Introduction

With the driving force to replace conventional vapor compression cooling technology with magnetic refrigeration, increasing interests have been placed on Heusler alloy, Ni2MnGa, and its off-stoichiometric solid solutions owing to their large magnetocaloric effect (MCE).[1] Magnetic refrigeration technology has the advantage of eliminating the greenhouse gases, enhancing cooling efficiency, and saving energy.[2,3] Compared to other magnetocaloric materials,[3] NiMnGa-based magnetocaloric alloys are inexpensive, easy to produce, and do not contain either rare earth or environmentally hazardous elements.

Isothermal entropy change, which is the figure of merit to compare MCEs in different materials, is proportional to the derivative of magnetization to temperature.[4] During the first order transformation between low temperature martensite and high temperature austenite phase, a large magnetization change is induced leading to large change in isothermal magnetic entropy. Since isothermal entropy change is proportional to the derivative of magnetization to temperature,[4] MCE at martensitic transformation temperature is very large; larger than that at ferromagnetic–paramagnetic transition.[5–7] It has been reported that by altering the composition, it is possible to bring the structural and magnetic phase transition temperatures close to each other. A very large MCE has been observed in NiMnGa-based alloys when this simultaneous structural and magnetic phase transition occurs.[1,6,8]

A better understanding of the martensitic transformation and martensitic structures is crucial in optimizing the MCE. Despite the intensive research on measurement of MCE and magnetic properties for Ni2+x Mn1−x Ga alloys,[1,5–10] only few investigations have focused on the crystallography associated with the phase transformations. Powder X-ray diffraction (XRD) has been performed on Ni2+x Mn1−x Ga alloys with x varying from 0.15 to 0.35, and documented the existence of non-modulated (NM) and seven-modulated (7 M, as the modulation period of the (1 1 0) planes in the austenitic phase is seven) martensite depending on the composition and heat treatment.[11] Compositional variation of martensite structures and phase transitions has been studied, by XRD and optical microscopy, by Jiang et al.[12] for arc-melted Ni2MnGa and replacing Ga by Mn atoms where they observed 5 M, 7 M, and non-modulated martensites. Similar studies have been performed by Panda et al.[13] using XRD and some transmission electron microscopy (TEM) with Mn substituting for Ni for melt spun ribbons of NiMnGa alloys. Empirical relationship among martensite transformation temperature, Curie temperature, saturation magnetization, valence electron concentration (e/a), composition etc., for NiMnGa alloys has been suggested by Jin et al.[14] via polynomial fitting of data. In all these studies, there are no mention of MCE and the potential influence of the structure and crystallography of the alloys, if there is any. In this investigation, we have chosen five polycrystalline Ni2+x Mn1−x Ga (x  = 0.14, 0.16, 0.19, 0.22, and 0.24) alloys to be examined by various techniques with an emphasis on TEM for detailed microstructural and crystallographic analyses on the martensitic phases. Magnetocaloric properties of some of the alloys (x  = 0.14 and 0.16) have been studied already, and one of the alloys (x  = 0.16) exhibited simultaneous structural and magnetic phase transformation at 340 K (67 °C).[1] In this study, we also attempt to explore the effects of microstructure and crystallography of martensites on the magnetocaloric property with extensive TEM analyses.

Experimental

Polycrystalline Ni2+x Mn1−x Ga alloys with nominal compositions of x  = 0.14, 0.16, 0.19, 0.22, and 0.24 were triple arc-melted in argon atmosphere, followed by homogenization at 1273 K (1000 °C) for 72 hours under high vacuum (10−6 Torr).

