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Diffusional and displacive transformations
Scripta
METALLURGICA
Vol. 21, pp. 1 0 1 7 - 1 0 2 2 , 1987 P r i n t e d in the U . S . A .
P e r g a m o n J o u r n a l s , Ltd. All rights reserved
VIEWPOINT
SET No.
ii
DIFFUSIONAL AND DISPLACI93K TRANSFORMATIONS
H. K. D. H. Bhadeshia University of Cambridge Department of Materials Science and Metallurgy Pembroke Street, Cambridge CB2 3QZ, U. K. ( R e c e i v e d M a y 12, 1987) ( R e v i s e d M a y 26, 1987) The aim of this paper is to summarise some important characteristics of diffusional and displacive transformations, with emphasis on the grey area where it sometimes seems difficult to identify the operative transformation mechanism. The mechanism of transformation can sometimes be confused with the processes controlling the rate of interface motion. We therefore begin by defining diffusion-controlled and interface-controlled growth, and the mechanisms of diffusional and displacive transformations. Interface Motion: Rate Controlling Processes The rate at which an interface moves depends both on its intrinsic mobility (related to the process of atom transfer across the interface) and on the ease with which any alloying elements partitioned during transformation diffuse ahead of the moving interface. The two processes are in series so that interface velocity as calculated from interface mobility always equals the velocity calculated from the diffusion of solute ahead of the interface. Both of these processes dissipate the free energy (AG') available for interface motion; when /KG' is primarily used up in driving the diffusion of solute ahead of the interface, growth is said to be diffusion-controlled. Interfacecontrolled growth occurs when most of /KG' is dissipated in the process of atom transfer across the interface. It is emphasised that the rate of interface motion is always under mixed control (since the two processes are in series) but is said to be diffusion-controlled when variations in interface parameters have virtually no effect on velocity. Similarly, interface-control implies that variations in diffusion parameters have negligible effect on the interface velocity. Mixed control arises when similar amounts of free energy are dissipated in the interface and diffusion processes. These concepts are discussed more fully in (I). The process controlling interface motion should not be confused with the mechanism of transformation; for example, Widmanst~tten ferrite forms by a displacive transformation mechanism in which only the interstitials are redistributed during the transformation, so that its lengthening rate is approximately controlled by the diffusion of carbon in the austenite ahead of the transformation interface (2). Characteristics of Diffusional and Displacive Transformations We consider next the essential differences between diffusional and martensitic transformations. All martensitie transformations involve co-ordinated movements of atoms and are diffusionless. Since the shape of the pattern in which the atoms of the parent crystals are arranged nevertheless changes in a way that is consistent with the change in crystal structure, it follows that there must
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be a physical change in the macroscopic shape of the parent crystal during transformation. Fig.1 compares diffusional and martensitic transformations in a substitutionally alloyed material. The transformation strain is for simplicity assumed to be an invariant-plane strain (IPS) and a fully coherent interface (the invariant-plane) exists between the parent and product lattices, irrespective of the mechanism of transformation.
FIG.I. Schematic illustration of the mechanisms of diffusional and martensitic transformations in a substitutionally alloyed material (3). The lines joining "atoms" connect corresponding directions of the parent and product lattices. For the martensitic transformation, the pattern of atomic arrangement is changed on transformation, and since the transformation is diffusionless, the macroscopic shape of the crystal changes. The shape deformation has the exact characteristics of an IPS. Fig.1 also shows that labelled rows of atoms in the parent crystal remain in the correct sequence in the martensite lattice, despite transformation. As there is no mixing up of atoms during transformation, it is possible to suggest that a particular atom of the martensite originated from a corresponding particular atom in the parent crystal. This property may be expressed by stating that there exists an atomic correspondence between the parent and product lattices. For the diffusional transformation, it is evident (Fig.l) that the product phase can (although it need not) be of a different composition from the parent phase. In addition, there has been much mixing up of atoms during transformation and there is no atomic correspondence between the parent and product lattices. Because the transformation involves a reconstruction of the parent lattice, atoms are able to diffuse and mix in such a way that the IPS shape deformation (and its attendant strain energy) does not arise. In interstitially alloyed materials, the substitutional lattice can transform without diffusion while the interstitials diffuse (4); this is displacive transformation. The diffusion of interstitials has no influence on the shape change accompanying transformation so that the macroscopic characteristics of martensite are retained. Only a partial atomic correspondence (between atoms on the substitutional lattice) exists between the parent and product lattices.
