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Kinetics of discontinuous coarsening of cellular precipitate in a Cu-15 wt% in alloy
Vol. 34, No. Printed in Great Britain
Actn metall.
7, pp. 1279-1287,
~1-4160~84
1986
$3.00 + 0.00
Pergamon Journals Ltd
KINETICS OF DISCONTINUOUS COARSENING OF CELLULAR PRECIPITATE IN A Cu-15 wt% In ALLOY S. P. GUPI’A Department of Metallurgical Engineering, Indian Institute of Technology. Kanpur, India (Received 25 .Jme 1985; in revi.~ed.fo~~l 20 October 1985)
Abstract-The morphology and growth kinetics of the cellular precipitate and discontinuously coarsened cellular precipitate have been studied in the temperature range 573-73 1K by utilizing optical and scanning electron microscopy and X-ray diffraction. In order to avoid precipitation of the Widmanstatten precipitate phase, which has a retarding effect on the rate of growth of primary cells, isothermal aging of the alloy was preferred. The Q-In alloy was observed to decompose completely by cellular precipitation reaction into a lamellar structure consisting of alternate lamellae of the a and 6 phases at all aging temperatures. The fine lamellar structure of the primary cells decomposed into a coarse lamellar structure consisting of the same two phases by a discontinuous coarsening or secondary reaction. Lattice parameter measurements indicated that whereas the depleted matrix was richer in solute than the equilibrium solvus during the primary reaction, it was very close to the equilibrium solvus during the secondary reaction. Analysis of the growth kinetics both of the primary and secondary cellular reaction indicated that the transformations are controlled by diffusion through the cell boundaries. R&aun&Nous avons &udi6 la mo~hologie et la cinCtique de croissance des prkcipitts cellulaires avant et apres un grossissement discontinu dam le domaine des temgratures comprises entre 573 et 731 K par microxopie optique, microscopic tlectronique a balayage et diffraction de rayons X. Pour tviter la pticipitation de la phase de Widmanstltten, qui retarde la vitesse de croissance des cellules primaires, nous avons choisi un vieillissement isotherme de l’alliage. L’alliage Q-In se dkcomposait compl&ement par prkcipitation cellulaire en une structure lamellaire constituee par des lamelles alternees des phases a et 6, pour toutes les temptratures de vieillissement. La fine structure lamellaire des cellules primaires se d&composait en une structure lamellaire grossikre des deux mimes phases, par grossissement discontinu ou rtaction secondaire. La mesure du paramttre reticulaire a montrC qu’alors que la matrice appauvrie ttait plus riche en solutb que le solvus d’bquilibre au tours de la rbaction primaire, elle &ait tr6s proche du solvus d’kquilibre au tours de la r&action secondaire. L’analyse de la cinttique de croissance des &actions cellulaires prim&ire et secondaire a montrt que les transformations 6taient contrB16es par la diffusion i travers les parois des cellules. ~~~m~fa~n&Mo~hologie und Wachstumskinetik zelluliren Ausscheidung und der diskontinuierlich vergrijberten Ausscheidung wurden im Tem~ratur~reich zwischen 573 und 731 K mittels optischer Mikroskopie, Rasterelektronenm~kroskopie und Riintgenbeugung untersucht. Urn die Bildung der WidmanstCtten-Phase zu vermeiden, weiches die Wachsumsrate der primlren Zellen verziigerm wiirde, wurde die isotherme Auslagerung bevonugt. Die Legierung Cu-In zerfiel vollsdndig iiber die Reaktion zellulCrer Ausscheidungen in eine lamellare Struktur, die aus alternierenden Lamellen der a- und d-Phasen besteht. Die feinlamellare Struktur der primlren Zellen zerfiel in eine groblamellare Struktur aus diesen beiden Phasen liber eine diskontinuierliche Vergriiberung oder sekundgre Reaktion. Messungen des Gitterparameters deuten darauf hin, dal3 die verarmte matrix wlhrend der primIren Reaktion reicher an gelBsten Atomen war als die Gleichgewichts-Solvuszusammensetzung, dal3 sie wahrend der sekundiiren Reaktion dagegen nahe an diesem Gleichgewicht lag. Die Analyse der Wachstumskinetik der ersten und der zweiten Reaktion wies darauf hin, daB die Transformationen durch die Diffusion durch die Zellwlinde hindurch kontrolliert werden.
1. INTRODUCTION
The phase transfo~ation in Cu-In alloys containing from 3.5 to 10.1 at% In has been studied by numerous investigators [l-6]. The transformation occurs by discontinuous or cellular precipitation when a supersaturated solid solution decomposes to the structurally identical but solute depleted matrix phase, c(, and a new precipitate phase 6. The microstructure consists of alternate lamellae of the two phases. The growth kinetics of the primary cellular reaction have been studied in alloys containing from 3.5 to 10.1 at% In by utilizing optical and transmission electron
microscopy [2,4,5]. The primary cellular reaction has been shown to be controlled by grain boundary diffusion of the solute. A discontinuous coarsening or secondary cellular reaction is observed in a number of alloy systems [7-121. The product of the secondary cellular reaction has a coarse lamellar structure which gradually replaces the fine lamellar structure of the primary cells. This investigation has been carried out to study the growth kinetics of discontinuous coarsening and compare it with the results obtained during cellular precipitation.
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2. EXPERIMENTAL
Alloys for this investigation were prepared by melting together appropriate amounts of copper and indium (both of 99.99% purity) in sealed quartz tubes under vacuum. In order to ensure homogeneity, quartz tubes were shaken a few times before solidification. Cylindrical rods of Cu-15 wt% In (8.9 at% In) prepared in this manner were lightly deformed and annealed at 700°C for 2 days. It was further deformed to obtain rods 6 mm diameter. Disc specimens 1.5 mm thick were cut from the rods and annealed for 24 h at 700°C. The average grain size of the annealed sample was 500 PM. In order to study the kinetics of discontinuous precipitation and coarsening, alloy specimens were first solution treated for 15 min at 565°C and then isothermally aged in the temperature range 573-73 1 K. A number of specimens were aged at each temperature and all heat treatments were carried out in salt baths maintained within +2”C. Isothermal aging was preferred over the normal quench and age procedure because preliminary experiments carried out on the alloy indicated that the Widmanstatten structure formed in the quenched and aged specimens effects the rate of growth of cells. The rate of growth of cell was determined by measuring perpendicular distance from the grain boundary to the leading edge of the cell by utilizing optical microscopy. The interlamellar spacing measurements were made by examining the bulk alloy specimen in a scanning electron microscope. Again, a large number of measurements were made at each temperature both for the primary and secondary cells. All measurements were made only from those regions where CI and 6 phases formed parallel lamellae. The composition of the depleted a matrix was determined by X-ray diffraction using CuK, radiation and Ni filter. The 20 values corresponding to {220} peak positions were determined at a scanning speed of 0.3”min’. The data were corrected for possible instrumentation error with silicon standard. The average indium concentration in the copper rich E phase associated with the primary and secondary cells was determined from lattice parameter measurements by correlation with the existing lattice parameter-concentration data [ 131.
