High-pressure synthesis of SmGe₃

2.1 Synthesis

SmGe₃ was synthesized under high-pressure high-temperature conditions. All sample handling, except for high-pressure synthesis itself, was performed in argon-filled glove boxes (MBraun, H₂O and O₂ < 0.1 ppm). The precursor mixture was prepared by arc melting of samarium (Lamprecht, 99.9%) and germanium (Chempur, 99.9999+%) in the ratio 1:3 plus 6% excess of samarium for the compensation of evaporation losses during heating. The material was ground and filled into BN crucibles before being transferred into MgO octahedra with an edge length of 18 mm. High-pressure high-temperature syntheses were conducted in a Walker-type module [25] for 30 min to 5 h at pressures between 9(1) to 9.5(10) GPa and temperatures from 1073(107) and 1273(127) K before quenching under load. The calibration of pressure and temperature has been realized prior to the experiments by the observation of resistance changes of bismuth [26] and thermocouple-calibrated runs, respectively.

2.2 Sample characterization

For metallographic analysis, samples were prepared by polishing with diamond powder disks (grain size 6, 3 and 0.25 μm) after embedding in paraffin. The investigation was realized with a Philips XL 30 scanning electron microscope (SEM) (LaB₆ cathode), comprising an EDAX Si(Li) detector for energy-dispersive X-ray spectroscopy (EDXS).

Differential scanning calorimetry (DSC) experiments were performed in a Netzsch DSC 404 C device (Netzsch-Gerätebau GmbH, Selb, Germany) operated with heating and cooling rates of 10 K/min under argon atmosphere using corundum crucibles.

Phase designation was conducted by X-ray powder diffraction experiments with a Huber Image Plate Guinier Camera G670 (Huber Diffraktionstechnik GmbH & Co. KG, Rimsting, Germany), using CuKα₁ radiation (λ = 1.54056 Å). X-ray diffraction experiments for structure refinement were realized with synchrotron radiation (λ = 0.20709 Å) at DESY Group PETRA III using beamline P02.1, and with a Stoe Stadi MP in Bragg-Brentano geometry. The diffractometer was equipped with a DECTRIS MYTHEN2 1K silicon strip detector and operated with Cu-Kα₁ radiation (λ = 1.54056 Å, curved germanium (111) Johann-type Monochromator). The sample with cylindrical shape was mounted on a zero background sample holder with one of the cross sectional area at its end oriented to the incident X-ray beam. For better data point statistics, the final powder pattern results from the sum of three individual intensity data sets, collected in the angular range 5.00° ≤ 2θ ≤ 120° (scan step = 0.06°, time pro step 40 s, t_total ≈ 24 h).

All crystallographic calculations including determination of diffraction peak positions as well as lattice parameter and structure refinements on basis of full diffraction profiles (Rietveld technique) were performed with the WinCSD program package [27].

Thin samples for the TEM study were prepared by the focused-ion-beam (FIB) lift-out technique. Thin cross-sections of micro-crystalline grains were extracted from a broken bulk fragment. Defined crystallographic oriented cross-sections were prepared perpendicular to the staking-faults visible at the fracture surface. The FIB lift-out technique was performed on a FEI Quanta 200 3D ion/electron dual beam device (FEI Company, Eindhoven, the Netherlands) equipped with an Omniprobe micro-manipulator (tungsten needle), and can be used both as a SEM and a scanning ion microscope (SIM). First, protecting Pt layers (24 × 2 µm thickness, 2 µm high) were deposited on selected parts (parallel and perpendicular to the c axis of microcrystalline arrays) using an acceleration voltage of 30 kV and a current of 0.1 nA. Each cross section (2 μm thickness) was prepared by applying a Ga-ion beam using an acceleration voltage of 30 kV and a current of 1–0.5 nA. The manufactured cut was transferred onto a copper Omniprobe TEM holder using the in-situ lift-out technique [3]. Finally, the cross section was thinned in several discrete steps down to a thickness of about 40 nm by applying an acceleration voltage of 30 kV with currents of 0.5–0.01 nA of the Ga-ion beam.

