Intermetallic phases with Ho₄Ir₁₃Ge₉-type structure

1 Introduction

The rare earth (RE) and electron-rich transition (T) metals form a large variety of metal-rich phosphides and silicides with a metal:metalloid ratio of close or exactly to 2:1. ^{1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11} The common structural motif of the many different structure types is the trigonal prismatic coordination of the phosphorus and silicon atoms. Due to the high metal content, these structures contain exclusively isolated phosphorus and silicon atoms, i. e., the structures exhibit no P–P or Si–Si bonding. The trigonal prisms are formed by the RE and T atoms, and they are capped on all rectangular faces, leading to coordination number 9 for the phosphorus and silicon atoms (so-called tri-capped trigonal prisms). The trigonal prisms show condensation via common edges or rectangular faces, leading to characteristic building units. Although this structural description by condensation of trigonal prisms is a purely geometrical one, it is extremely useful to distinguish the individual structure types.

A structure type that belongs to the family of rare earth-rich compounds is Ho₄Ir₁₃Ge₉, ¹² with the representatives (Table 1) Ce₄Rh₁₃Ge₉, ¹³ RE ₄Ir₁₃Si₉ (RE = Y, Sm, Gd–Lu) ¹⁴ and RE ₄Ir₁₃Ge₉ (RE = La–Nd, Sm). ^{15 , 16} Interestingly, also the uranium tetrelides U₄Rh₁₃Si₉, ¹⁷ U₄Ir₁₃Si₉ and U₄Ir₁₃Ge₉ ¹⁴ have been synthesized. The complex crystal structures with three crystallographically independent rare earth/uranium sites are associated with interesting magnetic properties. Gd₄Ir₁₃Si₉ (T _N = 4.5 K) and Tb₄Ir₁₃Si₉ (T _N = 4.3 K) show stable antiferromagnetic ground states and pronounced metamagnetic transitions in their 2 K magnetization isotherms. Susceptibility and specific heat measurements of U₄Ir₁₃Si₉ (T _m1 = 18 and T _m2 = 6.4 K) and U₄Ir₁₃Ge₉ (T _m1 = 25 and T _m2 = 7 K) ¹⁴ showed two successive magnetic phase transitions, and their gamma values classify them as strongly correlated electron systems. U₄Rh₁₃Si₉ is a 30 K antiferromagnet. ¹⁷

In continuation of our systematic phase analytical studies on rhodium- and iridium-rich rare earth tetrelides ^{18 , 19 , 20 , 21 , 22 , 23} we obtained a series of new Ho₄Ir₁₃Ge₉-type phases, completing the RE ₄Rh₁₃Si₉, RE ₄Rh₁₃Ge₉ and RE ₄Ir₁₃Ge₉ series. Bismuth and lead flux growth experiments in the ternary RE-T-P and RE-T-As systems ²⁴ afforded the first phosphides and the arsenide Eu₄Ir₁₃As₉ (Table 2) with Ho₄Ir₁₃Ge₉-type structure, nicely underpinning the close crystal-chemical relationship between the silicides and phosphides. The synthesis conditions and the structural chemistry of these phases are reported herein.

2 Experimental

2.2 X-ray diffraction

The polycrystalline Ho₄Ir₁₃Ge₉-type tetrelides were characterized through Guinier powder patterns. The Enraf-Nonius FR552 Guinier camera was operated with CuKα ₁ radiation and an image plate detection system (Fujifilm, BAS-1800). α-Quartz (a = 491.30 and c = 540.46 pm) was used as an internal standard. The orthorhombic lattice parameters (Table 1) were obtained from least-squares fits to the experimental 2θ data. The correct indexing of the reflections was ensured through parallel intensity calculations (program Lazy Pulverix ³¹ ). The experimental and simulated powder patterns of Tb₄Rh₁₃Ge₉ are presented as an example in Figure 1.

Figure 1:

Calculated (top) and experimental (bottom) Guinier powder patterns (CuKα ₁ radiation) of the Tb₄Rh₁₃Ge₉ sample.

