The ferromagnetic shape memory system Fe–Pd–Cu

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Acta Materialia 58 (2010) 5949–5961 www.elsevier.com/locate/actamat

The ferromagnetic shape memory system Fe–Pd–Cu S. Hamann a, M.E. Gruner b, S. Irsen c, J. Buschbeck d, C. Bechtold e, I. Kock f, S.G. Mayr f,g, A. Savan a, S. Thienhaus a, E. Quandt e, S. Fa¨hler d, P. Entel b, A. Ludwig a,* a Institute of Materials, Faculty of Mechanical Engineering, Ruhr-University Bochum, 44801 Bochum, Germany Faculty of Physics and Center for Nanointegration, CeNIDE, University of Duisburg-Essen, 47048 Duisburg, Germany c Forschungszentrum caesar, Electron Microscopy, 53175 Bonn, Germany d IFW Dresden, P.O. Box: 270116, 01171 Dresden, Germany e Inorganic Functional Materials, Christian-Albrechts-University, 24143 Kiel, Germany f I. Physikalisches Institut, Georg-August-University Go¨ttingen, 37077 Go¨ttingen, Germany g Leibniz-Institut fu¨r Oberfla¨chenmodifizierung eV, Translationszentrum fu¨r regenerative Medizin und Fakulta¨t fu¨r Physik und Geowissenschaften, University Leipzig, 04318 Leipzig, Germany b

Received 2 February 2010; received in revised form 2 July 2010; accepted 4 July 2010 Available online 30 July 2010

Abstract A new ferromagnetic shape memory thin film system, Fe–Pd–Cu, was developed using ab initio calculations, combinatorial fabrication and high-throughput experimentation methods. Reversible martensitic transformations are found in extended compositional regions, which have increased fcc–fct transformation temperatures in comparison to previously published results. High resolution transmission electron microscopy verified the existence of a homogeneous ternary phase without precipitates. Curie temperature, saturation polarization and orbital magnetism are only moderately decreased by alloying with nonmagnetic Cu. Compared to the binary system; enhanced Invar-type thermal expansion anomalies in terms of an increased volume magnetostriction are predicted. Complementary experiments on splat-fabricated bulk Fe–Pd–Cu samples showed an enhanced stability of the disordered transforming Fe70Pd30 phase against decomposition. From the comparison of bulk and thin film results, it can be inferred that, for ternary systems, the Fe content, rather than the valence electron concentration, should be regarded as the decisive factor determining the fcc–fct transformation temperature. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ferromagnetic shape memory alloys; Combinatorial methods; Ab initio calculations; Martensitic transformations; Invar effect

1. Introduction Since the discovery of the 10% magnetic-field-induced strain (MFIS) effect in Ni–Mn–Ga Heusler alloys [1,2], ferromagnetic shape memory alloys (FSMAs) have become a subject of intense scientific and technological interest [3,4]: although the necessary magnetic fields are higher compared to giant magnetostrictive materials, the MFIS of FSMA is more than one order of magnitude larger. The underlying mechanism of MFIS is based on a reorientation of martensitic variants which align their magnetic easy axis paral*

Corresponding author. Tel.: +49 234 32 27492. E-mail address: [email protected] (A. Ludwig).

lel to an external field. The basic requirements for MFIS are a substantial magnetocrystalline anisotropy in the martensite state, and a high mobility of martensitic twin boundaries. While MFIS can be observed in Ni–Mn–Ga near room temperature, for technical applications of FSMAs in sensor and actuator systems (e.g., for automotive industry) the development of new materials with improved properties is necessary. Development goals are materials with high transformation temperatures (martensite start temperature MS > 373 K), high Curie temperature (TC > 670 K), high magnetic saturation polarization (JS > 1 T) as well as high magnetocrystalline anisotropy. For reaching these goals, Fe-based alloys are promising. In Fe-rich alloys like metastable Fe70Pd30 [3] and Fe3Pt [5],

1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.07.011

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FSMA behavior is observed in a concentration range close to the onset of the martensitic instability (around 65– 75 at.% Fe), which is also known for magneto-volumetric anomalies such as the so-called Invar effect [6,7]. Fe70Pd30 shows a high TC of about 600 K and a saturation polarization of 1.5 T in the martensite phase [8], which is significantly higher compared to the Ni-based alloys. While Fe has a body centered cubic (bcc) structure at low temperatures, the ground state of ferromagnetic Febased alloys changes to face centered cubic (fcc) if the valence electron concentration e/a reaches values between 8.5 and 8.7. The consequence of this is a martensitic transformation from a face centered to a body centered cubic lattice taking place at finite temperatures. As a general trend in these alloys, it is observed that transformation temperatures increase with decreasing e/a. The compositional influence on the martensitic transition is often characterized in terms of e/a, i.e., the changing filling of the d-band, which also appears to work well for Ni- and Co-based Heusler FSMA [9]. In Fe-based FSMA, a slightly distorted face centered tetragonal (fct) intermediate phase appears between austenite and the ground state martensitic phase [8,10]. This phase provides the essential high mobility of twin boundaries in combination with significant magnetocrystalline anisotropy. For bulk Fe70Pd30, however, the largest MFIS of 3% is reported only for low temperatures of 77 K [5]. This is due to the comparatively low austenite start temperature (AS), in combination with the continuous decrease of tetragonality on approaching the martensitic transformation. A substantial increase of the transformation temperature of the martensitic transition is therefore a primary milestone on the way towards technological application. To achieve this, alloying with a third element is a promising route. The origin of the fcc–fct transition in binary Fe–Pd FSMA was linked by Opahle et al. [11] to a band-Jahn– Teller mechanism arising from a degeneracy of electronic states right at the Fermi level. Decreasing the symmetry by a tetragonal distortion lifts this degeneracy and leads to an effective gain in band energy of 14 meV atom1. A contribution of this size can influence the free energy in the vicinity of a martensitic transformation, where the energy landscape is supposed to be flat. Experimental evidence for such a flat energy landscape originates from the epitaxial growth of Fe70Pd30 on substrates with different misfits [12]. This allowed the stabilization of tetragonally distorted films, covering most of the Bain transformation path between bcc and fcc structure and is only possible if the corresponding elastic strain energy is very small. The importance of Fe states at the Fermi level is also underlined by another recent study of anomalies in the lattice dynamics of ordered Fe3Pt and Fe3Pd alloys [13]. In these systems, softening of the TA1 phonon branch in the [1 1 0] direction can be related in a similar fashion to a large density of Fe states at the Fermi level, which enables structural changes at low temperatures. The resulting transformation can be understood as an orthorhombic distortion of regu-

