Composition-dependent crystal structure and martensitic transformation in Heusler Ni–Mn–Sn alloys

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Acta Materialia 61 (2013) 4648–4656 www.elsevier.com/locate/actamat

Composition-dependent crystal structure and martensitic transformation in Heusler Ni–Mn–Sn alloys Hongxing Zheng a,b,⇑, Wu Wang a,b, Sichuang Xue a,b, Qijie Zhai b, Jan Frenzel c, Zhiping Luo d b

a Laboratory for Microstructures, Shanghai University, Shanghai 200072, China Shanghai Key Laboratory of Modern Metallurgy & Materials Processing, Shanghai University, Shanghai 200072, China c Institut fu¨r Werkstoffe, Ruhr-Universita¨t Bochum, 44801 Bochum, Germany d Department of Chemistry and Physics, Fayetteville State University, Fayetteville, NC 28301, USA

Received 27 November 2012; received in revised form 11 April 2013; accepted 11 April 2013 Available online 6 May 2013

Abstract In the present work, modulated four- and five-layered orthorhombic, seven-layered monoclinic (4O, 10M and 14M) and unmodulated double tetragonal (L10) martensites are characterized in Heusler Ni–Mn–Sn alloys using X-ray diffraction, high-resolution transmission electron microscopy, electron diffraction techniques and thermal analysis. All modulated layered martensites exhibit twins and stacking faults, while the L10 martensite shows fewer structural defects. The substitution of Sn with Mn in Ni50Mn37+xSn13x (x = 0, 2, 4) enhances the martensitic transition temperatures, while the transition temperatures decrease with increasing Mn content for constant Sn levels in Ni50yMn37+ySn13 (y = 0, 2, 4). The compositional dependence of the martensitic transition temperatures is mainly attributed to the valence electron concentration (e/a) and the unit-cell volume of the high-temperature phase. With increasing transition temperatures (or e/a), the resultant martensitic crystal structure evolves in a sequence of 4O ! 10M ! 14M ! L10 in bulk Ni–Mn–Sn alloys. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Martensitic transformation; Heusler Ni–Mn–Sn alloys; High resolution transmission electron microscopy (HRTEM); Compositional dependence; Crystal structure

1. Introduction Heusler Ni–Mn-based ferromagnetic shape memory alloys (FSMAs) have been widely studied as magnetically actuated materials [1,2]. Some years ago, a magnetocaloric effect was revealed in this alloy system which is based on two different solid-state transitions, the first-order martensitic transformation and the second-order magnetic transition of austenite [3–5]. The magnetocaloric properties of Ni–Mn-based alloys are comparable to those of conventional Gd5(GeSe)4 compounds [6,7]. In particular, Ni– Mn–Sn alloys show a high potential for large-scale engi⇑ Corresponding author at: Laboratory for Microstructures, Shanghai University, Shanghai 200072, China. Tel.: +86 21 56334045; fax: +86 21 56331218. E-mail address: [email protected] (H. Zheng).

neering applications. Other Heusler alloys are associated with higher costs because they contain expensive elements like Ga or In. For the design and processing of high quality Ni–Mn–Sn alloys, two key points should be addressed. The first key point is the complex crystal structure of the low-temperature martensite, as observed in Ni–Mn–Ga [8– 10] and Ni–Mn–In [11]. Sutou et al. [12] observed four-layered orthorhombic (4O) martensite in melt-spun Ni50Mn37.5Sn12.5. Krenke et al. [13] reported that the martensitic structure in bulk Ni0.50Mn0.50xSnx can be 10M (orthorhombic; using the new notation of Ref. [14], this structure could be denoted as 10O; however, the notation 10M will be used in the present study for the description of the five-layered orthorhombic structure in order to keep consistency), 14M (monoclinic) and L10 (unmodulated double tetragonal), depending on the Sn content. It is found that the structure of the martensite also depends