Fig. 1. Scanning electron micrograph showing primary cells, specimen isothermally aged at 695K for 11 h. position of the remaining 28 peaks corresponded with the reported [14] crystal structure and lattice parameter of the 6 phase. The nucleation occurred at a/x grain boundaries, which migrated under the influence of the available driving force leading to the growth of cells. Initially the cells were in the shape of roughly hemispherical
3. RESULTS AND DISCUSSION
3.1. Morphology The microstructure observed through the optical and scanning electron microscope revealed that the supersaturated solid solution decomposed into a and 6 phases at all aging temperatures in the range 573-731K. The product phases formed into a lamellar morphology by cellular phase transformation, Fig. 1. The X-ray diffraction data revealed that the tl phase is a f.c.c. solid solution of indium in copper and
35Fm
Fig. 2. Growth of the primary in the form of slabs, aged for 6 h at 665K.
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nodules; however. a number of them joined together and appeared as slabs with continued aging, Fig. 2. The impingement of cells originating from different boundaries occurred after completion of 60-70% of the transformation. At some stage between the impingement of primary cells and the complete transformation, a new transformation product with a larger interlamellar spacing
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appeared in the microstructure, Fig. 3(a). These also transformed by the discontinuous or cellular mode. The primary cell structure was gradually consumed by the moving cell boundaries of the secondaryprimary cells leading to a coarse lameffar structure throughout the specimen, Fig. 3(b). 3.2. Growth rate The primary and secondary cell growth rate (V, and V, respectively) data is shown in Table I and plotted in Fig. 4, as a function of AT, where AT is the difference in the equilib~um solvus and aging temperatures. The equilibrium solvus temperature used to evaluate AT is taken to be 520°C for Cu-8.9 at% In alloy. The cell growth rates show typical C-curve behavior both for primary and secondary c&s. The primary ~11 growth rate increases by an order of magnitude with the increase in temperature from 573 to 65X and then decreases again. The secondary cell growth rates are slower by 20-40 times the primary cell growth rate at all aging temperatures. The primary cell growth rate data of Shapiro and Kirkaldy [2] and Predel et al. [3,4] are also shown in Fig. 4 for comparison, The primary cell growth rate values are of the same order of magnitude but somewhat greater than the values obtained by Shapiro and Kirkaldy [2] for a 7.5 at% alloy and smaller than the values obtained by Predel and Gust !3,4] for a 10 at% alloy, Similar composition dependence on the rate of growth of primary cells has been reported for Fe-Zn alloys 112, IS].
-
/
0 PrmOry,tha stu*y 63 Shopso and Kirkaldyj +
Fig. 3(a) Initiation of the secondary at prior ajcx boundaries and cell boundaries, aged for 16 h at 665K. optical phntomicrograph. (b) .. Optical photomicrograph showing secondary cells, spectmen aged at 731K tbr 416 h.
I
0
2 ), 7%%ln
Predel and Gust (3.t.). TO%ln
I
I
,
I
I
200
100 A% K
Fig. 4. Growth rate of primary and secondary cells vs AT.
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Table I. Growth
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rate, interlamellar
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spacing and composition
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data for primary
and secondary
cells “1
“I (x 109ms-‘)
T(K)
2.02 3.38 7.12 11.5 5.83 2.71 1.0
731 712 695 665 626 598 573
(x 10’Oms-‘)
(x l%m)
SZ (x IO’m)
‘Xi
Sx;
x;
0.72 0.9 2.41 3.05 I .4 I .05 0.625
11.0 7.07 4.66 2.95 I .77 1.38 1.12
21.45 15.1 8.72 5.54 3.43 2.7 2.3
0.065 0.0515 0.041 0.0265 0.0195 0.01625 0.015
0.0557 0.045 0.0355 0.023 0.013 0.009 0.0085
0.057 0.0464 0.0365 0.0237 0.0138 0.0097 0.0095
3.3. Interlamellar spacing
The interlamellar spacing data both for primary and secondary cells (S, and S, respectively) are shown in Table 1 and plotted in Fig. 5 against AT. The interlamellar spacing values decrease continuously with decreasing temperature of aging as expected. The ratio S,/S,, however, remained more or less constant to a value 2 at all aging temperatures. In order to determine the functional relationship between S and AT, the interlamellar spacing data were plotted on a log-log scale, Fig. 6. The data falls on a straight line both for primary and secondary cells. The best line drawn through the experimental points gives a slope of - 1.8 which differs from observations made on Fe-Zn alloys [12] where a relationship of the type Sc((AT)-’ was observed. The primary interlamellar spacing values of this investigation are very close to the values obtained by Shapiro and Kirkaldy [2] but greater by less than an order of magnitude than the values obtained by Predel et al. [3,4]. 3.4. Composition of the depleted matrix
AT, K
The average composition of the CI phase in the primary and secondary cells were determined from
0
SECONDARY
Fig. 6. Log S vs log AT.
THIS STUD”
IX0
I
I
I
100
I
200
AT. K
Fig. 5. Interlamellar spacing vs AT
I
ATOM
PERCENT
In
Fig. 7. Composition of the depleted G(phase in primary and secondary cells and part of the equilibrium phase diagram.
