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The interfacial structure and habit plane of proeutectoid cementite plates
Acta metall, mater. Vol. 38, No. 12, pp. 2721 2732, 1990 Printed in Great Britain
0956-7151/90 $3.00 + 0.00 Pergamon Press plc
THE INTERFACIAL STRUCTURE AND HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES G. S P A N O S 1 and H. I. A A R O N S O N 2 IPhysical Metallurgy Branch of the Naval Research Laboratory, 4555 Overlook Avenue, SW, Washington. DC 20375-7500 and 2Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. (Received 6 February 1990; in revised form 22 June 1990)
Abstract--Three groups of previous investigators independently reported the anomalous result that the austenite habit plane of proeutectoid cementite plates, as determined with optical microscopy, is not unique. The present investigation utilized transmission electron microscopy (TEM) to study the interfacial structure and habit plane of proeutectoid cementite plates in a matrix of retained austenite in an Fe-0.81% C 12.3% Mn alloy in order to explain this unusual result. The broad faces of cementite plates were found to contain two types of structural feature: (1) large, kinked ledges with heights (h) of about 7 nm and spacings (21 between 30 and 100 nm, and (2) a finely spaced set of straight ledges, with h ~ 2 nm or less and 2 ~ 445 nm, whose direction is nearly [110]g II[010]c. Matching of atom spacings showed this to be a direction of good fit between the austenite and cementite lattices. The apparent habit plane, measured with conventional TEM techniques, was always less than 10° (and in most cases less than 5°) from (IT3)A I[(101)c. Atom matching studies also demonstrated that this pair of planes exhibits superior matching, and is thus likely to provide the conjugate atomic habit planes of the terraces of ledges. Thus, the non-uniqueness of the "optical microscopy apparent habit plane" of proeutectoid cementite plates appears to arise from the presence of arrays of ledges, combined with the sympathetic nucleation of new plates, on their broad faces. R6sum6--Trois groupes de chercheurs ont ind6pendamment rapport6 le r6sultat anormal suivant: le plan d'accolement de l'aust6nite de plaquettes de ckmentite proeutectoide, d&ermin6 par microscopie optique, n'est pas unique. La pr6sente 6tude a utilis6 la microscopic 61ectronique en transmission (MET) pour &udier la structure interfaciale et les plans d'accolement de plaquettes de ckmentite proeutecto'ide dans une matrice d'aust6nite r6siduelle dans un alliage Fe-0,81% C-12,3% Mn afin d'expliquer ce r6sultat inhabituel. On trouve que les faces larges des plaquettes de ckmentite pr6sentent deux types d'aspect structural: (1) de grandes marches avec des d6crochements, de hauteurs (h) d'environ 7 nm et d'espaccments (2) variant de 30 ~ 100 nm et (2) une s6ne de marches rapproch6es, avec h = 2 nm ou moins et 2 -~ 4-6 nm, dont les directions sont presque [110]A [][010]c. Les valeurs des distances atomiques montrent que ceci est une direction de bon accord entre les r6seaux de l'aust6nite et de la c6mentite. Le plan d'accolement apparent, mesur6 par las techniques classiques de MET. est toujours fi moins de l0 ° (et dans la plupart des cas fi moins de 5°) de (1T3)g II(101)c. L'&ude des distances interatomiques montre aussi que cette paire de plans conduit ~ un accord sup6rieur et a ainsi des chances de donner des plans atomiques d'accolement conjugu6s pour les terrasses des marches. Ainsi, la non-unicit6 du "plan d'accolement apparent par microscopic optique" des plaquettes de c6mentite proeutectoide parait provenir de la pr6sence d'arrangements de marches, combin6s avec la germination par sympathie de nouvelles plaquettes sur leurs faces larges. Zusammenfassung--Drei Autorengruppen berichteten friiher unabh~ngig iiber das anomale Ergebnis, dab die Austenit-Habitebene proeutektoider Zementitplatten, bestimmt mittels Lichtmikroskopie, nicht einheitlich sei. Um dieses ungew6hnliche Ergebnis zu iiberpriifen, werden in der vorliegenden Untersuchung Grenzfl/ichenstruktur und Habitebene yon proeutektoiden Zementitplatten in einer Matrix yon Restaustenit in einer Legierung Fe4),81% C-12,3% Mn mittels Durchstrahlungselektronenmikroskopie (TEM) analysiert. Die breiten Fl~chen der Zementitplatten enthalten zwei strukturelle Merkmale: (1) groBe, gekinkte Stufen in einer H6he (h) yon etwa 7 nm und mit Abs~nden (2) zwischen 30 und 100nm (2) einen engen Satz von feinen Stufen mit h = 2 nm oder weniger und 2 = 4-6 nm, dessen Richtung nahe [110]At]010C ist. l:berlegung zur Atompassung zeigen, dab diese Richtung eine gute Passung zwischen dem Austenit- und Zementitgitter vermittelt. Die scheinbare Habitebene, gemessen mit konventioneUen TEM-Veffahren, liegt inamer innerhalb yon 10" (und in den meisten F/illen innerhalb yon 5°) yon (ll3)All(101)c weg. Die Untersuchung der Atompassung zeigt auBerdem, dab dieses Ebenenpaar besonders gut zusammenpaBt und daher wahrscheinlich auch die konjugierte Habitebene der Terassen oder Stufen vorgibt. Also scheint die Nichteinheitlichkeit der "scheinbaren Habitebene im Lichtmikroskop" der proeutektoiden Zementitplatten yon den auf den breiten Fl/ichen vorhanden Stufem kombiniert mit der zugeh6rigen Bildung neuer Platten, herzurtihren.
1. INTRODUCTION Several previous groups of investigators [1-3] have independently utilized optical microscopy to d e m o n strate t h a t proeutectoid cementite plates formed in
hypereutectoid steels have m a n y austenite h a b i t planes, to the p o i n t where the h a b i t plane seems best described as " n o n - u n i q u e " (see Fig. 1). As pointed o u t by Heckel et al. [3], this result is a n o m a l o u s with respect to m o s t theories of precipitate m o r p h o l o g y
2721
2722
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES 10 20
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and lay within about 10° of the (001)c plane (where the subscript C will be used to denote the cementite phase). Previous TEM studies of proeutectoid cementite plates have been focussed primarily on determination of the orientation relationship between austenite and cementite [9-12]. Insofar as the present authors are aware, no detailed investigation of the interfacial structure of these plates has as yet been reported; although recently Cowley and Edmonds observed "linear defects" which exhibited "periodic image contrast" along cementite plates in an Fe-0.76% C-12.0% Mn steel [13]t. Pitsch [9, 10] obtained the following orientation relationship between cementite plates and the austenite matrix in an Fe-l.3% C-12.0% Mn alloy [lOO]c II [5~4]h
10
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Fig. 1. Results of previous investigations exhibiting the "non-uniqueness" of the apparent habit plane measured by optical microscopy. (a) Mehl et al. [1]; (b) Heckel et al. [3]. [1,4-6] as well as extensive experimental evidence in many other alloy systems [7, 8]. During the first two studies [1, 2], the habit plane of the broad faces of cementite plates was determined by indirect optical methods (since the remaining austenite matrix had transformed to martensite and/or to pearlite), while the third investigation [3] used X-ray diffraction to determine directly the orientation of the matrix (utilizing the small amount of austenite retained at room temperature). In none of these investigations were the planes in the c e m e n t i t e lattice, conjugate to the observed austenite habit planes, reported. However, Mehl et al. [1] dissolved away the matrix in which two cementite plates were embedded and utilized X-ray diffraction to show that the broad faces of the plates, as observed by optical microscopy, were "irregular" tUnless otherwise specified, all compositions reported in this paper are in wt%.
where A refers to the austenite matrix. In addition, Pitsch reported austenite habit planes, based on measurements made at a matrix of 20,000 x magnification, which again exhibited considerable variation from one plate to another. In a commercial steel, Thompson and Howell [11, 12] recently obtained a presumably different orientation relationship, but one which is similar in some respects to that of Pitsch. The purpose of the present investigation was to examine the crystallography a n d the interfacial structure of the broad faces of cementite plates in order to ascertain whether or not the habit plane, expressed relative to both the austenite a n d the cementite lattices, is really non-unique, particularly when considered on a near-atomic scale. A hypereutectoid, high-manganese Fe-C-Mn alloy was employed in order that the Ms lie well below room temperature and thus permit complete retention of the austenite matrix even in thin foils and in the carbon-depleted regions in contact with cementite plates. An examination of the atomic matching between various pairs of parallel (or nearly parallel) planes and directions in the austenite and cementite lattices was also undertaken in order to interpret the experimental results and complete deduction of the most probable conjugate atomic habit planes. It will now be useful to define three terms which will be used throughout the remainder of this paper. (1) The atomic habit plane (AHP) refers to the atomic-level habit plane corresponding to the terraces of ledges at an interphase boundary (see Fig. 2). (2) The TEM apparent habit plane (TApHP) is defined as the apparent habit plane, determined with conventional TEM techniques, passing through successive ledge terrace/riser intersections (see Fig. 2). (3) The optical apparent habit plane (OAHP) is the apparent habit plane evaluated by optical microscopy.
