Accommodation of transformation strain at cell interfaces during cubic to tetragonal transformation in a Ni-25at.%V alloy

Transcription

1 Accommodation of transformation strain at cell interfaces during cubic to tetragonal transformation in a Ni-25at.%V alloy J.B. Singh a, *, M. Sundararaman a, P. Mukhopadhyay a, N. Prabhu a,b a Materials Science Division, Bhabha Atomic Research Centre, Mumbai , India b Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology, Mumbai , India Abstract The ordering transformation in a stoichiometric Ni-25at.%V alloy involves a cubic (A1) to a tetragonal (DO 22 ) transformation. The microstructure essentially comprises cells (or colonies) of transformation twins corresponding to different variants of the ordered phase. Whereas it is well established that the formation of transformation twins reduces the strain energy associated with such cubic to noncubic transformations, the role of the interface separating two contiguous cells in further reducing the strain energy is generally overlooked. This paper presents some evidences of accommodation of strain at and in the vicinity of the intercell interfaces. Keywords: Ni 3 V; DO 22 structure; Ordering transformation; Strain accommodation 1. Introduction A disordered Ni-25at.%V alloy undergoes a cubic (A1) to tetragonal (DO 22 ) ordering transformation at temperatures below 1045 C by a first-order transformation process. This transformation leads to the generation of a significant amount of internal strain in the lattice. Domains of the ordered phase form with the [001] axis along any one of the h100i axes of the disordered matrix, giving rise to three mutually orthogonal variants (or transformation twins) of the Ni 3 V phase. Microstructural evolution in this alloy has been studied, starting from different initial microstructures [1,2]. At elevated temperatures (>600 C), the microstructure comprises colonies (or cells) of transformation twins, twinned along {110} fcc interfaces. Adjacent colonies meet along irregular interfaces [1]. The formation of transformation twins minimizes the strain energy within a cell. Tanner and Ashby [3] have discussed two mechanisms for the formation of these transformation twins: by h11 0i fcc {110} fcc glide and by diffusional rearrangement of atoms. They have argued that twin nucleation by the latter mechanism would be difficult because this process requires disordering and ordering of many atoms in a correlated manner within the cell. In spite of the fact that the magnitude of the twinning shear is relatively high for the glide twin, its nuc-

2 344 leation is relatively easy because of the inheritance of such dislocations from the disordered matrix. However, the issue of accommodation of strain at the cell interfaces does not appear to have been addressed. The present paper describes the results of a study on the accommodation of strain at and in the vicinity of the intercell interfaces. 2. Experimental Fingers of a polycrystalline alloy corresponding to the composition Ni-25at.%V were prepared from pure nickel and vanadium by electron beam melting followed by arc melting under argon atmosphere for homogenization. Repeated melting was carried out to homogenize the finger. Thin slices, cut from the fingers, were encapsulated in silica tubes filled with helium gas. The sealed slices were solution treated at 1100 C for 5 h followed by water quenching. The water-quenched samples were aged at 800 C for 1 h. For making transmission electron microscopy (TEM) specimens, heat-treated slices were first mechanically ground to a thickness of about mm. Discs of 3 mm diameter were punched out from these foils. The discs were then electropolished to perforation in a dual jet Tenupol unit using an electrolyte containing 1 part perchloric acid and 4 parts ethanol. The jetthinned samples were examined in a JEOL JEM 2000 FX transmission electron microscope. Different variants of the Ni 3 V phase were identified from the presence of their corresponding superlattice reflections in the [001] zone axis diffraction pattern at Fig. 1. Simulated [001] zone axis diffraction pattern showing the positions of superlattice reflections corresponding to the three variants, viz., I ([100]), II ([010]) and III ([001]), of the ordered Ni 3 V phase. Solid circles represent fundamental reflections, whereas solid squares represent superlattice reflections. Fig. 2. Typical microstructure of a Ni 3 V alloy showing a mosaic assembly of lamellar colonies, which met at irregular interfaces. positions shown in the simulated diffraction pattern (Fig. 1). 3. Results The typical microstructure of the Ni 3 V alloy after aging at 800 C for 1 h is shown in Fig. 2. The microstructure comprised a mosaic structure of many colonies (or cells), which met along irregular interfaces. Each of these colonies appeared to be internally twinned. Selected area diffraction patterns from these colonies indicated that they had formed within a single grain of the disordered phase and that the lamellae within each cell were transformation variants of the ordered phase. These lamellae were twin related along {101} fcc (or {102} DO22 ) planes; this was confirmed by using stereographic analysis of the interfaces between the transformation variants within a colony. A similar microstructure has been reported by Tanner [1] in ordered Ni 3 V. A large number of stacking faults, emanating from the cell interfaces and growing into either neighboring cell, were observed in the vicinity of these interfaces (Fig. 3). The bright field (BF) micrograph in Fig. 3a shows a cell interface and Fig. 3b shows a corresponding dark field (DF) micrograph imaged with the (020) reflection. The twin interfaces and the colony interface are invisible in this DF micrograph. The [001] zone axis diffraction pattern (Fig. 3c) reveals that the colonies contained domains corresponding to the [100] and [001] variants of the ordered phase. Stack-

