A novel ternary uranium-based intermetallic U34Fe4−xGe33: Structure and physical properties

Journal of Alloys and Compounds 606 (2014) 154–163

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A novel ternary uranium-based intermetallic U34Fe4xGe33: Structure and physical properties M.S. Henriques a,⇑, D. Berthebaud b,c, J.C. Waerenborgh a, E.B. Lopes a, M. Pasturel b, O. Tougait b, A.P. Gonçalves a a b c

Campus Tecnológico e Nuclear, Instituto Superior Técnico, Universidade de Lisboa, CFMC-UL, Estrada Nacional 10, 2695-066 Bobadela, Portugal Institut des Sciences Chimiques de Rennes, Chimie du Solide et Matériaux, Université Rennes 1, UMR CNRS 6226, 263 Avenue du Général Leclerc, 35042 Rennes, France CRISMAT, UMR CNRS 6508, 6 bd. Maréchal Juin, 14050 Caen, France

a r t i c l e

i n f o

Article history: Received 20 December 2013 Received in revised form 30 March 2014 Accepted 31 March 2014 Available online 13 April 2014 Keywords: Actinides alloys and compounds Crystal structure Electronic properties Magnetic measurements Mössbauer spectroscopy

a b s t r a c t The new ternary phase U34Fe4xGe33 has been synthesized and characterized by means of single crystal X-ray diffraction, magnetization, Mössbauer spectroscopy, specific heat, electrical resistivity, magnetoresistivity and thermopower measurements. It crystallizes in its own tetragonal structure type which can be described as derived from the one of the binary USi (U34Si34.5 structure-type, space group I4/mmm), with lattice parameters at room temperature, a = 10.873(5) Å and c = 25.274(3) Å. Structure refinement confirmed six inequivalent U atoms, occupying sites with dissimilar coordination, the Ge atoms staying on seven positions and Fe on two positions, one of the Fe sites with a partial occupancy. The U sub-lattice is composed by the stacking of a square cupola, two distorted cubes and a square orthobicupola. U34Fe4xGe33 with x = 0.68 undergoes a ferromagnetic-type transition below 28 K. Mössbauer spectroscopy shows that the magnetism is ruled by the U sub-lattice, as Fe atoms have no ordered moments. The Sommerfeld coefficient of the electronic specific heat is c = 131 mJ/(molU K2), whereas the estimated magnetic entropy at TC is 0.22Rln2. A residual resistivity of 314 lX cm and a resistivity ratio of 1.1 were found in the electrical resistivity curve, which also exhibits an upturn below TC that shifts towards higher temperatures with the applied magnetic field. This behavior may be related to some disorder in the nonmagnetic lattice and/or partial ordering of the magnetic lattice. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction In the last decades new investigations in crystal chemistry and physics of uranium-based intermetallics have been stimulated by a wide variety of properties displayed by this type of compounds. Fundamental aspects of their magnetism and the existence of highly correlated electron ground states have mainly triggered these efforts [1–3]. Perhaps the brightest example is magnetically mediated superconductivity in intermetallic uranium germanides [4,5]. These complex properties often occur when competing or overlapping energy scales are available. In the metallic state, it is commonly accepted that uranium has an open 5f electron shell, which allows interaction between spin, charge and lattice degrees of freedom [1]. When alloyed the picture is more intricate, since not only the f electrons can hybridize with other f electrons at different sites, but also with the outer s, p or d electrons of ligand atoms. ⇑ Corresponding author. Tel.: +351 219946000. E-mail address: [email protected] (M.S. Henriques). http://dx.doi.org/10.1016/j.jallcom.2014.03.189 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.

In a first approximation, direct f–f overlap is straight connected with the boundary between localized and itinerant character, as well as between magnetic and paramagnetic or superconducting ground-states, which is controlled by the 5f bandwidth. This parameter is also modified by hybridization with ligands. Recently, a systematic study of the ternary U–Fe–Ge system has revealed several new intermetallic compounds [6]. Their electronic properties clearly demonstrate the crucial role of the hybridization in which the 5f electrons are involved, both between themselves and with the outer electrons of ligand atoms. In the U9Fe7Ge24, U2Fe3Ge and U3Fe4Ge4 compounds the strong 5f hybridization results in the disappearance of the Fe ordered magnetic moment [7–10]. In U9Fe7Ge24 the 5f electronic states are sufficiently strongly delocalized due to f–p hybridization that no magnetic order was found in the uranium sublattice and the compound is a paramagnet [7]. By contrast, U2Fe3Ge and U3Fe4Ge4 are both strongly itinerant ferromagnets. U2Fe3Ge presents a special case since, in spite of the short U–U spacing, dU–U 6 3.2 Å, far below the Hill limit 3.4 Å for U [11], the magnetic order originates exclusively from the uranium sublattice.

M.S. Henriques et al. / Journal of Alloys and Compounds 606 (2014) 154–163 Table 1 Selected single crystal X-ray diffraction data collection, and refinement parameters for U34Fe4xGe33. Formula

U34Fe3.32Ge33

Molecular mass (g/mol) Crystalline system, space group Lattice parameters (Å)

10674.64 Tetragonal, I4/mmm (no 139) a = 10.873(5) c = 25.274(3) 2986(2) 2/11.865 108.96 Black 0.076⁄0.032⁄0.017 2.91–45 21 6 h 6 21 21 6 k 6 20 50 6 l 6 32 46354 /3560 Semi-empirical (MULTISCAN) 0.1415 68 1.040 0.0476/0.1191 0.000098 4.44/9.20

Volume (Å3) Z, calculated density (g/cm3) Absorption coefficient (cm1) Crystal color Crystal dimensions (mm) h Range (°) Data collection

Collected/unique reflections Absorption correction R(int) Refined parameters Goodness of the fit Final agreement factors [I > 2r(I)] R/xR2a Extinction coefficient Residual peaks (e/Å3)

1=4

a R(F) = R||Fo|–|Fc||/|Fc|, wR2 ¼ ½RwðF 20  F 2c Þ2=wF 40  P ¼ ½maxðF 20 ; 0Þ þ 2F 2c =3 þ 2F 2c =3.