Differential scanning calorimetry (TA Instruments™ Q2000 DSC) with a heating/cooling rate of 10  K/min was carried out for all alloys to identify the martensitic transformation temperature. The Curie temperature (T c) was also determined[1] from the magnetization versus temperature plot, and confirmed based on the inflection point of the DSC curves. The Curie temperatures of two alloys (Ni2+x Mn1−x Ga, where x  = 0.14 and 0.16) were verified to coincide with the data obtained from the magnetization versus temperature plots.[1]

For each alloy, specimens with approximate size of 5 mm × 5 mm × 3 mm were sectioned, and ground to 1200-grit SiC-paper to smoothen the surface. The specimens were then subjected to conventional X-ray diffraction (XRD, Rigaku D-Max B Diffractometer) with Cu Kα radiation to determine the crystal structures and lattice parameters. The specimens were then mounted in epoxy and metallographically polished down to 0.25 μm, followed by chemical etching with Marble’s Reagent to reveal the martensitic microstructure. Initial microstructural observation was carried out using optical microscopy (Olympus™ LEXT OLS-3000). The actual compositions of the five alloys were examined by X-ray energy dispersive spectroscopy (XEDS) equipped on a Zeiss™ Ultra 55 field emission scanning electron microscope (FE-SEM), and by chemical analysis via direct current plasma emission spectroscopy (DCPES) carried out at Luvak™ Incorporated. For the XEDS analysis, 20 random measurements were performed on each sample so as to obtain the average value with standard deviation.

TEM (FEI™ Tecnai F30 TEM) and scanning TEM equipped with high angle annular dark field (HAADF) detector, operating with accelerating voltage of 300 keV were employed to examine the details of microstructure and crystallography at room temperature. All the TEM foils were prepared via focus ion beam (FIB-FEI™ 200 TEM) in situ lift-out (INLO) technique, which is capable of selecting site-specific areas. For each alloy, up to four TEM foils were prepared by INLO-FIB for statistically confident TEM observations.

Results

The starting elemental compositions of Ni2+x Mn1−x Ga (x  = 0.14, 0.16, 0.19, 0.22, and 0.24) alloys, herein referred to as nominal composition, and the actual compositions measured by XEDS and DCPES are reported in Table I, and presented in the ternary phase diagram in Figure 1. Measurements from XEDS and DCPES give similar compositions, and both have a slightly higher Ga composition than the starting nominal composition. The e/a value was also calculated, with 10 valence electrons per atom for Ni, 7 for Mn, and 3 for Ga, as presented in Table I. The e/a ratio calculated using the measured compositions via XEDS and DCPES vary slightly, but the e/a increases as the Ni-content increases regardless of the measurement technique.

Table I Nominal Compositions (Atom Percent) and the e/a for Alloy Ni2+x Mn1−x Ga (x = 0.14, 0.16, 0.19, 0.22, and 0.24), Determined by XEDS and DCPES
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Fig. 1
figure 1

Nominal compositions and measured compositions in atomic percent by XEDS and DCPES presented on the ternary phase diagram

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Martensite start (M s) and finish (M f) and austenite start (A s) and finish (A f) temperatures were determined from DSC measurement as listed in Table II. Table II also lists the Curie temperature measured from magnetization curves.[1] Martensitic transformation temperature (T m) defined as T m = 1/2 (M s + M f) and austenitic transformation temperature (T a) defined as T a = 1/2 (A s + A f) are also reported in Table II. All specimens are observed to have a temperature hysteresis (ΔT = T a – T m) between the forward and reverse martensitic transformations. These transformation temperature increased as the Ni-content increased in the Ni2+x Mn1−x Ga (x  = 0.14, 0.16, 0.19, 0.22, and 0.24) alloys, with the Ni2.14Mn0.86Ga (x  = 0.14) alloy having the T m closest to the room temperature. Moreover, ΔT for the Ni2.14Mn0.86Ga (x  = 0.14) alloy is only 5 K, while that for other alloys is approximately 10 K. The T c also slightly increased as the Ni-content (or x) increased. The Ni2.16Mn0.84Ga (x  = 0.16) alloy had the structural transformation and magnetic transition temperatures to be nearly identical.[1]

