Transformation and slip behavior of Ni2FeGa
Highlights
► Ni2FeGa is a very promising new shape memory alloy. ► Transformation to martensite in Ni2FeGa was studied using atomistic simulations. ► The transformation path to 10M martensite involves shear and shuffle. ► Simulations point to APB (anti-phase boundaries) formation via dislocation slip. ► APBs were also discovered in deformed single crystals interrogated via TEM.
Introduction
Designing new shape memory materials that exhibit superior transformation characteristics remains a challenge. There needs to be a better fundamental basis for describing how reversible transformation (shape memory) works in the first place. Specifically, two aspects remain uncertain. The first is that the phase changes involve complex transformation paths with shear and shuffle (Ahlers, 2002) and the energy barrier levels corresponding to the transition are not well established. The second issue is that the determination of dislocation slip resistance (Olson and Cohen, 1975), which decides the reversibility of transformation of shape memory alloys, is very important and requires further study. Thus, this paper is geared towards establishing both the energy barriers in the phase changing of Ni2FeGa and the fault energies associated with dislocation slip for the same material.
Thermo-elastic phase transformation refers to a change in lattice structure upon exposure to stress or temperature and return of the lattice to the original state upon removal of stress or temperature (Delaey et al., 1974). Modern understanding of shape memory transforming materials has relied on the phenomenological theory of the martensitic transformation (Wechsler et al., 1953), which does not deal with the presence of dislocation slip. The presence of slip has been observed in experimental work at micro- and meso-scales (Otsuka and Wayman, 1998, Duerig et al., 1990), and incorporated in some of the continuum modeling approaches (Boyd and Lagoudas, 1996). A low transformation stress (Sehitoglu et al., 2000) and high slip resistance (Hamilton et al., 2004) are precursors to reversible martensitic transformation. Recently, theoretical developments at atomic length scales have been utilized (Hatcher et al., 2009, Kibey et al., 2009, Wagner and Windl, 2008) bringing into light the magnitude of energies of different phases and defect fault energies in NiTi.
NiTi is the most well known shape memory alloy that meets the requirement of excellent slip resistance in both martensite (Ezaz et al., 2011) and in austenite (Manchiraju and Anderson, 2010, Moberly et al., 1991, Norfleet et al., 2009, Pelton et al., 2012, Simon et al., 2010). The recent interest in the austenite slip behavior of NiTi is well founded because it is a key factor that influences the shape memory response.
We note that some of the other shape memory alloys of the Cu-variety (Damiani et al., 2002b, Malarria et al., 2009, Roqueta et al., 1997, Sade et al., 1988, Sittner et al., 1998) and the Fe-based (Maki, 1998a, Maki, 1998b, Morito et al., 2000, Jost, 1999, Tsuzaki et al., 1992) alloys possess large transformation strains but are susceptible to plastic deformation by slip. Plastic deformation has been incorporated into continuum energy formulations where the interaction of plastic strains and the transformation improves the prediction of overall mechanical response (Bartel et al., 2011, Idesman et al., 2000, Levitas, 2002). All these previous works point to the importance of dislocation slip resistance in shape memory alloys.
The Ni2FeGa alloys have large recoverable strains (Chumlyakov et al., 2008, Hamilton et al., 2007a, Hamilton et al., 2007b) and can potentially find some important applications like NiTi. In the case of Ni2FeGa alloys, stress-induced transformation to modulated martensite (Masdeu et al., 2005, Omori et al., 2004, Santamarta et al., 2006a, Santamarta et al., 2006b, Sutou et al., 2004) and the slip deformation of austenite (Hamilton et al., 2007a, Hamilton et al., 2007b) are two factors that dictate shape memory performance. The phase change in Ni2FeGa occurs primarily upon shape strains (Bain strain) in combination with shuffles to create a ‘modulated’ martensitic structure. The ‘modulated’ monoclinic structure has a lower energy than the ‘non-modulated’ lattice, and hence is preferred. We focus on atomic movements and the energy landscapes for transformation of L21 austenite to a 10M modulated martensite structure and establish the barrier for this change. We then investigate the dislocation slip barriers in [111] and [001] directions.
It is important to assess the transformation paths and energies associated with the austenite to martensite transformation simultaneously with dislocation slip behavior because the external shear stress that can trigger transformation can also result in dislocation slip. What we show is that the order strengthened Ni2FeGa alloy requires elevated stress levels for dislocation slip while undergoing transformation nucleation at much lower stress magnitudes (with lower energy barriers).
A schematic of pseudoelastic stress-strain response at constant temperature is given in Fig. 1. We note that the initial crystal structure at zero strain is that of austenite. Upon deformation, the crystal undergoes a phase transformation to a modulated martensitic structure. In the case of Ni2FeGa, the structures of austenite and martensite are cubic and monoclinic, respectively. Over the plateau stress region, austenite and martensite phases can coexist. In the vicinity of austenite to martensite interfaces, high internal stresses are generated to satisfy compatibility. Hence, slip deformation can occur in the austenite domains as illustrated in the schematic. Once the transformation is complete, the deformation of the martensitic phase occurs with an upward curvature. Upon unloading, the martensite reverts back to austenite as shown in the schematic. The strain recovers at the macroscale, but at the micro-scale residual slip deformation could remain as shown with TEM studies.