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Martensitie transformations can be regarded as a (diffusionless) subset of displacive transformations (5). Martensitic reactions are always interface-controlled whereas displacive or diffusional transformations need not be; their rate can for example be controlled by diffusion. With displacive and martensitic transformations, the product phase always has a thin-plate morphology since this minimises the strain energy associated with the shape deformation (6). The concept of a lattice correspondence has caused some confusion; a lattice correspondence can be defined between any two crystals, irrespective of the mechanism by which one crystal transforms to the other. It is a notional concept and is useful in for example, interface theory where the calculation of interface structure requires the definition of a (real or imaginary) transformation strain relating the two crystals. A real strain implies the existence of an atomic correspondence whereas a notional strain does not (p.70, 3). In a first order transformation, the partial derivative of the Gibbs free energy with respect to temperature is discontinuous at the transition temperature. There is thus a latent heat of transformation evolved at a 'sharp' transformation interface which separates the co-existing parent and product phases. The phase change occurs at a well defined interface separating perfect forms of the parent and product phases. The interface structure must dominate the mechanism of transformation and we now discuss the influence of interface structure in terms of austenite (FCC, Y) as the parent lattice and ferrite (BCC, ~) as the product lattice. Influence of interface structure The Y-9~ transformation is a first order transformation which occurs by the motion of well defined interfaces. The structure of the interface influences the way in which the atoms of the parent lattice move in order to generate the ~ lattice. It can be shown (7) that two arbitrary crystals can be joined by a stress-free coherent interface only if one of the crystals can be generated from the other by a homogeneous transformation strain which is an invariant-plane strain (IPS). This condition in turn requires that two of the principal strains of the pure strain part of the transformation strain be of opposite sign, the third being zero. By the addition of a suitable rigid body rotation, a pure strain like this can be converted into an IPS. The pure deformation which converts a FCC crystal to a BCC crystal, and which seems to involve the smallest atomic displacements, is the Bain strain (8). In steels, all of the principal strains of the Bain strain have finite values, two of them being positive and the third negative. Combination of the Bain strain with a rigid body rotation cannot therefore give a transformation strain which is an IPS. It follows that (x/Y interfaces must be semi-coherent or incoherent, except at the nucleation stage where the ~ may be forced into coherence. For larger areas of contact, the structure of the interface will in general consist of coherent patches separated periodically by discontinuities which prevent the misfit in the interface from accumulating over large distances. Glissile interfaces There are two kinds of semi-coherency (7,9) - if the discontinuities discussed above consist of a single set of screw dislocations, or dislocations whose Burgers vectors do not lie in the interface plane. This semi-coherency is of the kind associated with glissile interfaces. If the transformation strain is an invariant-line strain (consisting of the Bain strain and an appropriate rigid body rotation), and if the invariant-line lies in the interface, then the latter need only contain a single set of misfit dislocations. For martensitic transformations, the transformation strain has to be an invariant-line strain (or an invariant-plane strain) in order to ensure a glissile interface. A glissile interface also requires that the glide planes (of the misfit dislocations) associated with the ~ lattice meet the corresponding glide planes in the Y lattice edge to edge in the interface, alone the dislocation lines. A glissile oVY interface can move conservatively and when it
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does so, the interface dislocations inhomogeneously shear the volume of material swept by the interface in such a way that the macroscopic shape change accompanying transformation is an IPS even though the homogeneous lattice transformation strain is an invariant-line strain. Conservative motion of a glissile interface leads to martensitic or displacive transformation. We note that the criteria distinguishing glissile from sessile interfaces must be applied to the interface as a whole, taking account of every element of the interface in defining the interface plane (10).
