Massive transformations

Materials Science and Engineering, 25 ( 1 9 7 6 ) 119 - 125

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© Elsevier S e q u o i a S.A., L a u s a n n e - - P r i n t e d in t h e N e t h e r l a n d s

Massive Transformations*

T. B. M A S S A L S K I

Carnegie-Mellon University, Pittsburgh, Pa. 15213 (U.S.A.)

1. G E N E R A L B A C K G R O U N D

Among a number of possible modes of crystal structure change in the solid state, the process known as the massive transformation is now known to occur in numerous alloy systems and several pure metals [ 1, 2 ]. In this process, the parent crystal structure changes into a new structure during cooling or heating, and the growth of the new grains is accomplished through displacement of incoherent boundaries, often at speeds of several cm per second. This t y p e of transformation does, of course, involve the usual nucleation and growth characteristics b u t it also has some specific features. There is no change of the overall composition and there is no characteristic crystallographic orientation relationship between parent and product grains. Since only a few atomic jumps may be sufficient to transfer each atom from one structure to another, most of the atomic mobility is limited to the interface region. Massive transformations are, therefore, an example of predominantly interface-controlled reactions involving only localized diffusion. However, they exhibit nucleation and growth characteristics associated with thermal activation. The details of the atomic movements at the transformation interfaces are n o t well understood, b u t the process does n o t appear to involve co-operative shear-like movements. In transmission electron micrographs, the massive phase exhibits a low, and random, density of dislocations, as may be expected from a diffusional and thermally-activated process. Early experiments [3] have shown that, because of the above features, massive grains are initially difficult to nucleate. However, once nucleated without a crystallographic orientation relationship with respect to the * D e d i c a t e d t o the m e m o r y o f t h e late P r o f e s s o r R. F. Mehl.

parent matrix, they can grow rapidly without regard for prior parent grain boundaries. This situation allows several parent grains to be absorbed by one growing, massive grain. Hence, provided the flow of heat is controlled directionally and only one nucleus is encouraged to grow, it is possible for a sample to be convetted into a single crystal [4]. The microstructure in a specimen that has undergone a massive transformation usually exhibits "massive" patches of grains that are surrounded by irregular boundaries consisting of a mixture of planar and curving sections. It is this microstructural feature that has provided the original name for the massive transformation [3, 5]. Typical examples of microstructures are shown in Fig. l(a) and (b). It must be admitted that while the word massive is now in c o m m o n use to describe the transformation process, its origin is linked with the initial description of a microstructure. Thus, the name of the massive transformation is quite coincidental and does n o t convey any particular description of a specific transformation mechanism, a feature that seems to be the rule rather than the exception with most metallurgical terms [6]. The phase relationships leading to a possible massive transformation may be illustrated in terms of schematic phase diagrams as in Fig. 2; for alloys (see Fig. 2(b), (c) and (d)), the two different crystal structures are normally simple metallic structures that can be stable or metastable at the same composition but at different temperatures. These conditions are also satisfied during allotropic transformations in pure metals (see Fig. 2(a)), which therefore may also occur by a massive transformation. In this case, of course, composition invariance is automatic. Details of some typical massive transformations that have been reported in the literature are given in refs. 1 and 2.

120

(a)

(b) Fig. 1. (a) Microstructure resulting from a massive transformation in an Fe-0.002 wt.% C alloy quenched in iced brine from 1000 0(3.Etched in nital.(x350) (b) Massive 0tm phase (dark, mottled) formed at the boundaries and inside parent grains of ~ phase (light) during a partial massive transformation in a Cu-37.5 at.% Zn alloy [18].

I

opportunity for studying transformations in which most of the driving free energy for the transformation is dissipated in driving the transformation interfaces, rather than in diffusional processes in the bulk material near the interfaces. This is particularly true when interfaces move at high velocities, as in a typical massive transformation. The "interface-control" becomes then a predominant feature and it m a y lead to a departure from local equilibrium conditions at the interface, and to possible solute trapping [7, 8]. At high growth rates, and during continuous cooling, it is also possible to consider the nucleation aspect separately from the growth aspect [9]. Products of a massive transformation in ferrous alloys tend to be soft (i.e., ferrite in steels) and are, on the whole, detrimental to mechanical properties when compared with martensite. On the other hand the rate of transformation in such alloys is usually much slower than in non-ferrous alloys, allowing for the possibility that some transformationinduced enhanced flow will occur under an applied stress [10]. Finally, it is well known that in metallurgical processes which involve rapid heating or cooling, solid-state transformations may occur by different, and often competing, modes. One of the modes can be a composition-invariant massive transformation. A better understanding of this process, and of the nature of the transformation interfaces during rapid motion, will u n d o u b t e d l y advance our general knowledge of complex transformations during heat treatment of metals and alloys. Below, a few of the more specific aspects of massive transformations are discussed in further detail.