Small single crystals were selected under an optical microscope from the Gd₄Ir₁₃Ge₉, Sm₄Rh₁₃P₉, Sm₄Ir₁₃P₉, Gd₄Ir₁₃P₉, Yb₄Ir₁₃P₉ and Eu₄Ir₁₃As₉ samples. The crystals were fixed to thin glass fibers using beeswax and their quality was first tested by Laue photographs on a Buerger camera (white molybdenum radiation, image plate technique, Fujifilm, BAS-1800). Complete data sets were collected at room temperature on a STOE IPDS-II diffractometer (graphite-monochromatized MoKα radiation; oscillation mode). Numerical absorption corrections were applied to the data sets. The pnictide data sets showed severe trilling formation and their quality was not sufficient to perform reliable structure refinements. Therefore, only their lattice parameters are listed in Table 2. Details about the data collection and the structure refinement of Gd₄Ir₁₃Ge₉ are listed in Table 3.

Table 3:

Single crystal data and refinement parameters of Gd₄Ir₁₃Ge₉ at T = 300 K.

Formula	Gd4Ir13Ge9
Molar mass/g mol−1	3,781.2
Cell parameters
a/pm	397.76(2)
b/pm	1,120.97(6)
c/pm	1,935.52(10)
Cell volume/nm3	V = 0.8630
Crystal system	Orthorhombic
Space group; Z	Pmmn; 2
Pearson code	oP52
Calc. density/g cm−3	14.55
Crystal size/µm3	20 × 20 × 180
Diffractometer	STOE IPDS-II
Radiation; wave length/pm	MoKα; 71.073
Transm. ratio (min; max)	0.066; 0.396
Abs. coeff./mm−1	130.2
Detector dist./mm	80
Irradiation time/min	4
ω range; increment/deg	0–180; 1
Integr. param. (A; B; EMS)	12.0; −6.0; 0.030
F(000)/e	3,090
θ range/deg	2–32
hkl range	±5; ±16; ±28
No. refl.	15,555
Independent refl.; R int	2,537; 0.0626
Refl. with I ≥ 3 σ(I); R σ	1,569; 0.0432
Data; ref. parameters	2,537; 90
Goodness-of-fit	1.27
R1; wR2 (I ≥ 3 σ(I))	0.0287; 0.0619
R1; wR2 (all data)	0.0621; 0.0683
Domain ratio/%	90.9(5):7.4(3):1.7(4)
Extinct. coeff.	172(5)
Largest diff. peak; hole/e Å−3	5.16; −6.25

3 Structure refinement

The isotypy of Gd₄Ir₁₃Ge₉ with the orthorhombic Ho₄Ir₁₃Ge₉ type ¹² (space group Pmmn) was already evident from the Guinier powder pattern. The standardized atomic parameters of Ho₄Ir₁₃Ge₉ ¹² listed in the Pearson data base ³⁴ were taken as starting values and the structure was refined on F ² with the Jana2020 software package, ^{35 , 36} with anisotropic displacement parameters for all atoms. The data set showed trilling formation. The final refinement was conducted with the twin matrices M1 = (1 0 0, 0 1/2 −3/2, 0 1/2 1/2) and M2 = (1 0 0, 0 1/2 −3/2, 0 –1/2 −1/2) and smoothly converged to the residuals and domain ratios listed in Table 3. The final difference Fourier synthesis was contourless. Further details on the refinement, the positional and the displacement parameters and the interatomic distances are listed in Tables 3–5.

CCDC 2425314 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.

4 Crystal chemistry

Detailed phase analytical studies in the ternary systems RE-(Rh,Ir)-(Si,Ge) led to 16 new tetrelides with orthorhombic Ho₄Ir₁₃Ge₉-type ¹² structure (space group Pmmn). Parallel work in the respective pnictide systems furthermore revealed the phosphides Sm₄Rh₁₃P₉, Sm₄Ir₁₃P₉, Gd₄Ir₁₃P₉ and Yb₄Ir₁₃P₉ and the arsenide Eu₄Ir₁₃As₉. All these phases have the Pearson symbol oP52 and the Wyckoff sequence e ⁹ b ³ a ⁵.

