CRYSTAL STRUCTURE OF MARTENSITIC PHASES IN Ni±Mn±Ga SHAPE MEMORY ALLOYS

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1 Acta mater. 48 (2000) 3027± CRYSTAL STRUCTURE OF MARTENSITIC PHASES IN Ni±Mn±Ga SHAPE MEMORY ALLOYS J. PONS 1 {, V. A. CHERNENKO 2, R. SANTAMARTA 1 and E. CESARI 1 1 Departament de FõÂ sica, Universitat de les Illes Balears, Ctra. de Valldemossa km 7.5, E Palma de Mallorca, Spain and 2 Institute of Magnetism, National Academy of Sciences of Ukraine, Vernadsky Str. 36-B, Kiev, , Ukraine (Received 5 April 2000; accepted 27 April 2000) AbstractÐThe crystal structures of the di erent martensitic phases observed in a wide variety of Ni±Mn± Ga alloy compositions have been studied in detail. Similarly to the Ni±Al alloys, the non-modulated martensite can be well described by the L1 0 lattice, although it must be ``doubled'' in order to account for the L2 1 type of order of the parent phase. Concerning the well known ve- and seven-layered martensites, two approaches taken from the literature are analysed and discussed. The rst approach, widely accepted in Ni±Al alloys, describes the structure as long period stacking of {1} P close packed planes ( M and 14 M structures), while the second one considers lattices modulated by shu ing. The two approaches are shown to be very similar and, in many cases, indistinguishable by the di raction techniques using photographic recording. However, some physical arguments are given to interpret the ve- and seven-layered structures with the second and rst approaches, respectively. The structure of the ``new'' -layered martensite is studied, being described by a (55) stacking sequence of close-packed planes Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Crystal structure; Phase transformations (martensite); Ni±Mn±Ga alloys; Electron di raction; X-ray di raction (XRD) 1. INTRODUCTION { To whom all correspondence should be addressed. The Ni±Mn±Ga alloys with compositions close to the stoichiometric Ni 2 MnGa compound undergo a thermoelastic martensitic transformation and constitute a new family of shape memory alloys [1, 2]. These alloys nd additional interest due to the fact that they also exhibit a ferromagnetic transition at the Curie temperature, T c, which is located in the vicinity of 370 K and does not strongly depend on the alloy composition. The martensitic and magnetic transitions of this alloy system have been extensively studied in recent years [1±9]. A good shape memory e ect has been observed in bulk material as well as in meltspun thin ribbons [, 11]. Furthermore, the possibility of inducing a giant strain by means of an external magnetic eld has been recently observed [6, 12], which is especially promising from the point of view of applications. The crystal structure of the austenitic parent phase (P) in the stoichiometric compound has been determined by neutron di raction, being cubic with L2 1 (Heusler) atomic order [3]. The o -stoichiometric compounds have only been studied by X-ray or electron di raction and, due to the similar atomic scattering factors of the constituent atoms, the re ections indicating the second neighbour ordering (characteristic of the L2 1 structure) have not been found. Although the observed re ections indicate only rst neighbour ordering (B2 structure), indeed, the crystal lattice has been conventionally treated to be L2 1 ordered as in the stoichiometric compound [1, 2,, 11]. The structure of the martensitic phase for the stoichiometric compound was rst studied by neutron elastic scattering, providing a body centred tetragonal modulated lattice (bct, c/a < 1) and a hypothesis has been made that modulation should be along the h0i direction [3]. Further studies on alloys close to stoichiometric composition have con- rmed that the martensitic structure is formed by the tetragonal distortion of the initial cubic lattice (c/a < 1) and revealed that the martensitic lattice is subjected to periodic shu ing along the (1) [11 0] P system and the modulation period is ve (1) P planes ( ve-layered martensite ) [4, 5]. A sequence of stress-induced intermartensitic transformations to a body-centred monoclinic structure with seven (1) P -plane modulation (seven-layered /00/$ Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S (00)

