Ferromagnetic Shape Memory Materials: Underlying ... - CiteSeerX

Copyright © 2007 American Scientific Publishers All rights reserved Printed in the United States of America

SENSOR LETTERS Vol. 5, 229–233, 2007

Ferromagnetic Shape Memory Materials: Underlying Physics and Practical Importance V. A. Chernenko1 2 ∗ , S. Besseghini2 , P. Müllner3 , G. Kostorz4 , J. Schreuer5 , and M. Krupa1 1

INVITED RESEARCH ARTICLE

Institute of Magnetism, 36-b, Kiev 03142, Ukraine 2 CNR-IENI, Lecco 23900, Italy 3 Department of Materials Science and Engineering, Boise State University, Boise, ID 83725, USA 4 ETH Zurich, Department of Physics, CH-8093 Zurich, Switzerland 5 Ruhr University Bochum, 44780 Bochum, Germany (Received/Accepted: 2 July 2006) The underlying physics of the giant magnetic or mechanical field-induced-strains in Ni–Mn–Ga alloys are briefly discussed. For the purpose of illustrating some fundamental aspects, experimental data relative to lattice instability and composition dependence of magnetization are presented alongside reported results. An implementation of Ni–Mn–Ga single crystal as a strain sensor is described.

Keywords: Ferromagnetic Shape Memory Alloys, Lattice Instability, Magnetostress, Strain Sensor.

1. INTRODUCTION At present, various active materials such as (ferro-) piezoelectric, magnetostrictive, shape-memory alloys, rheological fluids, etc., are being used for sensing and actuation on a macro- and microscale.1–3 The most commercially developed examples of the first three classes are PZT ceramic, Terfenol-D, and Nitinol. The functionality of these materials is based on the physical mechanisms responsible for the electric, magnetic, or thermal energy transformations into mechanical work, which produce the actuation. The reverse energy conversion can be used for sensing. The efficiency, power density, and speed of the aforementioned types of energy conversion determine the advantages and drawbacks of these materials in the applications. As an example, a slow response due to thermal inertia is typical of shape-memory materials, while their advantage lies in the very large reversible strains (more than one order of magnitude larger, compared with other materials in question). Ideally, transducing materials should show large strains, high-force production, and fast dynamic response. These demands are met by the new class of materials denoted as ferromagnetic shape memory alloys (FSMAs) which ∗

Corresponding author; E-mail: [email protected]

Sensor Lett. 2007, Vol. 5, No. 1

combines the properties of ferromagnetism with those of a thermoelastic martensitic transformation.4–6 In particular, FSMAs in their martensitic state allow for a stressor magnetic-field-induced rearrangement of twin variants resulting in a giant magnetostrain, 5–10%.7–9 Prototype of the FSMAs is Ni2 MnGa Heusler alloy with its offstoichiometric derivatives.2–9 Other FSMA systems,6 such as Fe–Pd4 , Fe3 Pt4 , Ni–Mn–(Al, Sn, Sb, In),10 11 Co–Ni– (Al, Ga),12 13 Ni–Fe–(Al, Ga)14 15 are of increasing interest as well. So far, the best-working room-temperature easy-axisferromagnetic martensites in Ni–Mn–Ga alloys have been the subject of the most intense fundamental and applied research. For these alloys, a bulk single-crystalline technology was developed, which led to commercially available actuator products.16 Motivated by the auspicious results on bulk specimens, there is also a large interest in thin-film technology of FSMAs for microsystem applications.17 Hereafter, the underlying mechanisms of the giant magnetic or mechanical field-induced-strains (MFIS) in FSMAs are briefly explained. Some experimental results on the Ni–Mn–Ga alloys, both obtained in the present work and collected from the literature, are presented to highlight some fundamental aspects. An implementation

1546-198X/2007/5/229/005

doi:10.1166/sl.2007.085

229

Ferromagnetic Shape Memory Materials: Underlying Physics and Practical Importance

Chernenko et al.

of Ni–Mn–Ga single crystal as a strain sensor is described.

