IOP PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 42 (2009) 084018 (7pp)
doi:10.1088/0022-3727/42/8/084018
Heusler compounds as ternary intermetallic nanoparticles: Co2FeGa Lubna Basit1 , Changhai Wang1 , Catherine A Jenkins1 , Benjamin Balke1 , Vadim Ksenofontov1 , Gerhard H Fecher1 , Claudia Felser1 , Enrico Mugnaioli2 , Ute Kolb2 , Sergej A Nepijko3 , Gerd Sch¨onhense3 and Michael Klimenkov4 1
Johannes Gutenberg - Universit¨at, Institut f¨ur analytische und anorganische Chemie, 55099 Mainz, Germany 2 Johannes Gutenberg - Universit¨at, Institut f¨ur Physikalische Chemie, Elektronenmikroskopie-Zentrum Mainz (EMZM), 55099 Mainz, Germany 3 Johannes Gutenberg - Universit¨at, Institut f¨ur Physik, 55099 Mainz, Germany 4 Institut f¨ur Materialforschung I, Forschungszentrum Karlsruhe GmbH, 76021 Karlsruhe, Germany E-mail:
[email protected]
Received 11 October 2008, in final form 1 December 2008 Published 30 March 2009 Online at stacks.iop.org/JPhysD/42/084018 Abstract This work describes the preparation of ternary nanoparticles based on the Heusler compound Co2 FeGa. Nanoparticles with sizes of about 20 nm were synthesized by reducing a methanol impregnated mixture of CoCl2 · 6H2 O, Fe(NO3 )3 · 9H2 O and Ga(NO3 )3 · xH2 O after loading on fumed silica. The dried samples were heated under pure H2 gas at 900 ◦ C. The obtained nanoparticles—embedded in silica—were investigated by means of x-ray diffraction (XRD), transmission electron microscopy, temperature dependent magnetometry and M¨oßbauer spectroscopy. All methods clearly revealed the Heusler-type L21 structure of the nanoparticles. In particular, anomalous XRD data demonstrate the correct composition in addition to the occurrence of the L21 structure. The magnetic moment of the particles is about 5µB at low temperature in good agreement with the value of bulk material. This suggests that the half-metallic properties are conserved even in particles on the 10 nm scale. (Some figures in this article are in colour only in the electronic version)
materials science (for recent examples see [7] and articles there). Nanostructured magnetic materials are interesting in connection with ultrahigh-density magnetic recording, for advanced permanent magnets, as well as a wide range of applications from medical imaging to data storage. Most of the magnetic nanoparticles produced up to now are based on binary compounds or alloys. Examples for binary nanoparticles based on magnetic transition metal alloys are FePt [1] or FeCo [8–12]. Heusler compounds are magnetic materials that hold the greatest potential to achieve half-metallicity at room temperature and are also ideal for spintronics [13]. However, nanostructured Heusler compounds have not previously been prepared and investigated in terms of the size-dependent structures and magnetic properties. This work reports on the synthesis of ternary Heusler nanoparticles (Co2 FeGa). The half-metallicity of Heusler compounds is critically related to structural disorder at the atomic level. The decreased
1. Introduction Nanoparticles, in particular magnetic ones, are of considerable interest in many scientific disciplines [1]. Nanoscale magnetic particles demonstrate many novel physical and chemical properties mainly attributed to their small size and high surface to volume ratio. Those confinements in the length scale and interfacing materials interact with some threshold magnetic phenomenon as well [2, 3]. On the other hand, it also provides versatile possibilities to precisely tailor the magnetic properties with more degrees of freedom. Recently, great progress has been made in the synthesis, characterization and applications of the magnetic nanoparticles. However, the material systems are mainly limited to oxides [4], binary alloys [5] and core– shell structured materials [6]. The magnetic properties of nanoparticles are of high interest for basic research as well as applications in 0022-3727/09/084018+07$30.00
1
© 2009 IOP Publishing Ltd
Printed in the UK
J. Phys. D: Appl. Phys. 42 (2009) 084018
L Basit et al
