Structural, electronic and magnetic properties of

Journal of Solid State Chemistry 191 (2012) 121–128

Contents lists available at SciVerse ScienceDirect

Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc

Structural, electronic and magnetic properties of layered REB2C compounds (RE¼ Dy, Tm, Lu) Volodymyr Babizhetskyy a,b,n, Arndt Simon a, Constantin Hoch a, Kurt Hiebl c, Laurent Le Polle s d, Re´gis Gautier d,nn, Jean-Franc- ois Halet d,nn a

Max-Planck-Institut f¨ ur Festk¨ orperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany Department of Inorganic Chemistry, Ivan Franko National University of L’viv, Kyryla & Mefodiya Str. 6, UA-79005 Lviv, Ukraine c Arbeitsgruppe Neue Materialien, Universit¨ at Wien, W¨ ahringerstrasse 42, A-1090 Wien, Austria d Sciences Chimiques de Rennes, UMR 6226 CNRS, Ecole Nationale Supe´rieure de Chimie de Rennes, Universite´ de Rennes 1, Avenue du Geńe´ral Leclerc, F-35042 Rennes Cedex, France b

a r t i c l e i n f o

abstract

Article history: Received 15 December 2011 Received in revised form 21 February 2012 Accepted 25 February 2012 Available online 7 March 2012

The crystal structure of LuB2C has been determined from single crystal and powder X-ray diffraction ˚ b ¼ 6.7341(1) A, ˚ data. It crystallizes in the orthorhombic space group Pbam (a¼ 6.7429(1) A, ˚ Z¼ 4, R1¼ 0.024 (wR2 ¼0.059) for 436 reflections with Io 42s(Io)). The compounds c ¼3.5890(1) A, REB2C (RE ¼Y, Tb–Lu) are isotypic. The boron and carbon atoms form infinite, planar two-dimensional nets which alternate with sheets of rare-earth metal atoms. Inside the nonmetal atom nets, a coloring with fused B2C2 rhombuses and B5C2 heptagons is proposed, supported by NMR experiments and density functional theory calculations. The calculated density of states of LuB2C indicates this compound to be metallic. The magnetic properties of the isotypic compound TmB2C, has been measured in the temperature range 2 K o To 300 K and in various external fields up to B ¼ 7 T. The sample undergoes an antiferromagnetic (AFM) transition at TN ¼ 12 K, and at fields B 43 T a metamagnetic transition is encountered. The temperature dependence of the electrical resistivity proves the metallic character of the TmB2C compound as well as the AFM ordering. & 2012 Elsevier Inc. All rights reserved.

Keywords: Rare-earth metal boride carbide Crystal structure Electronic structure Density functional theory calculations Rare-earth metal magnetism

1. Introduction The structural chemistry of ternary rare earth metal boride carbides RExByCz (RE¼rare-earth or actinoid metal) is particularly rich. These compounds can be classified into three categories [1], depending upon the arrangement of the nonmetal atoms: (a) boron and carbon atoms form infinite, planar two-dimensional (2-D) nets, (b) boron and carbon are bonded in one-dimensional (1-D) zig-zag boron chains with carbon atoms attached, and (c) boron and carbon atoms are assembled in finite chains of different length. The dimensionality of the boron–carbon network in these compounds is related to the average valence electron concentration (VEC) per main group atom [2], assuming in a first

n Corresponding author at: Department of Inorganic Chemistry, Ivan Franko National University of L’viv, Kyryla & Mefodiya Str. 6, UA-79005 Lviv, Ukraine. Fax: þ 380 33 2 2323 6840. nn Corresponding authors at: Sciences Chimiques de Rennes, UMR 6226 CNRS Ecole Nationale Supe´rieure de Chimie de Rennes - Universite´ de Rennes 1, Avenue du Geńe´ral Leclerc, F-35042 Rennes Cedex, France. E-mail addresses: [email protected] (V. Babizhetskyy), [email protected] (R. Gautier), [email protected] (J.-F. Halet).

0022-4596/$ - see front matter & 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jssc.2012.02.062

approximation a Zintl–Klemm ionic bonding scheme [3] between the metal and the nonmetal atoms. Layered compounds of formula REB2C2 (LaB2C2 and ScB2C2 types of structures) [4–6], REB2C (YB2C, ThB2C, a-UB2C types) [7–11], RE2B3C2 (Gd2B3C2) [12] as well as Sc2B1.1C2.3 [13] belong to the first category [2]. In the tetragonal LaB2C2-type structure the B and C atoms form planar nets of four- and eight-membered rings stacked directly above one another with the metal atoms occupying positions between the eight-membered rings. In the orthorhombic structure of ScB2C2 the B/C layers consist of fused five and seven-membered rings with the metal atoms occupying positions between the larger rings. In both B/C nets all atoms are three-connected. Three structural types have been reported for the REB2C phases. While the structure type of ThB2C [10] is found with the early actinoid metals (Th, U, Np, Pu) [14] so far, CeB2C [15] is the only rare-earth metal compound with ThB2C structure which contains fused hexagonal and nine-membered rings. The boride carbides of the smaller rare-earth metals, (Sc, Tb–Lu)B2C, rather seem to crystallize in the YB2C-type with tetragonal symmetry (P42/mbc) according to early powder X-ray measurements, with successive nonmetal atom sheets composed of fused four-membered B2C2 and seven-membered B5C2 rings rotated by 901 along

