- Email: [email protected]
Evolution of microstructure in the stoichiometric Ni–25at.%V alloy
Intermetallics 11 (2003) 83–92 www.elsevier.com/locate/intermet
Evolution of microstructure in the stoichiometric Ni–25at.%V alloy J.B. Singha,*, M. Sundararamana, P. Mukhopadhyaya, N. Prabhub b
a Materials Science Division, Bhabha Atomic Research Centre, Mumbai- 400 085, India Department of Metallurgical Engineering and Materials Science, IIT Bombay, Mumbai- 400 076, India
Received 19 August 2002; received in revised form 18 September 2002; accepted 26 September 2002
Abstract The disorder-to-order reaction in the stoichiometric Ni3V alloy is a typical cubic-to-tetragonal type (A1 to D022) transformation. Microstructural evolution has been studied at different temperatures below the ordering temperature in samples of this alloy having the same initial microstructure produced by solution treatment followed by water quenching. The ordered phase has been observed to evolve through a series of structural changes, starting with the impingement and alignment of fine ordered domains corresponding to all the three variants of the ordered phase, followed by the appearance of a two-variant lamellar structure which ultimately gets converted to a structure in which each Ni3V grain comprises a single variant. The lamellar structure is found to be quite stable with regard to coarsening in response to heat treatments. Evidence has been found which indicates that a discontinuous coarsening type of reaction is one of the possible mechanisms driving the two-variant lamellar to single-variant morphological transition. It has also been observed that coarsening of domains takes place in a manner similar to Ostwald ripening wherein larger domains coarsen at the expense of smaller domains. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: A. Intermetallics, miscellaneous; B. Order/disorder transformation; F. Electron microscopy; Transmission
1. Introduction In the Ni–V binary system, the disordered fcc (A1) solid solution, at 25 at.% V (a=0.3567 nm), transforms below Tc=1045 C [1,2] to form an ordered body centered tetragonal (D022) phase (a0 =0.3542 nm, c0 /a0 =2.036) [3]. Fig. 1 shows the ordered Ni3V unit cell. Since the c0 direction of the tetragonal cell may align itself along any one of the three 4-fold axes (i.e., < 001> axes) of the cubic cell, the ordered D022 phase possesses three mutually orthogonal variants. These are called transformation variants [4]. The transformation variants of the Ni3V phase are perpendicular twin related to each other (c0 axes of two variants being perpendicular to each other) across {101}1 (or f102ÞD022 ) planes.
* Corresponding author. Tel.: +91-22-559-5061; fax: +91-22-5505151. E-mail address: [email protected] (J.B. Singh). 1 It is to be noted that all the indices used throughout this paper are expressed in terms of the fcc basis unless otherwise mentioned. The asymmetrical notation means that permutations are possible on the first two indices while the third is fixed.
If two contiguous regions of an ordered crystal of a given variant do not share the same unit cell orientation, they are in juxtaposition and their mutual interface is an intra-variant domain boundary (henceforth called an antiphase boundary (APB)). Lattice translations that can create APBs in the ordered Ni3V phase are shown in Fig. 1 and are given by 1 P1 ¼ ½a0 ; a0 ; 0D022 2 and P2 ¼
1 < 2a0 ; 0; c0 D022 4
APBs represented by P2 and P20 in the figure are equivalent. The two types of vectors, namely, P1 and P2, would create distinct APBs on a plane. Francois et al. [5] have estimated the energies of APBs created by these vectors on the (111) plane and have found these to be about 150 and 40 mJ/m2 respectively. Since the two APB types are associated with distinct APB energies,
0966-9795/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(02)00186-3
84
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
these are designated as ‘‘Type I’’ and ‘‘Type II’’ respectively. It should be pointed out here that both types of APBs created by P1 and P2 vectors on the (111) plane are conservative in nature and correspond to APBs of the ‘‘first kind’’ as per the nomenclature used in the literature [6]. Ordering in the stoichiometric Ni3V alloy is so fast that it cannot be suppressed even by melt-spinning [7]. Different morphologies are obtained in the microstructure on directly quenching the alloy from a solutionising temperature (> Tc) to different order annealing temperatures (< Tc) [2]. The evolution of these morphologies is attributed to the operation of different transformation mechanisms at different ordering temperatures. The microstructure developed during low temperature order annealing exhibits all the three variants of the ordered phase which arrange themselves in a mosaic assembly of prism shaped cells bounded by interfaces that approximate f102gD022 type orientations [2]. During high temperature order annealing, the ordered Ni3V phase assumes a lamellar shape with the lamellae bounded by f102gD022 planes. Each lamella corresponds to a rotational variant of the ordered phase. The long-range order parameter generally remains less than unity even after prolonged low temperature order annealing, whereas near perfect order is attained within a short time during high temperature annealing [2]. It is expected that the different microstructures evolved at different ordering temperatures (i.e., the three-variant structure and the two-variant lamellar structure) are related. In view of this, the
evolution of the microstructure has been studied at different temperatures in samples having the same initial microstructure, namely, that produced by solution treatment followed by water quenching. These studies have been carried out using diffraction contrast transmission electron microscopy (TEM).
2. Experimental procedure Buttons of the Ni–25 at.% V alloy were prepared by electron beam melting and arc melting of pure Ni and V. The alloy was remelted several times to improve homogeneity. The homogeneity in the composition of the alloy was confirmed by determining the composition at different points of the buttons using electron probe microanalysis (EPMA). Thin slices, cut from the cast buttons, were solution treated at 1150 C for 4 h and then water quenched. Solution treated samples were order annealed at different temperatures ranging from 650 to 950 C below Tc. X-ray diffraction examination of the solution treated specimen was carried out using a monochromatic copper Ka radiation source. For making TEM specimens, appropriately order annealed slices of the alloy were mechanically ground to a thickness of about 0.1 mm. Discs of 3 mm diameter were then punched out from these foils. The discs were electropolished at about 18 V to perforation in a dual jet Tenupol unit, using an electrolyte containing 1 part perchloric acid and 4 parts ethanol; the temperature of the electrolyte was maintained at about 35 C. The thinned samples were examined in a Jeol JEM 2000 FX electron microscope. The ordered Ni3V phase was identified from the presence of superlattice reflections at {100} and {1 1/2 0} positions in selected area diffraction (SAD) patterns corresponding to different zone axes, this being a characteristic feature of phases with the D022 structure.
3. Results 3.1. Microstructure of the solution treated alloy
Fig. 1. The Ni3V (D022) unit cell. Whereas P1 and P2 indicate the translation vectors which can create Type I and Type II APBs respectively, P2 and P20 indicate equivalent translations on two different planes which would both create Type II APBs.
The microstructure of the solution treated and water quenched alloy showed a fine dispersion of ordered particles, corresponding to all the three variants of the ordered phase, embedded in a disordered matrix (Fig. 2). Bright field (BF) micrograph [Fig. 2(a)] showed a tweed contrast. The ordered particles maintained perfect coherency with the disordered matrix. That all the three variants of the ordered phase were present within a single grain of the parent phase could be confirmed from the < 001 > zone axis SAD pattern [inset in Fig. 2(a)]. Superlattice reflections appeared to be quite intense. Dark field (DF) micrographs obtained by using superlattice reflections corresponding to one of the variants
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
[Fig. 2(b)] revealed that the ordered particles were aligned along < 110 > directions. X-ray diffraction study of this sample showed a significant splitting of the {200}fcc peak [Fig. 2(c)] into ð004ÞNi3 V and f200ÞNi3 V peaks at 2 values equal to 50.81 and 51.57 respectively. The lattice parameters, a0 and c0 of the ordered phase, deduced from these peaks are 0.3542 and 0.7182 nm respectively. 3.2. Microstructure of order-annealed alloy The microstructure in this alloy appeared to have evolved through impingement and alignment of fine ordered domains. Interfaces between ordered domains were devoid of any dislocations. This indicated that ordered and disordered regions remained fully coherent during the growth. Dark field imaging of different domains in samples order annealed for 1 h at 650 C showed domains of two sizes; the average size of the two types of domains differed by about an order of ten (Fig. 3). The fine ordered domains appeared to have coagulated to form the large domains. These large domains grew to form the lamellar structure. The
Fig. 2. (a) BF micrograph showing the tweed contrast in a solution treated and quenched sample. A [001] zone axis diffraction pattern showing the presence of all the three variants of the ordered phase is shown in the inset. (b) A DF micrograph, imaged with a superlattice reflection corresponding to one of the three variants of the Ni3V phase, showing the alignment of ordered particles along [110] and [110] directions. (c) X-ray diffraction showing a significant splitting of f200ÞNi3 V and ð004ÞNi3 V peaks in a solution treated sample.
