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Temperature stability of martensite and magnetic field induced strain in Ni–Mn–Ga
Scripta Materialia 46 (2002) 605–610 www.actamat-journals.com
Temperature stability of martensite and magnetic field induced strain in Ni–Mn–Ga N. Glavatska *, G. Mogylny, I. Glavatskiy, V. Gavriljuk Institute for Metal Physics, Ukrainian Academy of Sciences, Vernadsky Blvd. 36, Kiev-142 UA-03680, Ukraine Received 20 August 2001; received in revised form 14 December 2001; accepted 4 January 2002
Abstract In single crystal Ni2 MnGa that exhibits 4.6% magnetic field induced strain (MFIS) at 291 K, it is found that the effect lacks thermal stability. As the temperature rises, the MFIS decreases concomitantly with the lattice distortion. At the same time, the critical magnetic field necessary to activate twin boundary motion falls. A new intermediate martensitic phase is observed. Ó 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Magnetic shape memory; Ni2 MnGa; Martensite; Crystal structure; Thermal properties
1. Introduction In recent years many publications were focused on investigation of Ni–Mn–Ga ferromagnetic alloys. In these materials an enormous strain can be induced by the magnetic field, which makes them very attractive for applications as mechanical actuators. According to proposed models [1–3], the magnetic field induced strain (MFIS) observed in the martensitic phase of the Ni–Mn–Ga alloys is caused by the reorientation of the twinned martensite structure in a manner that is consistent with the direction of the applied field. The reversible MFIS is denoted as magnetic shape memory effect (MSME). Models for this effect predict that the maximal MSME is limited by the tetragonality of martensite (c=a ratio) because the field-induced * Corresponding author. Tel.: +380-44-444-6427; fax: +38044-444-3310. E-mail address: [email protected] (N. Glavatska).
replacement of unfavorable martensitic variants by those ones compatible with the applied magnetic field changes the direction of tetragonality in the sample. Recently a significant success has been achieved in the value of the field-induced strain, and Ni– Mn–Ga alloys exhibiting giant MFIS and MSME that are suitable for actuating elements are now available. Murray et al. [4] observed the fieldinduced strain of 6% in a single crystal specimen. MSME of 5.3% at 100% of the reverse strain after changing the field direction in a single crystal have been obtained in our investigation [5]. We also reported the large reversible magneto-mechanical shape memory effect of 2.5% at room temperature without changing the direction of the field. That effect was observed under mechanical stress and magnetic field simultaneously applied orthogonal to each other [5]. Prototypes of MSM actuators working at room temperature were demonstrated for the first time
1359-6462/02/$ - see front matter Ó 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 6 2 ( 0 2 ) 0 0 0 1 9 - 2
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at the international conferences in Balatonf€ ured (1999) and Bremen (2000) [6,7]. The alloy used by Ullakko et al., for these actuators has the phase transformation temperatures close to room temperature, As ¼ 305 K and Ms ¼ 299 K [6,7]. Other reported alloys also showed the giant magnetic field activated strain in the martensitic phase near T ¼ Ms . Their martensite-to-austenite transformation temperature is close to the ambient one: Ms ¼ 305 K in Ref. [5], Ms ¼ 318 K in Ref. [4], Ms ¼ 263 K in Ref. [8]. In view of the great potential of Ni–Mn–Ga alloys as actuators and sensors, it is important to study the temperature stability of the martensitic structure, and corresponding MSME at temperatures in the vicinity of the phase transformation. The aim of the present study is to clarify the thermal stability of the martensitic structure and of the MFIS in the Ni2 MnGa single crystal alloy that demonstrated a large MSME in the temperature range between room temperature and that of the martensite–austenite transformation.
