Equiatomic iron-based tetrelides TFeSi and TFeGe (T = Zr, Nb, Hf, Ta) – A ⁵⁷Fe Mössbauer-spectroscopic study

2.1 Synthesis

The iron-tetrelides TFetr (T=Zr, Nb, Hf, Ta; tr=Si, Ge) were synthesized directly from the elements by arc-melting. Starting materials were zirconium sponge (Johnson Matthey, 99.5%), niobium and tantalum sheets (WHS Sondermetalle, 99.5%), hafnium buttons (Smart Elements, >99.9%), iron granules (Alfa Aesar, 99.98%), silicon pieces (Merck, 99.9999%) and germanium pieces (Chempur, 99.999%) (all stated purities are metal-based). The elements were mixed in the ideal atomic ratio of T to Fe to X=1:1:1 and were arc-melted [19] under an argon pressure of 700–800 mbar using a water-cooled copper crucible. The argon (Westfalen, 99.998%) was purified over titanium sponge (T=900 K), silica gel, and molecular sieves. The ingots were turned over and re-melted several times to ensure homogeneity of the samples. Subsequently the product buttons were sealed under vacuum in silica tubes for oxidation protection and annealed at T=1273–1373 K for 240 h. Afterwards the samples were quenched in ice water. The polycrystalline, air-stable compounds show metallic lustre and could be obtained phase-pure based on the X-ray powder data.

2.2 X-ray image plate data and data collection

The polycrystalline samples were characterized by powder X-ray diffraction on a Guinier camera (Enraf-Nonius FR552 equipped with a Fuji-film image plate system, BAS-1800) using CuKα₁ radiation and α-quartz (a=491.30, c=540.46 pm) as an internal standard. The lattice parameters (Table 1) were refined from the powder data. The experimental patterns were compared to calculated ones in order to ensure correct indexing [20]. We observed good agreement with the literature data.

Crystal fragments were selected from the crushed annealed ZrFeSi, NbFeGe, HfFeGe, and TaFeGe samples and glued to quartz fibers using bees wax. Their quality for intensity data collection was first checked by Laue photographs on a Buerger camera (white Mo radiation, image plate technique, Fujifilm, BAS-1800). Complete data sets were then collected either on a Stoe IPDS-II two-circle diffractometer with graphite monochromatized MoKα radiation (λ=71.073 pm) or a STOE StadiVari diffractometer equipped with a Mo micro focus source and a Pilatus detection system. Due to a Gaussian-shaped profile of the latter X-ray source, scaling was applied along with the numerical absorption correction. All relevant crystallographic data and details of the data collections and evaluations are listed in Table 2.

2.3 EDX data

The single crystals studied on the diffractometers (as an example we show the NbFeGe single crystal in Fig. 1) were semi-quantitatively analysed by EDX using a Zeiss EVO^® MA10 scanning electron microscope in variable-pressure mode (60 Pa) with SiO₂, Fe, Zr, Nb, Ge, Hf, and Ta as internal standards. The analysis with a secondary electron detector at several points gave the experimental compositions 36±2 at.% Zr, 30±2 at.% Fe, 34±2 at.% Si (ZrFeSi crystal), 39±2 at.% Nb, 31±2 at.% Fe, 30±2 at.% Ge (NbFeGe crystal), 34±2 at.% Hf, 32±2 at.% Fe, 34±2 at.% Ge (HfFeGe crystal) and 39±2 at.% Ta, 32±2 at.% Fe, 29±2 at.% Ge (TaFeGe crystal). No impurity elements were detected.

Fig. 1:

Scanning electron microscopic picture (secondary electron detector) of the investigated single crystal of NbFeGe.

2.4 Physical property measurements

The property measurements were carried out with a Physical Property Measurement System (QuantumDesign PPMS-9). The magnetic susceptibilities of ZrFeSi, NbFeSi and HfFeGe were measured using the VSM option with an applied magnetic field of 10 kOe (1 kOe=7.96×10⁴ A m⁻¹) in the temperature range of 3–300 K. All three measurements were performed in the zero-field-cooled mode (ZFC). For NbFeSi and HfFeGe, additional measurements in field-cooled mode (FC) were carried out.

