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Crystal structure and magnetic properties of CeTe2
Journal of Alloys and Compounds 307 (2000) 101–110
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Crystal structure and magnetic properties of CeTe 2 ¨ * Klaus Stowe ¨ des Saarlandes, 66041 Saarbrucken ¨ FR 9.14, Anorganische Chemie und Analytische Chemie und Radiochemie, Universitat , Saarland, Germany Received 11 August 1999; received in revised form 7 February 2000; accepted 9 February 2000
Abstract X-ray diffraction single-crystal structure analysis of CeTe 2 prepared by chemical vapor transport reactions in the presence of mg-traces of iodine revealed superstructure reflections indicating a (23232) supercell of the basic anti-Fe 2 As type in contrast to the (23231) supercell found for LaTe 2 . The best interpretation of data set was obtained choosing for CeTe 2 the tetragonal space group P4 with the lattice parameters a5899.75(5) pm and c51821.2(1) pm (Z516). The doubling of the c axis compared to LaTe 2 is observed due to different polyanionic structural motifs in the heights z¯0 and z¯ ]12 . These are a herringbone pattern of [Te 2 ] dumbbell pairs — a topology which is also found in LaTe 2 — isolated [Te 4 ] four-membered rings in z¯ ]21 and additionally [Te 8 ] branched four-membered rings in z¯ ]12 . These structural elements give a diffraction pattern, which is all in all to be explained by a statistical superposition of the different elements. Magnetic susceptibility measurements revealed pronounced crystal field effects for the trivalent Ce ions, but apart from that are in agreement with former investigations finding a magnetic transition below T54 K due to ferrimagnetic ordering. A formerly observed spin sequence of the magnetic moments at different sites A and B of ABBA,A may now be well understood by a classification of the Ce ions into two types with different coordinational environment in the actual structure model. 2000 Elsevier Science S.A. All rights reserved. Keywords: Cerium ditelluride; Lanthanoid chalcogenides; X-ray diffraction single-crystal structure analysis; Magnetic susceptibility measurements
1. Introduction The observation of superstructure reflections indicating a (23231) supercell of the simple anti-Fe 2 As structure type made it necessary to redetermine the crystal structure of LaTe 2 by single-crystal analysis [1]. In contrast to former investigations revealing tetragonal or orthorhombic symmetry our analysis showed that LaTe 2 crystallizes monoclinic in space group P1c1 with the lattice parameters a5919.0(1), b5910.7(1), c5907.0(1) pm and b 5 90.04(1)8 (Z58). Compared to the anti-Fe 2 As basic structure the polyanionic square 4 4 nets are distorted in LaTe 2 into herringbone pattern of dimer pairs. These findings have put up the question, whether the compound CeTe 2 behaves homologously and shows superstructure reflections, too. But first of all we will give in the following a short review of the literature data known for CeTe 2 up to the present. Early reports of the compound CeTe 2 are due to Naderi Chirazi [2] in 1958, who was the first to synthesize the compound by the reaction of tellurium vapor with anhydr*Tel.: 149-681-302-3071; fax: 149-681-302-4233. ¨ E-mail address: [email protected] (K. Stowe)
ous cerium chloride in a hydrogen atmosphere at 8008C. At this temperature CeTe 2 grows in form of black–blue lamellae crystallizing with tetragonal symmetry with a5 450 and c5908 pm. Two years later Flahaut et al. [3] succeeded in identifying the crystal structure as anti-Fe 2 As type and determined approximate positional parameters from the powder diffraction pattern. Parallel to these investigations, in 1962 Bro and Andrellos [4,5] prepared crystals of the lanthanoid ditellurides LaTe 2 , CeTe 2 , PrTe 2 and NdTe 2 by chemical vapor transport reactions in the presence of iodine. In the phase diagram of the binary system Ce–Te, as determined by Chukalin et al. [6], CeTe 2 is formed by a peritectic reaction at 12508C. Moreover, indications for the existence of a 4:7 phase of formula Ce 4 Te 7 melting incongruently at 13408C and crystallizing in the tetragonal space group P4 /mbm were given, but compared to CeTe 2 with doubled a lattice parameter a5 899.8 and c5916.7 pm. From this we have to conclude that the structure of this compound might be closely related to that of CeTe 2 . After these early investigations CeTe 2 has attracted the interest of some groups once again in the last few years because of its remarkable transport and optical properties, which were measured by Kwon et al. [7–9] at several temperatures. Anomalous resistivity
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¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
effects of metallic CeTe 2 , especially in form of a very sharp maximum at T54.5 K, induced them to investigate the magnetic structure of the compound in detail. Neutron powder diffraction experiments at T52 K [10] clearly showed the presence of a magnetic superstructure with a doubled lattice parameter c9 5 2c. The RIETVELD refinement of the powder diffraction pattern resulted in a magnetic structure with a ferrimagnetic sequence of ABBA,A in planes normal to the c9 axis. The magnetic moments within the planes were determined as m (A)5 0.40(6) mB and m (B)50.98(6) mB . Even in this recent publication the unusual large anisotropic thermal motion of the Te(1) ions within the polyanionic 4 4 nets was emphasized. This encouraged us to reinvestigate the crystal structure of CeTe 2 , to redetermine its composition accurately and to compare its properties with former investigations in order to check whether there are further discrepancies.
2. Experimental details
2.1. Sample synthesis Black plate-like shaped single crystals of CeTe 2 with metallic luster up to an edge-length of several mm were obtained by chemical vapor transport reactions in silica ampules with I 2 as transporting agent in a temperature gradient from 9508C to 8508C starting from the elements Ce (ingot, 99.91%, Kelpin, Leimen, Germany) and Te (pieces, .99.999%, Fluka, Buchs, Switzerland) as already reported earlier [4,5]. The compound was handled under a dry and oxygen-free atmosphere of purified argon in a glove box, because it is moisture and air-sensitive.
2.2. Analytical characterization and measurements of physical properties For a further characterization of the compound CeTe 2 with respect to its composition atomic emission spectrometry with plasma excitation (ICP–AES, Perkin Elmer) was used. For the analysis samples consisting of selected single crystals were sealed in capillaries of 2 mm diameter, subsequently opened in an autoclave with a Teflon inlet and dissolved in a HNO 3 / HCl mixture. Further details are given in Ref. [11]. The analysis by ICP–AES of the product revealed a composition of CeTe 2.01( 3) . To support the analytical data the density of samples consisting of several single crystals was measured. This was done by a gas displacement pycnometer of type Accupyc 1330 / 1cc (Micromeritics) with helium as working gas. Because the samples were air and moisturesensitive, the complete pycnometer was placed in a glove box under a dried and oxygen-free argon atmosphere. The measurements on selected single crystals yielded an aver-
age density of rm 57.01(3) g cm 23 compared to a calculated density of rx 57.124 g cm 23 . ¨ Festkorper¨ Magnetic data were recorded at the MPI fur forschung, Stuttgart (Germany), with samples synthesized by chemical vapor transport reactions, which were sealed in Suprasil glass capillaries of 200 mm length and a reduction in the middle of the capillaries to hold the samples. Susceptibility measurements were performed with an MPMS SQUID magnetometer (Quantum Design) at two different magnetic fields of H50.1 and 1 T in the temperature interval of T52–350 K. Due to the paramagnetic behavior of the compound no diamagnetic corrections were applied.
