The title compound was prepared from the elements by arc-melting. The crystal structure was investigated by means of single-crystal X-ray diffraction. It crystallizes in the TbFeSi2 structure type, orthorhombic space group Cmmm, a = 4.0496(8), b = 16.416(2), c = 3.9527(6) Å, Z = 4, R1 = 0.041, wR2 = 0.11 for 207 unique reflections with Io > 2 σ(Io) and 19 refined parameters. The Fe position is not fully occupied and the refinement results in a composition GdFe0.68Si2 in agreement with a chemical analysis. The structure consists of zig-zag chains of Si(1) atoms which are terminally bound to additional Si(2) atoms. For an ordered variant GdFe0.5Si2 the Zintl concept can be applied which results in formal oxidation states Gd3+(Fe2+)0.5Si(1)1−Si(2)3−. The electronic structure of this variant GdFe0.5Si2 was analyzed using the tight-binding LMTO method and the results confirm the simple bonding picture.
Several ternary compounds with the approximate composition RT1−xSi2 (R=rare earth, T=transition element) have been reported during the last decades. Their crystal structures are characterized by a stacking of BaAl4 and AlB2 related slabs. Most compounds with T=Co–Cu crystallize in the CeNiSi2-type structure . Different structures were found for the RT1−xSi2 compositions. The early rare earth manganese RMn1−xSi2 (R=La–Sm) and iron RFe1−xSi2 (R=La–Tb) silicides crystallize in the LaMnSi2-type structure , , , a structure closely related to the CeNiSi2-type structure, and they are characterized by a site exchange between the transition-metal and the main-group elements within the BaAl4 block. The atomic positions in the LaMnSi2-type structure correspond to those in the TbFeSi2-type structure earlier discovered by Yarovets and Gorelenko . We use the earlier discovered type of structure for our denomination in the text. Investigations in quaternary systems R-T-T′-X led to the characterization of new isotypic representatives of the TbFeSi2-type structure with the composition RTT′0.5X1.5 (R=La–Sm; T=Mn, Co, Rh, Re; T′=Cu, Ni, Pd, Pt; X=Si, Ge) , , , , , . All compounds show the T′ substitution in the AlB2 slabs.
Paccard et al.  re-investigated TbFeSi2 first discovered by Yarovets and Gorelenko . From single-crystal X-ray diffraction data of the RFeSi2 (R=Ho, Tb, Dy) compounds, they concluded that these phases are non-stoichiometric and should rather be named as RFe0.5Si2 because an iron non-stoichiometry is evident. Due to the very small difference between the X-ray scattering factors for a fully occupied silicon site or a half-occupied iron site, this study does not clearly distinguish between the two site exchange variants, i.e. the TbFeSi2 and CeNiSi2 structure types. Norlidah et al.  using neutron diffraction and 57Fe Mössbauer spectroscopy for HoFe0.5Si2 have suggested that this compound crystallizes in the CeNiSi2-type structure and partially removed the uncertainties outlined by Paccard et al.  concerning the localization of the transition metal in the heavy rare earth RFe1−xSi2 compounds (R=Tb, Dy, Ho, Er, Lu). The TbFeSi2 structure type also has quaternary representatives in the R-Mn-T-Si systems: RMnPd0.5Si1.5 (R=La, Ce), RMnPt0.5Si1.5 (R=La, Ce, Pr), and RMnCu0.5Si1.5 (R=La, Ce–Nd) .
For the RT1−xX2 compounds with the CeNiSi2-type structure, the non-stoichiometry increases with the period number of the tetrele element with the same rare earth and transition metal element i.e.: HoFe0.5Si2, HoFe0.38Ge2, and HoFe0.14Sn2 . By fixing the rare earth and tetrele elements, the transition metal content increases with the group number of the transition metal i.e.: LuFe0.3Si2 , LuCo0.85Si2 , and LuNiSi2 .