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lattice parameter measurements using X-ray diffraction and are shown in Table 1 and plotted in Fig. 7. A part of the accepted equilibrium phase diagram of the Cu-In system is also shown in Fig. 7. The composition of the a phase of the primary cells, pXz,, was determined from samples consisting of about 90-95% primary cells and the remaining volume being occupied by some secondaries and untransformed regions. Ju and Fournelle [ 111,who have used X-ray diffraction technique in determining the composition of the depleted matrix associated with the primary cells must have experienced a similar situation in specimens they termed “primarily primary cells”. It is understood that since the secondary cells nucleate after about 60-70% of the transformation of the supersaturated solid solution is completed, the products of the secondary reaction are expected to be present in the microstructure as minor constituent at the termination stage of the primary reaction. The composition of the depleted a phase of the secondary reaction in equilibrium with the 6 phase was determined from samples consisting of N&90% secondary cells by volume. The remaining volume being occupied by the primary cells at this stage. The composition of the a phase, ‘Xi, was then computed from the relation X”
Sxl,=
B
_pp.p
I
vsB
where Xi is the composition of the a phase determined from the specimen consisting of 8&90% secondary cells by volume and V,Pand Vs are volume fractions of the primary and secondary cells respectively in the microstructure. This procedure was necessitated from the observation that the 6 phase started spheroidizing extensively during late stage of the transformation to secondary cells. However, since VF is small in comparison to VT and the difference between ‘XF and Xi is small, the true ‘Xl, differs from Xi by less than 10.0%. The procedure therefore does not lead to consequence of any serious nature but at the same time measures the true a phase composition associated with the secondary cells. 3.5. Primary cell growth kinetics A number of theories have been proposed to describe the kinetics of cellular phase transformation in alloys [1623, 281. Turnbull [16] was the first investigator to provide a quantitative theory of growth of the cellular precipitate by grain boundary diffusion based on a model developed by Zener [24] for volume diffusion. For the rate of growth, Turnbull’s treatment can be given by the following expression ‘Xl, -‘Xi VI =
IX” B
D,.6 ‘(s;)2
(2)
where 5; is the average width the tl. lamellae and ‘Xi is the equilibrium solvus composition at the aging
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temperature. Turnbull’s equation was modified by Aaronson and Liu [17] who proposed the following for the rate of growth (31 The composition of the 6 phase, Xi, is taken to be equal to 0.29 after Hansen and Anderko [25] and values of ‘XZ, are shown in Table 1 and Fig. 7. According to the theory of Petermann and Hornbogen [8] which is based on Lucke’s theory of grain boundary migration, the rate of growth of primary cells is given by v, =
_80,6.AGp RT.S;
Where AGp is the driving force used during primary cell growth and is described by
the
The first term on the right hand side of equation (5) is equivalent to pAGo used by Cahn [23], p being the fraction of the free energy used during the primary cell growth. In equation (5), y is the interfacial free energy of the a/6 interface and V, is the molar volume. Following Shapiro and Kirkaldy [18] and Predel and coworkers [3-51 a value of y = 0.4 J.rnm2 is used. This value of y corresponds to the interfacial free energy of a large angle grain boundary in Cu base alloys [27, 281. Shapiro and Kirkaldy [18] developed the theory of cellular phase transformation on the lines of eutectoid decomposition by assuming that the alloy system in which cellular phase transformation occurs behaves like a system with a metastable monotectoid. Their analysis relates the growth rate to the diffusivity by the following (6)
where
s,.= -2Yvm AGo (8) Values of D,,. 6 were calculated for the four theories described in the preceding paragraphs and are shown in Table 2 and plotted in Fig. 8. There appears to be quite a bit of scatter in the data especially at higher temperatures for the theories of cellular phase transformation proposed by Aaronson and Liu [17] and Turnbull [16]. Theories of Petermann and Hornbogen [7] and Shapiro and Kirkaldy [2] are better suited to describe the results.
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Table 2. Diffusivity, D,.b (102*m3s-l) for the primary and secondary cell growth T(K)
Tumbull
731 712 695 665 626 598 573
42.2 20.5 16.1 7.6 1.1 0.3 0.07
A and L” Sand 5.43 3.54 3.31 1.9 0.33 0.09 0.02
Kb
2100 910
P and H’ 896 200
680
105
330 63 19 5
28.7 3.7
0.84 0.2
Secondary Equation (I 1) Equation (9) 405 141 81 25 2.63 0.576 0.158
80.2 48.0 26.4 10.5 0.62 0.18 0.082
“Aaronson and Liu. %hapiro and Kirkaldy. CPetermann and Hornbogen.
There is a general lack of information in the literature about the grain boundary diffusion values for Cu-In alloys. However, from the work of Hoshino et al. [29] on the lattice diffusion on In in Cu for dilute alloys, the order of magnitude of the grain boundary diffusivity may be calculated. If we assume that the activation energy for diffusion is one half to two thirds of the value for lattice diffusion, then we expect Q6 to lie in the range 100-133 kJ mol-‘. Using these values and Do for volume diffusion from the work of Hoshino et al. [29], the grain boundary diffusivity is calculated to fall in the range 10-23-10-26m3/s at 650K. The cell boundary diffusivity at 650K has values in the range t0-20-10-23 m3js for the four theories used to analyse the experimentat data on primary cell growth. It is clear therefore that the cell boundary diffusivities are three to five orders of magnitude higher than the value calculated from diffusion data representative of the stationary grain boundary value. This is in agree-
OShopwo&K~rkaldy
(6)
n Petermonn&Hornbogen(L
F
0
Turnbull
0
Aaronson
(2)
ment with the results of recent studies [30-321 which have suggested that diffusion in migrating boundaries is 4-5 orders of magnitude faster than in stationary boundaries. Higher cell boundary diffusivity of the same order of magnitude has been reported for Fe-Zn alloys [12] during primary cell growth. The volume diffusivity at 650K is 8-10 orders of mag nitude lower than the cell boundary value. From the Arrhenius plot of Fig. 8, activation energy values were calculated for the four theories used to analyse results of the primary cell growth. The activation energy value falls in the range 135-160 kJ mol-I, being highest for the Petermann and Hornbogen theory [7]. There is a general agreement with the values of activation energy reported by Gust et al. [5] for Cu-In b&crystals. From the above considerations it is concluded that the grain boundary diffusion accounts for solute transport during cellular precipitation in Cu-In alloys. 3.6. Secondary cell growth kinetics The theory of discontinuous coarsening is based on the theory of primary cell growth by Petermann and Hornbogen [7]. Accordingly, the rate of growth of the secondary cell is given by [9]
& Liu(3)
where AC,, is the total available driving force for the cellular precipitation reaction, given as AG~=,TI’X:ln~~)+‘*Lln~~)]
Fig. 8.
D,.6
vs I/?’
for primary cell growth.
(10)
sX; in equation (10) is the concentration of indium in the depleted a phase after the secondary cellular reaction. In the derivation of equation (9) it is assumed that the discontinuous coarsening reaction also follows the Petermann and Hornbogen growth kinetics and is slow enough to use the chemical free energy remaining after the primary cell growth. From equation (9) it is clear that since I’, is larger than V, by more than an order of magnitude, the value of the term V,Si will dominate over V,Sz. The kinetics of discontinuous coarsening will be no different than that of the primary cell growth. The growth rate, interlameIiar spacing and chemical free energy data for the secondary cell growth
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chemical driving force during primary and secondary cell growth, it is difficult to predict the exact reason for the discrepancy at this time. The activation energy, Q, determined from the two sets of data are 160 k 5 kJ moi-’ as obtained for the primary cell growth. The Petermann and Hornbogen analysis [7] when applied to primary cell growth, generally, shows a larger activation energy than other theories of cellular phase transformation. Work carried out by Gust Predel and Roll [5] on Cu-In bi-crystals of known orientation indicates the value of Q in the range 1.53-174 kJ mall’ for the Petermann and Hornbogen theory in comparison to values in the range 128 to 153 kJmoll’ for the Aaronson and Liu [17] and 134-162 kJ mol-’ for Turnbull’s theory [16]. Results of this investigation on polycrystalline specimen where the cell growth data represents an average of a large number of grain boundary misorientations, indicate that the Q values indeed fall in the range reported by Gust et al. [5].
A PRIMARY 0
SECONDARY
( 9
1
0
SECONDARY
( II
)
3.7. Chemical free energy and mobility
Fig.