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES T~HP
~::r~i..~ g~"-i
~
~.P
Fig. 2. Schematic illustration of the TEM apparent habit plane (TApHP) and the atomic habit plane (AHP). 2. EXPERIMENTAL AND LATTICE MATCHING PROCEDURES
2.1. Experimental procedures The composition of the hypereutectoid F e 4 2 - M n alloy employed is given in Table 1. The isothermal heat treatment procedure is given in Ref. [14]. The isothermal reaction temperatures and times were chosen to ensure observation of sufficient numbers of cementite plates with TEM. Most studies were performed on specimens isothermally reacted at 500°C for 8 h; a single result is also reported, however, from a 550°C-2 h treatment. Discs 3 mm diameter x 0.25 mm thick were sparkcut from the heat treated specimens with an electrodischarge machine, using a hollow copper electrode, in order to avoid introduction of dislocations into the austenite matrix. The discs were then electrodished and finally jet polished in a twin-jet Fischione unit following the procedure of Hackney and Shiflet [15]. A second jet polishing technique, reported by Thompson and Howell [11], was also successfully employed and yielded somewhat better results. A brief summary of the trace analysis methods utilized to ascertain ledge directions and habit plane orientations relative to both the austenite and the cementite lattices will now be presented. The method for determining ledge directions is the following. (1) Obtain a Kikuchi pattern [16], a selected area electron diffraction pattern, and bright-field and/or dark-field images of the ledges using beam directions corresponding to slight tilts (so as to obtain two-beam diffraction conditions) from at least three zone axes in the austenite. Although only two zones are actually required for the trace analysis [17], at least three zones were always employed to ensure consistency. (2) Label the Kikuchi map and diffraction patterns relative to a standard f.c.c. Kikuchi triangle [18]. (3) Tilt to (or close to) parallel zone axes in austenite and cementite and obtain a selected area electron diffraction pattern, in order to ascertain the relative orientations of the cementite and austenite lattices. (4) Perform conventional trace analysis [17], using the information from steps (1) and (2), to determine the ledge direction in the austenite; the particular variant chosen is dictated by the standard Kikuchi triangle used in step (2). (5) Re-label the f.c.c. Kikuchi triangle Table 1. Alloy composition(wt%) C
0.81
Mn
12.3
P
0.0003
S
0.0006
2723
so that it is of the "correct" crystallographic variant in austenite corresponding to the common representation of the Pitsch orientation relationship (see Section 3.2 below), as determined in step (3). (6) Based on this triangle, choose the correct austenite variant of the ledge direction and the parallel direction in cementite, so that they correspond to the orientation relationship determined in step (3). The TEM apparent habit plane (TApHP) corresponding to the broad faces of cementite plates was determined by a similar technique to that employed for austenite:ferrite interfaces [19]. This procedure is as follows. (1) Ascertain the ledge direction as described in the preceding paragraph. (2) Determine the direction of the line of intersection between the plate and the foil surface by the method outlined above for the ledge direction. (3) Since both directions obtained in steps (1) and (2) must lie in the TApHP, determine the point of intersection of their great circles on a stereographic projection (or equivalently, calculate their cross product), which thus defines the TApHP. Since the "fine ledges" analyzed were usually so closely spaced and often had such small riser heights, it was impossible to determine unambiguously the line of intersection between their terrace plane and the foil surface for three austenite zones. Hence, this method could not be used to determine directly the atomic habit plane (AHP). On one cementite plate, this method was checked for consistency by re-determining the habit plane through application of a second procedure. The plate was tilted edge-on and the TApHP was determined by direct comparison with the corresponding diffraction pattern. The two methods yielded results within 3° of each other. Ledge heights were determined by utilizing an equation due to Gleiter [20], based on the measured displacement of interface fringes: h = m" sin ~ ' sin fl
(1)
where h = ledge height, m = fringe spacing, ~ = the angle between the thickness fringes and the projection of the ledges, and fl = the angle between the interphase boundary plane and the surface of the thin foil.
2.2. Lattice matching method A brief description of the procedure employed to determine parallel directions and planes of good matching between the austenite and cementite lattices will now be presented. In general, only the substitutional or M ( = Fe, Mn) atoms, were considered, as in a similar previous study [1]. This simplification appears to be required, since the interstitial sites utilized by carbon are incompletely occupied in the austenite lattice. Further, if the substitutional sites match between the two lattices along a given direction or plane, their interstices should lie in similar positions as well. The austenite and cementite lattices were taken to obey the Pitsch [9, 10] orientation relationship (see Section 3.2 below). The following lattice parameters for cementite were utilized: ac = 0.452 nm,
2724
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
L
70 nm
!
Fig. 3. Examples of coarse ledges, pointed out by arrows, near the edge of a cementite plate. b c = 0 . 5 0 9 n m and cc=0.674nm [21]. The corresponding lattice parameter of austenite was then deduced by analysis of selected area electron diffraction patterns which exhibited both austenite and cementite reflections. This procedure was employed since only the relative values of misalignment and/or misfit between austenite and cementite atoms were compared in this analysis (see Section 4), and accurate lattice parameter data for cementite and austenite as a function of temperature, carbon and manganese concentrations are not available. The atomic position coordinates for cementite were taken from Pearson [22]. In order to determine the quality of atomic matching between parallel planes in the two lattices, each lattice was sectioned along the appropriate plane and the atom positions were delineated graphically with the aid of a computer. Planar "slices" at very small distances ( < 0.1 nm) normal to this plane were also sometimes considered for the cementite lattice; the component atoms were then projected onto this plane. Such a procedure appeared necessary because the complexity of the cementite lattice (see Fig. 2 of Ref. [23]) makes the spacing between certain adjacent parallel planes quite small.
is seen to be accentuated along the line of intersection of the plate with the foil surface (see arrows in Fig. 3). Coarse ledge heights were determined to be approximately >~7nm while ledge spacings varied widely, but were in the range of 30-100 nm. Fine linear features were also repeatedly observed on the broad faces of cementite plates, as shown in Fig. 4. These features also exhibited the fringe displacements characteristic of ledges [20]. They exhibit a step-like appearance at the intersection of the interphase boundary with the foil surfaces where they terminate [see Fig. 4(a)]. Hence, this set of features probably is best described as ledges rather than interfacial dislocations, and thus will be referred to as "fine ledges" in the remainder of this papert. The fine ledges were usually much straighter and more uniformly spaced than the coarse ledges, with h ~ 2 nm or less$, and spacings between 4 and 6 nm. It is apparent from Fig. 4(a) that the atomic habit plane (AHP) corresponding to the terraces of the steps is different from the TEM apparent habit plane (TApHP), and that there are local variations in the TApHP due to changes in the inter-ledge spacing, 2 (and possibly also the ledge height). Figure 4(b) is another example of the stepped contrast from the fine ledges. Note the gradual change in the TApHP as ). decreases, effectively stepping the interface upward more sharply. Larger coarse ledges are pointed out by large arrows in Fig. 5. They may have resulted from
3. EXPERIMENTAL RESULTS 3.1. T E M observations o f interfacial structure Interfacial structure studies of the broad faces of cementite plates revealed two general types of feature. Coarse (i.e. of relatively large height) irregularly spaced ledges were observed at the broad faces (e.g. see Fig. 7 of Ref. [14]) and near the edges of cementite plates (Fig. 3). Note the displacement of interference fringes as they cross the ledges. This type of contrast is due to the difference in thickness of the terraces on either side of a riser and has been described in detail by Gleiter [20]. The stepped contrast of the interface tSome consequences of their alternate interpretation as dislocations are discussed in Section 6.3. :[:Someof the fine ledges appeared to have heights less than 2 nm, but the fringe displacement and/or step height was too small to permit accurate measurements to be made.
Fig. 4. Examples of "fine ledges", pointed out by arrows, at the broad faces of cementite plates. (a) TEM bright field micrograph revealing "fine ledges" at the austenite:cementite interface; (b) TEM dark field micrograph, taken from a I l l A reflection, also exhibiting the stepped nature of the interface.
SPANOS and AARONSON:
HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
Fig. 5, TEM dark field micrograph taken from a Ill A reflection revealing coarse ledges (large arrows) which may have formed due to accumulation of a finer set of ledges. coalescence of what appear to be a finer set of ledges (small arrows) which exhibit white on dark strain field contrast. This type of contrast has been demonstrated by Hackney and Shiflet [15] at ledges on the edges of pearlite colonies. Ledges and kinks have also been observed at a cementite:cementite boundary considered to be a remnant of the original austenite:cementite interface, before it was converted into a low-angle cementite:cementite boundary by the sympathetic nucleation [24, 25] of a second cementite crystal [14].
3.2. Crystallography and quantitative TEM results The orientation relationship between the cementite plates and the austenite matrix, as determined by analysis of selected area electron diffraction patterns from 8 different plates, was always within a few degrees of the Pitsch [9, 10] orientation relationship (e.g. see Fig. 6). The new orientation relationship recently reported by Thompson and Howell [11, 12] was not observed. This could be due to the significant difference in the alloy compositions used in the two investigations. Their steel contained 1.09% C, 2.3% Mn, 0.28% Cr, 0.26% Si and 0.18% Ni. Quantitative TEM analysis was performed on five plates upon which the fine ledges at the broad faces of the plates were not obscured by systems of coarse ledges. The fine ledge direction was determined relative to both the austenite and cementite lattices by the trace analysis method described in Section 2.1. An example of the intermediate results is presented in Figs 6-8. A typical selected area diffraction pattern required to determine the cementite orientation relative to the austenite matrix is presented in Fig. 6. Figure 7 is an example of the Kikuchi pattern obtained from the austenite matrix adjacent to the plate in Fig. 4(a~. Figure 8 demonstrates the three traces and their intersection, corresponding to the fine ledge direction for this particular example. The fine ledge direction determined in this manner was always very close to [I10]AII[010]C. It was 2° or less from [110]AII[010]c on four plates and about 5° from this direction on the fifth plate. Based on the average scatter in the intersections of the traces taken from each interface, it is estimated that the maxi-
2725
mum experimental error introduced during the trace analysis procedure is about 2 °. These results are represented stereographically in Fig. 9. The TEM apparent habit plane (TApHP) across the fine ledges on four of these plates (not enough information was obtained on the fifth) was determined using the procedure previously outlined. Due to local variations in the TApHPs, e.g. see Section 3.1 and Fig. 4(a) and (b), the habit plane trace analysis was always performed on a relatively planar portion of the interphase boundary. The results are presented in Fig. 10. The TApHP were within 5~' of (li3)A 11(101)¢ for three of the plates and about 10" from these planes for the fourth plate. 4. LATTICE MATCHING ANALYSIS The substitutional atoms ( M = F e , Mn) were found to exhibit particularly good matching between the austenite and cementite lattices along the [110]A II[010]C direction, as demonstrated in Fig. 11. The relative interatomic spacings are 0.253 nm in this direction in the austenite lattice, as compared to 0.254 nm for the parallel direction in cementite. However, the matching is not quite as good as this statement implies, since every other M atom in the cementite lattice is "shifted" by about 0.07 nm in the [100]c direction, i.e. normal to the "good matching" direction (Fig. 11).
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Fig. 6. A typical selected area electron diffraction pattern corresponding to the Pitsch orientation relationship [9, 10].
2726
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
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\ Fig. 7. A portion of the f.c.c. Kikuchi map taken from the austenite matrix adjacent to the cementite plate shown in Fig. 4(a). The quality of matching was investigated for various pairs in the two lattices in order to ascertain the most likely candidate(s) for the atomic habit plane (AHP). Since, from geometrical considerations, the fine ledge direction must lie in the A H P (i.e. the
[1101~ Fig. 8. Traces of the fine ledges shown in Fig. 4(a), indicating their direction, relative to both austenite and cementite. BL, B2 and B3 correspond to the electron beam directions (or zone axes used) and UI, U2 and U3 represent the projected ledge directions.
terrace plane), the survey was restricted to seven pairs of relatively low index planes which contain the experimentally determined [110]A II[010]c conjugate directions and which are within about 6 ° of being parallel in the presence of the Pitsch orientation relationship (or, alternatively, are parallel at deviations of approximately 6 ° or less from the Pitsch
11101A 0|/10+1~c Fig. 9. Fine ledge directions measured for five plates superimposed on a [101]A stereographic projection. Note that in all cases the ledges lie very close to [ll0]A U[010]o
SPANOS and AARONSON:
HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
2727
[110]A
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Fig. 11. Illustration of atomic positions of substitutional atoms (Fe, Mn) along the [010]c and [110]A directions.