fcc

~

2. FREE ENERGY CONSIDERATIONS

bcc ..........

r.,c0

(o~ ~

i

~

,,o,, '/I'""'

hop (d~

Solute c0ncentr0ti0n

Fig. 2. Schematic phase diagrams for (a) a pure metal,

and (b - d) three types o f alloys, that may undergo massive transformations [2 ].

Massive transformations are of interest for several reasons. As a subgroup of diffusional solid-state transformations they provide an

It is clear that a structural transformation can occur only if the free-energy conditions are favorable, i.e., when the Gibbs free energy of the product phase is lower than that of the parent phase, thus providing the driving force for the reaction. Being thermally activated, a massive transformation requires, however, n o t only an adequate driving force b u t also conditions under which this driving force is achieved at a temperature high enough for the rate of individual atomic movements to be

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appreciable. A schematic representation of the likely free-energy relationships in the temperature range at which massive transformations could occur, in a system involving a parent phase, ~, and a product phase, a, is shown in Fig. 3*. On cooling, transformations from ~ to a are, at least in principle, possible at any composition range within which the free-energy curve of the a phase lies below that of the ~. A H-phase alloy of composition c undercooled to temperature T1 can undergo an equilibrium phase separation into a l + ~1 phases, b u t there is no driving force for a composition-invariant reaction, ~c ~ ac, because the respective Gibbs free energies are equal at T 1 (i.e., T1 is located at the intersection of T O and c). If undercooling can be continued until T3 is reached without prior decomposition, the value of the free energy driving force

*The symbols ~ and c~ used here for the parent and product phases conform with the situation often encountered in phase diagrams based on the noble metals Cu, Ag, and Au. The ~ phase then represents the high temperature b.c.c, structure which is known to be highly unstable on cooling, and the 0t phase represents the f.c.c, primary solid solution.

i \i'-, -,i 0

a

GB

\

/

~ /T,

B2

A

C

B

Fig. 3. Free energy relationships related to a possible massive transformation.

for a composition-invariant transformation becomes AGSm. A massive transformation is now possible into an ~ phase of composition c, and the reaction can occur, at least in principle, with local equilibrium being maintained at the interface, because the composition line intersects the c~-phase free-energy curve in the single-phase region away from the tangent linking ~3 and ~3. However, if a compositioninvariant transformation were to occur at a higher temperature, for example, T2, there is, in addition to the driving force, AG 2 , for a massive transformation, also a larger driving force AG 2 representing an equilibrium phase separation into ~2 and ~2. Under these conditions, it is n o t possible, a priori, to decide which mode will prevail and, if a massive transformation is observed, it occurs as a composition-invariant mode in a two-phase field, which is most unusual. The driving force, AG~, is then dissipated primarily to bring a b o u t the reaction step at the interfaces and make them migrate, thereby effecting the crystal structure change, b u t n o t for any bulk diffusional processes of transporting A or B atoms individually. Hillert [11] points out that in this situation the driving free energy for one of the components at the interface may be of a wrong sign. For example, in Fig. 3, G~A-- G~ > 0 b u t G~ -- G~ < 0, so that at least for one of the components, the indicated direction of flow is against its own chemical potential. In order to obtain a positive value of the driving force for both components it may be convenient to assume that some diffusion takes place in the matrix just ahead of the migrating interface. This would allow a free energy construction whereby the composition of ~ is displaced locally until the tangents to the G ~ and G ~ curves do n o t intersect [11]. Whether this actually takes place in real massive transformations probably depends on whether the atomic species A and B cross the interfaces individually, or in some more complex cooperative manner. In any case, little is known, as yet, a b o u t the nature of the moving interfaces, although it appears quite likely that they become diffuse and widened as they move at high velocities [12]. Experimental evidence confirms, however, that massive transformations can occur in two-phase fields in many alloy systems; for example C u - Z n [13, 7], Cu-A1 [7], Ag-Cd [13], and F e Ni [8].