9. D,.fi vs I/T for secondary cell growth.
have been analysed using equation (9) and the results are plotted in Fig. 9. It is quite clear that the data follows the Petermann and Hornbogen theory of secondary cell growth kinetics very well in the whole range of temperature. The D,.6 value does not differ significantly from the diffusivity values obtained during primary cell growth also plotted in Fig. 9 for comparison. In order to avoid the influence of the parameters of primary cell growth, I’, and S,, on the kinetics of discontinuous coarsening, one can analyse results primarily from the data obtained during secondary cell growth. The relevant equation is given by v2 =
-GAG,
The various chemical free energy terms used in analysing primary and secondary cell growth kinetics are plotted in Fig. IO. With a decrease in the isothermal transformation temperature there is an increase in the chemical free energy available to drive the primary as well as the secondary cellular reaction. The difference in the interfacial free energy is much too small in comparison to either of the chemical free energies. This is the reason we did not attempt to analyse kinetics of discontinuous coarsening using theory of Livingston and Cahn [33], which explicitly assumes that difference in the interfacial free energy
(11)
2
where AC, is the driving force used during discontinuous coarsening reaction given as AG~=(~G~-~AG~)+~~-~j.
(12)
From the interlamellar spacing, growth rate and chemical free energy data obtained for the secondary cell growth, the diffusivity values, D,.6, were calculated. These are shown in Table 2 and plotted in Fig. 9. Although the L&.6 values show some scatter, they can be described by a straight line. Functionally, equations (9) and (11) are the same and diffusivity values calculated from the two equations should not differ. However. from uncertainties in the value of the
-800
50
150
loo
2w
AT.K
Fig. 10. Chemical free energy, interfacial free energy difference and fraction of the driving force vs A7’.
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Fig. 11. Cell boundary mobility vs I/T. between primary and secondary cells acts as a driving force for the discontinuous coarsening We can extend the analysis of primary and secondary cell growth by assuming a mobility controlled cell growth. Thus, we wilt evaluate mobilities for the Cu-In alloys and compare them with the mobilities obtained from other experiments [34,35] in copper base alloys. Assuming linear relationship to describe the cell boundary migration V=M*P
(13)
where V is the steady state growth rate under a force acting on the boundary, M is the constant of proportionality expressing the velocity per unit force. The force P is the chemical free energy AC, and AC, released during the primary and secondary reaction respectively. The mobility of the cell boundary are plotted in Fig. 11 along with the mobilities of grain boundary during grain growth in a c( brass [34]. From Fig. 11 it is clear that mobilities as obtained in the Cu-In alloy system during the growth of cellular precipitate are about three orders of magnitude lower than those from the grain growth data. Similar results have been shown by Perovic and Purdy [3S] during discontinuous precipitation of rods in Cu-Co alloys. The mobility data obtained in these experiments for the primary cell’ growth extrapolates to the mobility in the Cu-Co alloy system calculated at 873K. [Note: we could not directly use all the mobility data plotted by Perovic and Purdy [35] for the Cu-Co alloy (Fig. 13 in their publication) because values of 1000/r (in
Cu-In alloys containing 15 wt% In decompose completely by cellular mode of phase transformation into lamellar aggregate of o[and 6 phases when aged isothe~ally in the temperature range 573-73 1K. The diffusion of indium occurs through the advancing cell boundaries. The activation energy for cell boundary migration agrees well with the value reported by Gust et al. [5] for Cu-In bicrystals. It has been shown that not all of the available chemical free energy is used during the primary cell growth. Upon prolonged aging, the lamellar structure of the primary cells decomposes into a coarse lamellar structure of the secondary cells at all aging temperatures used in this investigation. The free energy remaining after completion of the primary reaction and a part of the interfacial free energy is used to drive the secondary cellular reaction. The solute diffusion again occurs by boundary diffusion in the advancing cell boundary interface. The diffusivity in the boundary is three to five orders of magnitude higher than the diffusivity through stationary boundaries in these alloys. REFERENCES 1. H. Bohm, 2. MetaNk. 52, 564 (1961). 2. J. M. Shapiro and J. S. Kirkaldy, Actn metnll. 16, 1239 (1968). 3. B. Predel and W. Gust, Mater. Sci. Engng 19, 229 (1975). 4. B. Predel and W. Gust, Mater. Scj. Engng 17,41 (1975). 5. W. Gust, B. Predel and U. Roll, Acfa metall. 28, 1395 (1980). 6. R. A. Fournelle and J. B. Clark, Metall. Trans. 3, 27.51 (1972). 7. J. Petermann and E. Hornbogen, 2. Metailk. 59, 814 (1948). 8. K. N. Melton and J. W. Edington, Acta metali. 22, 333 (1974).
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9. R. A. Fournelle, Acta metall. 27, 1147 (1979). IO. H. Tsabakino and R. Nazoto, Proc. Inc. Conf. Solid-Solid Phase Transformafion, p. 951. Am. Inst. Min. Metall. Petroleum Engrs (1982). 11. C. P. Ju and R. A. Foumelle, Acfa metall. 33, 71 (1985). 12. S. P. Gupta and G. T. Parthiban, 2. Metallk. July (1985). 13. R. 0. Jones and E. 0. Owen, J. Insr. Metaals 82, 445 (1953). 14. D. J. H. Corderoy and R. W. Honeycomb, J. Inst. Metals 92, 65 (1963). 15. G. R. Speich. Trans. Am. Inst. Min. Engrs. 242, 13.59 (1968). 16. D. Turnbull, Acta metali. 3, 55 (1955). 17. H. I. Aaronson and Y. C. Liu, Scripta mefall. 2, I (1968). 18. 1. M. Shapiro and J. S. Kirkaldy, Acta metali. 16, 579 (1968).
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19. B. E. Sundquist, Metall. Trans. 4, 1919 (1973). 20. M. Hillert in Mechanism of Phase Transformation in Crystalline Solids, p. 231. Inst. Metals, L&d. (1969). 21. M. Hillert, Metall. Trans. 3, 2729 (1972). 22. M. Hitlert, Acta metafl. 30, 1689 (1982).
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23. J. W. Cahn, Acta metall. 7, 18 (1959). 24. C. Zener, Trans. Am. Inst. Min. Engrs. 167, 550 (1946). 25. M. Hansen and K. Anderko, Constitution of Binary A/lop, 2nd ed. McGraw-Hill, New York (1958). 26. K. Kucke, Z. &Ierailk. 52, 1 (1961). 27. E. D. Hondros, Energetics of Solid Solution Interfaces (edited by R. C. Griggin). Int. Conf. Aust. Inst. Metals. Butterworth, Melbourne (1969). 28. M. C. Inman and H. R. Tipler, ~eff~~l. Rezl. 8, 105 (1963). 29. K. Hoshino, Y. Iijiyama and K. Hirano, Acfu meiall. 30, 265 (1982). 30. M. Hillert and G. R. Purdy, Acta metall. 26, 333 (1978). 31. Li Chongmo and M. Hillert, Atta metail. 29, 1949 (1981). 32. K. Smidoda, G. Gottschalk and H. Gleiter, Acta metoll. 26, 1833 (1978). 33. J. D. Livingston and J. W. Cahn, Acta metal/. 22, 495 (1974). 34. P. Feltham and G. J. Copley, Acta metali. 6,593 (1958). 35. A. Perovic and G. R. Purdy, Acta metull. 29, 53 (1981). 36. C. A. Mackliet, Phys. Rev. 109, 1964 (1958). 37. Y. C. Liu and H. 1. Aaronson, Actn metall. 16, 1343 (1968).