Table II Temperature (K) of the Martensite Start (M s), Martensite Finish (M f), Austenite Start (A s), Austenite Finish (A f), Martensitic Transformation (T m), Austenitic Transformation (T a), Curie (T c), and Thermal Hysteresis (ΔT) Measured by DSC for the Ni2+x Mn1−x Ga (x = 0.14, 0.16, 0.19, 0.22, and 0.24) Alloys
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Figure 2 presents the XRD patterns of all alloys at room temperature. The Ni2+x Mn1−x Ga alloys with x  = 0.16, 0.19, 0.22, and 0.24 show similar XRD patterns, which can be indexed according to the NM tetragonal structure. The indexing of these patterns is based on the same crystallographic axes as of the parent austenitic phase, so that the tetragonality ratio c/a is larger than 1. The lattice parameters of a and c, as well as c/a ratio, calculated for these alloys are listed in Table III, and plotted in Figure 3 to clarify the changes in lattice parameters with the e/a. As the e/a increases (i.e., substitution of Ni for Mn), lattice parameters a slightly decreases and c increases. Therefore, the tetragonality ratio, c/a also increases as the e/a increases, which is consistent with the results reported for other NiMnGa alloys.[15,16]

Fig. 2
figure 2

X-ray diffraction patterns from the Ni2+x Mn1−x Ga (x = 0.14, 0.16, 0.19, 0.22, and 0.24) alloys at room temperature

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Table III Crystal Structures and Lattice Parameters (Å) for the Ni2+x Mn1−x Ga (x = 0.14, 0.16, 0.19, 0.22, and 0.24) Alloys Determined by X-Ray Diffraction
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Fig. 3
figure 3

Lattice parameters, a and c, and tetragonality ratio c/a determined at room temperature for the Ni2+x Mn1−x Ga (x  = 0.14, 0.16, 0.19, 0.22, and 0.24) alloys as a function of e/a

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The XRD pattern for the Ni2.14Mn0.86Ga alloy with x  = 0.14 is clearly different from other alloys as shown in Figure 2. The diffraction pattern is indexed according to a monoclinic unit cell, which indicates that the martensite in this alloy has a modulated 7 M crystal structure. Table III listed the lattice parameter for Ni2.14Mn0.86Ga (x  = 0.14) alloy based on the 7 M structure.

Figure 4 presents the microstructure of all alloy specimens examined by optical microscopy. The grain size for these polycrystalline specimens varied from 200 μm to 1 to 2 mm. The martensitic lamellas appear to be plate- or spear-like in shape, which is typical for shape memory alloys.[13,17] However, typical width of martensitic lamellas for the Ni2.14Mn0.86Ga alloy appear to be smaller than that for other alloys as shown in Figure 4, with a higher density of martensitic lamellas within each grain. Similar observations have also been reported for NM and 7 M martensites with different compositions than this study.[12] Considering that the Ni2.14Mn0.86Ga (x  = 0.14) alloy has a 7 M martensite while others have NM martensites, according to XRD, it is possible that the width of a modulated martensitic variant is inherently thinner.

Fig. 4
figure 4

Optical micrograph from martensitic microstructures for the Ni2+x Mn1−x Ga (x  = 0.14, 0.16, 0.19, 0.22, and 0.24) alloys after chemical etching