The specific electrical resistivity of NbFeSi was measured by the van der Pauw method [21] in the temperature range of 2–300 K. The previously sintered, disc shaped sample was contacted to the ac-transport puck modified by Wimbush Science and Technology with a distance of the spring probes (gold plated nickel) of 2 mm, and the applied alternate current frequency was set to 31 Hz. The maximum currents were 15 mA for the first and 20 mA for the second channel.

2.5 Mössbauer spectroscopy

For the ⁵⁷Fe Mössbauer-spectroscopic investigations of the TFeSi and TFeGe (T=Zr, Nb, Hf, Ta) samples a ⁵⁷Co/Rh source was used. The samples were placed in thin walled PMMA containers with an optimized thickness according to Long et al. [22]. The measurements were conducted in usual transmission geometry at room temperature with measurement periods between 1 and 6 days for each sample. To fit the spectra the routine WinNormos for Igor6 was used [23].

3.1 Structure refinements

Isotypism of ZrFeSi and TaFeGe with the TiNiSi type (space group Pnma), of NbFeGe with the TiFeSi type (Ima2), and of HfFeGe with the ZrNiAl-type structure (P6̅2m) was already evident from the X-ray powder data. The systematic extinctions of the data sets were compatible with these space groups. The starting atomic positions were determined using the charge-flip algorithm [24] of SuperFlip [25] and the four structures were refined on F² with the Jana2006 [26] software package using anisotropic displacement parameters for all atoms. All occupancy factors were refined in separate cycles leading to full occupation within two standard deviations. The final difference Fourier analyses revealed no significant residual electron densities. Refinement of the correct absolute structures of NbFeGe and HfFeGe (non-centrosymmetric space groups) was ensured through calculation of the Flack parameters [27], [28], [29].

The single crystal of NbFeGe showed pseudo-hexagonal symmetry as it was already observed by Jeitschko for the prototype TiFeSi [30], [31]. The body-centred orthorhombic lattice possesses the general reflection conditions h+k+l=2n; h0l: only h=2n, l=2n, which is compatible with the space group Ima2 (no. 46). The formation of trillings is observed due to the translationsgleiche symmetry reduction of index 3 (t3) from space group P6̅2m of the aristotype Fe₂P into the orthohexagonal setting [32]. The trilling formation can be described by the following matrices:

M2=(1000−12320−12−12);  M3=(1000−12−32012−12)

The trilling domain ratios were refined separately, leading to an amount of M₁:M₂≈9:1 and a negligible contribution of the third domain (M₃≈0).

All positional parameters and interatomic distances are listed in Tables 3–6.

CCDC 1877715 (ZrFeSi), 1877716 (NbFeGe), 1877718 (HfFeGe) and 1877719 (TaFeGe) contain 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.

3.2 Crystal chemistry

In the present study we have investigated eight iron-based equiatomic silicides TFeSi and germanides TFeGe with T=Zr, Nb, Hf and Ta. Although the main focus on these phases lies in the ⁵⁷Fe Mössbauer-spectroscopic study (vide infra), we also characterized the samples through powder X-ray diffraction and additionally refined four structures from single crystal diffractometer data. Our data fully confirm the original literature. In that context, it is interesting to note, that a recent theoretical investigation [33] claimed the cubic half-Heusler phase structure for ZrFeSi. Our single crystal data, however, undoubtedly prove that ZrFeSi has the orthorhombic TiNiSi-type structure. The total energy calculations thus do not reproduce the ground state under ambient conditions correctly. In addition, the calculated cell volume of 0.0498 nm³ per formula unit is significantly higher (ca. 10%) than the value of 0.0454 nm³ determined in the present work. Keeping the small volume changes during phase transitions for such intermetallics in mind (typical examples are ErAgSn [34] or ScRuSi [35]), the theoretical results are highly questionable.

In the following discussion, we only briefly focus on the crystal chemical details, since these tetrelides crystallize in well-known prototypes [36]. Furthermore, we focus on the respective iron coordination, which is relevant for the discussion of the ⁵⁷Fe Mössbauer-spectroscopic data (vide infra). ZrFeSi, NbFeSi, HfFeSi, TaFeSi, ZrFeGe, and TaFeGe crystallize with the TiNiSi-type structure [37], space group Pnma. As an example, we present the iron coordination of ZrFeSi in Fig. 2. The structure contains only one crystallographic iron site, and each iron atom shows distorted tetrahedral silicon coordination with Fe–Si distances ranging from 236 to 249 pm. At least the shorter ones are close to the sum of the covalent radii for Fe+Si of 233 pm [38]. Substantially distorted trigonal prisms of zirconium atoms surround the FeSi₄ tetrahedra.