2 3028 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga martensite ) and a body-centred tetragonal structure having c/a > 1 without modulation (non-modulated martensite ) have been reported [1, 4, 5]. Recently, several o -stoichiometric Ni±Mn±Ga alloys have been studied by TEM and X-rays [9] and the observed di raction patterns have been analysed in terms of the M and/or 14 M structures already observed in Ni±Al alloys [13, 14], as being correspondent to the ve- and seven-layered martensites, respectively. It is worth noting that M and 14 M legends have been used in Ref. [9] in accordance with the new notation of Ref. [15]; the 14 M structure has been more often referred to as 7R or 7 M martensite [16±18]. In our previous works, the thermally induced martensites in a wide range of Ni±Mn±Ga alloy compositions have been identi ed mainly by means of TEM and electron di raction. The above mentioned types of layered structures appeared to be easy to distinguish owing to the extra spots on the electron di raction patterns along the direction corresponding to the h1i P plane. Brie y, the alloys with martensitic transformation temperatures (Ms ) well below 270 K showed a ve-layered martensite (this group includes the stoichiometric composition); the group with Ms near 270 K presented ve-layered and/or seven-layered martensite, while the group of alloys with Ms above room temperature exhibited the seven-layered martensite or the non-modulated structure or a new modulated structure with a period of (1) P planes (-layered martensite ) [, 19±21]. In those works, except for the layer periodicity, the martensitic crystal structures were not analysed. The present work is devoted to a detailed analysis of the crystal structures of the di erent martensitic phases that are typical for a wide variety of Ni± Mn±Ga alloy compositions. First, the two approaches that were commonly used for the description of the di erent martensitic structures in the Ni±Al system (i.e. M and 14 M structures) and in the Ni±Mn±Ga system, respectively, will be reviewed. Later, the experimental results will be presented and analysed within the two approaches. 2. CONSTRUCTION OF THE LAYERED STRUCTURES 2.1. Long period stacking approach for the martensitic structures in the Ni±Al system The B2 parent phase in Ni±Al alloys has only rst neighbour ordering. The basic martensitic structure (non-modulated) is most often described as face centred tetragonal with L1 0 lattice [22], schematised in Fig. 1(a). In binary alloys with Al content around 37.5 at.% Al, the formation of a sevenlayered structure is well known, being traditionally called 7R or 7 M (14 M in the new notation) [16, 17, 22]. Recently, in ternary alloys like Ni±Al±Mn, a ve-layered martensite, named M (in the new notation) has been observed, as well as structures with other periods like 12 or 15 layers [13, 14]. The di erently layered structures are commonly constructed as long period stackings of close-packed planes, derived from the {1}-type planes of austenite, or {111} planes of the L1 0 cell. The unit cell is described as a monoclinic lattice, the crystallographic axes being aligned along [1] (a-axis), [001] (b-axis) and [1] (c-axis) of the cubic austenite. Hereafter such axes will be referred to as ``monoclinic axes''. The stacking sequences of the 14 M and M structures are (52) 2 and (32) 2 in Zhdanov notation, respectively. The basal planes, {001}, are stacked along the c-axis in such a way that two consecutive planes are shifted along the a-axis a distance given by (1/3+d ) a, d being an adjustable parameter (d=0 corresponds to a perfect closepacked structure). The value of d and the stacking sequence determine the b angle of the monoclinic cell. A detailed description of the construction of these structures is presented in Ref. [13], from which the following lattice parameters are obtained: a 14M =0.425 nm, b 14M =0.278 nm, c 14M =2.97 nm, b 14M =94.78 and a M =0.424 nm, b M =0.283 nm, c M =2.05 nm, b M = In the new axes, the L1 0 structure has a three-layer periodicity (ABCtype stacking) and it is sometimes denoted as 3R (2 M in the new notation of Ref. [15]). If this scheme is applied to the Ni±Mn±Ga Fig. 1. (a) Scheme of the L1 0 cell. (b) Lattice correspondence between the ``cubic'' axes and those for the L1 0 cell.