1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.04.035

H. Zheng et al. / Acta Materialia 61 (2013) 4648–4656

on processing conditions; for example, Santos et al. [15,16] observed a seven-layered orthorhombic martensite in Ni50Mn37Sn13 produced by the melt-spinning rapid solidification technique, whereas Muthu et al. [17,18] observed a four-layered orthorhombic (4O) martensite in the conventional arc-melted bulk Ni50Mn37Sn13. Previous studies in Ni–Mn–Ga alloys show that the martensitic crystal structure strikingly determines the properties. Kakeshita et al. [19] observed that the rearrangement of martensite variants (RMV) in Ni–Mn–Ga alloys by magnetic fields occurs at any temperature for the 10M martensite, while it only occurs in a limited temperature range for the 14M martensite and was not observed at all for the 2M martensite. Sozinov et al. [20] reported that twinning stress, magnetic anisotropy and magnetic-field-induced strain response of Ni–Mn–Ga alloys strongly depend on the martensitic crystal structure. Therefore, it is important to characterize the martensitic crystal structure for the design of high-performance Ni–Mn–Sn alloys. However, the crystal structure characterization of martensite in Ni–Mn–Sn alloys has not been deeply investigated so far. Related investigations were mainly performed through X-ray diffraction [4,13,15,21] and, to date, only the four-layered orthorhombic (4O) martensite has been studied using conventional transmission electron microscopy [12,17,18,22] and neutron powder diffraction technique [23]. The second key point is the composition dependence of the martensitic transformation. Several investigations have been conducted in Heusler Ni–Mn-based alloys and some important factors have been revealed. Firstly, the valence electron concentration (e/a) is thought to be a key factor. Most experimental results suggest an almost perfect linear correlation between the phase transition temperatures and the e/a [24–26]. In terms of the band model, the effect of e/a can be explained as follows. The L21-structured austenite is stabilized because the Fermi surface just touches the (1 1 0) Brillouin zone. Increasing the e/a would overlap the Fermi surface and the (1 1 0) Brillouin zone, and electrons above the Fermi level move to the corner states of the Brillouin zone; as a consequence, the excessive increase in system energy leads to the lattice distortion to minimize the free energy, i.e. the formation of martensite [27]. Secondly, atom size effects must be taken into account and it is widely accepted that the unit-cell contraction of high-temperature austenite would promote the martensitic transformation owing to changes of the relative positions between the Fermi surface and the Brillouin zone. Han et al. [4] found that substituting smaller Ge (atomic radius, r = 0.140 nm) for larger isoelectronic Sn (r = 0.163 nm) atoms in Ni43Mn46Sn11xGex results in an increase of the phase transition temperatures. Kokorin et al. [28] observed similar results when replacing larger In (r = 0.166 nm) by smaller isoelectronic Ga (r = 0.141 nm) atoms in Ni2MnGaxIn1x. In some cases, these size effects dominate the phase transformation behavior. Kanomata et al. [29] found that the phase

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transformation was suppressed in Ni2xCuxMnGa, where the substitution of Cu (r = 0.128 nm) for Ni (r = 0.125 nm) results in a higher e/a ratio and a larger unit-cell volume. Feng et al. also observed such abnormal e/a dependence in Ni49xCuxMn39Sb12 alloys [30]. Combining both factors, Chen et al. [31] proposed to adopt the electron density n (n = (e/a)  N/Vcell) to describe the way in which the alloy composition influences the phase transformation based on the electronic theory of metals [32], where Vcell is the unit-cell volume and N is the average number of atoms contained within a unit cell, and it seems valid in Ni–Mn–Ga [31] and Ni– Mn–Sn [33]. However, additional factors need to be considered due to recent unexpected experimental results reported in the literature. Liu et al. found that the martensitic transition temperatures decrease even though the replacement leads to a higher e/a and a smaller unit-cell volume in Ni–Mn– Ga [34] and Ni–Mn–In–Sb [35]. Karaman et al. [36] proposed to use the magnetic valence number (Zm) to describe the transition temperatures based on the fact that the spinup d-band lies either entirely above or below the Fermi level in strong magnetic systems [37]. To the best of our knowledge, the effect mechanism of alloy composition remains controversial, and the role of the martensitic crystal structure requires further attention. Against this background, the objective of the present study is to address the effects of alloy composition on the phase transformation in Ni–Mn–Sn alloys, and special attention will be paid to the characterization of the martensitic crystal structure using high-resolution transmission electron microscopy and electron diffraction techniques. The aim is to provide more information for better understanding of the basic transformation in Ni–Mn–Sn alloys. 2. Materials and experimental procedures Five Ni–Mn–Sn ingots with a weight of 80 g and nominal compositions of Ni50Mn37+xSn13x (x = 0, 2, 4) and Ni50yMn37+ySn13 (y = 2, 4) were prepared using conventional arc-melting from Ni, Mn, Sn elements with purities of 99.99 wt.% under argon gas atmosphere. Additional 5 wt.% Mn was added to compensate for evaporation losses. All ingots were annealed at 1273 K for 4 h in a vacuum furnace followed by water quenching. X-ray diffraction (D/MAX2200V XRD) measurements using Cu Ka radiation were performed to identify phases and crystal structures. The crystal structure of martensite was further characterized using high-resolution transmission electron microscopy (JEM-2010F HRTEM) and the selected area electron diffraction (SAED) technique. Thin foil samples for TEM observation were prepared according to standard metallographic practice and double-jet electrochemical thinning. Differential scanning calorimetry (NETZSCH DSC 204 F1) measurements were carried out to examine the characteristic transition temperatures with heating/cooling rates of 10 K min1.