Finally, the RRuSi2-type compounds (R=La, Ce, Nd, Sm, Gd, Tb) and the stoichiometric RFeSi2-type compounds (R=Nd, Sm, Gd, Tb) adopt the NdRuSi2-type structure, a monoclinic variant of the CeNiSi2 type , , . The NdRuSi2-type structure family includes the non-stoichiometric CeNi1−xSi2 and CeNil−xSi2+x structures with vacancies or mixed occupations on the transition metal sites . The compounds CeRh1−xGe2+x (x=0.325) crystallize in a primitive orthorhombic cell with disordered substitution on half of the transition-metal sites , while the TmLi1−xGe2 (x=0.5) structure is another monoclinically distorted variant .
In the course of systematic phase-analytical studies of the Gd–Fe–Si system we have obtained new phases. A closer inspection of the new compound GeFe1−xSi2 became the subject of the present work.
Polycrystalline samples of different compositions GdFeSi2, GdFe0.8Si2, GdFe0.5Si2 and GdFe0.4Si2 were prepared from the commercially available pure elements: gadolinium metal with a claimed purity of 99.99 at.%, Alfa-Aesar, Johnson Matthey Company, sublimed bulk pieces; silicon as powder, purity >99.99 at.%, H. C. Starck, Germany; iron powder, purity 99.98 at.%, Fluka Chemicals. Suitable amounts of powders and freshly filed chips of the rare earth metal were mixed together and pressed into pellets. Arc-melting of the samples (1.00 g each) was performed on a water-cooled copper hearth under a purified argon atmosphere with Ti as the getter. To ensure homogeneity, the samples were turned over and re-melted three times. Weight losses were generally smaller than 0.5%. For further heat treatments, the pellets were wrapped in tantalum foil, sealed in evacuated quartz tubes, annealed at T=800°C for 1 month and subsequently quenched by submerging the tubes in cold water. Single crystals of the new gadolinium iron silicide, having a metallic luster and being unreactive towards air, were isolated by crushing the solidified samples.
2.2 Microprobe analysis
For metallographic inspection and for complementary qualitative phase analysis, energy dispersive X-ray spectroscopy (EDX) was employed. The samples were embedded in Wood’s metal (melting point of 75°C, Fluka Chemie, Switzerland). The embedded samples were polished on a nylon cloth using chromium oxide (Bühler Isomet) with grain sizes 1–5 μm. Quantitative and qualitative composition analyses of the polished samples were performed by energy-dispersive X-ray spectroscopy (EDX) on a scanning electron microscope TESCAN 5130 MM with an Oxford Si-detector. From the EDX analysis of the arc-melted sample GdFe0.4Si2 the composition Gd26.2(3)Fe18.0(3) Si55.6(3) was deduced. For the chemical microprobe, the polishing procedure had to be performed or repeated just before the measurements. The surface of the phases in the Gd–Fe–Si system appears to be quite stable in air. Metallographic investigation, X-ray powder diffraction and EDX analyses revealed the presence of the phases Gd2Fe3Si5  and Gd1.2Fe4Si9  besides the new compound GdFe1−xSi2 (x=0.32) (Fig. 1). After the annealing procedure, only Gd2Fe3Si5 and GdSi2  were found in the GdFe0.4Si2 sample.
2.3 X-ray diffraction and structure refinement
X-ray powder diffraction patterns were obtained on a powder diffractometer STOE STADI P with MoKα1 radiation, using sealed boron glass capillaries. The unit cell parameters were refined with the help of the WinCSD program package . The indexing of the X-ray powder patterns was ensured through intensity calculations taking the atomic positions determined from the single-crystal investigation. The unit cell parameters refined from X-ray powder data are a=4.05781(5), b=16.424(2), c=3.9652(4) Å. The small difference between the lattice parameters determined from single-crystal and powder diffraction, respectively, are quite normal.