2. Experimental The non-stoichiometric Ni49:0 Mn29:6 Ga21:4 alloy was melted in the argon atmosphere, thereafter homogenized (72 h at 1273 K) and annealed for ordering (1070 K for 48 h). Next, a single crystal specimen was cut from a large grain along {1 0 0} planes. A powder specimen for X-ray diffraction analysis was prepared from the same ingot and then annealed in a protecting atmosphere. The HUBER 2-circle X-ray diffractometer with a copper anode and graphite monochromator providing CuKa radiation was used to obtain the powder diffraction patterns. The crystallographic structure for each surface of the single crystal specimen was studied using a 3-circle X-ray diffractometer constructed on the DRON-3M base with the monochromatic CuKa radiation. An effect of temperature on the structure was examined by a h–2h analysis under heating in situ, using the HUBER diffractometer. A Peltier-element was used to provide for the heating and temperature control. The h–2h analysis of the diffraction reflections was made without rotation
of the sample. The phase transformation temperatures (TC , Ms , Mf , As , Af ) were determined using a high-sensitivity dilatometer of original construction with precise temperature control [9]. Strain of the specimens at different temperatures was measured using the same dilatometer with and without magnetic field from zero up to 1 T produced by the electromagnet. The resolution of the dilatometer is equal to 38 nm [9]. Before studying the effect of temperature on the crystal structure and MFIS, the specimen was heated to T > Af and cooled under the magnetic field to room temperature. As was found in [10], this treatment produces selection of the preferential martensite variant, which results in the increase of the MSME in the Ni2 MnGa alloy.
3. Results and discussion The phase transformation temperatures in the studied alloy as measured using dilatometer are the following: TC ¼ 369 K, As ¼ 310:7 K, Af ¼ 312:3 K, Ms ¼ 305:9 K, Mf ¼ 302:8 K. The X-ray powder diffraction patterns have shown that the austenitic phase has a Heusler-type structure with space group Fm3m and the lattice parameter of 0.584 nm. After comparing the X-ray powder diffraction pattern with a detailed analysis of the crystallographic orientations carried out using the 3-circle diffractometer, we have found that the martensite has a monoclinic crystal symmetry with the cell parameters a0 ¼ 0:4220 nm, b0 ¼ 0:5590 nm, c0 ¼ 2:0980 nm and b 90:3° at T ¼ 297 K. Deviations of the atomic positions from the ideal ones can be accounted for by a 5-layer structure. Fig. 1a illustrates the diffraction patterns for a(2; 0; 10) and b- (2; 0; 10) martensitic variants. The (0 4 0) variant indexed for a 5-layer monoclinic martensite corresponding to the (4 0 0) austenite peak is shown in Fig. 1b. Since the main goal of this study is to investigate how MFIS changes with temperature and its correlation with the lattice distortion (1 c=a), it is convenient to simplify matters by ignoring the 5-layer structure. This enables us to approximate the martensite phase as the tetragonal cell with a ¼ b ¼ 0:5951 nm, and c ¼ 0:5590 nm at T ¼ 297 K relating to the
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Fig. 1. In situ observations showing the effect of heating on the X-ray diffraction pattern for single crystal Ni2 MNGa {1 0 0} surfaces: (a) transformation of the (4 0 0) martensite peak to austenite; (b) transformation of the (0 0 4) martensite peak to austenite.
austenitic fcc phase. Thus the lattice distortion is ð1 c=aÞ 100 ¼ 6:2% at the above-mentioned temperature. Henceforth we will use descriptions of the martensite phase in terms of this tetragonal form of martensite. Due to cooling under applied magnetic field, as described previously, one surface of the specimen was obtained as (4 0 0) (Fig. 1a). A second surface in one of the orthogonal cubic directions had (0 0 4) orientation (Fig. 1b). Fig. 1a shows results of the in situ X-ray diffraction study of a change in the martensitic structure during heating from room temperature to T > As . Initially, at T < As , a shift in the position of both the (4 0 0) and (0 0 4) peaks occurs. From Fig. 1a one can see that the cell parameter a of the martensite lattice decreases significantly during heating up to T ¼ 309 K. Then at 311 K a new, more intensive peak with a different profile appears, corresponding to the tetragonal phase with a ¼ b ¼ 0:594 nm, and c ¼ 0:560 nm (Fig. 1a). At higher temperatures the martensite peaks eventually disappear because the specimen is transformed completely to the austenitic phase. These observations may be interpreted as evidence that a martensite-to-martensite transformation occurs at temperatures below As . Subsequently, the intermediate metastable martensite phase transforms to austenite. The cell parameter for the (0 0 4) variant of martensite increases during heating (Fig. 1b). The (0 0 4) martensite variant disappears at higher tempera-
ture and martensite-to-austenite transformation is completed. Fig. 2 shows the relative change of the a- and ccell parameters calculated from the X-ray h–2h measurements and its effect on the strain in the specimen measured as a function of temperature. The specimen is contracted in its a-direction with increasing temperature according to the decrease of the a-cell parameter (Fig. 2a). The length of the specimen measured parallel to the c-direction is expanded to a degree corresponding to the increase in the value of the c parameter. However, no precise quantitative correlation between changing Da=a (Dc=c) and strain is observed because the sample does not consist from one martensitic domain and, beside the preferential a- or c-orientation in direction of the strain measurement as induced by the preliminary magneto-thermal treatment, there are also some twin variants having other orientations. It is worth of noting that the large increase in the strain (0.5%) along the c-direction occurs within the relatively narrow temperature interval (Fig. 2b). The martensite tetragonality and the unit cell volume were also calculated using X-ray diffraction results. These are plotted as a function of temperature in Fig. 3. It is clear from these results combined with Fig. 2 that the crystal does not undergo a normal thermal expansion (the a parameter decreases). Hence the combined changes
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Fig. 2. Temperature dependence of the cell parameters and strain in the Ni2 MnGa single crystal: (a) relative change of the a-cell parameter and strain measured along a-axis; (b) relative change of the c-cell parameter and strain measured along c-axis.