2. THEORETICAL BACKGROUND OF GIANT FIELD-INDUCED STRAINS IN Ni–Mn–Ga ALLOYS


2.1. Lattice Instability A very general answer to the question why ferromagnetic Ni–Mn–Ga alloys show giant MFIS comes from considering their inherent lattice instability towards thermoelastic martensitic transformation (MT).18 19 This instability is ¯ shear often accommainly related to a uniform (110)[110] panied by shuffling in the same system. It belongs to a Zener-type instability typical of -alloys when a parent phase with bcc open lattice transforms during cooling into a lower-symmetry close-packed martensitic phase as a result of the invariant-plane Bain deformation. In order to accommodate stresses due to the large Bain strains, secondary invariant-lattice strains occur involving the same shear system, so that a twinned microstructure is formed. It is worth noting that the aforementioned shear in Ni– Mn–Ga intermetallics, as well as in other -alloys, is characterized by a low restoring force, that is to say, their shear modulus C is very small. Moreover, C has an abnormal descending temperature dependence during cooling in the cubic phase, reaching down to a minimum of about 10 GPa near MT.20 21 Figure 1 shows the variation in two close resonance frequencies f (f 2 is proportional to the shear modulus) within a wide temperature range. The data plotted in Figure 1 were extracted from the 3D-map shown in Figure 2. Figure 2 represents the results of resonant ultrasound spectroscopy for a (100)-oriented Ni519 Mn268 Ga213 single crystal exhibiting a 14 M-martensite with MT and Curie temperatures of Tm = 307 K and TC = 341 K, respectively.22 23 According to Figure 1, the total decrease

Fig. 1. Frequencies of the two lowest resonances as a function of decreasing temperature for Ni519 Mn268 Ga213 (Tm = 307 K, TC = 341 K). Data were extracted from the 3D-map shown in Figure 2. The arrow points at the kink resulting from the ferromagnetic ordering.

230

Fig. 2. Intensities of the resonances for a (100)-oriented cube of Ni519 Mn268 Ga213 single-crystal measured by resonant ultrasound spectroscopy at different temperatures.23

in high-frequency modulus in the cubic phase can be evaluated to be about 40%. In addition, this modulus exhibits a kink near TC . A similar anomaly was previously observed for the low-frequency modulus.20 One of the consequences of a small modulus, especially in the temperature range of structural transformations, is a considerably enhanced ordinary magnetostriction. For instance, at the parent-tointermediate phase transition in Ni2 MnGa, this is about 600 ppm.24 With MT in this compound, magnetostriction is about 10 times larger,24 which implies a predominant contribution of the reversible motion of twinning dislocation.25–27 Alongside an abnormally reduced elastic modulus, Ni–Mn–Ga alloys in single-crystalline form are characterised by extremely mobile twin boundaries accounting for very low yield stresses, y ∼ 1 MPa, in the martensitic state.26 27 Such a twinning stress appears smaller than the equivalent mechanical stress (magnetostress) produced by a magnetic field, which explains the giant magnetostrain effect. 2.2. The Magnetostress Concept In Ni–Mn–Ga alloys, MT is accompanied by a cubic-totetragonal unit cell distortion with a contracted c-axis and expanded a-axes. The magneto-elastic coupling described by a negative magnetostriction constant is responsible for the appearance of an easy-magnetization direction along the short c-axis, accompanied by the large uniaxial magnetic anisotropy. It is also responsible for the emergence of magnetostress. Some models suggesting the equivalence of magnetic field and stress in a ferromagnetic martensite are presented in Refs. [25, 28]. According to the phenomenological magnetoelastic model of ferromagnetic martensite,27–29 this equivalence stems from energy density terms like ∼M 2 describing magnetoelastic interaction, where M and are the appropriate components of magnetization vector and strain tensor, respectively. Basically, the above terms arise because spin exchange and spin–orbit interactions between electrons depend on the atom coordinates. The core structure of the Helmholtz free energy for ferromagnetic tetragonal martensite can be written Sensor Letters 5, 229–233, 2007


Chernenko et al.

as follows: 1 1 F = C 2ii + AMi2 − Mi2 ii − Mi Hi (1) 2 2 where C is the elastic modulus, A ∼ 1 − c/a is the magnetic anisotropy parameter, is a magnetoelastic energy parameter, and H is the magnetic field. Note, that in Eq. (1), the elastic and magnetoelastic energies are expressed for the cubic phase due to negligible ‘tetragonal corrections.’29 The fundamental equation of thermodynamics ik = F /ik T yields: ii = C ii + Mi2

(2)

Experimental results of the quasielastic reversible MFIS response up to 0.5% as presented in Ref. [24] are in complete agreement with expression (3). The field dependence of strain shown in Figure 3 is only reversible at low fields. The part of strain accumulated at high fields is irreversible. This is also irreversible on compression at zero field, as shown from stress–strain curves

Fig. 3. Magnetic-field-induced strain measured at T = 300 K along [100]C for a 10 M-martensitic specimen of a Ni510 Mn279 Ga211 singlecrystal with Tm = 314 K and TC = 370 K. Inset: compressive stress–strain curves measured under orthogonal magnetic field for the same specimen at T = 300 K (see Ref. [26] for details).