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Figures 5(a) and (b) presents typical low and high magnification bright field (BF) TEM micrographs of martensitic variants from the Ni2.14Mn0.86Ga (x  = 0.14) alloy. Selected area diffraction patterns (SADP) from a single martensitic variant and from the interface between two adjacent variants are presented in Figures 5(c) and (d), respectively. The thickness of the primary martensitic variants in this alloy varied from 100 nm to 300 nm, which is very thin and consistent with approximate observation from optical microscopy. Figure 5(b) also shows layered contrast with intervals of only a few nanometers, and indicates that the structure is modulated. Also shown in Figure 5(b) is a dark contrast at the interface between adjacent two primary variants, indicating that the boundary may be distorted. The SADP from the martensitic variant in Figure 5(c) shows six superlattice diffraction spots between the fundamental diffraction spots. Thus, the presence of modulated 7 M martensite is confirmed for the Ni2.14Mn0.86Ga (x  = 0.14) alloy. From the SADPs, the lattice parameter is determined to be a = 4.24 Å, b = 5.44 Å, c = 29.44 Å, and β = 93.2 deg for this monoclinic structure; this is quite close to that determined by XRD. The SADP with [2 1 0] zone axis from the boundary region indicates that two adjacent variants are twinned, where the twinning plane is \( \left( {1\bar{2}\bar{7}} \right) \).

Fig. 5
figure 5

(a) Bright field TEM micrograph from the Ni2.14Mn0.86Ga alloy showing the martensitic variants. (b) Bright field TEM micrograph from the twin variants and boundary. Selected area diffraction patterns of the Ni2.14Mn0.86Ga alloy from (c) individual martensitic variant and (d) twin boundary region

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High resolution TEM (HRTEM) micrographs from a single martensitic variant and from the twin boundary region were examined via fast Fourier transform (FFT) as presented in Figure 6. The thin-layered microstructure in Figure 6, consisting of only several atomic layers, is the modulated 7 M structure. In NiMnGa alloys, a perfect 7 M martensite typically has a \( \left( {5\bar{2}} \right) \) stacking sequence,[18,19] which forms secondary nano twins within the primary twin variants. However, the diffused spots in FFT indicate that the layered structure is locally imperfect, or some stacking faults might have been generated during the martensitic transformation. Figure 6(b) also shows the HRTEM micrograph from the boundary between two primary martensitic variants. This twin boundary appears to be not perfectly flat, with some distortion within a thickness range of a few atomic layers. This implies that the primary twin boundary is not coherent. Fast Fourier transformation from the boundary region shows that the two variants have basically the same 7 M crystal structure, as also seen from the SADP in Figure 5(d).

Fig. 6
figure 6

High resolution TEM micrographs and corresponding fast Fourier transform patterns from the Ni2.14Mn0.86Ga alloy: (a) individual martensitic variant and (b) twin boundary region

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TEM investigation from Ni2+x Mn1−x Ga alloys with x  = 0.16, 0.19, 0.22, and 0.24 showed similar microstructure and crystal structure, but very different from the Ni2.14Mn0.86Ga (x  = 0.14) alloy. Figure 7(a) presents a typical BF TEM micrograph taken from the Ni2.16Mn0.84Ga (x  = 0.16) alloy. The width of the primary martensitic variants for these samples is typically in the range of micrometers, and thicker than that for the Ni2.14Mn0.86Ga (x  = 0.14) alloy. In Figure 7(b), the SADP taken from the interface area, with the orientation of [111], indicates that the adjacent martensitic variants are twinned, with the twinning plane of \( \left( {20\bar{2}} \right) \). However, the dark contrast seen in Figure 7(a) at the interface between adjacent primary variants indicates that this boundary is also distorted.

Fig. 7
figure 7

(a) Bright field TEM micrograph of martensitic variants from Ni2.16Mn0.84Ga alloy and (b) the corresponding selected area diffraction pattern from [1 1 1] orientation at the twin boundary region

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Figure 7(a) also reveals that, within each primary martensitic variant, thinner secondary twin variants with straight boundaries exist. Figure 8 demonstrates by HR-TEM, taken from the orientation of [1 1 1], that the thickness of these secondary twins varies from 10 to 20 nm, and lead to some diffuse scattering in the corresponding FFT. The FFT also shows a similar pattern to the SADP taken from the twin boundary area at the orientation of [1 1 1]. Therefore, these secondary nanotwins in NM martensites have the same orientation relationship as in the primary twins, where the twinning plane is the same, \( \left( {20\bar{2}} \right) \), as highlighted in Figure 8.