3 345 faults at the interface and dislocations in the vicinity of the interface could be observed. In the BF micrograph, shown in Fig. 4b, which was imaged with the (200) reflection in the two beam condition, the twin interfaces and the colony interface are invisible. Within the twin lamellae, the density of stacking faults appeared to be quite high in the vicinity of the colony interface and decreased as one moved away from the interface (Fig. 5). The occurrence of d fringes could be noticed at the transformation twin interfaces. These fringes appeared due to a small variation in the diffraction deviation parameter, s, across the coherent interface due to the nonintegral value of the c/a ratio of the ordered Ni 3 V phase [4]. A great deal of work on the characterization of stacking faults and dislocations in the Ni 3 V phase has already been reported by earlier workers [5 8]. Whereas these faults are usually geometric stacking faults and are mostly intrinsic in nature, the dislocations observed in this phase are Fig. 3. (a) BF micrograph of an interface where two colonies met and (b) corresponding DF micrograph imaged with the (020) reflection under which the twin interfaces and the colony interface were invisible. Stacking faults emanating from the colony interface into each cell could be noticed. (c) [001] Zone axis diffraction pattern showing superlattice reflections belonging to the [100] and [001] variants of the Ni 3 V phase. ing faults emanating from the cell interface and propagating into the contiguous cells could be clearly seen in the micrographs. In addition to stacking faults, dislocations could also be noticed in the vicinity of the interface (Fig. 4). Fig. 4a shows a BF image where Fig. 4. (a) BF micrograph of an interface where faults at the interface and dislocations in the vicinity of the interface could be observed. (b) BF micrograph imaged with (200) reflection in the two beam condition when the twin interfaces and the colony interface were invisible.