lar Fe octahedra embedded in a simple cubic matrix of the Pt-group elements. Softening of the TA1 [1 1 0] phonons in the austenitic phase is a common anomaly present in SMA and is frequently regarded as a precursor to the martensitic transformation. In ordered Fe alloys, the distortions arising from these phonon modes are accompanied by an extensive reconstruction of the Fe-dominated parts of the Fermi surface which can be interpreted in the framework of a Kohn anomaly. This suggests a scenario in which the electronic instability related to the distortions is originating from the local electronic states of clusters of Fe atoms in a specific surrounding. In consequence, the thermoelastic transition would de facto be determined by the Fe content, while a suitable e/a ratio might be required to keep the responsible electronic states close to the Fermi level. For binary alloys, it is difficult to decide if the e/a ratio or the Fe content is decisive for the martensitic instability, since both parameters are equivalent. In ternary alloys this is, however, in general not the case and the influence of the Fe concentration on the formation of the fct phase might be separable in a systematic fashion from the dependency on the total valence electron concentration. Although the strategy to substantially improve the shape memory properties of Fe–Pd by alloying additional components is a straightforward idea, corresponding efforts were rather sparse up to now. The first reported attempt to systematically understand the influence of a third component in terms of the valence electron concentration was presented by Tsuchiya et al. [14], who reported the change of transition temperatures for Fe–Pd–X alloys by the addition of Co and Ni. In the ternary systems, the fcc–fct transition line is shifted to higher values of e/a, while upon addition of a few at.% Co, slightly higher transformation temperatures have been achieved. This was not confirmed by later experiments on melt-spun ribbons by Vokoun et al. [15], who were, on the other hand, investigating samples with smaller Pd content than Tsuchiya et al. Sa´nchez-Alarcos et al. [16] reported that replacement of 3 at.% Fe by Co in a Fe70Pd30 alloy decreases both the thermoelastic fcc–fct and the irreversible fct–bct transition temperatures, but effectively increases the temperature range of MFIS. Vokoun et al. also found that the substitution of Pd with Pt, which along with Ni is isoelectronic to Pd, also decreases the transformation temperatures in Fe70Pd(30X)PtX (0 < X < 8 at.%), in agreement with previous experiments by Wada and co-workers [17]. Recent combinatorial investigations of Fe–Pd thin films alloyed with Mn showed an increase of MS [18], while corresponding investigations of the ternary bulk system revealed that also small Mn additions favorably affect the non-thermoelastic fct–bct transition [19]. Previous combinatorial experiments by other groups concentrated on the structural mapping of the ternary Fe–Pd–Ga system, which provides a combination of two alloys with extraordinary magnetostrictive properties [20]. Additional studies are also available for Fe–Pd–Rh [21,22], however without providing conclusive information concerning the stability range of

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the fct phase. Several of these studies were also measuring the change of magnetic properties. Ref. [14], for instance, reports an increased saturation magnetization, in comparison to binary Fe70Pd30 [23] for Fe–Pd–Co and Fe–Pd–Ni, while it is decreased on addition of potentially antiferromagnetically interacting Mn [19]. Calculations of ordered L12 Fe3Pd(Pt) predict a strongly increased magnetocrystalline anisotropy energy for the ternary system [24]; this, however, was not reproduced experimentally, which the authors traced back to prevailing disorder. In fact, a later investigation proved disorder to affect even the easy direction of magnetization [25]. In the present investigation, we use the fcc element Cu as the third alloy component into the Fe–Pd-based FSMA, in order to (a) vary the e/a ratio, (b) change the volume of the unit cell, and (c) eventually stabilize the metastable and disordered Fe70Pd30 phase against decomposition. Generally, with increasing Cu content the e/a ratio is supposed to increase, as Cu has more valence electrons than either Pd or Fe. However, by increasing the Fe content at the expense of Pd, also smaller e/a ratios less than 8.6 can be achieved. This allows an increase of the Fe content while keeping e/a constant. Cu is known to form stable compounds with Pd and metastable compounds with Fe and thus their potential formation must be considered as well [26]. The addition of Cu into Fe–Pd was previously attempted by Kang and Ha [27] to enhance (1 0 0) orientation in thin films and to accelerate L10 ordering for lowering the annealing temperatures. The authors found that Cu preferentially substitutes for Fe and induces a (0 0 1) texture within thin films. Due to the smaller atomic radius of Cu compared to Pd, a change of the volume of the unit cell can also be expected. Furthermore, Cu can act as an austenite (fcc) stabilizer in the ternary alloy. Stabilization of the parental austenite Fe70Pd30 phase would simplify fabrication of Fe–Pd-based FSMA due to the decreased driving force of decomposition of the disordered fcc Fe70Pd30 phase to the stable L10 Fe50Pd50 and Fe(Pd)bcc phases known from the equilibrium phase diagram. Thus alloying of Fe70Pd30 with Cu could lead, apart from a better understanding of the relevant parameters, to a new ternary FSMA with enhanced intrinsic properties. In order to clarify the composition– structure–property relations in new FSMA systems such as Fe–Pd–Cu, a multitude of well-defined and comparable samples are needed. This is the strength of combinatorial and high-throughput technologies [28], which allow the influence of Cu alloying on Fe–Pd-based FSMA to be efficiently investigated. 2. Experimental 2.1. Fabrication and characterization of Fe–Pd–Cu samples Fe–Pd–Cu materials libraries covering compositional areas of interest within the ternary Fe–Pd–Cu system were fabricated using a combinatorial magnetron sputtering system (CMS 600/400LIN, DCA). The composition spreads