85
transformation to the lamellar structure often occurred through an intermediate coarse basket weave type structure, which will be discussed later. Selected area diffraction patterns from regions containing smaller domains often showed superlattice reflections corresponding to all the three variants, whereas those from the adjacent regions, containing larger domains, showed superlattice reflections corresponding to only one or two variants, depending upon the aperture size. This indicated that during the coarsening process, one or two of the variants had dissolved or had ‘‘switched’’ their orientations to those favoured by the large domains. < 001 > zone axis diffraction patterns from two adjacent large domains also indicated that the two domains corresponded to perpendicular twin related variants across {110} interfaces, with the c0 -axes in the two domains perpendicular to each other. Such perpendicular twin related domains are often produced during cubic to tetragonal transformations. Dark field micrographs of two such domains are shown in Fig. 3 (a) and (b). The observed perpendicular twin lamellar structure was nothing but a two-variant assembly of the Ni3V phase, which was produced by consuming the threevariant fine structure. The tendency of joining up of domains belonging to the same variant, leading to the formation of lamellae, was demonstrated by the arrangement of microdomains of each variant along < 110 > directions. Order-annealing the alloy for 10 h at 650 C revealed that barring a few regions, almost all the fine domains had coarsened. Fig. 4(a) shows a typical BF image obtained from such a specimen. A banded contrast with bands oriented in different directions could be observed. These bands corresponded to different variants of the ordered phase. Detailed microscopic analysis revealed some interesting features of this microstructure, which are described in the following. A SAD pattern from the region marked 1 showed superlattice reflections corresponding to all the three variants [Fig. 4(b)] whereas those from regions 2, 3 and 4 showed superlattice reflections corresponding to only two variants. However, the
Fig. 3. (a) and (b) DF micrographs, imaged respectively with (100) and (010) superlattice reflections, illustrating the coarsening of fine domains to form large domains in a sample aged for 1 h at 650 C.
86
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
three regions (regions 2, 3 and 4) all showed different combinations of two of the three variants. A [001] zone axis SAD pattern from region 2 showed superlattice reflections corresponding to [100] and [010] variants [Fig. 4(c)]. A [001] SAD pattern from the region 3 showed superlattice reflections corresponding to [010] and [001] variants whereas one from region 4 showed superlattice reflections corresponding to [100] and [001] variants. A careful look at regions 1, 3 and 4 also revealed that the three-variant arrangement observed in region 1 was, in fact, the consequence of the intersection of the two-variant structures corresponding to regions 3 and 4. Tanner [2] has suggested that the three variants are arranged in a prism shaped mosaic assembly, domains within which are bounded by interfaces that approximate ð102ÞD022 (or {101}fcc) orientations. Such an assembly of three variants in an < 111> orientation would have an angle of about 120 between them. However, the three-variant assembly could not be imaged clearly in this orientation, as the contrast associated with the different variants was rather weak. On the other hand, this arrangement could be imaged well in a < 001 > orientation (Fig. 5). Fig. 5(a) shows a BF micrograph from a region where the three variants were
Fig. 4. (a) A typical BF image of an alloy aged at 650 C for 10 h showing that a major fraction of the fine domains in the field of view had coarsened to yield lamellae comprising coarse domains. A banded structure arising due to the arrangement of lamellae with different variant combinations of two of the three variants could be seen. Circles encircling the numbers 1–4 show the aperture positions. A [001] zone axis SAD pattern from the region marked 1 showed superlattice reflections corresponding to all the three variants whereas SAD patterns from regions marked 2, 3 and 4 showed the presence of only two variants. (b) and (c) respectively show the [001] zone axis SAD patterns from regions 1 and 2 (see text for details).
arranged together. Evidently, the arrangement of the three variants in this orientation appeared to be cuboidal. If the arrangement of these variants were assumed to be prism shaped, such a cuboidal arrangement could indeed be expected on projecting the prism shaped assembly on a (001) plane. Dark field images of the different variants are shown in Fig. 5 (b)–(d). Interfaces between different variants were found to be of {101} type. Fig. 6 shows a set of BF and DF images of the area marked by a rectangle in Fig. 4. It is to be noted that the images in Fig. 6 have been arranged with a 90 anticlockwise orientation with respect to that in Fig. 4. Fig. 6(a) is a BF micrograph whereas Fig. 6 (b)–(d) are DF micrographs of different variants imaged with their corresponding superlattice reflections. Evidently, the DF images revealed two morphologies of the coarsened domains: one with the coarse basket-weave type morphology (marked I) and the other with the lamellar morphology (marked II). Selected area diffraction patterns from both the regions showed the presence of only two variants. In region I, the two domains, as revealed by the [001] SAD pattern, corresponded to [100] and [010] variants with interfaces lying along (110) and (110) planes whereas the domains in region II corresponded to [100] and [001] variants. Overall, all the three variants could be observed in this field of view. In addition, small regions having fine domains could also be observed in
Fig. 5. (a) A typical BF micrograph from a sample aged at 650 C for 10 h showing a cuboidal arrangement of the three variants, when viewed in a [001] projection; (b) to (d) show DF images of the different variants imaged with (100), (010) and (110) superlattice reflections respectively.
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
this sample. The microstructure observed throughout this specimen was similar in nature to that shown in Fig. 4. Another set of micrographs where the fine domains had coarsened to form a lamellar structure is shown in Fig. 7. Once the fine domains coarsened to form large domains, there appeared to be a competition between the large domains to coarsen further. Larger domains appeared to grow at the expense of smaller domains. Order annealing of the alloy at 800 C for 1 h resulted in an almost complete elimination of fine domains and the general microstructure was quite similar to that observed in the alloy aged for 10 h at 650 C. Once the fine domain structure was eliminated, further coarsening appeared to be quite sluggish. In samples aged for 10 h at 800 C, the basket-weave type morphology could still be observed in many regions (Fig. 8). Comparing this microstructure with that associated with region I in Fig. 6 would reveal an interesting change in the basket-weave morphology as coarsening occurred. It could be seen that in Fig. 6, the two variants in the basket weave morphology have comparable volume fractions whereas in Fig. 8, the volume fraction of one of the variants is significantly larger than that of the other. This indicated that, between the two variants present in the region, there was again a competition for
Fig. 6. A set of BF and DF images from the area marked by a rectangle in Fig. 4. (a) BF micrograph and (b), (c) and (d) DF micrographs of different variants imaged with (100), (010) and (110) superlattice reflections. The region marked I showed a coarse basketweave type morphology whereas the region marked II showed a lamellar structure forming as a result of the coarsening of fine domains.
87
dominating over each other as the transformation progressed. In the case under discussion, it was the [100] variant that dominated over the [010] variant. A similar competition could be expected between the domains in the lamellar morphology. The transformation of the basket-weave structure to the lamellar structure took place by a process of interface elimination. As mentioned earlier, two types of {110} interfaces were present in the basket-weave microstructure. However, as the transformation progressed, the microstructure appeared to have chosen only one of these interfaces in the later stages of ageing. This is illustrated in Fig. 9. Some remnants of domains arranged along the disappearing interface (marked by arrows) could also be seen in addition to a domain corresponding to the third variant. Further ageing would ultimately result in the lamellar arrangement of two variants. In fact, ageing at 950 C just for 1 h produced the lamellar structure. 3.3. Effect of prolonged order annealing The lamellar structure was quite stable against coarsening since the adjacent lamellae were separated by coherent {110} interfaces. However, on prolonged order annealing, the two-variant lamellar structure would tend to transform to a single variant structure. Tanner [2] has shown that such a transition may occur due to ‘‘recrystallization’’ of the ordered domains. Each
Fig. 7. Another region from a sample aged at 650 C for 10 h showing the coarsening of fine domains to form a lamellar structure. (a) BF image; (b) [001] zone axis SAD pattern; (c) and (d) DF micrographs imaged with (100) and (010) superlattice reflections.