length scale to the nanometre regime definitely increases the structural disorder. Nanostructured Heusler particles of different sizes and surface properties are a perfect model system for investigating the relationship between structural disorder and magnetic behaviour in ternary intermetallics. More importantly, less is understood on the impacts of the nanoscale on the structure and magnetic properties of Heusler compounds. This might be due to the complicated crystal structure and the difficulty in characterizing it. The significance of a systematic work along this approach is expected to be manifold: (1) a new material system (Heusler compounds) would come to the mainstream of nanoscience and technology; (2) unconventional crystal structure, degree of disorder and physical properties are expected; (3) a clear understanding of this novel material system would pave the way for potential applications. Polycrystalline bulk Co2 FeGa was earlier reported by Bushow et al [14, 15]. It has an ideal L21 structure with a lattice parameter of a = 5.737 Å. The saturation magnetization was reported to be 5.13µB at 5 K. The hyperfine fields were investigated by Jaggi et al using M¨oßbauer spectroscopy and nuclear magnetic resonance (NMR) studies [16]. The Curie temperature reported by Umetsu et al amounts to TC = 1093 K [17]. The magnetic and transport properties of polycrystalline Co2 FeGa were investigated by Zhang et al [18]. Details of the L21 structure were explained by Balke et al using extended x-ray absorption fine structure spectroscopy (EXAFS) [19]. Chen et al investigated the magnetic, transport and thermal properties of single crystalline Co2 FeGa [20]. The objective of this work is a systematic study on the synthesis and characterization of Heusler nanoparticles (Co2 FeGa) in terms of the relationship between the process parameters, crystal structure and magnetic properties.
2. Experimental details
Figure 1. Anomalous XRD of Co2 FeGa nanoparticles. The high resolution, anomalous diffraction pattern were taken at excitation energies close to the Co (a) or Fe (b) absorption K-edges using photon energies of 7.7077 keV or 7.112 keV, respectively. The off resonant diffraction data (c) were taken at hν = 7.05 keV. The inset compares the (2 2 0) reflexions taken from bulk material and the nanoparticles (7.05 keV). The broadening of the bulk reflexion is caused by the sample preparation.
The Co2 FeGa nanoparticles were synthesized as follows. The first step is the decomposition and reduction of the Co, Fe and Ga precursors. A solution of precursors Fe(NO3 )3 · 9H2 O (0.1616 g), CoCl2 · 6H2 O (0.2854 g) and Ga(NO3 )3 · xH2 O (0.1278 g) was prepared in 50 ml methanol. Fe(NO3 )3 · 9H2 O (99.99%), CoCl2 · 6H2 O (99.99%), and Ga(NO3 )3 · xH2 O (98.0%) were used as received from Sigma-Aldrich (Schnelldorf, Germany), fumed silica was obtained from Degussa (Essen, Germany). All other chemicals were used as received without further purification. 1.00 g of fumed silica powder was impregnated in the precursor solution and mixed in an ultrasonic bath for 1 h. The methanol was removed afterwards by evaporation on a rotary evaporator. The residue obtained was dried at 80 ◦ C for 1 h. This resulted in loading of Fe, Co and Ga species onto the high surface-area silica powder. The dried residue was ground to powder, which was placed in a quartz tube furnace and heated to 850 ◦ C under flow of H2 (g). This temperature and the H2 (g) flow were maintained for 5 h. The sample was then cooled to room temperature. Finally, the Co2 FeGa nanoparticles were collected. The structure of the samples was pre-characterized by powder x-ray diffraction (XRD) using Mo Kα radiation
(Bruker AXS D8). However, Mo Kα radiation reveals only the cubic structure but cannot distinguish the f cc-typical features due to the similar scattering factors of Co, Fe and Ga. To overcome this difficulty, anomalous XRD measurements were performed at the XPD beamline of the Brazilian synchrotron facility LNLS (Campinas). In the L21 structure with F m3m symmetry, the scattering factors of the (1 1 1) and (2 0 0) reflexions are given by: f1 1 1 = fFe − fGa and f2 0 0 = fFe + fGa − 2fCo , where fCo , fFe and fGa are the atomic scattering factors of the constituents. The factor of the main reflexion is f2 2 0 = fFe + fGa + 2fCo . The accompanied atomic scattering factor becomes small when approaching with the excitation energies a K absorption edge of one of the constituents. This enhances either the (1 1 1) or the (2 0 0) reflexion, in particular if the excitation energy comes close to the Fe or Co K-edges. This effect, known as anomalous XRD, makes it possible to identify the crystalline structure of Heusler compounds unambiguously [21]. It should be noted that f1 1 1 or f2 0 0 vanish independently of the excitation energy in the case of mixing either Fe and Ga or all three elements, respectively. Therefore, such types of disorder can be immediately excluded (see figure 1). 2
J. Phys. D: Appl. Phys. 42 (2009) 084018
L Basit et al
Figure 2. TEM image of Co2 FeGa nanoparticles. Shown are (a) Co2 FeGa particle in a silicon matrix, (b) diffraction pattern, (c) filtered IFFT of the particle and (d) FFT.