H. Zheng et al. / Acta Materialia 61 (2013) 4648–4656

40

50

60

70

10M(30 13)

10M(147)

10M(240)

14M(306) 10M(23 -3)

4O(023) 4O(123)

14M(12 -12) 10M(02 10) A(311)

A(332)

14M(12 -6)

14M(20 -5) 10M(125) 10M(109)

A(332)

A(220)

4O(400)

80

2 theta (degree)

90

40

50

A(400)

A(311)

A(220) A(511)

∗

A(422)

A(332) A(332)

∗

4O(221)

14M(11 10)

10M(0010) 10M(201)

4O(400)

4O(023) 4O(123) A(422)

∗

A(422)

A(222)

A(400)

∗

A(400)

∗

4O(023) 4O(123) 10M(147)

10M(02 10) A(222)

∗

A(220)

∗

(b) 14M(306)

14M(12 -12)

14M(12 -6)

14M(20 -5)

4O(400) A(220) 4O(221)

∗

4O(400) A(220) 4O(221)

Intensity (a.u.)

10M(0010)

10M(201) 10M(109) 10M(125)

14M(11 10)

(a)

14M(21 11) 14M(139)

4650

60

70

80

90

2 theta (degree)

Fig. 1. XRD patterns of as-cast Ni–Mn–Sn (a) and annealed at 1273 K for 4 h (b) at room temperature. The alloys from top to bottom are Ni50Mn41Sn9, Ni50Mn39Sn11, Ni50Mn37Sn13, Ni48Mn39Sn13 and Ni46Mn41Sn13, respectively.

3. Results and discussion 3.1. Phase and structure characterization Fig. 1 shows the X-ray diffraction (XRD) patterns of Ni–Mn–Sn alloys at room temperature, whereas the alloys from top to bottom are Ni50Mn41Sn9, Ni50Mn39Sn11, Ni50Mn37Sn13, Ni48Mn39Sn13 and Ni46Mn41Sn13, respectively. A(hkl), 4O(hkl), 10M(hkl) and 14M(hkl) indicate the Miller indices for the L21, 4O, 10M and 14M structures in Fig. 1, respectively. The XRD pattern of as-cast Ni50Mn37Sn13 is indexed to be a mixture of L21 cubic structure (austenite) [4] and four-layered orthorhombic (4O) structure (martensite) [21–23]. After homogenization annealing at 1273 K for 4 h, the A(2 2 0) peak disappears and the alloy shows almost a fully martensitic microstructure at room temperature where the austenitic peaks become very weak. Substituting Sn with Mn, both as-cast Ni50Mn39Sn11 and Ni50Mn41Sn9 are martensitic at room temperature. However, the crystal structures of these martensites are different. The former mainly corresponds to 10M orthorhombic, whereas two weak peaks from the 4O structure can be detected, and the latter is 14M monoclinic [13]. Both do not show significant changes after high-temperature annealing. On the other hand, when substituting Ni with Mn, an opposite effect can be observed. Although the XRD pattern of as-cast Ni48Mn39Sn13 is similar to that of as-cast Ni50Mn37Sn13, high-temperature annealing strengthens the A(2 2 0) peak, accompanied by an appreciable drop of both 4O(4 0 0) and 4O(2 2 1) peaks. For the ascast Ni46Mn41Sn13, these two 4O peaks completely dimin-