Magnetic susceptibility was measured using a polycrystalline sample of cylindrical shape (3.0 × 2.5 × 3.4 mm) on an SQUID magnetometer (MPMS XL‐7, Quantum Design) between 1.8 and 300 K in external fields of 0.01 to 3.5 T. Electrical resistivity measurements were conducted in a temperature range from 1.8 to 300 K by using the four-point probes method with a Keithley DC current source and a Hewlett Packard nanovoltmeter inside a helium flow cryostat at zero magnetic field. The contacting of the sample with Cu wire was done inside the glove box with Ag paint.

3.1 Composition and properties

The new samarium germanide is synthesized by high-pressure high-temperature treatment of pre-reacted Sm_25.4Ge_74.6 mixtures. The average chemical composition of the product as determined by energy dispersive X-ray spectroscopy amounts to Sm_25.5(5)Ge_74.5(5) or SmGe_2.92(8).

Differential scanning calorimetry measurements (Figure 1) of SmGe₃ reveal a decomposition into SmGe₂ [28], Sm₂Ge₅ [29] and a hitherto unknown phase at 470(5) K. The feature at 737(5) K is attributed to a reaction of the decomposition products into SmGe₂ [28] and Ge [30]. In full agreement with the ambient-pressure phase diagram [31], effects at 1030(5) K and 1103(5) K correspond to the peritectoid decomposition of SmGe₂ into Sm₂Ge₃ and Ge as well as to the melting of the resulting eutectic, respectively.

Figure 1:

Differential scanning calorimetry (DSC) curve of SmGe₃ taken on heating (red curve) and cooling (blue curve) in the temperature range from 300 to 1175 K with a heating rate of 10 K min⁻¹ at ambient pressure under argon atmosphere.

The magnetic susceptibility χ measured in an external field of μ₀H = 3.5 T between 1.8 and 300 K (Figure 2) indicates van Vleck-type paramagnetic behavior, denoting the influence of the external field on the wave function and the transition towards excited states. Under consideration of the slope of the experimental data, the typical minimum of χ(T) for Sm³⁺ compounds is expected to occur around 400 K. The electrical resistivity ρ at zero-field between 1.8 and 300 K (Figure 2, inset) denotes metallic behavior with a room temperature value ρ(300 K) of 122 µΩcm and an inflection, which is attributed to the reduced scattering of charge carriers in the magnetically ordered phase [32]. The ordered state is antiferromagnetic as indicated by the cusp at 23 K in χ(T).

Figure 2:

Magnetic susceptibility χ of SmGe₃ for μ₀H = 3.5 T at temperatures between 1.8 and 300 K. Inset: Electrical resistivity of SmGe₃ at zero-field in the same temperature range.

3.2 Substructure

X-ray powder diffraction patterns of SmGe₃ evidence that the strongest reflections indicate a Cu₃Au-type structure motif [33]. A similar atomic arrangement is also reported for analog phases MGe_3−x (x ≈ 0.15: M = Tb, Dy, Yb [34], [35]; x = 0: M = Ce [14], Np [36], Pu [37] and U [38], as well as for SmSn₃ [39]), the corresponding tin compound of samarium. The crystal structure represents an ordered variety of an fcc lattice, with germanium atoms occupying the centers of cube faces and samarium being positioned on the vertices.

The refinement of a Cu₃Au-type model using full diffraction profiles (Figure 3) results in a₀ = 4.337(3) Å with R(P) = 0.043 and wR(P) = 0.063. As some other isostructural phases exhibit germanium deficiencies, partial occupation of the Ge site has been tested. The refinement proceeds without improvement of the residuals so that the models for phases SmGe₃ and SmGe_2.84(2) yield R(P) = 0.0429 and wR(P) = 0.0629 in the substructure.