Fig. 3. Temperature dependence of: (a) martensite unit cell volume; (b) martensite tetragonality, as calculated from the h–2h X-ray analysis.
in the a- and c-cell parameters with temperature has a large effect on the tetragonality (c=a ratio) (Fig. 3b). As the MSME depends on tetragonality (or lattice distortion) [1–3], it is important to examine the effect of temperature on MFIS. Prior to making any strain measurements under field, the specimen was first magnetized in the direction orthogonal to that of the magnetic field to be applied during the measurements of strain. The results of measure MFIS at different temperatures are shown in Fig. 4a. MFIS in the martensite is caused essentially by a realignment of the crystal twins so there is an excessive proportion of the c-axis contributions to the dimensions of the specimen along
the direction of the applied field. The teragonality ratio c=a < 1; hence the specimen is contracted in the direction of the applied magnetic field and expanded orthogonal to it. The rise in strain with increasing applied field is being eventually saturated (Fig. 4a). Increase of temperature within a quite narrow temperature interval (12 K) slightly below As affects notably the strain behavior activated by the magnetic field causing shift the strainfield curves to the left (Fig. 4a). Several important conclusions can be drawn from the analysis of temperature effect on MFIS (Fig. 4a). Firstly, the lattice distortion (1 c=a) of martensite that defines the theoretical limit of MFIS, decreases linearly with temperature at a
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Fig. 4. Effect of temperature in the Ni2 MnGa martensite single crystal on: (a) MFIS; (b) lattice distortion calculated from the experimental data in comparison with the maximum MFIS.
Fig. 5. Effect of temperature on: (a) the critical magnetic field needed to activate the twin boundary motion; (b) the strain induced by the applied magnetic field at different values.
rate of 2:8 104 K1 , or a total of 0.34% over the 12 K measurement interval (Fig. 4b, upper line). The second important result is that, over the studied temperature range, the measured MFIS decreases linearly with T, and it is proportional to the lattice distortion (1 c=a). In Fig. 4b (lower line) it can be seen that the total change in the field-induced strain amounts to 0.27% in the temperature range between 291 and 303 K. We can also deduce from the maximum observed MFIS that it is smaller than its ideal value controlled by the lattice distortion at the same temperature. It
means that not all martensite in the specimen was preferable oriented after preliminary magnetization. Another noteworthy finding is that the value of the critical magnetic field required for activation of the twin boundary motion is decreased with temperature rise (Fig. 5a). This is also evident from the field–strain curves in Fig. 4a, where the onset of MFIS occurs at smaller magnetic field for higher temperatures. For instance, Fig. 5b shows that in between T ¼ 291 and 302 K the magnetic field H needed to produce the strain of 3.4% falls from 0.45 to 0.35 T.
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A final point to note is the difference in the temperature dependence of the inelastic part of MFIS as a function of the applied magnetic field value. After the critical field had been exceeded, there is a rapid, approximately linear rise in the strain (Fig. 4a). In this region of the field values the MFIS is controlled by the mobility of the twin boundaries and the strain magnitudes rise with temperature (Fig. 5b lower curve) at the same values of the magnetic field. Contrariwise, the saturated MFIS is controlled by the lattice distortion (1 c=a) of martensite and it falls with increasing temperature (Fig. 5b upper curve).