ish. Both annealed Ni50Mn39Sn11 and Ni50Mn41Sn9 are austenitic at room temperature. Besides the reflections from austenite and martensite, some extra peaks can be observed in the as-cast alloys (marked by asterisks in Fig. 1a); for example, in the XRD pattern of as-cast Ni46Mn41Sn13, the peak at 38.2° is from the (2 2 0) reflection of MnSn2, and two other peaks, at 44.5° and at 64.8°, are from the (1 1 0) and (2 0 0) reflections of MnNi, respectively. These extra peaks are also visible in the other as-cast alloys. However, they all disappear after annealing, indicating that the secondary phases are effectively eliminated. Based on the XRD results, one can conclude that three of the alloys are martensitic at room temperature. The least-squares method is used to refine the lattice parameters and the calculated results are listed in Table 1 for the following analysis of the electron diffraction patterns. Fig. 2a shows a typical low-magnification TEM bright-field image of plate-like martensite with a high density twins in as-cast Ni50Mn37Sn13. A HRTEM image is presented in Fig. 2b, where martensite (right) and austenite (left) coexist with an irregular interface at the atomic scale (dashed line). It is found that the unit cell along the c-axis direction contains four atomic layers, with the repeating distance c = 0.87 nm, which is consistent with data reported in the literature [12]. Planar defects of stacking faults exist, which is common in the layered structures. The crystal structures of austenite and martensite are identified as L21 cubic structure [17] and modulated four-layered orthorhombic structure (4O) [12,17,18,22], respectively, according to the respective SAEDPs in Fig. 2c and d. Fig. 2d displays three

H. Zheng et al. / Acta Materialia 61 (2013) 4648–4656

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Table 1 Crystal structures and lattice parameters at room temperature calculated using the XRD data of the as-cast Ni–Mn–Sn alloys. Alloy composition

Crystal structure

Lattice parameters a (nm)

b (nm)

c (nm)

b (°)

Ni50Mn41Sn9 Ni50Mn39Sn11 Ni50Mn37Sn13

14M 10M 4O L21

0.4328 0.4297 0.4383 0.5952

0.5634 0.5606 0.5640 0.5952

2.9934 2.1777 0.8704 0.5952

92.77 90 90 90

(b)

(a)

4 layers c = 0.87 nm

L21 4O

500 nm

10 nm

(d)

(c)

(0-22)

(004) Variant 1 (2-4-2) (000)

(000)

(2-2-4)

[311]L21

[0-10]4O

(004) Variant 2

Fig. 2. (a) TEM bright-field image of as-cast Ni50Mn37Sn13 at room temperature. (b) HRTEM image of L21 austenite (left) and 4O martensite (right). The SAEDPs of L21 austenite (c) and 4O martensite (d).

satellite spots between the fundamental maxima (marked by white arrows), which represent typical diffraction features of the modulated 4O structure. It includes two variants, with an angle near 90° between them. For the as-cast Ni50Mn39Sn11, similar plate-like twins are observed as shown in Fig. 3a and b. Besides the 4O and 10M martensites, some L10 martensites (unmodulated double tetragonal, white areas in Fig. 3a and b) are also visible. The corresponding SAEDPs of 4O, 10M and L10 martensites taken from the TEM bright-field images highlighted in Fig. 3a and b are shown in Fig. 3c–e, respectively. Fig. 3c corresponds to four-layered orthorhombic (4O) martensite, as observed in Fig. 2d. Fig. 3d is the SAEDP of five-layered martensite, named 10M (in the new notation

[14]), where four satellite spots are marked by white arrows. Fig. 3e represents the SAEDP of L10 martensite which has a three-layered periodicity (ABC-type stacking) and it is sometimes denoted as 3R (2M in the new notation [14]; L10 is used in the present study). The HRTEM images of 10M and L10 martensites are shown in Fig. 3f and g, respectively (4O martensite similar to Fig. 2b, not shown here). In Fig. 3f, two variants of 10M martensites can be found which intersect at the angle of almost 90°. In each variant, the image presents contrast modulations with a period of 10 atomic layers and a spacing c = 2.18 nm. Stacking faults are also visible along the c-axis. However, less structural defects are found in the L10 martensite (Fig. 3g). On the other hand, according to the XRD pat-

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H. Zheng et al. / Acta Materialia 61 (2013) 4648–4656

(b)

(a)

4O

(c)

10M

L10

500 nm

500 nm

(e)

(d)

(020)

(00 10) (00-2)

(004)

(-200) (000)

(000)

(000)

[0-10]4O

[010]10M 10M

(f) 10 layers c = 2.18 nm

10 layers c = 2.18 nm

(200)

(g)