3 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga 3029 alloys, as the parent phase has L2 1 order, the lattice parameter b must be doubled and the stacking must alternate basal planes with and without ``prime'' ('), i.e. an additional shift by 1 2 b along the b-axis between two consecutive planes has to be added. It is worth noting that the structures obtained following this scheme are best tted to the di raction patterns obtained using high quality X-ray or electron di raction equipment. However, the 14 M structure of Ni 62.5 Al 37.5 was re ned from neutron di raction experiments by Noda et al. [18], who described more sophisticated models to t the observed di raction peak intensities with better accuracy. Nevertheless, the modelling based on closepacked plane stacking has a reasonably good level of precision and it is widely accepted. Actually, HREM observations have con rmed the (52) or (32) stacking sequences [17, 23] Modulated lattices approach in Ni±Mn±Ga In this approach, described in Refs [4, 5], the L2 1 type order of the parent phase is considered. The martensitic structures are described, in the rst term, by body-centred unit cells, which do not include the modulation (they are deduced from the fundamental di raction spots). For the ve-layered martensite, the cell is body-centerd tetragonal with a = nm, c = nm (c/a < 1), while for the seven-layered martensite the cell is body-centred monoclinic with a = nm, b = nm, c = nm, g=90.58 (these are the parameters given in Ref. [5]; in the previous work [4], the cell was de ned as orthorhombic); nally, for the nonmodulated martensite the cell is body-centred tetragonal with a = nm and c = nm (c/a > 1). These results have been obtained in almost-stoichiometric compounds from X-ray di raction using photographic recording; thus, again, such structures are accurate up to the capabilities of this technique. It is very important to note that the crystallographic axes of these body-centred structures correspond to the axes of the austenite (cubic) structure. They are the same as the ``pseudo-orthorhombic'' axes de ned in Ref. [18]. Hereafter these axes will be referred to as ``cubic'' axes. The description of the layered structures is made with the crystallographic axes along [1], [001] and [1] (the same as the ``monoclinic axes'' of the Ni± Al-type unit cells). The cell is considered to be modulated by periodical shu ing of the basal planes along [1] (a-axis), the displacement of each j plane from its regular position being given by a function D j containing three harmonic terms: D j ˆ A sin 2pj=L B sin 4pj=L C sin 6pj=L, where L is the modulation period [4, 5]. The values of the constants A, B and C are adjusted to t the experimental relative intensities of the extra re ections appearing along the c -axis. For the ve-layered martensite, it is important to note that the new axes describing the modulation remain orthogonal, thus, the unit cell is orthorhombic. On the other hand, the Ni±Al-type M structure is slightly monoclinic. This fact o ers a way to distinguish both types of approaches. It is also important to note that the stacking sequence (32) 2 is incompatible with an orthorhombic cell. This would require the horizontal shift between two consecutive planes to be exactly 1 2 a (deviation parameter d=0.167), but this would lead to a two-layer periodicity. The case of the seven-layered structure is di erent; as it is built from a monoclinic cell in the ``cubic'' axes, the new axes containing the modulation are not orthogonal, giving rise to a monoclinic cell with b= This makes it more di cult to distinguish the two approaches for the seven-layered martensite. Concerning the non-modulated martensite, the structure reported in Refs [4, 5] is certainly the same as the L1 0 structure, they only di er in the selection of the crystallographic axes and the consideration of the parent phase as L2 1 ordered. The correspondence between both lattices (with B2-type order) is shown in Fig. 1(b) (this is the Bain-type distortion as a path from b.c.c. to f.c.c.), the relationship between the lattice constants being as follows: p a L ˆ p 2 abct ˆ 2 0:552 nm ˆ 0:781 nm; c L ˆ c bct ˆ 0:644 nm The numeric values correspond to the stoichiometric compound. Note that c L =a L ˆ 0:825 < 1, while c bct /a bct >1. 3. EXPERIMENTAL PROCEDURE The compositions and martensite start temperatures, Ms, of the alloys used in the present work are shown in Table 1. The alloys were prepared in an induction furnace under argon atmosphere from the constitutive metals (Ni of 99.99% purity, twiceremelted Cerac Mn and % purity Ga) and cast into a copper mould. For some of the alloys, Table 1. Composition of the alloys, together with their electron to atom ratio (e/a ) and nominal martensite start temperature (Ms ) Alloy Ni (at.%) Mn (at.%) Ga (at.%) e/a Ms (K)

4 3030 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga Fig. 2. (a) X-ray di raction spectrum obtained from bulk alloy 5 at room temperature. (b) Selected area electron di raction pattern (SAEDP) obtained in melt-spun alloy 8. The patterns have been indexed according to a ``double'' L1 0 lattice. rapidly solidi ed thin ribbons were obtained by the melt-spinning method. Details of the preparation of the ribbons can be found elsewhere [, 11]. The crystal structures were analysed by means of X-ray di raction (XRD; powder method, Siemens D5000 di ractometer with Cu Ka radiation) and TEM-selected area electron di raction (Hitachi H600 operating at 0 kv with in situ cooling stage). The available di ractometer does not have any cooling facility, so it could only be used for the alloys being in martensitic state at room temperature. The experimental interplanar distances, d hkl, were obtained from the XRD spectra after a peak deconvolution process using pseudo-voight functions. The re nement of the lattice constants was carried out with the least-squares method using a self-made computer program. In order to get more accurate information from the electron di raction patterns, the camera length of the electron microscope was calibrated. A stoichiometric Ni 2 MnGa melt-spun ribbon was used as standard, the lattice parameter of the austenite being previously determined by XRD. The obtained value for the lattice parameter (a = nm) is coincident with that reported in the literature ( nm) [3]. 