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Magnetic properties of stress-induced martensite and martensitic transformation in Ni–Mn–Ga magnetic shape memory alloy
Materials Science and Engineering A 378 (2004) 394–398
Magnetic properties of stress-induced martensite and martensitic transformation in Ni–Mn–Ga magnetic shape memory alloy Oleg Heczko∗ , Ladislav Straka Laboratory of Biomedical Engineering, Department of Engineering Physics and Mathematics, Helsinki University of Technology, Rakentajanaukio 2C, P.O. Box 2200, FIN-02015 Espoo, Finland
Abstract Thermoelastic and strain-induced martensitic transformations of single crystalline Ni49.7 Mn29.1 Ga21.2 magnetic shape memory alloys were investigated by simultaneous detection of the strain and magnetization. The transformation temperature to austenite was TA = 314 K. The thermoelastic transformation was shifted to higher temperature with increasing compressive stress with rate about 4 MPa/K. The effect of the moderate magnetic field up to 1 T on transformation was negligible. Very similar magnetic properties of thermally and stress-induced martensites measured in the field up to 1.2 T suggest an equivalence of the phases. Direct comparison of the magnetic properties of austenite and stress-induced martensite at constant temperature above the thermal martensitic transformation is made. At 317 K, the stress-induced martensite had a large uniaxial magnetic anisotropy, Ku = 1.2 × 105 J/m3 and the saturation magnetization increased, about 14%, compared with the parental austenite. © 2004 Published by Elsevier B.V. Keywords: Ni–Mn–Ga shape memory alloys; Martensitic transformation; Stress-induced martensite; Saturation magnetization of martensite; Magnetic anisotropy
1. Introduction Heusler Ni–Mn–Ga alloys are ferromagnetic materials, which undergo a reversible martensitic transformation resulting in a shape memory effect. Ferromagnetism in Heusler alloys was intensively studied long time ago [1]. It was established that the source of the ferromagnetism is the presence of Mn with Ni playing only minor part. It has appeared only recently that the coexistence of the shape memory properties and ferromagnetism gives unique opportunity to manipulate the structure not only by stress and temperature but also by magnetic field [2,3]. Renewed interest in martensitic Ni–Mn–Ga arises from now well-established fact that some of these alloys close to stoichiometry exhibit giant magnetic-field-induced strain up to 10% [4–6] called magnetic shape memory effect (MSME). This effect occurs in low temperature martensitic phase of a single crystal. The Ni–Mn–Ga alloys, as other shape memory alloys, exhibit large thermoelastic strain and superelastic properties upon austenite–martensite transformation [2,7,8]. The struc-
ture of the stress-induced martensite was studied by Martynov and Kokorin [9] and Martynov [10]. However, the characterization of the magnetic properties during thermoelastic and stress-induced transformations and interplay with the structure changes is still lacking. Moreover, the previously studied composition are invariably materials with Ni excess with lower Mn content and although the structure of these materials are similar to our investigated material it has not been demonstrated yet that these materials exhibit large MSME. A comprehension of the magnetic properties and their changes in the material exhibiting full MSME can facilitate better understanding of the principal austenite–martensite transformations and the origin of the MSME effect. Here, we investigate the stress–strain behavior and the changes of magnetic properties during the austenite–martensite transformation and during the superelastic straining of the alloy exhibiting MSME at room temperature.
2. Experimental ∗
Corresponding author. E-mail address: [email protected] (O. Heczko).
0921-5093/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.msea.2003.12.055
A nearly single crystalline Ni–Mn–Ga ingot was produced by AdaptaMat Ltd. using modified Bridgman
O. Heczko, L. Straka / Materials Science and Engineering A 378 (2004) 394–398
method. The ingot was encapsulated in evacuated quartz ampoule and annealed in two stages to achieve proper homogenization (1273 K for 2 days) and ordering (1073 K for 3 days) and then cooled in air. The composition of the ingot determined by electron dispersion spectroscopy (EDS) was Ni49.7 Mn29.1 Ga21.2 with precision about 0.5 at.%. Single crystal samples (approx. 2 mm × 2.5 mm × 7.5 mm) were cut along {1 0 0} planes from the ingot by spark erosion. Crystal orientation and structure studies were performed using X-ray X’Pert Philips diffractometer. To ensure the same initial conditions for all measurements, the sample was initially compressed at room temperature to achieve a single variant state, i.e. homogenous single crystalline state with only one martensitic variant with the orientation of c crystallographic axis along the stress direction. The single variant state of the sample was checked by polarized light microscopy. The residual variants with c axis perpendicular to stress were detected but their volume was very small. During cooling the single crystal samples transformed from parental cubic (Heusler) austenite L21 phase (high temperature phase) to martensitic phase, which has five-layered modulated tetragonal structure [11] similar to that observed in Ni51 Mn24 Ga25 [9]. Lattice parameters of austenite are aA = 0.584 nm at 323 K and martensite aM = 0.595 nm, cM = 0.560 nm at 293 K. No other intermartensitic transformation was detected down to 110 K by ac susceptibility measurement. The investigated alloy exhibited 6% MSME at room temperature [12,13]. Thermoelastic and stress-induced martensitic transformations were studied by the simultaneous measurements of dilatation and of magnetization under various compressive stresses and magnetic fields. The dilatation was measured by contactless dilatometer using laser vibrometer equipped with displacement sensor. The magnetization was measured using in-house-made vibrating coil magnetometer (VCM). The sample was placed inside a cylinder between two heated (fixed and movable) copper pistons. The sample was compressed with the piston driven by compressed air. Whole apparatus was installed inside a 12 in. magnet with the maximum field 1.15 T. This arrangement allows applying heat, stress and magnetic field simultaneously. The orientation of the magnetic field was perpendicular to the applied stress. The strain was measured along the axis of the compressive stress, the magnetization along magnetic field direction. Heating and cooling rate was about 6 K/min. The stress–strain curves were obtained by the application of monotonously increasing compressive stress and measuring the straining of the sample. This is different from a typical compression test, where strain is increasing linearly and stress is measured. The sample was compressed along one of the principal 1 0 0 axis of the parental austenitic phase along long dimension of the sample. The maximum stress was 60 MPa.