, where w1 ¼ ½r2 ðF 20 Þ þ 7:27P,

Equally interesting physics can be expected in other representatives of the U–Fe–Ge group. A new phase, U34Fe4xGe33, was found in the isothermal section at 900 °C of the ternary U–Fe–Ge phase diagram [6]. The present work reports on the synthesis and structural characterization of the U34Fe4xGe33 compound with x = 0.68 by single crystal X-ray diffraction. In order to obtain information on the nature of the 5f electronic states, a study of its magnetization, 57Fe Mössbauer spectroscopy, specific heat, resistivity, magnetoresistivity and thermopower has been performed. 2. Experimental details The synthesis of polycrystalline samples was accomplished by arc-melting the starting elements (with purities 99.5% for U and 99.99% for Fe and Ge) under a high purity TiZr-gettered argon atmosphere. The alloys were prepared with nominal compositions 9U:1Fe:10Ge and were turned and re-melted three times. Each sample was crushed two times before the first and the second re-melt to ensure better homogeneity. Mass losses during this process were found to be <0.5%. Powdered samples were studied by X-ray diffraction (XRD) with a Bruker AXS D8 Advance diffractometer (h2h Bragg–Brentano geometry) using monochromatized Cu Ka1 radiation (k = 1.5406 Å). The Powdercell software package [12] was used to first compare the experimental diffraction patterns with those generated for the known compounds and to first approach the unit cell parameters. The phase composition was analyzed in small polished pieces of the samples with an Oxford Link–Isis Si/Li energy dispersive X-ray spectrometer (EDS), coupled to the scanning electron microscope (SEM) JEOL-JSM 6400. The measurements were carried out with the electron beam operating at 15 kV and three points or areas (of about 0.5–0.6 mm2) were analyzed. Small single crystals suitable for X-ray diffraction were isolated from an as-cast sample, glued on the top of a glass fiber and mounted onto goniometer head. The single crystal used in this case had approximate dimensions 0.02  0.03  0.02 mm3. Single crystal X-ray diffraction intensities were collected using a Kappa CCD four circle diffractometer, equipped with a bidimensional detector using graphite monochromatized Mo Ka radiation (k = 0.71073 Å). The orientation matrix and the unit cell parameters were derived from the first ten measured frames of the data using the DENZO software [13]. The scaling and merging of redundant measurements of the different data sets as well as the cell refinement was performed using SCALEPACK [13]. Semi-empirical absorption corrections were made with the use of the MULTISCAN software [14]. Structural models for the compound were determined by direct methods with the help of SIR-97 [15]. The different structural refinements and Fourier syntheses were made with SHELXL-97 [16]. The atomic positions have been standardized using STRUCTURE TIDY [17]. Additional details of the data collection and structure refinement are given in Table 1. For further characterization, a polycrystalline U34Fe3.32Ge33 sample was then prepared using the above mentioned conditions. The as-cast sample was annealed into a sealed silica tube inside a resistance furnace at 900 °C for 1 week. Powder

155

X-ray patterns and SEM–EDS back-scattered electron of the annealed sample showed that the only phase present had a composition 48(2) U:5(1)Fe:47(2)Ge, which compares well to the nominal composition of U34Fe3.32Ge33. For this composition, the comparison between the calculated and the experimental X-ray diffraction patterns taken from the as-cast and annealed samples is shown in Fig. 1. Magnetization measurements were performed on a polycrystalline sample (fixed powder) using a Quantum Design MPMS-5 SQUID magnetometer, from 2 to 300 K under magnetic fields up to 5 T. The sample for Mössbauer spectroscopy was prepared using metallic iron 95.73% enriched in the 57Fe isotope (Chemgas). X-ray powder diffraction confirmed that this sample was a single phase and magnetization data showed the same behavior as the sample prepared with natural Fe. The 57Fe Mössbauer measurements were performed in transmission mode, between 1.6 and 295 K, using a conventional constant acceleration spectrometer and a 25 mCi 57Co source in a rhodium matrix. The velocity scale of the spectrometer was calibrated with reference to an a-Fe foil at different temperatures in the range 2–295 K. The Mössbauer absorber containing approximately 0.1 mg/cm2 of 57Fe was prepared from the powdered U34Fe4xGe33 enriched in 57Fe and mixed with Perspex. Low temperature studies were performed using a bath cryostat with the sample immersed in liquid He for measurements at 4.1 and 1.6 K and in He exchange gas for temperatures above 4.1 K. The obtained spectra were fitted to Lorentzian lines using a non-linear least-squares method [18]. Specific heat was measured at T = 2–300 K in a zero magnetic field by the relaxation method. The mass of the sample used in the measurement was 8 mg. Electrical resistivity measurements were performed on needle shaped pieces (dimensions 4  1  0.6 mm3) of the U34Fe3.32Ge33 polycrystalline sample by the four-point method in the temperature range 1.8–300 K in zero field and under magnetic field applied parallel to the current flow. The thermopower was measured by using a slow ac technique [19], by attaching two 25 lm diameter 99.99% pure Au wires (Goodfellow metals), thermally anchored to two quartz reservoirs, with Pt paint (Demetron 308A) to the extremities of the needle sample as in a previously described apparatus [20].