The cell volumes of the RE ₄(Rh,Ir)₁₃(Si,Ge)₉ tetrelides reported herein and of those known from literature (Table 1) are plotted in Figure 2 as a function of the sequence of the rare earth elements. Within the four series, the cell volumes decrease with increasing atomic number as expected from the lanthanide contraction. Inspection of the literature data shows that the cell volume reported for La₄Ir₁₃Ge₉ ¹⁶ is doubtful. The reported values of the lattice parameters are even smaller than those reported for Ce₄Ir₁₃Ge₉ and Pr₄Ir₁₃Ge₉. We have repeated the synthesis of a sample with the starting composition 4La:13Ir:9Ge by arc-melting and subsequent annealing at T = 1,170 K for 240 h. The arc-melted sample was mainly composed of LaIr₃Ge₂ ¹⁶ and a phase with a yet unknown composition. LaIr₃Ge₂ disappeared after annealing; however, we got no hint for the expected phase.

Figure 2:

Plot of the cell volumes of the tetrelide series RE ₄ T ₁₃ X ₉ (T = Rh, Ir and X = Si, Ge) with Ho₄Ir₁₃Ge₉-type structure. The underlying lattice parameters are summarized in Table 1.

The structure of Gd₄Ir₁₃Ge₉ was refined from single crystal X-ray diffractometer data and is discussed in the following. Although the Gd₄Ir₁₃Ge₉ structure contains 17 crystallographically independent atomic sites and seems complex at first sight, it can easily be described by condensation of germanium centered trigonal prisms Ge@Gd₄Ir₂ and Ge@Gd₂Ir₄ (Figure 3). These prisms are condensed via common edges within the bc plane, forming a chain of condensed shamrocks ³⁷ which extends in b direction. This building unit is inverted (due to many inversion centers of this centrosymmetric space group, e. g., 0, 0, 1/2 or 0, 1/2, 1/2), and, consequently, we obtain alternating strands of identical composition that are shifted with respect to each other by half the translation period a, emphasized by thin and thick lines in Figure 3.

Figure 3:

Projection of the Gd₄Ir₁₃Ge₉ and Sr₄In₁₃Au₉ structures along the short unit cell axes. Gadolinium (strontium), iridium (gold) and germanium (indium) atoms are drawn as medium grey, blue and magenta circles, respectively. All atoms lie on different mirror planes (x = 1/4 and 3/4 for Gd₄Ir₁₃Ge₉ and z = 0 and 1/2 for Sr₄In₁₃Au₉), accentuated by thin and thick lines. The trigonal prisms around the germanium (gold) atoms are emphasized. The empty Ir₆ (In₆) and filled Ir@Gd₆ (In@Sr₆) prisms are shaded.

The condensation of the Ge@Gd₄Ir₂ and Ge@Gd₂Ir₄ prisms leads to the formation of Ir8₄Ir3₂ and Gd2₄Gd3₂ trigonal prisms at the connection points of the shamrocks (shaded in Figure 3). The iridium-based trigonal prisms are too small to be occupied and thus remain empty. Those formed solely by gadolinium atoms are much larger and are filled with the Ir4 atoms. The Ir4 filled Gd2₄Gd3₂ trigonal prisms are the structural unit to be noted. These trigonal prisms seem to be too large for the Ir4 atoms and we observe a slightly enhanced U ₁₁ displacement towards the triangular faces of prisms. This peculiar behavior is most likely a geometrical constraint induced by the prism condensation and a kind of compromise for the Gd₄Ir₁₃Ge₉ structure. Many other metal-rich structures with related shamrock-like condensation patterns of trigonal prisms show similar displacements of the transition metal atoms with RE ₆ trigonal prisms. Typical examples are isotypic Er₄Ir₁₃Si₉ ¹⁴ or the phosphides Ce₁₃Ir_34.4P₂₄ ³⁸ and Y₇Ir₁₇P₁₂. ³⁹

The description of the Gd₄Ir₁₃Ge₉ structure with a condensation pattern of trigonal prisms is a purely geometrical one, however, this motif of prism condensation helps to distinguish the many related structure types of metal-rich tetrelides and pnictides. Compilations of such structure types based on the prismatic motifs are given in several overviews. ^{2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 40}