122

V. Babizhetskyy et al. / Journal of Solid State Chemistry 191 (2012) 121–128

b

b a

a

Fig. 1. Colorings I (experimental, Pbam, left) and II (hypothetical P4/mbm, right) for LuB2C.

the stacking direction [7–9]. Later, the crystal structure of HoB2C obtained on the basis of powder X-ray and neutron powder diffraction data was found to be different to the earlier proposed tetragonal YB2C-type [16]. Indeed, orthorhombic or monoclinic symmetry was assumed with B2C layers stacked directly above each other, as it is also found in the REB2C2 compounds [4]. This is confirmed according to a new investigation of REB2C (RE ¼Y, Tb–Lu) phases that we carried out recently [17]. Thus, the crystal structure of DyB2C has to be described with orthorhombic symmetry different from the tetragonal YB2C-type [18]. There is also the question of B/C distribution in the nonmetal layers. As the very weak X-ray scatters B and C coexist with the strong scatter rare-earth metal in the compound REB2C the problem of the distribution of B and C on the available crystallographic sites may arise. This problem called ‘‘the Coloring problem’’ by Burdett et al. [19], has been addressed several times in rare-earth metal borocarbides [5,20]. In the case of REB2C, several colorings can be envisioned. Two of them are sketched in Fig. 1: Coloring I proposed on the basis of X-ray single crystal diffraction studies and 11B solid-state NMR experiments [21] with B/C alternation in the rhombuses, and Coloring II with boron rhombuses. Here we present part of our work on REB2C compounds, in particular addressing the crystal and electronic structures of LuB2C as well as its 11B NMR spectrum and the magnetic and the electrical properties of TmB2C.

glass capillaries. These crystals were first examined by the Buerger precession technique in order to establish their suitability for the subsequent data collection. Single crystal diffraction data of LuB2C were collected at room temperature on a STOE IPDS II image plate diffractometer with monochromatized MoKa radiation. All relevant crystallographic data are listed in Table 1. The starting atomic parameters were derived via direct methods using the program SIR97 [22]. They were subsequently refined with the program SHELX-97 [23] within the WinGX program package [24] (full matrix least-squares on F2) with anisotropic atomic displacement factors for all atoms. The refinements converged well, and the light atoms could be located from difference Fourier maps. The atomic coordinates and thermal parameters are listed in Table 2, selected interatomic distances and bond angles are reported in Table 3. Drawings of the structure were prepared with the program DIAMOND [25]. The calculated X-ray powder diffraction patterns recorded on samples sealed in capillaries under dry argon were found to be in good agreement with the experimental patterns collected on a STOE STADI P with MoKa1 radiation. The diffraction profiles were collected in 48 h in the range 41o2y o751. Rietveld analysis of the X-ray diffraction profile and the unit cell parameters for all investigated samples of REB2C (RE ¼Y, Tb–Lu) were performed with the CSD software package [26]. The correct indexing of the X-ray patterns was ensured through intensity calculations using the orthorhombic symmetry and atomic positions from the single crystal refinement. The unit cell parameters for all investigated compounds REB2C (RE¼ Y, Tb–Lu) are presented in Table 4. 2.3. Magnetic and electric resistivity measurements Measurements of the magnetizations M and the magnetic susceptibilities, w ¼M/H, in external fields B r7 T were performed in the temperature interval 1.8–300 K using a MPMS XL-7 SQUID magnetometer (Quantum Design, Inc.). Measurements of the Table 1 Crystal data and structure refinement for LuB2C. LuB2C 208.59 Pbam oP16, 4

2. Experimental

Empirical formula Molar mass Space group Pearson symbol, Z Lattice parameters (powder pattern) ˚ a (A)

6.7341(1)

2.1. Synthesis and analysis

˚ b (A) ˚ c (A)

The compounds REB2C (RE¼ Y, Tb–Lu) were prepared from commercially available elements: RE 99.99 at%, Alfa – Aesar, Johnson Matthey Company, sublimed bulk pieces, crystalline boron powder (99.99 at%; H.C. Starck, Germany, graphite powder, 99.98 at%, Aldrich). The graphite and boron powders were outgased overnight at 950 1C, p o10 5 mbar. All handlings were carried out by Schlenk-technique or in a dry-box. Mixtures of the powders were compacted in stainless steel dies. The pellets of ca. 1 g were arc-melted under purified argon atmosphere on a water-cooled copper hearth, turned over and re-melted typically three times to improve homogeneity. The samples were then wrapped in molybdenum foil enclosed in an evacuated silica tube, annealed at 1270 K for one month, and then quenched in cold water. 2.2. X-ray diffraction and structure refinement

Unit cell volume (A˚ 3) Calculated density (g/cm3) Absorption coefficient (1/cm) Crystal size/mm3 ˚ Radiation and wavelength (A) Diffractometer Refined parameters Refinement 2ymax and (siny/l)max h, k, l

