A microstructural model of motion of macro-twin interfaces in Ni–Mn–Ga 10 M martensite

Highlights

• A simple model relating micromorphology and motion of macro-twins is presented.

• Some macro-twins can be pinned at energetically favourable positions.

• When applied to 10 M martensite of Ni–Mn–Ga, the model gives correct predictions.

• Three length-scales are considered: meso-, micro- and nano-scale (adaptive martensite).

• Validity of the model is supported by several experimental observations.

Abstract

We present a continuum-based model of microstructures forming at the macro-twin interfaces in thermoelastic martensites and apply this model to highly mobile interfaces in 10 M modulated Ni–Mn–Ga martensite. The model is applied at three distinct spatial scales observed in the experiment: meso-scale (modulation twinning), micro-scale (compound a–b lamination), and nano-scale (nanotwining in the concept of adaptive martensite). We show that two mobile interfaces (Type I and Type II macro-twins) have different micromorphologies at all considered spatial scales, which can directly explain their different twinning stress observed in experiments. The results of the model are discussed with respect to various experimental observations at all three considered spatial scales.

Introduction

Ferromagnetic shape memory alloys (FSMAs) of the Ni–Mn–Ga system (Chernenko et al., 1995, O'Handley et al., 2000, Heczko et al., 2000) are smart materials with potential for applications in actuation and micromanipulation. The decisive factor for magnetic shape memory effect is the high mobility of the twin boundaries, which enables fast actuation with large strain amplitudes. This high mobility was observed mainly in the five-layered (10 M) modulated martensite phase of Ni–Mn–Ga alloy. In particular, as recently shown by Sozinov et al. (2011) and Straka et al. (2011), two different types of mobile twin interfaces relevant for actuation can arise in the 10 M phase: Type I (twinning stress $\approx 1\mathrm{MPa}$ at room temperature and strongly temperature-dependent) and Type II (twinning stress less than 0.2 MPa and nearly temperature-independent). The respective temperature dependences were analyzed by Straka et al. (2012) and measured by Straka et al. (2013) and Heczko et al. (2013a). Understanding the difference between these two types requires a crystallographic analysis beyond the tetragonal approximation of the 10 M unit cell, taking into account the weak monoclinicity of the modulated phase (Lanska et al., 2004, Righi et al., 2007). In addition, as proved by X-ray microdiffraction in Straka et al. (2011) and Heczko et al. (2013b), and discussed ibid theoretically, these mobile interfaces are not simple twinning planes, but they are macro-twinning planes between fine 1st or 2nd order laminates. Furthermore, according to the so-called adaptive concept of martensite (Kaufmann et al., 2010, Kaufmann et al., 2011, Niemann et al., 2012), the 10 M modulated phase itself is built up from a stacking sequence of tetragonal unit cells of the non-modulated (NM) martensite, which adds even one more level of lamination. Thus, the observed mobile interfaces are in fact macro-twin boundaries between relatively complex twinned structures. This opens the questions how such microstructures can be connected compatibly over a single interface, and how the micromorphologies forming at these interfaces can affect their motion. Such analysis is the subject of this paper.

Recently, Faran and Shilo, 2011, Faran and Shilo, 2013 analyzed the kinetics of Type I and Type II interfaces under pulse-like magnetic loadings and obtained extensive data on mobility of both the types for a wide range of amplitudes of the driving force. They concluded that for small amplitudes of the applied magnetic pulses (small driving force, slow propagation), the kinetics of both the Type I and Type II interfaces is driven mainly by nucleation and growth of steps along the interfaces. This macroscopically appears as a smooth, continuous sideways motion of the mobile boundary. Under such condition, Faran and Shilo, 2011, Faran and Shilo, 2013 showed that the energy of such steps is smaller for the Type II twins, for which also the Peierls barrier seems to be smaller, and, consequently, the mobility to be higher. On the other hand, they did not take into account the complex microstructure of the analyzed macro-twins known from the experiments. The presence of fine lamination (possibly of higher orders) close to the interface does not contradict the concept of nucleation and growth of the steps. It is plausible that, in addition to the Peierls landscape, the microstructure can create energetic barriers against the nucleation and motion of such steps. Such conjecture is supported by the fact that Faran and Shilo (2013) have observed some variation of the mobility with periodicity of about $10–50\mathrm{\mu }\mathrm{m}$, which could be a characteristic length-scale of some particular microstructure. Similar periodicity was also detected on quasi-static curves for the Type I interface measured by Faran and Shilo (2012).

In this paper, we examine the influence of the complex microstructures on the quasi-static motion of the Type I and Type II boundaries. Within the frame of continuum mechanics, we present a theoretical model of such interfaces, employing the description of thermoelastic martensites. We solve the compatibility problems in the interfacial region where the two laminates meet, and discuss what effect the resulting microstructure can have on the motion of the macro-twin. Our discussion is restricted to the 1st order of lamination only; which is, however, sufficient for application of the model for the case of 10 M martensite of Ni–Mn–Ga. The reason is that the individual laminations in 10 M martensite appear at completely different spatial scales, and their interactions in the interfacial region can be, thus, discussed separately. By using this model, we obtain a multi-scale picture of the micromorphology at the studied macro-twin boundaries, and we are able to explain the possible origins of the different twinning stress.