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3. Results and discussion 3.1. Thermoelastic martensite transformation Fig. 1 shows the saturation magnetization (at 2 T) as a function of temperature measured during cooling and two magnetization curves of martensite at room temperature and austenite at 328 K. The direction of the magnetic field is always directed along one 1 0 0 direction of the parental austenite phase. The thermomagnetic curve exhibits one large jump indicating austenite-to-martensite transformation at mean transformation temperature TM = 306 K. Upon transformation, the saturation magnetization increases about 10%. The decrease of the saturation magnetization can be caused, apart of the suggested decrease of the atomic magnetic moment of Mn atoms, by lower Curie ferromagnetic temperature of austenite. The smoothness of the rest of the curve indicates that there is no other transformation down to 10 K. The presence of the intermartensitic transformation would result in small but distinctive sharp changes of the curve as shown in [14]. Additionally, the same character of the magnetization curve measured at 10 K is a strong indication that no other transformation occurs. The magnetization curve of martensite was measured in the direction along [0 1 0], i.e. perpendicular to c, short tetragonal axis, which is the easy magnetization axis [12,13]. The rectilinear curve is typical for material having large uniaxial magnetic anisotropy, in this case Ku ≈ 1.75×105 J/m3 . It should be stressed here that this kind of curve could be only obtained if the sample is in a single variant state. If more martensitic variants are present the curve is more round and magnetic anisotropy determination could be in error as in [2]. Negligible magnetic hysteresis shows that the principal mode of magnetization process is magnetization vector rotation. From the magnetization curve, it can be inferred that the magnetic field 1 T is strong enough to reach the magnetic saturation of martensite. The magnetization curve of austenite is square-like with fast approach to saturation
Fig. 1. Saturation magnetization as a function of temperature. The curve is measured during cooling. Insets shows the magnetization curves of martensite and austenite. The curve of the martensite was measured with magnetic field normal to c-axis of single variant sample. The magnetization curves are corrected for demagnetization.
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4
30MPa
2MPa
60MPa
strain (% )
3 2 1 0 290
300
310
320
330
340
350
temperature (K ) Fig. 2. Dilatation changes during thermal martensitic transformation under various loads.