Sensor Letters 5, 229–233, 2007

Fig. 4. Saturation magnetization measured at H = 1 T and T = 77 K as a function of composition for Ni–Mn–Ga alloys at a constant content of the third element. The straight lines are guides for the eye.

231


where a sum of the mechanical stress (first term) and magnetostress (second term) represents a generalized form of Hooke’s law for a stressed ferromagnetic crystal. Eq. (2) shows that the magnetoelastic coupling is responsible for the occurrence of magnetostress. On the other hand, the proportionality between stress and magnetization square confirms a magnetoelastic nature of the fieldinduced stress. These theoretical findings are supported experimentally.24 In the special case of a linear dependence of the magnetization process as a function of field and 1 − c/a, the magnetoelastic mechanism prescribes the dependence27–29 ∼ H2 (3)

in the inset to Figure 3. The results shown in Figure 3 and inset were obtained in Refs. [25, 26] for a 10 Mmartensitic specimen of Ni510 Mn279 Ga211 single crystal with Tm = 314 K and TC = 370 K. The microstructure of this material, studied in Ref. [26], consists of three martensitic variants, each with an equiprobable volume fraction. Under such conditions, the maximum strain during specimen compression is about 2%, whether magnetostress or mechanical force is applied (Fig. 3 and inset). This experimental fact is in line with the aforementioned equivalence principle. The fascinating phenomenon of magnetic-field-induced superelasticity arises when magnetic field and mechanical compression are applied orthogonally to the FSMA specimen, see curve at 2 T in the inset to Figure 3,26 and results of Ref. [27]. In this case, besides a reversible movement of twin interfaces resulting in a reversible macroscopic deformation of up to 10%,22 30 a magnetostress value, M , can be measured as the difference in yield stresses, which is shown in the inset to Figure 3. A good agreement is obtained between the measured magnetostress values and ones calculated from a magnetoelastic model.27 The largest measured value of M up to date (4 MPa) was obtained from 14 M martensite in a Ni519 Mn268 Ga213 single crystal.30 Notably, according to Eq. (2), magnetostress is dependent on the magnetoelastic parameter, magnetization, and the mutual orientation of the field and magnetization vectors. Parameter is suggested to be constant in the Ni– Mn–Ga alloy system24 so, among the material parameters, only the saturation magnetization value, Ms , can be controlled. In Refs. [31, 32], Ms was measured at room temperature and studied as a function of electron concentration. In the present work, we measured magnetization curves up to H = 1 T at 77 K for all the alloys described in Ref. [33]. The results for those alloys with an approximately constant content of the third element


Chernenko et al.


were selected and plotted in Figure 4 and inset. Figure 4 and inset show different trends of the off-stoichiometry influence on Ms . Substituting Ni or Ga for Mn increases or decreases Ms values, respectively, while at constant concentration of Mn, a substitution of Ni by Ga results in a nonmonotonous behavior of Ms . The maximum of Ms measured at 77 K is found in the vicinity of stoichiometric composition, which is in agreement with results obtained at room temperature.31 32 Thus, the maximum of magnetostress value for the tetragonal 10 M-martensite can be expected in the stoichiometric Ni2 MnGa compound.