Actn metall.
7, pp. 1279-1287,
~1-4160~84
1986
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KINETICS OF DISCONTINUOUS COARSENING OF CELLULAR PRECIPITATE IN A Cu-15 wt% In ALLOY S. P. GUPI’A Department of Metallurgical Engineering, Indian Institute of Technology. Kanpur, India (Received 25 .Jme 1985; in revi.~ed.fo~~l 20 October 1985)
Abstract-The morphology and growth kinetics of the cellular precipitate and discontinuously coarsened cellular precipitate have been studied in the temperature range 573-73 1K by utilizing optical and scanning electron microscopy and X-ray diffraction. In order to avoid precipitation of the Widmanstatten precipitate phase, which has a retarding effect on the rate of growth of primary cells, isothermal aging of the alloy was preferred. The Q-In alloy was observed to decompose completely by cellular precipitation reaction into a lamellar structure consisting of alternate lamellae of the a and 6 phases at all aging temperatures. The fine lamellar structure of the primary cells decomposed into a coarse lamellar structure consisting of the same two phases by a discontinuous coarsening or secondary reaction. Lattice parameter measurements indicated that whereas the depleted matrix was richer in solute than the equilibrium solvus during the primary reaction, it was very close to the equilibrium solvus during the secondary reaction. Analysis of the growth kinetics both of the primary and secondary cellular reaction indicated that the transformations are controlled by diffusion through the cell boundaries. R&aun&Nous avons &udi6 la mo~hologie et la cinCtique de croissance des prkcipitts cellulaires avant et apres un grossissement discontinu dam le domaine des temgratures comprises entre 573 et 731 K par microxopie optique, microscopic tlectronique a balayage et diffraction de rayons X. Pour tviter la pticipitation de la phase de Widmanstltten, qui retarde la vitesse de croissance des cellules primaires, nous avons choisi un vieillissement isotherme de l’alliage. L’alliage Q-In se dkcomposait compl&ement par prkcipitation cellulaire en une structure lamellaire constituee par des lamelles alternees des phases a et 6, pour toutes les temptratures de vieillissement. La fine structure lamellaire des cellules primaires se d&composait en une structure lamellaire grossikre des deux mimes phases, par grossissement discontinu ou rtaction secondaire. La mesure du paramttre reticulaire a montrC qu’alors que la matrice appauvrie ttait plus riche en solutb que le solvus d’bquilibre au tours de la rbaction primaire, elle &ait tr6s proche du solvus d’kquilibre au tours de la r&action secondaire. L’analyse de la cinttique de croissance des &actions cellulaires prim&ire et secondaire a montrt que les transformations 6taient contrB16es par la diffusion i travers les parois des cellules. ~~~m~fa~n&Mo~hologie und Wachstumskinetik zelluliren Ausscheidung und der diskontinuierlich vergrijberten Ausscheidung wurden im Tem~ratur~reich zwischen 573 und 731 K mittels optischer Mikroskopie, Rasterelektronenm~kroskopie und Riintgenbeugung untersucht. Urn die Bildung der WidmanstCtten-Phase zu vermeiden, weiches die Wachsumsrate der primlren Zellen verziigerm wiirde, wurde die isotherme Auslagerung bevonugt. Die Legierung Cu-In zerfiel vollsdndig iiber die Reaktion zellulCrer Ausscheidungen in eine lamellare Struktur, die aus alternierenden Lamellen der a- und d-Phasen besteht. Die feinlamellare Struktur der primlren Zellen zerfiel in eine groblamellare Struktur aus diesen beiden Phasen liber eine diskontinuierliche Vergriiberung oder sekundgre Reaktion. Messungen des Gitterparameters deuten darauf hin, dal3 die verarmte matrix wlhrend der primIren Reaktion reicher an gelBsten Atomen war als die Gleichgewichts-Solvuszusammensetzung, dal3 sie wahrend der sekundiiren Reaktion dagegen nahe an diesem Gleichgewicht lag. Die Analyse der Wachstumskinetik der ersten und der zweiten Reaktion wies darauf hin, daB die Transformationen durch die Diffusion durch die Zellwlinde hindurch kontrolliert werden.
1. INTRODUCTION
The phase transfo~ation in Cu-In alloys containing from 3.5 to 10.1 at% In has been studied by numerous investigators [l-6]. The transformation occurs by discontinuous or cellular precipitation when a supersaturated solid solution decomposes to the structurally identical but solute depleted matrix phase, c(, and a new precipitate phase 6. The microstructure consists of alternate lamellae of the two phases. The growth kinetics of the primary cellular reaction have been studied in alloys containing from 3.5 to 10.1 at% In by utilizing optical and transmission electron
microscopy [2,4,5]. The primary cellular reaction has been shown to be controlled by grain boundary diffusion of the solute. A discontinuous coarsening or secondary cellular reaction is observed in a number of alloy systems [7-121. The product of the secondary cellular reaction has a coarse lamellar structure which gradually replaces the fine lamellar structure of the primary cells. This investigation has been carried out to study the growth kinetics of discontinuous coarsening and compare it with the results obtained during cellular precipitation.
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2. EXPERIMENTAL
Alloys for this investigation were prepared by melting together appropriate amounts of copper and indium (both of 99.99% purity) in sealed quartz tubes under vacuum. In order to ensure homogeneity, quartz tubes were shaken a few times before solidification. Cylindrical rods of Cu-15 wt% In (8.9 at% In) prepared in this manner were lightly deformed and annealed at 700°C for 2 days. It was further deformed to obtain rods 6 mm diameter. Disc specimens 1.5 mm thick were cut from the rods and annealed for 24 h at 700°C. The average grain size of the annealed sample was 500 PM. In order to study the kinetics of discontinuous precipitation and coarsening, alloy specimens were first solution treated for 15 min at 565°C and then isothermally aged in the temperature range 573-73 1 K. A number of specimens were aged at each temperature and all heat treatments were carried out in salt baths maintained within +2”C. Isothermal aging was preferred over the normal quench and age procedure because preliminary experiments carried out on the alloy indicated that the Widmanstatten structure formed in the quenched and aged specimens effects the rate of growth of cells. The rate of growth of cell was determined by measuring perpendicular distance from the grain boundary to the leading edge of the cell by utilizing optical microscopy. The interlamellar spacing measurements were made by examining the bulk alloy specimen in a scanning electron microscope. Again, a large number of measurements were made at each temperature both for the primary and secondary cells. All measurements were made only from those regions where CI and 6 phases formed parallel lamellae. The composition of the depleted a matrix was determined by X-ray diffraction using CuK, radiation and Ni filter. The 20 values corresponding to {220} peak positions were determined at a scanning speed of 0.3”min’. The data were corrected for possible instrumentation error with silicon standard. The average indium concentration in the copper rich E phase associated with the primary and secondary cells was determined from lattice parameter measurements by correlation with the existing lattice parameter-concentration data [ 131.
