to happen through diffusion of excess vacancies, since selfdiffusion is an important factor only above

Ta = 200 OC for the annealing intervals considered.

( t , = 15 min). This is to be concluded from isochronal annealing after quenching from 3000C. In this case the vacancy concentration decreases to such a low value during annealing, that the few remaining vacancies d o not permit considerable s.r.0.-formation during the annealing intervals of t , = 15 min at

temperatures between T, = 160 OC and 200 OC. There- fore, the resistivity curve levels off below the equi- librium curve. Only above T, = 200 OC the concentration and mobility of thermal vacancies are so greatly increased that during one annealing step further s.r.0. and corresponding resistivity changes occur. The isochronal curve runs into the equilibrium curve.

If, however, the annealing time t, at each tempe- rature is extended sufficiently, as represented in this paper by the curve after quenching from T, = 250 OC

(here t, = 3 h), one finds that concentration and mobility of thermal vacancies permit detectable s.r.0.-formation after annihilation of surplus vacancies. This fact is demonstrated by the second resistivity increase at higher annealing temperatures

(T, 2 160 OC).

Further information about the influence of vacancies on s.r.0.-formation can be obtained through iso- thermal annealing experiments. In figures 2 and 3, the resistivity p is plotted as a function of the annealing time (versus log t ) during annealing at Ta = 80 OC

and 220 OC conducted after quenching from different temperatures (300 OC

<

Tq

<

750 OC).

FIG. 2. - Resistivity p us. annealing time t for different quenching

temperatures and a low annealing temperature (T, = 80 OC).

After quenching from high temperatures

Tq 2 500 OC, the resistivity runs through a maximum and reaches a final value which is the equilibrium value corresponding to the annealing temperature. This type of annealing curve has been investigated in detail by Schulze and Liicke [l, 21. In the opinion of these authors such curves must be interpreted as a superposition of an increase of resistivity due to s.r.0.-formation and a decrease due to annihilation of quenched-in vacancies (which is a well known fact for the pure components Au and Ag, compare e.g.

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SHORT-RANGE-ORDER FORMATION A N D VACANCY ANNIHILATION C7-353

, , , , , , , , , , , , , , , , ,

,,,I

5.8 0 5.7 9 8

lo-2 I - lo0 10' lo2

lo3

Annealing Time t lminl

FIG. 3. - Resistivity p us. annealing time r for different quench~ng

temperatures and a high annealing temperature (T, = 220°C).

quenched-in vacancy concentration decreases. and consequently the maximum disappears at medium quenching temperatures. Then the direct contribution of vacancies becomes neglectable. After quenching from low temperatures T,

<

450 OC the quenched-in vacancies are annealed out before the equilibrium of s.r.0. is established. If the concentration of the remaining thermal vacancies is very small (e.g. corresponding to an annealing temperature Ta = 80 OC as in figure 2),

the curves run into final values which are further and further below the equilibrium value in direct relation to the lower quenching temperature (e.g. the annihilating vacancy concentration).

However, at the high annealing temperature

Ta = 220oC in figure 3, all curves reach the equili-

brium resistivity since a sufficient concentration of thermal vacancies remains, and s.r.0.-formation occurs by selfdiffusion (I).

Another variation of isothermal treatment is the temperature change after the equilibrium value corresponding to one annealing temperature has been established. In figure 4 the relative resistivity change

( p

-

po)/po us. annealing time is given for a sample after a quench from T, = 650 OC during annealing

at Ta = 60 OC. After the equilibrium resistivity was

reached, the annealing temperature was raised by

20 OC to Ta = 80 OC, and the new (lower) equilibrium

( I ) That the resistivity increase appears to occur in two steps, is

only an effect of the logarithmic time scale. In a linear time scale one

obtains curves with a continuously decreasing slope (see figure 6 ) .

Annealing T ~ r n e t [ m ~ n ]

FIG. 4. - Relative resistivity change ( p - p,)/p, us. annealing

time I after sudden changes of the annealing temperatures between

60 OC and 80 OC.

value was adopted during further annealing. Then the degree of s.r.0. at T, = 60 0C was restored, and subsequently the annealing at Ta = 80 OC was repeated. It is easy to see, that now a longer annealing interval is required for assuming the equilibrium compared to the first annealing treatment at 80 OC.