A FEI Tecnai F20 transmission electron microscope equipped with a field emission gun was used for the investigation by transmission electron microscopy (TEM). The operation voltage was set to 200 kV resulting in a lateral resolution of 0.14 nm. High resolution TEM (HRTEM) and scanning TEM (STEM) were performed using a FEI Tecnai F30 ST TEM equipped with a high-angle angular dark field (HAADF) and energy dispersive x-ray (EDX) detectors. TEM images were recorded using a Gatan CCD camera (1024×1024 pixels). Nano-electron diffraction was performed to assure a semi-parallel electron beam (convergence angle approximately 0.3 mrad) using a C2 aperture of 10 µm and combined with STEM imaging [22]. The magnetic properties were investigated at low temperatures using a super conducting quantum interference device (SQUID, Quantum Design MPMS-XL-5). For magnetostructural investigations, 57 Fe M¨oßbauer measurements were performed using a conventional, constant-acceleration spectrometer at 85 K. For excitation, a 57 Co source was used delivering γ radiation with an energy of hν = 14.4 keV. The intrinsic line width of the source is E = 4.69 neV. Iron with a natural abundance of 2.2% 57 Fe was used for the samples of this study. The M¨oßbauer data were analysed using the program RECOIL [23].
of the constituents, XRD using typical laboratory sources is not useful because the typical reflexions of the face centred cubic fcc lattice are suppressed. Using energies at the K absorption edges of the constituents allows one to ‘switch off’ one of the scatterers and thus to enhance particular f cc superstructure reflexions (see section 2: experimental details). Figure 1 compares the anomalous XRD data of Co2 FeGa nanoparticles with a size of about 30 nm for different excitation energies. The energies were chosen to be close to the K absorption edges of iron and cobalt. The appearance of the (1 1 1) and (2 0 0) superstructure reflexions is typical for the f cc lattice and confirms the L21 structure of the nanoparticles. It is interesting to note that the (2 2 0) reflexion is sharper than the one observed for polycrystalline Co2 FeGa. The broadening of the (2 2 0) reflexion of the bulk material is caused by the preparation of the powder sample. Grinding of the compact ingots leads to a partial distortion of the structure and powder with inhomogeneous size distribution. The sharp (2 2 0) reflexion observed from the nanoparticles confirms the high crystalline quality of the nanoparticles. The lattice parameter was determined by a Rietveld refinement and is a = 0.573 10(8) nm at room temperature (300 K). This value is about 0.24% smaller than in polycrystalline bulk material [14] (compare the inset in figure 1). The slightly reduced lattice parameter may be explained by increased intrinsic pressure caused by the comparably high ratio of surface to bulk atoms in the nanoparticles. It is worthwhile to note that the chemical sensitivity of the anomalous XRD provides a sensitive test not
3. Results and discussion The crystalline structure of the nanoparticles was investigated by anomalous XRD. Due to the nearly equal scattering factors 3
J. Phys. D: Appl. Phys. 42 (2009) 084018
L Basit et al
Figure 3. Finding individual Co2 FeGa nanoparticles by TEM. (a) shows a large conglomerate of nanoparticles. (b) shows the marked area of (a) with higher resolution. The diffraction pattern taken from three particles marked in (b) are shown in panels (c), (e) and (g). (d), (f ) and (h) are the Fourier transforms of the images of the particles numbered in (b) by 1, 2 and 3, respectively.