Small and irregularly platelet-shaped single crystals for X-ray investigation were selected from the crushed arc-melted sample of GdFe0.4Si2. These crystals were first examined by the Buerger precession method in order to establish their suitability for intensity data collection. After the X-ray data collection on a STOE IPDS II image plate diffractometer, an EDX analysis of the single crystal revealed the composition Gd27.3(3)Fe19.1(3)Si53.6(3), which is in good agreement with the results obtained from the bulk sample, and the small difference indicates surface irregularities of single crystals.
Single-crystal X-ray data of GdFe1−xSi2 (x=0.32) was collected at room temperature on a Stoe IPDS II image plate diffractometer with monochromatized MoKα radiation in oscillation mode. The lattice parameters were determined from 3150 reflections in the region 4.8–58.98°. All relevant details concerning the data collection are listed in Table 1.
|Space group||Cmmm (No. 65)|
|Unit cell volume V, Å3||262.77(7)|
|Calculated density, g cm−3||6.81|
|Absorption coefficient, mm−1||31.1|
|Crystal size, mm3||0.12×0.09×0.02|
|Diffractometer||STOE IPDS II|
|2θmax, deg/(sinθ/λ)max, Å−1||58.21/0.684|
|hkl indices range||–5≤h≤5, –20≤k≤22, –5≤l≤5|
|Reflections with I>2 σ(I)||207|
|Final R1/wR2 [I>2σ(I)]a,b||0.041/0.119|
|Final R1/wR2 (all data)a,b||0.044/0.111|
|Goodness-of-fitc on F2||1.16|
|Largest diff. hole/peak, e− Å−3||–3.53/4.14|
aR1=Σ||Fo|–|Fc||/Σ|Fo|; bwR2=[Σw(Fo2–Fc2)2/Σw(Fo2)2]1/2, w=[σ2(Fo2)+(0.056P)2+1.938P]−1, where P=(Max(Fo2, 0)+2Fc2)/3; cGoF=S=[Σw(Fo2–Fc2)2/(nobs–nparam)]1/2.
The unit cell parameters and extinction rules suggested Cmmm as the most appropriate space group. The starting atomic parameters derived via Direct Methods using the program Sir 97  were subsequently refined with the program SHELXL-97  (full-matrix least-squares on F2) with anisotropic displacements parameters for the gadolinium atoms. Only 4 different atomic coordinates were obtained in 4c Wyckoff positions, equivalent to those of the CeNiSi2 and TbFeSi2 structure types , . First the Gd, Fe and Si atoms were assigned to the 4c (0, y, 1/4) positions, according to the CeNiSi2 structure. Refinement of the crystal structure with the SHELXL program in anisotropic approximation of the atomic displacement parameters showed non-positive values for the Si1 atoms at y=0.7499(3). There is a significant residual electron density peak in the difference Fourier map close to the Si1 atom (4.9 e− Å−3; 0.09 Å). However, the values of the anisotropic atomic displacement Uiso for the Fe site with y=0.185(3) is increased. Refinement of the occupancy (G) for this 4c site resulted in G=0.612(6). The final reliability factor for the CeNiSi2 structure model was R1=0.049 (wR2=0.131). Exchange of Si1 with Fe atoms led to a site variant of the CeNiSi2 type and considered as the TbFeSi2-type structure. In the next step the Gd, Fe and Si atoms were refined in 4c (0 y 1/4) positions, according to the TbFeSi2-type structure. The final difference Fourier synthesis was flat and the composition obtained from the structure refinement is in good agreement with the EDX results. Exchange of the Si1 atoms by Fe atoms and refinement of the site occupation for the iron positions led to an improvement of the anisotropic displacement parameters of all atoms with good R values and a satisfactory chemical composition with respect to the EDX analysis (R1=0.041; wR2=0.11; S=1.1; Gd27.3(3)Fe19.1(3)Si53.6(3)). The atomic coordinates and displacement parameters are given in Table 2. Selected interatomic distances and bond angles are reported in Table 3. The program Diamond was used for the drawing of the crystal structure .
|Atom||Occup.||y||Ueq or Uiso||U11||U22||U33|
aWyckoff site 4c in 0 y 1/4. bU23=U13=U12=0.