This factual situation indicates that surplus vacancies still are annihilating, and therefore, identical changes in s.r.0. are slowed down the longer the total annealing time. Figure 5 shows that similar changes of the annealing temperature in the temperature range

Ta

--

200 OC lead to reproducible curves, since here

vacancy concentration is in thermal equilibrium.

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C7-354 R. SCHEFFEL, H.. HEIDSIEK AND K. LUCKE

4. Quantitative analyses.

-

A quantitative ana-

lysis of the different isochronal and isothermal annealing curves can be carried out with two empirical equations proposed by Schulze and Liicke [2]. This method will be demonstrated below by analysing one isothermal annealing curve as a n example. A more detailed description will be given in a subsequent paper.

If the direct contribution of vacancies to the resistivity can be neglected, the rate of vacancy annihilation, and the rate of resistivity increase due to s.r.0.- formation, can be described by two simple equations with reaction orders a and /3 :

with

and

z, is the characteristic time for vacancy annihilation and 7, for s.r.0.-formation. z, is not a constant, since c is a function of the annealing time.

c, and po are the initial values of the vacancy concentration and the s.r.0. dependent resistivity corresponding to the quenching temperature Tq, whereas ce and p, are the equilibrium values dependent on annealing temperature. v is the jump frequency of a vacancy, and n its mean number of jumps before annihilation. m is the mean number of jumps of an atom until the equilibrium value of s.r.0. is reached. B is a constant with the dimension of a resistivity.

Since after quenching from Tq = 300 OC the resis- tivity changes occur only due to s.r.0.-formation, the results for the annealing curve at T, = 220 OC in

figure 3 can be analysed according to the above equa- tions. Figures 6a and 66 show this curve again. The total resistivity change has been normalized to one, and the time scale is either logarithmic (like in figure 3) or linear. Figure 6c shows the slope i/(pe

-

po) of the curve in figure 66 versus the normalized deviation from the equilibrium value ( ~ e

-

P)I(P~

-

PO) (2).

This normalized deviation is greatest (equal one) at the beginning of the isothermal experiment, and decreases with increasing order towards zero ; figure 6c should be read from right to left. The scale of both axes in figure 6c is logarithmic, because then, according to eq. (2), a differentiated isothermal curve

she-uld

give a straight line with the slope

fl

and the axis

(') In order to ease a comparison of figures 6b and 6c on top of figure 6c the corresponding normalized resistivity change

( p - p o ) / ( p . - p o ) is also given.

Annealing Time t [min]

a )

0 20 40 6 0 8 0 100

Annealing Time t Imin]

b)

FIG. 6a and 6b. - Normalized resistivity change vs. annealing time for one annealing cunre,from figure 3. The time scale is logarith-

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SHORT-RANGE-ORDER FORMATION A N D VACANCY ANNIHILATION C7-355

Normalized Resistivity Change ( p - % ) I ( ~ , - g ) intercept of the extrapolated straight line (broken line in figure 6c) a value for

7s = Tse ( v c ~ ) -

can be obtained. H , can then be determined for each

single annealing curve from tso and z,, corresponding

to

HF =

-

k

(ts017se)

T - 1 - T-1

a 9

( 5 )

Here one finds HF = 0.96 eV which agrees with the

value given in [2]. The full curves in figures 6 are theo- retical curves which have been found by fitting the five

TJ parameters (e.g. the two reaction orders a and

fi

and

the three characteristic times rs0, r,, and 7,). The activation enthalpy of vacancy migration

HM,

for example, derived from an Arrhenius plot af

7;'

-

v

-

exp

- -

(

:'?I

for a set of curves with T, = const, turns out to be

H M

= 0.75 eV in agreement with [2]. (Not shown here.)

If quenching and annealing temperature differ

(

e-p)l!p;po)

_{approximately lo0-30}_{O C}_{the bent part of the diffe-}

FIG. 6c. -Normalized slope P , ( ~ , - p,) for the curve from (b) rential annealing curves nearly disappears as can be

us. the normalized deviation ( p , - p)/(p, - p,) of the resistivity Seen in figure 7. This indicates that no large changes of

from the equilibrium value. vacancy concentration occur.

intercept l/.c,, if t, was a constant for the whole curve

(e.g. if the vacancy concentration was a constant (see eq. (4))).

