Magnetic field-induced twin boundary motion in polycrystalline Ni–Mn–Ga fibres

Magnetic field-induced twin boundary motion leading to large magnetic field-induced strain of ∼1.0% was established in polycrystalline Ni50.9Mn27.1Ga22.0 (at.%) fibres at room temperature (∼60–100 μm in diameter and ∼3 mm in length). The fibres' grains are as large as the fibre diameter and of random orientation. At room temperature, a ferromagnetic 5M martensite is found. Magnetic field-induced twin boundary motion was indicated by magnetic measurements and validated by electron backscatter diffraction (EBSD). The application of a magnetic field shifts the equilibrium temperature of martensite and austenite by ∼0.4 K T−1, which agrees with calculations using the Clapeyron–Clausius approach.


Introduction
The capability of magnetic shape memory (MSM) alloys to produce large magnetic fieldinduced strain of several per cent has recently excited significant research interest [1]- [3]. In MSM alloys, the large strain can either be caused by a magnetic field-induced grain boundary (usually twin boundary) motion or by a magnetic field-induced phase transformation. The former is mostly referred to as MSM effect, magnetoplasticity [4,5] or more precisely as magnetically induced reorientation (MIR) [6]. The magnetic field-induced phase transformation is correctly referred to as the MSM effect or as magnetically induced martensite/austenite (MIM/MIA). During MIR, twin boundaries move in order to allow those twin variants having a smaller angle between easy magnetization axis and applied field direction to grow, at the expense of unfavourably oriented twin variants [1,7].
The most investigated MSM material so far is the Heusler alloy Ni 2 MnGa, but also other MSM alloys and MSM-polymer-composites have been under scrutiny in order to overcome some of the disadvantages of (bulk) Ni 2 MnGa, e.g. brittleness, difficult preparation and cost [8]- [13]. In Ni-Mn-Ga alloys near the stoichiometric composition Ni 2 MnGa, MIR has been found in single crystals (resulting in up to ∼10% strain) [3], in polycrystalline foams (resulting in 0.115% strain) [5], in polycrystalline melt-spun ribbons (resulting in 0.025% strain) [14] and in thin films (no macroscopic strain, as film was constrained) [6].
In this work, large MIR strain of ∼1.0% in polycrystalline Ni 2 MnGa fibres is reported. These fibres could be ideal for magnetically controlled MSM-polymer-composites. Textured MSM-polymer-composites are relatively simple to prepare in near-net-shape form by mixing MSM particles with a polymer and curing the polymer within a desired mould with an applied magnetic field [11,12]. In these composites, stress-induced twin boundary motion has very recently been demonstrated by synchrotron x-ray and neutron diffraction [15,16], making them promising for magnetically controlled mechanical energy dampers. On the other hand, a large magnetically induced strain (e.g. by MIR) within the MSM particles, as reported here, can result in MSM-polymer-composites being applied as actuators. A further advantage is the reduction of eddy currents for high actuation frequencies due to the nonconductive polymer matrix.