2.3. X-ray single-crystal structure determination The data collections were carried out with a P4 singlecrystal diffractometer (Siemens, Karlsruhe, Germany). The unit cell was determined by refinement of the diffraction angles of 100 single-crystal reflections distributed uniformly in reciprocal space. All reflections of CeTe 2 could be ] ] indexed by a tetragonal primitive (2Œ232Œ232) supercell with a51272.44(7) and c51821.2(1) pm (Z532), which will be considered in the following as cell choice 1. But from all in all 34 318 measured reflections only 9 reflections with I . 4 ? s (I) did not suit the systematic extinction condition of a C-centering. From these 9 only the (0 9 0) reflection and its equivalents had a reliable intensity with I ¯ 10 ? s (I). Rotating about the plane normal of these reflections revealed apart from absorption effects no intensity changes, so that a Renninger effect could be ruled out. But all attempts to include all the 17 140 extinct reflections in the refinement procedure resulted only in a worsening of the R-values, whereas no general changes in the structure model were observed. Thus the refinements were performed assuming a C-centered lattice or, after transformation into a standard setting, a P-type lattice. This second (23232) supercell with a5899.75(5) and c51821.2(1) pm (Z516), in the following referred to as cell choice 2, was also the basis of all our subsequent structural discussions. Table 1 gives a summary of important measurement and refinement data. The structure refinements were performed with the computer program SHELX-97 [12,13]. The results are summarized in Tables 2 and 3. Group–subgroup relations with the space group of the anti-Fe 2 As type, P4 /nmm, as aristotype have lead us to a plausible structure solution in space group P4 (see Fig. 1). Due to the drastic reduction in symmetry, a lot of additional degrees of freedom for a distortion of the aristotype are produced, whereas the dropped symmetry elements are only pseudo-symmetry elements and valid for the averaged structure. In the space group P4 the polyanionic Te(1) ions, forming regular 4 4 nets in the undistorted anti-Fe 2 As type, occupy the general Wyckoff positions (4d). Already in the early stages of the refinement
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
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Table 1 Measurement and refinement data for CeTe 2 in the X-ray single-crystal structure analysis Measurement temperature Lattice parameters a c Number of formula units per cell Calculated density Measured density Space group Measured range of reciprocal space (Mo-K a ) Type of data collection / scan width No. of observed reflections No. of nonequivalent reflections Absorption correction Crystal color Crystal size Linear absorption coefficient Internal R value c Structure solution Structure refinement Program for structure solution and refinement Extinction parameter empirical with F* 5 F[1 1 0.002x F 2 / sin (2u )] 21 / 4 Number of independent parameters R values (w 5 1 /s (Fo )2 )
293 K 899.75(5) pm 1821.2(1) pm 16 7.124 gcm 23 7.01(3) gcm 23 P 4 (No. 75) 3,2u ,608 (all octants) v / 1.18 in 96 steps 17 178 4460 Numerical a,b Lustrous black 0.0830.1530.32 mm 3 275.9 cm 21 3.94% Transformed anti-Fe 2 As model Full matrix least-squares SHELX-97 d 0.00040(1) 177 wR 2 50.0738
a
W. Herrendorf, HABITUS, Program for the Optimization of the Crystal Description for a Numerical Absorption Correction on the Basis of Appropriate Psi-Scanned Reflections, Karlsruhe, Germany, 1992. b W. Alcock, P.J. Marks, and K.-G. Adams, ABSPSI, Absorption Correction and Refinement of the Crystal Habitus, Karlsruhe, Germany, 1994. c K.-G. Adams, MITTELN, Averaging Symmetry-Equivalent Reflections, Karlsruhe, Germany, 1995. d ¨ G.M. Sheldrick, SHELX-97, FORTRAN-77 Program for the Refinement of Crystal Structures from Diffraction Data, Gottingen, Germany, 1997; G.M. Sheldrick, Acta Cryst. A 46 (1990) 467.
difference electron density syntheses clearly showed several maxima around these Te(1) ions. These maxima indicate that even in the low symmetric space group P4 the structure refinement is complicated by microtwinning effects. From the observation of supercell reflections indicating a doubling of the c-axis we have to conclude that the polyanionic arrangement of the Te(1) ions in the distorted 4 4 nets has to be different in z9¯0 and z9¯ ]12 (formerly in the anti-Fe 2 As type z50 and z51). Correspondingly only one additional density maximum was found in z9¯0, but two maxima in z9¯ ]21 . Since the Te(1) ions at the additional density are not related to the original ones by symmetry elements, there is no possibility to find a simple twin law and to refine the structure e.g. with the twin refinement method implemented in the program SHELXL [12,13]. The only way to treat this type of microtwinning is by split positions, which was done in the following refinement procedure. To deal with the pseudocentrosymmetry of the data set, racemic twinning was included at the last stages of refinement, which resulted in a twin component ratio of 0.41(9) to 0.59(9). Refining with cell choice 2 the isotropic displacement factors Uiso independently with the constraints and restraints for the site occupation factors sof given in the footnote of Table 3 resulted in physically quite reliable and almost equal values for all the different Te(1) ions. From this no hint for a deviation of stoichiometry from the
assumed composition was given. But the existence of additional compounds with a composition very close to the 1:2 ratio, as e.g. Ce 4 Te 7 (see Introduction), made it necessary to perform an independent determination of the elemental composition of the synthesized samples. But the analysis by ICP–AES of selected single crystals of the product gave also no hints on a deviation of the assumed composition CeTe 2 . Moreover, this result was confirmed by pycnometric density measurements. On the other side, for the compound Ce 4 Te 7 , also proposed in the literature, we would expect a significantly smaller density of rx 5 6.50 gcm 23 [6] compared to the measured value of rm 5 7.01(3) g cm 23 .
3. Description of the crystal structure The difference of the actual structure model to former investigations lies entirely in the topology of the polyanionic square 4 4 nets (Te(1ni), n 5 1–4, i5A, B(, C); referring to the numbering, see footnote a in Table 2), whereas the other Te anions (Te(2n), n51–8) and the Ce cations (Ce(n), n51–8) remain almost at their positions as in the anti-Fe 2 As structure type. CeTe 2 in the anti-Fe 2 As type can be regarded as built up solely from 4 4 nets with a layer sequence of (4 4 )2 (Te(1)) 4 4 (Ce) 4 4 (Te(2)) 4 4 (Te(2))
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
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Table 2 Positional parameters a and equivalent isotropic displacement factors b (pm 2 ) of CeTe 2 Atom
Wyck.
x
y
z
sof c
Ueq
Te(11A) Te(11B) Te(12A) Te(12B) Te(13A) Te(13B) Te(13C) Te(14A) Te(14B) Te(14C) Te(21) Te(22) Te(23) Te(24) Te(25) Te(26) Te(27) Te(28) Ce(1) Ce(2) Ce(3) Ce(4) Ce(5) Ce(6) Ce(7) Ce(8)
4d 4d 4d 4d 4d 4d 4d 4d 4d 4d 1a 1a 1b 1b 2c 2c 4d 4d 1a 1a 1b 1b 2c 2c 4d 4d
0.2524(1) 0.2218(9) 0.5081(2) 0.4778(9) 0.5201(3) 0.4950(4) 0.4982(7) 0.2602(3) 0.2433(4) 0.2312(7) 0 0
0.9914(1) 0.0157(9) 0.2482(1) 0.2902(8) 0.2461(3) 0.2640(3) 0.2245(6) 0.9976(4) 0.9806(4) 0.0133(7) 0 0
0.866(2) 0.134(2) 0.866(2) 0.134(2) 0.446(1) 0.377(1) 0.177(2) 0.446(1) 0.377(1) 0.177(1)
1 ] 2 1 ] 2
1 ] 2 1 ] 2 1 ] 2 1 ] 2
0.9996(1) 0.9972(7) 0.9988(1) 0.0026(6) 0.5001(2) 0.4971(3) 0.5048(5) 0.4975(2) 0.4996(3) 0.5102(4) 0.3162(1) 0.8160(1) 0.3164(1) 0.8163(1) 0.3167(1) 0.8164(1) 0.1835(1) 0.6836(1) 0.1356(1) 0.6360(1) 0.1360(1) 0.6364(1) 0.1359(1) 0.6358(1) 0.3623(1) 0.8621(1)
0.0160(2) 0.0161(4) 0.0155(2) 0.0158(4) 0.0108(3) 0.0108(3) 0.0108(3) 0.0108(3) 0.0108(3) 0.0110(3) 0.0102(4) 0.0106(5) 0.0109(5) 0.0104(5) 0.0108(4) 0.0105(4) 0.0147(3) 0.0143(3) 0.0143(4) 0.0141(5) 0.0163(4) 0.0154(5) 0.0146(4) 0.0146(4) 0.0152(3) 0.0150(3)
0 0 0.2508(1) 0.2505(1) 0 0 1 ] 2 1 ] 2
0 0 0.2523(1) 0.2526(1)
0.2493(1) 0.2494(1) 0 0 1 ] 2 1 ] 2 1 ] 2 1 ] 2
0.2473(1) 0.2479(1)
1 ] 4 1 ] 4 1 ] 4 1 ] 4 1 ] 2 1 ] 2
1 1 1 ] 4 1 ] 4 1 ] 4 1 ] 4 1 ] 2 1 ] 2
1 1
a
To differentiate between the different types of Te(1) ions, a numbering as Te(1n) was used with Te(1n) (n51, 2) for Te(1) in z¯0 and Te(1m) (m53, 4) for Te(1) in z¯ ]12 . Additionally this numbering was expanded as Te(1ni) with i5A, B(, C) for the different split-up positions. b * 1 U 22 * 1 U 33 * ], with U ij* the orthogonalized tensor components. Equivalent isotropic Ueq calculated by ]13 [U 11 c The site occupation factors of all n sites Te(1ni) with i5A, B(, C) were constrained to equal values for n51, 2 and n53, 4, e.g. sof(Te(11A))5 sof(Te(12A)), and their sum restrained to unity with an effective standard deviation of 0.001, e.g. sof(Te(13A))1sof(Te(13B))1sof(Te(13C))51.