only of the structure but also of the composition. The results exclude that the particles consist of disordered binary alloys. Transmission electron microscopy (TEM, HRTEM, as well as STEM) was used to study the size and distribution of the nanoparticles. The contrast was slightly reduced but due to Bragg contrast the particles could be detected better because the particles were embedded in a silica matrix. Additionally, it is not straightforward to find the particles due to magnetic interactions. Figure 2 shows an individual nanoparticle of Co2 FeGa in the silica matrix with clearly resolved lattice planes. The fast Fourier transform (FFT) of the image allows the plane spacing to be measured as 0.21 nm (see figure 2(d)). The diffraction pattern confirms the high crystallinity of the particles (see 2(b))). Together with the filtered image (IFFT, 2(c) ), this underlines that the particles are single crystalline. More details will be shown below for a similar particle. The process of finding particles with different zone axes is illustrated in figure 3. The magnetic particles tend to cluster. Figures 3(a) and (b) show a large conglomerate of particles sticking together in the silica matrix. The zoom into this image is shown in (b) where single, bright particles are revealed in the
image taken with a smaller field of view. The STEM images provided in figure 3 show that the sample consists of a majority of high quality crystalline material in an amorphous matrix. In order to perform electron diffraction with a semi-parallel beam on selected single particles inside the agglomerates NED in STEM mode was used. Oriented particles producing a high Bragg contrast appear bright in STEM and were selected for diffraction. The orientation of those particles is seen in the electron diffraction patterns. After changing to TEM mode, the selected nanoparticles were found again and high resolution images were recorded as shown in figure 2. The Fourier transformation of the HRTEM images of individual particles is provided for comparison with the diffraction patterns as well in figure 3. The pattern of particles (1) to (3) exhibit nearly 4-fold, or 2-fold symmetry corresponding to particles being aligned approximately along the [0 0 1], [1 1 0] direction as well as unidentified directions of the cubic crystal structure. A particle with the quasi-6-fold pattern of the [1 1 1] direction is seen in figure 2. The appearance of those different axis alignments of the particles clearly indicates their f cc crystalline structure. Figure 4 shows another HRTEM image of a single Co2 FeGa nanoparticle and the corresponding Fourier 4
J. Phys. D: Appl. Phys. 42 (2009) 084018
L Basit et al
Figure 5. Size distribution of Co2 FeGa nanoparticles. Displayed is the number of particles as a function of size as counted from a TEM image.
The investigation by EDX was accomplished by the large amount of silica. Analysis of the EDX data taken with a field of view of (100 × 100) nm2 revealed a composition of Co : Fe : Ga = 2 : 1.1 : 1. This is in very good agreement with the nominal composition of Co2 FeGa, in particular considerably that the silica background amounted to about 60% of the total signal. The magnetic properties of the nanoparticles were investigated by temperature dependent magnetometry. Figure 6 displays the magnetization curve measured at low temperature (T = 5 K). The particles are soft magnetic as is seen in the inset (a) of figure 6 from the small hysteresis. The remanence and coercivity of the measurement shown in figure 6 amount to −1 Br = 77 mT and Hc = 7.7 kAm , respectively. The energy integral WH = H dB gives the hysteresis loss per cycle from a direct integration of the magnetization loop. The result for the investigated Co2 FeGa nanoparticle sample is WH = 130 Jm−3 at 5 K. This value may be compared with pure bulk Fe with WH = 60 Jm−3 and Hc = 0.8 Am−1 [24]. Increasing the temperature from 5–300 K causes a small decrease in the magnetic moment to 4.77µB (see inset (b) in figure 6). This only small change is in agreement with the high Curie temperature reported for bulk material [17]. The saturation magnetization at low temperature is equivalent to a magnetic moment of about 4.9µB in the primitive cell. The measured magnetic moment agrees well with the value found for polycrystalline bulk material. It is in accordance with the Slater–Pauling rule for localized moment systems. At 5 K, the value comes close to 5µB as expected for Co2 FeGa in the half-metallic ferromagnetic state. This suggests that the half-metallic ferromagnetic properties of Heusler compounds are conserved in nanoscaled materials. M¨oßbauer spectroscopy—as a magneto-structural method—is also suitable to confirm the Heusler-type character of the Co2 FeGa nanoparticles. The spectrum shown in figure 7 reveals a magnetic sextet with an isomer shift of v = 0.20 mm s−1 and hyperfine magnetic field of Hhff = 24.15 kAm−1 . The hyperfine magnetic field is in well agreement with the value obtained for bulk samples of Co2 FeGa.
