Accommodation of transformation strain at cell interfaces
during cubic to tetragonal transformation in a
Ni-25at.%V alloy
J.B. Singha,*, M. Sundararamana, P. Mukhopadhyaya, N. Prabhua,b
b
a
Materials Science Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology, Mumbai 400 076, India
Abstract
The ordering transformation in a stoichiometric Ni-25at.%V alloy involves a cubic (A1) to a tetragonal
(DO22) 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: Ni3V; DO22 structure; Ordering transformation; Strain accommodation
1. Introduction
A disordered Ni-25at.%V alloy undergoes a cubic
(A1) to tetragonal (DO22) 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
Ni3V 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
h11̄0ifcc{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-
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 0.1 – 0.2 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 Ni3V 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 Ni3V phase. Solid circles represent fundamental
reflections, whereas solid squares represent superlattice
reflections.
Fig. 2. Typical microstructure of a Ni3V 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 Ni3V 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 Ni3V. 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-
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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 Ni3V phase [4]. A great deal of work on the
characterization of stacking faults and dislocations in
the Ni3V 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
Ni3V 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.
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].
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 Ni3V phase (of
the order of 25 mJ/m2 [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]
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
Ni3V 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 Ni3V 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
Ni3V 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
s¼
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.
347
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 Ni3V 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.
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