l
/
0 FIG.2.
Diagram illustrating the shape change accompanying the movement of an epitaxially semi-
coherent interphase interface. Epitaxial semi-coherency If the intrinsic interface dislocations have Burgers vectors which lie in the interface plane, not parallel to the dislocation line, then the interface may be said to be epitaxially semi-coherent (Fig.2). The normal displacement of such an interface necessitates the thermally activated climb of the misfit dislocations, so that the interface can only move in a non-conservative manner with relatively restricted mobility at low temperatures. The nature of the shape change that accompanies the motion of an epitaxially semi-coherent interface is difficult to assess. As discussed by Christian (7,9), the upwards non-conservative motion of the boundary AB (Fig.2) to a new position C'D' should change the shape of a region ACDB of the parent crystal to a shape AC'D'B of the product phase. The shape change thus amounts to a uniaxial distortion normal to AB together with a shear component parallel to the interface plane (i.e., an IFS). Because of the dislocation climb implicit in the process, the total number of atoms in regions ACDB and AC'D'B will not be equal, the difference being removed by diffusion normal to the interface plane. Atom movements are therefore necessary over a distance (at least) equal to that moved by the boundary, corresponding to the thickness of the transformed region. If this constitutes the only diffusional flux that accompanies interface motion, then the shear component of the shape change will not be destroyed, and the transformation will exhibit surface relief effects (and corresponding strain energy) normally associated with displacive transformations (the product phase will have the morphology of a thin-plate). The mobility will, of course, be limited by the climb prooes~ A situation like this in effect amounts to an orderly removal of atoms as the interface migrates (i.e., removal of the extra half planes of the misfit dislocations) so that a partial atomic correspondence is still maintained between the parent and product phases. However, Christian (4) has pointed out that since atoms have to migrate over large distances when an epitaxially semi-coherent interface moves, they should also be able to produce a net flow parallel to the interface, thus eliminating the shear component of the shape change, and its associated strain energy. Referring to Fig.2, thls would involve the diffusion of matter contained in the region BF'D' to region AFC', in a direction parallel to the interface. Hence, it has been
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considered improbable that atomic correspondence can be maintained during non-conservative interface motion. Bhsdeshia (11) has suggested that this may not be true if the flow parallel to the interface has to occur through a distance much larger than that normal to the interface - after all, the length to thickness ratio of plates is always large. This argument would fail if the dislocation climb process draws vacancies form a large distance normal to the interface. Reconstructive diffusion From the above discussion it is evident that diffusion both parallel and normal to the interface plane is necessary if the migration of an epitaxially semi-coherent interface is to produce diffusional transformation. The diffusion processes have been described phenomenologically, but in reality, they should occur as the interface moves. Such diffusion is henceforth referred to as reconstructive diffusion, to describe the atomic mixing necessary to accomplish the lattice change without causing the macroscopic displacements characteristic of martensitic transformations in steels. It is emphasised that in diffusional transformations, reconstructive diffusion is necessary even if the parent and product phases have identical composition, or if the transformation occurs in a pure element. Diffusional transformation in effect represents transformation and recrystallisation occurring simultaneously, and reconstructive diffusion is the recrystallisation part of the process. During the formation of martensite, much of the driving force is used up in accommodating the elastic strains due to the shape change. Such strains are absent for diffusional transformations which can consequently occur at lower driving forces. The conservative motion of a glissile interface leads to martensitic transformation. If circumstances arise where a glissile interface exists but only diffusional reaction is possible, then the interface can move if reconstructive diffusion accompanies its motion. The displacive formation of bainite from austenite stops when the carbon-enriched austenite can no longer support such transformation; Bhadeshia (11) has shown that continued holding at isothermal transformation temperature causes the interfaces which initially led to displacive bainite growth to move at a much slower rate, as the residual austenite continues to diffusionally transform. Incoherent Interfaces As the misfit between adjacent crystals increases, the dislocations in the connecting interface become more closely spaced. They eventually coalesce so that the boundary consists of closely spaced 'vacancies' or 'dislocation cores'. Such a boundary is said to be incoherent; there is little correlation of atomic positions across the boundary. The motion of incoherent boundaries can only cause diffusional transformation, with no atomic correspondence between the parent and product phases. For incoherent boundaries, the free volume and diffusivity within the boundary may be sufficiently high to confine reconstructive processes to the close proximity of the boundary itself (unlike semi-coherent interfaces). Incoherent, coherent and semi-coherent boundaries can co-exist around a particle which has grown diffusionally; only semi-coherent and coherent boundaries can exist around a particle which has grown displacively. This is because if an atomic correspondence exists across a particular interface of a particle, then it necessarily does so across any other interface (7,12). Discussion We believe that the viewpoint presented above provides an adequate description of displacive and diffusional transformations, enabling phase transformations theory to be usefully applied in predicting rate-controlling processes and miorostruoture. The shape change accompanying the motion of an epitaxially semi-coherent interface does need further work to establish whether the diffusion necessary to enable the climb of intrinsic interface dislocations provides an opportunity for reconstructive diffusion to eliminate the shear component of the shape deformation.