Fig. 10. [110]A II[010]c stereographic projection with poles of experimentally determined TApHPs.
orientation relationship). These plane pairs are represented stereographically in Fig. 12. The pair of conjugate plains which exhibits the best matching is (lI3)A II(101)C (Fig. 13). These two planes are within 1° of being parallel in the presence of the Pitsch orientation relationship. Normal to the [110]A IJ[010]C "good fit" direction within the interface, i.e. in the [~32]A II[I01]C direction, there is also
relatively good matching. The misfit in this direction is 3.9%, corresponding to an extra half plane of atoms every 10.6nm. Two complications should, however, be considered. The previously discussed "shift" in the [100]c direction of every other atom lying in the row parallel to [110]A II[010]C is such that the "shifted" atoms lie slightly (0.06 nm) out of the plane (i.e. the x atoms in Fig. 13). Secondly, every other row of atoms lying along the [ll0]AII[010]C direction exhibits an additional small misalignment of about 0.01 nm in that direction (see row B of Fig. 13). Despite these complications, this interface was found
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2728
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
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to exhibit the best matching of all those investigated, and thus was concluded to be the best candidate for the conjugate atomic habit planes. The (I13)AIl(001)c plane pair was suggested by Mehl et al. [1] (long before Pitsch's [9, 10] determination of the orientation relationship) as a possible interface of good matching. For this pair to be perfectly parallel, a 4.5 ° deviation from the Pitsch orientation relationship is required; this is much greater than the <1 ° angle needed by the (Ii3)A II(101)c pair. Mehl et al. [1] found good matching between the (T13)AII(001)c planes in only one direction. Moreover, their model corresponds to an additional rotation, in the interface, of 16 ° from the Pitsch orientation relationship. During the present analysis, matching of the (il3)AIl(001)c planes was re-examined on the assumption that there is no "in-plane" deviation from the Pitsch orientation relationship; such a deviation is contrary to the experimental observations made on the present alloy (see Section 3.2 and Fig. 6) as well as to those previously reported by Pitsch [9, 10]. Again, there is good fit along the [II0]AII[010]C direction, and in this case, the 0.07 n m "shift" of every other atom takes place within the interface. The misfit in the interface in the direction normal to [110]A II[010]c, now [~3~]A II[100]c, is 7%, corresponding to an extra half plane of atoms approximately every 6.2 nm. This is considerably worse than for the analogous direction in the (lI3)AIl(001)c interface (compare Figs 13 and 14). In addition, every other row of atoms parallel to [110]A II[010]C now exhibits a misalignment of 0.125 n m in that direction, almost half the interatomic spacing of 0.254 n m (see row B of Fig. 14). This disregistry is much greater than the
0.01 n m misalignment observed at the (1T3)A II(001)c interface (see row B of Fig. 13), and would probably result in a very high energy interface, since every other row would contain substitutional atoms lying in essentially interstitial positions relative to the lattice on the opposite side of the interface. The only other interface which exhibited possibly significant matching in the direction normal to [110]A II[010]C is that corresponding to the (I10)A II(10T)c planar pair. The misfit in that direction is about 11.8%, corresponding to an extra half plane of atoms every 3.2 nm. This misfit is appreciably larger than the corresponding misfit in either of the other two conjugate pairs disucssed above. The present pair of planes also requires a 4 ° deviation from the Pitsch orientation relationship in order to be exactly parallel; again, this seems rather large. N o other interfaces, amongst those studied, exhibited adequate matching in the direction normal to [110]A II[010]c • 5. COMPARISON OF LATTICE MATCHING ANALYSIS WITH EXPERIMENTAL RESULTS A comparison of the experimental results and the lattice matching studies reveals that the fine ledges analyzed by T E M always lie essentially parallel to the particular variant of the close packed direction in austenite determined by the lattice matching analysis to exhibit good fit between the two lattices, i.e. the [110]A H[010]C direction (compare Figs 9 and 11). This is consistent with the model of the broad faces of cementite plates now to be developed. By definition, the fine ledge direction must lie within the terrace plane, i.e. the AHP, of the fine ledges (see Fig. 2). This plane should be an immobile, low energy interface ,I.° + ° . 4.22
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SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES [26], and would thus be expected to contain the direction of good atomic matching. As demonstrated in Fig. 10, the T A p H P was close to (lI3)AIl(101)c on all four of the plates at which both the fine ledges and the TApHPs were analyzed. Also as previously mentioned, the angular deflection of the TApHPs from the (1T3)A I1(101)c planes was usually 5° or less, and was 10° for one plane analyzed. These deviations are within the possible range estimated due to the presence of the fine ledges, ~< 26 °, deduced using ledge spacings and heights measured with TEM (see Section 3.1). Alternatively, the other two plane pairs which exhibited any reasonable matching normal to the [ll0]AII[010]C direction, (1T3)A II(001)c and (II0)A II(10T)c, deviated by much greater angles, as large as 61 and 70 °, respectively, from the experimentally determined TApHPs (compare Figs 10 and 12). These angles appear to be too great to be accounted for by the presence of ledges. Hence, based on the current experimental findings, the (1 ]'3)A [ (101)c plane pair appears to be the only plausible candidate for the AHP. This conclusion is in agreement with the results of the lattice matching analysis, in which it was demonstrated that the (1T3)A II(101)c pair provides the best atomic matching (of the seven conjugate pairs considered) between the two lattices (see Section 4). Finally, with the exception of (~25)A H(001)c, which yields no matching at all normal to the "good fit" direction and lies as much as 65 ° from the experimentally determined TApHPs, the (ll3)AII(101)C pair exhibits the smallest deviation ( < 1° as compared to ~>4 ° for all other possible pairs) from the repeatedly observed Pitsch orientation relationship (see Section 3.2 and Refs [9, 10, 14]), as demonstrated in Fig. 12. Hence, the present experimental observations, lattice matching analysis and the coincidence of this plane pair with the observed orientation relationship all strongly indicate that the atomic habit plane of proeutectoid cementite plates is (I13)A II(101)c6. DISCUSSION The results of this investigation suggest that ledges can cause differences between the TApHP and AHP of proeutectoid cementite plates (see Fig. 2). Face-to-
J
TApHP
Fig. 15. Schematic illustration of the OAHP and the TApHP of an aggregate of plates formed by face-to-face sympathetic nucleation. The OAHP of an aggregate is dictated by the TApHPs (which are determined by the ledge heights and ledge spacings, Fig. 2) and by the dimensions and relative positions of all the crystals in the array.
2729
Fig. 16. TEM micrograph showing ledges apparently being emitted from a cementite:cementite:austenite junction. face sympathetic nucleation [14] can evidently produce further deviation of the OAHP from the AHP, since the OAHP of an aggregate of sympathetically nucleated crystals can differ from the TApHP of the individual crystals in such an array, as demonstrated schematically in Fig. 15. In this vein, differences between the OAHP and the TApHP have also been reported for "stacks" of f-hydride (ZrHLs) plates formed in Z r - 2 . 5 % N b and in a Zrq2.11.0% Nb-3-3.5% Sn4).8-1.0% Mn alloy [27]. We now note that sympathetic nucleation can also expedite ledge formation at the junctions between "substrate" and sympathetically nucleated crystals [28, 29], in the same manner that ledges are generated at the intersections of impinged plates [30-33]. Figure 16 shows ledges being emitted from a cementite:cementite:austenite junction between two cementite plates, one of which was presumably nucleated sympathetically at the other. It appears from this micrograph that the ledges on the right side are travelling away from the junction between the two cementite plates, since they are stepped "down" from the source, corresponding to growth of the cementite plates into the austenite matrix. Hence, sympathetic nucleation may also affect the TApHP by increasing the ledge density on the broad faces of individual plates. 6. I. Previous habit plane investigations
The "non-uniqueness" of the optical apparent habit plane (OAHP) of cementite plates previously reported [1-3] will now be considered in more detail. The most direct results [3] of these investigations indicate that the OAHPs, reported relative to the austenite lattice only, lie in a group centered approximately about a {521}A plane, which lies only 8 ° from a { 113}A type plane [Fig. 1(b)]. The range of angular deviations from the {l13}A for 99% of the planes measured by Heckel et al. [3] is 0-15 ° [see Fig. l(b)]. The results of the more indirect study by Mehl et al. [1] also indicate that the OAHP always lies within 15 ° of a { 113}A plane. In addition, Cowley and Edmonds [13] recently reported TApHPs within 5° of {113 }A in an Fe-0.76% C-12.0% Mn alloy. These results are
2730
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
all consistent with the present deduction that the atomic habit plane (AHP) is (II3)AH(101)c. These deviations from {l13}A are within those previously discussed due to the presence of ledges, and probably also arise at least in part due to face-to-face sympathetic nucleation. It should be pointed out that as a result of the techniques employed, the previous investigators were able to report the habit plane relative to a general variant in the austenite lattice only, while the current TEM study determined the exact variant of the habit plane, relative to both austenite and cementite. The optical observation by Mehl et al. [1] that the "irregular" broad faces of two cementite plates isolated from the matrix were within about 10° of (001)c is in contrast to the present findings, and may again be a result of differences between the AHP and OAHP. Some differences between the previous habit plane investigations [1-3] and this one should, however, be briefly noted. The alloy compositions were considerably different, and the previous investigators employed continuous cooling transformation while isothermal reaction was utilized here. Continuous cooling is expected to increase the frequency of sympathetic nucleation, since the driving force for nucleation is continuously increasing with time. This factor should induce further scatter in the OAHPs. 6.2. The nature of the features observed at the austenite :cementite interface The coarse, often kinked [14], ledges are morphologically similar to growth ledges observed on a wide variety of precipitate plates in many alloy systems [26, 34] and presumably serve the same function. On the other hand, the fine ledges are very similar in appearance to and have heights similar to the "direction steps", observed on ferrite:cementite (c¢:C) interfaces in pearlite [35]. These steps were shown to cause local deviations of the pearlite lamellae from (113),11(001)c [35], in the same manner as the rotations of the TApHP away from (1T3)AII(101)c at the broad faces of cementite plates observed in the present investigation. The possibility that the fine ledges are structural ledges [19, 36, 37] will now be considered. Their linear appearance is consistent with this interpretation [19]. However, studies of f.c.c.:b.c.c. [19] and b.c.c.:h.c.p. [38] interfaces have demonstrated that the interplanar spacings in the direction normal to the structural ledge terraces must be essentially equal in the two phases and that the risers of structural ledges are usually between one and four atomic planes high. In contrast, the interplanar spacings normal to the (li3)^ll(101)c terraces are very dissimilar in the austenite and cementite lattices (see Fig. 17). In addition, the height of the fine ledges (approximately 2 nm or less) can be considerably greater than the (1T3)AIl(101)c interplanar spacings. Unless special circumstances intervene, such dissimilar interplanar spacings and relatively high risers would thus seem