88
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
‘‘recrystallised’’ grain would contain only one variant of the ordered phase. Investigations during the present study indicated that the transition from the two-variant lamellar to the single variant structure during prolonged annealing could as well take place via a process similar to discontinuous coarsening. Fig. 10 shows a case, in a sample annealed at 850 C for 50 h, where the lamellar two-variant structure was in the process of transforming to a single variant structure. The lamellae corresponded to the [010] and [001] variants of the ordered phase [inset in Fig. 10(a)]. Evidently, during coarsening the [001] variant grew at the expense of the [010] variant. Owing to the large grain size, it was difficult to intercept such a transformation in the vicinity of a grain boundary in TEM samples. However, the scanning electron microscopy image shown in Fig. 10(d) revealed that such a discontinuous transformation had occurred in many regions in this specimen. The mechanisms involved in this type of transformation have been discussed in detail elsewhere [7]. 3.4. Changes in APB character during order annealing In the course of the present investigations, APBs were observed to change their character during the ordering
Fig. 8. Micrographs (of an alloy aged for 10 h at 800 C) illustrating the growth of larger domains at the expense of smaller domains. (a) BF micrograph from a region where most of the area imaged showed a basket-weave structure and was growing at the expense of smaller domains in the lamellar region (visible at an angle to the edge of the figure); (b), (c) and (d) DF micrographs imaged with (100), (010) and (110) superlattice reflections respectively, showing the different variants in bright contrast.
process. They were found to be ‘‘isotropic’’ in nature to start with; but they appeared to acquire some anisotropy along particular directions during the later stages of the transformation. The fine domains shown in Figs. 3 and 6 appeared to have isotropic boundaries as reported by Tanner [2]. Fig. 11 shows APBs observed in coarsened domains in a sample order annealed for 10 h at 650 C. A comparison of these APBs with those observed in the fine domain structure suggested that APBs associated with coarsened domains were characterized by a significant amount of anisotropy: the curvature of APBs in the latter case appeared to be significantly smaller than that in the fine domain structure. Such observations suggested that the initially isotropic APBs had some tendency to become anisotropic with the progress of the transformation. This observation was in agreement with those reported by Tanner [2]. As mentioned earlier, two types of APBs occur in the Ni3V phase. Vectors for Type I and Type II APBs would be different for different variants of this phase. Antiphase boundary vectors responsible for the creation of these two types of APBs in the [001] domain of the Ni3V phase are listed in Table 1. The numbers would obviously need to be permuted to arrive at the corresponding vectors in the [100] and [010] ordered domains. This table can be used to characterize the nature of APBs in ordered domains with [001] orientation. It could be seen that whereas Type II APBs would
Fig. 9. Micrographs showing a later stage of the transformation after 10 h of ageing at 800 C; one of the two interfaces of the basket-weave structure disappeared to form to a two variant lamellar structure. (a) BF micrograph of the region; (b) and (c) DF micrographs of the two variants; (d) a domain corresponding to the [001] variant could also be seen within this region.
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
always be visible with all the superlattice reflections, Type I APBs would be invisible with {001} type reflections. In regions containing large domains, both types of APBs (i.e., Types I and II) were observed. Fig. 11 (b) and (c) shows an example each of Type I and Type II APBs (marked A and B respectively) in a [100] domain. It could be seen that the APB marked A was invisible with the (100) reflection whereas that marked B was visible with both the (1/2 1 0) and (100) reflections. This established the nature of these two APBs to be of Types I and II respectively. On the whole, APBs of Type II nature were found to be predominant. In samples annealed for 10 h at 850 C, all the APBs were observed to be in contrast with {100}-type as well as with {1/2 1 0}-type reflections which established that only Type II APBs were present in the later stages of transformation.
4. Discussion 4.1. Nucleation of ordered Ni3V domains The disorder to order transformation in the Ni3V alloy is a typical example of cubic to non-cubic trans-
Fig. 10. (a) BF micrograph from a region (of a sample aged at 850 C for 50 h) undergoing transformation from a two variant lamellar morphology to a single variant morphology by a discontinuous coarsening type mechanism. The inset shows a [001] zone axis diffraction pattern from the interface; (b) DF micrograph showing the coarsening [001] variant in bright contrast; (c) DF micrograph showing the [010] variant. (d) Scanning electron microscopy image suggesting that such a discontinuous transformation had occurred in many regions of the specimen.
89
formation. Such transformations are usually associated with a transformation strain energy [8]. In these transformations an ordered superlattice can be created from a disordered state by two different processes. These are: (1) nucleation and growth process, in which nuclei having a finite value of the order parameter are created, and, (2) continuous ordering process, in which a continuous increase in the order parameter occurs by the local rearrangements of atoms, occurring homogeneously throughout the lattice, to establish the final long-range order. In the former case, the strain energy associated with the transformation contributes to the activation barrier for the nucleation of the equilibrium ordered phase, while in the latter, it suppresses the instability temperature for continuous ordering. This results in a reduction in the kinetics of the phase transformation. Often the transformation takes a kinetic path between the two extreme modes of ordering by creating nuclei with low values of the order parameter and/or with such a c0 /a0 ratio which produces a strain smaller than that produced during the nucleation of the equilibrium ordered phase. This type of nucleation provides a relatively low nucleation barrier analogous to the case of non-classical nucleation in phase separating systems, as suggested by Cahn and Hilliard [9]. An estimation of the tetragonality in solution treated and water quenched samples from the {200)Ni3v and (004)Ni3v and peak splitting observed in the X-ray diffraction gives a c0 /a0 value of 2.028. This value of c0 /a0 ratio corresponds to a relatively high value of order in the material as inferred from the work of Tanner [2]. The measured c0 /a0 value was, in fact, a mean value
Fig. 11. DF micrographs of coarsened domains in a specimen aged for 10 h at 650 C showing APBs with a significant amount of anisotropy; (a) a [001] domain imaged with (110) reflection, (b) and (c) [100] domains imaged with (1/2 1 0) and (100) reflections respectively. APBs marked as A and B show an example each of Type I and Type II APBs respectively.
90
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
Table 1 Expected contrast from Type I and Type II APBs in Ni3V phase ([001] domain), when they are imaged with (001), {1 0 1/2) and {110) reflections. (V: Visible; I: Invisible) APB type
APB vector
Type I
11 11 10 10 01 01
Type II
0 0 1 1 1 1
Operating Reflections 001 I I V V V V
1 0 1/2 V V V V V V
1 0 1/2 V V V V V V
averaged over the whole sample, which included disordered regions (with a c0 /a0 value equal to zero) also. Therefore, it would not be unreasonable to assume that the c0 /a0 value within individual ordered domains would be close to the maximum, which is equal to 2.036 [3]. Therefore, it was likely that the fine ordered domains were individually in a highly ordered state. This was possible because the transition from the disordered to the completely ordered state is attended by a rather small change in volume ( 0.33%). Consequently, ordered nuclei, completely coherent with the disordered lattice, could form randomly throughout the bulk. Short-range order and excess vacancies, retained from above Tc, would have assisted the process: the former by providing embryos with a suitable atomic arrangement and the latter by enhancing atomic interchange within the lattice. 4.2. Growth of ordered Ni3V domains The extensive impingement of ordered domains (Fig. 2) observed in solution treated and quenched samples indicated that the growth of these domains was almost complete during water quenching. From the value of the long-range order parameter, Tanner [2] has estimated that at least 50% of the ordering transformation takes place during the initial stages when the alloy is directly quenched from the disordered state to an ordering temperature of 600 C. In the present study, the initial microstructure was produced from water quenching the alloy to room temperature from the solutionising temperature (1150 C). Therefore, it could be assumed that a much higher density of the ordered particles than that obtained in the study carried out by Tanner [2] would be available for growth on ageing. However, with this high density of particles, only a very limited growth would be needed for the impingement of these particles to occur. Two contiguously arranged fine ordered domains would correspond to either the same variant or to two different variants. During the growth, domains with the same orientation would impinge and coalesce to form a
0 1 1/2 V V V V V V
0 1 1/2 V V V V V V
110 V I V V V V
110 I V V V V V