Collected reflections Independent reflections Reflections with Io Z2s(Io) Final R1 indices (R1 all data)a Weighted wR2 factor(wR2 all data)b Goodness-of-fit on F2: Extinction coefficient Largest diff.peak and hole (e A˚ 3) a

Small irregularly shaped single crystals were selected from the crushed sample of LuB2C and sealed under argon atmosphere in

6.7429(1) 3.5890(1) 162.97(1) 8.502 59.95 0.10 0.08 0.02 Mo Ka, 0.71069 STOE IPDS II 26 F2 72.96, 0.762 11o h o11 9o k o 11 5o l o 5 4993 445 (Rint ¼0.057) 436 (Rs ¼ 0.022) 0.024 (0.025) 0.059 (0.060) 1.11 0.018(1) 3.00/ 3.55

R1(F) ¼ [S(9Fo9 9Fc9)]/S9Fo9. wR2(F2)¼ [S[w(F2o F2c )2/S[w(F2o)2]]1/2; [w-1 ¼ s2(Fo)2 þ(0.031)2 þ4.525P], where P¼(F2o þ2F2c )/3. b


123

Table 2 Atomic coordinates and displacement parameters (in A˚ 2) for LuB2C.a. Atom

Site

x

y

z

Ueq/Uiso

U11

U22

U33

U12

Lu C B1 B2

4h 4g 4g 4g

0.30878(4) 0.037(1) 0.094(1) 0.333(1)

0.30880(4) 0.332(1) 0.0.095(1) 0.037(1)

1/2 0 0 0

0.0028(1) 0.007(1) 0.004(1) 0.004(1)

0.0034(1) 0.006(3) 0.002(3) 0.004(3)

0.0039(1) 0.010(3) 0.005(2) 0.004(2)

0.0011(1) 0.006(3) 0.005(3) 0.005(3)

0.00034(7) 0.003(2) 0.001(2) 0.002(2)

a

U23 ¼ U13 ¼0.

Table 3 ˚ and B–C angles (deg) with multiplicities for LuB2C resulting Bond lengths (d, A) from X-ray diffraction studies and DFT optimization. Bond

Mult

d

opt

Bond

Mult

d/Angle

opt

Lu–Lu Lu–Lu Lu–Lu Lu–Lu Lu–B1 Lu–B1 Lu–B1 Lu–B2 Lu–B2 Lu–C Lu–C B1–B2 B1–B1

1 2 2 2 2 2 2 2 2 2 2 1 1

3.6443(4) 3.5890(1) 3.4632(4) 3.4591(4) 2.720(6) 2.711(6) 2.711(6) 2.551(5) 2.568(5) 2.567(6) 2.551(6) 1.66(1) 1.80(1)

3.632 3.595 3.485 3.421 2.705 2.716 2.734 2.592 2.613 2.531 2.562 1.708 1.808

C–B1 C–B2 C–B2

1 1 1

1.65(1) 1.63(1) 1.62(1)

1.595 1.611 1.621

C–B2–C C–B2–B1 C–B2–B1 C–B1–B2 C–B1–B1 B2–B1–B1 B2–C–B2 B2–C–B1 B2–C–B1

1 1 1 1 1 1 1 1 1

90.3(5) 135.7(6) 134.0(6) 116.8(6) 121.7(7) 121.5(7) 89.7(5) 134.4(6) 135.9(6)

99.1 129.3 131.6 117.3 121.0 121.6 80.9 138.7 140.4

Table 4 Unit cell parameters for REB2C. RE

˚ a (A)

˚ b (A)

˚ c (A)

V (A˚ 3)

Ref.

Sc Y Tb Dy Ho Er Tm Yb Lu

6.651 6.7815(3) 6.7844(3) 6.789 6.775 6.7515(4) 6.7323(5) 6.7212(6) 6.7429(1)

– 6.7904(4) 6.7907(3) 6.777 6.785 6.7807(6) 6.7452(5) 6.7304(7) 6.7341(1)

6.763 3.7535(1) 3.7883(2) 3.725 3.696 3.6585(3) 3.6383(3) 3.6268(4) 3.5890(1)

299.17 172.56(2) 174.53(3) 171.8 169.9 167.49(4) 165.22(4) 164.06(5) 162.97(1)

[9]

[18] [16]

electrical resistivity were carried out for TmB2C applying a common four-probe technique in the temperature range 7–300 K. Electrical contacts were made with commercial silver paint (Degussa, Hanau, Germany) and 25 mm gold wire.