4 4 (Ce), (4 4 )2 (Te(1)). By (4 4 )2 9 we denoted the polyanionic layers packed with twice the density of the other nets. These regular square Te(1) nets are believed to cause the metallic conductivity of the lanthanoid ditellurides of this structure type [14]. In the actual structure model the Te(1) nets have distorted into several different types of pattern. Corresponding to the number of electron density maxima in the two different layer heights we have two types A, B in z¯0 and three types A, B and C in z¯ ]21 . The only crystal chemically meaningful interpretation of the split positions in z¯0 is to assume a double herringbone pattern of [Te 2 ] dumbbells with an interatomic distance d(Te(11A)–Te(12A))5304.8 pm as in the homologous compound LaTe 2 (d5298.7, 303.6 pm) [1] superimposed by an arrangement of isolated [Te 4 ] fourmembered rings with point symmetry 4.. (see Fig. 2). Because of two independent (4d) positions Te(12B) and Te(11B) there are also two independent rings with interatomic distances of d5268.5 and d5283.0 pm, respectively. The interpretation of the split positions in z¯ ]12 is also clear cut (see Fig. 3). Apart from a double herringbone pattern of dimers [Te 2 ] (A) and four-membered rings [Te 4 ] (B) we have also as additional feature branched fourmembered rings [Te 8 ] (C). Although the topology of A
and B in z¯ ]21 is the same as in z¯0, there are somewhat different interatomic distances within the various types of bonding pattern. Within the dimers of the herringbone pattern the Te(1nA) ions with n53, 4 are now only 295.2 pm apart, and within the two different four-membered rings d(Te(13B))–Te(13B))5300.3 and d(Te(14B))– Te(14B))5310.6 pm. The branched four-membered rings are unique and they are found only in z¯ ]12 . They show interatomic of d5294.6 pm within the rings and d5306.5 pm from the ring ions to the neighboring Te ions. If we cancel the differentiation into these discrete structural motifs by averaging all interatomic distances within the distorted square sheets, we again get a simple anti-Fe 2 As type structure. Even in the actual structure model there is a large amount of pseudo-symmetry due the small distortions of the Te in the square sheets. This can also be seen from the numerous pseudo-extinction rules in cell choice 1 as well as cell choice 2. But a very careful inspection of these pseudo-extinction rules has let us to the realization that they are not strictly fulfilled. This brings us back to the question of the different cell choices. From the structure refinement we rejected the thesis of cell choice 1 and considered choice 2 as the more probable one. But in view of a microdomain structure of different structural motifs the question of the correct cell choice has to be
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe Table 3 Anisotropic displacement factors a ,b (pm 2 ) of CeTe 2
105
extended domain size with a stable instead of a random sequence of the layer types seems to be more realistic.
Atom
U11
U22
U33
U23
U13
U12
Te(11A) Te(11B) Te(12A) Te(12B) Te(13A) Te(13B) Te(13C) Te(14A) Te(14B) Te(14C) Te(21) Te(22) Te(23) Te(24) Te(25) Te(26) Te(27) Te(28) Ce(1) Ce(2) Ce(3) Ce(4) Ce(5) Ce(6) Ce(7) Ce(8)
178(4) 175(7) 176(4) 177(7) 117(5) 115(5) 115(5) 132(5) 135(5) 133(5) 93(5) 85(5) 86(5) 102(6) 96(7) 89(7) 170(6) 176(7) 168(5) 159(5) 185(5) 176(6) 164(7) 168(7) 136(5) 142(6)
192(4) 192(7) 180(5) 179(7) 118(5) 115(5) 115(5) 121(5) 120(5) 121(5) U 11 U 11 U 11 U 11 89(7) 110(7) 165(7) 178(8) U 11 U 11 U 11 U 11 170(7) 190(8) 132(5) 145(6)
109(4) 116(7) 108(4) 117(7) 90(5) 95(5) 94(5) 71(5) 68(5) 77(5) 120(9) 146(11) 155(11) 107(11) 138(9) 114(9) 107(5) 74(5) 95(9) 105(10) 119(9) 110(10) 104(7) 80(8) 187(5) 164(5)
218(6) 219(8) 226(6) 222(7) 17(5) 20(5) 17(5) 238(5) 238(5) 236(5) 0 0 0 0 0 0 1(4) 28(4) 0 0 0 0 0 0 230(4) 212(4)
217(5) 218(8) 34(6) 33(7) 15(5) 17(5) 15(5) 21(5) 15(5) 18(5) 0 0 0 0 0 0 22(4) 23(5) 0 0 0 0 0 0 3(4) 25(4)
21(4) 20(7) 22(4) 18(7) 18(4) 21(5) 18(5) 229(5) 230(5) 226(5) 0 0 0 0 23(4) 24(4) 2(7) 28(7) 0 0 0 0 217(4) 226(4) 13(6) 9(6)
a
Due to prominent correlation effects the thermal displacement parameters of split positions could not be refined without restraints. So the displacement parameters of all the Te(1ni) ions were coupled by giving an SIMU card, which restrained ions closer than 100 pm with an effective standard deviation of 10 pm 2 to have the same Uij components. Additionally the thermal motion of the Te(1) ions at the split positions had to be restricted by an ISOR instruction, which restrained the Uij components to isotropic behavior with the effective standard deviation of 30 pm 2 as implemented in the refinement program SHELXL-97 [12,13]. b The dimensions are in accordance with the following formula: 2 2p 2 ? o i o j Uij h i h j a *i a *j .
discussed again, because in principle also a mixture of different motifs within a single distorted square sheet is within the range of possibility. For instance the alternation of dumbbell pairs and 4-rings in [100] direction of cell 2 would lead to an enlargement of the unit cell and to cell 1. On the other side, from the very low intensity of the reflections not fulfilling the extinction rule of the Ccentering in unit cell choice 1 we have to conclude that this mixing of different structural elements is not very marked and cell choice 2 the more appropriate one. If there is perfect order among the different kind of structural motifs in CeTe 2 , the Laue monotonic scattering would be gathered exclusively into sharp superlattice reflections, otherwise, the scattering would also be diffusely distributed depending on the extent of local order that exists. But despite a somewhat enlarged FWHM of the axial reflections in direction of the c lattice vector, no hints for diffuse scattering in comparative q scans of reciprocal space were seen. From this, the assumption of a distribution of the structural motifs A, B and C in form of microlamellae of
4. Discussion of the crystal structure In the following section we will discuss the interatomic distances and interactions in more detail. The double herringbone pattern was first described for the homologous compound LaTe 2 [1], which crystallizes in a low symmetric monoclinic space group with two different interatomic distances within the dimers of d5298.7 and d5303.6 pm. The calculation of the Crystal Orbital Hamiltonian Population (COHP) function, which is the Hamiltonian population weighted density of states, suggested that, due to secondary interactions of d5313.0 pm, we have to regard the Te(1) sheet in LaTe 2 better as a simple herringbone arrangement of L-shaped [Te 4 ]-units. By the way of contrast no intermolecular distances between the dimers below 320 pm are found in CeTe 2 , so that we do not have to consider any pronounced further secondary interactions. With d5304.8 and 295.2 pm in z¯0 and z¯ ]12 , respectively, the observed intramolecular distances are not very different from those in LaTe 2 . In both compounds they are ¯10% longer than a single bond distance (e.g. d5271 pm in diphenylditelluride [15]). On the contrary, in the compounds LaSe 2 , which crystallizes also in a distorted antiFe 2 As type structure with an arrangement of the polyanionic partial structure in form of a simple herringbone pattern [16,17] (see Fig. 4, upper part), and La 10 Se 19 , whose structure is a ordered-defect variant of the antiFe 2 As type [18] (see Fig. 4, lower part), the [Se 2 ] 22 distances of d(Se–Se)5245.2 and 247.7 pm, respectively, are only ¯5% larger than the corresponding single bond distance (e.g. d5233 pm in p, p9-dichlorodiphenyl-ditelluride [19]). As expected for tellurides, the differentiation between the polyanionic interatomic distances within the distorted tellurium sheet is much less distinct than in the other polychalcogenides. Proceeding to the next arrangement, the four-membered rings, we are confronted with another new type of bonding pattern. The four-membered rings in CeTe 2 all have a point-symmetry 4.., but their interatomic Te–Te distances are relatively wide-spread (d(Te(1)–Te(1))5268.5, 283.0 pm in z¯0 and 300.3, 310.6 pm in z¯ ]12 , see Fig. 3). Since all other interatomic distances within the polyanionic sheet lie above 320 pm, we can neglect secondary interactions in a first approximation and compare these fragments with other molecular ones. Topologically similar [Te 4 ] rings are observed in literature as twofold positive charged species in compounds such as Te 4 (AlCl 4 ) 2 [20], Te 4 (HfCl 6 ) [21], Te 4 (MoOCl 4 ) 2 [22] or in the subhalogenide a-TeI [23]. In the last compound non-planar [Te 4 I 4 ] rings were found, which are interconnected by secondary interactions to infinite chains. The Te–Te distances within the rings with values of d5278.6, 280.7, 289.3 and 292.8 pm lie in the
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¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
Fig. 1. Symmetry relations between the space group of the anti-Fe 2 As structure type P4 /nmm and the actual space group of CeTe 2 P4.
