Internal friction associated with the structural phase transformations in Ni-Mn-Ga alloys

Pergamon PII: S1359-6454(%)00244-3

~cta outer. Vol. 45. No. 3. DD.999-1004, 1997 Copyright 0 i997 Acta’Metallurgica Inc. Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359-6454/97 $17.00 + 0.00

INTERNAL FRICTION ASSOCIATED WITH THE STRUCTURAL PHASE TRANSFORMATIONS IN Ni-Mn-Ga ALLOYS E. CESARI,‘? V. A. CHERNENKO: ‘Departament

V. V. KOKORIN,2 J. PONS’ and C. SEGUi’

de Fisica, Universitat de les Illes Balears, E-07071 Palma de Mallorca, of Magnetism, Vernadsky str. 36 B, Kiev 252680, Ukraine

Spain and *Institute

(Received 24 June 1996)

Abstract-A double peak in the temperature

dependence of internal friction (IF) and elastic modulus in some off-stoichiometric Ni2MnGa shape memory alloys has been observed both on cooling and heating between the parent and martensite phases. Transmission electron microscopy (TEM) observations have shown that these anomalies are related to structural transformations from the parent cubic phase (P) to an intermediate cubic modulated phase (I) and from the I phase to the martensitic one (M). As for the IF results, the I to M transformation has the characteristics of a first-order phase transition, whereas the P to I transformation shows some distinctive features, such as no temperature-rate dependence. Copyright ‘8 1997 Acta Metallurgica Inc.

1. INTRODUCTION There has been a lot of interest addressed to the shape memory ferromagnetic Heusler alloy NizMnGa in view of the peculiarities of the thermoelastic transformations (MT), precursor martensitic phenomena and soft mode behaviour that it exhibits [l-5]. Recently, it was shown [6] that according to the characteristics of MT, the off-stoichiometric N&MnGa alloys can be separated into three groups. Group I is characterized by a transformation start temperature M, well below room temperature (hence below the Curie temperature, which is about 380 K) and very low transformation heat (1.5 J/g on average); group II, in turn, is characterized by MS around room temperature and intermediate heat exchange (average 4.2 J/g), and finally alloys of group III show transformation temperatures above room temperature, usually above the Curie temperature, and high transformation heat (average 8 J/g). For the latter, the martensite start temperature (MS) can be higher than 600 K, and therefore these alloys have the potential to be developed as high temperature shape memory alloys. The Ni-Mn-Ga alloys belonging to the different groups also show different mechanical behaviour, both in the martensitic phase and in the transformation region. In particular, the alloys belonging to group I show two consecutive internal friction maxima and the corresponding Young’s modulus minima, which occur at different temperature ranges both on cooling and heating the samples. In this tTo whom

all correspondence

should

be addressed. 999

paper the results concerning this distinctive behaviour will be shown and analysed, and the characteristics and origin of the internal friction peaks will be discussed. 2. EXPERIMENTAL PROCEDURE Off-stoichiometric N&MnGa alloys with M, about 200 K and Curie temperature about 380 K (thus belonging to Group I in [6]) were involved as the subjects for investigation. The present study showed that all the alloys of the aforementioned group have similar IF behaviour near MT. Hence, the typical results presented below were obtained using mainly one of the alloys. The composition of the investigated single crystalline alloy is Ni-24.3 Mn-26.0 Ga in at. %. The martensitic transformation temperatures were measured by the low field magnetic susceptibility resulted in A4, = 175 K and technique and A, = 190 K, A, being the start temperature of the reverse transformation. In this case, the temperature of the specimen was monitored with a thermocouple welded to it. The dynamic mechanical properties of the alloys were studied in a three-point bending configuration using a Perkin-Elmer Dynamic Mechanical Analyser, DMA-7. Plate-like specimens of average dimensions 10 x 1.5 x 0.5 mm3 were sparkcut, mechanically polished by grinding and electropolished as a final stage of the preparation. The DMA-7 system applies a vibrational stress c = o,e/‘“’ causing a strain t = Ed.+‘+ ‘) of the specimen. The corresponding complex modulus is then E = CT/~= E’ + jE” where E’ and E” are the storage and loss moduli, respectively. The values of t,, and 6 are obtained