Hamiltonian populations (COHP) were computed with the scalar relativistic tight-binding linear muffin-tin orbital method in the atomic spheres approximation including the combined correction (LMTO) [30]. Exchange and correlation were treated in the local density approximation using the von Barth–Hedin local exchange correlation potential [31]. Normally, within the LMTO formalism, interatomic spaces were filled with interstitial spheres. Because of the close-packed character of the LuB2C crystallographic structures, no interstitial ‘‘empty’’ spheres were added. The full LMTO basis set consisted of 6s, 6p, 5d, and 4f functions for Lu spheres, and 2s, 2p, and 3d functions for B and C spheres. The eigenvalue problem was solved using the following minimal basis set ¨ obtained from the Lowdin downfolding technique: Lu (6s, 5d, 4f), C (2s, 2p), and B (2s, 2p). The k space integration was performed using the tetrahedron method [32]. Charge self-consistency and the average properties were obtained from 490 and 280 irreducible k points for Pbam and P4/mbm crystallographic structures, respectively. DOS and COHP curves were shifted to the Fermi level at 0 eV. Electric field gradient (EFG) calculations were carried out using PAW [33] method and the PBE generalized gradient approximation [28]. EFG calculations were checked for convergence with respect to the kinetic energy cut-off of the plane waves basis set and the k point grid used for integration over the Brillouin zone. Calculations were considered as converged when the maximum variation for the quadrupolar coupling constant and the asymmetry parameter of 11B nuclei did not exceed the values of 0.1 MHz and 0.05, respectively. PAW calculations were carried out with the CASTEP 5.5 code [27] using the same computational parameters as for geometry optimizations. A quadrupole moment Q for 11B equal to 40.59(10) mB was taken from ref. [34]. Since NMR is not sensitive to the sign of CQ at ambient temperature, absolute values of CQ were considered.

3. Results

2.4. Solid-state NMR

3.1. X-ray crystal structure of LuB2C

Experiments were carried out using a Bruker Avance 300 NMR spectrometer (7 T) equipped with a 2.5 mm MAS probe. Spectra were recorded using 11B rotor synchronized Hahn echo MAS experiments.

A crystal structure for LuB2C was first proposed on the basis of the YB2C structure [7–9] which is an ordered variant of the ThB4 structure [35], by removing the two out-of-plane B atoms from the B6 octahedra and replacing two of the remaining B atoms by C atoms to give B2C layers, composed of four-membered (B2C2) and seven-membered (B5C2) rings (Coloring I, see the left hand-side of Fig. 1). The B2C layers are stacked along [0 0 1] and rotated by 901 to each other generating tetragonal P42/mbc symmetry, and leading to a doubling of the c-axis [7–9]. This stacking was suggested for RE ¼Sc, Y and Tb–Lu [7–9], until powder X-ray and neutron diffraction data showed no evidence for a doubling of the c-axis for HoB2C [16]. In order to solve this discrepancy X-ray powder and for the first time, single crystal data of DyB2C [18] and LuB2C were analyzed. No doubling of the c-axis according to the earlier proposed YB2C unit cell was detected within the counting

2.5. Theoretical calculations Density functional theory (DFT) calculations were carried out using two different computational approaches. Geometry optimizations were performed using the CASTEP 5.5 code [27] with PBE generalized gradient approximation [28]. Pseudo-potentials were generated using the OTF ultrasoft pseudopotential generator included in the program. A cut-off energy of 900 eV and a Monkhorst-Pack k-point grid [29] of 7 7 11 permitted to achieve convergence. Default pseudopotential parameters were used for all elements. Density of states (DOS) and Crystal Orbital

124


statistics of the measurements even with prolonged X-ray exposure. All the reflections could be indexed in a tetragonal a a c/ 2 unit cell with a E6.7 and c E7.2 A˚ [7–9]. The metrics of the single crystal unit cell and measured data lead to the space group P4/mbm but with no alternating B and C atoms in the rhombuses, i.e., fused sheets of four-membered (B4) and seven-membered (B4C3) rings (Coloring II, see the left right-side of Fig. 1). The powder X-ray diffraction data also show no evidence for a doubling of the c-axis, however a close examination reveals that some peaks in the diffraction pattern are broadened. This can result from a lowering of symmetry. A series of profile matching using a pseudo-Voigt peak shape was carried out to determine crystal symmetry. The regions of the fits are shown in Fig. 2. Indeed, the reduced values of Rp ¼3.1% for orthorhombic symmetry (Fig. 2(a)) and high Rp ¼6.0% for tetragonal symmetry (Fig. 2(b)) indicate a significant improvement upon symmetry lowering. In particular the 161 reflections in the tetragonal system exhibit a splitting into 161 and 611 if normalized to the half-width of the nearly 223 reflections, see Fig. 2(a) and (b). No monoclinic distortion can be deduced from X-ray single crystal as well as powder diffraction data. Based on the orthorhombic symmetry obtained from Rietveld refinement for LuB2C the single crystal refinement was performed. The reflection conditions in the single crystal data clearly led to the space group Pbam, corresponding to the highest possible symmetry for correct ordering of B and C atoms (Coloring I, Fig. 1) and allowing an eclipsed stacking of the B/C sheets along the c-axis (Fig. 3). The final atomic and displacement parameters of LuB2C are listed

a

B2

C

B1

B1 B1 Lu

b c a Fig. 3. Perspective view of the crystal structure of LuB2C.

in Table 2, and selected bond distances and bond angles in Table 3. The bonding in the B/C layers is quite irregular. The fourmembered B2C2 rings have a two-fold symmetry with internal angles of 89.7 and 90.31 and B–C distances of 1.63 A˚ (Fig. 2). The seven-membered B5C2 rings have internal angles between 116.8 and 135.91 around the ideal value of 128.61 for a heptagon. The B– B and B–C distances show significant differentiation (see Table 3), suggesting a marked variation of bond order around the rings. 3.2. Electronic structure of LuB2C

b

Fig. 2. The 90–941 2y region of the X-ray powder diffraction pattern of LuB2C showing profil matching fits to the data assuming (a) orthorhombic Pbam and (b) tetragonal P4/mbm space group symmetry.