The experimental curve in figure 6c shows, that c is not constant throughout the whole experiment. At the

a0

beginning of the annealing treatment the sample I

contains the vacancy concentration co

-

exp

(H, is the enthalpy of formation for a vacancy). o,

n

Thus the characteristic time 7, of s.r.0.-formation is 3

according to eq. (4) V)

z

_N ZS = zso

-

(vco)-

'

.

.-

-

e

(62-

This value can be obtained directly from the inter-

₂

:

240°C cept of the differentiated curve in figure 6c at

( ~ e - P) (PC - PO) = 1

.

230'C

Along the bent p a n of this curve s.r.0.-formation

happens while vacancies are annihilating (at about 2 20.C 60

%

of the total resistivity change). Then the curve _lo3

indeed runs into a straight line, indicating that now 1 6' 1

o0

the vacancy concentration has decreased t o the equi- C P,-P)lCQ-K$

librium value c e Along the Straight line s.r.o.-for-

FIG, 7 -Normalized slop u.y, normalkd dcvlation ofthe r h -

mation Occurs with vacancies (selfdiffusion). _{livity from the equilibrium value for some curves similar to those}

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Furthermore the reaction order

P

turns out to be A n n e a l i n g T e m p e r a t u r e T,

['c]

approximately one ( 3 ) (see the broken line in figure 7),

and therefore an analysis with the presumption

fi

= 1 has been performed for the curvesin figure 7 and the

curve T, = 230 OC, T , = 200 OC in figure 5. The Au 1 5 a t % A g

resulting values for l / ~ , , have been plotted versus T;

'

in figure 8. From the slope of the straight line an activation enthalpy of Q = 1.72 eV is obtained, which

is the sum HM

+

HF according to eq. (4) (with

/?

= 1) :

₇

C

.-

H ,

+

HF E "Ce

-

l/Tsc =

-

rn U m u

-

Q =I72 eV

Further methods of evaluation for the activation enthalpies from the characteristic times are described

by H. Heidsiek, R. Scheffel and K. Liicke in [8]. 1

o - ~

=

I

t I I I I a L L L L I I I I I I ~ ~ L Y 5. Conclusions.

-

The present paper shows that 1.95 2.00 2.05 2.lO

information about vacancies in alloys can be obtained R e c i p r o c a l Annealing T e m p e r a t u r e 10001T,

[K-'1

from the analysis of s.r.0.-kinetics. BY means of a FIG. 8. - Reciprocal characteristic time r,' (calculated for P = I )

numerical evaluation it is even possible to deduce us. reciprocal annealing temperature 103/T, obta~ned from curves

values for the activation enthalpy of vacancy formation in figures 5 and 7.

from single isothermal annealing experiments.

Furthermore it turns out that the behaviour of

(') This confirms the results of Radelaar 191, who investigated annihilating surplus vacancies and thermal vacancies s.r.0.-induced resistivity changes of different Au-Ag alloys after must generally be taken into account when studying changing the annealing temperature. the kinetics of s.r.0.-formation.

References

[l] SCHULZE. H. A., L ~ ~ c K E , K., J. Appl. Phys. 39 (1968) 4860. [6] DAWSON, H. J., Acta Mer. 13 (1965)453.

[2] SCHULZE, H. A., L u c ~ , K., Acta Met. 20 (1972) 529. 171 DE JONG, M., KOEHLER, J. S., Phys. Rev. 129 (1963) 40; 129

[3] LUCKE, K., HAAS, H., Scripta Met. 7 (1973) 781. (1963) 50.

[4] LANG, E., Z. Metallkde 64 (1973) 56. [8] HEIDSIEK, H., S C H E ~ L , R., L ~ ~ c K E , K., J. Physique Colloq.

[5] LUCKE, K., HAAS,, H., SCHULZE, H. A,, J. Phys. Chem. Solid! 38 (1977) C7.