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ALLOYS 3. RESULTS

automatically from the registered values of deflection and phase angle, respectively, and the DMA-7 software package allows us to obtain simultaneously E’ and tanb, where E’ = (co/co) COSSand tans = (E”/ E’). Since the storage modulus gives the stored fraction, and the loss modulus the lost fraction of the overall energy in an oscillation cycle, it is obtained that

tans =

IN Ni-Mn-Ga

The temperature spectrum of internal friction and storage modulus of the studied alloy during cooling is presented in Fig. 1. The IF spectrum is fairly reproducible during consecutive temperature cycling. In the low temperature region the curves show the typical internal friction and modulus behaviour during MT, with a higher IF level in the martensitic phase (M) than in the parent phase (P) and an IF-peak concurrently with a modulus minimum at the transformation temperature range [7]. The same is true for the reverse MT, which proceeds with a hysteresis about 10 K. The most prominent feature shown in Fig. 1 is the presence of an additional IF-peak and corresponding modulus minimum at temperatures well above the MT. It was verified experimentally that all the alloys from group I irrespective of their single or polycrystalline state manifest, during cooling and heating, a double peak. On the contrary, however, according to the IF measurements, alloys of other groups in [6] do not exhibit any IF peak before the MT. The TEM observations performed at different temperatures support the idea that the two stages in IF and modulus spectra can be attributed to two separated structural transformations. At temperatures around 200 K and above (parent phase, P) the selected area electron diffraction patterns (SAEDP) correspond to a L2, ordered cubic structure with diffuse streaking along < 110 > directions. The bright field images show a fine “tweed” contrast (more easily visible near the extinction and bend contours). On cooling down, the streakings along < 110 > are observed to be gradually replaced by extra sharp reflections (satellites) which divide the reciprocal lattice spacings in all < 110 >-type directions in six equal parts, as seen in Fig. 2(a) (intermediate phase, I). Nevertheless, this change in the SAEDP is not accompanied by a notable microstructural change but a marked tweed contrast persists. The formation

-L Lw

2rl W’

where A W is the lost energy (i.e. the energy dissipated during the deformation cycle) and W is the amplitude value of the elastic energy (i.e. the stored energy), hence tand = Q-l is a measure of the internal friction (IF). The IF and modulus measurements were performed at frequency v = 1 or 2 Hz and oscillation amplitude about 10 -4. In most of the experiments the temperature dependence was studied at 5 K/min cooling and heating rates, but it is worth noting that during the IF measurements the temperature was monitored by a thermocouple located in a close neighbourhood of the specimen, and therefore the temperatures measured by the DMA-7 system are slightly shifted along the temperature axis with respect to those determined precisely by low field magnetic susceptibility measurements. Apart from the temperature dependence (at constant stress amplitude) of the internal friction, the stress amplitude dependence has also been studied at different constant temperatures. The whole set of experiments allows us to analyse the influence of external parameters on the IF results. The structural identification of the different phases was performed using a Transmission Electron Microscopy (Hitachi H600, 100 kV) equipped with single-tilt heating and cooling stages. The thin foils were prepared by double-jet electropolishing in 50% nitric acid in methanol at 8 V and 240 K.

,i‘;

co 3 z1.0

E

I

\ ’ ./

8 - 2.0

-

E3

r 0

’

IF L

L 150

200 TEMPERATURE

Fig. 1. Evolution

5

4 , 1.0 250

300

ot)

of the internal friction (IF) and modulus (E) during cooling alloy (i- = 5 K/min, v = 2 Hz, o0 = 2 MPa).

for the studied Ni-Mn-Ga

CESARI

et ~1.:

TRANSFORMATION

IN Ni-Mn-Ga

1001

ALLOYS

SAEDP reveal a tetragonal lattice with long period modulations along < 110 >paren, (Fig. 2(b)), which needs a further detailed investigation to clarify its stacking order structure, although it is clear that the modulation is different from the one observed in the intermediate phase. The whole P-I-M transformation path is reversible on in-situ heating. Thus, it is shown in the present work that forward P-+1 and reverse I--+P phase transformations, characterized by changes of the physical properties such as the IF and modulus, occur at temperatures above the martensitic transformation M-1. It is worth noting that the P-1 transformation takes place independently on the MT, as stated from IF and in situ TEM experiments, in which cooling was stopped between the two IF peaks and the specimen was heated back to the parent phase. The hysteresis of the P-1 transformation as measured from IF peaks resulted in about 3 K. Complementary DSC experiments were performed in which only the MT was detected, traces of the P-1 transformation being completely absent regardless the temperature rate. In view of the striking features of the parent-tointermediate phase transformation, complementary experiments were undertaken to obtain some new information about IF behaviour as a function of

Fig. 2. In-situ electron diffraction patterns obtained at different temperatures: (a) T= 183 K, I phase, zone axis [I 1 l]r indexed according to the L21 structure; (b) T = 128 K, M phase, zone axis [100]~ indexed according to a tetragonal lattice.

2.c

1.a

z of l/6 extra spots can be postulated as an indication of the I phase existence in Ni-Mn-Ga alloys, as was assumed in [l, 31 on the basis of electron microscopy observations. Recently, a further confirmation of the occurrence of the I phase was found by inelastic neutron scattering measurements [5]. According to the present data, the structure of the I phase can be regarded as a multi-cell or mosaic structure [8] characterized by < l/3 l/3 O> transverse displacement modulations of the parent cubic structure, which give rise to the observed satellites in the SAEDP. The HREM images in [5] show an inhomogeneous assembly of contiguous distorted regions of roughly 46 nm extent, each region consisting of alternating dark/light bands of approximately 1.2 nm width parallel to (220) or (220). The band width is consistent with the satellite spacings observed in the reciprocal space [5]. On further cooling, the transformation to martensite phase (M) is observed, with the development of a plate microstructure. The

0

x ti 5I

2.0

B E -

1.0

k a 3E

0

2.0

1.0

0 4

8

12

STRESS AMPIXIVDE (oe, Mpa) Fig. 3. Stress amplitude dependence of the internal friction (continuous lines) and strain (discontinuous lines) at constant temperature: (a) T = 132 K, M phase; (b) T = 187 K, I phase; (c) T = 190 K, I phase (v = 1 Hz. force rate 50 mN/min).

CESARI et al.: TRANSFORMATION IN Ni-Mn-Ga ALLOYS

1002

., l&l

li5

200 TEMPERATURE(K)

Fig. 4. Temperature evolution on cooling of the IF under different stress amplitudes (v = 1 Hz, P= 5 Kjmin).

change was stopped at (or close to) the peak temperatures for both the MT and the parent-tointermediate phase transitions. The results are shown in Fig. 5, indicating that a small but appreciable dependence on the temperature rate exists for the MT (Fig. 5(a)), while IF in the P+9 transition remains practically constant at f = 0 and, hence, it is temperature rate independent (Fig. 5(b)). The same result arises from systematic measurement of IF vs temperature at different temperature rates between 1 and 10 K/min. This result is opposite to that obtained for the martensitic transformation in Cu-based alloys, for which the temperature rate dependent contribution to the IF peak is by far the most important [7].

2.0 external parameters in martensite, I-phase and transformation regions. The high temperature region will not be discussed since neither high damping nor other special features are observed in this region. Figure 3 shows the stress amplitude dependence of tans and strain at three constant temperatures corresponding to the M phase (Fig. 3(a)) and I phase (Fig. 3(b,c)). It has to be emphasized that a critical stress amplitude (a,,) exists under which the IF is below the resolution of the experimental device, tand increasing afterwards and showing a tendency towards a saturation value. The maxima on curves (b) and (c) in Fig. 3 have to be attributed to the stress-induced I+M transformation, the value of co corresponding to the single maximum being linearly dependent on temperature with an approximate slope do/dT = 2.5 MPa/K. A similar value was obtained in uniaxial tension tests for stress-induced P to M transformation in group II Ni-Mn-Ga alloys [l]. Further cooling after the experiments which led to obtaining curves 3(b) or 3(c) did not result in any other IF peak, supporting the idea that 1-M transformation was stress induced at temperatures above IV,. Thus, it can be emphasized that the DMA measurements provided by the Perkin Elmer machine in the described configuration can be used in determining 0-T diagrams of MTs. Figure 4 shows internal friction as a function of temperature for different stress amplitudes. It can be observed that the IF level in the I phase and M phase temperature regions increases with increasing stress amplitude (which is consistent with Fig. 3). As for the IF peaks height, in the case of the I-+M transformation the maximum IF relative to the martensite level decreases with increasing stress amplitude, while the IF maximum during the P-+1 transition with respect to the I phase level remains nearly constant. The effect of temperature rate on the internal friction spectra was also checked by analysing the evolution of tans after the temperature