CCDC 1969021 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.
2.4 Electronic structure calculations
First principles electronic band structure calculations were performed for an ordered variant of GdFe0.5Si2 within the local density approximation  using the linear muffin-tin orbital (LMTO) method , ,  encoded in the TB-LMTO-ASA program . All calculations were checked for convergence of energies, orbital moments and magnetic moments with respect to the number of k-points used in the reciprocal space integrations. Spin orbit coupling was not included and relativistic effects were treated in terms of the scalar relativistic method. Three different classes of empty spheres were used to fill the space in the structure. In our calculations for GdFe0.5Si2 the basis set consisted of Gd 5d, Fe 3s,p,d and Si 3s,p states. The Gd 4f states were treated as semicore states. To examine the bonding around the Fermi level between the Si atoms and between the Si atoms and Fe atoms, we performed crystal orbital Hamiltonian population (COHP) analysis  which partitions the band structure energy (i.e. the sum of the Kohn-Sham orbital energies) into contributions between pairs of atomic orbitals. The COHP plots are presented under the convention in which positive and negative values refer to bonding and antibonding interactions, respectively.
3 Results and discussion
The crystal structure of GdFe1−xSi2 (x=0.32) is shown in a projection on the (001) plane in Fig. 2. Typical coordination polyhedra (CP) of the various atoms are drawn in Fig. 2a. The gadolinium atoms [GdGd6Fe4Si11] present a peculiar environment in the form of a hexagonal prism with additional atoms outside the prism faces. Their coordination number (CN) is therefore 21. The gadolinium atoms have close Si neighbors with Gd–Si distances between 3.011(3) and 3.127(4) Å and one Gd–Si distance of 3.464(8) Å (Table 3). The Gd–Fe distances cover the range between 3.108(4) and 3.137(4) Å for the four Fe neighbors of the Gd atom. The orthorhombic prisms with four centered lateral faces [FeGd4Fe4Si4] with CN=12 are the CPs of the iron atoms. They have four close Si atoms with Fe–Si1 distances between 2.245(5) and 2.290(5) Å and four Fe atoms with Fe–Fe distances of 2.8294(4) Å. The silicon atoms have nine metal atom neighbors, forming a trigonal prism with three additional atoms outside the rectangular faces of the prisms: [Si1Gd4Fe4Si1] and [Si2Gd6Si3]. Si–Si distances are in the range from 2.361(3) to 2.395(8) Å.
GdFe1−xSi2 (x=0.32) crystallizes in the TbFeSi2-type structure that is built up of an intergrowth of BaAl4 and AlB2 slabs. This structure type can be considered as a site exchange variant of the CeNiSi2-type structure by interchanging the silicon and the transition metal in the BaAl4 slab (Fig. 2). Both structures types TbFeSi2 and CeNiSi2 are geometrically similar with all atoms in 4c Wyckoff positions (space group Cmcm). Earlier presented results ,  based on powder X-ray diffraction data for the RFeSi2 compounds (R=Y, La–Nd, Tb, Ho, Er, Tm, Lu) were not sufficient for the consideration of structural details. From X-ray diffraction studies on single crystals of the RFeSi2 compounds (R=Ho, Tb, Dy), the authors in reference  concluded that these phases should rather be named RFe0.5Si2 since an important iron non-stoichiometry is evidenced. The half-occupation of the 4c site by an iron atom does not allow to clearly distinguishing between the two site exchange variants. Norlidah et al.  on the basis of 57Fe Mössbauer spectroscopy and neutron diffraction data suggested that the RFexSi2 (R=Tb, Dy, Ho, Er, Lu) compounds crystallize in the non-stoichiometric CeNiSi2-type structure, although the results of the crystal structure refinement were not presented.