same order of magnitude as those in CeTe 2 . Polyanionic fragments like [Te 4 ] 22 are found only as open chain species, e.g. in the compound (PPh 4 ) 2 Te 4 [24] with intrachain distances of d(Te–Te)5268.6, 270.5 and 276.1 pm. Theoretical calculations using the effective core potential model on square-planar [X 4 ] 21 , [X 4 ] 1 and [X 4 ] 0 (X5S, Se, Te) [25] have shown that the bond lengths increase dramatically with decreasing positive charge of the system. By an extensive population analysis Saethre and Gropen [25] found that this increase is almost exclusively due to the loss of bonding in the p system, whereas the bonding in the s system remains relatively unaltered. In coordination compounds as, e.g. CeTe 2 the antibonding
p contributions might be reduced by a covalent interaction of Te with the Ce neighbors. But further insights into the bonding characteristics in CeTe 2 will come from first principles band structure calculations similar to those, which we have already performed for the homologous compound LaTe 2 [1]. But this will be the topic of a subsequent paper. At the moment we can only state that the different intraring distances observed in CeTe 2 may indicate also quite different charges of the several Te ions. The last type of bonding pattern, the branched fourmembered rings which are exclusively found in z¯ ]12 , also reveals almost no secondary interactions, since all intermolecular distances lie well above 320 pm. The [Te 8 ] units
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
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Fig. 2. Polyanionic Te(1) sheets in the crystal structure of CeTe 2 in [001] projection at z¯0. Left side: Double herringbone type pattern (A). Right side: Four-membered Te rings (B; distances in pm).
also have a point symmetry 4.. with intramolecular distances of d5294.6 pm within the rings and an exocyclic bond distance of d5306.5 pm (see Fig. 3). They may be regarded as a molecular fragment of the planar [CsTe 6 ] sheets in the compound Cs 3 Te 22 [26]. The structure of these 2,3-connected [Te 6 ] sheets consists of linear and T-shaped Te ions with intraring distances of d5300.3 pm and two bond lengths of d5307.7 pm for the linear Te ion
connecting two four-membered rings (see Fig. 5). Following Zintl’s concept Liu et al. [27] assigned these [CsTe 6 ] sheets a formal twofold negative charge with partial charges of 21 for the linear Te and 2 ]41 for the T-shaped ring Te ions. To model this sheet Liu and co-workers also performed EH calculations at isolated [Te 4 Te 4 ] n 2 molecular units and varied the Te–Te–Te angle b for the Tshaped Te ions while maintaining the four-fold symmetry.
Fig. 3. Polyanionic Te(1) sheets in the crystal structure of CeTe 2 in [001] projection at z¯ ]21 . Left top side: Double herringbone type pattern (A). Right top side: Four-membered Te rings (B). Bottom: Branched four-membered rings (C; distances in pm).
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¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
Fig. 3. (continued)
They calculated that the b 5908 configuration is more stable than the b 51358 conformer if the molecule possesses a total charge of 25 to 29, whereas for larger charges the b 51358 configuration is more stable. For charges between 25 and 29, in all cases studied, the total energy was minimized at angles b ,908. In the case of Cs 3 Te 22 an angle of b 588.58 was found experimentally. In CeTe 2 the geometry of the [Te 8 ] unit does not differ significantly from that assumed by Liu et al. for their calculations on the [Te 4 Te 4 ] unit, which was taken from Cs 3 Te 22 . The bond distances are only 3–5 pm shorter in CeTe 2 , but the angle b (100.1(3)8) is somewhat larger than 908 indicating a relatively high charge (29 and higher) of the [Te 8 ] fragment. All in all we can summarize our results as follows: Compared to LaTe 2 , whose structure shows only [Te 2 ] dumbbells in the polyanionic Te(1) layers, we find a clear trend in CeTe 2 to reduce the localization and to increase the itinerancy in the distorted square nets. Apart from dumbbells of connectivity 1 also isolated four-membered rings of connectivity 2 and branched four-membered rings of connectivity 1 and 3 were observed in the crystal structure of CeTe 2 . Since the evaluation of the interatomic distances within the distorted square sheets revealed only very weak secondary interactions above 320 pm, we would expect CeTe 2 to be a semiconductor. But, as the homologous La compound, CeTe 2 is reported to be a metallic conductor [7–9]. In LaTe 2 this is due to an additional direct covalent La–La interaction leading to an energy lowering of a single La 5d x 2 2y 2 orbital around the Brillouin zone center G in band structure calculations [1]. Whether this is also the reason for the metallic conductivity of CeTe 2 , we intend to make clear by a subsequent paper.
Fig. 4. Distortion pattern for the selenium sheets in LaSe 2 in form of a herringbone pattern (top) and La 10 Se 19 with isolated Se 22 anions, vacancies and [Se 2 ] 22 dimers in the ratio 1:1:4 (bottom).
5. Magnetic susceptibility measurements In this context it might be very interesting to redetermine the magnetic properties of crystals of CeTe 2 synthesized by chemical vapor transport reactions and compare them with results reported earlier [7,10] on powder samples. These were prepared by using mineralization in an evacuated and sealed tungsten crucible at 15008C [7]. On the other side, CeTe 2 should melt incongruently at 12508C [6], so that there might be some uncertainties concerning the composition of the samples prepared by Kown et al. [7,10]. Between the magnetic susceptibility data in Kwon et al. [7] and ours (see Fig. 6) there is some relationship, but also distinct differences. In the high temperature regime above T¯100 K the re-
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
Fig. 5. Planar [CsTe 6 ] 22 sheets in the crystal structure of Cs 3 Te 22 [26]. Assignment of charges due to Liu et al. [27] (distances in pm).
ciprocal molar susceptibility given in Kown et al. [7] increases almost linearly with temperature, whereas our data suggest a magnetic moment decreasing with temperature. Fitting a straight line between T5250 and 350 K
109
gives a magnetic moment of m 52.18 mB and a positive paramagnetic Curie temperature of Qp 551 K, whereas extrapolation of the data in the interval T550–100 K gave m 52.62 mB and a negative Curie temperature of Qp 5 210 K. So in contrast to Kown et al. [7] we find quite pronounced crystal field effects for the trivalent Ce ions ( mS1L (Ce 31 )52.54 mB ). The negative Curie temperature of the midrange data together with the observation of a magnetic transition at an onset temperature of T¯4 K with 1 /xm ¯0 for T ,4 K implies a ferrimagnetic ordering in agreement with neutron diffraction data on powder samples at T52 K [10]. As already mentioned in the Introduction, these investigations resulted in magnetic superstructure reflections indicating a doubling of the magnetic unit cell compared to the crystallographic cell with magnetic moments lying along c in a spin sequence of ABBA,A with moments of m (A)50.40(6) mB and m (B)50.98(6) mB . Assuming an undistorted anti-Fe 2 As type structure for CeTe 2 , the finding of two different magnetic moments is quite unreasonable, because, even with a doubled c axis, all Ce ions would have the same capped tetragonal antiprismatic coordination environment. Referring to our crystal structure analysis, the crystal structure has revealed two basically different Ce environments for Ce coordinating Te(1) ions in z¯0 (Ce(n), n51,3,5,8) and z¯ ]12 (Ce(m), m52,4,6,7), so that the observation of different
Fig. 6. Reciprocal molar magnetic susceptibility of CeTe 2 in the temperature range T52–350 K at H50.1 and H51 T.
110
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
magnetic moments especially in a sequence ABBA,A now appears quite reasonable. With the redetermined crystal structure data some properties of CeTe 2 such as the ferrimagnetic ordering can now be understood, but others such as the metallic transport properties have still to be explained by theoretical calculations.
Acknowledgements The author is particularly indebted to Dr. R.K. Kremer ¨ ¨ and Mrs. E. Brucher from the Max-Planck-Institut fur ¨ Festkorperforschung in Stuttgart, Germany, for the magnetic susceptibility measurements. The Deutsche Forschungsgemeinschaft DFG and the Fonds der Chemischen Industrie FCI are gratefully acknowledged for financial support.
References ¨ [1] K. Stowe, F.R. Wagner, J. Solid State Chem. 149 (2000) 155. [2] A. Naderi Chirazi, Doctoral Thesis in Pharmaceutics, Paris, 1958. [3] J. Flahaut, M.P. Pardo, C. Naderi Chirazi, M. Guittard, Compt. Rend. 250 (1960) 857. [4] P. Bro, J. Electrochem. Soc. 109 (1962) 1110. [5] J.C. Andrellos, P. Bro, Solid State Electronics 5 (1962) 414. [6] V.I. Chukalin, E.I. Yarembash, A.I. Vilenskii, Izv. Akad. Nauk SSSR, Neorg. Mater. 3 (1967) 1538.