3. THE STRAIN-INDUCED MAGNETIZATION PROCESS IN FSMAS FOR SENSOR APPLICATIONS In the previous section, results of the uniaxial compression experiments under a constant orthogonal magnetic field of 2 T were presented in the inset to Figure 3 (see details in Ref. [26]). During the same experiments, it was shown that a nonsaturating field of 0.7 T was also sufficient to produce a hysteretic reversible stress–strain behavior.26 The measuring procedure at this field was then modified to register a stray field as a function of compressive strain.26 The stray field was measured by a Hall probe on the specimen side facing the applied field. The results are depicted in Figure 5. Upon deformation, magnetization reduces linearly by up to 30%. Upon unloading, the magnetization is restored to its initial value with a tiny hysteresis (Fig. 5). This effect is reversed with respect to the MFIS one. A large linear deformation-induced change in magnetization opens new paths towards the implementation of FSMAs in sensors26 34 and the generation of electric power.35 A prototype of a strain sensor based on a 10 Mmartensitic Ni520 Mn244 Ga236 crystal has been suggested in Ref. [34]. A sketch of this sensor design is shown in Figure 6. The parallelepiped-shaped (100)-oriented singlecrystal was initially trained (see, e.g., Ref. [9]) in order to obtain a specimen containing only a single-variant of

Fig. 6. Sketch of a strain sensor proposed in Ref. [34]: (1) 10 Mmartensitic parallelepiped of Ni520 Mn244 Ga236 crystal in a single-variant form; (2) insulating layer; (3) permalloy magnetoresistive gauge; (4) electric contacts; (5) amplifier of a differential signal.

tetragonal martensite. The stress–strain behavior under magnetic field and other characteristics of this specimen are studied in Ref. [27]. For the sensor shown in Figure 6, the compressive stress to be measured is applied to specimen 1 in a vertical direction. In the initial state, the short c-axis and magnetization vector of the specimen are lying along the horizontal direction in the figure plane. A constant field of about 0.3–0.4 T can be optionally applied in the same horizontal direction to get a reversible operation of the sensor. The magnetic flux change caused by a rotation of the magnetization vector under mechanical straining is registered by a magnetoresistive gauge glued onto the active edge of the specimen. The gauge is made of a permalloy foil with negligible magnetostriction and in-plane uniaxial magnetic anisotropy. A similar foil with its magnetization axis oriented 90 from the previous one is glued onto the opposite edge of specimen. A change in the differential electrical signal of the gauges is calibrated in terms of stress/strain. This signal does not depend on the applied magnetic fields. The sensor has its own noise of less than 10−10 V and can be used for both static and dynamic strain/stress measurements.

4. SUMMARY

Fig. 5. Magnetization change as a function of strain in the same series of experiments shown in Figure 3 (see Ref. [26] for details).

232

In the present paper, some fundamental issues related to the necessary and sufficient conditions of giant MFIS effect in FSMAs were addressed. A Zener type of lattice ¯ shear, instability, low restoring force towards (110)[110] the thermoelastic martensitic transformation in ferromagnetic matrix and low elastic shear modulus were considered as the necessary conditions for MFIS while both a low yield stress for twin variant rearrangements in martensite, ∼1 MPa, and high magnetostress exceeding this yield stress were taken as the sufficient conditions. The most studied prototype of Ni–Mn–Ga FSMA system was Sensor Letters 5, 229–233, 2007

Chernenko et al.


considered as a model to illustrate an adequate correspondence between experimentally observed phenomena and their theoretical treatment. A potential application of FSMA materials was demonstrated by an implementation in a stress sensor. Acknowledgments: VAC is grateful to Fondazione Cariplo for financial support (project 2004.1819A10.9251).