Acknowledgements This study was performed within the frames of the project INTAS 97-30921. The support of Academy of Science in Finland is also greatly appreciated. References [1] [2] [3] [4] [5]
4. Conclusions [6]
1. The lattice distortion of the martensite decreases linearly with increasing temperature. 2. The maximum attainable field-induced strain decreases with increasing temperature concomitantly with the lattice distortion of martensite. 3. The critical value of the magnetic field for activation of the twin boundary motion decreases with increasing temperature. 4. An intermediate martensite-to-martensite transformation occurs just before the martensite-toaustenite transformation in the alloy Ni2 MnGa.
[7]
[8] [9] [10]
Ullakko K. J Mater Eng Perform 1996;5:405. O’Handley RC. J Appl Phys 1998;83:3263. James RD, Wutting M. Philos Mag A 1998;77:1273. Murray SJ, Marioni M, Allen SM, O’Handley RC. Appl Phys Lett 2000;77:886. Heczko O, Glavatska N, Gavriljuk V, Ullakko K. In: Baryakhtar V, editor. European Magnetic Materials and Applications, Mater Sci Forum, vol. 373–376. Zuerich: Trans Tech Publications; 2001. p. 341. Ullakko K, Likhachev A, Heczko O, Sozinov A, Jokinen T, Forsman K, Aaltio I. Seventh International Conference on New Actuators, ACTUATOR 2000, June 19–21, 2000, Bremen, Germany. Ullakko K, S€ oderberg O, Heczko O, Sozinov A, Ezer Y, Aaltio I, et al. Second Hungarian Conference and Exhibition on Material Sciences, Testing and Informatics, 10–13 October, 1999, Balatonf€ ured, Hungary. Tickle R, James RD. J Magn Magn Mater 1999;195:627. Cherepin VT, Glavatska NI, Glavatskiy IN, Gavriljuk VG. Measurement Sci Technol 2002;13:174. S€ oderberg O, Glavatska N, Yakovenko P, Bersudsky E, Glavatskiy I, Ezer Y, et al. In: Proceedings of SMST-99 Conference Antwerpen, 5–9 September, 1999. p. 38.
Temperature stability of martensite and magnetic field induced strain in Ni–Mn–Ga N. Glavatska *, G. Mogylny, I. Glavatskiy, V. Gavriljuk Institute for Metal Physics, Ukrainian Academy of Sciences, Vernadsky Blvd. 36, Kiev-142 UA-03680, Ukraine Received 20 August 2001; received in revised form 14 December 2001; accepted 4 January 2002
Abstract In single crystal Ni2 MnGa that exhibits 4.6% magnetic field induced strain (MFIS) at 291 K, it is found that the effect lacks thermal stability. As the temperature rises, the MFIS decreases concomitantly with the lattice distortion. At the same time, the critical magnetic field necessary to activate twin boundary motion falls. A new intermediate martensitic phase is observed. Ó 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Magnetic shape memory; Ni2 MnGa; Martensite; Crystal structure; Thermal properties
1. Introduction In recent years many publications were focused on investigation of Ni–Mn–Ga ferromagnetic alloys. In these materials an enormous strain can be induced by the magnetic field, which makes them very attractive for applications as mechanical actuators. According to proposed models [1–3], the magnetic field induced strain (MFIS) observed in the martensitic phase of the Ni–Mn–Ga alloys is caused by the reorientation of the twinned martensite structure in a manner that is consistent with the direction of the applied field. The reversible MFIS is denoted as magnetic shape memory effect (MSME). Models for this effect predict that the maximal MSME is limited by the tetragonality of martensite (c=a ratio) because the field-induced * Corresponding author. Tel.: +380-44-444-6427; fax: +38044-444-3310. E-mail address: [email protected] (N. Glavatska).