Figure 3:

Synchrotron powder XRD pattern of SmGe_3−x (see main text) and the result of refining a Cu₃Au-type substructure using full diffraction profiles (Rietveld method).

3.3 Superstructure

Closer inspection of the substructure refinement reveals significant extra reflections not being accounted for by the Cu₃Au-aristotype, e.g., that at 2.36°. The finding points at a larger unit cell for SmGe₃ and motivated additional investigations of the crystal structure. For this purpose, annealed samples (55 h at 823 K and 9.5 GPa) are selected and cleaved in order to avoid peak broadening because of grinding. Nevertheless, transmission electron microscopy investigations of a selected lamella prepared by the focused ion-beam method still reveal the presence of extended structural defects in the microstructure (Figure 4a).

Figure 4:

a) TEM image of a FIB SmGe₃ lamella oriented along [213] direction. The inserted [213]* Selected area (electron) diffraction (SAED) pattern is taken from an area free of {111} stacking-faults, therefore, the diffuse lines along the [111]* direction are absent. In the TEM image, the [11-1] direction is indicated by the red arrow. Dark bands are inclined {111} stacking faults; SAED diffraction images for SmGe₃ phase (observed in almost all the FIB lamellar area) along the zone directions, b) [110]*, c) [112]* and d) [102]*. The observed reflection conditions are in agreement with the reflection conditions for a face-centered lattice. The diffuse lines in b) and c) originate from {111} stacking-faults/twin-boundaries.

SAED (Figure 4b–d) and X-ray powder diffraction patterns consistently evidence a 2a₀ × 2a₀ × 2a₀ superstructure (a₀ unit cell of the primitive cubic phase). Systematic absences are compatible with a face-centered lattice. As the synchrotron X-ray diffraction experiment evidences significant broadening of the diffraction profiles upon grinding of the material, subsequent X-ray measurements are performed with as-grown ingots at the cost of reduced powder average. Thus, diffraction data of several samples had to be collected in order to check for reproducibility of the intensity information. The best result has been achieved for a sample having been manufactured at 9.5 GPa by heating the starting mixture to 1273 K for 30 min before annealing at 823 K for 5 h to increase the size of the crystal domains. The corresponding diffraction patterns evidence a number of weak reflections, which are absent in the non-annealed samples. In order to test if the extra lines have to be attributed to (potentially incommensurate) modulations of the superstructure, metallographic investigations have been performed. The measurements reveal the presence of a small amount of a side product with composition Sm:Ge ≈ 1:2. As the diffraction peak positions of the previously reported compounds with similar composition do not match the extra lines, a reference sample was synthesized at the same conditions as the 1:3 phase. The X-ray powder diffraction diagram of this component is compatible with a Pu₃Pd₅-type [40] crystal structure and fits the extra lines in the pattern of SmGe₃. With these pieces of information at hand, a model for the superstructure of SmGe₃ was developed in space group Fm3¯m and refined (Tables 1 and 2 and Figure 5). Decrease to tetragonal symmetry (sg I4/mmm, a_t = √2 a₀, c_t = 2 a₀) does not result in improvements of the residuals of the least squares refinements. Further details on an ordered variety with presumably monoclinic symmetry and on the Pu₃Pd₅-type phase will be reported elsewhere.

Figure 5:

X-ray powder diffraction diagram of SmGe₃ measured in reflection alignment. Blue indices refer to the Cu₃Au-type substructure; green ones to the 2 × 2 × 2 superstructure. The tick marks below the experimental pattern and the difference curve indicate line positions for the main (black) and the side phase (ocean blue).