DFT geometry optimizations were carried out for each coloring with atomic positions and cell parameters free to relax. Optimized crystallographic parameters and bond distances are listed in Tables 3, 5, and 6. Optimization of the Pbam structure (Coloring I) leads to a small shortening of the cell parameter a and a weak lengthening of cell parameters b and c. The volume of the optimized cell is less than 1 A˚ 3 larger than the experimental one. This is below the 1–2% overestimation that is often computed with the PBE functional. Only B1–B2 and C–B1 are substantially affected by the optimization: The former is lengthened from 1.660 to 1.708 A˚ whereas C–B1 bond is shortened by ca. ˚ The total energy of the optimized Pbam structure of LuB2C 0.05 A. is close to that of the experimental structure (0.14 eV/formula unit in favor of the computed one). LMTO DOS and COHP curves of the X-ray structure of LuB2C are sketched in Fig. 4. The corresponding curves for the optimized Pbam structure are very similar (see Supporting Information). The Fermi level cuts a peak of the DOS as expected for a metallic compound. The fully occupied 4f levels of lutetium lie around 5 eV. Below the Fermi level, bands show significant contributions arising from light elements with bonding B–B and B–C characters. COHP curves indicate that B–C bonding is optimized. This is not the case for the B–B bonds since vacant bonding bands lie between þ5 and þ9 eV. The computed net charge of þ2.38 for the rare-earth metal atom shows a large electron donation towards the B2C net. This indicates a predominantly ionic interaction between the rare-earth and light elements. The alternative B/C distribution within the layers (P4/mbm symmetry), i.e., Coloring II (Fig. 1) was also theoretically analyzed


125

Table 5 X-ray and DFT-optimized cell parameters, atomic positions and total energy of LuB2C. X-ray

DFT-opt. Pbam

DFT-opt. P4/mbm

˚ a (A)

6.7429(1)

6.6528

6.6659

˚ b (A) ˚ c (A)

6.7341(1)

6.7684

6.6659

3.589(1)

3.6317

3.7351

162.97(1)

163.53

165.97

0.30878(4), 0.30880(4), ½ 0.037(1), 0.332(1), 0 0.094(1), 0.095(1), 0 0.333(1), 0.037(1), 0 0

0.31239, 0.30890, ½ 0.04102, 0.32282, 0 0.09690, 0.09367, 0 0.34612, 0.03336, 0 0.14

0.80371, 0.30371, ½ 0.91637, 0.58363, 0 0.96813, 0.81871, 0 þ 0.71

Volume (A˚ 3) Lu C B Relative DFT energy (eV/formula unit)

Table 6 ˚ with multiplicities for the hypothetical P4/ DFT-optimized bond lengths (d, A) mbm-LuB2C. Bond

Mult

DFT-optimized

Lu–Lu Lu–Lu Lu–Lu Lu–B Lu–B Lu–C Lu–C B–B C–B C–C

4 1 1 1 1 2 1 2 2 1

3.409 3.701 3.735 2.543 2.604 2.745 2.791 1.735 1.605 1.577

for LuB2C. Tables 5 and 6 list the optimized cell parameters and bond distances, respectively. Although the volume is only 3 A˚ 3 larger than that of the X-ray unit cell, the c parameter is almost 0.15 A˚ larger than that experimentally measured. Optimized distances are consistent with those encountered in the X-ray crystal structure of LuB2C as well as in other lutetium borocarbides [36]. The LMTO DOS curve (Supporting Information) suggests as well a metallic behavior for this compound. Interestingly, the COHP curve for C–C shows that some occupied bands lying between 2 and 4 eV exhibit substantial antibonding character. From the energetic point of view, this hypothetical structure of LuB2C (Coloring II) is unfavorable compared to the Pbam crystal structure (Coloring I) since its total energy is þ 0.71 and þ0.85 eV/formula unit higher than that of the X-ray and DFToptimized Pbam crystal structures, respectively. The same result was found earlier for YB2C [21].

3.3.

11

B solid-state NMR

11

B solid state NMR has proved to be a valuable tool to address cases where the location of light elements in a crystal structure is a challenge for diffraction techniques [21,37,38]. Because of the 3/2 spin value of 11B nucleus, a quadrupolar interaction must be anticipated in the NMR experiments. Since the quadrupolar interaction is very sensitive to the local environment of the atoms, 11B solid-state NMR experiments can provide valuable structural information, particularly if it is combined with firstprinciples calculations of quadrupolar interactions parameters. Such an approach has been successfully used to solve the coloring problem in YB2C [21]. 11B EFG parameters have been computed for different LuB2C crystal structures (Table 7). The effect of geometry optimization on computed quadrupolar parameters is rather small, especially for the quadrupolar coupling constant. However, the differences of the computed quadrupolar parameters of the two boron atoms of the Pbam crystal structure might be large enough to be distinguished using 11B NMR.