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were prepared by co-sputtering from elemental targets (100 mm diameter, purity 99.99%, focal point at the middle of the substrate, 45° tilt, target-substrate distance 185 mm) on thermally oxidized 400 Si substrates [28]. The 1.5 lm thick SiO2 layer acts as a diffusion barrier between Fe– Pd–Cu films and Si during later annealing. The base pressure before deposition was <4.8  105 Pa. Pd and Cu were sputtered in rf mode while Fe was sputtered in dc mode on the unheated substrate with an Ar pressure of 0.665 Pa. Fe–Pd–Cu thin films had a thickness between 280 nm and 400 nm depending on the measurement location due to the complex pattern of intersecting thickness wedges coming from each tilted source (sputter time 5500 s). A lift-off process was used to structure the films into an array of discrete 3 mm  3 mm squares. After deposition, the materials libraries were annealed in a furnace (Schmetz IU 54 1F) at 1123 K for 1 h under N2 atmosphere at 80 kPa and then quenched from 1123 K to room temperature in N2 overpressure (40 kPa) with a cooling rate of approximately 15 K s1 to achieve the metastable transforming phase and to avoid decomposition. This procedure was verified by prior experiments with Fe70Pd30 thin films. Additionally, bulk samples of selected compositions identified by thin film screening were fabricated by splat quenching. Ingots were prepared by arc melting in an Ar atmosphere and homogenized by turning them over and remelting them six times. Subsequently, the ingot was divided into samples of about 0.18 g each, which were remelted in the arc melter to form small spheres for splat quenching [29,30]. The samples were melted inductively in Ar (60 kPa) and subsequently projected between two Cu pistons, leading to rapid solidification of splats having a thickness of about 60 lm. These were annealed at 1123 K for 1 h and cooled with different rates. Sample compositions were determined by automated energy dispersive X-ray spectroscopy (EDX) using a Zeiss Supra 55 FEG-SEM equipped with an Oxford Inca system. The accuracy is <1 at.% after calibrating the system with an Fe70Pd30 standard. In order to identify transforming compositions in annealed Fe–Pd–Cu thin films, measurements of the temperature-dependent electrical resistance, R(T), in the range from 253 K to 443 K, were performed using an automated high-throughput test stand [31]. From such R(T) curves, transformation temperatures (error <5 K) were deduced using the tangential method [32]. For microstructural investigations, automated X-ray diffraction (XRD) was performed using a Bruker-AXS system (area detector, Cu Ka, spot size 0.5 mm, integration time 300 s, 2H area range from 35° to 65°). Temperature-dependent X-ray diffraction, XRD(T), in the range from 253 K to 373 K (10 K steps) was used to verify and analyze martensitic transformations and transition temperatures determined by R(T) measurements. During XRD(T), the temperature was measured with a NiCr–Ni thermocouple (error <0.5 K). Low-temperature measurements were conducted using an evacuated Be dome to prevent ice formation on the samples

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(chamber pressure <0.15 Pa). An additional measurement at 293 K was performed in air without the Be dome to identify peaks originating from the dome itself. Magnetization measurements were conducted using a Physical Property Measurement System (PPMS, Quantum Design) equipped with a temperature-dependent vibrating sample magnetometer (VSM) unit. For this measurement, the materials library was cut into 4.5 mm  4.5 mm pieces, which were glued to a quartz sample holder. Saturation polarization was extracted from in-plane hysteresis measurements, performed in a field range from 2 kOe to 2 kOe (25 Oe s1 sweep rate) in the martensite (243 K) and the austenite (393 K) state. The Curie temperature, TC, was determined from temperaturedependent magnetization measurements between 315 K and 500 K (sweep rate 10 K min1) in an applied magnetic field of 0.5 kOe using Kuz’min’s fit [33]. A Zeiss Libra 200 (CRISP) transmission electron microscope (TEM) was used for high resolution imaging and spectroscopic analysis. Cross-sectional TEM lamellae were prepared by a 5 kV Ga-Ion focused ion beam (Zeiss XB1540 Workstation (FIB)) and afterwards polished with 500 eV Ar ions using a low voltage Ar gun (PHI-AES970). Compositional depth profiles within the thin films were measured using a scanning Auger microscope (PHI-AES970) having an error <1 at.%.

LMU Munich [34,35]. The calculations employed the generalized gradient approximations (GGA) for the description of the exchange correlation potential in the formulation of Perdew et al. [36]. Separate calculations were carried out for all compositions exhibiting martensitic transformations as determined in the experiments. For each composition, the equilibrium lattice constants for the austenite ferromagnetic and magnetically disordered configuration were determined; the latter was simulated by mixing Fe species of different spin orientations by means of CPA, in spirit of the disordered local moment approach [37,38]. Furthermore, spin and orbital magnetic moments were obtained assuming a ferromagnetic spin configuration as the ground state. In the angular momentum expansion, orbitals were included up to lmax = f states; 1639 irreducible k-points were used for the Brillouin zone integration. In a separate calculation, magnetic exchange parameters were determined for use within a Heisenberg model [39]. From this we obtained Curie temperatures within the mean-field approximation, which allows a comparison of compositional trends between theory and experiment. 3. Results and discussion 3.1. Structural behavior of Fe–Pd–Cu alloys

2.2. Ab initio calculations of disordered Fe–Pd–Cu alloys In order to obtain a characterization of the basic magnetic and magnetoelastic properties which are difficult to access using the present experimental setup, first-principles calculations in the framework of density functional theory (DFT) were performed. The calculations were carried out with the Korringa–Kohn–Rostoker Green-function method (KKR) in connection with the atomic sphere approximation (ASA) and the coherent potential approximation (CPA) for the description of configurational disorder, as implemented within the fully relativistic SPR–KKR package from