showing that the austenite phase is magnetically soft and its magnetic anisotropy is very small [13,14]. Fig. 2 shows the thermoelastic transformation measured for three different loads 2, 30 and 60 MPa. As the de-twinning stress of the alloy is lower than 2 MPa, the initial state was always single variant martensite with c-axis in the direction of the stress as confirmed by polarized light microscopy. The additional proof that the sample was indeed in one variant state was provided by the measurement of the magnetization curve, which was rectilinear, similar to curve shown in Fig. 1. During transformation a large thermoelastic strain is generated (Fig. 2) due to large difference of lattice constants of martensite and austenite. The maximum deformation calculated from tetragonal distortion is ε = (aA − aM )/aM = 4.1% which corresponds well to the value observed. During reverse austenite-to-martensite transformation the compressive stress assists in nucleation of preferred variant and the sample always transforms to the homogenous (single variant) state with short c-axis along the stress direction [15]. The transformation is very sharp for the nearly free sample (2 MPa) with well-defined mean transformation temperatures TM = 305 K and TA = 314 K denoting the transformation to martensite and to austenite, respectively. The transformation temperature increases and progressively spreads out with increasing load (Fig. 2). The shift determined from experimental data using the mean temperature of transformation is about 4 MPa/K. Using the Clausius–Clapeyron relation [8] the increase of the transformation temperature by application of 60 MPa stress was calculated to be 20 K, which gives reasonable agreement. Transformation enthalpy used was 4.5 J/g determined from DSC measurement and the strain, ε = 0.04. When cycling over the transformation temperatures the character of the transformation stay basically the same but the mean transformation temperatures TM and TA vary within two degrees especially in martensite-to-austenite transformation. This variation can be caused by slightly inhomogeneous temperature distribution during heating/
cooling but it can also reflect different states from which the transformation started. This variation was observed previously [15]. The transformation broadens with increasing load. One reason for the broadening can be inhomogeneous stress distribution in the sample due to slightly irregular sample shape. It may also suggest the change of the nucleation and growth mechanism of a new phase with increasing compressive stress. The sharp transformation suggests that the new phase nucleates only at few places and the transformation occurs principally by moving phase boundary. Increasing compressive stress may block the phase boundary movement and more nucleation sites appear with increasing temperature. From Fig. 2, it is also clear that the full transformation to austenite was not reached even at 350 K when 60 MPa stress was applied. We also measured the strain changes during combined load of compressive stress and magnetic field of 1 T. It was found previously that the effect of moderate magnetic field (up to 1 T) on the transformation temperature is small [15]. The transformation temperatures (TM , TA ) are lowered by application of the magnetic field for about 1–2 K but the shape of the strain recovery is about the same. The martensite transformation is accompanied by the large change of the susceptibility, e.g. [11] and saturation magnetization as shown in Fig. 1. When martensite transforms to austenite the susceptibility and low field magnetization increase since the magnetic anisotropy of austenite phase is one order of magnitude smaller than of martensite [13]. On the other hand, in high magnetic field above saturation, the magnetization decreases during the transformation to austenite. But if the magnetic field is lower than saturation field and therefore the measured sample is not saturated, an increase of the magnetization during transformation can be observed as it is often the case. 3.2. Stress-induced martensite Above transition temperature the austenite could be transformed to stress-induced martensite (SIM) by compression. When decreasing the compressive stress the martensite transforms back to austenite leading to large reversible strain changes—superelastic behavior. The stress–strain curves were measured from 309 to 350 K with and without 1 T magnetic field. As the maximum magnitude of the compressive stress is limited, the interval where the martensite can be induced is small, about 15 K above the TA . An example of the stress–strain curve and magnetization as a function of stress at constant temperature in 1 T magnetic field is shown in Fig. 3. The onset of the formation of SIM is indicated by deviation from the linear dependence, i.e. by the end of elastic straining. From the magnitude of the strain (Fig. 3) we can ascertain that most of austenite transformed to martensite by 60 MPa compression. The maximum value of the strain, about 4%, agrees with the value determined from the lattice constants of austenite and martensite.
O. Heczko, L. Straka / Materials Science and Engineering A 378 (2004) 394–398
0
1,00 1,02
-1
strain (%)
1,04 1,06
-2
1,08 -3
1,10 1,12
-4
rel. magnetization (1)
0,98
1,14 0
10
20
30
40
50
60
70
compressive stress (MPa) Fig. 3. Stress-induced transformation. Strain (stress–strain curve) and saturation magnetization (line with points) at 1 T as a function of compressive stress of single crystal Ni–Mn–Ga at 317 K. Compression axis of initial cubic phase is [1 0 0].
0
T = 319 K -1
strain (%)
From the linear initial part of the stress–strain curve, the elastic modulus of austenite can be determined. The modulus decreases when approaching the temperature of the transformation from about 5 GPa at 323 K to just 1.5 GPa at 314 K in the vicinity of the transformation. The decrease of the elastic modulus is the sign of the elastic instability of austenitic lattice when approaching the transformation [8]. The modulus of the stress-induced martensite determined from the quasi-linear final part of the stress–strain curve is about two to three times higher and it is about the same or even increasing with decreasing temperature. At lower temperature below TA , but above martensitic start temperature Ms , the compression caused irreversible transformation to martensite. Once the sample was transformed by the stress, further cooling did not lead to additional transformation as indicated by strain and magnetic measurements. This suggests that the stress-induced martensite is identical to the thermally induced martensite. This agrees with Martynov [10] who, by X-ray diffraction, confirmed that the stress-induced martensite possesses the same structure as thermally induced martensite in Ni–Mn–Ga alloys with Ni excess. The structural changes revealed by the stress–strain curves are followed by large magnetic changes. The formation of the SIM is accompanied by the decrease of the initial susceptibility and the increase of saturation magnetization, about 14%. The decrease of the initial susceptibility is due to an increase of the magnetic anisotropy of the SIM. The saturation magnetization as a function of the stress is shown in Fig. 3. To facilitate the comparison with the stress–strain curve the scale of magnetization is inverted. The constant magnetization at the beginning of straining corresponds to the elastic straining of austenite. An increase of the magnetization at constant field signifies the formation of martensite. The return branch of magnetization has initially constant
397
H=0T -2
H=1T
-3
-4 0
10
20
30
40
50
60
70
compressive stress (MPa) Fig. 4. Effect of magnetic field on stress-induced martensite transformation at 319 K. Strain in 1 T magnetic field (full line), strain without field (dotted line).