122 3. M I C R O S T R U C T U R A L F E A T U R E S

Optical microscopy studies of massive transformations reveal a wide variety of microstructures. When the transformation is completed without interference from alternative competing modes, the usual appearance is that of numerous irregular grains as in Fig. 1. In m a n y non-ferrous systems massive transformations result from the decomposition of the high temperature b.c.c. (~) phase to either the f.c.c. (~), or the h.c.p. (f) structure of the same composition, or a mixture of both (~ "-~ Otto; ~ -'~ ~m o r ~ "-~ O/m/~m)*. The latter feature has been observed, for example, in the systems Cu-Ga (Fig. 4), or Ag-Cd, where both the f.c.c, and the h.c.p, structures can form in the same composition region. Many of the resulting microstructures then reveal the presence of fine duplex units referred to as "feathers" [14]. Individual feathery units consist of twinned halves, involving a singular twin (1011) plane, the structure on both sides consisting of stacks of fine plates (or slabs) of various lengths and thicknesses, the plates being either f.c.c, or h.c.p., of the same composition as the original ~ parent phase, and matching coherently along their respective (111)~ or (00.1)~ close-packed planes (Fig. 5). An atomistic model for the growth of such units, involving two-dimensional nucleation *The subscript m is commonly used to indicate that the product phase 0tm or ~'m is the result of a massive transformation.

9oo: 800

-

t

~'700 I..5OO 4OO 300

-I I I I I I I I I I I 22 24 26 28 30 20 Atomic Per Cent Gallium

18 Cu

32

Fig. 4. Portion of the phase diagram C u - G a in the region of the massive transformation.

(a)

(000 l ) ~ \1i l ~ ~ ( i\ \ ~k~l l TwiOe~1)

Fig. 5. (a) Duplex " f e a t h e r " units formed in a Cu 21.0 at.% Ga alloy, quenched from the ~-phase field. (b) Schematic drawing in three dimensions of a feather unit [15].

and growth of close-packed planes, has been proposed by Gleiter and Massalski [15]. It appears that two dimensional-nucleation at the interfaces, accompanied by rapid growth of ledges, can be a prominent feature of typical massive transformations [16, 17]. A first clear indication for the lack of a fixed orientation relationship between the parent and product phases is provided by microstructural features. Following a massive transformation, the resulting grains are seen to cross the parent grain boundaries without hindrance. This is easily verified on the microstructure if only a partial transformation is involved (as in Fig. l(b)), because the parent grain boundaries are still visible. However, even after a complete transformation, the original parent boundaries can be "seen" outlined by precipitation of another phase that has occurred prior to the massive transformation (Fig. 6), or by thermal grooves etched on the polished surface of the parent phase during the high-temperature annealing treatment {Fig. 7). Nevertheless, a more accurate confirmation of the "lack of orientation relation-

123 800

700

I--


Fig. 6. Microstructure obtained following a massive transformation in a ternary C u - G a - G e alloy. Precipitation of the 7 phase has occurred at parent ~-phase grain boundaries and inside ~ grains, prior to the massive transformation [ 3 ].

15

2O

25

50

35

ATOMIC % AI

Fig. 8. Portion of the phase diagram Ag-A1 in the region of the massive transformation.

Fig. 7. Mierostructure obtained following a massive transformation in an Fe-5.0 at.% Ni alloy after air cooling from the ")'-phase field at approximately 7 °C/s [8].

ship feature" requires X-ray work [ 3 ] , or electron diffraction [18].

4. KINETICS AND MODELS OF GROWTH

Kinetic studies of the ~(b.c.c.) to am (f.c.c.) massive transformation in C u - Z n alloys have been reported by Karlyn, Cahn and Cohen [19] and by Ayers and Massalski [ 2 0 ] . Pulseheating techniques were employed in both of these studies whereby a specimen of previously