large domain, which might or might not have an APB within it whereas domains with different orientations would meet along a common interface. The interfacial as well as the surface energy associated with the fine domain structure would be strongly dependent on the degree of order within these domains. This is primarily because of the fact that the increase in the chemical order parameter would be accompanied by an increase in the tetragonal distortion (c0 /a0 ratio). Therefore, this structure would have a strong tendency to reduce its strain and surface energy by allowing the growth of its constituent domains and such structures do so by aggregating fine domains to form an assembly of perpendicular twin related domains [8]. In this configuration adjacent domains are separated by {110} (i.e., f102gD022 ) type interfaces with adjacent domains having their tetragonal axes perpendicular to each other [8]. The same was observed in the present case as well. The creation of a group of parallel lamellae of perpendicular twin related domains which replaced the three-variant fine domain structure would, therefore, bring about a significant reduction in the surface and the strain energy. The resultant microstructure would exhibit twin related lamellae. The subsequent growth of such twin related lamellae would essentially involve ‘‘switching’’ of domain orientations ahead of the advancing front of coarsening lamellae. The switching process would encompass atomic jumps from one set of lattice positions to another, resulting in a rotation of the c0 -axis. The fact that the order parameter within the fine domains was quite high indicated that growth process (which involved a transition from a three-variant fine domain structure to a two-variant lamellar structure) was not primarily driven by the difference in the order parameter between the initial and the product structures. 4.3. Coarsening of ordered Ni3V domains The main factors that influence a disorder to order transformations are: (1) an increase in the degree of long-range order, (2) the magnitude of the ordering
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
strain energy and (3) a reduction in the interfacial energy associated with APBs and inter-variant domain boundaries (henceforth termed as ‘‘domain boundaries’’). As discussed earlier, the degree of order within the fine domains was quite high. Therefore, it was unlikely that an increase in the order parameter contributed very significantly to the coarsening of domains. Most of the strain arising during the ordering reaction was due to the change in the crystal structure from cubic to tetragonal. During the growth process, when two domains corresponding to different perpendicular variants would meet along {110} type interfaces, most of the accompanying ordering strain would get accommodated. Therefore, the major driving force for domain coarsening originated from the reduction in the interfacial energy associated with APBs and domain boundaries; this inference was also consistent with experimental observations. There was a significant difference in the density of APBs in coarsened domains in comparison to that in fine domains (Fig. 3). Coarsening of domains was observed to take place homogeneously throughout the grain. Many such coarsened regions could be observed within a grain in samples annealed for 10 h at 650 C (Fig. 4). When these regions grew, colonies or twin clusters with different variant combinations formed and subsequently impinged on other clusters within the originally disordered, parent grain. The two coarsening processes (viz., reduction of APB area and reduction of domain boundary area) occurred simultaneously. Large domains (thicker lamellae) grew at the expense of smaller domains. The driving force for such a coarsening mechanism can be assessed by considering the contributions of the interfacial energy of domain boundaries to the total strain energy of the system. According to Khachaturyan [8], the strain energy of an assembly of twin related tetragonal domains separated by (110) type interfaces is given by l ¼ ð110Þ
2V e€
where ð110Þ is the surface energy of the interfaces, V is the volume of the assembly and l is the period of the domain array, i.e., the distance between two consecutive domain boundaries. It follows from this expression that thinner lamellae would be associated with a larger accumulated strain energy as compared to thicker lamellae. This is in conformity with the results reported by Ling and Starke [10] in the Ni4Mo alloy. They have concluded that the strain in a lattice decreases with increasing domain size. Therefore, the removal of thinner domains would result in large reduction in the strain energy. From this discussion it could, therefore, be inferred that larger domains would grow at the expense of smaller domains in a manner similar to Ostwald ripening [11].
91
It was observed that the formation of the lamellar structure was often preceded by the formation of a coarse basket-weave type structure comprising two variants (Figs. 6, 8 and 9). As mentioned above, two variants of the ordered phase met along a {110} interface in order to accommodate the transformation strain. For any combination of two perpendicular variants (say, [100] and [010] variants), these variants could meet along two possible {110} interfaces (i.e., (110) and (110) interfaces), which were perpendicular to each other. This would result in the formation of a lamellar structure consisting of these variants for which lamellae boundaries would be perpendicular to each other and would give the appearance of the coarse basket-weave type morphology. The two interfaces being crystallographically equivalent, they would have the same interface energy. Experimental evidences indicated that the transformation from the basket-weave to the lamellar structure took place by the elimination of one of the two interfaces. Interfaces bounding thinner domains would be preferentially eliminated. Progressively the coarsened domains would assume a lamellar morphology as depicted in Fig. 9. The lamellar structure would ultimately coarsen to yield a single domain (variant) covering the whole grain (Fig. 10). 4.4. Role of antiphase boundaries during coarsening Crystallographically APBs can be expressed in terms of the reappearance of those symmetry operations, which are lost during the ordering process. The lost symmetry operations can be identified on the basis of the theoretical formulation developed earlier [12]. The translational symmetry lost during ordering appears as APBs. The number of translational variants, t, is given by the ratio Vo/Vd, where Vo and Vd represent the volumes of the primitive unit cells of the ordered and the disordered structures respectively [12]. For nonprimitive unit cells, the multiplicity of the respective structures should be taken into account. The number of APBs associated with different translational variants is then given by t-1. Using this formalism, the number of APBs calculated for Ni3V was found to be 3. These three APBs would appear as faults created by three different 1/2 < 110> translational vectors and are categorized as having Types I and II nature in the present case. The energies of these types of APBs have been determined to be about 150 and 40 mJ/m2, respectively [5,13]. A reduction in the number density of APBs would, therefore, result in a reduction in the internal energy. APBs associated with high energy could be expected to get eliminated faster as compared to APBs with low energy. Therefore, Type I APBs would be eliminated first. During the nucleation and growth process, a near perfect lattice registry across the interface between the ordered and disordered regions was maintained. This
92
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
resulted in the evolution of a large number of ordered regions per unit volume. Since Ni and V atoms could order on different sublattices, the independently nucleated domains would often be ‘out-of-phase’ (i.e., in antiphase juxtaposition). When these domains grew and impinged, APBs across which atoms had the ‘wrong’ kind of neighbours were formed. The isotropic nature of APBs observed in the initial stages of ordering appeared to be the result of the impingement of fine ordered domains that corresponded to the same orientation but were ‘out-of-phase’. In the coarsened domains, a few APBs of Type I nature were observed. However, these APBs were completely eliminated in samples aged for 10 h at 800 C. The fact that no Type I APBs could be observed in these samples indicated that, as the transformation progressed, APBs of Type I nature were completely eliminated. All the APBs were associated with some curvature even in the later stages of coarsening. These results demonstrated that Type II APBs were more stable than Type I APBs. These observations were consistent with the value of the energy of deformation induced APBs estimated by Francois et al. [5]. According to them, at high temperatures, these APBs do not show any pronounced anisotropy either on (111) or (001) planes, unlike in the case of Al3Ti alloy [14]. The elimination of all types of APBs, anyway, would contribute to the driving force in the later stages of the coarsening process.
5. Conclusions The evolution of microstructure in a Ni–25 at.% V alloy occurs through a series of structural changes, starting with fine ordered domains corresponding to all the three Ni3V variants and ending with a single variant covering the entire grain of the ordered phase, via the formation of a two variant lamellar structure. The two variant lamellar structure is quite stable until a ‘‘recrystallization’’ process or discontinuous type of coarsening
process intervenes to coarsen it to a structure in which each grain comprises a single Ni3V variant. Coarsening of domains takes place in a manner similar to Ostwald ripening wherein larger domains coarsen at the expense of smaller domains. APBs of Type II nature are found to be thermally more stable in comparison to APBs of Type I nature.
Acknowledgements The authors are grateful to the Head, Materials Science Division and Director, Materials Group, for their keen interest in this study. The help rendered by Mrs. P.S. Agashe in printing the micrographs is also gratefully acknowledged.
References [1] Massalski TB. Binary alloys phase diagrams, vol.3. ASM Intl., 1992. [2] Tanner LE. Physica Stat Sol 1968;30:685. [3] Villars P, Calvert LD. Pearson’s handbook of crystallography data for intermetallic phases, vol. 3. Metals Park (OH): ASM; 1986. p. 2907. [4] Buerger MJ. Am Mineralogist 1945;30:469. [5] Francois A, Hug G, Veyssiere P. Philos mag A 1992;66:269. [6] Marcinkowski MJ. In: Thomas G, Washburn J, editors. Electron microscopy and strength of crystals, Interscience Publ.; 1963. p. 333. [7] Singh JB, Sundararaman M, Mukhopadhyay P, Banerjee S. Communicated to Acta Materialia. [8] Khachaturyan AG. Theory of structural transformations in solids. New York: John Wiley & Sons; 1983. p. 368. [9] Cahn JW, Hilliard JE. J Chem Phys 1959;31:688. [10] Ling FW, Starke Jr EA. Acta Metall 1971;19:759. [11] Cahn RW, Haasen P. Physical metallurgy, vol. 2. Amesterdam: North-Holland; 1996. p. 1436. [12] van Tendeloo G, Amelinckx S. Acta Cryst A 1974;30:431. [13] Vanderschaeve G, Escaig B. J Phys Lett 1978;39:74. [14] Hug G, Doulin J, Veyssiere P. High temperature ordered intermetallic alloys III. In: Liu CT, Taub AL, Stoloff NS, Koch CC, editors. MRS Symposia Proceedings, vol. 133. 1989. p. 125.