replacement of unfavorable martensitic variants by those ones compatible with the applied magnetic field changes the direction of tetragonality in the sample. Recently a significant success has been achieved in the value of the field-induced strain, and Ni– Mn–Ga alloys exhibiting giant MFIS and MSME that are suitable for actuating elements are now available. Murray et al. [4] observed the fieldinduced strain of 6% in a single crystal specimen. MSME of 5.3% at 100% of the reverse strain after changing the field direction in a single crystal have been obtained in our investigation [5]. We also reported the large reversible magneto-mechanical shape memory effect of 2.5% at room temperature without changing the direction of the field. That effect was observed under mechanical stress and magnetic field simultaneously applied orthogonal to each other [5]. Prototypes of MSM actuators working at room temperature were demonstrated for the first time
1359-6462/02/$ - see front matter Ó 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 6 2 ( 0 2 ) 0 0 0 1 9 - 2
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at the international conferences in Balatonf€ ured (1999) and Bremen (2000) [6,7]. The alloy used by Ullakko et al., for these actuators has the phase transformation temperatures close to room temperature, As ¼ 305 K and Ms ¼ 299 K [6,7]. Other reported alloys also showed the giant magnetic field activated strain in the martensitic phase near T ¼ Ms . Their martensite-to-austenite transformation temperature is close to the ambient one: Ms ¼ 305 K in Ref. [5], Ms ¼ 318 K in Ref. [4], Ms ¼ 263 K in Ref. [8]. In view of the great potential of Ni–Mn–Ga alloys as actuators and sensors, it is important to study the temperature stability of the martensitic structure, and corresponding MSME at temperatures in the vicinity of the phase transformation. The aim of the present study is to clarify the thermal stability of the martensitic structure and of the MFIS in the Ni2 MnGa single crystal alloy that demonstrated a large MSME in the temperature range between room temperature and that of the martensite–austenite transformation.
2. Experimental The non-stoichiometric Ni49:0 Mn29:6 Ga21:4 alloy was melted in the argon atmosphere, thereafter homogenized (72 h at 1273 K) and annealed for ordering (1070 K for 48 h). Next, a single crystal specimen was cut from a large grain along {1 0 0} planes. A powder specimen for X-ray diffraction analysis was prepared from the same ingot and then annealed in a protecting atmosphere. The HUBER 2-circle X-ray diffractometer with a copper anode and graphite monochromator providing CuKa radiation was used to obtain the powder diffraction patterns. The crystallographic structure for each surface of the single crystal specimen was studied using a 3-circle X-ray diffractometer constructed on the DRON-3M base with the monochromatic CuKa radiation. An effect of temperature on the structure was examined by a h–2h analysis under heating in situ, using the HUBER diffractometer. A Peltier-element was used to provide for the heating and temperature control. The h–2h analysis of the diffraction reflections was made without rotation
of the sample. The phase transformation temperatures (TC , Ms , Mf , As , Af ) were determined using a high-sensitivity dilatometer of original construction with precise temperature control [9]. Strain of the specimens at different temperatures was measured using the same dilatometer with and without magnetic field from zero up to 1 T produced by the electromagnet. The resolution of the dilatometer is equal to 38 nm [9]. Before studying the effect of temperature on the crystal structure and MFIS, the specimen was heated to T > Af and cooled under the magnetic field to room temperature. As was found in [10], this treatment produces selection of the preferential martensite variant, which results in the increase of the MSME in the Ni2 MnGa alloy.
3. Results and discussion The phase transformation temperatures in the studied alloy as measured using dilatometer are the following: TC ¼ 369 K, As ¼ 310:7 K, Af ¼ 312:3 K, Ms ¼ 305:9 K, Mf ¼ 302:8 K. The X-ray powder diffraction patterns have shown that the austenitic phase has a Heusler-type structure with space group Fm3m and the lattice parameter of 0.584 nm. After comparing the X-ray powder diffraction pattern with a detailed analysis of the crystallographic orientations carried out using the 3-circle diffractometer, we have found that the martensite has a monoclinic crystal symmetry with the cell parameters a0 ¼ 0:4220 nm, b0 ¼ 0:5590 nm, c0 ¼ 2:0980 nm and b 90:3° at T ¼ 297 K. Deviations of the atomic positions from the ideal ones can be accounted for by a 5-layer structure. Fig. 1a illustrates the diffraction patterns for a(2; 0; 10) and b- (2; 0; 10) martensitic variants. The (0 4 0) variant indexed for a 5-layer monoclinic martensite corresponding to the (4 0 0) austenite peak is shown in Fig. 1b. Since the main goal of this study is to investigate how MFIS changes with temperature and its correlation with the lattice distortion (1 c=a), it is convenient to simplify matters by ignoring the 5-layer structure. This enables us to approximate the martensite phase as the tetragonal cell with a ¼ b ¼ 0:5951 nm, and c ¼ 0:5590 nm at T ¼ 297 K relating to the
N. Glavatska et al. / Scripta Materialia 46 (2002) 605–610
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Fig. 1. In situ observations showing the effect of heating on the X-ray diffraction pattern for single crystal Ni2 MNGa {1 0 0} surfaces: (a) transformation of the (4 0 0) martensite peak to austenite; (b) transformation of the (0 0 4) martensite peak to austenite.