3. Results and discussion 3.1. Phase formation and X-ray diffraction The existence of the new phase U34Fe4xGe33 was first found in an as-cast sample with nominal composition 9U:1Fe:10Ge during the systematic investigation of the U–Fe–Ge ternary system [6]. X-ray powder diffraction patterns showed that it was not a structure related to a possible solubility of Fe in the binary compound UGe since the pattern could not be indexed with the ThIn structure-type [21]. Moreover, this phase was found to be the major phase in the as-cast sample, becoming the single phase present after annealing, according to X-ray diffraction data and SEM-EDS analysis.

Fig. 1. Experimental powder X-ray diffraction pattern for the annealed sample of U34Fe3.32Ge33 (red open symbols) with the Rietveld calculated pattern (black line) and the difference profile (bottom blue line). It shows the calculated Bragg positions of U34Fe3.32Ge33 (green vertical bars). (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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For resolving the crystalline structure, a single crystal was taken from the as-cast sample. This crystal had the composition 48(2)U:5(1)Fe:47(2)Ge as indicated by EDS analysis, which corresponds to U34Fe3.55Ge33.3, agreeing within the resolution of the technique the crystallographic formula given thereafter. First results after the automatic indexing and least-square refinement of the reflections collected for U34Fe3.32Ge33 pointed out that it crystallizes in a body centered tetragonal system, with cell parameters converging to a = 10.873(5) Å and c = 25.274(3) Å. Examination of systematic extinctions for the hkl indices, h + k + l – 2n, and structure determination were successfully done within the space group I4/mmm (n°139). The Wyckoff positions attributed by this structural model are 4e, 8f, 8j, 16m, and two 16n for the U atoms, 2a, 4c, 4e, 8h, 16m, two 16n for the Ge atoms, and two 4e sites for the Fe atoms (Table 2). The first refinement cycle for this structure was performed considering full occupancy of all the atomic sites in the cell. Nevertheless, this procedure revealed a high isotropic displacement parameter for the Fe atoms in one of the 4e positions (Fe2), thus pointing to a partial occupancy. Indeed, the subsequent refinement of the electronic density leads to occupancy of 66%. The residual positive density in the Fourier map is 4.44 e/Å3 corresponding to the position (0.5, 0.5, 0.1475) and located at 0.3 Å far from the Fe2 position. However, this small value excludes the presence of another atom in that position and can be considered as usual for uranium compounds with high cell volumes, as in the case of U9Fe7Ge24 [9]. The crystallographic formula obtained from the refinement was U34Fe3.32Ge33, which is in good agreement with the EDS data. Details on the data collection and structure refinements can be found in Table 1, while atomic positions and the equivalent isotropic and anisotropic displacement parameters are gathered in Tables 2 and 3, respectively. U34Fe4xGe33 crystallizes in a new structure type, which can be regarded as derived from the tetragonal structure of U34Si34.5 (space group I4/mmm, a = 10.622 Å, c = 24.262 Å) [22]. In the structure of the binary uranium silicide, 68 U atoms are located in six positions of the I4/mmm space group (4e, 8f, 8j, 16m and 16n) and 70 Si atoms are distributed in eight positions (2a, 4c, 4e, 4e, 8h, 16m, 16n and 16n). The site 2a, in which the Si atom is located, has only half occupation. In U34Fe4xGe33, the Si atoms are substituted by Ge atoms except in the 4e position, which is filled by a Fe atom. An additional 4e position, in relation to the binary type, is observed in the ternary compound and it is partially occupied by a Fe atom. The U lattice is similar in both binary and ternary compounds. It is worth noting that this compound is not an extension of the binary compound UGe since the latter adopts the orthorhombic ThIn structure-type. The binary structure-type USi is thus

Table 3 Anisotropic displacement parameters U (102 Å2)a, and their estimated standard deviation for U34Fe4xGe33. Atom

U11

U22

U33

U12

U13

U23

U1 U2 U3 U4 U5 U6 Ge1 Ge2 Ge3 Ge4 Ge5 Ge6 Ge7 Fe1 Fe2

17.05(6) 19.80(8) 16.66(1) 15.9(2) 16.84(3) 17.6(2) 16.6(5) 16.7(5) 19.9(3) 16.1(4) 16.9(6) 18.1(1) 17.8(8) 17.4(8) 39(3)

17.11(5) 27.2(2) 16.11(5) 15.9(2) 16.84(3) 17.6(2) 22.7(5) 16.4(5) 19.9(3) 16.1(4) 16.9(6) 16.3(9) 17.8(8) 17.4(8) 39(3)

19.26(4) 18.98(5) 19.81(5) 19.7(2) 18.7(2) 45.3(6) 20.7(5) 21.4(5) 21.4(5) 21.9(6) 37.6(4) 19.1(9) 21.5(3) 22.6(3) 88(8)

0 0 0.92(2) 0 0.46(7) 0 0 0 1.7(4) 0.2(5) 0 0 0 0 0

0.34(1) 0 0.6(8) 0 0.12(1) 0 0 0 1.0(3) 0 0 0 0 0 0

0 0.52(4) 0.6(8) 0 0.12(11) 0 0 0 1.0(3) 0 0 0 0 0 0

a The anisotropic displacement factors Uij are defined by exp[2p2(h2a  U11+...+ 2hka  b  U12)].