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Fig. 17. Illustration of relative interplanar spacings in austenite and cementite normal to (1~3)A[1(101)c. not to provide the most efficient arrangement, from the standpoint of interracial energy, for causing the repetition of coherent regions at shorter lateral distances, the usual function of structural ledges [36]. 6.3. On the Compensation of misfit at (173)A II (lO1)c The question then arises as to how the misfit between the austenite and cementite lattices is accommodated at the (II3)AII(101)C interface. It may be possible that the fine ledges lying along [110]a II [100]c could provide at least some misfit compensation, and thus might also be interpreted as dislocations, as in the case of Shockley partial "dislocation/ledges" on the broad faces and edges of y' (h.c.p.) plates precipitated from an f.c.c, matrix in an A1-15% Ag alloy [30, 39]. The Burgers vector of these dislocation/ ledges lies in the atomic habit plane [30, 39] and can thus accommodate misfit. Misfit compensating ledges apparently also play a role at fl(b.c.c.):~t(h.c.p.) interfaces corresponding to the broad faces of proeutectoid ct plates and grain boundary allotriomorphs in a Ti~i.62 at.% Cr alloy [38]. The complexity of the cementite lattice (see Ref. [23]) limits the possibilities of modelling the "fine ledges" at austenite:cementite interfaces as dislocations; as far as the present authors are aware. Burgers vectors for dislocations in cementite have yet to be reported, either theoretically or experimentally, nevertheless, considering for the moment only the austenite lattice and possible unit (1/2(110)) or partial (1/6(112)) dislocations lying in the (II3)A II(010)c interface, 1/21110]AII[101]C is the only 1/2(110) type Burgers vector lying in this plane. It lies along the "good fit" direction and would thus not accommodate any misfit in the direction of "poorest fit", [~32]AII[T01]C- There are two possible Shockley partial dislocations lying in this interface, 1/61i21] and 1/612ii], but there are no rational directions in the cementite lattice corresponding to these austenite directions (following the Pitsch [9, 10] orientation relationship). Thus, even though ledges at interphase interfaces can often be interpreted equivalently as dislocations [30, 38, 39], in the present case, a complete dislocation description of the "fine ledges" is not readily apparent. 6.4. Comparison with habit plane behavior in other transformations The last major question to be considered is why the non-uniqueness of the OAHP [1-3] should appear to
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
Fig. 18. TEM dark field image taken from a 220A reflection revealing four cementite plates in the face-to-face morphological arrangement. characterize only proeutectoid cementite plates. One possible explanation for this is that face-to-face sympathetic nucleation may occur much more readily during the formation of cementite plates than in other precipitation processes so far examined from this viewpoint. This mode of sympathetic nucleation was thus observed with TEM at the majority of plates examined in this investigation. Figure 18 is a typical example of four plates stacked atop one another in this mannert. In contrast, in Ti-X alloys transformed at high reaction temperatures, proeutectoid ~(h.c.p.) plates obeying the Burgers [40] orientation relationship with the fl(b.c.c.) matrix and exhibiting a near{111}~ habit plane, frequently exhibit sympathetic nucleation, but predominantly in the edge-to-edge and edge-to-face modes [25]. These forms of sympathetic nucleation should have a negligible effect on the OAHP. In particular, the habit planes of individual precipitate crystals in edge-to-face arrangements should be much easier to identify separately, even with optical microscopy (see Fig. 2 of Ref. [14]). On the other hand, face-to-face sympathetic nucleation, resulting in the formation of "sheaves" of plates, has been well documented during the formation of both upper bainite [24,41] and lower bainite [41,42]. The scatter in the habit plane of bainite plates when examined with optical microscopy at a given temperature and its gradual change x~ith decreasing temperature [8, 43] thus seem #Although some of the plates in Fig. 18 appeared to be separated from one another (e.g. plates Nos 1 and 2), when they were followed far enough back in the foil, a point of contact was almost always observed (e.g. plates Nos 2 and 3); in the few cases where it was not, it is believed that the plates were probably in contact either in the thicker, non-transparent regions of the thin foil, or above or below the plane of the foil. Additionally, impingement was minimized by employing relatively small undercoolings and short isothermal reaction times; both of which avoided a high number density of individually nucleated cementite plates [14].
2731
likely to result at least in part from physically meaningless OAHPs established by face-to-face sympathetic nucleation (see Fig. 15). Variations in the modes and kinetics of sympathetic nucleation with temperature could easily contribute to changes in the OAHP of sheaves. Hence, the behavior of the OAHP of cementite plates seems not to be entirely "unique", and may well be found in still other alloy systems when more detailed experimental studies are extended to them. Another source of the non-uniqueness of the cementite OAHP may be the relatively high h/2 ratio of ledges on the broad faces of these plates, since tan 0 = hi2 (where 0 is the angle between the TApHP and the AHP). In particular, this ratio can be especially high for the fine ledges, ~< about 0.5, as a result of their relatively small values of 2. By comparison, h/2 falls in the range of 0.0144).029 for ledges on y A1-Ag 2 plates [44] and 0.158-0.325 for the closely spaced structural ledges on ferrite plates [19]. It should be noted that these data are not only quite limited but also exhibit appreciable scatter. While experimental data on hi2 are not yet available on a wide range of diffusional transformations, this remains another possible reason why a non-unique OAHP may be more evident for proeutectoid cementite plates than for plates in other alloy systems. A third cause of non-uniqueness may be that multiple habit planes do exist, even at the atomic level. Although the deduction of the present investigation is that (li3)A 11(101)c represents the unique conjugate atomic habit planes of cementite plates, this remains to be confirmed with atomic resolution techniques. It is anticipated that this experiment may prove to be difficult to perform in the present alloy system, however, due to difficulties of obtaining TEM foils with extremely thin areas, which are required for such studies, in both the austenite and (particularly in) the cementite phases. Notwithstanding, the current results do make a non-unique AHP for cementite plates seem considerably less likely than before. 7. CONCLUSIONS The interfacial structure, habit plane and orientation relationship of proeutectoid cementite plates in an Fe-0.81% C-12.3% Mn alloy have been investigated with transmission electron microscopy, supplemented with optical microscopy. The Pitsch [9, 10] orientation relationship was shown to be obeyed. The broad faces and edges of these plates were found to be ledged. Two types of features were observed: (1) coarse ledges with h (height) on the order of 7 nm and widely varying spacings, 2, in the range 30-100 nm, and (2) finer, straighter ledges with h ~ 2 nm or less and 2 in the range of 4-6 nm. TEM analysis on relatively planar portions of the broad faces of cementite plates, selected so as to avoid complications in determining the habit plane due to undulations sometimes observed at these
2732
SPANOS and AARONSON:
HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
broad faces as a result of variations in ledge spacings (and presumably heights), revealed the fine ledge direction to be [110]A II[010]C. Lattice matching studies, accomplished by superimposing substitutional atom positions in the cementite and austenite lattices, revealed this to be a direction of " g o o d fit" between the two structures. Similar studies of pairs of planes sharing the [ll0]All[101]c zone axis showed that (Ii3)A II (101)c is by far the most closely matching and thus the most probable pair of conjugate atomic habit planes (AHPs) corresponding to the terraces of ledges. In agreement with this analysis, T E M apparent habit planes (TApHPs), i.e. those measured by conventional T E M methods, were always less than 10 ° (and in most cases less than 5 °) from (li3)A II(101) c, while they were between 50 and 61 ° from the next closest conjugate pair exhibiting any reasonable atomic matching. In addition, the (li3)A II(101)c plane pair exhibits the smallest deviation, < I °, from the Pitsch orientation relationship [9, 10]; all other viable conjugate pairs investigated by lattice matching are 4 ° or more from being parallel in the presence of this relationship. Although the possibility remains that true deviations of the atomic habit plane (AHP) from (li3)A II(101)c exist, it was concluded that the well established [1-3] non-uniqueness of the observed habit plane of proeutectoid cementite plates is most likely due to two effects: (1) the presence of ledges which can yield substantial deviations from the atomic habit plane, in the same manner as similar ledges observed on ferrite:cementite interfaces in pearlite [35], and (2) the strong tendency for face-toface sympathetic nucleation, which can cause substantial further deviations. Particularly when the apparent habit plane is measured with optical microscopy or low resolution T E M , the habit plane of the resulting composite plate can easily be mistaken for the AHP. Acknowledgements--The authors express their appreciation to the National Science Foundation for support of this work through grant DMR81-19507 to the CMU MRL; the (partial) funding support of the contributions of G. Spanos by the Office of Naval Research is also gratefully acknowledged. The authors also wish to thank Professor Gary Shiflet (University of Virginia) for supplying the Fe4).81% C-12.3% Mn alloy and Dr Tael Kim for use of computer programs which were subsequently modified for the lattice matching analysis. Finally, appreciation is expressed to Dr Tadashi Furuhara and Professor W. T. Reynolds Jr for many helpful discussions.
REFERENCES 1. R. F. Mehl, C. S. Barrett and D. W. Smith, Trans. Am. Inst. Min. Engrs 105, 215 (1933). 2. A. B. Greninger and R. Trioiano, Trans. Am. Inst. Min. Engrs 140, 307 (1940). 3. R. W. Heckel, J. H. Smith and H. W. Paxton, Trans. Am. Inst. Min. Engrs 218, 566 (1960). 4. C. S. Barrett, The Structure o f Metals. McGraw-Hill, New York (1952).