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The implications of the shape change as discussed in the viewpoint are sometimes not accepted (e.g., Ref.13). It has been proposed that an IPS surface relief effect, of the type associated with martensitic transformations, arises even during a diffusional transformations, simply due to the existence of a sessile semi-coherent or coherent interface which is displaced by the movement of "disordered" ledges (13). The ledges themselves are considered to have an incoherent structure. We believe that this proposal is fundamentally incorrect: the very existence of an IPS relief implies co-ordinated movements of atoms, inconsistent with the concept of a diffusional transformation (and its associated reconstructive diffusion) and with the structure of the incoherent boundary (ledge) whose motion leads to transformation. Christian and Edmonds (12) have shown that the proposal also implies the existence of an atomic correspondence across just the sessile part of the interface, and this is an impossible concept since atomic correspondence is a property of the particle as a whole. The proposal also leads to detailed contradictions with experimental evidence (10,14). The second main point of controversy concerns factors determining the morphology of precipitates, especially in steels. The shape change accompanying the formation of Widmanst~tten ferrite and bainite in steels is known to be an IPS with a large shear component (15,16). The strain energy due to this shape deformation causes the plates to adopt a thin-plate morphology. Aaronson and co-workers have ignored the influence of the shape change on morphology, and instead claim that the plate morphology is a consequence of variation of interface mobility as a function of interface orientation. Their ideas do not explain the lack of a plate morphology in the case of allotriomorphic ferrite which grows diffusionally, but which can otherwise be similar to Widmanst~tten ferrite (10). References I. H. K. D. H. Bhadeshia, Progress in Materials Science 29, 321 (1985). 2. H. K. D. H. Bhadeshia, Materials Science and Technology I, 497 (1985). 3. H. K. D. H. Bhadeshia, Geometry of Crystals, Institute of Metals, London (and Brookfield, U. S. A.) (1987). 4. J.W. Christian, 'Decomposition of Austenite by Diffusional Processes', eds. V.F. Zaokay and H.I. Aaronson, Intersoience, New York, (1962) p.371. 5. M. Cohen, G.B. Olson and P.C. Clapp, Proc. of Int. Conf. on Martensitic Transformations, ICOMAT 79, Boston, Massachusetts, (1979) p.1. 6. J.W. Christian, Acta Metall., 6, 377 (1958). 7. J.W. Christian, 'Theory of Transfm. in Metals and Alloys', Pt.1, 2nd ed., Pergamon Press, Oxford, (1975). 8. E.C. Bain, Trans. AIMME, 70, 25 (1924). 9. J.W. Christian, 'Mech. of Phase Transf. in Cryst. Solids', Institute of Metals, London, Monograph 13, (1969) p.129. 10. H.K.D.H. Bhadeshia, Scrlpta Metall., 17, 1475 (1983). 1 I. H.K.D.FL Bhadeshia, Journal de Physique, 43, C4-437 (1982). 12. J.W. Christian and D.V. Edmonds, Phase Transformations in Ferrous Alloys, p.293, eds. A. R. Marder and J. I. Goldstein, TMS-AIME, Warrendale, Pennsylvania, (1984). 13. K.R. Kinsman, E. Eichen and H.I. Aaronson, Metall. Trans. A, 6A, 303 (1975). 14. H.K.D.H. Bhadeshia, Scripta Metall., 14, 821 (1980). 15. J.D. Watson and P.G. McDougall, Aeta Metall., 21, 961 (1973). 16. T. Ko and S.A. Cottrell, JISI, 307, 172 (1952).
METALLURGICA
Vol. 21, pp. 1 0 1 7 - 1 0 2 2 , 1987 P r i n t e d in the U . S . A .