Evolution of microstructure in the stoichiometric Ni–25at.%V alloy J.B. Singha,*, M. Sundararamana, P. Mukhopadhyaya, N. Prabhub b
a Materials Science Division, Bhabha Atomic Research Centre, Mumbai- 400 085, India Department of Metallurgical Engineering and Materials Science, IIT Bombay, Mumbai- 400 076, India
Received 19 August 2002; received in revised form 18 September 2002; accepted 26 September 2002
Abstract The disorder-to-order reaction in the stoichiometric Ni3V alloy is a typical cubic-to-tetragonal type (A1 to D022) transformation. Microstructural evolution has been studied at different temperatures below the ordering temperature in samples of this alloy having the same initial microstructure produced by solution treatment followed by water quenching. The ordered phase has been observed to evolve through a series of structural changes, starting with the impingement and alignment of fine ordered domains corresponding to all the three variants of the ordered phase, followed by the appearance of a two-variant lamellar structure which ultimately gets converted to a structure in which each Ni3V grain comprises a single variant. The lamellar structure is found to be quite stable with regard to coarsening in response to heat treatments. Evidence has been found which indicates that a discontinuous coarsening type of reaction is one of the possible mechanisms driving the two-variant lamellar to single-variant morphological transition. It has also been observed that coarsening of domains takes place in a manner similar to Ostwald ripening wherein larger domains coarsen at the expense of smaller domains. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: A. Intermetallics, miscellaneous; B. Order/disorder transformation; F. Electron microscopy; Transmission
1. Introduction In the Ni–V binary system, the disordered fcc (A1) solid solution, at 25 at.% V (a=0.3567 nm), transforms below Tc=1045 C [1,2] to form an ordered body centered tetragonal (D022) phase (a0 =0.3542 nm, c0 /a0 =2.036) [3]. Fig. 1 shows the ordered Ni3V unit cell. Since the c0 direction of the tetragonal cell may align itself along any one of the three 4-fold axes (i.e., < 001> axes) of the cubic cell, the ordered D022 phase possesses three mutually orthogonal variants. These are called transformation variants [4]. The transformation variants of the Ni3V phase are perpendicular twin related to each other (c0 axes of two variants being perpendicular to each other) across {101}1 (or f102ÞD022 ) planes.
* Corresponding author. Tel.: +91-22-559-5061; fax: +91-22-5505151. E-mail address: [email protected] (J.B. Singh). 1 It is to be noted that all the indices used throughout this paper are expressed in terms of the fcc basis unless otherwise mentioned. The asymmetrical notation means that permutations are possible on the first two indices while the third is fixed.
If two contiguous regions of an ordered crystal of a given variant do not share the same unit cell orientation, they are in juxtaposition and their mutual interface is an intra-variant domain boundary (henceforth called an antiphase boundary (APB)). Lattice translations that can create APBs in the ordered Ni3V phase are shown in Fig. 1 and are given by 1 P1 ¼ ½a0 ; a0 ; 0D022 2 and P2 ¼
1 < 2a0 ; 0; c0 D022 4
APBs represented by P2 and P20 in the figure are equivalent. The two types of vectors, namely, P1 and P2, would create distinct APBs on a plane. Francois et al. [5] have estimated the energies of APBs created by these vectors on the (111) plane and have found these to be about 150 and 40 mJ/m2 respectively. Since the two APB types are associated with distinct APB energies,
0966-9795/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(02)00186-3
84
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
these are designated as ‘‘Type I’’ and ‘‘Type II’’ respectively. It should be pointed out here that both types of APBs created by P1 and P2 vectors on the (111) plane are conservative in nature and correspond to APBs of the ‘‘first kind’’ as per the nomenclature used in the literature [6]. Ordering in the stoichiometric Ni3V alloy is so fast that it cannot be suppressed even by melt-spinning [7]. Different morphologies are obtained in the microstructure on directly quenching the alloy from a solutionising temperature (> Tc) to different order annealing temperatures (< Tc) [2]. The evolution of these morphologies is attributed to the operation of different transformation mechanisms at different ordering temperatures. The microstructure developed during low temperature order annealing exhibits all the three variants of the ordered phase which arrange themselves in a mosaic assembly of prism shaped cells bounded by interfaces that approximate f102gD022 type orientations [2]. During high temperature order annealing, the ordered Ni3V phase assumes a lamellar shape with the lamellae bounded by f102gD022 planes. Each lamella corresponds to a rotational variant of the ordered phase. The long-range order parameter generally remains less than unity even after prolonged low temperature order annealing, whereas near perfect order is attained within a short time during high temperature annealing [2]. It is expected that the different microstructures evolved at different ordering temperatures (i.e., the three-variant structure and the two-variant lamellar structure) are related. In view of this, the
evolution of the microstructure has been studied at different temperatures in samples having the same initial microstructure, namely, that produced by solution treatment followed by water quenching. These studies have been carried out using diffraction contrast transmission electron microscopy (TEM).
2. Experimental procedure Buttons of the Ni–25 at.% V alloy were prepared by electron beam melting and arc melting of pure Ni and V. The alloy was remelted several times to improve homogeneity. The homogeneity in the composition of the alloy was confirmed by determining the composition at different points of the buttons using electron probe microanalysis (EPMA). Thin slices, cut from the cast buttons, were solution treated at 1150 C for 4 h and then water quenched. Solution treated samples were order annealed at different temperatures ranging from 650 to 950 C below Tc. X-ray diffraction examination of the solution treated specimen was carried out using a monochromatic copper Ka radiation source. For making TEM specimens, appropriately order annealed slices of the alloy were mechanically ground to a thickness of about 0.1 mm. Discs of 3 mm diameter were then punched out from these foils. The discs were electropolished at about 18 V to perforation in a dual jet Tenupol unit, using an electrolyte containing 1 part perchloric acid and 4 parts ethanol; the temperature of the electrolyte was maintained at about 35 C. The thinned samples were examined in a Jeol JEM 2000 FX electron microscope. The ordered Ni3V phase was identified from the presence of superlattice reflections at {100} and {1 1/2 0} positions in selected area diffraction (SAD) patterns corresponding to different zone axes, this being a characteristic feature of phases with the D022 structure.
3. Results 3.1. Microstructure of the solution treated alloy
Fig. 1. The Ni3V (D022) unit cell. Whereas P1 and P2 indicate the translation vectors which can create Type I and Type II APBs respectively, P2 and P20 indicate equivalent translations on two different planes which would both create Type II APBs.
The microstructure of the solution treated and water quenched alloy showed a fine dispersion of ordered particles, corresponding to all the three variants of the ordered phase, embedded in a disordered matrix (Fig. 2). Bright field (BF) micrograph [Fig. 2(a)] showed a tweed contrast. The ordered particles maintained perfect coherency with the disordered matrix. That all the three variants of the ordered phase were present within a single grain of the parent phase could be confirmed from the < 001 > zone axis SAD pattern [inset in Fig. 2(a)]. Superlattice reflections appeared to be quite intense. Dark field (DF) micrographs obtained by using superlattice reflections corresponding to one of the variants
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
[Fig. 2(b)] revealed that the ordered particles were aligned along < 110 > directions. X-ray diffraction study of this sample showed a significant splitting of the {200}fcc peak [Fig. 2(c)] into ð004ÞNi3 V and f200ÞNi3 V peaks at 2 values equal to 50.81 and 51.57 respectively. The lattice parameters, a0 and c0 of the ordered phase, deduced from these peaks are 0.3542 and 0.7182 nm respectively. 3.2. Microstructure of order-annealed alloy The microstructure in this alloy appeared to have evolved through impingement and alignment of fine ordered domains. Interfaces between ordered domains were devoid of any dislocations. This indicated that ordered and disordered regions remained fully coherent during the growth. Dark field imaging of different domains in samples order annealed for 1 h at 650 C showed domains of two sizes; the average size of the two types of domains differed by about an order of ten (Fig. 3). The fine ordered domains appeared to have coagulated to form the large domains. These large domains grew to form the lamellar structure. The
Fig. 2. (a) BF micrograph showing the tweed contrast in a solution treated and quenched sample. A [001] zone axis diffraction pattern showing the presence of all the three variants of the ordered phase is shown in the inset. (b) A DF micrograph, imaged with a superlattice reflection corresponding to one of the three variants of the Ni3V phase, showing the alignment of ordered particles along [110] and [110] directions. (c) X-ray diffraction showing a significant splitting of f200ÞNi3 V and ð004ÞNi3 V peaks in a solution treated sample.