Fig. 1. Scanning electron micrograph showing primary cells, specimen isothermally aged at 695K for 11 h. position of the remaining 28 peaks corresponded with the reported [14] crystal structure and lattice parameter of the 6 phase. The nucleation occurred at a/x grain boundaries, which migrated under the influence of the available driving force leading to the growth of cells. Initially the cells were in the shape of roughly hemispherical
3. RESULTS AND DISCUSSION
3.1. Morphology The microstructure observed through the optical and scanning electron microscope revealed that the supersaturated solid solution decomposed into a and 6 phases at all aging temperatures in the range 573-731K. The product phases formed into a lamellar morphology by cellular phase transformation, Fig. 1. The X-ray diffraction data revealed that the tl phase is a f.c.c. solid solution of indium in copper and
35Fm
Fig. 2. Growth of the primary in the form of slabs, aged for 6 h at 665K.
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nodules; however. a number of them joined together and appeared as slabs with continued aging, Fig. 2. The impingement of cells originating from different boundaries occurred after completion of 60-70% of the transformation. At some stage between the impingement of primary cells and the complete transformation, a new transformation product with a larger interlamellar spacing
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appeared in the microstructure, Fig. 3(a). These also transformed by the discontinuous or cellular mode. The primary cell structure was gradually consumed by the moving cell boundaries of the secondaryprimary cells leading to a coarse lameffar structure throughout the specimen, Fig. 3(b). 3.2. Growth rate The primary and secondary cell growth rate (V, and V, respectively) data is shown in Table I and plotted in Fig. 4, as a function of AT, where AT is the difference in the equilib~um solvus and aging temperatures. The equilibrium solvus temperature used to evaluate AT is taken to be 520°C for Cu-8.9 at% In alloy. The cell growth rates show typical C-curve behavior both for primary and secondary c&s. The primary ~11 growth rate increases by an order of magnitude with the increase in temperature from 573 to 65X and then decreases again. The secondary cell growth rates are slower by 20-40 times the primary cell growth rate at all aging temperatures. The primary cell growth rate data of Shapiro and Kirkaldy [2] and Predel et al. [3,4] are also shown in Fig. 4 for comparison, The primary cell growth rate values are of the same order of magnitude but somewhat greater than the values obtained by Shapiro and Kirkaldy [2] for a 7.5 at% alloy and smaller than the values obtained by Predel and Gust !3,4] for a 10 at% alloy, Similar composition dependence on the rate of growth of primary cells has been reported for Fe-Zn alloys 112, IS].
-
/
0 PrmOry,tha stu*y 63 Shopso and Kirkaldyj +
Fig. 3(a) Initiation of the secondary at prior ajcx boundaries and cell boundaries, aged for 16 h at 665K. optical phntomicrograph. (b) .. Optical photomicrograph showing secondary cells, spectmen aged at 731K tbr 416 h.
I
0
2 ), 7%%ln
Predel and Gust (3.t.). TO%ln
I
I
,
I
I
200
100 A% K
Fig. 4. Growth rate of primary and secondary cells vs AT.
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Table I. Growth
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rate, interlamellar
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spacing and composition
PRECIPITATE
data for primary
and secondary
cells “1
“I (x 109ms-‘)
T(K)
2.02 3.38 7.12 11.5 5.83 2.71 1.0
731 712 695 665 626 598 573
(x 10’Oms-‘)
(x l%m)
SZ (x IO’m)
‘Xi
Sx;
x;
0.72 0.9 2.41 3.05 I .4 I .05 0.625
11.0 7.07 4.66 2.95 I .77 1.38 1.12
21.45 15.1 8.72 5.54 3.43 2.7 2.3
0.065 0.0515 0.041 0.0265 0.0195 0.01625 0.015
0.0557 0.045 0.0355 0.023 0.013 0.009 0.0085
0.057 0.0464 0.0365 0.0237 0.0138 0.0097 0.0095
3.3. Interlamellar spacing
The interlamellar spacing data both for primary and secondary cells (S, and S, respectively) are shown in Table 1 and plotted in Fig. 5 against AT. The interlamellar spacing values decrease continuously with decreasing temperature of aging as expected. The ratio S,/S,, however, remained more or less constant to a value 2 at all aging temperatures. In order to determine the functional relationship between S and AT, the interlamellar spacing data were plotted on a log-log scale, Fig. 6. The data falls on a straight line both for primary and secondary cells. The best line drawn through the experimental points gives a slope of - 1.8 which differs from observations made on Fe-Zn alloys [12] where a relationship of the type Sc((AT)-’ was observed. The primary interlamellar spacing values of this investigation are very close to the values obtained by Shapiro and Kirkaldy [2] but greater by less than an order of magnitude than the values obtained by Predel et al. [3,4]. 3.4. Composition of the depleted matrix
AT, K
The average composition of the CI phase in the primary and secondary cells were determined from
0
SECONDARY
Fig. 6. Log S vs log AT.
THIS STUD”
IX0
I
I
I
100
I
200
AT. K
Fig. 5. Interlamellar spacing vs AT
I
ATOM
PERCENT
In
Fig. 7. Composition of the depleted G(phase in primary and secondary cells and part of the equilibrium phase diagram.
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lattice parameter measurements using X-ray diffraction and are shown in Table 1 and plotted in Fig. 7. A part of the accepted equilibrium phase diagram of the Cu-In system is also shown in Fig. 7. The composition of the a phase of the primary cells, pXz,, was determined from samples consisting of about 90-95% primary cells and the remaining volume being occupied by some secondaries and untransformed regions. Ju and Fournelle [ 111,who have used X-ray diffraction technique in determining the composition of the depleted matrix associated with the primary cells must have experienced a similar situation in specimens they termed “primarily primary cells”. It is understood that since the secondary cells nucleate after about 60-70% of the transformation of the supersaturated solid solution is completed, the products of the secondary reaction are expected to be present in the microstructure as minor constituent at the termination stage of the primary reaction. The composition of the depleted a phase of the secondary reaction in equilibrium with the 6 phase was determined from samples consisting of N&90% secondary cells by volume. The remaining volume being occupied by the primary cells at this stage. The composition of the a phase, ‘Xi, was then computed from the relation X”
Sxl,=
B
_pp.p
I
vsB
where Xi is the composition of the a phase determined from the specimen consisting of 8&90% secondary cells by volume and V,Pand Vs are volume fractions of the primary and secondary cells respectively in the microstructure. This procedure was necessitated from the observation that the 6 phase started spheroidizing extensively during late stage of the transformation to secondary cells. However, since VF is small in comparison to VT and the difference between ‘XF and Xi is small, the true ‘Xl, differs from Xi by less than 10.0%. The procedure therefore does not lead to consequence of any serious nature but at the same time measures the true a phase composition associated with the secondary cells. 3.5. Primary cell growth kinetics A number of theories have been proposed to describe the kinetics of cellular phase transformation in alloys [1623, 281. Turnbull [16] was the first investigator to provide a quantitative theory of growth of the cellular precipitate by grain boundary diffusion based on a model developed by Zener [24] for volume diffusion. For the rate of growth, Turnbull’s treatment can be given by the following expression ‘Xl, -‘Xi VI =
IX” B
D,.6 ‘(s;)2
(2)
where 5; is the average width the tl. lamellae and ‘Xi is the equilibrium solvus composition at the aging
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temperature. Turnbull’s equation was modified by Aaronson and Liu [17] who proposed the following for the rate of growth (31 The composition of the 6 phase, Xi, is taken to be equal to 0.29 after Hansen and Anderko [25] and values of ‘XZ, are shown in Table 1 and Fig. 7. According to the theory of Petermann and Hornbogen [8] which is based on Lucke’s theory of grain boundary migration, the rate of growth of primary cells is given by v, =
_80,6.AGp RT.S;
Where AGp is the driving force used during primary cell growth and is described by
the
The first term on the right hand side of equation (5) is equivalent to pAGo used by Cahn [23], p being the fraction of the free energy used during the primary cell growth. In equation (5), y is the interfacial free energy of the a/6 interface and V, is the molar volume. Following Shapiro and Kirkaldy [18] and Predel and coworkers [3-51 a value of y = 0.4 J.rnm2 is used. This value of y corresponds to the interfacial free energy of a large angle grain boundary in Cu base alloys [27, 281. Shapiro and Kirkaldy [18] developed the theory of cellular phase transformation on the lines of eutectoid decomposition by assuming that the alloy system in which cellular phase transformation occurs behaves like a system with a metastable monotectoid. Their analysis relates the growth rate to the diffusivity by the following (6)
where
s,.= -2Yvm AGo (8) Values of D,,. 6 were calculated for the four theories described in the preceding paragraphs and are shown in Table 2 and plotted in Fig. 8. There appears to be quite a bit of scatter in the data especially at higher temperatures for the theories of cellular phase transformation proposed by Aaronson and Liu [17] and Turnbull [16]. Theories of Petermann and Hornbogen [7] and Shapiro and Kirkaldy [2] are better suited to describe the results.