4. EXPERIMENTAL RESULTS 4.1. Non-modulated martensite This structure has been observed in the alloys with relatively high Ms values, so they are in martensitic state at room temperature and they could be studied by XRD. An analysis of the X-ray and electron di raction patterns indicates that the structure is the face-centred L1 0. Figure 2 contains examples of the typical patterns indexed according to the lattice obtained from the L2 1 order for the parent phase (``double'' L1 0 cell), although the second neighbour order is not revealed in the patterns. The lattice parameters obtained by XRD in the di erent alloys are shown in Table 2. Figure 3 Table 2. Lattice parameters of the non-modulated martensite and tetragonality (c/a ) Alloy a (nm) c (nm) c/a Fig. 3. Plots of Ms and e/a ratio as a function of tetragonality c/a.

5 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga 3031 shows the plots of the transformation temperature (Ms ) and the electron-to-atom ratio (e/a ) as a function of the tetragonality ratio (c/a ), and an interesting correlation between these parameters is revealed. The microstructure of this martensite consists of plates, most of them being internally twinned with the f111g L twinning plane. There are, however, some minor twinning-free zones giving di raction patterns like that of Fig. 2(b). The internal twinning is not regular across the material: there are zones with a rather regular distribution of relatively thick twins and zones with a high density of irregular and very ne twins. It is important to emphasise that these di erent zones are very often encountered in the same main martensite plate. An example is shown in the zones labelled as A and B in Fig. 4(a), which exhibit a di erent di raction pattern [Figs 4(b) and 4(c)]. In zone A, the pattern is typical for two twinrelated variants, while in zone B (irregular ne twins) the pattern shows a di use scattering intensity along the h111i L direction (which becomes the c-axis of the layered structures). Zone C is the interface with a small nely twinned area having an almost orthogonal twinning plane. Such interfaces are, usually, non-planar. The corresponding di raction pattern [Fig. 4(d)] shows the di use scattering along the two directions, including some di use and not regularly placed satellites. The nely twinned areas having satellites in the di use scattering are Fig. 4. (a) Bright eld TEM image of a melt-spun alloy 8; (b) SAEDP from region A; (c) SAEDP from region B; (d) SAEDP from region C.

6 3032 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga the electron di raction patterns of the melt-spun ribbons again show a non-modulated structure [Fig. 2(b)]. These changes in the martensitic structure will be discussed in the next section Five-layered martensite Fig. 5. SAEDP of the ve-layered martensite obtained in alloy 3 in situ cooled to 77 K. mostly placed in the thicker parts of the TEM foil. Sometimes the position of the satellites is irregular [as in Fig. 4(d)] and in other cases the satellites are regularly placed, giving rise to the di raction pattern corresponding to the -layered martensite (which will be described below). A similar behaviour to that depicted in Fig. 4 has also been found in Ni±Al alloys [24, 25]. In Ref. [25], the existence of zones giving di raction patterns like those of the -layered structure is also reported. A very interesting result has been obtained in alloy 8. In the bulk state, the XRD patterns indicate a non-modulated tetragonal structure for the martensite [similar to Fig. 2(a)], while the patterns obtained in the melt-spun ribbons of the same nominal composition are clearly di erent [see Fig. 6(b)]. As it will be mentioned below, such patterns correspond to the seven-layered martensite. However, This martensite appears only in the alloys transforming at temperatures well below room temperature (alloys 1±3 in Table 1), so it was only possible to study them by TEM and electron di raction. The observed patterns (a typical example is shown in Fig. 5) are very similar to those reported in the Ni±Al±Mn alloys [13, 14], where the structure has been reported as M. Particularly, the relative intensities of the four extra spots along the c -axis, which depend on the close-packed stacking sequence, are like those of the Ni±Al±Mn alloys [13, 14], being best tted with the (32) stacking sequence. However, it is important to note that these relative intensities are also the same as those obtained by the modulated lattice approach [4, 5]. As it was mentioned at the end of Section 2, the angle b between the a- and c-axes is important to distinguish between the two approaches. In the present work, the studied alloys have compositions near the stoichiometry and only the melt-spun Ni± 23.6 at.% Mn±24.9 at.% Ga ribbon exhibited a b angle di erent from 908 (it is between 908 and 918). Although the selected-area electron di raction does not allow a high accuracy, the values measured for the other lattice parameters (a = 0.42 nm, b = 0.55 nm, c = 2. nm) are very close to those given in Refs [4, 5], after a translation to the ``monoclinic'' axes. Fig. 6. (a) SAEDP of the seven-layered martensite obtained in melt-spun alloy 4 in situ cooled to 77 K. (b) X-ray di raction spectrum obtained in the melt-spun alloy 8 at room temperature, indexed according to the 14 M structure.