We capture the energetics of the transformation through ab initio density functional theory (DFT) calculations. In Fig. 2(a), the initial lattice constant is ao and the monoclinic lattice constants are a, b and c with a monoclinic angle. We incorporate shears and shuffles for the case of transformation from L21 to 10M. A typical transformation path is described in Fig. 2(a). The martensite has lower energy than the austenite. To reach the martensitic state, there exists an energy barrier (corresponding to in Fig. 2(a)) that needs to be overcome. This barrier is dictated by the energy at the transition state (TS) as shown in Fig. 2(a). A smaller barrier is desirable to allow transformation at stress levels well below dislocation mediated plasticity. Along the transformation path, we find a rather small energy barrier (8.5 mJ/m2 for the L21 to 10M transformation in Ni2FeGa).
Dislocation slip resistance in the L21 austenite can be understood by consideration of energetics of slip displacements in the [111] direction associated with the motion of the dissociated dislocations. Ribbons of anti-phase boundaries (APBs) form by dissociation of superdislocations in the L21 parent lattice. We compute the separation distance of the superpartials via equilibrium considerations and show the presence of these APBs from TEM observations. The energy barriers are manifested via generalized stacking fault energy curves (GSFE) and decide the slip resistance of the material. We check the GSFE curves in two possible dislocation slip systems and calculate theoretical resolved shear stress.
The fundamental descriptions of the APB formation in ordered cubic materials point to decomposition of full dislocations (Koehler and Seitz, 1947, Marcinkowski and Brown, 1961). For the Ni2FeGa, as atoms are sheared over other atoms in neighboring planes the energy landscape indicates the decomposition of the full dislocation to four partials resulting in APBs. The partial dislocations are not zig zag type as in face centered cubic systems but are in the same direction as the full dislocation. This is illustrated in Fig. 2(b). It is easiest to see the APB formation with a [110] projection (Fig. 2(b)). The x-axis is [001] and the y-axis is in this case. In this view atoms on only two planes (in-plane and out-of-plane) are noted (a different view will be illustrated later). Because we have twice as many Ni atoms then Fe and Ga, in the direction every second column has all Ni atoms. When slip occurs with vector 1/4 the original ordering of the lattice no longer holds. The passage of the first partial 1/4 results in disordering of the atomic order at near neighbors. The passage of the second partial restores the original stacking of next to near neighbor atoms. Upon a slip displacement of 1/2 the columns with all Ni atoms are restored but other columns do not have the original ordering (Fig. 2(b)). Upon displacement of the original lattice structure with long range order of the matrix is recovered. The fault energy barriers corresponding to Fig. 2(b) have several minima (metastable equilibrium points) corresponding to the passages of the partial dislocations (Fig. 2(c)). More details will be given later in the text. In Fig. 2(b) refers to the unstable fault energy and and describe the nearest-neighbor (NN) and next-nearest neighbor (NNN) APB energies respectively. The fault energy barriers are moderately high (>400 mJ/m2 in Ni2FeGa) and point to the considerable slip resistance in Ni2FeGa. We provide TEM evidence of the presence of APBs in the austenitic phase for samples that have undergone pseudoelastic cyclic deformation.
Section snippets
Fundamentals of Cubic to Modulated (10M) Transformation in Ni2FeGa
The martensitic structure is critical to the properties of ferro-magnetic shape memory alloys. Their tetragonality c/a, twinning stress and magnetocrystalline anisotropy constant determine the magnetic-field-induced strain (MFIS) (Luo et al., 2011b, Morito et al., 2005). However, large MFIS originates mainly from the contribution of the modulated martensites (Han et al., 2007). Experiments have shown that the cubic structure (L21) undergoes the phase transformation to martensitic phases,
The (011)<111> case
The generalized stacking fault energy (GSFE), first introduced by Vitek (1968), is a comprehensive definition of the fault energy associated with dislocation motion. In fcc alloys, a single layer intrinsic stacking fault is formed by the passage of partial dislocations in the direction on the {111} plane. The fault energy of different sheared lattice configurations can be computed as a function of displacement ux. The generalized stacking fault energy (GSFE) is represented by a surface
Experimental results
Single crystal Ni54Fe19Ga27 with [0 01] orientation was utilized in this work. After single crystal growth, the samples were heat treated at 900 °C for 3 h and subsequently water quenched. The details of the processing and heat treatment are described in our previous work (Hamilton et al., 2006). The Ni2FeGa is characterized by the forward and reverse transformation temperatures obtained via differential scanning calorimetry. The reverse transformation temperature (martensite to austenite) for the
Implication of Results
Based on the GSFE results the ideal stress levels for dislocation slip were calculated for <111> and <001> directions and the magnitudes are shown in Table 2. We note that the stress magnitudes for slip nucleation, , are rather high precluding significant slip within austenite. However, the stresses at the austenite -martensite interfaces can be sufficiently high to generate dislocation slip in the austenite domains. Furthermore, Fisher (1954) made a first order estimate of the
Acknowledgements
The work was supported by the NSF grant CMMI-09-26813 and partly by DMR-08-03270.
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