Fig. 8
figure 8

High resolution TEM micrograph and corresponding fast Fourier transform pattern from the Ni2.16Mn0.84Ga alloy

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Discussion

Both NM and 7 M martensites formed hierarchical twins-secondary twins within the primary twins. Secondary twins form at the habit plane so as to minimize the lattice elastic strain energy during the austenite-to-martensite transformation. For both NM and 7 M martensites, the coherency of the primary twin boundary was lost, corresponding to higher boundary energy for the primary twin variants. The primary twin variants with different alignment with respect to the secondary twins were also observed in this study, despite their higher boundary energy. Formation of the primary twin variants can help reduce the strains perpendicular to the habit plane during phase transformation.[20]

There are microstructural differences between 7 M and NM martensites. In 7 M martensites, the secondary twins have a width of a few atomic layers, and the primary twins have a width of a few hundred nanometers, as seen in Figures 5 and 6, respectively. For the NM martensites, the width for the secondary twins is about 10 to 20 nm and that for the primary twins is in the micrometer scales, as shown in Figures 7 and 8, respectively. Clearly, the thickness of the twins in 7 M martensites is thinner than that in the NM martensites, and correspond to a higher number of twin boundaries. Li et al.[21,22] previously reported that 7 M martensite had thinner lamellas compared to the NM martensite in a polycrystalline NiMnGa alloy, in which the 7 M martensite, NM martensite and austenite coexisted in one grain. Thus it is plausible that the twin boundary energy for the 7 M martensite is lower than that for the NM martensite. During martensitic transformation, more twin boundaries can form in 7 M martensite so as to further minimize the transformation strain at the habit plane. Also, lower temperature may favor the formation of 7 M martensites because of its lower twin boundary energy. This may account for why the Ms for transformation from austenite to 7 M martensite is lower than that for transformation from austenite to NM martensite, as observed in this study and in other NiMnGa alloys.[23]

As reported earlier, the MCE for Ni2.16Mn0.84Ga (x  = 0.16) is higher than that for Ni2.14Mn0.86Ga (x  = 0.14) due to the concurrence of structural and magnetic transformation. The crystal structures of the martensite for these two alloys are very different, one being the modulated structure and the other non-modulated structure. The transformation to a modulated structure might be directly related to the low thermal hysteresis as observed in Ni2.14Mn0.86Ga (x  = 0.14) as shown in Table II. The small twin width and high density of twins in the 7 M martensites can reduce the interfacial energy during phase transformation, and leads to a smaller hysteresis.[20,24] The small hysteresis is beneficial to a reduction in energy loss.[24] Further studies are being carried out to elucidate whether one structure is superior to the other with respect to MCE properties.

Summary

A series of Ni2+x Mn1−x Ga (x  = 0.14, 0.16, 0.19, 0.22, and 0.24) polycrystalline alloys were prepared and characterized for microstructural and crystallographic analyses. Martensitic transformation temperatures were found to increase with an increase of e/a, and Ni2.16Mn0.84Ga alloy had the closest transition temperature to the room temperature. While modulated 7 M martensites were observed in Ni2.14Mn0.86Ga alloy, only the NM martensites were found in all other alloys at room temperature. The lattice parameters for the NM martensites were determined by XRD, and the c/a ratio was found to increase with an increase in e/a ratio. Both NM and 7 M martensites consisted of twin variants with different orientations. The thickness of the variants in 7 M martensites was smaller than that for NM martensites. For NM martensites, the primary twin variant thickness was in the micrometer scale, and each variant consisted of very fine secondary twin variants with a thickness of few tens of nanometer. For 7 M martensites, the primary twin variant thickness was in the nanometer scale, and the variant consisted of very fine structure that has only a few atomic layers corresponding to the structural modulation.