7 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga Seven-layered martensite Again, the alloys exhibiting this martensite usually have an Ms below room temperature. This kind of martensite has been observed by electron di raction in alloy 4. Figure 6(a) shows an example of the typical di raction patterns. In alloy 3, a mixture of ve- and seven-layered martensite has been found. As in the ve-layered structure, the observed electron di raction patterns are practically identical to those reported for the 14 M structure in Ni±Al± Mn, although the modulated lattice approach also leads to the same relative intensities of the extra re ections. This fact will be covered in the next section. As it was mentioned in Section 4.1, the melt-spun ribbon of alloy 8 exhibited XRD patterns di erent from those of the same bulk alloy. An example of such an XRD pattern is presented in Fig. 6(b). This pattern can be well indexed on the base of the 14 M structure with the following lattice parameters (obtained after a least-squares tting procedure): a = nm, b = nm, c = nm, b= Using these lattice parameters and assuming a (52) 2 stacking, the deviation parameter d is determined to be The vertical distance between two basal planes is given by (c sin b )/14=0.2 nm Ten-layered martensite This structure has been observed in alloys with transformation temperatures above room temperature, but only by electron di raction (material in thin-foil condition) [, 11, 21]. Typical di raction patterns are shown in Fig. 7. As commented above, the -layered martensite is often observed in coexistence with the non-modulated martensite (in alloys 5 and 7). The electron di raction patterns from alloy 7 were analysed in terms of the ``monoclinic'' axes, resulting in the following lattice constants: a = 0.43 nm, b = 0.54 nm, c = 2. nm, b=908 (the lattice is orthorhombic). The structure will now be analysed following the Ni±Al-type scheme, i.e. in terms of long period stacking of close-packed planes, in a similar way as in Ref. [13] for the M structure ( ve-layered). All the possible stacking sequences with a period of planes can be classi ed in the following families: {91}, {82}, {73}, {64} and {55} fmng stands for the family of sequences having a total of m shifts in the + direction along the a-axis, and n shifts in the opposite direction). Using the value for the deviation parameter, d, obtained in the seven-layered structure (d=0.08), the only family which results in an orthorhombic cell is {55} (this family always gives an orthorhombic cell, independently of the value of d ). This result rules out the other families. The di erent stacking sequences of the {55} family are detailed in Table 3, together with the positions of the successive basal planes in the unit cell (in relation to the lattice parameter a ). With these positions, the theoretical intensities of the re ections can be calculated as the square modulus of the structure factor (dynamical e ects for the electron Fig. 7. Examples of SAEDP of -layered martensite obtained in melt-spun alloy 7. Fig. 8. Experimental intensities along the 12 l row for the -layered martensite and scheme of the calculated intensities for the (55) stacking sequence model.