The measured compositions of the ternary Fe–Pd–Cu materials libraries are depicted in a partial composition diagram in Fig. 1a (600 samples). Open light grey circles represent compositions measured by EDX, while the black lines indicate the calculated e/a ratios of the respective samples. Filled circles represent all samples showing a thermoelastic non-linearity in the R(T) measurement, with the martensite start temperature being indicated by colour coding. The composition area investigated is centered around Fe70Pd30 (from Fe40 to Fe94) with variation of Cu from 1 to 18 at.%. In order to identify compositions showing

Fig. 1. (a) Partial Fe–Pd–Cu composition diagram showing the compositional area covered by the materials libraries. Constant e/a ratios are defined by black lines. Light grey circles denote the fabricated samples of the materials libraries. Transforming samples are indicated by filled circles, with colourcoding indicating the martensite start temperature MS. (b) Example R(T) curve of the transforming sample Fe71.8Pd26.6Cu1.6. The determination of transformation temperatures by the tangential method is indicated. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

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phase transformations, all compositions were tested by R(T) screening. Fig. 1b shows an example R(T) curve from the sample Fe71.8Pd26.6Cu1.6, which indicates a phase transformation due to its non-linear S-shaped R(T) curve, from which transformation temperatures were determined by the tangential method [32]. In order to assign the observed non-linearities in the R(T) curves to a martensitic transformation, XRD(T) was performed. Fig. 2 shows an example of the XRD(T) data for the sample Fe71.8Pd26.6Cu1.6. At 253 K (1 1 1) and (2 0 0) fct reflections are observed, as expected for a polycrystalline martensitic structure comparable to binary Fe70Pd30 [40]. No additional peaks are observed, which indicates the absence of large precipitates. With increasing temperature, the (1 1 1) fct peak does not change; instead the (2 0 0) fct peak decreases while the (2 0 0) fcc peak starts to grow, starting at approximately 293 K. With further increasing temperature, the (2 0 0) fcc peak continues to increase in intensity up to 343 K. For temperatures above 343 K, no further growth of the (2 0 0) fcc peak is observed. Thus, martensitic transformation temperatures deduced from non-linearities in the R(T) measurement is confirmed by the structural analysis. The transformation temperatures determined by these methods showed no significant differences. In order to determine the (micro-) structure of the samples, room temperature XRD mapping of the Fe–Pd–Cu samples was performed. Fig. 3a shows the ternary Fe– Pd–Cu composition diagram, indicating all investigated compositions. Transforming compositions are colour coded according to their martensite start temperature, MS, while the symbols classify the occurring phases. The squares in Fig. 3a define single phase compositions showing a non-linearity in the R(T) measurement. Diamonds designate multi-phase samples where the transforming Fe70Pd30 phase dominates but additional precipitate phases occur and are thus not considered further. The dark grey triangles represent samples having a Fe50Pd50 structure with additional Fe–Cu and Pd–Cu precipitates. For Fe concentrations above 72.5 at.% only a bcc structure and precipitate phases (a-Fe, Fe–Cu and Pd–Cu) are present

(light grey circles). Open squares indicate samples having a Fe70Pd30 austenite phase with additional Fe–Cu and Pd–Cu precipitates present at larger Cu contents, and not showing a non-linearity in R(T) measurement. All single phase compositions are located in a zone with Fe content between 69 and 72 at.%, while the Cu content increases from 1 to 5 at.%. Due to the region, defined by transforming samples, a substitution of Cu for Pd is assumed. Samples with Cu contents <5 at.% transform up to a maximum Fe content of 72 at.%. For binary films an expansion of the transforming region from Fe70Pd30 to Fe72Pd28 was previously observed [41]. However, in the ternary system, we observe a considerably larger maximum MS = 359 K for compositions around Fe71.8Pd26.6Cu1.6. In order to understand how Cu alloying into the Fe–Pd system affects the structure, a binary cut was defined through the ternary composition diagram (blue arrow). Along this line, Cu and Pd contents vary, while the Fe content remains constant at 70 at.%. Fig. 3b illustrates the structural change of these samples, in the form of a colour coded (red = high intensity, blue = low intensity) top view on the diffraction patterns. A martensitic structure with (1 1 1) and (2 0 0) peaks is observed at room temperature up to 6 at.% Cu. No additional peaks, e.g., from precipitate phases, are observed. For Cu contents above 6 at.%, a (1 1 0) bcc phase occurs in addition to the transforming fct/fcc phase. At 8 at.% Cu, the (1 1 0) Fe8Cu2 peak appears. Due to composition change, a slight shift of the (1 1 1) fct/fcc peak is observed over the whole range of Fig. 3b. While austenitic Fe70Pd30 exhibits a lattice constant of a = 0.3756 nm [8], alloying with small amounts of Cu should cause this to change. The lattice constant a of the austenite fcc phase was determined from the (2 0 0) fcc peak for selected Fe–Pd–Cu samples using XRD at 373 K. Fig. 4 presents lattice constants determined from experiments (black) and calculation (red)1 for selected Fe–Pd–Cu samples having constant Fe contents (Fe70: squares; Fe71: triangles; Fe72: circles), while the inset shows the locations of the experimental samples in the ternary composition diagram. Since the atomic radius for Cu (0.128 nm) lies between that of Fe (0.126 nm) and Pd (0.137 nm), a decrease of lattice constants with adding small amounts of Cu should occur [42]. As expected, the lowest lattice constant is observed for samples with the smallest Pd and highest Cu content. However, the lattice parameters of the Fe–Pd system are known to deviate from Vegard’s law [43] and at elevated temperatures the Invar behavior of Fe–Pd leads to a significant reduction of the thermal expansion coefficient in a broad range of temperature. In fact, the calculated values for a (determined for the ferromagnetic ground state) are slightly higher than the lattice constants measured experimentally. Since calculations represent the state at 0 K and measurements were performed up to 373 K, this is opposite to what one would

Fig. 2. XRD(T) of the sample Fe71.8Pd26.6Cu1.6 measured between 253 K and 373 K.