Fig. 2:

Coordination of the iron atoms in the structures of NbFeGe, ZrFeSi and HfFeGe. The Wyckoff positions, the site symmetries, and the crystallographically independent sites are indicated. Zirconium (hafnium, tantalum), iron and silicon (germanium) atoms are drawn as black, blue and red circles, respectively.

HfFeGe adopts the ZrNiAl type [39], [40], [41], space group P6̅2m. This structure also contains only one iron site; again with tetrahedral germanium coordination. The Fe–Ge distances of 245 and 254 pm are slightly longer than the sum of the covalent radii for Fe+Ge of 238 pm [38]. This bonding situation is similar to that of ZrFeSi discussed above. In contrast to the silicide, we observe a symmetrical trigonal Hf₆ prism around the FeGe₄ tetrahedron.

The corresponding niobium compound NbFeGe is structurally closely related to HfFeGe, however, we observe a small structural distortion. If the sizes of the three elements forming a ZrNiAl related compound do not exactly match, puckering of the atoms (and this is not necessarily a function of the electron count) leads to superstructure formation [42], [43]. However, of the more than 1000 ZrNiAl related phases [11] only 11 were ascribed to the HfRhSn-type superstructure, space group P6̅2c [11], [42] and 38 to the TiFeSi-type superstructure, space group Ima2 [11], [31]. NbFeGe adopts the latter ordering variant. So far, only the prototype itself and the isotypic stannide ScAgSn [44] were studied on the basis of single crystal diffraction data. The group-subgroup relation has been discussed for ScAgSn. The first translationengleiche symmetry reduction induces the formation of trillings. In the TiFeSi-type superstructure the iron site splits into two crystallographically independent sites 8c and 4a with individual distortions. This is readily evident from the different Fe–Ge distances within the FeGe₄ tetrahedra with slightly shorter ones for Fe1 (Table 6).

The three different structures do not only have the tetrahedral tetrel coordination of the iron atoms in common. We also observe weak Fe–Fe contacts for all four compounds studied. Each iron atom has two closer iron neighbors at Fe–Fe distances ranging from 275 to 298 pm, distinctly longer than in bcc iron, where each iron atoms has eight neighbors at 248 pm [45].

3.3 Magnetic properties of ZrFeSi, NbFeSi and HfFeGe

The temperature dependence of the magnetic susceptibility of ZrFeSi, NbFeSi and HfFeGe is presented in Fig. 3. The three compounds show almost temperature-independent Pauli-paramagnetic behavior due to substantial contributions from the conduction electrons, over-compensating the intrinsic diamagnetism. The measured molar susceptibilities at T=300 K are 4.15(2)×10⁻⁴ (ZrFeSi), 12.0(1)×10⁻⁴ (NbFeSi) and 8.63(2)×10⁻⁴ emu mol⁻¹ (HfFeGe). The slight increases of χ below 50–100 K are due to small amounts of paramagnetic impurities (Curie tails). Since the FC and ZFC measurement curves of NbFeSi and HfFeGe are superimposed, we can rule out ferromagnetic interactions caused by iron particles at the grain boundaries.

Fig. 3:

Temperature dependences of the molar magnetic susceptibility of ZrFeSi (black), NbFeSi (red) and HfFeGe (blue) at an external magnetic field strength of 10 kOe in the temperature range of 3–300 K.

Again we compare our experimental data for ZrFeSi with electronic-structure calculations [33]. The band structure analyses revealed high spin polarization for ZrFeSi in a half-Heusler-type structure. This finding also contradicts the Pauli paramagnetism correctly determined in the present work.

3.4 Electrical properties of NbFeSi

The reduced resistivity R(T)/R(300 K) of NbFeSi measured in the range 2–300 K is presented in Fig. 4. The resistivity decreases with decreasing temperature. Down to ca. 50 K the decrease is almost linear, while we observe proportionality to ~ T⁵ in the 2–50 K regime, in agreement with Bloch’s theory (increasing electron phonon coupling with increasing temperature). At T=2 K the residual-resistivity ratio (RRR, defined as R(300 K)/R(T)) is 12.2, classifying NbFeSi as a good metal.