8 3034 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga di raction are not considered in the present analysis) and compared with the observed intensities. The computer calculations have been done for the 12 l and 20 l rows of re ections resulting in (55) as the unique sequence having a good correlation between observed and calculated intensities (see Fig. 8). The unit cell corresponding to this sequence is schematised in Fig. 9 (the L2 1 order of the parent phase is considered). The structure factor is given by the following expression: with F hkl ˆ F b (1 exp 2pi 0:4133h k 2 l exp 2pi 0:8266h 2l exp 2pi 0:2399h k 2 3l exp 2pi 0:6532h 4l exp 2pi 0:0665h k 2 5l exp 2pi 0:6532h 6l exp 2pi 0:2399h k 2 7l exp 2pi 0:8266h 8l exp 2pi 0:4133h k 2 9l ) Fig. 9. Unit cell corresponding to the (55) stacking sequence model of the -layered martensite. rms the (55) sequence as the correct one. For this sequence, the variation of d from 0 to 0.1 was also studied. It is important to note that the t between the experimental and calculated relative intensities is reasonably good only for values of d ranging between 0.08 and Using the notation of Ref. [15], this structure could be denoted as O (Orthorhombic). To our knowledge, the observation of a - layered martensite in Ni±Al alloys has been reported only once [25] and it has never been analysed. F b ˆ f Ga f Mn exp 2pi k h f Ni exp 2pi 2 2 k 4 h exp 2pi 2 3k 4 It is worth noting that the stacking sequence families other than {55} could lead to an orthorhombic unit cell, provided the parameter d is variable. The suitable values for d are such that the horizontal shift between two consecutive planes (1/ 3+d ) is 1/2, 1/4, 1/6 or 1/8. This results in: d=0.167 for {64}; d= or for {73}; d= or for {82} and d=0.2083, or for {91}. As mentioned above, the value results in two-layer periodicity and the value seems too large compared to 1/3. Anyway, the structure factors for all the di erent possibilities were also calculated, but did not t well with the observed intensities. This fact further con- Fig.. Comparison of the unit cells obtained from the modulated lattice approach [4, 5] and Ni±Al-type approach for the ve-layered (a) and seven-layered (b) martensites.

9 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga 3035 Table 3. Positions of the atomic layers in the unit cell (in relation to the a parameter) for the di erent stacking sequences in the family {55} Stacking sequence Layer Stacking sequence Layer Stacking sequence Layer DISCUSSION The two approaches describing the layered structures are very di erent in their construction: the Ni±Al-type is based on long period stacking of close-packed planes, while the second approach considers a modulated structure by shu ing, the modulation being given by a function with three harmonic terms. However, the resulting structures are not much di erent. Indeed, if we transform the unit cells given in Ref. [5] from the ``cubic'' to the ``monoclinic'' axes we obtain the following lattice parameters: a 5lay =0.417 nm, b 5lay =0.554 nm, c 5lay =2.08 nm, b 5lay =908; a 7lay =0.423 nm, b 7lay =0.551 nm, c 7lay =2.94 nm, b 7lay = These lattice parameters are almost the same as those of the M and 14 M structures (the b parameter is doubled by the L2 1 order of the austenite). Regarding the atom positions inside the unit cell, a high similarity between the two approaches also exists, as it can be seen in Fig.. This leads to the very similar relative values for the structure factor of the extra re ections along the c -axis in the two approaches, in such a way that the two can be valid to interpret the patterns obtained by photographic recording (selected area electron di raction, or the X-ray technique used in Refs [4, 5]). As an example, Table 4 shows the intensities j F hkl j 2 of the 20 l re ections obtained with the modulated lattice approach for the seven-layered martensite (values taken from Table 2 in Ref. [5]) and those calculated for the same lattice with the atom positions corresponding to the (52) stacking sequence [depicted in

10 3036 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga Fig. (b)]. For such lattice, the value of the deviation parameter d is The high similarity of both approaches makes it impossible to distinguish between them according to the photographic diffraction patterns. As mentioned above, they can be distinguished only in the case of the ve-layered structure by the value of the angle b. In our work, we have obtained b=908 in most of the cases, thus, the modulated lattice approach seems to be more suitable for the description of the ve-layered martensite. The case in which the cell has been observed to be slightly monoclinic (b between 908 and 918) could be explained by a modulated structure obtained from a slightly orthorhombic cell (rather than tetragonal) in the ``cubic'' axes. Besides the crystallography, there is a physical argument also favouring the interpretation of the ve-layered martensite as a modulated structure. The argument is based on the existence of a premartensitic