[7] Y.S. Kwon, T.S. Park, K.R. Lee, J.M. Kim, Y. Haga, T. Suzuki, J. Magn. Magn. Mater. 140–144 (1995) 1173. [8] M.H. Jung, Y.S. Kwon, T. Kinoshita, S. Kimura, Physica B 230–232 (1997) 151. [9] M.H. Jung, Y.S. Kwon, T. Suzuki, Physica B240 (1997) 83. [10] J.-G. Park, I.P. Swainson, W.J.L. Buyers, M.H. Jung, Y.S. Kwon, Physica B 241–243 (1998) 684. ¨ [11] K. Stowe, Z. Anorg. Allg. Chem. 622 (1996) 1419. [12] G.M. Sheldrick, SHELX-97, FORTRAN 77 Program for the Determination and Refinement of Crystal Structures from Diffraction ¨ Data, Gottingen, 1997. [13] G.M. Sheldrick, Acta Cryst. A46 (1990) 467. [14] A. Kikuchi, J. Phys. Soc. Jpn. 67 (1998) 1308. [15] G. Llabres, O. Dideberg, L. Dupont, Acta Cryst. B 28 (1972) 2438. ´ ´ P. Laruelle, Acta Cryst. B 38 (1982) 33. [16] P.S. Benazeth, D. Carre, ´ ´ P. Laruelle, Acta Cryst. B 38 (1982) 37. [17] P.S. Benazeth, D. Carre, [18] M. Grupe, W. Urland, J. Less-Common Met. 170 (1991) 271. [19] F.H. Kruse, R.E. Marsh, J.D. McCullough, Acta Cryst. 10 (1957) 201. [20] T.W. Couch, D.A. Lokken, J.D. Corbett, Inorg. Chem. 11 (1972) 357. [21] J. Beck, K.-J. Schlitt, Chem. Ber. 128 (1995) 763. [22] J. Beck, Z. Naturforsch. 45b (1990) 1610. [23] R. Kniep, D. Mootz, A. Rabenau, Z. Anorg. Allg. Chem. 422 (1976) 17. ¨ [24] H. Wolkers, B. Schreiner, R. Staffel, U. Muller, K. Dehnicke, Z. Naturforsch 46b (1991) 1915. [25] L.J. Saethre, O. Gropen, Can. J. Chem. 70 (1992) 348. [26] W.S. Sheldrick, M. Wachhold, Angew. Chem. Int. Ed. Engl. 34 (1995) 40. [27] Q. Liu, N. Goldberg, R. Hoffmann, Chem. Eur. J. 2 (1996) 390.
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Crystal structure and magnetic properties of CeTe 2 ¨ * Klaus Stowe ¨ des Saarlandes, 66041 Saarbrucken ¨ FR 9.14, Anorganische Chemie und Analytische Chemie und Radiochemie, Universitat , Saarland, Germany Received 11 August 1999; received in revised form 7 February 2000; accepted 9 February 2000
Abstract X-ray diffraction single-crystal structure analysis of CeTe 2 prepared by chemical vapor transport reactions in the presence of mg-traces of iodine revealed superstructure reflections indicating a (23232) supercell of the basic anti-Fe 2 As type in contrast to the (23231) supercell found for LaTe 2 . The best interpretation of data set was obtained choosing for CeTe 2 the tetragonal space group P4 with the lattice parameters a5899.75(5) pm and c51821.2(1) pm (Z516). The doubling of the c axis compared to LaTe 2 is observed due to different polyanionic structural motifs in the heights z¯0 and z¯ ]12 . These are a herringbone pattern of [Te 2 ] dumbbell pairs — a topology which is also found in LaTe 2 — isolated [Te 4 ] four-membered rings in z¯ ]21 and additionally [Te 8 ] branched four-membered rings in z¯ ]12 . These structural elements give a diffraction pattern, which is all in all to be explained by a statistical superposition of the different elements. Magnetic susceptibility measurements revealed pronounced crystal field effects for the trivalent Ce ions, but apart from that are in agreement with former investigations finding a magnetic transition below T54 K due to ferrimagnetic ordering. A formerly observed spin sequence of the magnetic moments at different sites A and B of ABBA,A may now be well understood by a classification of the Ce ions into two types with different coordinational environment in the actual structure model. 2000 Elsevier Science S.A. All rights reserved. Keywords: Cerium ditelluride; Lanthanoid chalcogenides; X-ray diffraction single-crystal structure analysis; Magnetic susceptibility measurements
1. Introduction The observation of superstructure reflections indicating a (23231) supercell of the simple anti-Fe 2 As structure type made it necessary to redetermine the crystal structure of LaTe 2 by single-crystal analysis [1]. In contrast to former investigations revealing tetragonal or orthorhombic symmetry our analysis showed that LaTe 2 crystallizes monoclinic in space group P1c1 with the lattice parameters a5919.0(1), b5910.7(1), c5907.0(1) pm and b 5 90.04(1)8 (Z58). Compared to the anti-Fe 2 As basic structure the polyanionic square 4 4 nets are distorted in LaTe 2 into herringbone pattern of dimer pairs. These findings have put up the question, whether the compound CeTe 2 behaves homologously and shows superstructure reflections, too. But first of all we will give in the following a short review of the literature data known for CeTe 2 up to the present. Early reports of the compound CeTe 2 are due to Naderi Chirazi [2] in 1958, who was the first to synthesize the compound by the reaction of tellurium vapor with anhydr*Tel.: 149-681-302-3071; fax: 149-681-302-4233. ¨ E-mail address: [email protected] (K. Stowe)
ous cerium chloride in a hydrogen atmosphere at 8008C. At this temperature CeTe 2 grows in form of black–blue lamellae crystallizing with tetragonal symmetry with a5 450 and c5908 pm. Two years later Flahaut et al. [3] succeeded in identifying the crystal structure as anti-Fe 2 As type and determined approximate positional parameters from the powder diffraction pattern. Parallel to these investigations, in 1962 Bro and Andrellos [4,5] prepared crystals of the lanthanoid ditellurides LaTe 2 , CeTe 2 , PrTe 2 and NdTe 2 by chemical vapor transport reactions in the presence of iodine. In the phase diagram of the binary system Ce–Te, as determined by Chukalin et al. [6], CeTe 2 is formed by a peritectic reaction at 12508C. Moreover, indications for the existence of a 4:7 phase of formula Ce 4 Te 7 melting incongruently at 13408C and crystallizing in the tetragonal space group P4 /mbm were given, but compared to CeTe 2 with doubled a lattice parameter a5 899.8 and c5916.7 pm. From this we have to conclude that the structure of this compound might be closely related to that of CeTe 2 . After these early investigations CeTe 2 has attracted the interest of some groups once again in the last few years because of its remarkable transport and optical properties, which were measured by Kwon et al. [7–9] at several temperatures. Anomalous resistivity
0925-8388 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 00 )00799-4
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¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
effects of metallic CeTe 2 , especially in form of a very sharp maximum at T54.5 K, induced them to investigate the magnetic structure of the compound in detail. Neutron powder diffraction experiments at T52 K [10] clearly showed the presence of a magnetic superstructure with a doubled lattice parameter c9 5 2c. The RIETVELD refinement of the powder diffraction pattern resulted in a magnetic structure with a ferrimagnetic sequence of ABBA,A in planes normal to the c9 axis. The magnetic moments within the planes were determined as m (A)5 0.40(6) mB and m (B)50.98(6) mB . Even in this recent publication the unusual large anisotropic thermal motion of the Te(1) ions within the polyanionic 4 4 nets was emphasized. This encouraged us to reinvestigate the crystal structure of CeTe 2 , to redetermine its composition accurately and to compare its properties with former investigations in order to check whether there are further discrepancies.
2. Experimental details
2.1. Sample synthesis Black plate-like shaped single crystals of CeTe 2 with metallic luster up to an edge-length of several mm were obtained by chemical vapor transport reactions in silica ampules with I 2 as transporting agent in a temperature gradient from 9508C to 8508C starting from the elements Ce (ingot, 99.91%, Kelpin, Leimen, Germany) and Te (pieces, .99.999%, Fluka, Buchs, Switzerland) as already reported earlier [4,5]. The compound was handled under a dry and oxygen-free atmosphere of purified argon in a glove box, because it is moisture and air-sensitive.
2.2. Analytical characterization and measurements of physical properties For a further characterization of the compound CeTe 2 with respect to its composition atomic emission spectrometry with plasma excitation (ICP–AES, Perkin Elmer) was used. For the analysis samples consisting of selected single crystals were sealed in capillaries of 2 mm diameter, subsequently opened in an autoclave with a Teflon inlet and dissolved in a HNO 3 / HCl mixture. Further details are given in Ref. [11]. The analysis by ICP–AES of the product revealed a composition of CeTe 2.01( 3) . To support the analytical data the density of samples consisting of several single crystals was measured. This was done by a gas displacement pycnometer of type Accupyc 1330 / 1cc (Micromeritics) with helium as working gas. Because the samples were air and moisturesensitive, the complete pycnometer was placed in a glove box under a dried and oxygen-free argon atmosphere. The measurements on selected single crystals yielded an aver-
age density of rm 57.01(3) g cm 23 compared to a calculated density of rx 57.124 g cm 23 . ¨ Festkorper¨ Magnetic data were recorded at the MPI fur forschung, Stuttgart (Germany), with samples synthesized by chemical vapor transport reactions, which were sealed in Suprasil glass capillaries of 200 mm length and a reduction in the middle of the capillaries to hold the samples. Susceptibility measurements were performed with an MPMS SQUID magnetometer (Quantum Design) at two different magnetic fields of H50.1 and 1 T in the temperature interval of T52–350 K. Due to the paramagnetic behavior of the compound no diamagnetic corrections were applied.