Fig. 4:

Reduced electrical resistivity R(T)/R(300 K) of NbFeSi measured in the temperature range 2–300 K.

3.5 ⁵⁷Fe Mössbauer spectroscopy

Figure 5 shows the ⁵⁷Fe Mössbauer spectra of the equiatomic iron-tetrelides TFeX (T=Zr, Nb, Hf, Ta; X=Si, Ge) at room temperature along with transmission integral fits. The underlying fitting parameters are listed in Table 7. Although the eight tetrelides crystallize with three different structure types, the tetrahedral tetrel coordination of the iron atoms is their common structural motif. Thus, we have a small model system to systematically study small changes in the iron coordination by ⁵⁷Fe Mössbauer spectroscopy.

Fig. 5:

⁵⁷Fe Mössbauer spectra of the tetrelides TFeSi and TFeGe (T=Zr, Nb, Hf, Ta) at room temperature.

In the following we discuss the isomer shift values which are a measure for the electron density at the iron nuclei, and the quadrupole splitting (ΔE_Q) values which reflect the degree of asymmetry of the iron coordination. The isomer shifts vary from ca. 0 mm s⁻¹ for most TiNiSi-type compounds to ca. 0.2 mm s⁻¹ for the ZrNiAl type germanides, indicating higher electron density at the iron nuclei in the latter [46], [47]. However, the isomer shifts show no direct correlation with the electron count, most likely due to small differences induced by the different structure types.

A readily visible difference concerns the quadrupole splitting parameters which cover the broad range from 0.142 to 0.693 mm s⁻¹ (Table 7). We can relate these differences with the Fetr₄ tetrahedra and first focus on the structures of ZrFeSi, HfFeGe and TaFeGe refined in the present work. The Fe–Ge distances in TaFeGe (237 and 242 pm) and HfFeGe (245 and 254 pm) show small ranges and this is directly expressed in quadrupole splitting parameters of 0.204 mm s⁻¹ for HfFeGe and 0.306 mm s⁻¹ for TaFeGe. The asymmetry of the iron coordination is caused by the differences in the Fe–Ge distances, the Ge–Fe–Ge bond angles and the hafnium, respectively tantalum coordination around the tetrahedra. The latter is much more asymmetric in TiNiSi-type TaFeGe (compare the distorted trigonal prism of ZrFeSi shown in Fig. 2) than in HfFeGe which has a regular polyhedron, explaining the higher ΔE_Q value for TaFeGe.

As a second example, we compare the isotypic structures of TaFeGe and ZrFeSi. The iron atoms in the silicide have 3+1 tetrahedral silicon coordination with three closer Fe–Si distances of 2×236 and 1×240 and a fourth one at 249 pm. TaFeGe shows a much smaller range with 2×237, 1×241 and 1×241 pm. This leads to a significantly higher quadrupole splitting parameter of 0.648 mm s⁻¹ for ZrFeSi. An even higher ΔE_Q value of 0.693 mm s⁻¹ has been refined for HfFeSi and we can expect a similar structural distortion for the FeSi₄ tetrahedra in this silicide.

Finally, we turn to the NbFeGe superstructure. The symmetry reduction leads to a 2:1 splitting of the subcell iron site to Fe1 on 8c and Fe2 on 4a. The NbFeGe spectrum shows a slightly broader signal because of the superposition of two separate sub-signals. The spectrum could be reproduced by two signals in an intensity ratio of 2 to 1 of which the blue one (for Fe1 on 8c) shows a slightly higher quadrupole splitting. This is consistent with the course of the interatomic distances, i.e. a slightly more asymmetric 1:1:1:1 coordination for Fe1 and a 2:2 coordination for Fe2 (Table 6).

Summing up, we observed well-resolved ⁵⁷Fe Mössbauer spectra for the series of TFeX (T=Zr, Nb, Hf, Ta; X=Si, Ge) tetrelides. The small structural distortions within and around the different Fetr₄ tetrahedra are directly expressed in the ⁵⁷Fe spectra. Thus, ⁵⁷Fe Mössbauer spectroscopy is a suitable complementary tool for structure elucidation of intermetallic iron compounds.