The shortest interatomic distances in the Gd₄Ir₁₃Ge₉ structure are found between the iridium and germanium atoms. The Ir–Ge distances range from 240 to 260 pm, comparable to the sum of the covalent radii ⁴¹ of 248 pm for Ir + Ge. Similar distances have been observed for CeIrGe ⁴² (256–275 pm Ir–Ge) and Ce₉Ir₃₇Ge₂₅ ⁴³ (239–262 pm Ir–Ge). Each iridium atom in the Gd₄Ir₁₃Ge₉ structure has between three and five germanium neighbors, and both atom types build up a three-dimensional [Ir₁₃Ge₉] ^δ− polyanionic network (Figure 4). The three crystallographically independent gadolinium atoms fill slightly distorted hexagonal prisms within the [Ir₁₃Ge₉] ^δ− network. The rectangular faces of the hexagonal prisms are all capped by iridium and gadolinium atoms at much longer Gd–Ir and Gd–Ge distances. The prisms filled by the Gd2 and Gd3 atoms form a trimeric unit. This leads to the Ir@Gd₆ prism discussed above which shows the slightly enhanced displacement parameter U ₁₁ for the Ir4 atoms.

Figure 4:

Projection of the Gd₄Ir₁₃Ge₉ structure onto the bc plane. Gadolinium, iridium and germanium atoms are drawn as medium grey, blue and magenta circles, respectively. The three-dimensional [Ir₁₃Ge₉] network is emphasized. Atom designations are given at the right-hand part of the drawing.

The high iridium content in the Gd₄Ir₁₃Ge₉ structure (50 at%) naturally leads to a variety of Ir–Ir interactions. The various Ir–Ir distances (except the isolated Ir4 atoms discussed above) range from 274–294 pm. The shorter ones are close to the Ir–Ir distance of 272 pm in fcc iridium. ⁴⁴ This is the typical range in iridium-rich tetrelide and pnictide structures. Closely related structures are, e. g., Ce₉Ir₃₇Ge₂₅ (275–294 pm Ir–Ir), ⁴³ Lu₃Ir₇P₅ (271–301 pm Ir–Ir) ⁴⁵ or La₅Ir₁₉P₁₂ (282–296 pm Ir–Ir). ⁴⁶ Thus, the [Ir₁₃Ge₉] ^δ− network in Gd₄Ir₁₃Ge₉ is stabilized by Ir–Ge and Ir–Ir bonding as well.

The germanium atoms are located within their Gd₄Ir₂ and Gd₂Ir₄ trigonal prisms and show no Ge–Ge bonding. As a consequence of the geometrical constraints of the Ge1@Gd₂Ir₄ and Ge4@Gd₂Ir₄ prism condensation forming the empty Ir₆ prism (Figure 3), the Ge1 and Ge4 centers slightly move towards each other. Nevertheless, the resulting Ge1–Ge4 (291 pm) and Ge4–Ge4 (291 pm) distances are both significantly longer than the 245 pm Ge–Ge single bond distance in the diamond-type modification of germanium, ⁴⁴ and are no bonding contacts.

Finally, we turn towards the known coloring variants of the Ho₄Ir₁₃Ge₉-type ¹² structure. Tables 1 and 2 list the known representatives of this structure type. In the family of tetrelides, examples are known with the transition metals rhodium and iridium and the tetrels silicon and germanium. A few pnictides have also been synthesized. The phosphides Sm₄Rh₁₃P₉ and RE ₄Ir₁₃P₉ (RE = Sm, Gd, Yb) as well as the arsenides Ca₄Rh₁₃As₉, Sm₄Rh₁₃As₉ and Eu₄Ir₁₃As₉ are strictly isotypic with Ho₄Ir₁₃Ge₉. Just the tetrel sites are substituted with the pnicogen atoms. This is different for the platinides Ce₄Al₁₃Pt₉ ²⁶ and Sr₄In₁₃Pt₉, ²⁷ which are isopointal ^{47 , 48} but not isotypic. The more electronegative platinum atoms occupy the pnicogen sites and thus, this is another example for so-called anti-type structures. The most prominent example concerns the fluorite (CaF₂) and anti-fluorite type (Li₂O). This coloring principle is not that rare in the field of intermetallic compounds. Typical examples are the pairs Hf₂Co₄P₃ ⁴⁹ versus Sr₂In₄Au₃ ⁵⁰ or Eu₅In₉Pt₇ ²⁷ versus Sc₅Pt₉Si₇, ⁵¹ i.e., phosphide versus auride and platinide versus silicide character. The coloring in all these variants is driven by the course of the electronegativities.