retained ~ phase at room temperature is "upquenched" to a selected reaction temperature. Reaction rate data in the former study were obtained by metallographic measurements, and in the latter by electrical resistivity measurements. The results of such studies, as well as direct observation of moving interfaces with an optical microscope in C u - G a alloys (~ + ~m transformation) [21], indicate that the overall interface velocities during the transformation are very rapid, i.e., of the order of 1 - 2 cm/s. More recently, kinetics of the ~(b.c.c.) ~, ~m (h.c.p.) transformation were studied in the Ag-A1 system by Perepezko and Massalski [16]. This transformation not only has all the features of a typical massive transformation b u t also, at the composition of A g - 2 4 . 5 at.% A1, a congruent phase relationship exists between the product and parent phases, as shown in Fig. 8. This situation obviates the necessity for prior rapid quenching of the phase to room temperature. Instead, since there is no equilibrium two-phase field to cross, the ~ phase may be transferred directly to a reaction temperature in the ~-phase field. A technique was used for studying the progress with time of a single ~/~m reaction interface by growing single crystals*. The velocity *The key to the production of single crystals is t h e directional control of the growth of a single grain. Three important features are needed to achieve this:

124

AG-245

at % A L

I20

100

E "~80

o

40

20

~ 1

40

60

-

80 1 UndercooHng (z~ T,°C )

I

Fig. 9. Relationship between interface velocity and undercooling during the ~ "* ~rn reaction in a Ag-24.5 at.% A1 alloy [16].

of the ~/~m transformation interface was measured at different amounts of undercooling, AT, below the To temperature at which the free energies of the ~ and ~ phases are equal, and at different cooling rates, T = dT/dt. For a massive transformation, the temperature at which a thermal arrest inflection occurs during cooling is related to the magnitude of the imposed cooling rate. An increase in cooling rate tends to depress the transformation temperature and increase the amount of undercooling [22]. A typical relationship obtained between the interface velocity and the a m o u n t of undercooling for a Ag-24.5 at.% A1 alloy is shown in Fig. 9. A range of velocities was recorded covering nearly two orders of magnitude; a low value of 0.29 mm/s at 1 °C undercooling to a maximum value of 12.0 mm/s at 18 °C undercooling. At low undercoolings, the velocity increases rapidly with increased undercooling, b u t b e y o n d an undercooling of a b o u t 10 °C, the rate of increase of velocity with undercooling diminishes and the velocity appears to be approaching a maximum value. The measured undercooling can be related to the driving free energy for the ~ -~ [m massive reaction. In the Ag-A1 alloys, AG ~ ~ varies linearly from 1.25 cal/mole at AT = 1 °C, to 25.0 cal/mole at AT = 20 °C, which are quite substantial driving free energies compared, for example, with typical values for migration of boundaries during grain growth [23] which does not involve a crystal structure change. Thus, during a massive transformation, iman apparatus involving a temperature gradient, a convenient specimen geometry and preparation procedure, and a controlled heat-treatment schedule [4 ].

purity drag effects of the kind observed during grain growth are unlikely to be of importance. For incoherent interfaces, such as those involved in a typical massive transformation, one can envisage two possible ways in which migration of the interface normal to itself can occur. In the first of these, atoms are able to cross the interface and attach themselves randomly to all points of the advancing boundary. There is thus a continuous, or uniform, growth at all positions along the boundary. In the second mechanism, the interface is stepped on the atomic scale and atoms are attached predominantly at these steps. The interface then migrates by the lateral motion of ledges associated with a two-dimensional nucleation process. These ideas axe similar to those proposed for the growth of crystals from supercooled liquids. The forward growth rate, v, can be written as an exponential function of temperature, T, and undercooling, AT. For growth with two-dimensional nucleation supplying the required steps, a plot of In v against (TAT)-1 should be linear; which is the case in Ag-A1 alloys over a fairly wide range of velocity [16]. The data for undercooling exceeding about 10 °C tend to deviate from the above behavior and a continuous growth by random atom attachment appears to be the dominating process. The velocity can then be related to the mobility, M, and the driving free energy, AG, which, in turn, are functions of temperature, undercooling and diffusivity [ 16]

5. NUCLEATION FEATURES

Experimental work indicates that there exists a well-defined relationship between the transformation temperature of a massive transformation and the rate of cooling [1, 22]. In the single-crystal experiments, the transformation temperature corresponds to the temperature at the interface, Ti, measured during the passage of a single transformation front under given thermal conditions. In the continuous cooling experiments, the transformation temperature corresponds to the thermal arrest temperature observed on an oscillographicallyrecorded cooling curve. In both cases, it is possible to estimate, therefore, the amount of time a specimen spends between To and the transformation temperature. During continuous cooling, this time, t, consists of t w o parts: t,,