Fig. 4. LMTO DOS and COHP curves for LuB2C (X-ray crystal structure).

Table 7 Computed quadrupolar NMR structures of LuB2C.

X-ray DFT-opt. Pbam DFT-opt. P4/mbm

11

B parameters for X-ray and DFT-optimized crystal

CQ (MHz)

ZQ

1.55 1.56 1.49 1.57 1.53

0.38 0.75 0.24 0.34 0.19

In the case of LuB2C, the main interactions involved in the 11B NMR lineshape are presumably not only quadrupolar interactions but also metallic shift interaction because of its metallic properties. 11B solid-state NMR experiments were carried out on a

126


60

1/χ (103kg/m3)

40

20

0

Fig. 5.

11

50

100

150 T (K)

200

250

300

Fig. 7. Reciprocal susceptibility vs. temperature for TmB2C in fields B¼ 0.1 T (open. symbols) and B¼7 T (filled symbols). Lines show the least-squares fit.

B MAS NMR spectrum recorded at a MAS rate of 15 kHz.

150

150

7T 100

3T 1T 100

M (Am2/kg)

M (Am2/kg)

0

50

50 0 -50

-100 0

-150 0

50

100

150 T (K)

200

250

-7

300

-6

-5

-4

-3

-2

-1

0 1 B (T)

2

3

4

5

6

7

Fig. 6. Magnetization vs. temperature for TmB2C in various applied fields. Open symbols in ZFC, filled symbols in FC conditions.

Fig. 8. Isothermal magnetization vs. applied field at T¼ 2 K. Open symbols in increasing fields, filled symbols in decreasing fields.

powder sample of LuB2C in order to confirm the arrangement of boron and carbon atoms in the nonmetal sheets. The simulation of 11B MAS NMR spectra generated by second-order quadrupolar broadening using the EFG values presented in Table 7 does not allow to distinguish between the two possible geometries: The lineshape sketched in Fig. 5 is not dominated by second-order quadrupolar broadening which represents only about 10% of the total linewidth. The lineshape is presumably dominated by short T2 relaxation times. This hinders to draw a conclusion based on the comparison with DFT-computed EFG. Anyway, considering a lineshape dominated by isotropic metallic shift (comparable to results obtained in ref. [38]), the NMR lineshape clearly exhibits two contributions that are in favor of a structural elucidation in the Pbam space-group.

applied magnetic fields. The effective paramagnetic moment is calculated by a least squares fit according to the general formula

3.4. Magnetic properties of TmB2C The temperature dependence of the magnetization, M, for a powder sample of TmB2C was measured under field cooled (FC) and zero-field cooled (ZFC) conditions in various fields as shown in Fig. 6. The magnetization passes a pronounced maximum at T¼12 K in external fields B o1 T and in increasing as well as in decreasing temperatures. This observation is attributed to the onset of an antiferromagnetic order. In elevated magnetic fields B 43 T the temperature dependence of the magnetization is reminiscent of a ferromagnetic transition, and a tendency of saturation at the lowest temperatures is observed. The inverse susceptibility, 1/w-, versus temperature reveals a Curie–Weiss behavior above 150 K and is shown in Fig. 7 for two different

w ¼

C w0 T y

where C is the Curie constant, y is the paramagnetic Curie temperature and w0 is an additional term representing the diamagnetism of the core electrons, Pauli paramagnetism, etc. The derived value meff ¼7.41 mB together with y ¼56.6 K is in good agreement with the theoretical moment value of 7.56 mB of localized 4f electrons in the Tm3 þ ion. The isothermal magnetization was measured at T¼2 K and is presented in Fig. 8. In low magnetic field the magnetization increases linearly due to the antiferromagnetic ground state. However, in higher fields (B42 T) the values of M dramatically rise and saturate above B45 T stemming from a metamagnetic transition. We note a fully reversible magnetization curve. Similarly to an earlier work on the isostructural compound ErB2C [39] we interpret this finding with a basic two-sublattice antiferromagnetic structure of TmB2C. Two-dimensional sheets of ferromagnetically coupled rare-earth atoms – the positive paramagnetic Curie temperature, y, supports this assumption – separated by the planar networks of the boron and carbon atoms are coupled antiferromagnetically. This negative exchange interaction is however much weaker than the inplane interaction, which gives rise to a spin flip in elevated fields leading to a three-dimensional ferromagnetism. The saturation moment of 5.5 mB/Tm is less than that of the free Tm3 þ ion gJ¼7 mB. Such a moment reduction is usually observed in measurements of


127

helpful discussions. The French GENCI (Grand Equipement National de Calcul Intensif) centre is acknowledged for high performance computing resources of CINES (Grant 2010-86170).

1.0

300

0.8 0.6

Appendix A. Supporting information

0.64 0.63

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jssc.2012.02.062.

