Changes of free energy in the process of discontinuous precipitation in deformed FCC solid solution

Scripta METALLURGICA

Vol. 13, pp. 791-794, 1979 Printed in the U.S.A.

Pergamon Press Ltd. All rights reserved.

CHANGES OF FREE ENERGY IN THE PROCESS OF DISCONTINUOUS PRECIPITATION IN DEFORMED FCC SOLID SOLUTION A.Paw~owski Institute for Metal Research of the Polish Academy of Sciences Krak6w, u l . Reymonta 2 5 , P o l a n d (Received February 12, 1979) (Revised July I0, 1979) Introduction Plastic deformation of a quenched solid solution increases the driving force of discontinuous precipitation associated with the change of free energy introduced by plastic deformation. This problem has been expressed quantitatively by H o r n b o g e n [1] who s t a t e d t h a t i n t h e c a s e when t h e c e l l u l a r precipitation precedes reorystallization the driving force of the transferN a t i o n i s e q u a l t o t h e sum o f t h e d r i v i n g f o r c e o f p r e c i p i t a t i o n and t h e driving force resulting from the inoreeee of lattice defects in the solution. The l a t t i c e force is equal to the driving force of reor~tallizationwhioh o c c u r s on t h e f r o n t o f a c o l o n y o f d i s c o n t i n u o u s p r e c i p i t a t e s and a c c e l e r a t e s the precipitation. I n t h e p r e s e n t p a p e r a method o f d e f o r m a t i o n o f t h e S n o r e se of the driving force of discontinuous precipitation in a deformed solid solution and a verification of the method in FCC alloys is prebented. Results The method of the analysis of the kinetics of discontinuous precipitation in the growth period was applied in the aluminium-zino alloys(containing 40% wt Zn, 50% wt Zn and 65% wt Zn~an aluminium-silver alloy containing 4 0 % w t Ag ; a silver-copper alloy containing 8% wt Cui and a copper-silver alloy containing 8% wt Ag. The alloys were subjected to cold rolling and then ageing a~ the o temperatures ranges: 50°0 - 188u0 in the ~aae ~f Al-Zn alloys, at 180vC-220 C in the case of the AI-Ag alloy and at 200v-300~C in the case of Ag-Ou alloys. The rate of increase of the cellular precipitation was determined from of electric resistance measurements and X-ray phase analysis, the results of which agreed well with the rate determined by the method of observation in situ. The structure of alloys after plastic deformation and ageing was investigated by means of the transmission electron microscopy. On ~he basis of the changes of rate IG) of discontinuous precipitation in the growth period at various ageing temperatures, the equations of the type: G = Gn exp {-AHm/RT) for the particular strain values for each alloy were eatabl~shed. It has-been found that the deformation does not cause an7 changes in the activation energy of the precipitation while it definitely effects the value of the pre-exponential factor G~. In order to give a phTeloal interpretation of this value the Machlin-depen~ence given by Christian [2] was applied: FG G = ~'V • RT . exp ( - A i t m / R T ) (1) where: AHm - activation energy of transformation, frequency, ~F ~ - driving force of transformation, interface.

- characteristic k - distance across the

791 C OQ36-9Z4~/79/090791-04502.00/O o p y r l g h t (cj 1979 Pergamon P r e s s Ltd,

792

FREE ENERGY CHANGES IN PRECIPITATION

Vol. 13, No. 9

The value of the driving force of transformation in an undeformed alloy was determined from the relation given by Cahn ~3j: FG