stabilized by the presence of a small quantity of Fe (5 at.%) in the lattice. The crystal structure of U34Fe4xGe33 is depicted in Fig. 2 and it is difficult to describe in terms of simple geometric forms due to the large number of atoms in the coordination spheres. As a consequence, only the environment of the six distinct U atoms in the lattice will be described. The relevant interatomic distances are listed in Table 4. As shown in Fig. 3, the U1, U2, U3 and U4 atoms have 13 nearest neighbors, whereas U5 has 12 and U6 has 16, the highest coordination number among all the six inequivalent U atoms found within this structure. U1 atom is surrounded by four U atoms, eight Ge atoms and one Fe atom. The U2 environment is composed of seven Ge atoms and six U atoms. The refined distances U1–U1 and U2–U2 are 3.173(1) Å and 2.887(1) Å, respectively. The latter distance is shorter than the sum of atomic radii (rU = 1.53 Å [23]) and both are below the Hill limit, pointing to a strong interaction between the f orbitals. The U3 and U4 are located in the center of a distorted pentagonal-based bipyramid, formed only by Ge atoms, surrounded by other six atoms (five U atoms and one Fe atom for U3 and six U atoms for U4). The distances U4–Ge4 and U4–Ge6 are 2.89 Å and 2.85 Å, respectively, i.e. below the sum of the atomic radii of the elements (rGe = 1.39 Å [23]). U5 is located in the center of a regular octahedron composed of eight Ge atoms, in which each face is capped by one U atom at distances ranging from 3.3 Å to 3.6 Å from U5. U6 is positioned at the center of a

Table 2 Positional and equivalent isotropic displacement parameters for U34Fe4xGe33.

a

Atoms

Wyckoff positions

Occupation

x

y

z

Ueq (Å2)a

U1 U2 U3 U4 U5 U6 Ge1 Ge2 Ge3 Ge4 Ge5 Ge6 Ge7 Fe1 Fe2

16n 16n 16m 8j 8f 4e 16n 16n 16m 8h 4e 4c 2a 4e 4e

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.66(3)

0 0 0.1795(1) 0.2618(1) 1/4 0 0 0 0.1410(1) 0.2357(1) 0 0 0 0 0

0.2542(1) 0.3672(1) 0.1795(1) 1/2 1/4 0 0.2502(1) 0.3785(1) 0.1410(1) 0.2357(1) 0 1/2 0 0 0

0.0628(1) 0.1911(1) 0.3840(1) 0 1/4 0.2388(1) 0.2973(1) 0.4003(1) 0.1535(1) 0 0.4348(1) 0 0 0.1023(2) 0.3407(5)

0.0173(1) 0.0218(1) 0.0175(1) 0.0170(1) 0.0173(1) 0.0267(2) 0.0199(2) 0.0145(2) 0.0203(2) 0.0180(3) 0.0234(5) 0.0176(7) 0.0185(6) 0.0187(6) 0.055(4)

Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

M.S. Henriques et al. / Journal of Alloys and Compounds 606 (2014) 154–163

157

Fig. 2. Projections of the unit cell of U34Fe4xGe33 into (a) the (ac) plane and (b) the (ab) plane.

square-based anti-prism. The bases are topped by one U atom each and only four intercalated triangular faces have one U atom each. In U6 coordination, the U6–Fe2 distance is 2.57 Å, i.e. smaller than the sum of the atomic radii (rFe = 1.26 Å [23]). This short distance is rather due to the large vibrations allowed to the Fe2 atoms owing to the partial site occupancy than to significant hybridization between 5f and 3d orbitals. Concerning the Fe1 atoms, 50% of them are strongly hybridized with the Ge atoms, as the U–Ge spacing is shorter than 2.6 Å. From the interatomic distances listed in Table 4, it can be seen that 21 U atoms out of the 68 in the unit cell have U–U interatomic distances above 3.5 Å, thus pointing to a weak interaction between their 5f wave-functions. The opposite situation occurs in the case of the binary USi or UGe compounds, in which 60% of the U atoms in the structure are involved in U–U distances below 3.4 Å. Most of the U–Ge distances range from 3.02 and 3.19 Å (two exceptions are mentioned above) and lie well within the range of distances reported for other binary and ternary uranium germanides. The arrangement of the U sub-lattice in the structure is presented in Fig. 4. It can be seen as a stacking of three different types of layers. The first layer is formed by a square cupola, in which U4 atoms form the square base and U1 form the top irregular octagon. Square cupolae are a class of convex polyhedra (Johnson solid) where each face is a regular polygon, but which is not uniform [24]. In this case it is made by the arrangement of 4 + 1 squares, 4 triangles and an octagon. Concerning the U lattice, the square base has an edge length equal to the distance between the U4 atoms, dU4–U4 = 3.66 Å, whereas the other 4 squares plus the 4 alternating triangles composing the cupola have edge lengths equal to the distance between U1 atoms, dU1–U1 = 3.66 Å and 5.34 Å, respectively. Thus the top octagon is irregular. The second layer is made by four interconnected U5 coordination spheres. U5 is in the center of an irregular cube build up from U2, U3 and U6 atoms. The distance between U5 and U2 is 2.35 Å, while U3 and U6 are positioned at distances above 3.6 Å. The third layer is located in the center of the unit cell and is composed by a square orthobicupola built from U1 and U4 atoms. Square orthobicupolae are another class of Johnson solids closely related with cupolae, as they can be constructed by joining two square cupolae along their octagonal bases, matching like faces [24]. At this point, in each one of the cupolae U1 atoms form the squared base and U4 form the shared irregular octagon in the center.