[100]L10 L10

Variant 1

Variant 2

5 nm

5 nm

Fig. 3. (a) and (b) TEM bright-field images of as-cast Ni50Mn39Sn11 at room temperature. (c–e) The corresponding SAEDPs of 4O, 10M and L10 martensites taken from the areas highlighted in (a) and (b) marked by white circles. (f and g) HRTEM images of 10M and L10 martensites.

tern of as-cast Ni50Mn39Sn11 bulk alloy in Fig. 1, the appearance of L10 martensite is not expected. Pons et al. [8] observed an interesting result that all the martensites in the TEM thin foil show the L10 structure although the XRD pattern obtained from the melt-spun Ni–Mn–Ga only indicates 14M martensite. They ascribed the finding to the large stress introduced during rapid solidification, which makes it difficult for the L21 austenite and the L10 martensite to accommodate, and this leads to further microtwinning. Once the stress is relaxed in thin foil condition, the macroscopic twinning and non-layered L10 martensite would recover again. Therefore, the appearance of L10 martensites in the present study might also be associ-

ated with internal stresses caused by the rapid waterquenching of the bulk sample. In the case of the as-cast Ni50Mn41Sn9, most of the martensites correspond to monoclinic structure (14M), and a few L10 martensites can still be found in the TEM thin foil sample (Fig. 4a). The SAEDP of the 14M martensite is shown in Fig. 4b where two variants of 14M martensites can be identified, and six satellite spots can be seen between the fundamental maxima (marked by white arrows). Fig. 4c presents a typical HRTEM image taken from the thin foil sample where three zones are labelled as A, B and C, respectively. Both zones A and B are identified as the 14M martensite, and

H. Zheng et al. / Acta Materialia 61 (2013) 4648–4656

(a)

4653

(b) 14M

(22-4) (02 -14)

500 nm

(c)

(000)

[-571]14M

(d)

A-14M 14 layers c = 2.99 nm C-L10

14 layers c = 2.99 nm

B-14M

5 nm

500 nm

Fig. 4. (a) TEM bright-field image of as-cast Ni50Mn41Sn9 at room temperature. (b) The corresponding SAEDP taken from the area highlighted in (a) marked by a white circle. (c) HRTEM image of 14M and L10 martensites. (d) TEM bright-field image of intersected 14M martensites, the inserted SAEDP taken from the area highlighted in (d) marked by a white circle.

in each variant, the image presents contrast modulations with a period of 14 atomic layers and a spacing c = 2.99 nm. The zone C is internal nanotwin-free L10 martensite without structural defects. In Fig. 4d, the martensite is highly twinned primarily along two directions. The inserted SAEDP taken from the intersection area highlighted in Fig. 4d shows superlattice reflections along three directions. Two of them correspond to the two martensite variants, and the third one originates from the double diffraction of the overlapped twins. 3.2. Compositional dependence of martensitic transformation The DSC results of the annealed Ni–Mn–Sn alloys are presented in Fig. 5a. The DSC chart of Ni46Mn41Sn13 is shifted down to negative heat flow values for clarity. Except for Ni46Mn41Sn13, large exothermic and endothermic peaks during cooling and heating corresponding to direct and reverse martensitic transformations can be observed. Taking Ni50Mn39Sn11 as an example, the characteristic transition temperatures, including the austenite

start and finish (As and Af), and martensite start and finish (Ms and Mf) temperatures can be determined, as shown in Fig. 5a. With Mn replacing Sn on the basis of Ni50Mn37Sn13, the transformation peaks strongly shift towards the high-temperature regime. In contrast, the substitution of Ni with Mn leads to a strong decrease. No endothermic/ exothermic peak is detected for Ni46Mn41Sn13 within the experimental temperature range (123–373 K), and it can be inferred that the martensitic transformation is strongly suppressed. This is in line with the XRD result in Fig. 1. Additionally, it is very important to note the following two points on Fig. 5. (i) Small humps can be clearly discerned from the DSC heat flow curve of Ni50Mn39Sn11, whether in heating or in cooling (marked by single arrows), which is invisible in other three alloys. This is related to the internal transformation kinetics and can be interpreted well from the fact that the alloy consists of 10M and 4O mixed martensites (see XRD pattern in Fig. 1 and TEM analysis in Fig. 3). Small humps are still visible even after five thermal cycles, as shown in Fig. 5b. (ii) In case of both Ni46Mn41Sn13 and Ni48Mn39Sn13, weak exothermic and endothermic peaks can be identified at about 298 K and

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H. Zheng et al. / Acta Materialia 61 (2013) 4648–4656 0.4

exo

(a)