P e r g a m o n J o u r n a l s , Ltd. All rights reserved
VIEWPOINT
SET No.
ii
DIFFUSIONAL AND DISPLACI93K TRANSFORMATIONS
H. K. D. H. Bhadeshia University of Cambridge Department of Materials Science and Metallurgy Pembroke Street, Cambridge CB2 3QZ, U. K. ( R e c e i v e d M a y 12, 1987) ( R e v i s e d M a y 26, 1987) The aim of this paper is to summarise some important characteristics of diffusional and displacive transformations, with emphasis on the grey area where it sometimes seems difficult to identify the operative transformation mechanism. The mechanism of transformation can sometimes be confused with the processes controlling the rate of interface motion. We therefore begin by defining diffusion-controlled and interface-controlled growth, and the mechanisms of diffusional and displacive transformations. Interface Motion: Rate Controlling Processes The rate at which an interface moves depends both on its intrinsic mobility (related to the process of atom transfer across the interface) and on the ease with which any alloying elements partitioned during transformation diffuse ahead of the moving interface. The two processes are in series so that interface velocity as calculated from interface mobility always equals the velocity calculated from the diffusion of solute ahead of the interface. Both of these processes dissipate the free energy (AG') available for interface motion; when /KG' is primarily used up in driving the diffusion of solute ahead of the interface, growth is said to be diffusion-controlled. Interfacecontrolled growth occurs when most of /KG' is dissipated in the process of atom transfer across the interface. It is emphasised that the rate of interface motion is always under mixed control (since the two processes are in series) but is said to be diffusion-controlled when variations in interface parameters have virtually no effect on velocity. Similarly, interface-control implies that variations in diffusion parameters have negligible effect on the interface velocity. Mixed control arises when similar amounts of free energy are dissipated in the interface and diffusion processes. These concepts are discussed more fully in (I). The process controlling interface motion should not be confused with the mechanism of transformation; for example, Widmanst~tten ferrite forms by a displacive transformation mechanism in which only the interstitials are redistributed during the transformation, so that its lengthening rate is approximately controlled by the diffusion of carbon in the austenite ahead of the transformation interface (2). Characteristics of Diffusional and Displacive Transformations We consider next the essential differences between diffusional and martensitic transformations. All martensitie transformations involve co-ordinated movements of atoms and are diffusionless. Since the shape of the pattern in which the atoms of the parent crystals are arranged nevertheless changes in a way that is consistent with the change in crystal structure, it follows that there must
1017 0036-9748/87 $3.00 C o p y r i g h t (c) 1987 P e r g a m o n
+ .00 Journals
Ltd.
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TRANSFORMATIONS
Vol.
21, No.
8
be a physical change in the macroscopic shape of the parent crystal during transformation. Fig.1 compares diffusional and martensitic transformations in a substitutionally alloyed material. The transformation strain is for simplicity assumed to be an invariant-plane strain (IPS) and a fully coherent interface (the invariant-plane) exists between the parent and product lattices, irrespective of the mechanism of transformation.
FIG.I. Schematic illustration of the mechanisms of diffusional and martensitic transformations in a substitutionally alloyed material (3). The lines joining "atoms" connect corresponding directions of the parent and product lattices. For the martensitic transformation, the pattern of atomic arrangement is changed on transformation, and since the transformation is diffusionless, the macroscopic shape of the crystal changes. The shape deformation has the exact characteristics of an IPS. Fig.1 also shows that labelled rows of atoms in the parent crystal remain in the correct sequence in the martensite lattice, despite transformation. As there is no mixing up of atoms during transformation, it is possible to suggest that a particular atom of the martensite originated from a corresponding particular atom in the parent crystal. This property may be expressed by stating that there exists an atomic correspondence between the parent and product lattices. For the diffusional transformation, it is evident (Fig.l) that the product phase can (although it need not) be of a different composition from the parent phase. In addition, there has been much mixing up of atoms during transformation and there is no atomic correspondence between the parent and product lattices. Because the transformation involves a reconstruction of the parent lattice, atoms are able to diffuse and mix in such a way that the IPS shape deformation (and its attendant strain energy) does not arise. In interstitially alloyed materials, the substitutional lattice can transform without diffusion while the interstitials diffuse (4); this is displacive transformation. The diffusion of interstitials has no influence on the shape change accompanying transformation so that the macroscopic characteristics of martensite are retained. Only a partial atomic correspondence (between atoms on the substitutional lattice) exists between the parent and product lattices.