The atomic arrangement of the 2a₀ × 2a₀ × 2a₀ superstructure represents a new variety of the Cu₃Au-type. The decrease of symmetry with respect to the lt-Cu₃Au type [33] adds a degree of freedom to the positions of the germanium atoms. While germanium is coordinated by eight germanium and four metal atoms at the same distance in the undistorted lt-Cu₃Au arrangement (corresponding to 12 distances of a₀/√2 = 3.067(2) Å for the substructure), the distances amount to d₁(Ge–Ge) = 2.903(2) Å and d₂(Ge–Ge) = 3.229(2) Å, while the contacts d(Sm–Ge) = 3.0682(1) Å remain essentially unchanged in the superstructure of SmGe₃ (Figure 6).

Figure 6:

Crystal structure of SmGe₃. (left) Segment visualizing the distortion of the germanium substructure; (right) coordination sphere of the germanium atom.

The symmetry relation between the sub- and the superstructure is concisely described by a group subgroup relationship [41], [42] evidencing a klassengleiche transition of order 2. The relationship considering also some other fcc varieties is summarized in form of a small family tree (Figure 7) and the atomic arrangements are shown (Figure 8).

Figure 7:

Group-subgroup schemes for the structures of ht- and lt-Cu₃Au [43], [33], CuPt₇ [44], [45], SrPb₃ [46] and SmGe₃. Indices for klassengleiche (k) and translationengleiche (t) symmetry reductions, unit cell transformations, and atomic positions are given.

Figure 8:

Segments of the crystal structures of (left) lt-Cu₃Au [33] and (right) the 2 × 2 × 2 superstructure of SmGe₃. The unit cells are indicated by black lines. The atomic arrangement of SrPb₃ [46] corresponds to that of lt-Cu₃Au with a subtle tetragonal distortion (c/a = 1.014).

Within the series of rare earth metal trigermanides MGe₃ (M = La, Ce, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22] and their variants MGe_3−x (M = Tb, Dy, Yb) [34], [35] and MGe_3+x (M = Nd, Pr) [21], different structural motifs are observed. The overview (Figure 9) illustrates that the selected parameters do not allow for a clear separation, but a general tendency comes to light. The extended stability field of the DyGe₃ type includes the heavier rare-earth metal trigermanides (M = Tb, Dy, Ho, Er; Tm and Lu, but except Yb). The compounds of the lighter rare-earth metals among these form at ambient pressure, only the Tm and Lu compound require high-pressure synthesis. Light rare-earth metals (M = Ce, Tb, Dy; but also Yb) form dense-packed lt-Cu₃Au-type arrangements at elevated pressures.

Figure 9:

Average interatomic distances d(Ge–Ge) of selected compounds MGe₃ (M = La; rare-earth metal except Pm) [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [35]. Only bond distances resulting from crystal structure refinements (except lt-Cu₃Au) are considered. Filled symbols denote compounds synthesized by high-pressure methods, empty ones phases synthesized at ambient pressure. The grey field indicates distances d(Ge–Ge) of compounds being assigned to the lt-Cu₃Au type. References to the crystal structures are given in form of structure types.

The interatomic distances d(Ge–Ge) of all structure types except Cu₃Au fall into the range from 2.4 to roughly 3 Å (Figure 9). Within the series of isotypic DyGe₃-type compounds, the distances d(Ge–Ge) remain more or less constant (distances d(M–Ge) decrease with increasing atomic number in accordance with the lanthanide contraction, not shown). Compounds, which are reported to adopt the lt-Cu₃Au-type structure, exhibit unusually long interatomic distances d(Ge–Ge). This abnormality is attenuated by the symmetry breaking in the new SmGe₃-type arrangement. The distortion induces a subdivision of the Ge–Ge distances into two groups. The shorter contacts, representing half of the distances d(Ge–Ge), fall now into the upper part of the range observed for DyGe₃-type compounds and phases REGe_3+x (RE = Pr, Nd). Whether the underlying reason for the distortion is the formation of Ge–Ge bonds or the stereochemical activity of lone pairs located at the Ge⁻ species (assuming the electron balance Sm³⁺[Ge⁻]₃) will be the topic of future investigations by quantum chemical methods.