austenitic fcc phase. Thus the lattice distortion is ð1 c=aÞ 100 ¼ 6:2% at the above-mentioned temperature. Henceforth we will use descriptions of the martensite phase in terms of this tetragonal form of martensite. Due to cooling under applied magnetic field, as described previously, one surface of the specimen was obtained as (4 0 0) (Fig. 1a). A second surface in one of the orthogonal cubic directions had (0 0 4) orientation (Fig. 1b). Fig. 1a shows results of the in situ X-ray diffraction study of a change in the martensitic structure during heating from room temperature to T > As . Initially, at T < As , a shift in the position of both the (4 0 0) and (0 0 4) peaks occurs. From Fig. 1a one can see that the cell parameter a of the martensite lattice decreases significantly during heating up to T ¼ 309 K. Then at 311 K a new, more intensive peak with a different profile appears, corresponding to the tetragonal phase with a ¼ b ¼ 0:594 nm, and c ¼ 0:560 nm (Fig. 1a). At higher temperatures the martensite peaks eventually disappear because the specimen is transformed completely to the austenitic phase. These observations may be interpreted as evidence that a martensite-to-martensite transformation occurs at temperatures below As . Subsequently, the intermediate metastable martensite phase transforms to austenite. The cell parameter for the (0 0 4) variant of martensite increases during heating (Fig. 1b). The (0 0 4) martensite variant disappears at higher tempera-
ture and martensite-to-austenite transformation is completed. Fig. 2 shows the relative change of the a- and ccell parameters calculated from the X-ray h–2h measurements and its effect on the strain in the specimen measured as a function of temperature. The specimen is contracted in its a-direction with increasing temperature according to the decrease of the a-cell parameter (Fig. 2a). The length of the specimen measured parallel to the c-direction is expanded to a degree corresponding to the increase in the value of the c parameter. However, no precise quantitative correlation between changing Da=a (Dc=c) and strain is observed because the sample does not consist from one martensitic domain and, beside the preferential a- or c-orientation in direction of the strain measurement as induced by the preliminary magneto-thermal treatment, there are also some twin variants having other orientations. It is worth of noting that the large increase in the strain (0.5%) along the c-direction occurs within the relatively narrow temperature interval (Fig. 2b). The martensite tetragonality and the unit cell volume were also calculated using X-ray diffraction results. These are plotted as a function of temperature in Fig. 3. It is clear from these results combined with Fig. 2 that the crystal does not undergo a normal thermal expansion (the a parameter decreases). Hence the combined changes
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Fig. 2. Temperature dependence of the cell parameters and strain in the Ni2 MnGa single crystal: (a) relative change of the a-cell parameter and strain measured along a-axis; (b) relative change of the c-cell parameter and strain measured along c-axis.
Fig. 3. Temperature dependence of: (a) martensite unit cell volume; (b) martensite tetragonality, as calculated from the h–2h X-ray analysis.
in the a- and c-cell parameters with temperature has a large effect on the tetragonality (c=a ratio) (Fig. 3b). As the MSME depends on tetragonality (or lattice distortion) [1–3], it is important to examine the effect of temperature on MFIS. Prior to making any strain measurements under field, the specimen was first magnetized in the direction orthogonal to that of the magnetic field to be applied during the measurements of strain. The results of measure MFIS at different temperatures are shown in Fig. 4a. MFIS in the martensite is caused essentially by a realignment of the crystal twins so there is an excessive proportion of the c-axis contributions to the dimensions of the specimen along
the direction of the applied field. The teragonality ratio c=a < 1; hence the specimen is contracted in the direction of the applied magnetic field and expanded orthogonal to it. The rise in strain with increasing applied field is being eventually saturated (Fig. 4a). Increase of temperature within a quite narrow temperature interval (12 K) slightly below As affects notably the strain behavior activated by the magnetic field causing shift the strainfield curves to the left (Fig. 4a). Several important conclusions can be drawn from the analysis of temperature effect on MFIS (Fig. 4a). Firstly, the lattice distortion (1 c=a) of martensite that defines the theoretical limit of MFIS, decreases linearly with temperature at a
N. Glavatska et al. / Scripta Materialia 46 (2002) 605–610
609
Fig. 4. Effect of temperature in the Ni2 MnGa martensite single crystal on: (a) MFIS; (b) lattice distortion calculated from the experimental data in comparison with the maximum MFIS.