Several of the ternary compounds with the approximate compositions RT1−xSi2 crystallize in the CeNiSi2, NdRuSi2 and TbFeSi2 types, characterized by different stackings of elementary blocks characteristic of the AlB2 and BaAl4 crystal structures. The RT1−xSi2 structures are related to one of the well-known ThCr2Si2 or CaBe2Ge2 structure types , . As the atomic composition is different from 1:2:2, only one part of the structures can be compared. In the CeNiSi2, NdRuSi2 and TbFeSi2 structures the BaAl4 blocks display two different arrangements as a function of the relative positions (sequence) of the T and X elements (Fig. 2). While the spatial distribution within the sheets is always a XTTX elemental block in the ThCr2Si2 type, alternating XTTX and TXXT sequences occur in the CaBe2Ge2 type. This atomic distribution generates Si–Si pairs in ThCr2Si2, whereas no Ge–Ge bonding occurs in one of the sheets in CaBe2Ge2.
The XTTX elemental block is characterized by a transition metal occupying the center of the BaAl4 block, in tetrahedral X coordination, while the TXXT layer is characterized by a site inversion between the T and X elements. The XTTX elemental block is mainly encountered in the ThCr2Si2- and TbFeSi2-type structures while the TXXT layer is encountered in the CeNiSi2 and NdRuSi2-type structures (Fig. 2). The relative stability of the XTTX and TXXT sequences, is one of the most intriguing problems encountered in the crystal chemistry of these layered compounds. According to Zheng and Hoffmann , the elemental RT2X2 block is characterized by different band dispersivity of the T and X sites, the more lattice dispersive site being the one that engenders more overlaps between equivalent sites, i.e. the separation between the equivalent sites is smaller than that of other sites. As shown in Fig. 2, in the XTTX block, the T metal occupies the more dispersive site while this site is occupied by the X element in the TXXT elemental block. This leads to important consequences for the relative stability of each block. Depending on the degree of band filling, the more electronegative atom will enter or avoid the more dispersive sites. Hence, for a T metal less electronegative than the X element and for a large band filling, the XTTX block will be more stable than the TXXT elemental block since the latter will have a higher Fermi energy. The numerous compounds crystallizing in the ThCr2Si2-type structure account for the great stability of the XTTX block. The stability of the CaBe2Ge2-type structure has been investigated by electronic structure calculations by Zheng and Hoffmann . According to this study, the occurrence of compounds with the CaBe2Ge2-type structure should be related to the T–X interlayer interactions between the XTTX and TXXT elemental blocks, favoring their simultaneous presence.
For the calculation of the electronic structure of GdFexSi2 based on the LMTO method we have used an ordered and refined structural variant with the composition GdFe0.5Si2 in space group Amm2, a subgroup of Cmcm, to avoid the statistical occupation of the Fe site (Table 4). The structure contains zig-zag chains of Si(1) with Si–Si distances of 2.359 Å with terminally bonded Si(2) atoms, as shown in Fig. 3. Based on the Zintl concept formal oxidation states can be assigned resulting in a reasonable formula Gd3+(Fe2+)0.5Si(1)1−Si(2)3−. The DOS (density of states) curve indicates that GdFe0.5Si2 is a metal. The occupied Si states are distributed from –11 eV to the Fermi level, whereas the occupied Fe 3d states are located between –5 eV and 0 eV. The calculated COHP curves for the important interactions in GdFe0.5Si2 are shown in Fig. 3. There is a strong bonding interaction between the Fe and Si(2) atoms. The Fe–Si(1) interactions are very weak because of the large Fe–Si(1) distances and are therefore not shown in Fig. 4. Strong Si(1)–Si(1) and Si(2)–Si(1) interactions are found as expected from the analyses based on the Zintl concept (above) whereas the Si(2)–Si(2) interactions are negligibly small. The top valence electrons are all in bonding orbitals and any further filling with electrons, e.g. by additional Fe atoms, will lead to a significant occupation of antibonding states. As the d electron count increases across the first transition series, the electronegativity rises as well (1.55, 1.83, 1.88, 1.91 and 1.90 for Mn, Fe, Co, Ni and Cu, versus 1.9 for Si in Pauling scale). Not only the dispersivity favors the CeNiSi2 structure (less electronegative atoms occupy the less dispersive sites), but also the d electrons start to fill the antibonding states above the Fermi level indicated in Fig. 3, thus any higher d electron count further favors the CeNiSi2 structure.
aG (site occupancy)=0.5.