5. H. I. Aaronson, The Mechanism o f Phase Transformations in Crystalline Solids, pp. 270-281. Inst of Metals, London (1969). 6. H. W. Paxton, J. chem. Phys. 26, 1769 (1957). 7. A. H. Geisler, Phase Transformations in Solids, pp. 387-535. Wiley, New York (1951). 8. J. S. Bowles and C. S. Barrett, Prog. Met. Phys. 3, 1 (1952). 9. W. Pitsch, Acta metall. 10, 897 (1962). I0. W. Pitsch, Arch. Eisenhiitt. 34, 381 (1963). 11. S. W. Thompson and P. R. Howell, Scripta metall. 21, 1353 (1987). 12. S. W. Thompson and P. R. Howell, Scripta metall. 22, 229 (1988). 13. S. A. Cowley and D. V. Edmonds, Proc. 1987 Solid-Solid Phase Transformations Conf. (edited by G. Lorimer), pp. 459-461. Inst. of Metals, London (1988). 14. G. Spanos and H. I. Aaronson, Scripta metall. 22, 1537 (1988). 15. S. A. Hackney and G. J. Shiflet, Acta metall. 35, 1007 (1987). 16. S. Kikuchi, Japan J. Phys. 5, 83 (1928). 17. M. H. Loretto and R. E. Smallman, Defect Analysis in Electron Microscopy. Wiley, New York (1975). 18. G. Thomas and M. J. Goringe, Transmission Electron Microscopy o f Materials. Wiley, New York (1979). 19. J. M. Rigsbee and H. I. Aaronson, Acta metall. 27, 365 (1979). 20. H. Gleiter, Acta metall. 17, 565 (1969). 21. K. W. Andrews, J. Iron Steel Inst. 203, 721 (1965). 22. W. B. Pearson, Handbook of Lattice Spacings and Structures o f Metals and Alloys. Pergamon Press, Oxford (1958). 23. S. B. Hendricks, Z. Kristallogr. 74, 534 (1930). 24. H. I. Aaronson and C. Wells, Trans. Am. Inst. Min. Engrs 206, 1216 (1956). 25. E. S. K. Menon and H. I. Aaronson, Acta metall. 35, 549 (1987). 26. H. I. Aaronson, C. Laird and K. R. Kinsman, Phase Transformations, pp. 313-396. Metals Park, Ohio (1970). 27. V. Perovic, G. C. Weatherly and C. J. Simpson, Acta metall. 31, 1381 (1983). 28. H. I. Aaronson, H. B. Aaron and K. R. Kinsman, Metallography 4, 1 (1971). 29. H. I. Aaronson, D. Eylon and F. H. Froes, Scripta metall. 21, 1241 (1987). 30. J. M. Howe, H. I. Aaronson and R. Gronsky, Acta metall. 33, 639 (1985). 31. R. Sankaran and C. Laird, Acta metall. 22, 957 (1974). 32. G. C. Weatherly, Can. Metall. Q. 8, 105 (1969). 33. U. Dahmen and K. H. Westmacott, Physica status solidi (A) 80, 249 (1983). 34. H. I. Aaronson, J. Microsc. 102, 275 (1974). 35. S. A. Hackney and G. J. Shifiet, Acta metall. 35, 1019 (1987). 36. M. G. Hall, H. I. Aaronson and K. R. Kinsman, Surf. Sci. 31, 257 (1972). 37. J. M. Rigsbee and H. I. Aaronson, Acta metall. 27, 351 (1979). 38. T. Furahara, Ph.D. thesis, Carnegie Mellon Univ., Pittsburgh, Pa (1989). 39. J. M. Howe, H. I. Aaronson and R, Gronsky, Acta metall. 33, 649 (1985). 40. W. G. Burgers, Physica I, 561 (1934). 41. J. M. Oblak and R. F. Hehemann, Transformation and Hardenability in Steels, pp. 15-38. Climax Molybdenum Co., Ann Arbor, Mich (1967). 42. R. F. Hehemann, Phase Transformations, pp. 397-432. Metals Park, Ohio (1970). 43. G. V. Smith and R. F. Mehl, Trans. Am. lnst. Min. Engrs 150, 211 (1942). 44. C. Laird and H. I. Aaronson, Acta metall. 17, 505 (1969).
0956-7151/90 $3.00 + 0.00 Pergamon Press plc
THE INTERFACIAL STRUCTURE AND HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES G. S P A N O S 1 and H. I. A A R O N S O N 2 IPhysical Metallurgy Branch of the Naval Research Laboratory, 4555 Overlook Avenue, SW, Washington. DC 20375-7500 and 2Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. (Received 6 February 1990; in revised form 22 June 1990)
Abstract--Three groups of previous investigators independently reported the anomalous result that the austenite habit plane of proeutectoid cementite plates, as determined with optical microscopy, is not unique. The present investigation utilized transmission electron microscopy (TEM) to study the interfacial structure and habit plane of proeutectoid cementite plates in a matrix of retained austenite in an Fe-0.81% C 12.3% Mn alloy in order to explain this unusual result. The broad faces of cementite plates were found to contain two types of structural feature: (1) large, kinked ledges with heights (h) of about 7 nm and spacings (21 between 30 and 100 nm, and (2) a finely spaced set of straight ledges, with h ~ 2 nm or less and 2 ~ 445 nm, whose direction is nearly [110]g II[010]c. Matching of atom spacings showed this to be a direction of good fit between the austenite and cementite lattices. The apparent habit plane, measured with conventional TEM techniques, was always less than 10° (and in most cases less than 5°) from (IT3)A I[(101)c. Atom matching studies also demonstrated that this pair of planes exhibits superior matching, and is thus likely to provide the conjugate atomic habit planes of the terraces of ledges. Thus, the non-uniqueness of the "optical microscopy apparent habit plane" of proeutectoid cementite plates appears to arise from the presence of arrays of ledges, combined with the sympathetic nucleation of new plates, on their broad faces. R6sum6--Trois groupes de chercheurs ont ind6pendamment rapport6 le r6sultat anormal suivant: le plan d'accolement de l'aust6nite de plaquettes de ckmentite proeutectoide, d&ermin6 par microscopie optique, n'est pas unique. La pr6sente 6tude a utilis6 la microscopic 61ectronique en transmission (MET) pour &udier la structure interfaciale et les plans d'accolement de plaquettes de ckmentite proeutecto'ide dans une matrice d'aust6nite r6siduelle dans un alliage Fe-0,81% C-12,3% Mn afin d'expliquer ce r6sultat inhabituel. On trouve que les faces larges des plaquettes de ckmentite pr6sentent deux types d'aspect structural: (1) de grandes marches avec des d6crochements, de hauteurs (h) d'environ 7 nm et d'espaccments (2) variant de 30 ~ 100 nm et (2) une s6ne de marches rapproch6es, avec h = 2 nm ou moins et 2 -~ 4-6 nm, dont les directions sont presque [110]A [][010]c. Les valeurs des distances atomiques montrent que ceci est une direction de bon accord entre les r6seaux de l'aust6nite et de la c6mentite. Le plan d'accolement apparent, mesur6 par las techniques classiques de MET. est toujours fi moins de l0 ° (et dans la plupart des cas fi moins de 5°) de (1T3)g II(101)c. L'&ude des distances interatomiques montre aussi que cette paire de plans conduit ~ un accord sup6rieur et a ainsi des chances de donner des plans atomiques d'accolement conjugu6s pour les terrasses des marches. Ainsi, la non-unicit6 du "plan d'accolement apparent par microscopic optique" des plaquettes de c6mentite proeutectoide parait provenir de la pr6sence d'arrangements de marches, combin6s avec la germination par sympathie de nouvelles plaquettes sur leurs faces larges. Zusammenfassung--Drei Autorengruppen berichteten friiher unabh~ngig iiber das anomale Ergebnis, dab die Austenit-Habitebene proeutektoider Zementitplatten, bestimmt mittels Lichtmikroskopie, nicht einheitlich sei. Um dieses ungew6hnliche Ergebnis zu iiberpriifen, werden in der vorliegenden Untersuchung Grenzfl/ichenstruktur und Habitebene yon proeutektoiden Zementitplatten in einer Matrix yon Restaustenit in einer Legierung Fe4),81% C-12,3% Mn mittels Durchstrahlungselektronenmikroskopie (TEM) analysiert. Die breiten Fl~chen der Zementitplatten enthalten zwei strukturelle Merkmale: (1) groBe, gekinkte Stufen in einer H6he (h) yon etwa 7 nm und mit Abs~nden (2) zwischen 30 und 100nm (2) einen engen Satz von feinen Stufen mit h = 2 nm oder weniger und 2 = 4-6 nm, dessen Richtung nahe [110]At]010C ist. l:berlegung zur Atompassung zeigen, dab diese Richtung eine gute Passung zwischen dem Austenit- und Zementitgitter vermittelt. Die scheinbare Habitebene, gemessen mit konventioneUen TEM-Veffahren, liegt inamer innerhalb yon 10" (und in den meisten F/illen innerhalb yon 5°) yon (ll3)All(101)c weg. Die Untersuchung der Atompassung zeigt auBerdem, dab dieses Ebenenpaar besonders gut zusammenpaBt und daher wahrscheinlich auch die konjugierte Habitebene der Terassen oder Stufen vorgibt. Also scheint die Nichteinheitlichkeit der "scheinbaren Habitebene im Lichtmikroskop" der proeutektoiden Zementitplatten yon den auf den breiten Fl/ichen vorhanden Stufem kombiniert mit der zugeh6rigen Bildung neuer Platten, herzurtihren.
1. INTRODUCTION Several previous groups of investigators [1-3] have independently utilized optical microscopy to d e m o n strate t h a t proeutectoid cementite plates formed in
hypereutectoid steels have m a n y austenite h a b i t planes, to the p o i n t where the h a b i t plane seems best described as " n o n - u n i q u e " (see Fig. 1). As pointed o u t by Heckel et al. [3], this result is a n o m a l o u s with respect to m o s t theories of precipitate m o r p h o l o g y
2721
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SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES 10 20
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and lay within about 10° of the (001)c plane (where the subscript C will be used to denote the cementite phase). Previous TEM studies of proeutectoid cementite plates have been focussed primarily on determination of the orientation relationship between austenite and cementite [9-12]. Insofar as the present authors are aware, no detailed investigation of the interfacial structure of these plates has as yet been reported; although recently Cowley and Edmonds observed "linear defects" which exhibited "periodic image contrast" along cementite plates in an Fe-0.76% C-12.0% Mn steel [13]t. Pitsch [9, 10] obtained the following orientation relationship between cementite plates and the austenite matrix in an Fe-l.3% C-12.0% Mn alloy [lOO]c II [5~4]h
10
[010]c I1[110]S
(b)
[00 llc II[2251A III
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//~ 5*C/s
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~ IOO
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Fig. 1. Results of previous investigations exhibiting the "non-uniqueness" of the apparent habit plane measured by optical microscopy. (a) Mehl et al. [1]; (b) Heckel et al. [3]. [1,4-6] as well as extensive experimental evidence in many other alloy systems [7, 8]. During the first two studies [1, 2], the habit plane of the broad faces of cementite plates was determined by indirect optical methods (since the remaining austenite matrix had transformed to martensite and/or to pearlite), while the third investigation [3] used X-ray diffraction to determine directly the orientation of the matrix (utilizing the small amount of austenite retained at room temperature). In none of these investigations were the planes in the c e m e n t i t e lattice, conjugate to the observed austenite habit planes, reported. However, Mehl et al. [1] dissolved away the matrix in which two cementite plates were embedded and utilized X-ray diffraction to show that the broad faces of the plates, as observed by optical microscopy, were "irregular" tUnless otherwise specified, all compositions reported in this paper are in wt%.
where A refers to the austenite matrix. In addition, Pitsch reported austenite habit planes, based on measurements made at a matrix of 20,000 x magnification, which again exhibited considerable variation from one plate to another. In a commercial steel, Thompson and Howell [11, 12] recently obtained a presumably different orientation relationship, but one which is similar in some respects to that of Pitsch. The purpose of the present investigation was to examine the crystallography a n d the interfacial structure of the broad faces of cementite plates in order to ascertain whether or not the habit plane, expressed relative to both the austenite a n d the cementite lattices, is really non-unique, particularly when considered on a near-atomic scale. A hypereutectoid, high-manganese Fe-C-Mn alloy was employed in order that the Ms lie well below room temperature and thus permit complete retention of the austenite matrix even in thin foils and in the carbon-depleted regions in contact with cementite plates. An examination of the atomic matching between various pairs of parallel (or nearly parallel) planes and directions in the austenite and cementite lattices was also undertaken in order to interpret the experimental results and complete deduction of the most probable conjugate atomic habit planes. It will now be useful to define three terms which will be used throughout the remainder of this paper. (1) The atomic habit plane (AHP) refers to the atomic-level habit plane corresponding to the terraces of ledges at an interphase boundary (see Fig. 2). (2) The TEM apparent habit plane (TApHP) is defined as the apparent habit plane, determined with conventional TEM techniques, passing through successive ledge terrace/riser intersections (see Fig. 2). (3) The optical apparent habit plane (OAHP) is the apparent habit plane evaluated by optical microscopy.