value corresponding to stable SIM. The decrease of magnetization indicates the reverse formation of austenite. The measurement reveals that there is a linear correspondence between measured strain and magnetization change during SIM formation. By measuring the saturation magnetization it is therefore possible to monitor the phase transformation and directly evaluate the amount of the transformed phase in the bulk material. The effect of magnetic field on the stress-induced martensite transformation is shown in Fig. 4. There are very small changes during loading, i.e. during SIM formation but in the reverse process the austenite formation occurs at higher stress when magnetic field is applied. The effect of the field can be explained as follows. The external stress produces the single variant martensite with c crystallographic axis in the direction of the stress. Further we can assume that the stress-induced martensite has negative magnetostriction similar to thermally induced martensite [14]. In the single variant martensite, the direction of magnetization is along the c-axis (easy magnetization axis). In magnetic field, the magnetization rotates from the easy axis to the field direction normal to the stress. Due to magnetoelastic coupling, the rotation of the magnetization produces a stress which counteracts the external stress and lowers the internal effective stress in the martensite. As a result the martensite transforms back to austenite at higher external stress. A rough estimation gives magnitude of the magnetoelastic stress to be about 3 MPa assuming λ = 270 ppm and elastic constant of martensite E = 12 GPa, which is about the observed difference between curves with and without magnetic field. The described effect saturates in moderate magnetic field (about 1 T) when magnetization fully rotates away from easy axis to the direction of the field (magnetic saturation). The effect, based on magnetoelastic coupling, has a different origin than magnetically-induced-transformation at very high field about 10 T. In that case, the driving force of the transformation is the difference of saturation magnetization between austenite and martensite phases [2].
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T = 317 K
2
-1
magnetization (Am kg )
80
60 MPa 2 MPa
40 0
agrees with observation made by Martynov and Kokorin [9]. The results show that by compression we can attain the martensite state above TA and in such way to expand the whole interval where the magnetic properties of the martensite can be evaluated. Moreover, it also allows the direct comparison of austenite and martensite at the same temperature.
-40 -80
Acknowledgements -1,0
-0,5 0,0 0,5 magnetic field µ0H (T)
1,0
Fig. 5. Magnetization curves of the stress-induced martensite (60 MPa) and parental austenite (2 MPa) at 317 K. The magnetic field was normal to stress direction. The curves are not corrected for demagnetization. The tilt of the curve of the austenite is due to demagnetization.
The changes of magnetic properties of Ni–Mn–Ga material due to the formation of SIM are summarized in Fig. 5. The figure shows the magnetization curves of the nearly free (2 MPa) sample—parental austenite and of the sample compressed by 60 MPa at 317 K. The compression leads to the formation of the SIM in homogenous single variant state with easy axis in the stress direction. The saturation magnetization of the SIM is about 14% higher than of the austenite in agreement with Fig. 3. The curve of the martensite is very similar to the curve measured at room temperature (inset of Fig. 1). The linear character of the curve indicates that the anisotropy is uniaxial with one anisotropy constant [13]. The single variant state allows the direct determination of magnetic anisotropy of stress-induced martensite from the magnetization curve. The magnetic anisotropy of martensite Ku = 1.2 × 105 J/m3 at 317 K was calculated from the anisotropy field corrected for demagnetization using the magnetization curve of magnetically soft austenite. Compared with room temperature the anisotropy of the stress-induced martensite at 317 K decreases about one third. The magnitude and rate of the decrease of the measured magnetic anisotropy is in agreement with the extrapolated value determined from [13]. This gives strong evidence of the likeness of the phases, which
The authors would like to acknowledge the funding support by the National Technology Agency of Finland (Tekes) as well as their industrial research partners (Metso Oyj, Nokia Research Centre and AdaptaMat Ltd.).