64

170

TIME (minutes) 3.0T

ti; 2.5 # l

I

214

(b)

2.0 IF

g ’ & 1.5 \ ;

\. 1.0

\.

._._.T._

2 _ 0.5 !Z

i 0

200

r 10.0 TIME (minutes)

Fig. 5. Effect of the temperature rate on the IF; the time evolution of tans after the temperature rate is decreased to zero is studied in the MT transformation transformation (b).

(a) and the P-1

CESARI et al.:

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TRANSFORMATION IN Ni-Mn-Ga ALLOYS

4. DISCUSSION Three terms are known [7,9-121 to contribute to the IF peak caused by MT. The first is a transient contribution (IF,,) which exists only during cooling or heating. It depends on external parameters like temperature rate, frequency and stress amplitude, and is related to the influence of alternating stress on the processes of nonequilibrium nucleation and growth. It depends on the transformation kinetics and is therefore proportional to the volume fraction transformed per unit time. The second contribution to the IF-peak at MT is a non-transient or stationary part, IF,, which is related to mechanisms of the phase transformation, which are independent of the temperature rate, such as the displacement of parent/martensite interfaces. Different approaches can be found in the literature for an explanation of IF,, but according to [IO] it is related to the amount of transformed volume fraction per stress unit. The third component, IF,,,, is not directly associated with MT, but it corresponds to the intrinsic damping generated in each of the coexisting phases. It is related to the mobility of defects, including mobile intervariant boundaries, under the effect of an oscillating stress, hence it is stress amplitude dependent. This scheme can be applied to any first order transformation. In the present case, the MT and the parent-tointermediate phase transformation must be considered separately. As a first approach, the different contributions to the IF peaks have been evaluated for each case from the described experiments as follows: the intrinsic part arises from the stress amplitude dependence of the internal friction in either an intermediate or martensitic condition (Fig. 3) and also from the internal friction level in temperature dependent IF experiments performed at different stress levels (Fig. 4). The phase transition contribution (transient plus stationary contributions) to the IF peak associated with the P-+1 and 1-M transformations was calculated subtracting the intrinsic IF level in the I and M phases respectively from the corresponding internal friction peak height. The obtained values are shown in Fig. 6 as a function of the stress amplitude. For the martensitic 1-M transformation, the intrinsic contribution increases and the non-intrinsic contribution decreases with increasing stress amplitude (Fig. 6(a)). As for the transient contribution, IF,,, the experiments like those in Fig. 5(a) indicate a small but non-zero contribution of about 10% of the overall peak height. Even though this result is much lower than that obtained for other alloys undergoing an MT, it agrees with the general scheme of a first-order transformation. Concerning the P--+1 transformation, however, Fig. 6(b) shows that both the intrinsic and phase transition contributions increase with stress amplitude. No temperature rate dependent contribution to the IF was

0

2

4 Stress amplitude

0.1

6

8

IO

(MPa)

,

(b)

1 $ 0.04 + 0.02

01 0

2

4 Stress amplitude

6

8

10

(MPa)

Fig. 6. Stress amplitude dependence of the different contributions to the IF for the MT (a) and the P--t1 transformation (b).