2.3. X-ray single-crystal structure determination The data collections were carried out with a P4 singlecrystal diffractometer (Siemens, Karlsruhe, Germany). The unit cell was determined by refinement of the diffraction angles of 100 single-crystal reflections distributed uniformly in reciprocal space. All reflections of CeTe 2 could be ] ] indexed by a tetragonal primitive (2Œ232Œ232) supercell with a51272.44(7) and c51821.2(1) pm (Z532), which will be considered in the following as cell choice 1. But from all in all 34 318 measured reflections only 9 reflections with I . 4 ? s (I) did not suit the systematic extinction condition of a C-centering. From these 9 only the (0 9 0) reflection and its equivalents had a reliable intensity with I ¯ 10 ? s (I). Rotating about the plane normal of these reflections revealed apart from absorption effects no intensity changes, so that a Renninger effect could be ruled out. But all attempts to include all the 17 140 extinct reflections in the refinement procedure resulted only in a worsening of the R-values, whereas no general changes in the structure model were observed. Thus the refinements were performed assuming a C-centered lattice or, after transformation into a standard setting, a P-type lattice. This second (23232) supercell with a5899.75(5) and c51821.2(1) pm (Z516), in the following referred to as cell choice 2, was also the basis of all our subsequent structural discussions. Table 1 gives a summary of important measurement and refinement data. The structure refinements were performed with the computer program SHELX-97 [12,13]. The results are summarized in Tables 2 and 3. Group–subgroup relations with the space group of the anti-Fe 2 As type, P4 /nmm, as aristotype have lead us to a plausible structure solution in space group P4 (see Fig. 1). Due to the drastic reduction in symmetry, a lot of additional degrees of freedom for a distortion of the aristotype are produced, whereas the dropped symmetry elements are only pseudo-symmetry elements and valid for the averaged structure. In the space group P4 the polyanionic Te(1) ions, forming regular 4 4 nets in the undistorted anti-Fe 2 As type, occupy the general Wyckoff positions (4d). Already in the early stages of the refinement
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
103
Table 1 Measurement and refinement data for CeTe 2 in the X-ray single-crystal structure analysis Measurement temperature Lattice parameters a c Number of formula units per cell Calculated density Measured density Space group Measured range of reciprocal space (Mo-K a ) Type of data collection / scan width No. of observed reflections No. of nonequivalent reflections Absorption correction Crystal color Crystal size Linear absorption coefficient Internal R value c Structure solution Structure refinement Program for structure solution and refinement Extinction parameter empirical with F* 5 F[1 1 0.002x F 2 / sin (2u )] 21 / 4 Number of independent parameters R values (w 5 1 /s (Fo )2 )
293 K 899.75(5) pm 1821.2(1) pm 16 7.124 gcm 23 7.01(3) gcm 23 P 4 (No. 75) 3,2u ,608 (all octants) v / 1.18 in 96 steps 17 178 4460 Numerical a,b Lustrous black 0.0830.1530.32 mm 3 275.9 cm 21 3.94% Transformed anti-Fe 2 As model Full matrix least-squares SHELX-97 d 0.00040(1) 177 wR 2 50.0738
a
W. Herrendorf, HABITUS, Program for the Optimization of the Crystal Description for a Numerical Absorption Correction on the Basis of Appropriate Psi-Scanned Reflections, Karlsruhe, Germany, 1992. b W. Alcock, P.J. Marks, and K.-G. Adams, ABSPSI, Absorption Correction and Refinement of the Crystal Habitus, Karlsruhe, Germany, 1994. c K.-G. Adams, MITTELN, Averaging Symmetry-Equivalent Reflections, Karlsruhe, Germany, 1995. d ¨ G.M. Sheldrick, SHELX-97, FORTRAN-77 Program for the Refinement of Crystal Structures from Diffraction Data, Gottingen, Germany, 1997; G.M. Sheldrick, Acta Cryst. A 46 (1990) 467.
difference electron density syntheses clearly showed several maxima around these Te(1) ions. These maxima indicate that even in the low symmetric space group P4 the structure refinement is complicated by microtwinning effects. From the observation of supercell reflections indicating a doubling of the c-axis we have to conclude that the polyanionic arrangement of the Te(1) ions in the distorted 4 4 nets has to be different in z9¯0 and z9¯ ]12 (formerly in the anti-Fe 2 As type z50 and z51). Correspondingly only one additional density maximum was found in z9¯0, but two maxima in z9¯ ]21 . Since the Te(1) ions at the additional density are not related to the original ones by symmetry elements, there is no possibility to find a simple twin law and to refine the structure e.g. with the twin refinement method implemented in the program SHELXL [12,13]. The only way to treat this type of microtwinning is by split positions, which was done in the following refinement procedure. To deal with the pseudocentrosymmetry of the data set, racemic twinning was included at the last stages of refinement, which resulted in a twin component ratio of 0.41(9) to 0.59(9). Refining with cell choice 2 the isotropic displacement factors Uiso independently with the constraints and restraints for the site occupation factors sof given in the footnote of Table 3 resulted in physically quite reliable and almost equal values for all the different Te(1) ions. From this no hint for a deviation of stoichiometry from the
assumed composition was given. But the existence of additional compounds with a composition very close to the 1:2 ratio, as e.g. Ce 4 Te 7 (see Introduction), made it necessary to perform an independent determination of the elemental composition of the synthesized samples. But the analysis by ICP–AES of selected single crystals of the product gave also no hints on a deviation of the assumed composition CeTe 2 . Moreover, this result was confirmed by pycnometric density measurements. On the other side, for the compound Ce 4 Te 7 , also proposed in the literature, we would expect a significantly smaller density of rx 5 6.50 gcm 23 [6] compared to the measured value of rm 5 7.01(3) g cm 23 .
3. Description of the crystal structure The difference of the actual structure model to former investigations lies entirely in the topology of the polyanionic square 4 4 nets (Te(1ni), n 5 1–4, i5A, B(, C); referring to the numbering, see footnote a in Table 2), whereas the other Te anions (Te(2n), n51–8) and the Ce cations (Ce(n), n51–8) remain almost at their positions as in the anti-Fe 2 As structure type. CeTe 2 in the anti-Fe 2 As type can be regarded as built up solely from 4 4 nets with a layer sequence of (4 4 )2 (Te(1)) 4 4 (Ce) 4 4 (Te(2)) 4 4 (Te(2))
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
104
Table 2 Positional parameters a and equivalent isotropic displacement factors b (pm 2 ) of CeTe 2 Atom
Wyck.
x
y
z
sof c
Ueq
Te(11A) Te(11B) Te(12A) Te(12B) Te(13A) Te(13B) Te(13C) Te(14A) Te(14B) Te(14C) Te(21) Te(22) Te(23) Te(24) Te(25) Te(26) Te(27) Te(28) Ce(1) Ce(2) Ce(3) Ce(4) Ce(5) Ce(6) Ce(7) Ce(8)
4d 4d 4d 4d 4d 4d 4d 4d 4d 4d 1a 1a 1b 1b 2c 2c 4d 4d 1a 1a 1b 1b 2c 2c 4d 4d
0.2524(1) 0.2218(9) 0.5081(2) 0.4778(9) 0.5201(3) 0.4950(4) 0.4982(7) 0.2602(3) 0.2433(4) 0.2312(7) 0 0
0.9914(1) 0.0157(9) 0.2482(1) 0.2902(8) 0.2461(3) 0.2640(3) 0.2245(6) 0.9976(4) 0.9806(4) 0.0133(7) 0 0
0.866(2) 0.134(2) 0.866(2) 0.134(2) 0.446(1) 0.377(1) 0.177(2) 0.446(1) 0.377(1) 0.177(1)
1 ] 2 1 ] 2
1 ] 2 1 ] 2 1 ] 2 1 ] 2
0.9996(1) 0.9972(7) 0.9988(1) 0.0026(6) 0.5001(2) 0.4971(3) 0.5048(5) 0.4975(2) 0.4996(3) 0.5102(4) 0.3162(1) 0.8160(1) 0.3164(1) 0.8163(1) 0.3167(1) 0.8164(1) 0.1835(1) 0.6836(1) 0.1356(1) 0.6360(1) 0.1360(1) 0.6364(1) 0.1359(1) 0.6358(1) 0.3623(1) 0.8621(1)
0.0160(2) 0.0161(4) 0.0155(2) 0.0158(4) 0.0108(3) 0.0108(3) 0.0108(3) 0.0108(3) 0.0108(3) 0.0110(3) 0.0102(4) 0.0106(5) 0.0109(5) 0.0104(5) 0.0108(4) 0.0105(4) 0.0147(3) 0.0143(3) 0.0143(4) 0.0141(5) 0.0163(4) 0.0154(5) 0.0146(4) 0.0146(4) 0.0152(3) 0.0150(3)
0 0 0.2508(1) 0.2505(1) 0 0 1 ] 2 1 ] 2
0 0 0.2523(1) 0.2526(1)
0.2493(1) 0.2494(1) 0 0 1 ] 2 1 ] 2 1 ] 2 1 ] 2
0.2473(1) 0.2479(1)
1 ] 4 1 ] 4 1 ] 4 1 ] 4 1 ] 2 1 ] 2
1 1 1 ] 4 1 ] 4 1 ] 4 1 ] 4 1 ] 2 1 ] 2
1 1
a
To differentiate between the different types of Te(1) ions, a numbering as Te(1n) was used with Te(1n) (n51, 2) for Te(1) in z¯0 and Te(1m) (m53, 4) for Te(1) in z¯ ]12 . Additionally this numbering was expanded as Te(1ni) with i5A, B(, C) for the different split-up positions. b * 1 U 22 * 1 U 33 * ], with U ij* the orthogonalized tensor components. Equivalent isotropic Ueq calculated by ]13 [U 11 c The site occupation factors of all n sites Te(1ni) with i5A, B(, C) were constrained to equal values for n51, 2 and n53, 4, e.g. sof(Te(11A))5 sof(Te(12A)), and their sum restrained to unity with an effective standard deviation of 0.001, e.g. sof(Te(13A))1sof(Te(13B))1sof(Te(13C))51.