References [1] J.G. Booth, in: E.P. Wohlfarth, K.H.J. Bushow (Eds.), Ferromagnetic Materials, vol. 4, Elsevier, Amsterdam, 1988, pp. 212–308. [2] A.N. Vasil’ev, A.D. Bozhko, V.V. Khovailo, I.E. Dikshtein, V.G. Shavrov, V.D. Buchelnikov, M. Matsumoto, S. Suzuki, T. Takagi, J. Tani, Phys. Rev. B 59 (1999) 1113. [3] K. Ullakko, J.K. Huang, C. Kantner, R.C. O’Handley, V.V. Kokorin, Appl. Phys. Lett. 69 (1996) 1966. [4] O. Heczko, A. Sozinov, K. Ullakko, IEEE Trans. Mag. 36 (2000) 3266. [5] S.J. Murray, M. Marioni, S.M. Allen, R.C. O’Handley, T.A. Lograsso, App. Phys. Lett. 77 (2000) 886. [6] A. Sozinov, A.A. Likhachev, N. Lanska, K. Ullakko, Appl. Phys. Lett. 80 (2002) 1746. [7] V.A. Chernenko, A. Amengual, E. Cesari, V.V. Kokorin, I.K. Zasimchuk, J. Phys. III 5 (1995) C2–95. [8] V.A. Cherneko, V. L’vov, J. Pons, E. Cesari, J. Appl. Phys. 93 (2003) 2394. [9] V. Martynov, V.V. Kokorin, J. Phys. III (1992) 739. [10] V.V. Martynov, J. Phys. IV 5 (1995) C8. [11] O. Heczko, A. Sozinov, N. Lanska, O. Söderberg, K. Ullakko, J. Magn. Magn. Mater. 242–245 (2002) 1449. [12] O. Heczko, L. Straka, N. Lanska, K. Ullakko, J. Enkovaara, J. Appl. Phys. 91 (2002) 8228. [13] L. Straka, O. Heczko, J. Appl. Phys. 93 (2003) 8636. [14] R. Tickle, R.D. James, J. Magn. Magn. Mater. 195 (1999) 627. [15] L. Straka, O. Heczko, V. Novák, N. Lanska, J. Phys. IV 112 (2003) 911.
Magnetic properties of stress-induced martensite and martensitic transformation in Ni–Mn–Ga magnetic shape memory alloy Oleg Heczko∗ , Ladislav Straka Laboratory of Biomedical Engineering, Department of Engineering Physics and Mathematics, Helsinki University of Technology, Rakentajanaukio 2C, P.O. Box 2200, FIN-02015 Espoo, Finland
Abstract Thermoelastic and strain-induced martensitic transformations of single crystalline Ni49.7 Mn29.1 Ga21.2 magnetic shape memory alloys were investigated by simultaneous detection of the strain and magnetization. The transformation temperature to austenite was TA = 314 K. The thermoelastic transformation was shifted to higher temperature with increasing compressive stress with rate about 4 MPa/K. The effect of the moderate magnetic field up to 1 T on transformation was negligible. Very similar magnetic properties of thermally and stress-induced martensites measured in the field up to 1.2 T suggest an equivalence of the phases. Direct comparison of the magnetic properties of austenite and stress-induced martensite at constant temperature above the thermal martensitic transformation is made. At 317 K, the stress-induced martensite had a large uniaxial magnetic anisotropy, Ku = 1.2 × 105 J/m3 and the saturation magnetization increased, about 14%, compared with the parental austenite. © 2004 Published by Elsevier B.V. Keywords: Ni–Mn–Ga shape memory alloys; Martensitic transformation; Stress-induced martensite; Saturation magnetization of martensite; Magnetic anisotropy
1. Introduction Heusler Ni–Mn–Ga alloys are ferromagnetic materials, which undergo a reversible martensitic transformation resulting in a shape memory effect. Ferromagnetism in Heusler alloys was intensively studied long time ago [1]. It was established that the source of the ferromagnetism is the presence of Mn with Ni playing only minor part. It has appeared only recently that the coexistence of the shape memory properties and ferromagnetism gives unique opportunity to manipulate the structure not only by stress and temperature but also by magnetic field [2,3]. Renewed interest in martensitic Ni–Mn–Ga arises from now well-established fact that some of these alloys close to stoichiometry exhibit giant magnetic-field-induced strain up to 10% [4–6] called magnetic shape memory effect (MSME). This effect occurs in low temperature martensitic phase of a single crystal. The Ni–Mn–Ga alloys, as other shape memory alloys, exhibit large thermoelastic strain and superelastic properties upon austenite–martensite transformation [2,7,8]. The struc-
ture of the stress-induced martensite was studied by Martynov and Kokorin [9] and Martynov [10]. However, the characterization of the magnetic properties during thermoelastic and stress-induced transformations and interplay with the structure changes is still lacking. Moreover, the previously studied composition are invariably materials with Ni excess with lower Mn content and although the structure of these materials are similar to our investigated material it has not been demonstrated yet that these materials exhibit large MSME. A comprehension of the magnetic properties and their changes in the material exhibiting full MSME can facilitate better understanding of the principal austenite–martensite transformations and the origin of the MSME effect. Here, we investigate the stress–strain behavior and the changes of magnetic properties during the austenite–martensite transformation and during the superelastic straining of the alloy exhibiting MSME at room temperature.
2. Experimental ∗
Corresponding author. E-mail address: [email protected] (O. Heczko).