=

P ~Fo

+

$2 ~

v

and when the value of G O is known the factor

can be calculated. Assuming further on that this factor is constant with increasing strain values the conclusion was drawn that the increase in the transformation rate with the increase of plastic strain results from the incre-ase of the driving force. The fact that the factor ~ remains constant with increasing degree of deformation is justified by the changes of entropy being small and by the observations of small changes of the width of the grain boundary in the process of plastic deformation. On the basis of the assumptions that have been made and of the accepted method of interpretation, the value of the total driving force of cell transformation in an alloy after rolling has been calculated. The relation between its value and the degree of plastic strain in the aluminium alloys is shown in Fig.1. The existence of two ranges has been found: the first range in which no changes of A F ~ were observed, and the other one with a continuous change of the drivin~ force. In the AIZn50 alloy we may distinguish, moreover, s third range above 60% strain. Fig.2 shows a similar relation concerning the silver-copper alloys. In the AgCu8 alloy one can observer two, in the CuAg8 alloy - three ranges of changes. A characteristic feature of this relation is the discontinuous nature of the chang~of AF x occurring between the particular stages. They result, as we can conclude from the investigations of the structure [41 from the migration of the lattice defects to boundaries formed in the process of deformation. As a result of this process, in the areas where the cell transformation takes place the concentration of defects is lower when compared with its value in an quenched alloy. In aluminium alloys these boundaries are created as a result of the formation of deformation bands of a shear type, and in the silver and copper alloys the incoherent boundaries are formed as a result of further deformation of broad deformation twins. In thg copper alloy, however, shear bands were also observed. Admitting Hornbogen s principle concerning the summing up of the effects of precipitation and deformation, a quantitative evaluation of the drivingforce and its increase caused by deformation has been calculated. The incr2ase corresponds to the difference between the value of the driving force &F ~ and its minimum value occurring at the beginning of each deformation range. It has been established that this procedure defines a state of reference with respect to the lowest density of lattice defects in the given range. The values of the driving force determined in this way should correspond to the driving force of recrystsllization, occurring in the process of cellular transformation of an alloy deformed st the boundary of the colony. The method of determination the value AF ~ was verified using Hornbogen s statement that the value of the ~riving force of recrystallization AF R cannot exceed the value of AF ~, as otherwise recrystallization would precede the process of discontinuous precipitation. Thus applying the above rule, it has been found that in the AI-Zn, AI-Ag alloys this regularity is retained below 80% of strain and so the changes of the factor ~ ~ are small. In the AgCu8 alloy minimal changes of ~V have been found below 60% of strain, and in the CuAg8 alloy below 70%. To introduce a correction resulting from the changes of ~V a modified Machlin relation was applied which expressed the effect of plastic deformation on the change of the driving force of cell transformation. This correction describes the increase of the pre-exponential factor resulting from deformation. It is the product of the acceleration parameter Pz of the transformation and of the change of the deformation degree described in ~4] • The parameter Pz is expressed by the relation: AF I Pz =(I/z I - Zolln - ~ . The modified relation expresssing the dependence of the transformation rat~ upon ageing temperatures is as follows: G

=

~~e

PAzAF"

~r-

exp I-~--~--'/

(2)

The values of A F x determined in this way are smaller than those_shown in Fig.1 and 2. The ~alues of AF R calculated from the formula &FR =~F m -AFG satisfy Hornbogen s condition 6FR ~ &F ~ in the whole range of plastic strain.

Vol.

13, No.

9

FREE ENERGY CHANGES

AF"

IN P R E C I P I T A T I O N

AZ l nSO/

[cOV~o,] 100 -

793

~F" AgCu8

/

[coV.~] 2~o

temp. 200°C

90-

temp.

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20~C

200

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180 160 60-

120

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100-

30-

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70-

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20-

0

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0

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reduchon

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,

,

10

per

:

.

.

.

.

.

0

20 3O /.0 50 60 70 Rolhng reOuct,on m per cent

cent

80

90

Fig.l, Fig.2. The d r i v i n g f o r c e o f a d i a o o n t i n u p u = t r a n s f o r m a t i o n ae a f u n c t i o n o f t h e d e ~ r e e o f d e f o r m a t i o n i n : 1 / t h e a l u m i n i u m - z i n o and a l u m i n i u m - s i l v e r alloys, 2/ the silver-copper and c o p p e r - s i l v e r alloys.

a~ [c°'/mo,]r • ,co z2°1

a~

8O

ceV,,~ ]

70-

¢uag

:t

=

60"

o

[o=/~d 4.0

50

AgCu8

i

~0

50-

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35

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L0-

/

00

30"

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-20 Cu

CuAg8

-15

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,10

0

o

it Y / /

10-

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Zo

~b

reduction

sb

6b

in p e r

cent

7b

86

90

0

I0

/

20 30 60 50 60 Rothng recluctlon m per cent

~5 70

80

90

Fig.3, Fig.4. The driving force of_ a discontinuous reorystallization as a function of the degree of deformation in: 3/ the aluminium-zino and aluminium-silver alloys, 4/ the silver-copper and copper-silver alloys.

794

FREE ENERGY CHANGES IN PRECIPITATION

Vol. 13, No. 9

Conclusions I. The driving force of cellular transformation in a deformed alloy increase8 continuously as a result of plastic deformation which introduces subgrains, end microtwins. 2. The lowering of the driving force cf a deformed alloy when compared with its value in an undeformed alloy is caused by the incoherent boundaries of deformation bands and by the boundaries of the broad deformation twins. 3. The increase of the driving force of transformation S F~ resulting from deformation can be determined by the method given in the pre~ent paper. A constant increase of & F R with plastic strain has been found. 4. The dependence of the precipitation rate on temperature, given by Maohlin, can be applied with great accuracy to the precipitation in a deformed alloy after introducing the correction involving the increase of the factor ~ with a plastic strain. Acknowledgement The author is indebted to prof. W.Truszkowski for his valuable advice in the course of the preparation of this paper. References I. E.Hornbogen, Met.Trans. 3, 2217 (1972~ 2. J.W.Christian, The Theory of Transformations in Metals and Alloys, p. 736 Pergamon P r e s s , Oxford 1965. 3. J.W.Oahn, Acts Met. 7, 18 (1958). 4. A.Paw~owski, Aroh.Hutn. I , 161 ~978).