Figure 4. TEM image of Co2 FeGa nanoparticles. (a) displays a particle with a size of 18 nm, (b) shows a part of the nanoparticle (see square in (a)) on an enlarged scale, and (c) is the Fourier transform of the image.
transformation. The complete nanoparticle as shown in (a) is nearly spherical and has a diameter of d = 18 nm. The Fourier transformed image (b) reveals a 6-fold symmetry. It corresponds to six [1 1 0]-like planes perpendicular to the {1 1 1}-like direction of a cubic lattice. Figure 4(c) displays a part of the particle on an enlarged scale to make the lattice planes better visible. The lattice distance d2 2 0 of the 2 2 0planes is about 0.2 nm. At the given resolution, this is in reasonable agreement to the high resolution XRD data. TEM was also used to determine the size distribution of the nanoparticles. Figure 5 displays the distribution of the particles with different sizes counted from an image with a field of view of few micrometres. The distribution exhibits a maximum at particles with a size of 10–15 nm. A statistical analysis results in a mean particle size of dm = 26.6 nm with a standard deviation of σ = 47.3 nm and skewness γ = 162. This rather wide distribution explains the narrow XRD pattern as well as the line broadening observed by M¨oßbauer spectroscopy. The distribution, however, reflects only a very small part of the sample and may not be representative for samples of a few milligrams as used in the integral methods of investigation. Work is in progress to have a better control and selection of the particle size. 5
J. Phys. D: Appl. Phys. 42 (2009) 084018
L Basit et al
superparamagnetism. This feature depends on the particle size and the dispersion media [8, 9, 11]. It is expected that smaller Co2 FeGa nanoparticles will also show a transition from ferro- to paramagnetism. To obtain such particles will make an improved selection of smaller sized particles necessary. Actually, the embedding in silica has the advantage of preventing oxidation of the particles as observed for FePt [25]. Its disadvantage is, indeed, that the size selection is not well controllable. Experiments are on the way to remove the silica by HF etching and to coat the particles to prevent oxidation. Coating by carbon would allow one to functionalize the particles, in addition [26].
4. Summary Figure 6. Magnetization of Co2 FeGa nanoparticles. Shown is the low temperature magnetization of the nanoparticles at T = 5 K. The inset (a) shows the hysteresis close to the origin on an enlarged scale. Inset (b) shows the temperature dependence of the magnetization.
In this work, the synthesis, preparation and characterization of ternary intermetallic nanoparticles based on the Heusler compound Co2 FeGa were demonstrated. Co2 FeGa nanoparticles on the 10 nm scale were prepared in fused silica using the Fe(NO3 )3 · 9H2 O (0.1616 g), CoCl2 · 6H2 O (0.2854 g) and Ga(NO3 )3 · xH2 O (0.1278 g) dissolved in methanol as precursor. This results in nanoparticles embedded in a silica matrix. The investigations by means of XRD, transmission electron microscopy and M¨oßbauer spectroscopy revealed unambiguously the Heusler-type L21 structure and correct stoichiometry of the nanoparticles. From magnetometry at 5 K, it was found that the particles are soft magnetic but slightly harder compared with polycrystalline bulk material. The Curie temperature is clearly far above room temperature. The low temperature magnetic moment of the particles is about 5µB at low temperature in good agreement with the value of bulk material. This suggests that the half-metallic properties are conserved in particles on the 10 nm scale.
Figure 7. M¨oßbauer spectrum of Co2 FeGa nanoparticles. Shown is the spectrum taken at 85 K, the lines are the result of a fit with two sextets.
Acknowledgments The authors thank Gustavo Azevedo and Fabio Furlan Ferreira (LNLS Campinas, Brazil) for help with the experiments at LNLS. Financial support by the DFG (Research Unit FOR 559, project P 1) and DAAD (D06/33952) is gratefully acknowledged. Further support of this work was provided by the Brazilian Synchrotron Light Laboratory (LNLS) under proposals D04B-XAFS1-3304, D04B-XAFS1-6699 and D10B-XPD-6689.