0.62

0.4

0.61 0.60

0.2 0.0

0

5

10

15

20

25

30

References 0

50

100

150

200

250

300

T (K) Fig. 9. Electrical resistivity (r) vs. temperature for TmB2C. Inset: Low temperature resistivity data (enlarged scale). Solid line calculated after r ¼ r0 þATa.

bulk samples. Experimentally, for compounds exhibiting easy-axis anisotropy usually only ½ of the full moment is found, and hence we suggest that the moments of TmB2C are rather aligned in the (a, b) plane. Neutron diffraction analyses of the related compounds DyB2C and HoB2C [40] support this assumption, whereas for ErB2C the moments are found aligned parallel to the c-axis [39]. 3.5. Electrical resistivity of TmB2C The results of the normalized resistivity data versus temperature are presented in Fig. 9. The compound reveals the typical shape of a magnetic metal. The values of the measured resistivities decrease with falling temperatures down to T50 K stemming from a reduction of the electron–phonon scattering, pass a shallow minimum at T 30 K until a relative maximum is reached at the Neel temperature TN ¼12 K. Such a behavior is commonly attributed to ‘‘super zone’’ scattering [41]. Upon lowering the temperature the resistivity decreases again due to the reduction of the electron scattering in the magnetically ordered state. The resistivity data could be fitted according the formula r ¼ r0 þAT4.5. Such an exponent (a ¼4.5) is typical for antiferromagnets.

4. Conclusion LuB2C prepared from pure elements by melting and subsequent heating at 1270 K is a new member of the rare-earth metal boride carbide series in which the boron and carbon atoms form infinite, planar two-dimensional nets which alternate with sheets of rare-earth metal atoms. The study of X-ray single crystal and powder structure determination shows that LuB2C compound crystallizes in orthorhombic symmetry, and the B2C layers are stacked directly on top of each other, as found in REB2C2 (RE¼Y, Tb–Lu) and HoB2C compounds. Inside the nonmetal atom sheets, a coloring with fused B2C2 rhombuses and B5C2 heptagons is proposed and supported by NMR experiments and theoretical calculations. TmB2C which adopts the same arrangement, undergoes an antiferromagnetic transition at TN ¼12 K and at elevated fields (B4 3 T) a metamagnetic transition is encountered. The plot of the electrical resistivity confirms the metallic character as well as the AFM order of the compound TmB2C.

Acknowledgments The authors gratefully thank M. Babizhetska for the sample ¨ preparation, E. Brucher, G. Siegle for the magnetization and electrical resistivity measurements and Dr. Hj. Mattausch for