A last topic concerns pnictides and an auride that exhibit the same stoichiometry but a different crystal structure. The silicide phosphides RE ₄Co₁₃(Si,P)₉ (RE = Sm, Gd–Er) and U₄Fe₁₃P₉ ⁵² and the auride Sr₄In₁₃Au₉ ⁵³ have a composition similar to Ho₄Ir₁₃Ge₉, however, a different connectivity pattern of the trigonal prisms (Figure 3). First, the pair Ho₄Ir₁₃Ge₉ versus Sr₄In₁₃Au₉ is another example for an electronegativity driven anti-type, similar to the just discussed example. Second, the refined structures of Gd₄Co₁₃(Si,P)₉ and Sr₄In₁₃Au₉ show slightly enhanced U ₃₃ displacements for the 1c sites (Co in Gd₄Co₁₃(Si,P)₉ and In in Sr₄In₁₃Au₉). Again, these atoms reside in Gd₆ respectively Sr₆ prisms that are formed as centers of the condensed shamrock unit, similar to Gd₄Ir₁₃Ge₉, underpinning the close structural relationship.

5 Magnetic properties of Tb₄Ir₁₃Ge₉

The temperature dependence of the magnetic susceptibility of Tb₄Ir₁₃Ge₉ measured at 10 kOe is presented in Figure 5. Tb₄Ir₁₃Ge₉ shows Curie-Weiss behavior above 25 K. A fit of the data (25–300 K range) with a modified Curie-Weiss law yielded an experimental magnetic moment of 10.4(1) µ_B Tb atom⁻¹, a Weiss constant of −6.4(1) K and a temperature-independent contribution of χ ₀ = −0.01390(7) emu mol⁻¹. The experimentally derived moment is slightly larger than the free ion value of Tb³⁺ (9.72 µ_B). ⁵⁴ Such slightly enhanced values have been observed for a variety of intermetallic terbium compounds. ⁵⁵ The negative Weiss constant is indicative of antiferromagnetic interactions in the paramagnetic range.

Figure 5:

Temperature dependence of the magnetic susceptibility (χ and χ ⁻¹ values) of Tb₄Ir₁₃Ge₉ measured at 10 kOe. The insert shows a 100 Oe measurement that clearly manifests the antiferromagnetic ordering.

The low-field measurement at 100 Oe (insert of Figure 5) clearly reveals antiferromagnetic ordering of the terbium magnetic moments below a Néel temperature of T _N = 4.7(1) K, slightly higher than the one observed for the isotypic silicide Tb₄Ir₁₃Si₉ (4.3 K). ¹⁴ The magnetization behavior is shown in Figure 6. At 50, 100 and 150 K, well above the magnetic ordering temperature, we observe a linear increase of the magnetization with increasing field strength as it is usual for a paramagnetic material. A first curvature occurs in the 10 K isotherm which is still above the Néel temperature. The 3 K isotherm in the magnetically ordered regime shows a two-step metamagnetic behavior (with negligible hysteresis) and thus underpins the antiferromagnetic ground state. The first (poorly pronounced) plateau is around a magnetization of ∼2 µ_B per Tb atom. The highest magnetization value at 3 K and 80 kOe of 5.61(1) µ_B per Tb atom is much lower than the theoretical saturation moment of 9 µ_B per Tb atom according to g _J × J. ⁵⁴ Keeping the three crystallographically independent terbium sites 2a, 4e and 2b in mind, it might be possible, that the first step of the 3 K isotherm corresponds to the antiparallel-to-parallel spin realignment of one of the two-fold sites. This magnetization behavior is similar to that observed for Tb₄Ir₁₃Si₉. ¹⁴ A quantitative analyses of the terbium spin structure is only possible via neutron diffraction.

Figure 6:

Magnetization isotherms of Tb₄Ir₁₃Ge₉ measured at T = 3, 10, 50, 100 and 150 K.