Ni50Mn41Sn9 Ni50Mn39Sn11 Ni50Mn37Sn13

Heat flow (mW/mg)

0.2 Ni48Mn39Sn13

cooling Mf

Tc

0.0

As

Ms Af heating

-0.2

Ni46Mn41Sn13

Tc

-0.4

100

200

300

400

500

600

Temperature (K)

(b) Heat flow (mW/mg)

0.2

cooling

0.0

heating -0.2

325

350

375

400

425

450

475

500

Temperature (K)

Fig. 5. (a) DSC curves of annealed Ni–Mn–Sn alloys. The curve of Ni46Mn41Sn13 is shifted down to negative heat flow values for clarity. (b) Five cyclic DSC curves of Ni50Mn39Sn11 showing clear humps. All heating/cooling rates are 10 K min1.

305 K upon cooling and heating, respectively, which correspond to the magnetic transition of austenite, Tc (marked by double arrows, Fig. 5a) [22]. We now discuss the compositional dependence of the phase transition temperatures. Firstly, the martensite start temperature is plotted as a function of the e/a ratio, as shown in Fig. 6. Data from literature are also included [13,17,18,21], whereas only data from arc-melted bulk alloys are cited in order to reduce scatter caused by pro-

Martensitic start temperature (K)

800 Present work [13] [17,18] [21]

700 600

L10

500

14M

14M

400 10M+ a few 4O

10M 4O

300

4O 4O

4O

200

4O

8.00

8.05

8.10

8.15

8.20

8.25

8.30

8.35

8.40

e/a Fig. 6. Dependence of the martensite start temperature on valence electron concentration (e/a) martensitic crystal structure (including data from literature [13,17,18,21]). The dash line is a guide to the eye.

cessing techniques as introduced in Section 1 of this paper [15–18,38]. The phase transition temperature demonstrates a linear dependence of 16.6 K with a change of +0.01 in e/a, which well agrees with the e/a-dependence rule [24–26]. Here it is assumed that the valence electrons per atom are 10 (3d84s2) for Ni, 7 (3d54s2) for Mn and 4 (5s25p2) for Sn, respectively. Secondly, from the view of size effects, the atom radii are 0.125 nm for Ni, 0.135 nm for Mn, and 0.163 nm for Sn, respectively. When replacing Sn with Mn, the unit-cell of high-temperature austenite is expected to shrink. Substituting Mn for Ni would lead to a larger unit-cell volume, which can also be reflected from the fact that the XRD strongest peak A(2 2 0) shifts towards low angles with increasing Mn level at room temperature (Fig. 1b). One can conclude that the atom size effect provides a similar effect on the transition temperatures as the e/a ratio. Thirdly, the magnetic valence numbers are 0, 3 and 4 for Ni, Mn and Sn, respectively [37], and the calculated Zm for Ni–Mn–Sn alloys does not fit with the rule obtained by Karaman et al. in Co–Ni–Ga alloys [36]. We suggest that this is associated with the magnetism to a large extent. The phase transition temperatures of Co–Ni–Ga alloys studied in Ref. [36] are below the magnetic transition temperature of austenite, that is, the martensitic transformation takes place in almost similar magnetism states. However, this is not the same case in the present study. The ferromagnetic transition of austenite occurs prior to the martensitic transformation only in Ni48Mn39Sn13 and Ni46Mn41Sn13, so that the structural transition takes place between ferromagnetic austenite and weak magnetic martensite. According to previous studies on the effect of alloy composition on the magnetic transition behaviour of Ni–Mn– Sn alloys [12,13], one can conclude that for Ni50Mn37Sn13, it is very possible that the magnetic transition of austenite and the martensitic transformation couple within the same temperature range, while both Ni50Mn41Sn9 and Ni50Mn39Sn11 directly transform from paramagnetic austenite to weak magnetic martensite. That is, the magnetization discrepancy (DM) between austenite and martensite varies greatly so that the indicator of Zm does not apply to this study. Lastly, the crystal structure information of the resultant martensite is incorporated into Fig. 6 [13,17,18,21]. It is clearly that with increasing transition temperature (or e/a), the crystal structure of the martensite evolves in a sequence of 4O ! 10M ! 14M ! L10 during the phase transformation of bulk Ni–Mn–Sn alloys. Fig. 7 presents the variations of the transformation latent heat (|DH|) and entropy change (|DS|) as a function of the e/a ratio. |DH| almost linearly increases with increasing e/a, while |DS| increases first and then drops slightly for Ni50Mn41Sn9. Firstly, |DS| is influenced by the transformation-induced unit-cell volume change between austenite and martensite. As mentioned above, the crystal structure of martensite formed in Ni–Mn–Sn alloys varies with alloy composition (or e/a), and the change of the unit-cell vol-

