Noteworthy, according to data presented in (4) the lattice parameter (hence, the size ... These configurations correspond to the periodic table and are commonly ...
Scripta Materialia, Vol. 40, No. 5, pp. 523–527, 1999 Elsevier Science Ltd Copyright © 1999 Acta Metallurgica Inc. Printed in the USA. All rights reserved. 1359-6462/99/$–see front matter
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COMPOSITIONAL INSTABILITY OF b-PHASE IN Ni-Mn-Ga ALLOYS V.A. Chernenko1 Institute of Magnetism, Vernadsky st. 36, Kiev 252680, Ukraine (Received September 16, 1998) (Accepted in revised form December 12, 1998) Introduction The ferromagnetic Heusler alloys of stoichiometric Ni2MnGa and nonstoichiometric Ni-Mn-Ga chemical compositions though not containing a noble-metal, indeed, belong to b-alloys which lattice stability is decided by the Hume-Rothery mechanism: electron concentration e/a measuring the decrease of the electron energy due to the pseudogap formation and size factor. Like Cu-, Ag- and Au-based alloys they exhibit during cooling a martensitic transformation (MT) from an open bcc L21-type ordered structure to a close-packed ordered structure. This transformation appears as a lattice distortion through the (110) [11# 0] shear with periodic shuffling accompanied by a small volume change (1–3). Due to the thermoelastic nature of MT the Ni-Mn-Ga alloys have been found to exhibit a perfect shape memory and superelasticity effect in a concentration range of each constituent amounting about 10% of variation around the stoichiometric composition (1,3–5). A profound understanding of phase stability and transformation behaviour in this alloy system is important from the fundamental viewpoint since this system can be treated as a model object for studying the soft mode behaviour (6,7), interaction between the magnetic and structural state (8), static long-periodic lattice modulation problem (9), etc. The intriguing feature of Ni-Mn-Ga alloys similarly to Ti-Ni (10), Cu-Al-Be (11) and Ni-Al (12) alloys arises that transformation temperature, Ms, is dramatically dependent on concentration reflecting an extremely high sensitivity of the lattice stability toward the content variation (4). Noteworthy, according to data presented in (4) the lattice parameter (hence, the size factor) is not varied significantly and regularly as a function of content change in Ni-Mn-Ga system unless special alloy modifying is employed (13). It was shown in (13) that the replacement of Ga atoms by isoelectron In atoms having, according to (14), about 15% larger metallic radius was correlated with the lattice parameter increase and resulted in Ms supression down to complete stabilisation of b-phase. The main purpose of present paper is an analysis of previous data (4) concerning the compositional dependence of Ms from the viewpoint of searching for empirical correlation between the electron concentration and stability of b-phase in Ni-Mn-Ga system. This analysis will provide a confirmation of the feasibility of a reasonable explanation of seemingly random collection of alloys grouped with respect to their Ms values as well as other features in the manner suggested in (4). The alloys of compositional range studied in (4) are added here to a few alloys including ones doped with V and Ge
1
Current address: Departament de Fı´sica, Universitat de les Illes Balears, Ctra. de Valldemossa km 7.5, E-07071 Palma de Mallorca.
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TABLE 1. Compositions (in at.%), Martensitic Transformation Temperature (Ms), Curie Temperature (TC) and Electron Concentration (e/a) for Ni-Mn-Ga Alloys Alloy
Ni
Mn
Ga
V
Ge
Ms, K
TC, K
e/a
1 2 3 4 5 6 7
50.6 51.7 50 50 50 52.1 46.3
24.8 21.7 21 19 18 23.9 30.2
24.0 24.7 25 25 25 21.6 23.5
0.6 1.9 4 6 7 — —
— — — — — 2.4 —
152 189 89 67 ,4.2 223 157
380 375 370 363 361 363 380
7.55 7.52 7.42 7.38 7.36 7.60 7.46
to ensure the decisive role of e/a ratio on Ms. Original results about the temperature dependent resistance behaviour are presented as well. Experimental Procedure The Ni-Mn-Ga alloys studied in (4) were treated on the subject of the correlation between the electron concentration and Ms temperature. The Ms vs e/a evolution plotted in the next Section served as a guide for the preparation of alloy series including alloys doped with V and Ge elements to ensure the total basic trend especially in a low-temperature region. The compositions, nominal for the alloys 3–5 and for the other alloys given according to X-ray fluorescence analysis, are presented in Table 1. The polycrystalline ingots of 120 g weight and the specimens for examination were manufactured as described in (4). The low field magnetic susceptibility method was used to determine both the Ms and TC which are given in Table 1. The four-probe resistance measurement technique was used to detect the anomalies produced by phase transformations. Electron concentration (see Table 1 and Fig. 1) was calculated assuming the following configurations of the valence electrons and their number per atom (in brackets): for Ni: core 1 3d84s2 (10); for Mn: core 13d54s2 (7); for Ga: core 1 4s24p1 (3); for V: core 1 3d34s2 (5); for Ge: core 1 4s24p2 (4). These configurations correspond to the periodic table and are commonly used in band calculations of the electron structures for the Heusler alloys (see, e.g., (15)).