Experimental
Ni 50.9 Mn 27.1 Ga 22.0 (at.%, determined by inductively coupled plasma optical emission spectroscopy) fibres were prepared by crucible melt extraction. Their size is about 60-100 µm in diameter and several millimetres in length and they are polycrystalline. The fibres were annealed at 1100 • C for 2 h for homogenization and to stimulate grain growth. Their martensite-austenite transformation and Curie temperatures are well above room temperature (M s = 320 K, A s = 328 K and T C = 371 K). The martensite at room temperature has a pseudo tetragonal crystal structure with the modulation type 5M and uniaxial magnetocrystalline anisotropy. The fibres' actual crystallographic unit cell is slightly monoclinic, which was also found in a detailed XRD study of Ni 48.75 Mn 29.75 Ga 21.5 powder by Righi et al [17]. More information on the properties of the fibres can be found in [12]. Grain, (twin) boundary and texture information were obtained by scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) (LEO 1530 FEG-SEM equipped with a HKL Channel 5 EBSD unit). The unit cell used for the EBSD analysis was a = b = a/ √ 2 = 4.20 Å, c = c = 5.58 Å and space group I 4/mmm (139) (see figure 1(c)) [18]. In the EBSD maps, black lines are drawn between any two pixels, whenever their misorientation is an 86 • rotation around rotation axis 110 , short 86 • 110 , (with a 2 • error for angle and axis). This corresponds to a twin misorientation 86 • 100 on twin planes, when the unit cell is described with austenite's L2 1 cubic coordinate system having c < a = b (see figure 1(c)). The theoretical misorientation angle between twin variants is 2 · arctan(c/a) = 86.4 • . EBSD measurements are shown for two fibres. One fibre (length ∼1 mm) was embedded in epoxy and polished to study the inside of the fibre. A second fibre (length ∼3.5 mm) was placed on a silicon wafer and fixed with silver paste on one end. In this case, the EBSD patterns were collected from the fibre's surface. All EBSD maps shown are as-measured, apart from a removal of 'wild spikes' (one orientation pixel is surrounded totally by different orientations) and from filling single empty pixels, when surrounded totally by one orientation. The magnetic properties of this fibre were measured by a vibrating sample magnetometer (VSM) within a physical property measurement system (PPMS, Quantum Design). Figure 1 shows the fibres' bamboo-like grain structure with grains as large as the fibre diameter. Within the individual grains several twin boundaries are present and are marked in the EBSD map by black lines. There is no preferred crystallographic orientation of the grains, with respect to grain shape and fibre axis. As the fibre is rigidly fixed within the epoxy resin, a large MIR cannot be expected as it would be accompanied by a large strain. However, a small MIR was  are twin related (with 'orange' twin boundary) by an 86.4 • rotation around the rotation axis lying nearly within the sheet plane. The newly created, 'red' twin lamella has nearly the same orientation as the 'orange' twin variant (misorientation ∼7 • ). The rotation necessary to get from the 'yellow' to the 'red' twin variant is the same as to get from the 'yellow' to the 'orange' twin variant, except with an opposite sense of rotation (−86.4 • , 'red' twin boundary), which explains the ∼7 • misorientation between the 'red' and 'orange' twin variants, 2(90 • − 86.4 • ) = 7.2 • . The observed angles between twin boundaries are due to their projection to the observation (polished) plane (figure 2(d)).

Results and discussion
A large MIR strain of ∼1.0% was found in a not constrained, polycrystalline and randomly textured fibre by magnetizing the fibre parallel and perpendicular to the fibre axis (by measuring M(H ) dependence up to 2 T). The fibre was only mounted on one end. The orientation distribution along the complete free length of the fibre was mapped by EBSD (figure 3) in order to determine those regions showing MIR. Three regions (grains) of the fibre were identified to show significant MIR, in each case over a length of ∼100-200 µm (table 1). The regions I-III yield a total MIR strain of (24 ± 2) µm along the fibre axis. The entire free part of the fibre (∼2800 µm) produces a MIR strain of (29 ± 2) µm, which corresponds to ∼1.0% strain. The additional strain most likely originates from several other smaller regions, which exhibit MIR and are not seen in the EBSD maps. The MIR strain was determined from EBSD maps (step size 1 µm, therefore error is assumed as ±2 µm) and supported by SEM images.
The resulting strain ε in the X -direction (fibre axis) for a certain unit cell orientation can be estimated using the maximum theoretical strain along the crystallographic c-axis, ε 0 = 1 − (a/c) = 6.1%, and the angle α between the crystallographic c-axis and the X-direction to ε = ε 0 · cos(α). The obtained values for each of the three regions, given in table 1, give an upper bound of ∼25 µm total strain to be expected along the fibre axis, which agrees well with the measured strain of (24 ± 2) µm.
During magnetization of the fibre, typical MIR jumps were observed in the M(H ) curves shown in figure 4(a). These jumps represent a sudden volume increase of one crystallographic  figure 3.