References and Notes

Sensor Letters 5, 229–233, 2007

233


1. M. Kohl, Shape Memory Microactuators, Springer-Verlag, Berlin, Heidelberg (2004). 2. R. D. James and M. Wuttig, Proceedings of the SPIE Symposium on Smart Structures and Materials, edited by V. V. Varadan and J. Chandra (1996), Vol. 2715, p. 420. 3. M. Pasquale, Sens. Act. A 106, 142 (2003). 4. T. Kakeshita and K. Ullakko, MRS Bulletin 2, 105 (2002). 5. A. N. Vasil’ev, V. D. Buchel’nikov, T. Takagi, V. V. Khovailo, and E. A. Estrin, Physics - Uspekhi 46, 559 (2003). 6. E. Cesari, J. Pons, R. Santamarta, C. Segui, and V. A. Chernenko, Archives Metal. Mater. 49, 791 (2004). 7. S. J. Murray, M. Marioni, S. M. Allen, R. C. O’Handley, and T. A. Lograsso, Appl. Phys. Lett. 77, 886 (2000). 8. O. Heczko, A. Sozinov, and K. Ullakko, IEEE Trans. Magn. 36, 3266 (2000). 9. P. Müllner, V. A. Chernenko, and G. Kostorz, Mat. Sci. Eng. A 387–389, 965 (2004). 10. F. Gejima, Y. Sutou, R. Kainuma, and K. Ishida, Metall. Mater. Trans. A 30, 2721 (1999). 11. Y. Sutou, Y. Imano, N. Koeda, T. Omori, R. Kainuma, K. Ishida, and K. Oikawa, Appl. Phys. Lett. 85, 4358 (2004). 12. K. Oikawa, L. Wulff, T. Iijima, F. Gejima, T. Ohmori, A. Fujita, K. Fukamichi, R. Kainuma, and K. Ishida, Appl. Phys. Lett. 79, 3290 (2001). 13. M. Wuttig, J. Li, and C. Craciunescu, Scr. Mater. 44, 2393 (2001). 14. K. Oikawa, T. Ota, Y. Sutou, T. Ohmori, R. Kainuma, and K. Ishida, Mat. Trans. 43, 2360 (2002).

15. K. Oikawa, Y. Imano, V. A. Chernenko, F. Luo, T. Omori, Y. Sutou, R. Kainuma, T. Kanomata, and K. Ishida, Mat. Trans. 46, 734 (2005). 16. J. Tellinen, I. Suorsa, A. Jääskeläinen, I. Aaltio, and K. Ullakko, Actuator 2002 Conference, Bremen, Germany (2002), Vol. 8, p. 566. 17. M. Kohl, D. Brugger, M. Ohtsuka, and T. Takagi, Sens. Act. A 114, 445 (2004). 18. P. G. Webster, K. R. A. Ziebeck, S. L. Town, and M. S. Peak, Phil. Mag. B 49, 295 (1984). 19. V. A. Chernenko, Scripta Mater. 40, 523 (1999). 20. V. A. Chernenko, J. Pons, C. Seguí, and E. Cesari, Acta Mater. 50, 53 (2002). 21. M. Stipcich, Ll. Mañosa, A. Planes, M. Morin, J. Zarestky, T. Lograsso, and C. Stassis, Phys. Rev. B 70, 054115 (2004). 22. V. A. Chernenko, P. Müllner, M. Wollgarten, J. Pons, and G. Kostorz, J. Phys. IV 112, 951 (2003). 23. V. A. Chernenko, J. Schreuer, and P. Müllner, unpublished. 24. V. A. Chernenko, V. A. L’vov, M. Pasquale, C. P. Sasso, S. Besseghini, and D. A. Polenur, Int. J. Appl. Electromagn. Mechanics 12, 1 (2000). 25. P. Müllner, V. A. Chernenko, M. Wollgarten, and G. Kostorz, J. Appl. Phys. 92, 6708 ( 2002). 26. P. Müllner, V. A. Chernenko, and G. Kostorz, Scr. Mater. 49, 129 (2003). 27. V. A. Chernenko, V. A. L’vov, P. Müllner, G. Kostorz, and T. Takagi, Phys. Rev. B 69, 134410 (2004). 28. V. A. L’vov, S. P. Zagorodnyuk, and V. A. Chernenko, Eur. Phys. J. B 27, 55 (2002). 29. V. A. Chernenko, V. A. L’vov, S. P. Zagorodnyuk, and T. Takagi, Phys. Rev. B 67, 064407 (2003). 30. P. Müllner, V. A. Chernenko, and G. Kostorz, J. Appl. Phys. 95, 1531 (2004). 31. X. Jin, M. Marioni, D. Bono, S. M. Allen, R. C. O’Handley, and T. Y. Hsu, J. Appl. Phys. 91, 8222 (2002). 32. J. Enkovaara, O. Heczko, A. Ayuela, and R. M. Nieminen, Phys. Rev. B 67, 212405 (2003). 33. V. A. Chernenko, E. Cesari, V. V. Kokorin, and I. N. Vitenko, Scr. Met. Mat. 33 1239 (1995). 34. M. M. Krupa and V. A. Chernenko, Patent of Ukraine UA 717551 A. Priority 04-12-2004. Bulletin 12, 124 (2004). 35. I. Suorsa, J. Tellinen, K. Ullakko, and E. Pagounis, J. Appl. Phys. 95, 8054 (2004).