1 For interpretation of colour in Fig. 4, the reader is referred to the web version of this article.

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Fig. 3. (a) Partial ternary diagram of the Fe–Pd–Cu system showing the distribution of phases (symbols) and the transforming compositions (MS colour coded). The blue arrow indicates a constant Fe content. Diffractograms along this composition are summarized in (b). For Cu > 6 at.% the transforming fct/fcc structure decomposes into a bcc structure with Fe8Cu2 precipitates.

expect from normal thermal expansion and thus another indication for the presence of Invar-related anomalies in the films. This observation is of importance for the interpretation of the influence of substrate-induced stress on the martensitic transformation and will be discussed in detail in Section 3.4. 3.2. Transmission electron microscopy

Fig. 4. Calculated and experimentally determined lattice constants for fixed Fe contents (70–72 at.%) in dependence of Cu. Inset: lattice constants a of the fcc cubic austenite phase (measured at 373 K) for single phase transforming Fe–Pd–Cu samples within the composition diagram.

Transmission electron microscopy was used to confirm the existence of a single ternary phase in the sample Fe69.5Pd26.7Cu3.8. The prepared lamella (not shown) consist of the following layers: SiO2 substrate layer, a thin FeOx diffusion layer, the homogeneous Fe–Pd–Cu layer and a Pt-protection layer deposited during FIB preparation. The thin oxidized Fe layer at the film–substrate interface is related to diffusion effects during annealing and has a

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Fig. 5. High resolution transmission electron microscope (HRTEM) image shows twinned lattice planes of the Fe–Pd–Cu film. The inset shows the fast Fourier transform revealing the twinned microstructure.

thickness of approximately 40 nm. The grain structure of the layer, revealed by diffraction contrast, verified a homogenous chemical composition in the Fe–Pd–Cu layer. Fig. 5 shows the HRTEM image of a selected region of the Fe–Pd–Cu layer. The martensitic twin structure can be seen in the lattice image as well as on the fast Fourier transform (inset in Fig. 5). Summarizing these results, Cu is homogeneously dissolved in the Fe–Pd matrix. In the investigated area, no composition or phase segregation was detected. These results were confirmed by Auger-electron spectroscopy depth profiles (not shown). 3.3. Magnetic properties of Fe–Pd–Cu alloys Since determination of magnetic anisotropy is hampered by the polycrystalline microstructure of the present films,

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our experimental investigation concentrate on the other key properties, saturation polarization, JS, and Curie temperature, TC. In Fig. 6a, saturation polarization as a function of Cu content (colour coding indicates the Fe content) is presented for both the martensitic (squares, determined at 243 K) and the austenitic (triangles, determined at 393 K) structure. Error bars indicate a maximum variance <5% of JS. Generally, we find a saturation polarization for Fe–Pd–Cu samples which is about 10% lower than for Fe70Pd30 (1.5 T for martensite and 1.35 T for austenite phase [8]). The higher JS of the martensite phase compared to the austenite reflects the expected decrease of spontaneous magnetization with increased thermal fluctuations. For both martensite and austenite, JS has a general tendency to decrease with increasing Cu content, which is in agreement with the composition dependence of the ground state magnetic moments obtained from ab initio calculations. However, for Cu contents from 5 to 6 at.% the experimental JS values increase abruptly to a maximum of 1.1 T for the austenite and 1.35 T for the martensite phase. Although a direct evidence of precipitates was not observed with XRD, the rather unexpected increase of JS indicates that the formation of small precipitates below the sensitivity of XRD already starts at 5 at.% Cu. Below 5 at.% the homogeneous solution of Cu, which has a filled d-shell and thus shows only a negligible induced spin-polarization in the order of 0.08 lB, decreases magnetization. At Cu contents between 5 and 6 at.%, decomposition of the Fe– Pd–Cu sample into a Fe70Pd30 phase with a high JS and Cu-rich precipitate phases results in the overall increase of magnetization. When Cu content >6 at.% the volume fraction of non magnetic precipitates increases and thus leads to decrease JS. This agrees well with observations for the Fe–Pd–Cu splats with a Cu content >5 at.% presented in Section 3.5. Fig. 6b shows the experimentally determined and calculated Curie temperatures, TC, as a function of the Cu content, which are in both cases pre-

Fig. 6. (a) Saturation polarization for both the martensite fct and austenite fcc phase determined at 243 K and 393 K, respectively, in comparison to the calculated ground state total (spin + orbital) magnetic moments, for selected compositions along the path marked in Fig. 3. The straight line through the experimental data is shown to illustrate the deviations from a simple behavior. (b) Normalized Curie temperature TC in dependence of Cu content determined by calculation and experiments.