4 346 Fig. 5. A BF image showing stacking faults within the twin lamellae. Characteristic d fringe contrast at domain boundaries could also be noticed. mostly of Shockley partial types. A few evidences of the presence of superpartial dislocations of 1/2h110i type are also reported [5 8]. 4. Discussion A significant result of this investigation pertains to the accommodation of strain at and in the vicinity of cell interfaces during the evolution of the ordered Ni 3 V phase. The disorder to order transformation in this alloy is a typical case of a cubic to tetragonal structural phase transformation. Such transformations invariably result in the generation of a significant amount of internal strain in the lattice [9]. Microstructure in this alloy develops by the nucleation and growth of the ordered Ni 3 V phase. During the evolution process, the ordered particles always try to maintain coherency with the disordered matrix. It is well established that as these particles grow beyond a critical size, they lose coherency by generating misfit dislocations at the interface [10,11]. The critical size at which the loss of coherency occurs depends upon the magnitude of the coherency strain. On similar lines, it can be argued that in the case of the ordered Ni 3 V phase, as the ordered particles grow beyond a certain size and a critical value of the transformation strain, they are likely to relieve the strain by the formation of transformation twins. The formation of these (transformation) twins accommodates the transformation strain arising due to the lattice mismatch between the parent disordered matrix and the ordered phase. When two growing cells impinge on each other, it is unlikely that a perfect registry would be maintained at the interface in view of the different orientations of the twins within each of them. Such a failure to maintain perfect registry may introduce a considerable amount of strain at the interface. This strain could be relieved by the generation of misfit dislocations at the interface. In addition, the misfit could also be relieved by the generation of stacking faults when the stacking fault energy of the material is low, which indeed is the case for the Ni 3 V phase (of the order of 25 mj/m 2 [8]). The formation of faults and dislocations near the cell interfaces could also occur due to the accommodation of the transformation strain as the twin lamellae grow. When a twin lamella nucleates, it tapers to an edge at its sides in order to accommodate the shape change brought about by the twinning. The resulting twin has a lens shape [12]. The elastic strain field due to a lens-shaped twin can be modeled by considering an appropriate array of dislocations at the tip. If a lamella is thin and tapered, a pileup of dislocations on a single plane will represent the stress adequately at distances large compared to the thickness of the lamella. If h is the thickness of the lamella at any point, then the shear stress, s, due to a pileup of a number of dislocations at a sufficiently large distance, r, from the head of the pileup is given by [12] s ¼ mhg 2pr where m is the shear modulus and g is the magnitude of the shear. The product hg determines the magnitudes of the accommodation stresses and strain. It is clear from this expression that the twin lamellae experience a large elastic strain at the twin tip. This strain at the tip is often accommodated by the generation of dislocations at the tip or by the throwing out of emissary dislocations into the surrounding matrix, as in the case of bcc metals [13]. In a situation of this type, blunt twin plates with incoherent interfaces are predicted. At distances far away from the twin tip, where the twin is perfectly coherent, hardly any dislocations are produced at the interface; thus, most of the dislocations are observed near the twin tip only. When the stacking fault energy of the material is low, some of the elastic strain could also be accommodated by the generation of faults from the transformation twin interfaces near the tip. These considerations suggest that a considerable amount of strain is accommodated in the vicinity of the interfaces by stacking faults and dislocations.

5 Conclusion The observations presented here indicate that despite the generation of transformation twins, a considerable amount of transformation strain gets accumulated at and in the vicinity of cell interfaces. In the case of the ordered Ni 3 V phase, this strain is relieved by the generation of misfit dislocations and stacking faults. Acknowledgements The authors wish to thank Drs. S. Banerjee (Director, Materials Group) and P.K. De (Head, Materials Science Division) for their keen interest in this study. They also thank Mrs. Pushpa S. Agashe for her help in the preparation of the manuscript. References [1] Tanner LE. The ordering of Ni 3 V. Phys Status Solidi 1968;30:376. [2] Singh JB. Microstructural evolution during ordering transformations and micromechanisms of deformation in Ni-V and Ni-V-Nb alloys. PhD dissertation. IIT Bombay; [3] Tanner LE, Ashby MF. On the relief of ordering strain by twinning. Phys Status Solidi 1969;33:59. [4] Gevers R, Delavignette P, Blank H, van Landuyt J, Amelinckx S. Electron microscope transmission images of coherent domain boundaries. Phys Status Solidi 1964;5:595. [5] Singh JB, Sundararaman M, Mukhopadhyay P. Propagation of stacking faults across domain boundaries in Ni-V and Ni-V-Nb alloys with DO 22 structure. Philos Mag A 2000;80:1983. [6] Vanderschaeve G, Sarrazin T, Escaig B. Effect of domain size on the mechanical properties of ordered Ni 3 V. Acta Metall 1979;27:1251. [7] Vanderschaeve G, Escaig B. Cross-slip of twinning dislocations on crossing domain boundaries in ordered Ni 3 V. Philos Mag A 1983;48:265. [8] Francois A, Hug G, Veyssiere P. The fine structure of dislocations in Ni 3 V. Philos Mag A 1992;66:265. [9] Khachaturyan AG. Theory of structural transformations in solids. New York: Wiley; p [10] Weatherly GC, Nicholson RB. An electron microscope investigation of the interfacial structure of semi-coherent precipitates. Philos Mag 1968;17:801. [11] Brooks H. Metal interfaces. Cleveland: ASM; p. 20. [12] Kelly A, Groves GW, Kidd P. Crystallography and crystal defects. England: Wiley; p [13] Sleeswyk AW. Emissary dislocations: theory and experiments on the propagation of deformation twins in a-iron. Acta Metall 1962;10:705.