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES T~HP
~::r~i..~ g~"-i
~
~.P
Fig. 2. Schematic illustration of the TEM apparent habit plane (TApHP) and the atomic habit plane (AHP). 2. EXPERIMENTAL AND LATTICE MATCHING PROCEDURES
2.1. Experimental procedures The composition of the hypereutectoid F e 4 2 - M n alloy employed is given in Table 1. The isothermal heat treatment procedure is given in Ref. [14]. The isothermal reaction temperatures and times were chosen to ensure observation of sufficient numbers of cementite plates with TEM. Most studies were performed on specimens isothermally reacted at 500°C for 8 h; a single result is also reported, however, from a 550°C-2 h treatment. Discs 3 mm diameter x 0.25 mm thick were sparkcut from the heat treated specimens with an electrodischarge machine, using a hollow copper electrode, in order to avoid introduction of dislocations into the austenite matrix. The discs were then electrodished and finally jet polished in a twin-jet Fischione unit following the procedure of Hackney and Shiflet [15]. A second jet polishing technique, reported by Thompson and Howell [11], was also successfully employed and yielded somewhat better results. A brief summary of the trace analysis methods utilized to ascertain ledge directions and habit plane orientations relative to both the austenite and the cementite lattices will now be presented. The method for determining ledge directions is the following. (1) Obtain a Kikuchi pattern [16], a selected area electron diffraction pattern, and bright-field and/or dark-field images of the ledges using beam directions corresponding to slight tilts (so as to obtain two-beam diffraction conditions) from at least three zone axes in the austenite. Although only two zones are actually required for the trace analysis [17], at least three zones were always employed to ensure consistency. (2) Label the Kikuchi map and diffraction patterns relative to a standard f.c.c. Kikuchi triangle [18]. (3) Tilt to (or close to) parallel zone axes in austenite and cementite and obtain a selected area electron diffraction pattern, in order to ascertain the relative orientations of the cementite and austenite lattices. (4) Perform conventional trace analysis [17], using the information from steps (1) and (2), to determine the ledge direction in the austenite; the particular variant chosen is dictated by the standard Kikuchi triangle used in step (2). (5) Re-label the f.c.c. Kikuchi triangle Table 1. Alloy composition(wt%) C
0.81
Mn
12.3
P
0.0003
S
0.0006
2723
so that it is of the "correct" crystallographic variant in austenite corresponding to the common representation of the Pitsch orientation relationship (see Section 3.2 below), as determined in step (3). (6) Based on this triangle, choose the correct austenite variant of the ledge direction and the parallel direction in cementite, so that they correspond to the orientation relationship determined in step (3). The TEM apparent habit plane (TApHP) corresponding to the broad faces of cementite plates was determined by a similar technique to that employed for austenite:ferrite interfaces [19]. This procedure is as follows. (1) Ascertain the ledge direction as described in the preceding paragraph. (2) Determine the direction of the line of intersection between the plate and the foil surface by the method outlined above for the ledge direction. (3) Since both directions obtained in steps (1) and (2) must lie in the TApHP, determine the point of intersection of their great circles on a stereographic projection (or equivalently, calculate their cross product), which thus defines the TApHP. Since the "fine ledges" analyzed were usually so closely spaced and often had such small riser heights, it was impossible to determine unambiguously the line of intersection between their terrace plane and the foil surface for three austenite zones. Hence, this method could not be used to determine directly the atomic habit plane (AHP). On one cementite plate, this method was checked for consistency by re-determining the habit plane through application of a second procedure. The plate was tilted edge-on and the TApHP was determined by direct comparison with the corresponding diffraction pattern. The two methods yielded results within 3° of each other. Ledge heights were determined by utilizing an equation due to Gleiter [20], based on the measured displacement of interface fringes: h = m" sin ~ ' sin fl
(1)
where h = ledge height, m = fringe spacing, ~ = the angle between the thickness fringes and the projection of the ledges, and fl = the angle between the interphase boundary plane and the surface of the thin foil.
2.2. Lattice matching method A brief description of the procedure employed to determine parallel directions and planes of good matching between the austenite and cementite lattices will now be presented. In general, only the substitutional or M ( = Fe, Mn) atoms, were considered, as in a similar previous study [1]. This simplification appears to be required, since the interstitial sites utilized by carbon are incompletely occupied in the austenite lattice. Further, if the substitutional sites match between the two lattices along a given direction or plane, their interstices should lie in similar positions as well. The austenite and cementite lattices were taken to obey the Pitsch [9, 10] orientation relationship (see Section 3.2 below). The following lattice parameters for cementite were utilized: ac = 0.452 nm,
2724
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
L
70 nm
!
Fig. 3. Examples of coarse ledges, pointed out by arrows, near the edge of a cementite plate. b c = 0 . 5 0 9 n m and cc=0.674nm [21]. The corresponding lattice parameter of austenite was then deduced by analysis of selected area electron diffraction patterns which exhibited both austenite and cementite reflections. This procedure was employed since only the relative values of misalignment and/or misfit between austenite and cementite atoms were compared in this analysis (see Section 4), and accurate lattice parameter data for cementite and austenite as a function of temperature, carbon and manganese concentrations are not available. The atomic position coordinates for cementite were taken from Pearson [22]. In order to determine the quality of atomic matching between parallel planes in the two lattices, each lattice was sectioned along the appropriate plane and the atom positions were delineated graphically with the aid of a computer. Planar "slices" at very small distances ( < 0.1 nm) normal to this plane were also sometimes considered for the cementite lattice; the component atoms were then projected onto this plane. Such a procedure appeared necessary because the complexity of the cementite lattice (see Fig. 2 of Ref. [23]) makes the spacing between certain adjacent parallel planes quite small.
is seen to be accentuated along the line of intersection of the plate with the foil surface (see arrows in Fig. 3). Coarse ledge heights were determined to be approximately >~7nm while ledge spacings varied widely, but were in the range of 30-100 nm. Fine linear features were also repeatedly observed on the broad faces of cementite plates, as shown in Fig. 4. These features also exhibited the fringe displacements characteristic of ledges [20]. They exhibit a step-like appearance at the intersection of the interphase boundary with the foil surfaces where they terminate [see Fig. 4(a)]. Hence, this set of features probably is best described as ledges rather than interfacial dislocations, and thus will be referred to as "fine ledges" in the remainder of this papert. The fine ledges were usually much straighter and more uniformly spaced than the coarse ledges, with h ~ 2 nm or less$, and spacings between 4 and 6 nm. It is apparent from Fig. 4(a) that the atomic habit plane (AHP) corresponding to the terraces of the steps is different from the TEM apparent habit plane (TApHP), and that there are local variations in the TApHP due to changes in the inter-ledge spacing, 2 (and possibly also the ledge height). Figure 4(b) is another example of the stepped contrast from the fine ledges. Note the gradual change in the TApHP as ). decreases, effectively stepping the interface upward more sharply. Larger coarse ledges are pointed out by large arrows in Fig. 5. They may have resulted from
3. EXPERIMENTAL RESULTS 3.1. T E M observations o f interfacial structure Interfacial structure studies of the broad faces of cementite plates revealed two general types of feature. Coarse (i.e. of relatively large height) irregularly spaced ledges were observed at the broad faces (e.g. see Fig. 7 of Ref. [14]) and near the edges of cementite plates (Fig. 3). Note the displacement of interference fringes as they cross the ledges. This type of contrast is due to the difference in thickness of the terraces on either side of a riser and has been described in detail by Gleiter [20]. The stepped contrast of the interface tSome consequences of their alternate interpretation as dislocations are discussed in Section 6.3. :[:Someof the fine ledges appeared to have heights less than 2 nm, but the fringe displacement and/or step height was too small to permit accurate measurements to be made.
Fig. 4. Examples of "fine ledges", pointed out by arrows, at the broad faces of cementite plates. (a) TEM bright field micrograph revealing "fine ledges" at the austenite:cementite interface; (b) TEM dark field micrograph, taken from a I l l A reflection, also exhibiting the stepped nature of the interface.
SPANOS and AARONSON:
HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
Fig. 5, TEM dark field micrograph taken from a Ill A reflection revealing coarse ledges (large arrows) which may have formed due to accumulation of a finer set of ledges. coalescence of what appear to be a finer set of ledges (small arrows) which exhibit white on dark strain field contrast. This type of contrast has been demonstrated by Hackney and Shiflet [15] at ledges on the edges of pearlite colonies. Ledges and kinks have also been observed at a cementite:cementite boundary considered to be a remnant of the original austenite:cementite interface, before it was converted into a low-angle cementite:cementite boundary by the sympathetic nucleation [24, 25] of a second cementite crystal [14].
3.2. Crystallography and quantitative TEM results The orientation relationship between the cementite plates and the austenite matrix, as determined by analysis of selected area electron diffraction patterns from 8 different plates, was always within a few degrees of the Pitsch [9, 10] orientation relationship (e.g. see Fig. 6). The new orientation relationship recently reported by Thompson and Howell [11, 12] was not observed. This could be due to the significant difference in the alloy compositions used in the two investigations. Their steel contained 1.09% C, 2.3% Mn, 0.28% Cr, 0.26% Si and 0.18% Ni. Quantitative TEM analysis was performed on five plates upon which the fine ledges at the broad faces of the plates were not obscured by systems of coarse ledges. The fine ledge direction was determined relative to both the austenite and cementite lattices by the trace analysis method described in Section 2.1. An example of the intermediate results is presented in Figs 6-8. A typical selected area diffraction pattern required to determine the cementite orientation relative to the austenite matrix is presented in Fig. 6. Figure 7 is an example of the Kikuchi pattern obtained from the austenite matrix adjacent to the plate in Fig. 4(a~. Figure 8 demonstrates the three traces and their intersection, corresponding to the fine ledge direction for this particular example. The fine ledge direction determined in this manner was always very close to [I10]AII[010]C. It was 2° or less from [110]AII[010]c on four plates and about 5° from this direction on the fifth plate. Based on the average scatter in the intersections of the traces taken from each interface, it is estimated that the maxi-
2725
mum experimental error introduced during the trace analysis procedure is about 2 °. These results are represented stereographically in Fig. 9. The TEM apparent habit plane (TApHP) across the fine ledges on four of these plates (not enough information was obtained on the fifth) was determined using the procedure previously outlined. Due to local variations in the TApHPs, e.g. see Section 3.1 and Fig. 4(a) and (b), the habit plane trace analysis was always performed on a relatively planar portion of the interphase boundary. The results are presented in Fig. 10. The TApHP were within 5~' of (li3)A 11(101)¢ for three of the plates and about 10" from these planes for the fourth plate. 4. LATTICE MATCHING ANALYSIS The substitutional atoms ( M = F e , Mn) were found to exhibit particularly good matching between the austenite and cementite lattices along the [110]A II[010]C direction, as demonstrated in Fig. 11. The relative interatomic spacings are 0.253 nm in this direction in the austenite lattice, as compared to 0.254 nm for the parallel direction in cementite. However, the matching is not quite as good as this statement implies, since every other M atom in the cementite lattice is "shifted" by about 0.07 nm in the [100]c direction, i.e. normal to the "good matching" direction (Fig. 11).