85
transformation to the lamellar structure often occurred through an intermediate coarse basket weave type structure, which will be discussed later. Selected area diffraction patterns from regions containing smaller domains often showed superlattice reflections corresponding to all the three variants, whereas those from the adjacent regions, containing larger domains, showed superlattice reflections corresponding to only one or two variants, depending upon the aperture size. This indicated that during the coarsening process, one or two of the variants had dissolved or had ‘‘switched’’ their orientations to those favoured by the large domains. < 001 > zone axis diffraction patterns from two adjacent large domains also indicated that the two domains corresponded to perpendicular twin related variants across {110} interfaces, with the c0 -axes in the two domains perpendicular to each other. Such perpendicular twin related domains are often produced during cubic to tetragonal transformations. Dark field micrographs of two such domains are shown in Fig. 3 (a) and (b). The observed perpendicular twin lamellar structure was nothing but a two-variant assembly of the Ni3V phase, which was produced by consuming the threevariant fine structure. The tendency of joining up of domains belonging to the same variant, leading to the formation of lamellae, was demonstrated by the arrangement of microdomains of each variant along < 110 > directions. Order-annealing the alloy for 10 h at 650 C revealed that barring a few regions, almost all the fine domains had coarsened. Fig. 4(a) shows a typical BF image obtained from such a specimen. A banded contrast with bands oriented in different directions could be observed. These bands corresponded to different variants of the ordered phase. Detailed microscopic analysis revealed some interesting features of this microstructure, which are described in the following. A SAD pattern from the region marked 1 showed superlattice reflections corresponding to all the three variants [Fig. 4(b)] whereas those from regions 2, 3 and 4 showed superlattice reflections corresponding to only two variants. However, the
Fig. 3. (a) and (b) DF micrographs, imaged respectively with (100) and (010) superlattice reflections, illustrating the coarsening of fine domains to form large domains in a sample aged for 1 h at 650 C.
86
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
three regions (regions 2, 3 and 4) all showed different combinations of two of the three variants. A [001] zone axis SAD pattern from region 2 showed superlattice reflections corresponding to [100] and [010] variants [Fig. 4(c)]. A [001] SAD pattern from the region 3 showed superlattice reflections corresponding to [010] and [001] variants whereas one from region 4 showed superlattice reflections corresponding to [100] and [001] variants. A careful look at regions 1, 3 and 4 also revealed that the three-variant arrangement observed in region 1 was, in fact, the consequence of the intersection of the two-variant structures corresponding to regions 3 and 4. Tanner [2] has suggested that the three variants are arranged in a prism shaped mosaic assembly, domains within which are bounded by interfaces that approximate ð102ÞD022 (or {101}fcc) orientations. Such an assembly of three variants in an < 111> orientation would have an angle of about 120 between them. However, the three-variant assembly could not be imaged clearly in this orientation, as the contrast associated with the different variants was rather weak. On the other hand, this arrangement could be imaged well in a < 001 > orientation (Fig. 5). Fig. 5(a) shows a BF micrograph from a region where the three variants were
Fig. 4. (a) A typical BF image of an alloy aged at 650 C for 10 h showing that a major fraction of the fine domains in the field of view had coarsened to yield lamellae comprising coarse domains. A banded structure arising due to the arrangement of lamellae with different variant combinations of two of the three variants could be seen. Circles encircling the numbers 1–4 show the aperture positions. A [001] zone axis SAD pattern from the region marked 1 showed superlattice reflections corresponding to all the three variants whereas SAD patterns from regions marked 2, 3 and 4 showed the presence of only two variants. (b) and (c) respectively show the [001] zone axis SAD patterns from regions 1 and 2 (see text for details).
arranged together. Evidently, the arrangement of the three variants in this orientation appeared to be cuboidal. If the arrangement of these variants were assumed to be prism shaped, such a cuboidal arrangement could indeed be expected on projecting the prism shaped assembly on a (001) plane. Dark field images of the different variants are shown in Fig. 5 (b)–(d). Interfaces between different variants were found to be of {101} type. Fig. 6 shows a set of BF and DF images of the area marked by a rectangle in Fig. 4. It is to be noted that the images in Fig. 6 have been arranged with a 90 anticlockwise orientation with respect to that in Fig. 4. Fig. 6(a) is a BF micrograph whereas Fig. 6 (b)–(d) are DF micrographs of different variants imaged with their corresponding superlattice reflections. Evidently, the DF images revealed two morphologies of the coarsened domains: one with the coarse basket-weave type morphology (marked I) and the other with the lamellar morphology (marked II). Selected area diffraction patterns from both the regions showed the presence of only two variants. In region I, the two domains, as revealed by the [001] SAD pattern, corresponded to [100] and [010] variants with interfaces lying along (110) and (110) planes whereas the domains in region II corresponded to [100] and [001] variants. Overall, all the three variants could be observed in this field of view. In addition, small regions having fine domains could also be observed in
Fig. 5. (a) A typical BF micrograph from a sample aged at 650 C for 10 h showing a cuboidal arrangement of the three variants, when viewed in a [001] projection; (b) to (d) show DF images of the different variants imaged with (100), (010) and (110) superlattice reflections respectively.
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
this sample. The microstructure observed throughout this specimen was similar in nature to that shown in Fig. 4. Another set of micrographs where the fine domains had coarsened to form a lamellar structure is shown in Fig. 7. Once the fine domains coarsened to form large domains, there appeared to be a competition between the large domains to coarsen further. Larger domains appeared to grow at the expense of smaller domains. Order annealing of the alloy at 800 C for 1 h resulted in an almost complete elimination of fine domains and the general microstructure was quite similar to that observed in the alloy aged for 10 h at 650 C. Once the fine domain structure was eliminated, further coarsening appeared to be quite sluggish. In samples aged for 10 h at 800 C, the basket-weave type morphology could still be observed in many regions (Fig. 8). Comparing this microstructure with that associated with region I in Fig. 6 would reveal an interesting change in the basket-weave morphology as coarsening occurred. It could be seen that in Fig. 6, the two variants in the basket weave morphology have comparable volume fractions whereas in Fig. 8, the volume fraction of one of the variants is significantly larger than that of the other. This indicated that, between the two variants present in the region, there was again a competition for
Fig. 6. A set of BF and DF images from the area marked by a rectangle in Fig. 4. (a) BF micrograph and (b), (c) and (d) DF micrographs of different variants imaged with (100), (010) and (110) superlattice reflections. The region marked I showed a coarse basketweave type morphology whereas the region marked II showed a lamellar structure forming as a result of the coarsening of fine domains.
87
dominating over each other as the transformation progressed. In the case under discussion, it was the [100] variant that dominated over the [010] variant. A similar competition could be expected between the domains in the lamellar morphology. The transformation of the basket-weave structure to the lamellar structure took place by a process of interface elimination. As mentioned earlier, two types of {110} interfaces were present in the basket-weave microstructure. However, as the transformation progressed, the microstructure appeared to have chosen only one of these interfaces in the later stages of ageing. This is illustrated in Fig. 9. Some remnants of domains arranged along the disappearing interface (marked by arrows) could also be seen in addition to a domain corresponding to the third variant. Further ageing would ultimately result in the lamellar arrangement of two variants. In fact, ageing at 950 C just for 1 h produced the lamellar structure. 3.3. Effect of prolonged order annealing The lamellar structure was quite stable against coarsening since the adjacent lamellae were separated by coherent {110} interfaces. However, on prolonged order annealing, the two-variant lamellar structure would tend to transform to a single variant structure. Tanner [2] has shown that such a transition may occur due to ‘‘recrystallization’’ of the ordered domains. Each
Fig. 7. Another region from a sample aged at 650 C for 10 h showing the coarsening of fine domains to form a lamellar structure. (a) BF image; (b) [001] zone axis SAD pattern; (c) and (d) DF micrographs imaged with (100) and (010) superlattice reflections.