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sented relative to TC of binary Fe70Pd30. Experimentally, TC was extrapolated from a fit of the temperature dependence of saturation curves to Kuz’min’s parameterization [33,34,44]. Because accurate results cannot be achieved by a simultaneous fit of the shape parameters s and p and the critical exponent of the magnetization b, while determining the spontaneous magnetization M0 and TC by extrapolating the magnetization curve, we restrict the values to s = 1, p = 5/2 and b = 1/3 as determined previously in Ref. [12] for a larger temperature interval. The choice of a large value s = 1 (also valid for other 3d transition metals) is consistent with the largely decreased spin-wave stiffness of Fe–Pd alloys reported in the vicinity of the fcc–fct transition [45]. It should also be noted that the calculated TC are systematically too large on an absolute scale, since we used the mean-field approximation to the Heisenberg model, which furthermore neglects Invar-typical longitudinal spin fluctuations. Nevertheless, both approaches show the same trend – a slight decrease as a function of composition for Cu concentrations below 4 at.%. This is again expected from the dilution of the magnetic sites by the Cu-atoms, but it obviously does not lead to a severe degradation of the magnetic properties, which could jeopardize the FSMA properties. Between 4 and 5 at.% Cu, a kink to lower TC/TC(Fe70Pd30) ratios is observed in the experimental data – similar to the anomaly in the magnetization presented in Fig. 6a. This kink is again attributed to the decomposition of the single ternary phase into a multiphase structure for Cu > 5 at.%. The highest TC of 560 K for a single phase is observed at a composition with 72 at.% Fe. This value is slightly lower compared to 600 K for Fe70Pd30 [30]. Samples having a Cu content of 5 at.% exhibit a smaller TC – but following the previous arguments this is very likely attributed to the formation of a complex phase mixture. In addition, we expect uncertainties originating from slight changes of the composition due to the limited accuracy of the EDX measurements and the formation of interfacial layers. Decisive for a large MFIS is a strong coupling between the orientation of magnetic moments and the tetragonal distortion of the martensitic twins, which usually arises from spin–orbit coupling. This can be quantified in terms of the magnetocrystalline anisotropy energy, which is connected to the change of orbital moments upon variation of the magnetization direction. These quantities are particularly difficult to measure in a high-throughput approach and therefore further experimental characterization of orbital magnetism of the Fe–Pd–Cu system must be left for future work. Fully relativistic first-principles calculations as employed in our investigation, however, provide an easy and straightforward approach to grasp the principal trends on related quantities, such as orbital moments with composition. Fig. 7 provides the variation of the total orbital moment per atom for all compositions of interest. The obtained variations are small and at the limits of the methodological resolution. Nevertheless, a few discernable trends are discussed below. The total orbital moment of the

Fig. 7. Total orbital moments lorb of Fe–Pd–Cu as a function of composition obtained from first-principles calculations. Only moderate variations of lorb are encountered within the martensitically transforming concentration range.

binary reference composition Fe70Pd30 is with 0.054 lB atom1 among the largest values for the considered concentration range and thus it can be concluded that addition of Cu is not likely to improve the magnetocrystalline anisotropy of the material. Slightly larger values are only obtained for compositions with an Fe content of about 72 at.% and low Cu content. The Fe species provide the largest orbital moment of about 0.065 lB atom1 with an overall variation on the order of 1%. Thus, changes of its fractional contribution according to composition will provide the most relevant trend. The Pd atoms exhibit an orbital moment of about 0.025 lB atom1 (with variation of 5% over all compositions), which is proportional to the magnitude of the Pd-spin moment. The latter, in turn, is induced by the surrounding Fe moments. This raises the expectation that a large Fe content should have a beneficial influence on the magnetocrystalline anisotropy, since it is commonly traced back to the hybridization of the 3d and 4d electrons in this alloy. Cu exhibits only a small induced moment, which is connected with a rather tiny orbital contribution of the order of 0.01 lB atom1. 3.4. Substrate-induced stress and Invar effect In comparison to bulk samples, the thin films exhibit considerably higher transformation temperatures, regardless of their composition. This can partly be attributed to the high stress state of the films due to different thermal expansion coefficients of thin film and substrate. It is known that Fe–Pd FSMA thin films on SiO2 and MgO substrates are subject to high tensile stresses [46–49]. These lead to stress-induced martensitic transformations at systematically increased transformation temperatures. Kato et al. [50] estimated a proportionality factor of 4.8 MPa K1 for the Fe–Pd system. From other experiments on Fe70Pd30 thin films fabricated and processed in a similar way as in the present study, tensile stresses in the range of 200–300 MPa after annealing were observed [46]. This value, however, is

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sensitive to the composition and decreases systematically with increasing Fe content [51]. This behavior was attributed to the Invar effect, i.e., the anomalous reduction of thermal expansion which is also present in Fe–Pd alloys in this composition range. The Invar effect originates from a thermodynamic repopulation of electronic configurations, which are characterized by different local magnetic moments and equilibrium volumes. This effect becomes increasingly prominent for Fe-rich compositions [52] and may even lead to negative thermal expansion coefficients. The Invar properties of the ternary alloy are – apart from the changing Fe content – also influenced by Cu addition. As measurements of thermal expansion coefficients are difficult in film/substrate composites, we calculated the spontaneous volume magnetostriction, xs0, to give a qualitative indication. The quantity xs0 is defined as the relative change (VFM–VPM)/VPM between the volume VFM of the ferromagnetic phase and the volume VPM of the paramagnetic phase, both extrapolated to T = 0. Alternatively, xs0 can be interpreted as the relative volume expansion induced by the onset of ferromagnetism below TC, which is measured in comparison to a (hypothetical) reference alloy which remains paramagnetic at all temperatures. Fig. 8 shows the variation of xs0 as a function of the ternary composition, demonstrating an increase of up to 10% with Fe concentration as the dominating trend in the transforming composition range. As a secondary trend, at constant Fe content, we observe an increase of xs0 with increasing Cu concentration, which is in the opposite direction in terms of the resulting valence electron concentration e/a. This clearly demonstrates that the moment–volume interaction in the ternary system cannot be consistently interpreted as a function of e/a alone. We rather conclude that increasing Fe as well as Cu content will enhance the Invar-typical anomalies and thus further reduce thermal expansion and elastic constants below TC. Thus, the addition of Cu can be expected to further decrease the tensile stress compared to a binary film with the same Fe content.

Fig. 8. Calculated spontaneous volume magnetostriction xs0 of Fe–Pd– Cu as a function of composition. A clear increase of xs0 of about 10% is encountered for increasing Fe concentrations.