Although the coordination of the six independent U atoms is similar in U34Fe4xGe33 and in USi, the first has a different range of U–U distances. Thus the extension of the 5f overlap is expected to be different in the ternary compound and it should be reflected in the electronic properties. 3.2. Magnetic measurements Fig. 5a presents the temperature dependence of the magnetization of U34Fe3.32Ge33, measured on a fixed powder sample in a low applied field of 0.25 T. The increase of magnetization with decreasing temperature is related to the onset of ferro or ferrimagnetism. The Curie temperature of the compound was determined to be TC = 28(2) K according to the minimum of the temperature derivative of the magnetization. No sign of other magnetic transitions can be seen in the studied temperature range. The same temperature for the ferromagnetic transition was found in the magnetic susceptibility curves in zero-field cooled (ZFC) and field cooled (FC) (l0H = 0.25 T) modes, as shown in the inset to Fig. 5a. The difference between ZFC and FC modes in the low field magnetization gives a hint of thermomagnetic irreversibility which is a feature of magnetocrystalline anisotropy. The field dependence of the magnetization for applied magnetic fields up to 5 T at 2 K is shown in Fig. 5b. The magnetization at low temperature increases practically linearly with field up to 5 T. The substantial slope corresponds to the susceptibility v = 2.6  107 m3/mol. The behavior at low fields is influenced by a large hysteresis with coercive field l0Hc = 0.59 T, pointing to a high anisotropy and pinning of narrow domain walls. Those explain also the difference between FC and ZFC behavior. The value of the spontaneous moment per U atom is merely 0.18 lB, which brings a suspicion that the ground-state may be actually ferromagnetic, or some U atoms do not carry magnetic moment. In the paramagnetic state (T > 60 K), the susceptibility data can be well described by a modified Curie–Weiss law, v–v0 = C/(T–hp), where C = Curie constant, hp = Curie–Weiss temperature and v0 = temperature-independent susceptibility. The fitting curve is shown as a red line in Fig. 4c and it yielded v0 = 4  107 m3/mol and positive hp = 8 K, as expected for a compound showing predominantly ferromagnetic-type interactions. Nevertheless, the difference between TC and hp reflects that the compound cannot be purely ferromagnetic, being consistent with an

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Table 4 Interatomic distances for U, Fe and Ge atoms in the U34Fe4xGe33 with x = 0.68 compound. Atom pair

Distance (Å)

Atom pair

Distance (Å)

Atom pair

Distance (Å)

U1

1 2 2 1 2 1 1 1 2

Fe1 Ge4 Ge3 Ge6 Ge2 U1 Ge7 U2 U3

2.939(1) 3.021(1) 3.021(1) 3.108(1) 3.123(1) 3.173(1) 3.187(1) 3.469(1) 3.805(1)

U6

1 4 4 1 4

Fe2 Ge3 Ge1 Fe1 U5

2.574(14) 3.058(2) 3.097(2) 3.451(4) 3.854(1)

Ge5

1 4 4 1

U2

1 1 2 2 2 2 1 2

U2 Ge1 Ge2 Ge3 Ge1 U5 U1 U2

2.887(1) 2.970(1) 3.028(1) 3.050(1) 3.089(1) 3.351(1) 3.469(1) 3.608(1)

Ge1

1 1 2 2 2 1

Fe2 U2 U5 U3 U2 U6

2.933(5) 2.970(2) 2.970(1) 3.033(1) 3.089(1) 3.097(2)

Ge6

2 U4 4 Ge2 4 U1

2.845(1) 2.847(1) 3.108(1)

U3

1 2 1 2 1 1 1 2 2

Ge3 Ge2 Fe2 Ge1 Ge5 Ge4 U5 U4 U1

2.919(2) 2.943(1) 2.969(5) 3.033(1) 3.043(2) 3.209(1) 3.557(1) 3.579(1) 3.805(1)

Ge2

1 1 2 1 2 2

Ge2 Ge6 U3 U4 U2 U1

2.641(3) 2.845(1) 2.943(1) 2.946(1) 3.028(1) 3.123(1)

Ge7

2 Fe1 8 U1 4 Ge4

2.585(4) 3.187(1) 3.614(1)

U4

1 2 2 2 4 2

Ge6 Ge4 Ge2 Ge5 U3 U4

2.847(1) 2.888(2) 2.946(1) 3.070(2) 3.579(1) 3.662(1)

Ge3

1 1 1 2 2 1 2

Fe1 U3 U5 U1 U2 U6 Ge3

2.526(2) 2.919(2) 2.958(1) 3.021(1) 3.050(1) 3.058(2) 3.067(1)

Fe1

4 1 4 1

Ge3 Ge7 U1 U6

2.526(2) 2.585(4) 2.939(1) 3.451(4)

U5

2 4 4 2

Ge3 Ge1 U2 U3

2.958(1) 2.970(1) 3.351(1) 3.557(1)

Ge4

2 U4 4 U1 2 U3

2.888(2) 3.021(1) 3.209(1)