0921-5093/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.msea.2003.12.055
A nearly single crystalline Ni–Mn–Ga ingot was produced by AdaptaMat Ltd. using modified Bridgman
O. Heczko, L. Straka / Materials Science and Engineering A 378 (2004) 394–398
method. The ingot was encapsulated in evacuated quartz ampoule and annealed in two stages to achieve proper homogenization (1273 K for 2 days) and ordering (1073 K for 3 days) and then cooled in air. The composition of the ingot determined by electron dispersion spectroscopy (EDS) was Ni49.7 Mn29.1 Ga21.2 with precision about 0.5 at.%. Single crystal samples (approx. 2 mm × 2.5 mm × 7.5 mm) were cut along {1 0 0} planes from the ingot by spark erosion. Crystal orientation and structure studies were performed using X-ray X’Pert Philips diffractometer. To ensure the same initial conditions for all measurements, the sample was initially compressed at room temperature to achieve a single variant state, i.e. homogenous single crystalline state with only one martensitic variant with the orientation of c crystallographic axis along the stress direction. The single variant state of the sample was checked by polarized light microscopy. The residual variants with c axis perpendicular to stress were detected but their volume was very small. During cooling the single crystal samples transformed from parental cubic (Heusler) austenite L21 phase (high temperature phase) to martensitic phase, which has five-layered modulated tetragonal structure [11] similar to that observed in Ni51 Mn24 Ga25 [9]. Lattice parameters of austenite are aA = 0.584 nm at 323 K and martensite aM = 0.595 nm, cM = 0.560 nm at 293 K. No other intermartensitic transformation was detected down to 110 K by ac susceptibility measurement. The investigated alloy exhibited 6% MSME at room temperature [12,13]. Thermoelastic and stress-induced martensitic transformations were studied by the simultaneous measurements of dilatation and of magnetization under various compressive stresses and magnetic fields. The dilatation was measured by contactless dilatometer using laser vibrometer equipped with displacement sensor. The magnetization was measured using in-house-made vibrating coil magnetometer (VCM). The sample was placed inside a cylinder between two heated (fixed and movable) copper pistons. The sample was compressed with the piston driven by compressed air. Whole apparatus was installed inside a 12 in. magnet with the maximum field 1.15 T. This arrangement allows applying heat, stress and magnetic field simultaneously. The orientation of the magnetic field was perpendicular to the applied stress. The strain was measured along the axis of the compressive stress, the magnetization along magnetic field direction. Heating and cooling rate was about 6 K/min. The stress–strain curves were obtained by the application of monotonously increasing compressive stress and measuring the straining of the sample. This is different from a typical compression test, where strain is increasing linearly and stress is measured. The sample was compressed along one of the principal 1 0 0 axis of the parental austenitic phase along long dimension of the sample. The maximum stress was 60 MPa.
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3. Results and discussion 3.1. Thermoelastic martensite transformation Fig. 1 shows the saturation magnetization (at 2 T) as a function of temperature measured during cooling and two magnetization curves of martensite at room temperature and austenite at 328 K. The direction of the magnetic field is always directed along one 1 0 0 direction of the parental austenite phase. The thermomagnetic curve exhibits one large jump indicating austenite-to-martensite transformation at mean transformation temperature TM = 306 K. Upon transformation, the saturation magnetization increases about 10%. The decrease of the saturation magnetization can be caused, apart of the suggested decrease of the atomic magnetic moment of Mn atoms, by lower Curie ferromagnetic temperature of austenite. The smoothness of the rest of the curve indicates that there is no other transformation down to 10 K. The presence of the intermartensitic transformation would result in small but distinctive sharp changes of the curve as shown in [14]. Additionally, the same character of the magnetization curve measured at 10 K is a strong indication that no other transformation occurs. The magnetization curve of martensite was measured in the direction along [0 1 0], i.e. perpendicular to c, short tetragonal axis, which is the easy magnetization axis [12,13]. The rectilinear curve is typical for material having large uniaxial magnetic anisotropy, in this case Ku ≈ 1.75×105 J/m3 . It should be stressed here that this kind of curve could be only obtained if the sample is in a single variant state. If more martensitic variants are present the curve is more round and magnetic anisotropy determination could be in error as in [2]. Negligible magnetic hysteresis shows that the principal mode of magnetization process is magnetization vector rotation. From the magnetization curve, it can be inferred that the magnetic field 1 T is strong enough to reach the magnetic saturation of martensite. The magnetization curve of austenite is square-like with fast approach to saturation
Fig. 1. Saturation magnetization as a function of temperature. The curve is measured during cooling. Insets shows the magnetization curves of martensite and austenite. The curve of the martensite was measured with magnetic field normal to c-axis of single variant sample. The magnetization curves are corrected for demagnetization.