[1] (a) J. Bauer, J.-F. Halet, J.-Y. Saillard, Coord. Chem. Rev. 178-180 (1998) 723–753; (b) J.-F. Halet, in: M.G. Davidson, A.K. Hugues, T.B. Marder, K. Wade (Eds.), Contemporary Boron Chemistry, Royal Society of Chemistry, Cambridge, 2000, pp. 514–521; (c) M. Ben Yahia, J. Roger, X. Rocquefelte, R. Gautier, J. Bauer, R. Gue´rin, J.-Y. Saillard, J.-F. Halet, J. Solid State Chem. 179 (2006) 2779–2786. [2] F. Wiitkar, S. Kahlal, J.-F. Halet, J.-Y. Saillard, J. Bauer, P. Rogl, J. Am. Chem. Soc. 116 (1994) 251–261. [3] (a) E. Zintl, Angew. Chem. 52 (1939) 1–6; (b) W. Klemm, Proc. Chem. Soc. London (1958) 329–364; ¨ ¨ (c) H. Schafer, B. Eisenmann, W. Muller, Angew. Chem. Int. Ed. 12 (1973) 694–712; (d) S.M. Kauzlarich (Ed.), Chemistry, Structure, and Bonding of Zintl Phases and Ions, VCH, New York, 1996. [4] T. Onimaru, H. Onodera, K. Ohoyama, H. Yamauchi, Y. Yamaguchi, J. Phys. Soc. Jpn. 68 (1999) 2287–2291. [5] X. Rocquefelte, S.E. Boulfelfel, M. Ben Yahia, J. Bauer, J.-Y. Saillard, J.-F. Halet, Angew. Chem. 117 (2005) 7714–7717; X. Rocquefelte, S.E. Boulfelfel, M. Ben Yahia, J. Bauer, J.-Y. Saillard, J.-F. Halet, Angew. Chem. Int. Ed. 44 (2005) 7542–7545. [6] G.S. Smith, Q. Johnson, P.C. Nordine, Acta Crystallogr. 19 (1965) 668–673. [7] J. Bauer, H. Nowotny, Monatsh. Chem. 102 (1971) 1129–1145. [8] J. Bauer, J. Debuigne, J. Inorg Nucl. Chem. 37 (1975) 2473–2476. [9] J. Bauer, J. Less-Common Met. 87 (1982) 45–52. [10] P. Rogl, P.J. Fischer, Solid State Chem. 78 (1989) 294–300. [11] P. Rogl, P.J. Fischer, Solid State Chem. 90 (1991) 285–290. [12] F. Wiitkar, J.-F. Halet, J.-Y. Saillard, P. Rogl, J. Bauer, Inorg. Chem. 33 (1994) 1297–1305. [13] (a) Y. Shi, A. Leithe-Jasper, L. Bourgeois, Y. Bando, T. Tanaka, J. Solid State Chem. 148 (1999) 442–449; (b) T. Mori, M. Tansho, Y. Onoda, Y. Shi, T. Tanaka, Phys. Rev. B 62 (2000) 7587–7592. [14] P. Rogl, in: Nitrides, R. Freer Borides (Eds.), The Physics and Chemistry of Carbides, Kluwer Acad. Publ., Dordrecht, The Netherlands, 1990, pp. 269–277. [15] J. Bauer, D. Ansel, F. Bonhomme, P. Gosselin, J. Less-Common Met. 157 (1990) 109–120. [16] J. van Dujn, J.P. Attfield, R. Watanuki, K. Suzuki, J. Phys. Chem. Solids 62 (2001) 1423–1429. [17] V. Babizhetskyy, K. Hoch, Hj. Mattausch, A. Simon, 11th International Conference of Intermetallic Compounds, Lviv, Ukraine, May 30–June 2, 2010. P57. [18] V. Babizhetskyy, M. Babizhetska, B. Kotur, A. Simon, Visnyk Lviv Univ. Ser. Chem. 52 (2011) 54–61. [19] J.K. Burdett, S. Lee, T.J. McLarnan, J. Am. Chem. Soc. 107 (1985) 3083–3089. [20] J.K. Burdett, E. Canadell, T. Hughbanks, J. Am. Chem. Soc. 108 (1986) 3971–3976. [21] J. Cuny, S. Messaoudi, V. Alonzo, E. Furet, J.-F. Halet, E. Le Fur, S.E. Ashbrook, C.J. Pickard, R. Gautier, L. Le Polle s, J. Comput. Chem. 29 (2008) 2279–2287. [22] A. Altomare, M.C. Burla, M. Camalli, B. Carroccini, G.L. Cascarano, C. Giacovazzo, A. Guagliardi, A.G. Moliterni, G. Polidori, R. Rizzi, J. Appl. Crystallogr. 32 (1999) 115–119. [23] G.M. Sheldrick, SHELXL-97: Program for the Refinement of Crystal Structures, ¨ University of Gottingen, Germany, 1997. [24] L.J. Farrugia, J. Appl. Crystallogr. 32 (1999) 837–838. [25] K. Brandenburg, DIAMOND Version 2.1e, Crystal Impakt Gbr, Bonn, Germany, 1996–2001. [26] L.G. Akselrud, Yu.N. Grin, P.Yu. Zavalii, V.K. Pecharskii, Mater. Sci. Forum 133136 (1993) 335–340. http://imr.chem.binghamton.edu/zavalij/csd.html. [27] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717–2744. [28] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [29] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188–5192. [30] (a) O.K. Andersen, Phys. Rev. B 12 (1975) 3060–3083; (b) O.K. Andersen, Europhys.News 12 (1981) 4–8; (c) O.K. Andersen, The Electronic Structure of Complex Systems, in: P. Phariseau, W.M. Temmerman (Eds.), Plenum Publishing Corporation, New York, 1984; (d) O.K. Andersen, O. Jepsen, Phys. Rev. Lett. 53 (1984) 2571–2574;

128

[31] [32] [33] [34] [35] [36]


(e) O.K. Andersen, O. Jepsen, M. Sob, in: M. Yussouf (Ed.), Electronic Band Structure and Its Applications, Springer-Verlag, Berlin, 1986; (f) H.L. Skriver, The LMTO Method, Springer-Verlag, Berlin, 1984. U. von Barth, L. Hedin, J. Phys. C 5 (1972) 1629–1642. ¨ P.E. Blochl, O. Jepsen, O.K. Andersen, Phys. Rev. B 49 (1994) 16223–16233. ¨ P.E. Blochl, Phys. Rev. B 50 (1994) 17953–17979. ¨ Mol. Phys. 99 (2001) 1617–1629. P. Pyykko, A. Zalkin, D.H. Templeton, Acta Crystallogr. 6 (1953) 269–272. O. Oeckler, C. Jardin, Hj. Mattausch, A. Simon, J.-F. Halet, J.-Y. Saillard, J. Bauer, Z. Anorg. Allg. Chem. 627 (2001) 1389–1394.

[37] F. Mauri, N. Vast, C.J. Pickard, Phys. Rev. Lett. 87 (2001) 085506. [38] J. Roger, V. Babizhetskyy, S. Cordier, J. Bauer, K. Hiebl, L. Le Polle s, S.E. Ashbrook, J.-F. Halet, R. Gue´rin, J. Solid State Chem. 178 (2005) 1851–1863. [39] R. Watanuki, K. Suzuki, J. van Duijn, J.P. Attfield, Phys. Rev. B 69 (2004) 064433. [40] J. van Duijn, J.P. Attfield, R. Watanuki, K. Suzuki, R.K. Heenan, Phys. Rev. Lett. 90 (2003) 087201. [41] G.T. Meaden, Contemp. Phys. 12 (1971) 313–337.