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the time required to nucleate the massive phase, and tg, the time taken to grow a certain minimum amount. A detailed study of these relative times, based on an assessment of various cooling experiments, shows that for the high interface velocities obtained during a massive transformation, tg is practically negligible compared with tn (i.e., tn >> tg), and that t ~ tn. This is the experimental basis of a theory describing nucleation during continuous cooling [9]. Under conditions pertaining to a massive transformation, a parabolic form relationship is obtained between the undercooling and the cooling rate, ~v = K(AT)2, where K is a constant related to the initial shape of the nucleus, the driving force, and other properties of the material. This relationship is in good agreement with the experimental data for many massive transformations. It suggests that nucleation of the massive phase is the rate controlling process [9]. Results obtained during isothermal transformations in Ag-AI [16] indicate that there is also a delay time interval (incubation period) measured from the placement of the specimens at the reaction temperature, during which no transformation is detected. Such delay times vary between 0.4 and 0.05 s as undercooling is increased by about 30 °C. The trend of the delay times appears to follow a C-curve pattern usually associated with thermally activated transformation modes. It is very much like the nucleation time trend, tn, during continuous cooling [ 2 4 ] . Hence, nucleation is again the predominant feature. Other interesting features associated with nucleation occur in certain ternary alloys [ 2 5 ] . REFERENCES 1 T. B. Massalski, in Phase Transformations, Am.

Soc. Metals, Metals Park, Ohio, 1970, p. 433. 2 T. B. Massalski, Metals Handbook, Voi. 8, Am. Soc. Metals, Metals Park, Ohio, 1973, p. 186. 3 T. B. Massalski, Acta Metall., 6 (1958) 243. 4 J. H. Perepezko and T. B. Massalski, J. Mater. Sci., 9 (1974) 899. 5 A. B. Greninger, Trans. Metail. Soc. AIME, 133 (1939) 204. 6 R. B. G. Yeo, Trans. Am. Soc. Met., 58 (1965) 115. 7 T. B. Massalski, A. J. Perkins and J. Jaklovsky, Metall. Trans., 3 (1972) 687. 8 T. B. Massalski, J. H. Perepezko and J. Jaklovsky, Mater. Sci. Eng., 18 (1975) 193. 9 S. K. Bhattacharyya, J. H. Perepezko and T. B. Massalski, Acta Metall., 22 (1974) 879. 10 T. B. Massalski, J. H. Perepezko and S. K. Bhattacharyya, to be published. 11 M. Hillert, in H. I. Aaronson (ed.), Lectures on the Theory of Phase Transformations, Am. Inst. Mech. Eng., New York, 1975. 12 J. H. Perepezko and T. B. Massalski, Scr. Metall., 6 (1972) 743. 13 J. D. Ayers and T. B. Massalski, Metall. Trans., 3 (1971) 261. 14 G. A. Sargent, L. Delaey and T. B. Massalski, Acta Metall., 16 (1968) 723. 15 H. Gleiter and T. B. Massalski, Acta Metall., 18 (1970) 649. 16 J. H. Perepezko and T. B. Massalski, Acta Metall., 23 (1975) 621. 17 G. Bar6, J. H. Perepezko, H. Gleiter and T. B. Massalski, J. Mater. Sci. Eng., in the press. 18 E. B. Hawbolt and T. B. Massalski, Metall. Trans., 1 (1970) 2315. 19 D. A. Karlyn, J. W. Cahn and M. Cohen, Trans. Metall. Soc. AIME, 245 (1969) 197. 20 J. D. Ayers and T. B. Massalski, Metall. Trans., 3 (1972) 3185. 21 J. E. Kitti and T. B. Massalski, Acta Metall., 15 (1967) 161. 22 S. K. Bhattacharyya, J. H. Perepezko and T. B. Massalski, Scr. Metall., 7 (1973) 485. 23 C. G. Dunn and J. L. Walter, Recrystallization, Grain Growth and Textures, Am. Soc. Metals, Metals Park, Ohio, 1966, p. 461. 24 E. B. Hawbolt and T. B. Massalski, Metall. Trans., 2 (1971) 1771. 25 A. J. Perkins and T. B. Massalski, Metall. Trans., 2 (1971) 2701.