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4
30MPa
2MPa
60MPa
strain (% )
3 2 1 0 290
300
310
320
330
340
350
temperature (K ) Fig. 2. Dilatation changes during thermal martensitic transformation under various loads.
showing that the austenite phase is magnetically soft and its magnetic anisotropy is very small [13,14]. Fig. 2 shows the thermoelastic transformation measured for three different loads 2, 30 and 60 MPa. As the de-twinning stress of the alloy is lower than 2 MPa, the initial state was always single variant martensite with c-axis in the direction of the stress as confirmed by polarized light microscopy. The additional proof that the sample was indeed in one variant state was provided by the measurement of the magnetization curve, which was rectilinear, similar to curve shown in Fig. 1. During transformation a large thermoelastic strain is generated (Fig. 2) due to large difference of lattice constants of martensite and austenite. The maximum deformation calculated from tetragonal distortion is ε = (aA − aM )/aM = 4.1% which corresponds well to the value observed. During reverse austenite-to-martensite transformation the compressive stress assists in nucleation of preferred variant and the sample always transforms to the homogenous (single variant) state with short c-axis along the stress direction [15]. The transformation is very sharp for the nearly free sample (2 MPa) with well-defined mean transformation temperatures TM = 305 K and TA = 314 K denoting the transformation to martensite and to austenite, respectively. The transformation temperature increases and progressively spreads out with increasing load (Fig. 2). The shift determined from experimental data using the mean temperature of transformation is about 4 MPa/K. Using the Clausius–Clapeyron relation [8] the increase of the transformation temperature by application of 60 MPa stress was calculated to be 20 K, which gives reasonable agreement. Transformation enthalpy used was 4.5 J/g determined from DSC measurement and the strain, ε = 0.04. When cycling over the transformation temperatures the character of the transformation stay basically the same but the mean transformation temperatures TM and TA vary within two degrees especially in martensite-to-austenite transformation. This variation can be caused by slightly inhomogeneous temperature distribution during heating/
cooling but it can also reflect different states from which the transformation started. This variation was observed previously [15]. The transformation broadens with increasing load. One reason for the broadening can be inhomogeneous stress distribution in the sample due to slightly irregular sample shape. It may also suggest the change of the nucleation and growth mechanism of a new phase with increasing compressive stress. The sharp transformation suggests that the new phase nucleates only at few places and the transformation occurs principally by moving phase boundary. Increasing compressive stress may block the phase boundary movement and more nucleation sites appear with increasing temperature. From Fig. 2, it is also clear that the full transformation to austenite was not reached even at 350 K when 60 MPa stress was applied. We also measured the strain changes during combined load of compressive stress and magnetic field of 1 T. It was found previously that the effect of moderate magnetic field (up to 1 T) on the transformation temperature is small [15]. The transformation temperatures (TM , TA ) are lowered by application of the magnetic field for about 1–2 K but the shape of the strain recovery is about the same. The martensite transformation is accompanied by the large change of the susceptibility, e.g. [11] and saturation magnetization as shown in Fig. 1. When martensite transforms to austenite the susceptibility and low field magnetization increase since the magnetic anisotropy of austenite phase is one order of magnitude smaller than of martensite [13]. On the other hand, in high magnetic field above saturation, the magnetization decreases during the transformation to austenite. But if the magnetic field is lower than saturation field and therefore the measured sample is not saturated, an increase of the magnetization during transformation can be observed as it is often the case. 3.2. Stress-induced martensite Above transition temperature the austenite could be transformed to stress-induced martensite (SIM) by compression. When decreasing the compressive stress the martensite transforms back to austenite leading to large reversible strain changes—superelastic behavior. The stress–strain curves were measured from 309 to 350 K with and without 1 T magnetic field. As the maximum magnitude of the compressive stress is limited, the interval where the martensite can be induced is small, about 15 K above the TA . An example of the stress–strain curve and magnetization as a function of stress at constant temperature in 1 T magnetic field is shown in Fig. 3. The onset of the formation of SIM is indicated by deviation from the linear dependence, i.e. by the end of elastic straining. From the magnitude of the strain (Fig. 3) we can ascertain that most of austenite transformed to martensite by 60 MPa compression. The maximum value of the strain, about 4%, agrees with the value determined from the lattice constants of austenite and martensite.
O. Heczko, L. Straka / Materials Science and Engineering A 378 (2004) 394–398
0
1,00 1,02
-1
strain (%)
1,04 1,06
-2
1,08 -3
1,10 1,12
-4
rel. magnetization (1)
0,98
1,14 0
10
20
30
40
50
60
70
compressive stress (MPa) Fig. 3. Stress-induced transformation. Strain (stress–strain curve) and saturation magnetization (line with points) at 1 T as a function of compressive stress of single crystal Ni–Mn–Ga at 317 K. Compression axis of initial cubic phase is [1 0 0].