Fig. 5. Effect of temperature on: (a) the critical magnetic field needed to activate the twin boundary motion; (b) the strain induced by the applied magnetic field at different values.
rate of 2:8 104 K1 , or a total of 0.34% over the 12 K measurement interval (Fig. 4b, upper line). The second important result is that, over the studied temperature range, the measured MFIS decreases linearly with T, and it is proportional to the lattice distortion (1 c=a). In Fig. 4b (lower line) it can be seen that the total change in the field-induced strain amounts to 0.27% in the temperature range between 291 and 303 K. We can also deduce from the maximum observed MFIS that it is smaller than its ideal value controlled by the lattice distortion at the same temperature. It
means that not all martensite in the specimen was preferable oriented after preliminary magnetization. Another noteworthy finding is that the value of the critical magnetic field required for activation of the twin boundary motion is decreased with temperature rise (Fig. 5a). This is also evident from the field–strain curves in Fig. 4a, where the onset of MFIS occurs at smaller magnetic field for higher temperatures. For instance, Fig. 5b shows that in between T ¼ 291 and 302 K the magnetic field H needed to produce the strain of 3.4% falls from 0.45 to 0.35 T.
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A final point to note is the difference in the temperature dependence of the inelastic part of MFIS as a function of the applied magnetic field value. After the critical field had been exceeded, there is a rapid, approximately linear rise in the strain (Fig. 4a). In this region of the field values the MFIS is controlled by the mobility of the twin boundaries and the strain magnitudes rise with temperature (Fig. 5b lower curve) at the same values of the magnetic field. Contrariwise, the saturated MFIS is controlled by the lattice distortion (1 c=a) of martensite and it falls with increasing temperature (Fig. 5b upper curve).
Acknowledgements This study was performed within the frames of the project INTAS 97-30921. The support of Academy of Science in Finland is also greatly appreciated. References [1] [2] [3] [4] [5]
4. Conclusions [6]
1. The lattice distortion of the martensite decreases linearly with increasing temperature. 2. The maximum attainable field-induced strain decreases with increasing temperature concomitantly with the lattice distortion of martensite. 3. The critical value of the magnetic field for activation of the twin boundary motion decreases with increasing temperature. 4. An intermediate martensite-to-martensite transformation occurs just before the martensite-toaustenite transformation in the alloy Ni2 MnGa.
[7]
[8] [9] [10]
Ullakko K. J Mater Eng Perform 1996;5:405. O’Handley RC. J Appl Phys 1998;83:3263. James RD, Wutting M. Philos Mag A 1998;77:1273. Murray SJ, Marioni M, Allen SM, O’Handley RC. Appl Phys Lett 2000;77:886. Heczko O, Glavatska N, Gavriljuk V, Ullakko K. In: Baryakhtar V, editor. European Magnetic Materials and Applications, Mater Sci Forum, vol. 373–376. Zuerich: Trans Tech Publications; 2001. p. 341. Ullakko K, Likhachev A, Heczko O, Sozinov A, Jokinen T, Forsman K, Aaltio I. Seventh International Conference on New Actuators, ACTUATOR 2000, June 19–21, 2000, Bremen, Germany. Ullakko K, S€ oderberg O, Heczko O, Sozinov A, Ezer Y, Aaltio I, et al. Second Hungarian Conference and Exhibition on Material Sciences, Testing and Informatics, 10–13 October, 1999, Balatonf€ ured, Hungary. Tickle R, James RD. J Magn Magn Mater 1999;195:627. Cherepin VT, Glavatska NI, Glavatskiy IN, Gavriljuk VG. Measurement Sci Technol 2002;13:174. S€ oderberg O, Glavatska N, Yakovenko P, Bersudsky E, Glavatskiy I, Ezer Y, et al. In: Proceedings of SMST-99 Conference Antwerpen, 5–9 September, 1999. p. 38.