Fe2

1 1 4 4

Ge5 U6 U3 Ge1

2.378(14) 2.596(14) 2.933(5) 2.969(5)

antiferromagnetic component integrated in a ferro/ferrimagnetic arrangement. The effective magnetic moment deduced from the Curie constant (as C ¼ N A l2eff =3kB , with NA and kB being Avogadro and Boltzmann constants, respectively) is leff = 2.3lB/U, assuming that only U atoms contribute to the magnetism, and averaging over all the U atoms in the unit cell. This value is lower than the moment for the free ions in U3+ or U4+ configurations on the basis of the Russel– Saunders coupling (leff(U3+) = 3.62 lB and leff(U4+) = 3.58 lB [27]). Nevertheless, values in the range 2.8–3.4 lB are regularly found for uranium intermetallic compounds, in which the band character of the 5f states leads to an effective moment reduction [25]. Although the U–U distances in U34Fe4xGe33 are not generally below the critical distance for 5f electron delocalization, the same is not true for U–Ge distances. In this compound most of the U atoms have 6–8 Ge atoms in their coordination spheres at distances in the range of 2.85–3.1 Å. U1 is the exception, since it only has five Ge atoms at a distance close to the sum of the metallic radii. Consequently, for all the other five independent U atoms, extended hybridization between f and p wave functions is likely to occur, which may cause the reduction of the estimated U magnetic moments. This feature is also found in the binary compound USi crystallizing in a closely related structure and being a paramagnet with leff = 1.8 lB/U [26]. Regarding the Fe sub-lattice, it is unlikely that it can give a significant contribution to the magnetism of U34Fe4xGe33. Not only Fe atoms constitute less than 5% of the total amount of atoms in the unit cell, but in addition they hybridize strongly with Ge (Fe1) or Ge and U (Fe2) atoms. Moreover, the low Curie temperature and the strong magnetic hysteresis also give evi-

Fe2 U3 U4 Ge5

2.378(14) 3.043(2) 3.070(2) 3.287(1)

dence that the main contribution to the magnetism might rather come from the U sub-lattice. To verify this assumption 57Fe Mössbauer spectroscopy measurements were undertook at several temperatures. 3.3.

57

Fe Mössbauer spectroscopy

Mössbauer spectra taken in the temperature range 1.6–295 K for U34Fe4xGe33 consist of a single absorption peak (Fig. 6). This peak may be analyzed as a single quadrupole doublet. The estimated quadrupole splittings (Table 5) are lower than the line widths, thus explaining why the two peaks of the doublet are not resolved. The non-zero quadrupole splitting is consistent with Fe atoms located on positions with symmetry lower than cubic. According to X-ray data Fe is present in two unequally populated crystallographic sites. Since in the Mössbauer spectra only one quadrupole doublet is observed the electronic state of Fe in both sites is expected to be very similar. At 30 K, at the onset of the magnetic transition observed in magnetization data, an asymmetric broadening of the spectrum is clearly visible (Fig. 6). This broadening gradually increases, although very little, as the temperature decreases and becomes more evident at 4 K and 1.6 K. The spectra below 30 K cannot be fitted with a symmetric quadrupole doublet as those above this temperature. Two explanations may be considered: either the slowing down of the relaxation frequency of the Fe magnetic moments directions polarized by the magnetically ordered U sub-lattice as in U3Fe4Ge4 [9,10] or the establishment of long-range magnetic correlations among the Fe magnetic moments, lFe. If the

M.S. Henriques et al. / Journal of Alloys and Compounds 606 (2014) 154–163

159

Fig. 3. Coordination spheres for the six distinct U atoms in the structure of U34Fe4xGe33.

latter is assumed lFe would be frozen in the Mössbauer time scale. The 4 K spectrum should then be fitted by an octet. The sextet approximation is excluded because the quadrupole and magnetic interactions are similar and the former cannot be considered as a perturbation of the magnetic interaction. Since all the octet peaks overlap, due to the very low splitting arising from both the magnetic and quadrupole interactions, the analysis of the spectrum is not unique. On the other hand the low splitting implies that the estimated magnetic hyperfine field, Bhf, cannot be higher than 1.6 T. Considering hyperfine constants in the range 15–11.3 T/lB

[27], typical of intermetallics, these Bhf would be consistent with lFe < 0.15 lB. As already mentioned, the interatomic distances between Fe and Ge nearest neighbors (Table 4) are shorter than the sum of Fe and Ge metallic radii, considering a coordination number 10 [23] suggesting partially localized bonding between Fe and Ge atoms. The relatively high isomer shift (IS) of both Fe atoms may therefore be related to a strong hybridization between Fe and Ge, shifting the 4s electron density in Fe towards the more electronegative Ge atom [28]. Similar isomer shift values are also found for

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Fig. 4. The network of U atoms in the unit cell of U34Fe4xGe33 is constituted of three types of layers. The first layer is an inverted square cupola, whereas the second layer is the coordination sphere of the two U5, and the third layer is a square orthobicupola.

0.25

(a)

U34Fe3.32Ge33 -7 3 χ (10 m /mol)

M (μB /U)

0.20 0.15 0.10 0.05 0.00

10

20

5

30

40

FC ZFC

4 3 2 1 0

μ0H = 0.25 T 0

magnetization data of U34Fe3.32Ge33, as those of U2Fe3Ge [31] and U3Fe4Ge4 [9,10], cannot be explained by the corresponding Fe sub-lattices. They can only derive from the U sub-lattice. As far as we know the only U–Fe–Ge intermetallic compound where magnetic splittings are clearly observed (Bhf > 2.5 T) is UFe6Ge6 [30]0 in which all the U–Fe interatomic distances are higher than 3.1 Å A.