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3.5. Fe–Pd–Cu splats In order to transfer and confirm results from the thin film materials libraries to bulk-like samples, Fe–Pd–Cu splats were fabricated, processed and investigated. The samples were produced by the splat quenching technique (with a cooling rate of 106 K s1) to obtain thin foils in a metastable phase and to avoid demixing during cooling. It is known that a high cooling rate is beneficial for the formation of the fct phase [23]. The splats were post-annealed to improve their microstructure and transformation behavior. The influence of quenching and post-annealing on binary Fe–Pd splats was described by Kock et al. [53]. Fig. 9 presents room temperature XRD data of different splats with the nominal compositions of Fe70Pd30, Fe68.4Pd29.3Cu2.3 and Fe70Pd23.8Cu6.2. All splats were annealed at the same temperature and time (1123 K, 1 h) as used for the thin film materials libraries. In order to investigate the stability of the metastable phase in the Fe–Pd–Cu splats, cooling rates were varied and compared with the results from Fe70Pd30 splats. For rapid cooling (>100 K s1), the splats, which were sealed in quartz tubes under inert gas, were water-quenched. For slow cooling, the splats were cooled in air (<0.5 K s1), while for very slow cooling the splats rested in the furnace after annealing until room temperature was reached (cooling rate <0.2 K s1, temperature after 12 h–300 K). The binary Fe70Pd30 splats show the transforming Fe70Pd30 phase for both, the quenched and air-cooled samples, indicated by the (1 1 1) and (2 0 0) fcc peaks. No additional precipitate phases are observed. The oven-cooled Fe70Pd30 splat shows fractions of the Fe50Pd50 and a-Fe phase besides the transforming Fe70Pd30 phase. The Fe68.4Pd29.3Cu2.3 splats, which were water-quenched and air-cooled, show a single phase structure in Fig 9. Two additional peaks from Fe50Pd50 and Fe8Cu2 phases occur only for the very slowly cooled splats, with the highest fraction occurring in the Fe70Pd30 sample. Comparing the (1 1 1) fcc and (1 1 1) Fe50Pd50 peaks for the oven-cooled Fe70Pd30 in comparison to the Fe68.4Pd29.3Cu2.3 splat, a significant decrease in the (1 1 1) fcc peak intensity (and corresponding increase in (1 1 1) Fe50Pd50 peak intensity) is observed. Thus a high fractional decomposition from the transforming Fe70Pd30 phase into the Fe50Pd50 equilibrium phase and precipitates occurs for the binary Fe70Pd30 splat upon very slow cooling. By addition of Cu, this decomposition can be partially suppressed. In contrast, the water-quenched Fe70Pd23.8Cu6.2 splat does not show the single transforming phase: instead the (1 1 1) fcc/fct peak is shifted to higher angles and shows a broad peak at 42.9° which is correlated to the (1 1 0) bcc phase. For the oven-cooled sample, a further decomposition into precipitate phases (Fe50Pd50 and Fe8Cu2) occurs. Thus the decomposition of the high-temperature and metastable phase to equilibrium phases is suppressed by the addition of small amounts of Cu into binary Fe–Pd FSMA, even for slow cooling rates. In contrast, Fe70Pd23.8Cu6.2 splats do not show a single ternary phase due to decomposition upon cooling.

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Fig. 9. XRD patterns of Fe70Pd30, Fe68.4Pd29.3Cu2.3 and Fe70Pd23.8Cu6.2 splats processed with different cooling rates after annealing (quenched in water, air-cooled and oven-cooled).

Fig. 10 shows the change of lattice constants as a function of temperature during the martensitic transformation for a water-quenched Fe68.4Pd29.3Cu2.3 splat. Lattice constants were determined from XRD(T) measurements by peak fitting. The error for these results is smaller than the size of the symbols presented in Fig. 10. From 128 K (cfct = 0.360 ± 0.001 nm, afct = 0.382 ± 0.001 nm) to 233 K, only the low temperature tetragonal martensite (fct) phase occurs. Within this range an increase of c and a decrease of a is observed as the structure comes close to the transformation temperature. At 230 K the transition from the martensite to austenite phase starts, along with the appearance of (2 0 0), (2 2 0) and (3 1 1) fcc peaks (not shown here). With further increasing temperature, the (2 0 0), (0 0 2), (2 0 2) and (3 1 1) martensite peaks decrease and finally disappear at 238 K. With a further increase of temperature a growing intensity of (2 0 0), (2 2 0) and (3 1 1) fcc austenite peaks is

observed, which finishes at 278 K. At 300 K the lattice constant for the austenite phase was determined to be afcc = 0.374 ± 0.001 nm. At 128 K the Fe68.4Pd29.3Cu2.3 splat has a tetragonality of c/a = 0.942 which is higher than reported for a Fe68.8Pd31.2 single crystal [5]. Due to the change of the lattice constants for Fe68.4Pd29.3Cu2.3, a shape change consisting of an expansion of (a128K  a300K)/ a300K = 2.14% along the a-axis and a contraction of (c128K  a300K)/a300K = 3.74% can be estimated. Thus a maximum strain caused by conversion of the variants upon cooling from 300 K to 128 K of approximately 5.88% can estimated. This is slightly lower than the value of about 6% known for the Fe68.8Pd31.2 single crystal [5]. Since these investigations were performed on polycrystalline samples, where grain boundaries hinder magnetic-field-induced strain and the influence of micro-stress on the transformational behavior was not investigated, these values just give an upper estimate for MFIS in Fe68.4Pd29.3Cu2.3. 4. Discussion

Fig. 10. Change of lattice constants by the transformation from the low temperature (fct) to the high-temperature phase (fcc), determined by XRD(T) for a water-quenched Fe68.4Pd29.3Cu2.3 splat.

Fe–Pd–Cu thin film materials libraries were fabricated covering a range of 40 < Fe < 95 at.%, 5 < Pd < 55 at.% and 1 < Cu < 18 at.% and exhibiting transformation temperatures of up to 359 K. TEM confirmed the presence of a single ternary phase and showed the occurrence of nano-twins. XRD investigation of Fe68.4Pd29.3Cu2.3 splats, processed with different cooling rates after annealing, showed an enhanced stability against decomposition of the high-temperature metastable phase in comparison to Fe70Pd30. Ab initio calculations and experiments reveal the same trends for TC and JS, which are not significantly affected by the dilution of the magnetic sites in the ternary alloy. Slightly decreased orbital moments and an enhanced volume magnetostriction are predicted from ab initio calculations for Cu-enriched compositions.