02--2A
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,
,
? 022-A ,yo~-~,~ TTT~
/ ,
I I
~ ~
z z =~
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Fig. 6. A typical selected area electron diffraction pattern corresponding to the Pitsch orientation relationship [9, 10].
2726
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
\
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\ Fig. 7. A portion of the f.c.c. Kikuchi map taken from the austenite matrix adjacent to the cementite plate shown in Fig. 4(a). The quality of matching was investigated for various pairs in the two lattices in order to ascertain the most likely candidate(s) for the atomic habit plane (AHP). Since, from geometrical considerations, the fine ledge direction must lie in the A H P (i.e. the
[1101~ Fig. 8. Traces of the fine ledges shown in Fig. 4(a), indicating their direction, relative to both austenite and cementite. BL, B2 and B3 correspond to the electron beam directions (or zone axes used) and UI, U2 and U3 represent the projected ledge directions.
terrace plane), the survey was restricted to seven pairs of relatively low index planes which contain the experimentally determined [110]A II[010]c conjugate directions and which are within about 6 ° of being parallel in the presence of the Pitsch orientation relationship (or, alternatively, are parallel at deviations of approximately 6 ° or less from the Pitsch
11101A 0|/10+1~c Fig. 9. Fine ledge directions measured for five plates superimposed on a [101]A stereographic projection. Note that in all cases the ledges lie very close to [ll0]A U[010]o
SPANOS and AARONSON:
HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
2727
[110]A
vk,._Jx--J
Fig. 11. Illustration of atomic positions of substitutional atoms (Fe, Mn) along the [010]c and [110]A directions.
Fig. 10. [110]A II[010]c stereographic projection with poles of experimentally determined TApHPs.
orientation relationship). These plane pairs are represented stereographically in Fig. 12. The pair of conjugate plains which exhibits the best matching is (lI3)A II(101)C (Fig. 13). These two planes are within 1° of being parallel in the presence of the Pitsch orientation relationship. Normal to the [110]A IJ[010]C "good fit" direction within the interface, i.e. in the [~32]A II[I01]C direction, there is also
relatively good matching. The misfit in this direction is 3.9%, corresponding to an extra half plane of atoms every 10.6nm. Two complications should, however, be considered. The previously discussed "shift" in the [100]c direction of every other atom lying in the row parallel to [110]A II[010]C is such that the "shifted" atoms lie slightly (0.06 nm) out of the plane (i.e. the x atoms in Fig. 13). Secondly, every other row of atoms lying along the [ll0]AII[010]C direction exhibits an additional small misalignment of about 0.01 nm in that direction (see row B of Fig. 13). Despite these complications, this interface was found
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(~,,, oOl)c (225) A _
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2728
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
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to exhibit the best matching of all those investigated, and thus was concluded to be the best candidate for the conjugate atomic habit planes. The (I13)AIl(001)c plane pair was suggested by Mehl et al. [1] (long before Pitsch's [9, 10] determination of the orientation relationship) as a possible interface of good matching. For this pair to be perfectly parallel, a 4.5 ° deviation from the Pitsch orientation relationship is required; this is much greater than the <1 ° angle needed by the (Ii3)A II(101)c pair. Mehl et al. [1] found good matching between the (T13)AII(001)c planes in only one direction. Moreover, their model corresponds to an additional rotation, in the interface, of 16 ° from the Pitsch orientation relationship. During the present analysis, matching of the (il3)AIl(001)c planes was re-examined on the assumption that there is no "in-plane" deviation from the Pitsch orientation relationship; such a deviation is contrary to the experimental observations made on the present alloy (see Section 3.2 and Fig. 6) as well as to those previously reported by Pitsch [9, 10]. Again, there is good fit along the [II0]AII[010]C direction, and in this case, the 0.07 n m "shift" of every other atom takes place within the interface. The misfit in the interface in the direction normal to [110]A II[010]c, now [~3~]A II[100]c, is 7%, corresponding to an extra half plane of atoms approximately every 6.2 nm. This is considerably worse than for the analogous direction in the (lI3)AIl(001)c interface (compare Figs 13 and 14). In addition, every other row of atoms parallel to [110]A II[010]C now exhibits a misalignment of 0.125 n m in that direction, almost half the interatomic spacing of 0.254 n m (see row B of Fig. 14). This disregistry is much greater than the
0.01 n m misalignment observed at the (1T3)A II(001)c interface (see row B of Fig. 13), and would probably result in a very high energy interface, since every other row would contain substitutional atoms lying in essentially interstitial positions relative to the lattice on the opposite side of the interface. The only other interface which exhibited possibly significant matching in the direction normal to [110]A II[010]C is that corresponding to the (I10)A II(10T)c planar pair. The misfit in that direction is about 11.8%, corresponding to an extra half plane of atoms every 3.2 nm. This misfit is appreciably larger than the corresponding misfit in either of the other two conjugate pairs disucssed above. The present pair of planes also requires a 4 ° deviation from the Pitsch orientation relationship in order to be exactly parallel; again, this seems rather large. N o other interfaces, amongst those studied, exhibited adequate matching in the direction normal to [110]A II[010]c • 5. COMPARISON OF LATTICE MATCHING ANALYSIS WITH EXPERIMENTAL RESULTS A comparison of the experimental results and the lattice matching studies reveals that the fine ledges analyzed by T E M always lie essentially parallel to the particular variant of the close packed direction in austenite determined by the lattice matching analysis to exhibit good fit between the two lattices, i.e. the [110]A H[010]C direction (compare Figs 9 and 11). This is consistent with the model of the broad faces of cementite plates now to be developed. By definition, the fine ledge direction must lie within the terrace plane, i.e. the AHP, of the fine ledges (see Fig. 2). This plane should be an immobile, low energy interface ,I.° + ° . 4.22
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SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES [26], and would thus be expected to contain the direction of good atomic matching. As demonstrated in Fig. 10, the T A p H P was close to (lI3)AIl(101)c on all four of the plates at which both the fine ledges and the TApHPs were analyzed. Also as previously mentioned, the angular deflection of the TApHPs from the (1T3)A I1(101)c planes was usually 5° or less, and was 10° for one plane analyzed. These deviations are within the possible range estimated due to the presence of the fine ledges, ~< 26 °, deduced using ledge spacings and heights measured with TEM (see Section 3.1). Alternatively, the other two plane pairs which exhibited any reasonable matching normal to the [ll0]AII[010]C direction, (1T3)A II(001)c and (II0)A II(10T)c, deviated by much greater angles, as large as 61 and 70 °, respectively, from the experimentally determined TApHPs (compare Figs 10 and 12). These angles appear to be too great to be accounted for by the presence of ledges. Hence, based on the current experimental findings, the (1 ]'3)A [ (101)c plane pair appears to be the only plausible candidate for the AHP. This conclusion is in agreement with the results of the lattice matching analysis, in which it was demonstrated that the (1T3)A II(101)c pair provides the best atomic matching (of the seven conjugate pairs considered) between the two lattices (see Section 4). Finally, with the exception of (~25)A H(001)c, which yields no matching at all normal to the "good fit" direction and lies as much as 65 ° from the experimentally determined TApHPs, the (ll3)AII(101)C pair exhibits the smallest deviation ( < 1° as compared to ~>4 ° for all other possible pairs) from the repeatedly observed Pitsch orientation relationship (see Section 3.2 and Refs [9, 10, 14]), as demonstrated in Fig. 12. Hence, the present experimental observations, lattice matching analysis and the coincidence of this plane pair with the observed orientation relationship all strongly indicate that the atomic habit plane of proeutectoid cementite plates is (I13)A II(101)c6. DISCUSSION The results of this investigation suggest that ledges can cause differences between the TApHP and AHP of proeutectoid cementite plates (see Fig. 2). Face-to-
J
TApHP
Fig. 15. Schematic illustration of the OAHP and the TApHP of an aggregate of plates formed by face-to-face sympathetic nucleation. The OAHP of an aggregate is dictated by the TApHPs (which are determined by the ledge heights and ledge spacings, Fig. 2) and by the dimensions and relative positions of all the crystals in the array.