Angle between (c and X )/(c and Y)
Strain in X -direction  orientation favourably oriented to the field direction, i.e. the growth of one twin variant by twin boundary motion [7,19]. Since these jumps were only seen during the initial magnetization along one axis and were reversible by changing the applied field direction by 90 • , they are a clear indication for MIR and are consistent with the EBSD results. The critical field (or switching field) for MIR parallel to the fibre axis is ∼130 mT, which is particularly low, mainly due to the nearly zero demagnetization field in this fibre direction (aspect ratio of fibre >30). An even lower critical field needed for MIR was recently reported for an orthorhombic Ni 52 Mn 23 Ga 25 thin film and ascribed to the film's purity [6]. In the perpendicular direction, three MIR jumps are apparent, quite likely corresponding to the three MIR showing regions I-III observed in EBSD. A demagnetization correction for the perpendicular direction using N = 0.5 shows that the internal critical magnetic field for MIR is similar for the perpendicular and parallel directions.
Neither the constrained nor the free fibre showed MIR during the first magnetic field applications. The MIR shown here has been obtained after applying a field of 1.5-2 T several times (∼5 times) in different directions. The application of a magnetic field in different directions generates an alternating force on the twin boundaries, which can increase the twin boundary mobility. For the free fibre, MIR has been achieved after an additional cooling from austenite to martensite in a saturation field of 2 T (in VSM) followed again by a magnetic field application in different directions (∼4 times). As different twin boundaries may hinder each others movement, cooling to the martensite in a saturation magnetic field H favours the generation of one twin variant (with c H). Because of this, fewer twin boundaries are present, which can increase the twin boundary mobility. MIR was reversible and constant for at least ∼5 cycles thereafter. It is likely that training the fibres with many more cycles can further increase the MIR exhibiting fraction of the fibre.
Although the preparation method of the fibres yields a rather homogeneous composition distribution, the martensite-austenite transformation of the free, single fibre shows a stepwise character in high resolution M(T ) measurements ( figure 4(b)). These steps might be caused by different transformation temperatures of individual grains suggesting slight compositional differences between them.
Additionally, the M(T ) curve at 2 T (sample is saturated) is shifted to higher temperatures by slightly less than ∼1 K compared to the M(T ) curve at 10 mT. In a saturation magnetic field H , the higher saturation magnetization M sat of the martensite (compared to austenite) results in a lower Zeeman energy −M sat · H of the martensite. This shifts the martensite-austenite transformation temperatures to higher temperatures. The The theoretical temperature shift T can be calculated by the Clapeyron-Clausius approach as T = µ 0 · M sat · T m · H/Q [21] (anisotropy energy neglected), where M sat = (7.0 ± 0.1) Am 2 kg −1 is the difference of saturation magnetization between the austenite and martensite, µ 0 H = 2 T is the applied magnetic field, T m = T 10 mT m = 323.96 K and Q = (5.5 ± 0.2) × 10 3 J kg −1 is the latent heat of the martensite-austenite transformation (determined from differential scanning calorimetry (DSC) measurements). The calculated shift T = (0.82 ± 0.05) K agrees well with the measured value T m .

Summary
In summary, magnetic field-induced twin boundary motion (MIR) has been observed in meltextracted polycrystalline Ni 50.9 Mn 27.1 Ga 22.0 (at.%) fibres, in both constrained and free states, resulting, in the case of the free fibre, in a large macroscopic strain of ∼1.0%. The fibres' grains 8 are as large as the fibre diameter and randomly oriented. As the fibres preferentially and easily break along grain boundaries, single crystalline MSM particles capable of MIR can be obtained. Thus, these fibres are an ideal precursor for the preparation of MSM-polymer-composites for magnetic field controlled actuators and dampers. A magnetic field of 2 T shifts the equilibrium temperature of the martensite and austenite by ∼0.8 K, which agrees with calculations using the Clapeyron-Clausius approach.