88
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
‘‘recrystallised’’ grain would contain only one variant of the ordered phase. Investigations during the present study indicated that the transition from the two-variant lamellar to the single variant structure during prolonged annealing could as well take place via a process similar to discontinuous coarsening. Fig. 10 shows a case, in a sample annealed at 850 C for 50 h, where the lamellar two-variant structure was in the process of transforming to a single variant structure. The lamellae corresponded to the [010] and [001] variants of the ordered phase [inset in Fig. 10(a)]. Evidently, during coarsening the [001] variant grew at the expense of the [010] variant. Owing to the large grain size, it was difficult to intercept such a transformation in the vicinity of a grain boundary in TEM samples. However, the scanning electron microscopy image shown in Fig. 10(d) revealed that such a discontinuous transformation had occurred in many regions in this specimen. The mechanisms involved in this type of transformation have been discussed in detail elsewhere [7]. 3.4. Changes in APB character during order annealing In the course of the present investigations, APBs were observed to change their character during the ordering
Fig. 8. Micrographs (of an alloy aged for 10 h at 800 C) illustrating the growth of larger domains at the expense of smaller domains. (a) BF micrograph from a region where most of the area imaged showed a basket-weave structure and was growing at the expense of smaller domains in the lamellar region (visible at an angle to the edge of the figure); (b), (c) and (d) DF micrographs imaged with (100), (010) and (110) superlattice reflections respectively, showing the different variants in bright contrast.
process. They were found to be ‘‘isotropic’’ in nature to start with; but they appeared to acquire some anisotropy along particular directions during the later stages of the transformation. The fine domains shown in Figs. 3 and 6 appeared to have isotropic boundaries as reported by Tanner [2]. Fig. 11 shows APBs observed in coarsened domains in a sample order annealed for 10 h at 650 C. A comparison of these APBs with those observed in the fine domain structure suggested that APBs associated with coarsened domains were characterized by a significant amount of anisotropy: the curvature of APBs in the latter case appeared to be significantly smaller than that in the fine domain structure. Such observations suggested that the initially isotropic APBs had some tendency to become anisotropic with the progress of the transformation. This observation was in agreement with those reported by Tanner [2]. As mentioned earlier, two types of APBs occur in the Ni3V phase. Vectors for Type I and Type II APBs would be different for different variants of this phase. Antiphase boundary vectors responsible for the creation of these two types of APBs in the [001] domain of the Ni3V phase are listed in Table 1. The numbers would obviously need to be permuted to arrive at the corresponding vectors in the [100] and [010] ordered domains. This table can be used to characterize the nature of APBs in ordered domains with [001] orientation. It could be seen that whereas Type II APBs would
Fig. 9. Micrographs showing a later stage of the transformation after 10 h of ageing at 800 C; one of the two interfaces of the basket-weave structure disappeared to form to a two variant lamellar structure. (a) BF micrograph of the region; (b) and (c) DF micrographs of the two variants; (d) a domain corresponding to the [001] variant could also be seen within this region.
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
always be visible with all the superlattice reflections, Type I APBs would be invisible with {001} type reflections. In regions containing large domains, both types of APBs (i.e., Types I and II) were observed. Fig. 11 (b) and (c) shows an example each of Type I and Type II APBs (marked A and B respectively) in a [100] domain. It could be seen that the APB marked A was invisible with the (100) reflection whereas that marked B was visible with both the (1/2 1 0) and (100) reflections. This established the nature of these two APBs to be of Types I and II respectively. On the whole, APBs of Type II nature were found to be predominant. In samples annealed for 10 h at 850 C, all the APBs were observed to be in contrast with {100}-type as well as with {1/2 1 0}-type reflections which established that only Type II APBs were present in the later stages of transformation.
4. Discussion 4.1. Nucleation of ordered Ni3V domains The disorder to order transformation in the Ni3V alloy is a typical example of cubic to non-cubic trans-
Fig. 10. (a) BF micrograph from a region (of a sample aged at 850 C for 50 h) undergoing transformation from a two variant lamellar morphology to a single variant morphology by a discontinuous coarsening type mechanism. The inset shows a [001] zone axis diffraction pattern from the interface; (b) DF micrograph showing the coarsening [001] variant in bright contrast; (c) DF micrograph showing the [010] variant. (d) Scanning electron microscopy image suggesting that such a discontinuous transformation had occurred in many regions of the specimen.
89
formation. Such transformations are usually associated with a transformation strain energy [8]. In these transformations an ordered superlattice can be created from a disordered state by two different processes. These are: (1) nucleation and growth process, in which nuclei having a finite value of the order parameter are created, and, (2) continuous ordering process, in which a continuous increase in the order parameter occurs by the local rearrangements of atoms, occurring homogeneously throughout the lattice, to establish the final long-range order. In the former case, the strain energy associated with the transformation contributes to the activation barrier for the nucleation of the equilibrium ordered phase, while in the latter, it suppresses the instability temperature for continuous ordering. This results in a reduction in the kinetics of the phase transformation. Often the transformation takes a kinetic path between the two extreme modes of ordering by creating nuclei with low values of the order parameter and/or with such a c0 /a0 ratio which produces a strain smaller than that produced during the nucleation of the equilibrium ordered phase. This type of nucleation provides a relatively low nucleation barrier analogous to the case of non-classical nucleation in phase separating systems, as suggested by Cahn and Hilliard [9]. An estimation of the tetragonality in solution treated and water quenched samples from the {200)Ni3v and (004)Ni3v and peak splitting observed in the X-ray diffraction gives a c0 /a0 value of 2.028. This value of c0 /a0 ratio corresponds to a relatively high value of order in the material as inferred from the work of Tanner [2]. The measured c0 /a0 value was, in fact, a mean value
Fig. 11. DF micrographs of coarsened domains in a specimen aged for 10 h at 650 C showing APBs with a significant amount of anisotropy; (a) a [001] domain imaged with (110) reflection, (b) and (c) [100] domains imaged with (1/2 1 0) and (100) reflections respectively. APBs marked as A and B show an example each of Type I and Type II APBs respectively.
90
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
Table 1 Expected contrast from Type I and Type II APBs in Ni3V phase ([001] domain), when they are imaged with (001), {1 0 1/2) and {110) reflections. (V: Visible; I: Invisible) APB type
APB vector
Type I
11 11 10 10 01 01
Type II
0 0 1 1 1 1
Operating Reflections 001 I I V V V V
1 0 1/2 V V V V V V
1 0 1/2 V V V V V V
averaged over the whole sample, which included disordered regions (with a c0 /a0 value equal to zero) also. Therefore, it would not be unreasonable to assume that the c0 /a0 value within individual ordered domains would be close to the maximum, which is equal to 2.036 [3]. Therefore, it was likely that the fine ordered domains were individually in a highly ordered state. This was possible because the transition from the disordered to the completely ordered state is attended by a rather small change in volume ( 0.33%). Consequently, ordered nuclei, completely coherent with the disordered lattice, could form randomly throughout the bulk. Short-range order and excess vacancies, retained from above Tc, would have assisted the process: the former by providing embryos with a suitable atomic arrangement and the latter by enhancing atomic interchange within the lattice. 4.2. Growth of ordered Ni3V domains The extensive impingement of ordered domains (Fig. 2) observed in solution treated and quenched samples indicated that the growth of these domains was almost complete during water quenching. From the value of the long-range order parameter, Tanner [2] has estimated that at least 50% of the ordering transformation takes place during the initial stages when the alloy is directly quenched from the disordered state to an ordering temperature of 600 C. In the present study, the initial microstructure was produced from water quenching the alloy to room temperature from the solutionising temperature (1150 C). Therefore, it could be assumed that a much higher density of the ordered particles than that obtained in the study carried out by Tanner [2] would be available for growth on ageing. However, with this high density of particles, only a very limited growth would be needed for the impingement of these particles to occur. Two contiguously arranged fine ordered domains would correspond to either the same variant or to two different variants. During the growth, domains with the same orientation would impinge and coalesce to form a
0 1 1/2 V V V V V V
0 1 1/2 V V V V V V
110 V I V V V V
110 I V V V V V