The absence of a quadrupole splitting of the spectrum unambiguously indicates the cubic environment of the iron atoms and confirms the Oh symmetry of the Fe sites expected in the Heusler-type L21 structure. The data show some amount of magnetic impurities. The fit revealed a contribution of 17% of a foreign magnetic phase. This might be caused by impurities or different magnetic environments at the Co2 FeGa–Silica interface, presumably in the form of superparamagnetic oxidized iron. M¨oßbauer spectroscopy is a local probe in the sense that it is sensitive to the local environment of the Fe atoms. This local environment changes if going from the silica embedded surface to the bulk of the particles. Further, it should be noted that the spectrum has slightly broadened resonance lines that apparently correspond to the grain size distribution being shifted a bit by the few larger particles. The Co2 FeGa particles with a size of about 10 nm are ferromagnetic. Small, binary CoFe nanoparticles exhibit
References [1] Lu A-H, Salabas E L and Sch¨uth F 2007 Angew. Chem. (Int. Edn) 46 1222 [2] Soler M A G, da Silva S W, Garg V K, Oliveira A C, Azevedo R B, Pimenta A C M, Lima E C D and Morais P C 2005 Surf. Sci. 575 12 [3] Campos A F C, Tourinho F A, Aquino R and Depeyrot J 2007 J. Magn. Magn. Mater. 310 2847 [4] Sohn B H, Cohen R E and Papaefthymiou G C 1998 J. Magn. Magn. Mater. 182 216
6
J. Phys. D: Appl. Phys. 42 (2009) 084018
L Basit et al
[17] Umetsu R Y, Kobayashi K, Fujita A, Oikawa K, Kainuma R, Ishida K, Endo N, Fukamichi K and Sakuma A 2005 Phys. Rev. B 72 214412 [18] Zhang M, Br¨uck E, de Boer F R, Li Z Z and Wu G H 2004 J. Phys. D: Appl. Phys. 37 2049 [19] Balke B, Wurmehl S, Fecher G H, Felser C, Alves M C M, Bernardi F and Morais J 2007 Appl. Phys. Lett. 90 172501 [20] Chen P, Wu G H and Zhang X X 2008 J. Alloys Compounds 454 52 [21] Ravel X B, Cross B, Raphael J O, Harris M P, Ramesh V G and Saraf R V 2002 Appl. Phys. Lett. 81 2812 [22] Kolb U, Gorelik T, K¨ubel C, Otten M T and Hubert D 2007 Ultramicroscopy 107 507 [23] Lagarec K and Tancourt D G 1997 Nucl. Instrum. Methods Phys. Res. B 129 266 [24] Lide D R (ed) 2001 CRC Handbook of Chemistry and Physics 82 edn (Boca Raton, FL: CRC Press) [25] Basit L, Nepijko S A, Shukoor I, Ksenofontov V, Klimenkov M, Fecher G H, Sch¨onhense G, Tremel W and Felser C 2008 Appl. Phys. A at press doi:10.1007/s00339-008-4874-7 [26] Xu Y et al 2008 Nanotechnology 19 435102
[5] Baldi G, Bonacchi D, Innocenti C, Lorenzi G and Sangregorio C 2007 J. Magn. Magn. Mater. 311 10 [6] Zhang H, Sun S H, Li J, Wang Z L and Liu J P 2004 Appl. Phys. Lett. 285 792 [7] Fiorani D 2008 J. Phys. D: Appl. Phys. 41 130301 [8] Ennas G, Falqui A, Marras S, Sangregorio C and Marongiu G 2004 Chem. Mater. 16 5659 [9] Corrias A, Casula M F, Falqui A and Paschina G 2004 Chem. Mater. 16 3130 [10] Ennas G, Falqui A, Paschina G and Marongiu G 2005 Chem. Mater. 17 6486 [11] Reiss G and H¨utten A 2005 Nature Mater. 4 725–6 [12] Wei X W, Zhu G X, Liu Y Z, Ni Y H, Song Y and Xu Z 2008 Chem. Mater. 20 6248 [13] Felser C, Fecher G H and Balke B 2007 Angew. Chem. Int. Edn 46 668 [14] Buschow K H J and van Engen P G 1981 J. Magn. Magn. Mater. 25 90–6 [15] Buschow K H J, van Engen P G and Jongebreur R 1983 J. Magn. Magn. Mater. 38 1–22 [16] Jaggi N K, Rao K R P M, Grover A K, Gupta L C, Vijayaraghavan R and Dang Le Khoi 1978 Hyperfine Interact. 4 402
7