transition of austenite into an intermediate phase preceding the transformation into a velayered martensitic structure. This argument can be rationalised as follows: the premartensitic transition has been observed in Ni±Mn±Ga alloys close to the stoichiometric composition, transforming at temperatures well below room temperature. At temperatures above Ms, the L2 1 parent phase structure is modulated by transverse waves of atomic displacements with wave vector qkh1i and polarisation vector ekh1i (TA 2 acoustic phonon branch). Among the di erent wavelengths, there is a predominance of the h1/3 1/3 0i mode (wavelength of six times the distance between the {220} P planes), which results in the characteristic ``tweed'' contrast of the bright eld TEM images. The electron diffraction patterns exhibit di use intensity along the h1i direction and di use maxima located at 1/6 distance between the fundamental spots in this direction. On cooling, the di use maxima increase in intensity and decrease in width, until sharp satellites (without di use intensity) are formed as a result of the transition into the intermediate phase. The structure of the intermediate phase is described as a modulation of the L2 1 cubic lattice by static transverse waves with a wavelength of six {1} P planes. The parent to intermediate phase transition is of a weakly rst order nature and is considered as a condensation of the soft h1/3 1/3 0i phonon mode [19, 21, 26, 27]. So, the interpretation of the ve-layered martensite as a modulated structure is reinforced by the fact that it is originated from the intermediate phase, which is also modulated. Thus, the martensitic transformation brings about a symmetry reduction (cubic to tetragonal) and a change in the period of modulation (from six to ve planes). It is worth noting that a similar kind of { In the original work, the choice of the a- and b- axes (hence the parameters a and b ) is reversed. premartensitic transition has been observed in Ni± Al±Mn alloys as well [14], also being a precursor to the ve-layered martensite formation. Although the authors considered the martensitic structure to be M, the above discussion could be applied to this alloy system as well. On the other hand, for the seven-layered martensite there is a physical argument favouring its interpretation as a 14 M structure, (52) stacking, instead of a modulated structure. This was clearly explained by Khachaturyan et al. [28], where the seven-layered martensite was treated as an ``adaptive'' phase. In this model, the (52) stacking is considered as a microtwinning mode of the L1 0 structure (the basal plane of the stacking coincides with the f111g L twinning plane). When the lamellae of the two twin-related variants that form a martensite plate are reduced to the dimensions comparable with the interatomic distance, a microtwinned lattice is obtained. It was demonstrated that, in the microtwinning mode, the lattice parameters of the microtwins are changed to a lower symmetry cell, in order to obtain an invariant plane strain with the parent phase [28]. For the case of a tetragonal martensite (like L1 0 ), the adaptive phase unit cell should be orthorhombic with the following lattice parameters: a ad =a t +c t a c ; b ad =a c ; c ad =a t ; a t, c t and a c being the lattice parameters of the tetragonal martensite (L1 0 ) and the cubic parent phase, respectively.{ All these lattice parameters are related to the ``cubic'' axes. For the Ni±Al alloys, the calculated lattice parameters of the adaptive phase were practically the same as those of the 14 M phase [28] (in the original work, it is denoted as 7R). Thus, the seven planes with (52) stacking sequence are considered as the two microtwin lamellae, ve and two atomic planes in thickness. We can do the same calculations with the lattice parameters obtained for the Ni±Mn±Ga alloy 8, for which we have the L1 0 structure in bulk state and the 14 M structure in melt-spun condition. Converting the experimental 14 M and L1 0 lattice parameters to the ``cubic'' axes we have: a 14M =0.622 nm, b 14M =0.577 nm, c 14M =0.543 nm; a t =0.541 nm, c t =0.661 nm. According to the for- Table 4. Reported intensities j F hkl j 2 of the 20 l re ections of the seven-layered martensite for the modulated lattice approach [5] and intensities calculated for the same cell with a (52) stacking sequence of basal planes. The latter values have been normalised in order to be coincident with the modulation approach for the fundamental 200 re ection h k l Modulation [5] Stacking (+5 2)