0
T = 319 K -1
strain (%)
From the linear initial part of the stress–strain curve, the elastic modulus of austenite can be determined. The modulus decreases when approaching the temperature of the transformation from about 5 GPa at 323 K to just 1.5 GPa at 314 K in the vicinity of the transformation. The decrease of the elastic modulus is the sign of the elastic instability of austenitic lattice when approaching the transformation [8]. The modulus of the stress-induced martensite determined from the quasi-linear final part of the stress–strain curve is about two to three times higher and it is about the same or even increasing with decreasing temperature. At lower temperature below TA , but above martensitic start temperature Ms , the compression caused irreversible transformation to martensite. Once the sample was transformed by the stress, further cooling did not lead to additional transformation as indicated by strain and magnetic measurements. This suggests that the stress-induced martensite is identical to the thermally induced martensite. This agrees with Martynov [10] who, by X-ray diffraction, confirmed that the stress-induced martensite possesses the same structure as thermally induced martensite in Ni–Mn–Ga alloys with Ni excess. The structural changes revealed by the stress–strain curves are followed by large magnetic changes. The formation of the SIM is accompanied by the decrease of the initial susceptibility and the increase of saturation magnetization, about 14%. The decrease of the initial susceptibility is due to an increase of the magnetic anisotropy of the SIM. The saturation magnetization as a function of the stress is shown in Fig. 3. To facilitate the comparison with the stress–strain curve the scale of magnetization is inverted. The constant magnetization at the beginning of straining corresponds to the elastic straining of austenite. An increase of the magnetization at constant field signifies the formation of martensite. The return branch of magnetization has initially constant
397
H=0T -2
H=1T
-3
-4 0
10
20
30
40
50
60
70
compressive stress (MPa) Fig. 4. Effect of magnetic field on stress-induced martensite transformation at 319 K. Strain in 1 T magnetic field (full line), strain without field (dotted line).
value corresponding to stable SIM. The decrease of magnetization indicates the reverse formation of austenite. The measurement reveals that there is a linear correspondence between measured strain and magnetization change during SIM formation. By measuring the saturation magnetization it is therefore possible to monitor the phase transformation and directly evaluate the amount of the transformed phase in the bulk material. The effect of magnetic field on the stress-induced martensite transformation is shown in Fig. 4. There are very small changes during loading, i.e. during SIM formation but in the reverse process the austenite formation occurs at higher stress when magnetic field is applied. The effect of the field can be explained as follows. The external stress produces the single variant martensite with c crystallographic axis in the direction of the stress. Further we can assume that the stress-induced martensite has negative magnetostriction similar to thermally induced martensite [14]. In the single variant martensite, the direction of magnetization is along the c-axis (easy magnetization axis). In magnetic field, the magnetization rotates from the easy axis to the field direction normal to the stress. Due to magnetoelastic coupling, the rotation of the magnetization produces a stress which counteracts the external stress and lowers the internal effective stress in the martensite. As a result the martensite transforms back to austenite at higher external stress. A rough estimation gives magnitude of the magnetoelastic stress to be about 3 MPa assuming λ = 270 ppm and elastic constant of martensite E = 12 GPa, which is about the observed difference between curves with and without magnetic field. The described effect saturates in moderate magnetic field (about 1 T) when magnetization fully rotates away from easy axis to the direction of the field (magnetic saturation). The effect, based on magnetoelastic coupling, has a different origin than magnetically-induced-transformation at very high field about 10 T. In that case, the driving force of the transformation is the difference of saturation magnetization between austenite and martensite phases [2].
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T = 317 K
2
-1
magnetization (Am kg )
80
60 MPa 2 MPa
40 0
agrees with observation made by Martynov and Kokorin [9]. The results show that by compression we can attain the martensite state above TA and in such way to expand the whole interval where the magnetic properties of the martensite can be evaluated. Moreover, it also allows the direct comparison of austenite and martensite at the same temperature.
-40 -80
Acknowledgements -1,0
-0,5 0,0 0,5 magnetic field µ0H (T)
1,0
Fig. 5. Magnetization curves of the stress-induced martensite (60 MPa) and parental austenite (2 MPa) at 317 K. The magnetic field was normal to stress direction. The curves are not corrected for demagnetization. The tilt of the curve of the austenite is due to demagnetization.
The changes of magnetic properties of Ni–Mn–Ga material due to the formation of SIM are summarized in Fig. 5. The figure shows the magnetization curves of the nearly free (2 MPa) sample—parental austenite and of the sample compressed by 60 MPa at 317 K. The compression leads to the formation of the SIM in homogenous single variant state with easy axis in the stress direction. The saturation magnetization of the SIM is about 14% higher than of the austenite in agreement with Fig. 3. The curve of the martensite is very similar to the curve measured at room temperature (inset of Fig. 1). The linear character of the curve indicates that the anisotropy is uniaxial with one anisotropy constant [13]. The single variant state allows the direct determination of magnetic anisotropy of stress-induced martensite from the magnetization curve. The magnetic anisotropy of martensite Ku = 1.2 × 105 J/m3 at 317 K was calculated from the anisotropy field corrected for demagnetization using the magnetization curve of magnetically soft austenite. Compared with room temperature the anisotropy of the stress-induced martensite at 317 K decreases about one third. The magnitude and rate of the decrease of the measured magnetic anisotropy is in agreement with the extrapolated value determined from [13]. This gives strong evidence of the likeness of the phases, which
The authors would like to acknowledge the funding support by the National Technology Agency of Finland (Tekes) as well as their industrial research partners (Metso Oyj, Nokia Research Centre and AdaptaMat Ltd.).
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