observed for this transformation, according to Fig. 5(b). The stress amplitude dependence of the transient and stationary contributions to the IF in MT can be analysed following two different models [12]; one of them considers the strain change to be proportional to the tranformed volume fraction in an oscillation cycle and results in a crom2dependence of (IF,, + IF,); the other model considers the strain change to be proportional both to the instantaneous stress and the transformed volume fraction, resulting in a oO- ’ dependence. To discern whether the MT in the studied alloys corresponds to one or the other model, more data than available would be necessary. Further work is in progress to elucidate this point, In [5], after analysing the phonon dispersion curves at different temperatures, Zheludev et al. concluded that the P-+1 is a weak first-order transition, and indeed, the existence of a corresponding IF peak and modulus minimum, points, in principle, to such a conclusion. Nevertheless, some of the presented results depart from the characteristics of a first-order transition, for example (i) the absence of temperature rate dependence of IF (null IF,, contribution); (ii) the absence of a discontinuous microstructural change accompanying the transformation and (iii) the absence of detectable latent heat. In systems like La, _ ,Nd,P5014 (LNPP), an internal friction peak related to a recognized second-order ferroelastic phase transition was experimentally observed [13]. The internal friction in that case was

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CESARI et al.: TRANSFORMATION IN Ni-Mn-Ga ALLOYS

attributed to the appearance of domains of the new phase and to the domain walls’ mobility. In the present case, no other interfaces, boundaries or domain walls but those of the 4-6 nm size regions reported in [5], composing the mosaic structure of the intermediate phase, have been observed. Therefore, the origin of the IF peak corresponding to the P-1 transition remains unclear and could only tentatively be attributed to the movement of those boundaries under the effect of the oscillating stress. 5. CONCLUSIONS Two successive maxima in the temperature spectrum of the internal friction and modulus have been detected in certain off-stoichiometric Ni,MnGa alloys. According to the TEM observations, these anomalies are attributed to two structural transformations, namely P-1 and I++M, where I is an intermediate cubic phase obtained by < l/3 l/3 O> transverse displacement modulations of the parent P phase. The results indicate that the 1-M transition behaves as a first-order phase transition, whereas the P-1 transition features depart from those typical for a first-order transition. Further work should be concerned with the elucidation of the relationship between IF behaviour and the microstructure genesis in these N&MnGa alloys. Acknowledgements-V.A. Chernenko is grateful to the Universitat de les Illes Balears for financing his stay at the Departament de Fisica, UIB. Partial financial support from

the Spanish CICYT (research project MAT93-0188) and DGICYT (PB94-1173) is gratefully acknowledged.

REFERENCES 1. I. N. Vitenko, V. V. Kokorin, V. V. Martynov and V. A.

Chernenko, Martensitic transformations in Heusler alloy-NizMnGa, Preprint IMP 35.89, Kiev, p. 22 (1989). 2. V. V. Kokorin, V. V. Martynov and V. A. Chernenko, Scripta Met. et Mat. 26, 175 (1992). 3. V. A. Chernenko and V. V. Kokorin, Proc. of Int. Conf. on Martensitic Transformations ICOMAT-92 (edited by C. M. Wayman and J. Perkins) p. 1205, Monterey Inst. for Advanced Studies (1993). 4. G. Fritsch, V. V. Kokorin and J. Kempf, J. Phys: Condens. Matter 6, L107 (1994).

5. A. Zheludev, S. M. Shapiro, P. Wochner, A. Schwarz, M. Wall and L. E. Tanner, Phys Rev. B51,11310 (1995) and J. de Physique IV 5, C8-1139 (1995). 6. V. A. Chernenko, E. Cesari, V. V. Kokorin and I. N. Vitenko, Scripta Met. et Mut. 33, 1239 (1995). 7. J. Van Humbeeck, Proc. 9th Int. Conf. on Internal Friction and Ultrasonic Attenuation in Solids (edited by T. S. Ke) p. 337, International Academic Publishers (1989). 8. Z. Xu, Dwight Viehland and D. A. Payne, J. Mater. Res. 10, 453 (1995).

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’

12. J. Stoiber, These, Lausanne, EPFL (1992). 13. W. Ye-Ning, C. Xiao-Hua and S. Hui-Min, Proc. 9th Int. Conf. on Internal Friction and Ultrasonic Attenuation in Solids (edited by T. S. Ke) p. 305, International

Academic Publishers (1989).