H. Zheng et al. / Acta Materialia 61 (2013) 4648–4656

20

0.08 ΔHc

15

ΔHt

0.06

10 ΔSc

5

ΔSt

0 -5 8.05

8.10

8.15

8.20

0.04

ΔS (J/gK)

ΔH (J/g)

(3) With increasing transition temperatures (or e/a), the resultant low-temperature martensitic crystal structure evolves in a sequence of 4O ! 10M ! 14M ! L10 in bulk Ni–Mn–Sn alloys.

0.10

25

4655

0.02

0.00 8.25

e/a

Fig. 7. Dependence of transformation latent heat |DH| and enthalpy change |DS| on valence electron concentration (e/a).

ume caused by the structural transformation would be different [35], thus leading to the change of |DS|. Secondly, it has been argued that the character of the e/a dependence of |DS| is related to the magnetic contribution that relies on the difference in the magnetic exchange below and above Ms [39]. It is generally known that the magnetic exchange is closely connected to the Mn–Mn interatomic distance. In the present work, the L21 cubic unit cell of austenite shrinks with increasing e/a, thus the Mn–Mn interatomic distance would shorten and produce positive effect on the magnetic exchange. Additionally, the magnetism (magnetization discrepancy) of (between) austenite (paramagnetic or ferromagnetic) and martensite (various structures) also largely affects the magnetic exchange. It is worth performing more investigations to clarify this point. 4. Conclusions In summary, the phase transformation behaviour of bulk Ni–Mn–Sn alloys is investigated through X-ray diffraction, transmission electron microscopy and thermal analysis. The following conclusions are obtained. (1) The crystal structures of martensites are confirmed to be seven-layered monoclinic (14M) for Ni50Mn41Sn9, four-, five-layered orthorhombic and unmodulated double tetragonal (4O + 10M + L10) for Ni50Mn39Sn11 and four-layered orthorhombic (4O) for Ni50Mn37Sn13, respectively. All modulated layered martensites are nanotwinned in nature and less structural defects are observed inside the L10 martensite. (2) Substituting Sn with Mn is favourable to increase the phase transition temperatures in Ni50Mn37+xSn13x (x = 0, 2, 4). In contrast, when Sn content is a constant in Ni50yMn37+ySn13 (y = 0, 2, 4), increasing the Mn concentration lowers the transition temperatures dramatically. The compositional dependence of the transition temperatures is mainly attributed to the changes of the e/a and the unit-cell volume of hightemperature austenite.