Figure 1. Martensitic transformation temperature (Ms) and Curie temperature (TC) for the different Ni-Mn-Ga alloys as a function of electron concentration (e/a). The symbols are the same used in (4) and correspond to the alloys of the different groups listed in (4). Alloys from the Table 1 are labelled by open squares accompanied by their number position in Table 1. Diamonds represent the Curie temperatures of all alloys. Uncertainty for each symbol is shown by horizontal limiting bar.
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Results and Discussion The Ms and TC values measured in present work as well as taken from (4) are plotted as a function of e/a in Fig. 1. It follows from Fig. 1 that the low-temperature Ni-Mn-Ga alloys listed in Table 1 fit fairly well the corresponding data from (4).The alloy 5 from Table 1 and alloys 22 and 23 from (4) do not transform martensitically, so, they are conventionally placed in Fig. 1 at T 5 0 K though this is a rough assumption. The change in Ms with e/a being quite scattered with 6 0.3% uncertainty of element concentration in alloys (4) (shown as the limiting bars in Fig. 1) turned out to have a monotonous increasing dependence, which reflects the deepening of b-phase instability. This dependence consists of two parts which may be represented in a first approximation by straight lines of different slopes. The linear regression analysis yields the slopes of 937 K/(e/a) with R-factor equal to 0.893 and 515 K/(e/a) (R 5 0.831) for low- and high-temperature alloys, respectively. It is worth noting that the low- and high-temperature parts of Ms dependence in Fig. 1, divided by a vertical dotted line, are build up of alloys belonging to Group I (solid circles), Group II (crosses) and Group III (solid triangles), respectively, as they have been classified in (4). Inasmuch as different groups of Ni-Mn-Ga alloys manifest the different transformation behaviour (4,6,9,16) the lines in Fig. 1 may be treated as the quasiequilibrium phase boundaries between the ferromagnetic parent bcc L21-type ordered b-phase (precisely speaking between soft mode condensed phase (6)) and typically 5-layered close-packed tetragonal martensitic phase for low-temperature alloys (2,16) and between paramagnetic bcc L21-type ordered b-phase and high order modulated martensitic structures (9,16) for high-temperature alloys. It is instructive to mention that the imaginative bending point on Ms 5 f (e/a) dependence which is situated near the vertical dotted line in Fig. 1 also appears in close neighbourhood to the cross point with the smeared maximum on ferromagnetic second order transformations line drawn through the diamonds in Fig. 1 and represented by polynomial with R 5 0.749. Experimentally, alloys with Ms , TC (e/a , 7.7, Group I) and alloys with Ms . TC (e/a . 7.7, Group III) show essentially different transformation characteristics than alloys of Group II (e/a > 7.55–7.7) possessing somewhat intermediate position (4,6,9,16). Briefly, the low-temperature alloys including stoichiometric compound Ni2MnGa exhibit soft mode condensation accompanied by the formation of a multi-cell intermediate phase, I-phase, prior to the MT (6,7). The alloys of Group II display the high sensitivity of their crystal structure towards the mechanical stress (5) and magnetic field (17). The transformation behaviour of high-temperature alloys is characterised by two-step MT. So, the phase diagram in Fig. 1 can be further detailed by exposing the line corresponding to the transformations into the I-phase in case of the low-temperature alloys and the line of the intermartensitic phase transformations in high-temperature alloys. The typical r(T) experimental results depicted in Fig. 2 provide the further evidence of the different transformation behaviour between alloys belonging to the different groups. Namely, no anomaly caused by MT in Group I (the low temperature deflection on curve 1, probably, can be related to the soft mode condensation), 5% and 20 –25% change due to MT in Group II and Group III alloys, respectively, are obtained (Fig. 2). The mechanism of the electrical conductivity change in Ni-Mn-Ga alloys can be associated with the difference in scattering on a vibrational motion of the lattice between the parent and martensitic phase and electronic structure reconstruction, particularly, pseudogap onset near Fermi surface. The resistance behaviour near TC when ferromagnetic order present in parent phase (Fig. 2, curves 1 and 2) is typical for Heusler alloys. The TC as well as Ms values marked in Fig. 2 by arrows coincide with the data given in (4). There are no anomalies of r(T) near TC on curve 3 and Ms on curve 1, so these values shown in Fig. 2 were extracted from (4). Thus, resistance measurements are not indicative in looking for the ferromagnetic and martensitic transformations for alloys of Group III and alloys of Group I, respectively.