6

50

0

10 20 30 40 50 60 70 80

60

70

80

90

100

T (K)

1/(χ− χ ) (107 mol/m3) 0

M (μB/U)

0.4

(b)

0.3 0.2

T=2K

0.1 0.0

0

1

2

3

μ0H (T)

4

5

3.4. Specific heat

T (K)

4

(c)

3 2 1 0

μ0H = 0.25 T 0

100

200

300

T (K)

Fig. 5. (a) Temperature dependence of the magnetization of U34Fe4xGe33 in a magnetic field of 0.25 T. The inset shows the magnetic susceptibility measured in the modes of zero-field cooling (ZFC) and field cooling (FC) in a magnetic field of 0.25 T. (b) Magnetization as a function of the applied magnetic field measured at T = 2 K with increasing field (d) and decreasing field (s). (c) Reciprocal magnetic susceptibility versus temperature measured in the same magnetic field as in (a). The red line is the data fitting by a modified Curie–Weiss law. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

other U–Fe–Ge intermetallics such as U3Fe4Ge4 [9,10], UFeGe [29], and UFe6Ge6 [30]. Whether in the absence of strong magnetic correlations among the lFe or in the case that frozen lFe are lower than 0.14 lB the

The magnetic transition in U34Fe3.32Ge33 is also seen in the specific heat measurements as a small anomaly around 27 K (Fig. 7). Below TC the specific heat data follows Cp = c T + b T 3, where c T is the electronic contribution to the heat capacity and b T 3 is the lattice contribution. The best fit between 2 and 18 K was obtained for c = 131 mJ/(molU K2) and b = 0.3 mJ/molU K4 (red line, inset to Fig. 7). The value obtained for c classifies this compound as a moderate heavy fermion system. At room temperature, Cp = 1824 J/mol K, which matches within 4% the calculated Dulong–Petit limit (1754 J/ mol K). The apparent effective mass enhancement (averaged over all the non-equivalent U-atoms of this structure) observed in U34Fe3.32Ge33 can be related to the formation of a moderate-heavy fermion state or can be a direct consequence of some inherent atomic disorder in the Fe/Ge sub-lattice due to the insertion of Fe in the Ge lattice derived from the binary type. Moreover, one of the Fe positions is not fully occupied. Although no other meaningful disorder is seen in the XRD data, this possibility cannot be excluded. It is known that even compounds with a defined stoichiometry might have their groundstate physical properties changed by an amount of crystallographic disorder [32,33]. Moreover, U-based compounds which might exhibit some degree of disorder in the non-magnetic sub-lattice, show a delicate interplay between the crystallographic disorder and the strong electronic correlations. The magnetic entropy at TC was estimated to be Smag = 1.3 J/molU K by the integration of the area below the peak in the Cp/T versus T curve using the Debye integral, considering the estimated c-value at low temperature and the Debye temperature hD = 230 K, to approximate the non-magnetic specific heat (blue line,

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U34Fe3.32Ge33

0.5

TC

2

1000

C p /T (J/mol U K )

Cp (J/mol K)

1500

500

0.4 0.3 0.2 0.1

0

10

20

30

40

T (K)

0

0

50

100

150

200

250

T (K) Fig. 7. Temperature dependence of the specific heat Cp of U34Fe4xGe33, showing a small anomaly near the Curie temperature. The inset shows Cp/T versus T for T 6 40 K. The solid lines are an estimation of the non-magnetic contribution according to the Debye model (blue) and the low temperature (T 6 18 K) fitting procedure used to estimate the Sommerfeld coefficient (red). Further details are given in the text. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. 57Fe Mössbauer spectra of U34Fe4xGe33 taken at different temperatures, showing a single absorption peak and no magnetic splitting of the Fe sub-lattice.

Table 5 Fitted parameters of the Mössbauer spectra of U34Fe4xGe33 taken at different temperatures. T (K)

IS (mm/s)

QS (mm/s)

QUA (mm/s)

Bhf (T)

295 130 90 20 10 4 1.6

0.13 0.27 0.29 0.33 0.34 0.34 0.34

0.15 0.16 0.18 – – – –

– – – 0.12 0.13 0.12 0.13

– – – 1.2 1.5 1.6 1.6

IS: isomer shift relative to metallic a-Fe at 295 K; QS: quadrupole splitting; QUA = e2VZZQ/2, quadrupole interaction. Bhf: magnetic hyperfine field. Estimated errors are 60.02 mm/s for IS and QS. Values h = 0 and / = 0°, polar and azimuthal angles of Bhf relative to the main axes of the EFG, as well as g = 0.80, asymmetry parameter, were kept constant during the fitting procedure. These values correspond to those leading to the best final adjustments.

inset in Fig. 7). The magnetic entropy is thus only 0.22 of R ln2 corresponding to the filling up of the doublet ground-state. The lattice contribution has been estimated in the absence of a non-magnetic counterpart which is required for a more accurate value of Smag.

Nevertheless, this small value of the magnetic entropy can arise (i) whether from an avering of the specific heat over all the atoms present in the structure and is probably much higher on the magnetically ordering lattice or (ii) from the above discussed structural disorder. Both hypotheses can also contribute to a less well defined k-type anomaly at TC. The low magnetic entropy of U34Fe3.32Ge33 is comparable with the ones found for weak itinerant ferromagnets of similar systems, as URhGe (Smag = 0.46 R ln2), U3Fe4Ge4 (Smag = 0.5 R ln2) or UCoGe (Smag = 0.04 R ln2) [5,9,34]. As shown in the inset of Fig. 7, there is a gap between the phonon extrapolated curve (blue) and the experimental data points above TC, although the extrapolated curve approaches the experimental curve and both merge at 62 K. This behavior might be related with the importance of the magnetic degrees of freedom which might start to be relevant for the specific heat even above TC, for instance due to enhanced spin fluctuations in the paramagnetic state when the magnetic transition approaches. Moreover, this effect might also be understood by many possible degrees of freedom in this material (more than 140 atoms per unit cell) since the Debye model is an oversimplification for fitting the entire lattice contribution, which may contribute to possible underestimation of the low temperature lattice contribution. This behavior is common in many U compounds, e.g. the case of URu2Si2 (TN = 17.5 K) and the non-magnetic counterpart ThRu2Si2, in which the two curves only coincide above 100 K [35]. In URu2Si2, spin fluctuations are said to set in at a characteristic temperature of 70 K. To gain further insight into the electronic properties, the electrical transport properties were also studied for this compound. 3.5. Electrical resistivity, magnetoresistivity and thermopower The temperature dependence of the electrical resistivity q(T) measured between 290 and 1.4 K for a polycrystalline sample of U34Fe3.32Ge33 is shown in Fig. 8. The curve has a metallic-like character between 290 and 26 K. Centered at this temperature a broad minimum occurs in the curve and then q(T) increases with decreasing temperature down to 1.4 K. However, the overall