4 4 (Ce), (4 4 )2 (Te(1)). By (4 4 )2 9 we denoted the polyanionic layers packed with twice the density of the other nets. These regular square Te(1) nets are believed to cause the metallic conductivity of the lanthanoid ditellurides of this structure type [14]. In the actual structure model the Te(1) nets have distorted into several different types of pattern. Corresponding to the number of electron density maxima in the two different layer heights we have two types A, B in z¯0 and three types A, B and C in z¯ ]21 . The only crystal chemically meaningful interpretation of the split positions in z¯0 is to assume a double herringbone pattern of [Te 2 ] dumbbells with an interatomic distance d(Te(11A)–Te(12A))5304.8 pm as in the homologous compound LaTe 2 (d5298.7, 303.6 pm) [1] superimposed by an arrangement of isolated [Te 4 ] fourmembered rings with point symmetry 4.. (see Fig. 2). Because of two independent (4d) positions Te(12B) and Te(11B) there are also two independent rings with interatomic distances of d5268.5 and d5283.0 pm, respectively. The interpretation of the split positions in z¯ ]12 is also clear cut (see Fig. 3). Apart from a double herringbone pattern of dimers [Te 2 ] (A) and four-membered rings [Te 4 ] (B) we have also as additional feature branched fourmembered rings [Te 8 ] (C). Although the topology of A
and B in z¯ ]21 is the same as in z¯0, there are somewhat different interatomic distances within the various types of bonding pattern. Within the dimers of the herringbone pattern the Te(1nA) ions with n53, 4 are now only 295.2 pm apart, and within the two different four-membered rings d(Te(13B))–Te(13B))5300.3 and d(Te(14B))– Te(14B))5310.6 pm. The branched four-membered rings are unique and they are found only in z¯ ]12 . They show interatomic of d5294.6 pm within the rings and d5306.5 pm from the ring ions to the neighboring Te ions. If we cancel the differentiation into these discrete structural motifs by averaging all interatomic distances within the distorted square sheets, we again get a simple anti-Fe 2 As type structure. Even in the actual structure model there is a large amount of pseudo-symmetry due the small distortions of the Te in the square sheets. This can also be seen from the numerous pseudo-extinction rules in cell choice 1 as well as cell choice 2. But a very careful inspection of these pseudo-extinction rules has let us to the realization that they are not strictly fulfilled. This brings us back to the question of the different cell choices. From the structure refinement we rejected the thesis of cell choice 1 and considered choice 2 as the more probable one. But in view of a microdomain structure of different structural motifs the question of the correct cell choice has to be
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe Table 3 Anisotropic displacement factors a ,b (pm 2 ) of CeTe 2
105
extended domain size with a stable instead of a random sequence of the layer types seems to be more realistic.
Atom
U11
U22
U33
U23
U13
U12
Te(11A) Te(11B) Te(12A) Te(12B) Te(13A) Te(13B) Te(13C) Te(14A) Te(14B) Te(14C) Te(21) Te(22) Te(23) Te(24) Te(25) Te(26) Te(27) Te(28) Ce(1) Ce(2) Ce(3) Ce(4) Ce(5) Ce(6) Ce(7) Ce(8)
178(4) 175(7) 176(4) 177(7) 117(5) 115(5) 115(5) 132(5) 135(5) 133(5) 93(5) 85(5) 86(5) 102(6) 96(7) 89(7) 170(6) 176(7) 168(5) 159(5) 185(5) 176(6) 164(7) 168(7) 136(5) 142(6)
192(4) 192(7) 180(5) 179(7) 118(5) 115(5) 115(5) 121(5) 120(5) 121(5) U 11 U 11 U 11 U 11 89(7) 110(7) 165(7) 178(8) U 11 U 11 U 11 U 11 170(7) 190(8) 132(5) 145(6)
109(4) 116(7) 108(4) 117(7) 90(5) 95(5) 94(5) 71(5) 68(5) 77(5) 120(9) 146(11) 155(11) 107(11) 138(9) 114(9) 107(5) 74(5) 95(9) 105(10) 119(9) 110(10) 104(7) 80(8) 187(5) 164(5)
218(6) 219(8) 226(6) 222(7) 17(5) 20(5) 17(5) 238(5) 238(5) 236(5) 0 0 0 0 0 0 1(4) 28(4) 0 0 0 0 0 0 230(4) 212(4)
217(5) 218(8) 34(6) 33(7) 15(5) 17(5) 15(5) 21(5) 15(5) 18(5) 0 0 0 0 0 0 22(4) 23(5) 0 0 0 0 0 0 3(4) 25(4)
21(4) 20(7) 22(4) 18(7) 18(4) 21(5) 18(5) 229(5) 230(5) 226(5) 0 0 0 0 23(4) 24(4) 2(7) 28(7) 0 0 0 0 217(4) 226(4) 13(6) 9(6)
a
Due to prominent correlation effects the thermal displacement parameters of split positions could not be refined without restraints. So the displacement parameters of all the Te(1ni) ions were coupled by giving an SIMU card, which restrained ions closer than 100 pm with an effective standard deviation of 10 pm 2 to have the same Uij components. Additionally the thermal motion of the Te(1) ions at the split positions had to be restricted by an ISOR instruction, which restrained the Uij components to isotropic behavior with the effective standard deviation of 30 pm 2 as implemented in the refinement program SHELXL-97 [12,13]. b The dimensions are in accordance with the following formula: 2 2p 2 ? o i o j Uij h i h j a *i a *j .
discussed again, because in principle also a mixture of different motifs within a single distorted square sheet is within the range of possibility. For instance the alternation of dumbbell pairs and 4-rings in [100] direction of cell 2 would lead to an enlargement of the unit cell and to cell 1. On the other side, from the very low intensity of the reflections not fulfilling the extinction rule of the Ccentering in unit cell choice 1 we have to conclude that this mixing of different structural elements is not very marked and cell choice 2 the more appropriate one. If there is perfect order among the different kind of structural motifs in CeTe 2 , the Laue monotonic scattering would be gathered exclusively into sharp superlattice reflections, otherwise, the scattering would also be diffusely distributed depending on the extent of local order that exists. But despite a somewhat enlarged FWHM of the axial reflections in direction of the c lattice vector, no hints for diffuse scattering in comparative q scans of reciprocal space were seen. From this, the assumption of a distribution of the structural motifs A, B and C in form of microlamellae of
4. Discussion of the crystal structure In the following section we will discuss the interatomic distances and interactions in more detail. The double herringbone pattern was first described for the homologous compound LaTe 2 [1], which crystallizes in a low symmetric monoclinic space group with two different interatomic distances within the dimers of d5298.7 and d5303.6 pm. The calculation of the Crystal Orbital Hamiltonian Population (COHP) function, which is the Hamiltonian population weighted density of states, suggested that, due to secondary interactions of d5313.0 pm, we have to regard the Te(1) sheet in LaTe 2 better as a simple herringbone arrangement of L-shaped [Te 4 ]-units. By the way of contrast no intermolecular distances between the dimers below 320 pm are found in CeTe 2 , so that we do not have to consider any pronounced further secondary interactions. With d5304.8 and 295.2 pm in z¯0 and z¯ ]12 , respectively, the observed intramolecular distances are not very different from those in LaTe 2 . In both compounds they are ¯10% longer than a single bond distance (e.g. d5271 pm in diphenylditelluride [15]). On the contrary, in the compounds LaSe 2 , which crystallizes also in a distorted antiFe 2 As type structure with an arrangement of the polyanionic partial structure in form of a simple herringbone pattern [16,17] (see Fig. 4, upper part), and La 10 Se 19 , whose structure is a ordered-defect variant of the antiFe 2 As type [18] (see Fig. 4, lower part), the [Se 2 ] 22 distances of d(Se–Se)5245.2 and 247.7 pm, respectively, are only ¯5% larger than the corresponding single bond distance (e.g. d5233 pm in p, p9-dichlorodiphenyl-ditelluride [19]). As expected for tellurides, the differentiation between the polyanionic interatomic distances within the distorted tellurium sheet is much less distinct than in the other polychalcogenides. Proceeding to the next arrangement, the four-membered rings, we are confronted with another new type of bonding pattern. The four-membered rings in CeTe 2 all have a point-symmetry 4.., but their interatomic Te–Te distances are relatively wide-spread (d(Te(1)–Te(1))5268.5, 283.0 pm in z¯0 and 300.3, 310.6 pm in z¯ ]12 , see Fig. 3). Since all other interatomic distances within the polyanionic sheet lie above 320 pm, we can neglect secondary interactions in a first approximation and compare these fragments with other molecular ones. Topologically similar [Te 4 ] rings are observed in literature as twofold positive charged species in compounds such as Te 4 (AlCl 4 ) 2 [20], Te 4 (HfCl 6 ) [21], Te 4 (MoOCl 4 ) 2 [22] or in the subhalogenide a-TeI [23]. In the last compound non-planar [Te 4 I 4 ] rings were found, which are interconnected by secondary interactions to infinite chains. The Te–Te distances within the rings with values of d5278.6, 280.7, 289.3 and 292.8 pm lie in the
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Fig. 1. Symmetry relations between the space group of the anti-Fe 2 As structure type P4 /nmm and the actual space group of CeTe 2 P4.