11 PONS et al.: MARTENSITIC PHASES IN Ni±Mn±Ga 3037 mulae given above we can obtain the value of a c as: a c =b 14M =0.577 nm. The calculations of the other lattice parameters of the adaptive phase reveal: a ad =0.625 nm, c ad =0.541 nm; which are very similar to the values obtained for a 14M and c 14M. Moreover, considering the parameter o 0, de ned in Ref. [28] (related to the volume fraction of one of the twin variants in a martensite plate), in the microtwinning mode the following equation (given in Ref. [28]) holds: o o ˆ m 1 o o n where m and n are integers (number of atomic planes of each microtwin variant). In our case, the value of o o (calculated in the way described in Ref. [28]) is Then, o o /(1 o o )= The closest ratio of integers giving this value is 2/5 (as in Ref. [28]). Thus, in Ni±Mn±Ga alloys, the seven-layered structure also ts very well as an adaptive phase, which strongly favours the interpretation of the structure as a (52) stacking of close-packed planes rather than a modulated structure. It is also worth mentioning that the complete soft-mode condensation characteristic of the premartensitic transition has not been observed in the compositions giving the seven-layered martensite. Finally, the strange behaviour of alloy 8 can now be understood: the composition is such that the parent phase and the L1 0 martensite cells can be accommodated with normal (``macroscopic'') twinning, then, the L1 0 structure is formed in bulk condition. However, the grain size reduction and other internal stresses introduced by the rapid solidi cation make the accommodation of the L1 0 lattice in the melt-spun ribbons di cult, and microtwinning becomes necessary (i.e. the formation of the 14 M structure, as observed by XRD). These stresses are relaxed (at least partially) in the thin foil condition for TEM observation, then, the macroscopic twinning and non-layered L1 0 martensite is again recovered. The above calculations can be performed again to check for the adaptive phase nature of the -layered martensite. Converting the lattice parameters of the -layered martensite obtained by electron di raction to the ``cubic axes'' we have: a lay =b lay =0.60 nm and c lay =0.54 nm (tetragonal lattice). The parameters of the L1 0 martensite of alloy 7 in the ``cubic'' axes given in Table 2 are: a t =0.537 nm and c t =0.654 nm. Assuming again a c =b lay =0.60 nm, we have for the theoretical adaptive phase: a ad =0.591 nm and c ad =0.537 nm, which are very similar to the measured values for a lay and c lay. In this case the tting is worse than for the 14 M structure, but it has to be taken into account that the lattice parameters of the - layered cell were obtained by selected area electron di raction, which gives a lower accuracy. It is interesting to note that, in this case, the adaptive cell is tetragonal (with c/a < 1), which means that a t +c t =2a c. The value of o o /(1 o o ), calculated according to Ref. [28], is now 1.16 (i.e. very close to 1). The closest ratio of integers (whose sum is ) giving this number is 5/5, consistently with the obtained (55) sequence. Thus, the -layered structure also seems to be an adaptive phase for the composition range where the transformation temperatures are above room temperature. In turn, it is worth noting that a similar calculation using the lattice parameters of the ve-layered martensite results in a clear disagreement between the theoretical lattice parameters for the adaptive phase and the experimental ones, which further supports the consideration of the ve-layered lattice as a modulated structure rather than a periodic stacking of basal planes. The presence of nely twinned regions with -layered di raction patterns embedded in the L1 0 martensite further con rms the microtwinned nature of the -layered martensite. Finally, the observed correlation of the tetragonality of the L1 0 martensitic structure with the Ms temperature and e/a ratio for the Ni±Mn±Ga system has been, to our knowledge, rstly reported in the present work, although the correlation of Ms with e/a has already been discussed in Ref. [29]. However, the role of the tetragonality is already well known and discussed in other alloy systems undergoing thermoelastic martensitic transformations [14, 28, 30]. 6. CONCLUSIONS The crystal structures of the di erent martensites observed in the Ni±Mn±Ga alloys have been identi ed. As in the Ni±Al system, the non-modulated martensite can be well described by a L1 0 -type lattice with ``double size'' unit cell, due to the L2 1 type of atomic order of the parent phase. A correlation of the tetragonality with the Ms temperature and e/a ratio has been observed, as in other alloys undergoing thermoelastic martensitic transformations. The ve- and seven-layered martensites (also known in Ni±Al and Ni±Al±Mn alloys) have been analysed in terms of structures modulated by shuf- ing (approach already applied to Ni±Mn±Ga alloys [4, 5]) or periodic stacking of {1} P -type close-packed planes (Ni±Al-type approach). The whole set of results suggests an interpretation of the ve-layered martensite as a shu ing modulated structure, and the seven-layered one as a period stacking of basal planes with (52) 2 sequence (14 M structure). As for Ni±Al, the 14 M cell of the Ni± Mn±Ga alloys ts very well with the concept of an adaptive microtwinned phase, introduced in Ref. [28]. The ``new'' -layered structure has been analysed for the rst time, being suitably described as a stacking of basal planes with (55) sequence and

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