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Martensitie transformations can be regarded as a (diffusionless) subset of displacive transformations (5). Martensitic reactions are always interface-controlled whereas displacive or diffusional transformations need not be; their rate can for example be controlled by diffusion. With displacive and martensitic transformations, the product phase always has a thin-plate morphology since this minimises the strain energy associated with the shape deformation (6). The concept of a lattice correspondence has caused some confusion; a lattice correspondence can be defined between any two crystals, irrespective of the mechanism by which one crystal transforms to the other. It is a notional concept and is useful in for example, interface theory where the calculation of interface structure requires the definition of a (real or imaginary) transformation strain relating the two crystals. A real strain implies the existence of an atomic correspondence whereas a notional strain does not (p.70, 3). In a first order transformation, the partial derivative of the Gibbs free energy with respect to temperature is discontinuous at the transition temperature. There is thus a latent heat of transformation evolved at a 'sharp' transformation interface which separates the co-existing parent and product phases. The phase change occurs at a well defined interface separating perfect forms of the parent and product phases. The interface structure must dominate the mechanism of transformation and we now discuss the influence of interface structure in terms of austenite (FCC, Y) as the parent lattice and ferrite (BCC, ~) as the product lattice. Influence of interface structure The Y-9~ transformation is a first order transformation which occurs by the motion of well defined interfaces. The structure of the interface influences the way in which the atoms of the parent lattice move in order to generate the ~ lattice. It can be shown (7) that two arbitrary crystals can be joined by a stress-free coherent interface only if one of the crystals can be generated from the other by a homogeneous transformation strain which is an invariant-plane strain (IPS). This condition in turn requires that two of the principal strains of the pure strain part of the transformation strain be of opposite sign, the third being zero. By the addition of a suitable rigid body rotation, a pure strain like this can be converted into an IPS. The pure deformation which converts a FCC crystal to a BCC crystal, and which seems to involve the smallest atomic displacements, is the Bain strain (8). In steels, all of the principal strains of the Bain strain have finite values, two of them being positive and the third negative. Combination of the Bain strain with a rigid body rotation cannot therefore give a transformation strain which is an IPS. It follows that (x/Y interfaces must be semi-coherent or incoherent, except at the nucleation stage where the ~ may be forced into coherence. For larger areas of contact, the structure of the interface will in general consist of coherent patches separated periodically by discontinuities which prevent the misfit in the interface from accumulating over large distances. Glissile interfaces There are two kinds of semi-coherency (7,9) - if the discontinuities discussed above consist of a single set of screw dislocations, or dislocations whose Burgers vectors do not lie in the interface plane. This semi-coherency is of the kind associated with glissile interfaces. If the transformation strain is an invariant-line strain (consisting of the Bain strain and an appropriate rigid body rotation), and if the invariant-line lies in the interface, then the latter need only contain a single set of misfit dislocations. For martensitic transformations, the transformation strain has to be an invariant-line strain (or an invariant-plane strain) in order to ensure a glissile interface. A glissile interface also requires that the glide planes (of the misfit dislocations) associated with the ~ lattice meet the corresponding glide planes in the Y lattice edge to edge in the interface, alone the dislocation lines. A glissile oVY interface can move conservatively and when it
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does so, the interface dislocations inhomogeneously shear the volume of material swept by the interface in such a way that the macroscopic shape change accompanying transformation is an IPS even though the homogeneous lattice transformation strain is an invariant-line strain. Conservative motion of a glissile interface leads to martensitic or displacive transformation. We note that the criteria distinguishing glissile from sessile interfaces must be applied to the interface as a whole, taking account of every element of the interface in defining the interface plane (10).