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The combinatorial thin film approach delivers a comprehensive overview of the compositional dependence of the martensitic transformation temperatures. The complete analysis, however, must consider that a systematic influence by substrate-induced stresses may be present. On the other hand, the fabrication of bulk-like splats cannot produce the large amount of data necessary to reveal the relevant trends. Therefore, it is worthwhile to bring together the results of both approaches and combine them with values from the literature for the binary systems. This has been done in Fig. 11, which summarizes the martensite start temperature, MS, as a function of the composition in a three-dimensional diagram. The composition is defined in terms of the valence electron concentration e/a (see Fig. 1 for the whole materials library) and Fe content. In the introduction, these quantities were identified as the two most influential parameters determining the physics of the martensitic transformation in the ternary alloy. Since the full three-dimensional representation (small figure on the right of Fig. 11) is difficult to interpret, we restrict the discussion to projections of the data onto each of the three base planes, which cover the essential physics and are shown exclusively in the large diagram on the left of Fig. 11. The bulk samples (69 at.% < Fe < 71 at.% and 8.575 < e/a < 8.613), published by Cui et al. [8], show a linear distribution within all three planes, depicted by a black dashed line. For the Fe–Pd–Cu thin film

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martensite temperatures we observe a clear linear dependence on both the Fe content and the e/a ratio. The slope for these ternary thin films is considerably less than for the binary reference data. As discussed in Section 3.4, this can be traced back to the tensile stresses, which are largest for the samples with the smallest Fe content and significantly decreases with increasing Fe content. Tensile stresses can also be partially responsible for the considerable increase of the transformation temperatures with respect to bulk material. Splats as bulk reference show much lower transformation temperatures in comparison to Fe–Pd–Cu thin films. For Fe68.4Pd29.3Cu2.3 MS is 334 K for the thin film and 238 K for the splat, while for the binary composition, MS of splat and bulk systems coincide. If we attribute the observed difference of MS between film and splat solely to the stress state of the film, we obtain a reasonable value in the range of 460 MPa using the factor of 4.8 MPa K1 determined by Kato et al. [50]. A maximum MS of 359 K was observed for a sample with an Fe content of 71.8 at.% and an e/a ratio of 8.58. To our knowledge, this is the largest value obtained in the Fe–Pd system so far and significantly larger than the values obtained for corresponding binary systems [41], demonstrating that addition of Cu can substantially improve the relevant FSMA properties. This trend cannot be ascribed to a stress-related variation of the martensitic transformation temperature, since, as shown in Section 3.4, the Invar-related

Fig. 11. Martensite start temperatures, MS, as a function of e/a ratio and Fe content presented in a 3D graph with colour coded Cu content. Binary systems are shown by black symbols (squares and triangles). For clarity, only projections of the 3D data onto three different planes are depicted in the main diagram on the left; the spatial distribution of the data is given in the small diagram on the right. (Circles refer to the MS obtained from our thin film experiments in this study, while diamonds refer to values obtained for splats.) For comparison, literature data for binary alloys [8,41] are included (black open squares and black filled triangles). Black lines are guides to the eyes and meant to visualize the general compositional trends for the three kinds of data. Red dotted lines mark the border lines beyond which Cu-rich ternary thin films decompose into different phases. Outside of this volume, only data points corresponding to single phase samples are presented.

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reduction of thermal expansion, which partially compensates tensile stresses, is in fact enhanced in the Cu-doped alloys. The clear linear dependence between MS and the compositional parameters vanishes if the Fe content reaches a threshold value (indicated in Fig. 11 by red dotted lines), below which no transforming single component samples were obtained. Above the critical concentration, the stability region is characterized by a triangle (marked by the broken black lines on the bottom plane of Fig. 11). In comparison to results concerning binary bulk samples [8] and thin films [41] the compositional range in which single phase transforming samples can be found is significantly extended to lower Fe contents. From the discussion of the binary alloys and ternary thin films alone, it cannot be decided whether the Fe content or the valence electron concentration represents the most important variable which needs to be optimized in order to improve the FSMA behavior in a ternary system. However, a first conclusive indication comes from the splat experiments. Here, the MS value of the ternary splats coincides with the extrapolation of the data from the work of Cui et al. [8], if plotted versus the Fe content, while it deviates significantly to larger e/a values from the respective projection of the bulk values. This interpretation is also supported by the thin film data of Inoue et al. [41] which, however, does not show a defined linear behavior. This may be related to the variation of the fabrication parameters and the changing film thicknesses of the samples. Nevertheless, in the range between 70.5 and 71.5 at.% Fe, the MS values of the binary thin films (film thickness 200 nm) fall almost on top of Fe–Pd–Cu data if plotted against the Fe content, but deviates for the e/a projection. The films with low Fe content agree better with the bulk curve because of the higher film thickness (2 and 4 lm). Based on these observations, we conclude that a very promising route to develop improved Fe–Pd-based FMSAs is to add elements like Cu that extend the stability of the thermoelastically transforming phase to Fe concentration up to 72 at.% and beyond, and which we expect will increase the martensitic transformation temperatures to values which are suitable for technological applications. Acknowledgements The authors acknowledge the support from the Deutsche Forschungsgemeinschaft (DFG) within the priority programme SPP 1239, as well as the Heisenberg programme (A. Ludwig) and thank Dr J. Feydt from the Electronmicroscopy and Analysis group at Forschungszentrum caesar for temperature-dependent X-ray diffraction and Auger measurements. References [1] Ullakko K, Huang JK, Kantner C, O’Handley RC, Kokorin VV. Appl Phys Lett 1996;69:1966. [2] Sozinov A, Likhachev AA, Lanska N, Ullakko K. Appl Phys Lett 2002;80:1746.

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