In summary, a new ternary silicide GdFe1−xSi2 (x=0.32) has been synthesized from the elements by arc-melting. It crystallizes in space group Cmmm and represents a TbFeSi2-type structure. The Fe position is not fully occupied and the structure refinement results in a composition GdFe0.68Si2 in agreement with a chemical analysis. The structure consists of zig-zag chains of Si(1) atoms which are terminally bound to additional Si(2) atoms. For an ordered variant of GdFe0.5Si2, the Zintl concept can be applied which results in formal oxidation states Gd3+(Fe2+)0.5Si(1)1−Si(2)3−. This assignment is confirmed by results of calculations based on the LMTO method, which also indicate that GdFe0.5Si2 is a metal. A more detailed computational analysis will be presented in a separate publication.
Dedicated to:Professor Arndt Simon on the occasion of his 80th birthday.
 O. I. Bodak, E. I. Gladyshevskii, Sov. Phys. Crystallogr. 1970, 14, 859.Search in Google Scholar
 G. Venturini, B. Malaman, M. Meot-Meyer, D. Fruchart, G. Le Caer, D. Malterre, B, Roques, Rev. Chim. Miner. 1986, 23, 162.Search in Google Scholar
 V. I. Yarovets, Yu. K. Gorelenko, Vestn. L’vovsk. Univ., Ser. Khim. 1981, 23, 20.Search in Google Scholar
 L. V. Krivulya, O. I. Bodak, Y. K. Gorelenko, Inorg. Mater. 1986, 22, 1685.Search in Google Scholar
 V. Pavlyuk, O. Bodak, A. Sobolev, Sov. Phys. Crystallogr. 1991, 36, 493.Search in Google Scholar
 O. I. Bodak, E. I. Gladyshevskii, V. I. Yarovets, V. M. Davydov, T. V. Il’chuk, Inorg. Mater.1978, 14, 366.Search in Google Scholar
 E. I. Gladyshevskii, O. I. Bodak, V. I. Yarovets, Yu. K. Gorelenko, R. V. Skolozdra, Ukr. Fiz. Zh. (Russ. Ed.).1978, 23, 77.Search in Google Scholar
 L. Akselrud, Y. Grin, WinCSD (version 4), Software Package for Crystallographic Calculations, Max-Planck-Institut für Chemische Physik fester Stoffe, Dresden (Germany) 2014. See also: L. Akselrud, Y. Grin, J. Appl. Crystallogr. 2014, 47, 803.10.1107/S1600576714001058Search in Google Scholar
 A. Altomare, M. C. Burla, M. Camalli, G. L. Cascarano, C. Giacovazzo, A. Guagliardi, A. G. G. Moliterni, G. Polidori, R. Spagna, J. Appl. Crystallogr. 1999, 32, 115.10.1107/S0021889898007717Search in Google Scholar
 G. M. Sheldrick, Acta Crystallogr.2015, C71, 3.Search in Google Scholar
 K. Brandenburg, Diamond (version 2.1c), Crystal and Molecular Structure Visualization, Crystal Impact - H. Putz & K. Brandenburg GbR, Bonn (Germany) 1999.Search in Google Scholar
 O. Jepsen, O. K. Andersen, The Stuttgart TB-LMTO-ASA programm (version 47), Max-Plank-Institut für Festkörperforschung, Stuttgart (Germany) 2000.Search in Google Scholar
©2020 Walter de Gruyter GmbH, Berlin/Boston