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360

U34 Fe 3.32 Ge 33

350

4T 2T 1T 0.2 T 0T

340

318

330

316

ρ (μΩ cm)

ρ (μΩ cm)

duction. The thermopower decreases with temperature and does not present a maximum as one would expect from a Kondo system. Around TC a small increase in the slope of the thermopower curve is visible, signaling the magnetic transition. The U34Fe3.32Ge33 compound presents globally an important resistivity value with a very low RRR. All together with the low thermopower global value and the apparent high electronic coefficient of the specific heat, points to the presence of disorder in the crystallographic structure. The partial Fe occupancy is probably the key feature. As to the magnetism, the only type of ordering that can be excluded is simple antiferromagnetism. Other scenarios might be non-collinear ferromagnetic structures or ferromagnetic ordering only on some U sites, which would explain the low magnetic entropy.

320

314 312 310

310

10

300

0

50

100

150

20

T (K)

200

30

4. Conclusion

40

250

300

T (K) Fig. 8. Temperature dependence of the resistivity for U34Fe4xGe33 measured under various magnetic fields. The inset highlights the increase in resistivity and Curie temperature with the applied field in the low temperature region.

U34 Fe 3.32 Ge 33

S ( μ V/K)

6

4

TC

2 0

50

100

150

200

250

300

T (K) Fig. 9. Temperature dependence of the thermopower for U34Fe4xGe33, showing the change in slope near TC.

change in the resistivity is small as the temperature is decreased and the residual resistivity ratio RRR = q (290 K)/q (1.4 K) is of about 1.1. Remarkably, the residual resistivity itself is quite large, being equal to q0 = 314 lX cm. All the features of the electronic transport properties of U34Fe3.32Ge33 are in line with the specific heat results. Although other reasons might provide a satisfactory description of these results, the upturn in q(T) around TC might as well be explained either by the influence of disorder in the Fe/Ge sub-lattice of the compound probably combined with the presence of ferro/ferrimagnetism inducing the gapping of the Fermi surface. As it can be seen in the inset to Fig. 8, the sharp minimum in the q(T) curve shifts towards higher temperatures with the applied magnetic field, while the magnitude of the upturn does not significantly change. The temperature dependence of the thermopower between 18 and 300 K is presented in Fig. 9. The thermopower values are small and positive in good agreement with metallic-like character observed in the resistivity and indicative of hole-dominated con-

A novel U-based intermetallic phase U34Fe4xGe33 was found in the U–Fe–Ge ternary system. Single crystal X-ray diffraction has shown that this compound crystallizes in the tetragonal lattice system (space group I4/mmm), with cell parameters a = 10.873(5) Å and c = 25.274(5) Å. It adopts a new structure type derived from the binary USi. Although the U sub-lattice remains similar to the binary silicide, Fe/Ge lattice can introduce some disorder in the new ternary structure of U34Fe4xGe33. Regarding the analysis of the interatomic distances and the complexity of this structure, an interesting possibility is that different U atoms might carry different magnetic moments due to differential extent of hybridization from site to site. Magnetization measurements have shown that U34Fe4xGe33 orders magnetically below TC = 28 K, with magnetization behavior more likely encountered for ferro or ferrimagnets. The main contribution to the magnetic ordered state comes from the U lattice in agreement with 57Fe Mössbauer spectroscopy. An anomaly in the specific heat and a minimum in the resistivity and a change in slope in the thermopower also indicate the magnetic ordering temperature. Moreover, the minimum in the resistivity curve below TC and shifting to higher temperatures under increasing fields, together with high residual resistivity, low RRR, an enhanced electronic contribution to the specific heat and a small magnetic entropy involved in the transition, might support the possible influence of local disorder within Fe/Ge sub-lattice in the physical properties and/or the competition between a partially ordered sublattice below the Curie temperature. A clear distinction of the origin of the features of this compound might be achieved after further experimental work such as neutron diffraction or dynamic magnetic studies. Acknowledgements M.S. Henriques acknowledges the kind help of D. Gorbunov (Institute of Physics, ASCR) dealing with the specific heat measurements, and the support of the Portuguese Foundation for Science and Technology through the grant SFRH/BD/66161/2009. This work was supported by the exchange Program CNRS/FCT (PICS SCR-ITN) 2011–2013. References [1] A.J. Arko, J.J. Joyce, L. Havela, 5f-Electron phenomena in the metallic state, in: L.R. Morss, N.M. Edelstein, J. Fuger, J.J. Katz (Eds.), The Chemistry of Actinides and Transactinide Elements, third ed., vol. 4, Springer, The Netherlands, 2008, p. 2308. [2] G. Zwicknagl, P. Fulde, The dual nature of 5f electrons and the origin of heavy fermions in U compounds, J. Phys.: Condens. Matter 15 (2003) S1911. [3] B.R. Cooper, Y.-L. Lin, Q.-G. Sheng, Magnetic ordering in strongly correlatedelectron uranium systems: consequences of two kinds of f-electron-band– electron states, J. Appl. Phys. 85 (1999) 5338.

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