l
/
0 FIG.2.
Diagram illustrating the shape change accompanying the movement of an epitaxially semi-
coherent interphase interface. Epitaxial semi-coherency If the intrinsic interface dislocations have Burgers vectors which lie in the interface plane, not parallel to the dislocation line, then the interface may be said to be epitaxially semi-coherent (Fig.2). The normal displacement of such an interface necessitates the thermally activated climb of the misfit dislocations, so that the interface can only move in a non-conservative manner with relatively restricted mobility at low temperatures. The nature of the shape change that accompanies the motion of an epitaxially semi-coherent interface is difficult to assess. As discussed by Christian (7,9), the upwards non-conservative motion of the boundary AB (Fig.2) to a new position C'D' should change the shape of a region ACDB of the parent crystal to a shape AC'D'B of the product phase. The shape change thus amounts to a uniaxial distortion normal to AB together with a shear component parallel to the interface plane (i.e., an IFS). Because of the dislocation climb implicit in the process, the total number of atoms in regions ACDB and AC'D'B will not be equal, the difference being removed by diffusion normal to the interface plane. Atom movements are therefore necessary over a distance (at least) equal to that moved by the boundary, corresponding to the thickness of the transformed region. If this constitutes the only diffusional flux that accompanies interface motion, then the shear component of the shape change will not be destroyed, and the transformation will exhibit surface relief effects (and corresponding strain energy) normally associated with displacive transformations (the product phase will have the morphology of a thin-plate). The mobility will, of course, be limited by the climb prooes~ A situation like this in effect amounts to an orderly removal of atoms as the interface migrates (i.e., removal of the extra half planes of the misfit dislocations) so that a partial atomic correspondence is still maintained between the parent and product phases. However, Christian (4) has pointed out that since atoms have to migrate over large distances when an epitaxially semi-coherent interface moves, they should also be able to produce a net flow parallel to the interface, thus eliminating the shear component of the shape change, and its associated strain energy. Referring to Fig.2, thls would involve the diffusion of matter contained in the region BF'D' to region AFC', in a direction parallel to the interface. Hence, it has been
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considered improbable that atomic correspondence can be maintained during non-conservative interface motion. Bhsdeshia (11) has suggested that this may not be true if the flow parallel to the interface has to occur through a distance much larger than that normal to the interface - after all, the length to thickness ratio of plates is always large. This argument would fail if the dislocation climb process draws vacancies form a large distance normal to the interface. Reconstructive diffusion From the above discussion it is evident that diffusion both parallel and normal to the interface plane is necessary if the migration of an epitaxially semi-coherent interface is to produce diffusional transformation. The diffusion processes have been described phenomenologically, but in reality, they should occur as the interface moves. Such diffusion is henceforth referred to as reconstructive diffusion, to describe the atomic mixing necessary to accomplish the lattice change without causing the macroscopic displacements characteristic of martensitic transformations in steels. It is emphasised that in diffusional transformations, reconstructive diffusion is necessary even if the parent and product phases have identical composition, or if the transformation occurs in a pure element. Diffusional transformation in effect represents transformation and recrystallisation occurring simultaneously, and reconstructive diffusion is the recrystallisation part of the process. During the formation of martensite, much of the driving force is used up in accommodating the elastic strains due to the shape change. Such strains are absent for diffusional transformations which can consequently occur at lower driving forces. The conservative motion of a glissile interface leads to martensitic transformation. If circumstances arise where a glissile interface exists but only diffusional reaction is possible, then the interface can move if reconstructive diffusion accompanies its motion. The displacive formation of bainite from austenite stops when the carbon-enriched austenite can no longer support such transformation; Bhadeshia (11) has shown that continued holding at isothermal transformation temperature causes the interfaces which initially led to displacive bainite growth to move at a much slower rate, as the residual austenite continues to diffusionally transform. Incoherent Interfaces As the misfit between adjacent crystals increases, the dislocations in the connecting interface become more closely spaced. They eventually coalesce so that the boundary consists of closely spaced 'vacancies' or 'dislocation cores'. Such a boundary is said to be incoherent; there is little correlation of atomic positions across the boundary. The motion of incoherent boundaries can only cause diffusional transformation, with no atomic correspondence between the parent and product phases. For incoherent boundaries, the free volume and diffusivity within the boundary may be sufficiently high to confine reconstructive processes to the close proximity of the boundary itself (unlike semi-coherent interfaces). Incoherent, coherent and semi-coherent boundaries can co-exist around a particle which has grown diffusionally; only semi-coherent and coherent boundaries can exist around a particle which has grown displacively. This is because if an atomic correspondence exists across a particular interface of a particle, then it necessarily does so across any other interface (7,12). Discussion We believe that the viewpoint presented above provides an adequate description of displacive and diffusional transformations, enabling phase transformations theory to be usefully applied in predicting rate-controlling processes and miorostruoture. The shape change accompanying the motion of an epitaxially semi-coherent interface does need further work to establish whether the diffusion necessary to enable the climb of intrinsic interface dislocations provides an opportunity for reconstructive diffusion to eliminate the shear component of the shape deformation.