2729
Fig. 16. TEM micrograph showing ledges apparently being emitted from a cementite:cementite:austenite junction. face sympathetic nucleation [14] can evidently produce further deviation of the OAHP from the AHP, since the OAHP of an aggregate of sympathetically nucleated crystals can differ from the TApHP of the individual crystals in such an array, as demonstrated schematically in Fig. 15. In this vein, differences between the OAHP and the TApHP have also been reported for "stacks" of f-hydride (ZrHLs) plates formed in Z r - 2 . 5 % N b and in a Zrq2.11.0% Nb-3-3.5% Sn4).8-1.0% Mn alloy [27]. We now note that sympathetic nucleation can also expedite ledge formation at the junctions between "substrate" and sympathetically nucleated crystals [28, 29], in the same manner that ledges are generated at the intersections of impinged plates [30-33]. Figure 16 shows ledges being emitted from a cementite:cementite:austenite junction between two cementite plates, one of which was presumably nucleated sympathetically at the other. It appears from this micrograph that the ledges on the right side are travelling away from the junction between the two cementite plates, since they are stepped "down" from the source, corresponding to growth of the cementite plates into the austenite matrix. Hence, sympathetic nucleation may also affect the TApHP by increasing the ledge density on the broad faces of individual plates. 6. I. Previous habit plane investigations
The "non-uniqueness" of the optical apparent habit plane (OAHP) of cementite plates previously reported [1-3] will now be considered in more detail. The most direct results [3] of these investigations indicate that the OAHPs, reported relative to the austenite lattice only, lie in a group centered approximately about a {521}A plane, which lies only 8 ° from a { 113}A type plane [Fig. 1(b)]. The range of angular deviations from the {l13}A for 99% of the planes measured by Heckel et al. [3] is 0-15 ° [see Fig. l(b)]. The results of the more indirect study by Mehl et al. [1] also indicate that the OAHP always lies within 15 ° of a { 113}A plane. In addition, Cowley and Edmonds [13] recently reported TApHPs within 5° of {113 }A in an Fe-0.76% C-12.0% Mn alloy. These results are
2730
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
all consistent with the present deduction that the atomic habit plane (AHP) is (II3)AH(101)c. These deviations from {l13}A are within those previously discussed due to the presence of ledges, and probably also arise at least in part due to face-to-face sympathetic nucleation. It should be pointed out that as a result of the techniques employed, the previous investigators were able to report the habit plane relative to a general variant in the austenite lattice only, while the current TEM study determined the exact variant of the habit plane, relative to both austenite and cementite. The optical observation by Mehl et al. [1] that the "irregular" broad faces of two cementite plates isolated from the matrix were within about 10° of (001)c is in contrast to the present findings, and may again be a result of differences between the AHP and OAHP. Some differences between the previous habit plane investigations [1-3] and this one should, however, be briefly noted. The alloy compositions were considerably different, and the previous investigators employed continuous cooling transformation while isothermal reaction was utilized here. Continuous cooling is expected to increase the frequency of sympathetic nucleation, since the driving force for nucleation is continuously increasing with time. This factor should induce further scatter in the OAHPs. 6.2. The nature of the features observed at the austenite :cementite interface The coarse, often kinked [14], ledges are morphologically similar to growth ledges observed on a wide variety of precipitate plates in many alloy systems [26, 34] and presumably serve the same function. On the other hand, the fine ledges are very similar in appearance to and have heights similar to the "direction steps", observed on ferrite:cementite (c¢:C) interfaces in pearlite [35]. These steps were shown to cause local deviations of the pearlite lamellae from (113),11(001)c [35], in the same manner as the rotations of the TApHP away from (1T3)AII(101)c at the broad faces of cementite plates observed in the present investigation. The possibility that the fine ledges are structural ledges [19, 36, 37] will now be considered. Their linear appearance is consistent with this interpretation [19]. However, studies of f.c.c.:b.c.c. [19] and b.c.c.:h.c.p. [38] interfaces have demonstrated that the interplanar spacings in the direction normal to the structural ledge terraces must be essentially equal in the two phases and that the risers of structural ledges are usually between one and four atomic planes high. In contrast, the interplanar spacings normal to the (li3)^ll(101)c terraces are very dissimilar in the austenite and cementite lattices (see Fig. 17). In addition, the height of the fine ledges (approximately 2 nm or less) can be considerably greater than the (1T3)AIl(101)c interplanar spacings. Unless special circumstances intervene, such dissimilar interplanar spacings and relatively high risers would thus seem
(101) e
(I'T3)A
3 Cernentlte
1.o8/~
Austenlte
Fig. 17. Illustration of relative interplanar spacings in austenite and cementite normal to (1~3)A[1(101)c. not to provide the most efficient arrangement, from the standpoint of interracial energy, for causing the repetition of coherent regions at shorter lateral distances, the usual function of structural ledges [36]. 6.3. On the Compensation of misfit at (173)A II (lO1)c The question then arises as to how the misfit between the austenite and cementite lattices is accommodated at the (II3)AII(101)C interface. It may be possible that the fine ledges lying along [110]a II [100]c could provide at least some misfit compensation, and thus might also be interpreted as dislocations, as in the case of Shockley partial "dislocation/ledges" on the broad faces and edges of y' (h.c.p.) plates precipitated from an f.c.c, matrix in an A1-15% Ag alloy [30, 39]. The Burgers vector of these dislocation/ ledges lies in the atomic habit plane [30, 39] and can thus accommodate misfit. Misfit compensating ledges apparently also play a role at fl(b.c.c.):~t(h.c.p.) interfaces corresponding to the broad faces of proeutectoid ct plates and grain boundary allotriomorphs in a Ti~i.62 at.% Cr alloy [38]. The complexity of the cementite lattice (see Ref. [23]) limits the possibilities of modelling the "fine ledges" at austenite:cementite interfaces as dislocations; as far as the present authors are aware. Burgers vectors for dislocations in cementite have yet to be reported, either theoretically or experimentally, nevertheless, considering for the moment only the austenite lattice and possible unit (1/2(110)) or partial (1/6(112)) dislocations lying in the (II3)A II(010)c interface, 1/21110]AII[101]C is the only 1/2(110) type Burgers vector lying in this plane. It lies along the "good fit" direction and would thus not accommodate any misfit in the direction of "poorest fit", [~32]AII[T01]C- There are two possible Shockley partial dislocations lying in this interface, 1/61i21] and 1/612ii], but there are no rational directions in the cementite lattice corresponding to these austenite directions (following the Pitsch [9, 10] orientation relationship). Thus, even though ledges at interphase interfaces can often be interpreted equivalently as dislocations [30, 38, 39], in the present case, a complete dislocation description of the "fine ledges" is not readily apparent. 6.4. Comparison with habit plane behavior in other transformations The last major question to be considered is why the non-uniqueness of the OAHP [1-3] should appear to
SPANOS and AARONSON: HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
Fig. 18. TEM dark field image taken from a 220A reflection revealing four cementite plates in the face-to-face morphological arrangement. characterize only proeutectoid cementite plates. One possible explanation for this is that face-to-face sympathetic nucleation may occur much more readily during the formation of cementite plates than in other precipitation processes so far examined from this viewpoint. This mode of sympathetic nucleation was thus observed with TEM at the majority of plates examined in this investigation. Figure 18 is a typical example of four plates stacked atop one another in this mannert. In contrast, in Ti-X alloys transformed at high reaction temperatures, proeutectoid ~(h.c.p.) plates obeying the Burgers [40] orientation relationship with the fl(b.c.c.) matrix and exhibiting a near{111}~ habit plane, frequently exhibit sympathetic nucleation, but predominantly in the edge-to-edge and edge-to-face modes [25]. These forms of sympathetic nucleation should have a negligible effect on the OAHP. In particular, the habit planes of individual precipitate crystals in edge-to-face arrangements should be much easier to identify separately, even with optical microscopy (see Fig. 2 of Ref. [14]). On the other hand, face-to-face sympathetic nucleation, resulting in the formation of "sheaves" of plates, has been well documented during the formation of both upper bainite [24,41] and lower bainite [41,42]. The scatter in the habit plane of bainite plates when examined with optical microscopy at a given temperature and its gradual change x~ith decreasing temperature [8, 43] thus seem #Although some of the plates in Fig. 18 appeared to be separated from one another (e.g. plates Nos 1 and 2), when they were followed far enough back in the foil, a point of contact was almost always observed (e.g. plates Nos 2 and 3); in the few cases where it was not, it is believed that the plates were probably in contact either in the thicker, non-transparent regions of the thin foil, or above or below the plane of the foil. Additionally, impingement was minimized by employing relatively small undercoolings and short isothermal reaction times; both of which avoided a high number density of individually nucleated cementite plates [14].
2731
likely to result at least in part from physically meaningless OAHPs established by face-to-face sympathetic nucleation (see Fig. 15). Variations in the modes and kinetics of sympathetic nucleation with temperature could easily contribute to changes in the OAHP of sheaves. Hence, the behavior of the OAHP of cementite plates seems not to be entirely "unique", and may well be found in still other alloy systems when more detailed experimental studies are extended to them. Another source of the non-uniqueness of the cementite OAHP may be the relatively high h/2 ratio of ledges on the broad faces of these plates, since tan 0 = hi2 (where 0 is the angle between the TApHP and the AHP). In particular, this ratio can be especially high for the fine ledges, ~< about 0.5, as a result of their relatively small values of 2. By comparison, h/2 falls in the range of 0.0144).029 for ledges on y A1-Ag 2 plates [44] and 0.158-0.325 for the closely spaced structural ledges on ferrite plates [19]. It should be noted that these data are not only quite limited but also exhibit appreciable scatter. While experimental data on hi2 are not yet available on a wide range of diffusional transformations, this remains another possible reason why a non-unique OAHP may be more evident for proeutectoid cementite plates than for plates in other alloy systems. A third cause of non-uniqueness may be that multiple habit planes do exist, even at the atomic level. Although the deduction of the present investigation is that (li3)A 11(101)c represents the unique conjugate atomic habit planes of cementite plates, this remains to be confirmed with atomic resolution techniques. It is anticipated that this experiment may prove to be difficult to perform in the present alloy system, however, due to difficulties of obtaining TEM foils with extremely thin areas, which are required for such studies, in both the austenite and (particularly in) the cementite phases. Notwithstanding, the current results do make a non-unique AHP for cementite plates seem considerably less likely than before. 7. CONCLUSIONS The interfacial structure, habit plane and orientation relationship of proeutectoid cementite plates in an Fe-0.81% C-12.3% Mn alloy have been investigated with transmission electron microscopy, supplemented with optical microscopy. The Pitsch [9, 10] orientation relationship was shown to be obeyed. The broad faces and edges of these plates were found to be ledged. Two types of features were observed: (1) coarse ledges with h (height) on the order of 7 nm and widely varying spacings, 2, in the range 30-100 nm, and (2) finer, straighter ledges with h ~ 2 nm or less and 2 in the range of 4-6 nm. TEM analysis on relatively planar portions of the broad faces of cementite plates, selected so as to avoid complications in determining the habit plane due to undulations sometimes observed at these
2732
SPANOS and AARONSON:
HABIT PLANE OF PROEUTECTOID CEMENTITE PLATES
broad faces as a result of variations in ledge spacings (and presumably heights), revealed the fine ledge direction to be [110]A II[010]C. Lattice matching studies, accomplished by superimposing substitutional atom positions in the cementite and austenite lattices, revealed this to be a direction of " g o o d fit" between the two structures. Similar studies of pairs of planes sharing the [ll0]All[101]c zone axis showed that (Ii3)A II (101)c is by far the most closely matching and thus the most probable pair of conjugate atomic habit planes (AHPs) corresponding to the terraces of ledges. In agreement with this analysis, T E M apparent habit planes (TApHPs), i.e. those measured by conventional T E M methods, were always less than 10 ° (and in most cases less than 5 °) from (li3)A II(101) c, while they were between 50 and 61 ° from the next closest conjugate pair exhibiting any reasonable atomic matching. In addition, the (li3)A II(101)c plane pair exhibits the smallest deviation, < I °, from the Pitsch orientation relationship [9, 10]; all other viable conjugate pairs investigated by lattice matching are 4 ° or more from being parallel in the presence of this relationship. Although the possibility remains that true deviations of the atomic habit plane (AHP) from (li3)A II(101)c exist, it was concluded that the well established [1-3] non-uniqueness of the observed habit plane of proeutectoid cementite plates is most likely due to two effects: (1) the presence of ledges which can yield substantial deviations from the atomic habit plane, in the same manner as similar ledges observed on ferrite:cementite interfaces in pearlite [35], and (2) the strong tendency for face-toface sympathetic nucleation, which can cause substantial further deviations. Particularly when the apparent habit plane is measured with optical microscopy or low resolution T E M , the habit plane of the resulting composite plate can easily be mistaken for the AHP. Acknowledgements--The authors express their appreciation to the National Science Foundation for support of this work through grant DMR81-19507 to the CMU MRL; the (partial) funding support of the contributions of G. Spanos by the Office of Naval Research is also gratefully acknowledged. The authors also wish to thank Professor Gary Shiflet (University of Virginia) for supplying the Fe4).81% C-12.3% Mn alloy and Dr Tael Kim for use of computer programs which were subsequently modified for the lattice matching analysis. Finally, appreciation is expressed to Dr Tadashi Furuhara and Professor W. T. Reynolds Jr for many helpful discussions.
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