Acknowledgements The authors gratefully acknowledge the support from the National Natural Science Foundation of China (51201096), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20123108120019) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. HX Zheng thanks funding from the Alexander von Humboldt (AvH) Foundation of Germany. References [1] Man˜osa Ll, Moya X, Planes A, Krenke T, Acet M, Wassermann EF. Mater Sci Eng A 2008;481–482:49–56. [2] Wang JM, Jiang CB. Scripta Mater 2010;62:298–300. [3] Moya X, Man˜osa Ll, Planes A, Krenke T, Duman E, Acet M, et al. J Magn Magn Mater 2007;316:e572–4. [4] Han ZD, Wang DH, Zhang CL, Xuan HC, Zhang JR, Gu BX, et al. Mater Sci Eng B 2009;157:40–3. [5] Wu DZ, Xue SC, Frenzel J, Eggeler G, Zhai QJ, Zheng HX. Mater Sci Eng A 2012;534:568–72. [6] Kumar DMR, Raja MM, Gopalan R, Singh AK, Chandrasekaran V, Suresh KG. Intermetallics 2009;18(4):518–22. [7] Bru¨ck E, Tegus O, Thanh DTC, Buschow KHJ. J Magn Magn Mater 2007;310:2793–9. [8] Pons J, Chernenko VA, Santamarta R, Cesari E. Acta Mater 2000;48:3027–38. [9] Righi L, Albertini F, Pareti L, Paoluzi A, Calestani G. Acta Mater 2007;55:5237–45. [10] Pons J, Santamarta R, Chernenko VA, Cesari E. J Appl Phys 2005;97:083516. [11] Miyamoto T, Ito W, Umetsu RY, Kainuma R, Kanomata T, Ishida K. Scripta Mater 2010;62:151–4. [12] Sutou Y, Imano Y, Koeda N, Omori T, Kainuma R, Ishida K, et al. Appl Phys Lett 2004;85(19):4358–60. [13] Krenke T, Acet M, Wassermann EF, Moya X, Man˜osa Ll, Planes A. Phys Rev B 2005;72:014412. [14] Otsuka K, Ohba T, Tokonami M, Wayman CM. Scripta Metall Mater 1993;29:1359. [15] Santos JD, Sa´nchez T, Alvarez P, Sanchez ML, Sa´nchez Llamazares JL, Hernando B, et al. J Appl Phys 2008;103:07B326. [16] Hernando B, Sa´nchez Llamazares JL, Santos JD, Sa´nchez ML, Escoda Ll, Sun˜ol JJ, et al. J Magn Magn Mater 2009;321:763–8. [17] Muthu SE, Rao NVR, Rao DVS, Raja MM, Devarajan U, Arumugam S. J Appl Phys 2011;110:023904. [18] Muthu SE, Rao NVR, Raja MM, Kumar DMR, Radheep DM, Arumugam S. J Phys D Appl Phys 2010;43:425002. [19] Okamoto N, Fukuda T, Kakeshita T. Mater Sci Eng A 2008;481– 482:306–9. [20] Sozinov A, Likhachev AA, Lanska N, So¨derberg O, Ullakko K, Lindroos. Proc SPIE 2003;5053:586–94. [21] Fukushima K, Sano K, Kanomata T, Nishihara H, Furutani Y, Shishido T, et al. Scripta Mater 2009;61:813–6. [22] Zheng HX, Wu DZ, Xue SC, Frenzel J, Eggeler G, Zhai QJ. Acta Mater 2011;59(14):5692–9. [23] Brown PJ, Gandy AP, Ishida K, Kainuma R, Kanomata T, Neumann K-U, et al. J Phys Condens Matter 2006;18:2249.

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H. Zheng et al. / Acta Materialia 61 (2013) 4648–4656

[24] Moya X, Man˜osa Ll, Planes A, Krenke T, Acet M, Wassermann EF. Mater Sci Eng A 2006;438–440:911–5. [25] Krenke T, Moya X, Aksoy S, Acet M, Entel P, Man˜osa Ll, et al. J Magn Magn Mater 2007;310:2788–9. [26] Zayak AT, Adeagbo WA, Entel P, Rabe KM. Appl Phys Lett 2006;88:111903. [27] Smit J. J Phys F Metal Phys 1978;8:2139. [28] Kokorin VV, Osipenko IA, Shirina TV. Phys Metals Metallogr 1989;67:173–6. [29] Kanomata T, Nozawa T, Kikuchi D, Nishihara H, Koyama K, Watanabe K. Int J Appl Electrom 2005;21:151–7. [30] Feng WJ, Zuo L, Li YB, Wang YD, Gao M, Fang GL. Mater Sci Eng B 2011;176:621–5. [31] Chen XQ, Yang FJ, Lu X. Qin ZX. Phys Status Solidi (b) 2007;244(3):1047–53.

[32] Hook JR, Hall HE. Solid state physics. 2nd ed. New York: Wiley; 2003. [33] Wang RL, Yan JB, Xiao HB, Xu LS, Marchenkov VV, Xu LF, et al. J Alloys Compd 2011;509:6834–7. [34] Liu ZH, Zhang M, Wang WQ, Wang WH, Chen JL, Wu GH, et al. J Appl Phys 2002;92(9):5006–10. [35] Liu ZH, Wu ZG, Yang H, Liu YN, Liu EK, Zhang HW, et al. Intermetallics 2010;18:1690–4. [36] Dogan E, Karaman I, Singh N, Chivukula A, Thawabi HS, Arroyave R. Acta Mater 2012;60:3545–58. [37] Williams AR, Moruzzi VL, Malozemoff AP, Terakura K. IEEE Trans Magn 1983;19(5):1983–8. [38] Frenzel J, George EP, Dlouhy A, Somsen Ch, Wagner MF-X, Eggeler G. Acta Mater 2010;58:3444–58. [39] Khovailo VV, Oikawa K, Abe T, Tagaki T. J Appl Phys 2003;93:8483.