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Table 2. Diffusivity, D,.b (102*m3s-l) for the primary and secondary cell growth T(K)
Tumbull
731 712 695 665 626 598 573
42.2 20.5 16.1 7.6 1.1 0.3 0.07
A and L” Sand 5.43 3.54 3.31 1.9 0.33 0.09 0.02
Kb
2100 910
P and H’ 896 200
680
105
330 63 19 5
28.7 3.7
0.84 0.2
Secondary Equation (I 1) Equation (9) 405 141 81 25 2.63 0.576 0.158
80.2 48.0 26.4 10.5 0.62 0.18 0.082
“Aaronson and Liu. %hapiro and Kirkaldy. CPetermann and Hornbogen.
There is a general lack of information in the literature about the grain boundary diffusion values for Cu-In alloys. However, from the work of Hoshino et al. [29] on the lattice diffusion on In in Cu for dilute alloys, the order of magnitude of the grain boundary diffusivity may be calculated. If we assume that the activation energy for diffusion is one half to two thirds of the value for lattice diffusion, then we expect Q6 to lie in the range 100-133 kJ mol-‘. Using these values and Do for volume diffusion from the work of Hoshino et al. [29], the grain boundary diffusivity is calculated to fall in the range 10-23-10-26m3/s at 650K. The cell boundary diffusivity at 650K has values in the range t0-20-10-23 m3js for the four theories used to analyse the experimentat data on primary cell growth. It is clear therefore that the cell boundary diffusivities are three to five orders of magnitude higher than the value calculated from diffusion data representative of the stationary grain boundary value. This is in agree-
OShopwo&K~rkaldy
(6)
n Petermonn&Hornbogen(L
F
0
Turnbull
0
Aaronson
(2)
ment with the results of recent studies [30-321 which have suggested that diffusion in migrating boundaries is 4-5 orders of magnitude faster than in stationary boundaries. Higher cell boundary diffusivity of the same order of magnitude has been reported for Fe-Zn alloys [12] during primary cell growth. The volume diffusivity at 650K is 8-10 orders of mag nitude lower than the cell boundary value. From the Arrhenius plot of Fig. 8, activation energy values were calculated for the four theories used to analyse results of the primary cell growth. The activation energy value falls in the range 135-160 kJ mol-I, being highest for the Petermann and Hornbogen theory [7]. There is a general agreement with the values of activation energy reported by Gust et al. [5] for Cu-In b&crystals. From the above considerations it is concluded that the grain boundary diffusion accounts for solute transport during cellular precipitation in Cu-In alloys. 3.6. Secondary cell growth kinetics The theory of discontinuous coarsening is based on the theory of primary cell growth by Petermann and Hornbogen [7]. Accordingly, the rate of growth of the secondary cell is given by [9]
& Liu(3)
where AC,, is the total available driving force for the cellular precipitation reaction, given as AG~=,TI’X:ln~~)+‘*Lln~~)]
Fig. 8.
D,.6
vs I/?’
for primary cell growth.
(10)
sX; in equation (10) is the concentration of indium in the depleted a phase after the secondary cellular reaction. In the derivation of equation (9) it is assumed that the discontinuous coarsening reaction also follows the Petermann and Hornbogen growth kinetics and is slow enough to use the chemical free energy remaining after the primary cell growth. From equation (9) it is clear that since I’, is larger than V, by more than an order of magnitude, the value of the term V,Si will dominate over V,Sz. The kinetics of discontinuous coarsening will be no different than that of the primary cell growth. The growth rate, interlameIiar spacing and chemical free energy data for the secondary cell growth
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chemical driving force during primary and secondary cell growth, it is difficult to predict the exact reason for the discrepancy at this time. The activation energy, Q, determined from the two sets of data are 160 k 5 kJ moi-’ as obtained for the primary cell growth. The Petermann and Hornbogen analysis [7] when applied to primary cell growth, generally, shows a larger activation energy than other theories of cellular phase transformation. Work carried out by Gust Predel and Roll [5] on Cu-In bi-crystals of known orientation indicates the value of Q in the range 1.53-174 kJ mall’ for the Petermann and Hornbogen theory in comparison to values in the range 128 to 153 kJmoll’ for the Aaronson and Liu [17] and 134-162 kJ mol-’ for Turnbull’s theory [16]. Results of this investigation on polycrystalline specimen where the cell growth data represents an average of a large number of grain boundary misorientations, indicate that the Q values indeed fall in the range reported by Gust et al. [5].
A PRIMARY 0
SECONDARY
( 9
1
0
SECONDARY
( II
)
3.7. Chemical free energy and mobility
Fig.