large domain, which might or might not have an APB within it whereas domains with different orientations would meet along a common interface. The interfacial as well as the surface energy associated with the fine domain structure would be strongly dependent on the degree of order within these domains. This is primarily because of the fact that the increase in the chemical order parameter would be accompanied by an increase in the tetragonal distortion (c0 /a0 ratio). Therefore, this structure would have a strong tendency to reduce its strain and surface energy by allowing the growth of its constituent domains and such structures do so by aggregating fine domains to form an assembly of perpendicular twin related domains [8]. In this configuration adjacent domains are separated by {110} (i.e., f102gD022 ) type interfaces with adjacent domains having their tetragonal axes perpendicular to each other [8]. The same was observed in the present case as well. The creation of a group of parallel lamellae of perpendicular twin related domains which replaced the three-variant fine domain structure would, therefore, bring about a significant reduction in the surface and the strain energy. The resultant microstructure would exhibit twin related lamellae. The subsequent growth of such twin related lamellae would essentially involve ‘‘switching’’ of domain orientations ahead of the advancing front of coarsening lamellae. The switching process would encompass atomic jumps from one set of lattice positions to another, resulting in a rotation of the c0 -axis. The fact that the order parameter within the fine domains was quite high indicated that growth process (which involved a transition from a three-variant fine domain structure to a two-variant lamellar structure) was not primarily driven by the difference in the order parameter between the initial and the product structures. 4.3. Coarsening of ordered Ni3V domains The main factors that influence a disorder to order transformations are: (1) an increase in the degree of long-range order, (2) the magnitude of the ordering
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
strain energy and (3) a reduction in the interfacial energy associated with APBs and inter-variant domain boundaries (henceforth termed as ‘‘domain boundaries’’). As discussed earlier, the degree of order within the fine domains was quite high. Therefore, it was unlikely that an increase in the order parameter contributed very significantly to the coarsening of domains. Most of the strain arising during the ordering reaction was due to the change in the crystal structure from cubic to tetragonal. During the growth process, when two domains corresponding to different perpendicular variants would meet along {110} type interfaces, most of the accompanying ordering strain would get accommodated. Therefore, the major driving force for domain coarsening originated from the reduction in the interfacial energy associated with APBs and domain boundaries; this inference was also consistent with experimental observations. There was a significant difference in the density of APBs in coarsened domains in comparison to that in fine domains (Fig. 3). Coarsening of domains was observed to take place homogeneously throughout the grain. Many such coarsened regions could be observed within a grain in samples annealed for 10 h at 650 C (Fig. 4). When these regions grew, colonies or twin clusters with different variant combinations formed and subsequently impinged on other clusters within the originally disordered, parent grain. The two coarsening processes (viz., reduction of APB area and reduction of domain boundary area) occurred simultaneously. Large domains (thicker lamellae) grew at the expense of smaller domains. The driving force for such a coarsening mechanism can be assessed by considering the contributions of the interfacial energy of domain boundaries to the total strain energy of the system. According to Khachaturyan [8], the strain energy of an assembly of twin related tetragonal domains separated by (110) type interfaces is given by l ¼ ð110Þ
2V e€
where ð110Þ is the surface energy of the interfaces, V is the volume of the assembly and l is the period of the domain array, i.e., the distance between two consecutive domain boundaries. It follows from this expression that thinner lamellae would be associated with a larger accumulated strain energy as compared to thicker lamellae. This is in conformity with the results reported by Ling and Starke [10] in the Ni4Mo alloy. They have concluded that the strain in a lattice decreases with increasing domain size. Therefore, the removal of thinner domains would result in large reduction in the strain energy. From this discussion it could, therefore, be inferred that larger domains would grow at the expense of smaller domains in a manner similar to Ostwald ripening [11].
91
It was observed that the formation of the lamellar structure was often preceded by the formation of a coarse basket-weave type structure comprising two variants (Figs. 6, 8 and 9). As mentioned above, two variants of the ordered phase met along a {110} interface in order to accommodate the transformation strain. For any combination of two perpendicular variants (say, [100] and [010] variants), these variants could meet along two possible {110} interfaces (i.e., (110) and (110) interfaces), which were perpendicular to each other. This would result in the formation of a lamellar structure consisting of these variants for which lamellae boundaries would be perpendicular to each other and would give the appearance of the coarse basket-weave type morphology. The two interfaces being crystallographically equivalent, they would have the same interface energy. Experimental evidences indicated that the transformation from the basket-weave to the lamellar structure took place by the elimination of one of the two interfaces. Interfaces bounding thinner domains would be preferentially eliminated. Progressively the coarsened domains would assume a lamellar morphology as depicted in Fig. 9. The lamellar structure would ultimately coarsen to yield a single domain (variant) covering the whole grain (Fig. 10). 4.4. Role of antiphase boundaries during coarsening Crystallographically APBs can be expressed in terms of the reappearance of those symmetry operations, which are lost during the ordering process. The lost symmetry operations can be identified on the basis of the theoretical formulation developed earlier [12]. The translational symmetry lost during ordering appears as APBs. The number of translational variants, t, is given by the ratio Vo/Vd, where Vo and Vd represent the volumes of the primitive unit cells of the ordered and the disordered structures respectively [12]. For nonprimitive unit cells, the multiplicity of the respective structures should be taken into account. The number of APBs associated with different translational variants is then given by t-1. Using this formalism, the number of APBs calculated for Ni3V was found to be 3. These three APBs would appear as faults created by three different 1/2 < 110> translational vectors and are categorized as having Types I and II nature in the present case. The energies of these types of APBs have been determined to be about 150 and 40 mJ/m2, respectively [5,13]. A reduction in the number density of APBs would, therefore, result in a reduction in the internal energy. APBs associated with high energy could be expected to get eliminated faster as compared to APBs with low energy. Therefore, Type I APBs would be eliminated first. During the nucleation and growth process, a near perfect lattice registry across the interface between the ordered and disordered regions was maintained. This
92
J.B. Singh et al. / Intermetallics 11 (2003) 83–92
resulted in the evolution of a large number of ordered regions per unit volume. Since Ni and V atoms could order on different sublattices, the independently nucleated domains would often be ‘out-of-phase’ (i.e., in antiphase juxtaposition). When these domains grew and impinged, APBs across which atoms had the ‘wrong’ kind of neighbours were formed. The isotropic nature of APBs observed in the initial stages of ordering appeared to be the result of the impingement of fine ordered domains that corresponded to the same orientation but were ‘out-of-phase’. In the coarsened domains, a few APBs of Type I nature were observed. However, these APBs were completely eliminated in samples aged for 10 h at 800 C. The fact that no Type I APBs could be observed in these samples indicated that, as the transformation progressed, APBs of Type I nature were completely eliminated. All the APBs were associated with some curvature even in the later stages of coarsening. These results demonstrated that Type II APBs were more stable than Type I APBs. These observations were consistent with the value of the energy of deformation induced APBs estimated by Francois et al. [5]. According to them, at high temperatures, these APBs do not show any pronounced anisotropy either on (111) or (001) planes, unlike in the case of Al3Ti alloy [14]. The elimination of all types of APBs, anyway, would contribute to the driving force in the later stages of the coarsening process.
5. Conclusions The evolution of microstructure in a Ni–25 at.% V alloy occurs through a series of structural changes, starting with fine ordered domains corresponding to all the three Ni3V variants and ending with a single variant covering the entire grain of the ordered phase, via the formation of a two variant lamellar structure. The two variant lamellar structure is quite stable until a ‘‘recrystallization’’ process or discontinuous type of coarsening
process intervenes to coarsen it to a structure in which each grain comprises a single Ni3V variant. Coarsening of domains takes place in a manner similar to Ostwald ripening wherein larger domains coarsen at the expense of smaller domains. APBs of Type II nature are found to be thermally more stable in comparison to APBs of Type I nature.
Acknowledgements The authors are grateful to the Head, Materials Science Division and Director, Materials Group, for their keen interest in this study. The help rendered by Mrs. P.S. Agashe in printing the micrographs is also gratefully acknowledged.
References [1] Massalski TB. Binary alloys phase diagrams, vol.3. ASM Intl., 1992. [2] Tanner LE. Physica Stat Sol 1968;30:685. [3] Villars P, Calvert LD. Pearson’s handbook of crystallography data for intermetallic phases, vol. 3. Metals Park (OH): ASM; 1986. p. 2907. [4] Buerger MJ. Am Mineralogist 1945;30:469. [5] Francois A, Hug G, Veyssiere P. Philos mag A 1992;66:269. [6] Marcinkowski MJ. In: Thomas G, Washburn J, editors. Electron microscopy and strength of crystals, Interscience Publ.; 1963. p. 333. [7] Singh JB, Sundararaman M, Mukhopadhyay P, Banerjee S. Communicated to Acta Materialia. [8] Khachaturyan AG. Theory of structural transformations in solids. New York: John Wiley & Sons; 1983. p. 368. [9] Cahn JW, Hilliard JE. J Chem Phys 1959;31:688. [10] Ling FW, Starke Jr EA. Acta Metall 1971;19:759. [11] Cahn RW, Haasen P. Physical metallurgy, vol. 2. Amesterdam: North-Holland; 1996. p. 1436. [12] van Tendeloo G, Amelinckx S. Acta Cryst A 1974;30:431. [13] Vanderschaeve G, Escaig B. J Phys Lett 1978;39:74. [14] Hug G, Doulin J, Veyssiere P. High temperature ordered intermetallic alloys III. In: Liu CT, Taub AL, Stoloff NS, Koch CC, editors. MRS Symposia Proceedings, vol. 133. 1989. p. 125.