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The implications of the shape change as discussed in the viewpoint are sometimes not accepted (e.g., Ref.13). It has been proposed that an IPS surface relief effect, of the type associated with martensitic transformations, arises even during a diffusional transformations, simply due to the existence of a sessile semi-coherent or coherent interface which is displaced by the movement of "disordered" ledges (13). The ledges themselves are considered to have an incoherent structure. We believe that this proposal is fundamentally incorrect: the very existence of an IPS relief implies co-ordinated movements of atoms, inconsistent with the concept of a diffusional transformation (and its associated reconstructive diffusion) and with the structure of the incoherent boundary (ledge) whose motion leads to transformation. Christian and Edmonds (12) have shown that the proposal also implies the existence of an atomic correspondence across just the sessile part of the interface, and this is an impossible concept since atomic correspondence is a property of the particle as a whole. The proposal also leads to detailed contradictions with experimental evidence (10,14). The second main point of controversy concerns factors determining the morphology of precipitates, especially in steels. The shape change accompanying the formation of Widmanst~tten ferrite and bainite in steels is known to be an IPS with a large shear component (15,16). The strain energy due to this shape deformation causes the plates to adopt a thin-plate morphology. Aaronson and co-workers have ignored the influence of the shape change on morphology, and instead claim that the plate morphology is a consequence of variation of interface mobility as a function of interface orientation. Their ideas do not explain the lack of a plate morphology in the case of allotriomorphic ferrite which grows diffusionally, but which can otherwise be similar to Widmanst~tten ferrite (10). References I. H. K. D. H. Bhadeshia, Progress in Materials Science 29, 321 (1985). 2. H. K. D. H. Bhadeshia, Materials Science and Technology I, 497 (1985). 3. H. K. D. H. Bhadeshia, Geometry of Crystals, Institute of Metals, London (and Brookfield, U. S. A.) (1987). 4. J.W. Christian, 'Decomposition of Austenite by Diffusional Processes', eds. V.F. Zaokay and H.I. Aaronson, Intersoience, New York, (1962) p.371. 5. M. Cohen, G.B. Olson and P.C. Clapp, Proc. of Int. Conf. on Martensitic Transformations, ICOMAT 79, Boston, Massachusetts, (1979) p.1. 6. J.W. Christian, Acta Metall., 6, 377 (1958). 7. J.W. Christian, 'Theory of Transfm. in Metals and Alloys', Pt.1, 2nd ed., Pergamon Press, Oxford, (1975). 8. E.C. Bain, Trans. AIMME, 70, 25 (1924). 9. J.W. Christian, 'Mech. of Phase Transf. in Cryst. Solids', Institute of Metals, London, Monograph 13, (1969) p.129. 10. H.K.D.H. Bhadeshia, Scrlpta Metall., 17, 1475 (1983). 1 I. H.K.D.FL Bhadeshia, Journal de Physique, 43, C4-437 (1982). 12. J.W. Christian and D.V. Edmonds, Phase Transformations in Ferrous Alloys, p.293, eds. A. R. Marder and J. I. Goldstein, TMS-AIME, Warrendale, Pennsylvania, (1984). 13. K.R. Kinsman, E. Eichen and H.I. Aaronson, Metall. Trans. A, 6A, 303 (1975). 14. H.K.D.H. Bhadeshia, Scripta Metall., 14, 821 (1980). 15. J.D. Watson and P.G. McDougall, Aeta Metall., 21, 961 (1973). 16. T. Ko and S.A. Cottrell, JISI, 307, 172 (1952).