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Figure 2. Temperature dependence of electrical resistance, r, for polycrystalline Ni-Mn-Ga alloys belonging to different groups and listed in (4) as alloy 3 (curve 1, Group I), alloy 8 (curve 2, Group II) and alloy 17 (curve 3, Group III).
It has been already assumed that the electronic concentration plays an important role not only in stabilizing Heusler structure and defining the magnetic order but also in driving the structural phase transformation in Ni2MnGa (18). The strong dependence of Ms vs e/a (Fig. 1) as well as the formation of different martensitic structures for the different aforementioned critical values of e/a ratios justify such a hypothesis. In terms of band model these critical e/a ratios correspond to the situation when Fermi surface touches the Brillouin zone boundary. In this view of the occupancy of electron states, electrons above the Fermi level move to the corner states of the Brillouin zone. In case of the excessive increasing of energy of system the lattice gets the minimum of the free energy by distortion to accommodate these corner states within a new zone pattern. Moreover, nesting behaviour on Fermi surface as a function of electron concentration can account for the different lattice modulation in Ni-Mn-Ga alloys observed in (2,5,9,16) likewise it was shown for TiPd alloys (19). The various magnitudes of entropy difference, DS, between the initial bcc b-phase and product martensite for the different groups of Ni-Mn-Ga alloys can be inferred using the transformation heat data (Q) presented in (4). The calculated entropy change falls around two values: DS ' 8 z 1023 J/gK and DS ' 1.4 z 1022 J/gK for Group I and Group II alloys, respectively, reflecting the different martensitic structures (2,20) they exhibit. The martensitic structures arising in Ni-Mn-Ga system still remains a subject of current and future studies. Actually, in the high-temperature alloys studied by electron microscopy four martensites have been detected so far (9). Therefore MT in Group III alloys is accompanied by DS which varies considerably throughout this group (4). In b-phase Cu-Al-Mn alloys, for instance, it was experimentally shown as well that e/a ratio determines the low-temperature phase which develops, so that, at e/a # 1.45 and e/a $ 1.47 fcc- and hcp-type close-packed martensitic structures are formed, respectively (21). Besides, it was found that the entropy difference DS controlling the b-phase stability depends only on resulting martensitic structure and has a vibrational origin with the main contribution arising from the low-lying acoustic transversal TA2 phonon branch. Bearing in mind the experimental observation of the presence of intense diffuse streaking on the electron diffraction patterns for all the groups of Ni-Mn-Ga alloys and low values of shear elastic moduli in parent phase (3,9) the same considerations concerning the nature of b-phase instability can be applied for Ni-Mn-Ga system. So, increasing of e/a results in change of martensitic crystal structure. This change gives rise to the increase of difference in densities of vibrational states between b-phase and corresponding martensite. Apparently, the reconstruction of phonon spectrum for the different martensites can produce the different values of resistance anomaly as was observed experimentally (Fig. 2).
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Conclusions The correlation between the electron concentration of Ni-Mn-Ga alloys and their transformation behaviour and transformation characteristics has been empirically established whereby giving evidence to classification proposed in (4) and introducing an order in a seemingly chaotic distribution of chemical concentrations responsible for the continuous evolution of transformation temperatures. The growing of b-phase instability towards the close-packed martensitic phases while electron concentration increments is inherent for this alloy system. Increasing of electron concentration was experimentally shown to induce increasing of both electrical resistance and entropy discontinuities at MT, thus, confirming the growing of the first order character of MT. Acknowledgments The author is grateful to the DGES (SAB 1995-0640) for financing his stay at the Departament de Fı´sica, UIB. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
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