same order of magnitude as those in CeTe 2 . Polyanionic fragments like [Te 4 ] 22 are found only as open chain species, e.g. in the compound (PPh 4 ) 2 Te 4 [24] with intrachain distances of d(Te–Te)5268.6, 270.5 and 276.1 pm. Theoretical calculations using the effective core potential model on square-planar [X 4 ] 21 , [X 4 ] 1 and [X 4 ] 0 (X5S, Se, Te) [25] have shown that the bond lengths increase dramatically with decreasing positive charge of the system. By an extensive population analysis Saethre and Gropen [25] found that this increase is almost exclusively due to the loss of bonding in the p system, whereas the bonding in the s system remains relatively unaltered. In coordination compounds as, e.g. CeTe 2 the antibonding
p contributions might be reduced by a covalent interaction of Te with the Ce neighbors. But further insights into the bonding characteristics in CeTe 2 will come from first principles band structure calculations similar to those, which we have already performed for the homologous compound LaTe 2 [1]. But this will be the topic of a subsequent paper. At the moment we can only state that the different intraring distances observed in CeTe 2 may indicate also quite different charges of the several Te ions. The last type of bonding pattern, the branched fourmembered rings which are exclusively found in z¯ ]12 , also reveals almost no secondary interactions, since all intermolecular distances lie well above 320 pm. The [Te 8 ] units
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Fig. 2. Polyanionic Te(1) sheets in the crystal structure of CeTe 2 in [001] projection at z¯0. Left side: Double herringbone type pattern (A). Right side: Four-membered Te rings (B; distances in pm).
also have a point symmetry 4.. with intramolecular distances of d5294.6 pm within the rings and an exocyclic bond distance of d5306.5 pm (see Fig. 3). They may be regarded as a molecular fragment of the planar [CsTe 6 ] sheets in the compound Cs 3 Te 22 [26]. The structure of these 2,3-connected [Te 6 ] sheets consists of linear and T-shaped Te ions with intraring distances of d5300.3 pm and two bond lengths of d5307.7 pm for the linear Te ion
connecting two four-membered rings (see Fig. 5). Following Zintl’s concept Liu et al. [27] assigned these [CsTe 6 ] sheets a formal twofold negative charge with partial charges of 21 for the linear Te and 2 ]41 for the T-shaped ring Te ions. To model this sheet Liu and co-workers also performed EH calculations at isolated [Te 4 Te 4 ] n 2 molecular units and varied the Te–Te–Te angle b for the Tshaped Te ions while maintaining the four-fold symmetry.
Fig. 3. Polyanionic Te(1) sheets in the crystal structure of CeTe 2 in [001] projection at z¯ ]21 . Left top side: Double herringbone type pattern (A). Right top side: Four-membered Te rings (B). Bottom: Branched four-membered rings (C; distances in pm).
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Fig. 3. (continued)
They calculated that the b 5908 configuration is more stable than the b 51358 conformer if the molecule possesses a total charge of 25 to 29, whereas for larger charges the b 51358 configuration is more stable. For charges between 25 and 29, in all cases studied, the total energy was minimized at angles b ,908. In the case of Cs 3 Te 22 an angle of b 588.58 was found experimentally. In CeTe 2 the geometry of the [Te 8 ] unit does not differ significantly from that assumed by Liu et al. for their calculations on the [Te 4 Te 4 ] unit, which was taken from Cs 3 Te 22 . The bond distances are only 3–5 pm shorter in CeTe 2 , but the angle b (100.1(3)8) is somewhat larger than 908 indicating a relatively high charge (29 and higher) of the [Te 8 ] fragment. All in all we can summarize our results as follows: Compared to LaTe 2 , whose structure shows only [Te 2 ] dumbbells in the polyanionic Te(1) layers, we find a clear trend in CeTe 2 to reduce the localization and to increase the itinerancy in the distorted square nets. Apart from dumbbells of connectivity 1 also isolated four-membered rings of connectivity 2 and branched four-membered rings of connectivity 1 and 3 were observed in the crystal structure of CeTe 2 . Since the evaluation of the interatomic distances within the distorted square sheets revealed only very weak secondary interactions above 320 pm, we would expect CeTe 2 to be a semiconductor. But, as the homologous La compound, CeTe 2 is reported to be a metallic conductor [7–9]. In LaTe 2 this is due to an additional direct covalent La–La interaction leading to an energy lowering of a single La 5d x 2 2y 2 orbital around the Brillouin zone center G in band structure calculations [1]. Whether this is also the reason for the metallic conductivity of CeTe 2 , we intend to make clear by a subsequent paper.
Fig. 4. Distortion pattern for the selenium sheets in LaSe 2 in form of a herringbone pattern (top) and La 10 Se 19 with isolated Se 22 anions, vacancies and [Se 2 ] 22 dimers in the ratio 1:1:4 (bottom).
5. Magnetic susceptibility measurements In this context it might be very interesting to redetermine the magnetic properties of crystals of CeTe 2 synthesized by chemical vapor transport reactions and compare them with results reported earlier [7,10] on powder samples. These were prepared by using mineralization in an evacuated and sealed tungsten crucible at 15008C [7]. On the other side, CeTe 2 should melt incongruently at 12508C [6], so that there might be some uncertainties concerning the composition of the samples prepared by Kown et al. [7,10]. Between the magnetic susceptibility data in Kwon et al. [7] and ours (see Fig. 6) there is some relationship, but also distinct differences. In the high temperature regime above T¯100 K the re-
¨ / Journal of Alloys and Compounds 307 (2000) 101 – 110 K. Stowe
Fig. 5. Planar [CsTe 6 ] 22 sheets in the crystal structure of Cs 3 Te 22 [26]. Assignment of charges due to Liu et al. [27] (distances in pm).
ciprocal molar susceptibility given in Kown et al. [7] increases almost linearly with temperature, whereas our data suggest a magnetic moment decreasing with temperature. Fitting a straight line between T5250 and 350 K
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gives a magnetic moment of m 52.18 mB and a positive paramagnetic Curie temperature of Qp 551 K, whereas extrapolation of the data in the interval T550–100 K gave m 52.62 mB and a negative Curie temperature of Qp 5 210 K. So in contrast to Kown et al. [7] we find quite pronounced crystal field effects for the trivalent Ce ions ( mS1L (Ce 31 )52.54 mB ). The negative Curie temperature of the midrange data together with the observation of a magnetic transition at an onset temperature of T¯4 K with 1 /xm ¯0 for T ,4 K implies a ferrimagnetic ordering in agreement with neutron diffraction data on powder samples at T52 K [10]. As already mentioned in the Introduction, these investigations resulted in magnetic superstructure reflections indicating a doubling of the magnetic unit cell compared to the crystallographic cell with magnetic moments lying along c in a spin sequence of ABBA,A with moments of m (A)50.40(6) mB and m (B)50.98(6) mB . Assuming an undistorted anti-Fe 2 As type structure for CeTe 2 , the finding of two different magnetic moments is quite unreasonable, because, even with a doubled c axis, all Ce ions would have the same capped tetragonal antiprismatic coordination environment. Referring to our crystal structure analysis, the crystal structure has revealed two basically different Ce environments for Ce coordinating Te(1) ions in z¯0 (Ce(n), n51,3,5,8) and z¯ ]12 (Ce(m), m52,4,6,7), so that the observation of different
Fig. 6. Reciprocal molar magnetic susceptibility of CeTe 2 in the temperature range T52–350 K at H50.1 and H51 T.
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magnetic moments especially in a sequence ABBA,A now appears quite reasonable. With the redetermined crystal structure data some properties of CeTe 2 such as the ferrimagnetic ordering can now be understood, but others such as the metallic transport properties have still to be explained by theoretical calculations.
Acknowledgements The author is particularly indebted to Dr. R.K. Kremer ¨ ¨ and Mrs. E. Brucher from the Max-Planck-Institut fur ¨ Festkorperforschung in Stuttgart, Germany, for the magnetic susceptibility measurements. The Deutsche Forschungsgemeinschaft DFG and the Fonds der Chemischen Industrie FCI are gratefully acknowledged for financial support.
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