9. D,.fi vs I/T for secondary cell growth.
have been analysed using equation (9) and the results are plotted in Fig. 9. It is quite clear that the data follows the Petermann and Hornbogen theory of secondary cell growth kinetics very well in the whole range of temperature. The D,.6 value does not differ significantly from the diffusivity values obtained during primary cell growth also plotted in Fig. 9 for comparison. In order to avoid the influence of the parameters of primary cell growth, I’, and S,, on the kinetics of discontinuous coarsening, one can analyse results primarily from the data obtained during secondary cell growth. The relevant equation is given by v2 =
-GAG,
The various chemical free energy terms used in analysing primary and secondary cell growth kinetics are plotted in Fig. IO. With a decrease in the isothermal transformation temperature there is an increase in the chemical free energy available to drive the primary as well as the secondary cellular reaction. The difference in the interfacial free energy is much too small in comparison to either of the chemical free energies. This is the reason we did not attempt to analyse kinetics of discontinuous coarsening using theory of Livingston and Cahn [33], which explicitly assumes that difference in the interfacial free energy
(11)
2
where AC, is the driving force used during discontinuous coarsening reaction given as AG~=(~G~-~AG~)+~~-~j.
(12)
From the interlamellar spacing, growth rate and chemical free energy data obtained for the secondary cell growth, the diffusivity values, D,.6, were calculated. These are shown in Table 2 and plotted in Fig. 9. Although the L&.6 values show some scatter, they can be described by a straight line. Functionally, equations (9) and (11) are the same and diffusivity values calculated from the two equations should not differ. However. from uncertainties in the value of the
-800
50
150
loo
2w
AT.K
Fig. 10. Chemical free energy, interfacial free energy difference and fraction of the driving force vs A7’.
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Fig. 11. Cell boundary mobility vs I/T. between primary and secondary cells acts as a driving force for the discontinuous coarsening We can extend the analysis of primary and secondary cell growth by assuming a mobility controlled cell growth. Thus, we wilt evaluate mobilities for the Cu-In alloys and compare them with the mobilities obtained from other experiments [34,35] in copper base alloys. Assuming linear relationship to describe the cell boundary migration V=M*P
(13)
where V is the steady state growth rate under a force acting on the boundary, M is the constant of proportionality expressing the velocity per unit force. The force P is the chemical free energy AC, and AC, released during the primary and secondary reaction respectively. The mobility of the cell boundary are plotted in Fig. 11 along with the mobilities of grain boundary during grain growth in a c( brass [34]. From Fig. 11 it is clear that mobilities as obtained in the Cu-In alloy system during the growth of cellular precipitate are about three orders of magnitude lower than those from the grain growth data. Similar results have been shown by Perovic and Purdy [3S] during discontinuous precipitation of rods in Cu-Co alloys. The mobility data obtained in these experiments for the primary cell’ growth extrapolates to the mobility in the Cu-Co alloy system calculated at 873K. [Note: we could not directly use all the mobility data plotted by Perovic and Purdy [35] for the Cu-Co alloy (Fig. 13 in their publication) because values of 1000/r (in
Cu-In alloys containing 15 wt% In decompose completely by cellular mode of phase transformation into lamellar aggregate of o[and 6 phases when aged isothe~ally in the temperature range 573-73 1K. The diffusion of indium occurs through the advancing cell boundaries. The activation energy for cell boundary migration agrees well with the value reported by Gust et al. [5] for Cu-In bicrystals. It has been shown that not all of the available chemical free energy is used during the primary cell growth. Upon prolonged aging, the lamellar structure of the primary cells decomposes into a coarse lamellar structure of the secondary cells at all aging temperatures used in this investigation. The free energy remaining after completion of the primary reaction and a part of the interfacial free energy is used to drive the secondary cellular reaction. The solute diffusion again occurs by boundary diffusion in the advancing cell boundary interface. The diffusivity in the boundary is three to five orders of magnitude higher than the diffusivity through stationary boundaries in these alloys. REFERENCES 1. H. Bohm, 2. MetaNk. 52, 564 (1961). 2. J. M. Shapiro and J. S. Kirkaldy, Actn metnll. 16, 1239 (1968). 3. B. Predel and W. Gust, Mater. Sci. Engng 19, 229 (1975). 4. B. Predel and W. Gust, Mater. Scj. Engng 17,41 (1975). 5. W. Gust, B. Predel and U. Roll, Acfa metall. 28, 1395 (1980). 6. R. A. Fournelle and J. B. Clark, Metall. Trans. 3, 27.51 (1972). 7. J. Petermann and E. Hornbogen, 2. Metailk. 59, 814 (1948). 8. K. N. Melton and J. W. Edington, Acta metali. 22, 333 (1974).
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9. R. A. Fournelle, Acta metall. 27, 1147 (1979). IO. H. Tsabakino and R. Nazoto, Proc. Inc. Conf. Solid-Solid Phase Transformafion, p. 951. Am. Inst. Min. Metall. Petroleum Engrs (1982). 11. C. P. Ju and R. A. Foumelle, Acfa metall. 33, 71 (1985). 12. S. P. Gupta and G. T. Parthiban, 2. Metallk. July (1985). 13. R. 0. Jones and E. 0. Owen, J. Insr. Metaals 82, 445 (1953). 14. D. J. H. Corderoy and R. W. Honeycomb, J. Inst. Metals 92, 65 (1963). 15. G. R. Speich. Trans. Am. Inst. Min. Engrs. 242, 13.59 (1968). 16. D. Turnbull, Acta metali. 3, 55 (1955). 17. H. I. Aaronson and Y. C. Liu, Scripta mefall. 2, I (1968). 18. 1. M. Shapiro and J. S. Kirkaldy, Acta metali. 16, 579 (1968).
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19. B. E. Sundquist, Metall. Trans. 4, 1919 (1973). 20. M. Hillert in Mechanism of Phase Transformation in Crystalline Solids, p. 231. Inst. Metals, L&d. (1969). 21. M. Hillert, Metall. Trans. 3, 2729 (1972). 22. M. Hitlert, Acta metafl. 30, 1689 (1982).
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23. J. W. Cahn, Acta metall. 7, 18 (1959). 24. C. Zener, Trans. Am. Inst. Min. Engrs. 167, 550 (1946). 25. M. Hansen and K. Anderko, Constitution of Binary A/lop, 2nd ed. McGraw-Hill, New York (1958). 26. K. Kucke, Z. &Ierailk. 52, 1 (1961). 27. E. D. Hondros, Energetics of Solid Solution Interfaces (edited by R. C. Griggin). Int. Conf. Aust. Inst. Metals. Butterworth, Melbourne (1969). 28. M. C. Inman and H. R. Tipler, ~eff~~l. Rezl. 8, 105 (1963). 29. K. Hoshino, Y. Iijiyama and K. Hirano, Acfu meiall. 30, 265 (1982). 30. M. Hillert and G. R. Purdy, Acta metall. 26, 333 (1978). 31. Li Chongmo and M. Hillert, Atta metail. 29, 1949 (1981). 32. K. Smidoda, G. Gottschalk and H. Gleiter, Acta metoll. 26, 1833 (1978). 33. J. D. Livingston and J. W. Cahn, Acta metal/. 22, 495 (1974). 34. P. Feltham and G. J. Copley, Acta metali. 6,593 (1958). 35. A. Perovic and G. R. Purdy, Acta metull. 29, 53 (1981). 36. C. A. Mackliet, Phys. Rev. 109, 1964 (1958). 37. Y. C. Liu and H. 1. Aaronson, Actn metall. 16, 1343 (1968).