Indides RE₃T₂In₄ (RE = Y, Gd–Tm, Lu; T = Ni, Ru, Rh) with a ZrNiAl superstructure

1 Introduction

The ZrNiAl structure [1], [2], [3], a ternary ordered version of the Fe₂P type [4] is one of the basic structure types for equiatomic intermetallic compounds RETX and TT′X (RE=rare earth element, T=transition metal; X=element of the 3^rd, 4^th, or 5^th main group). More than 1300 representatives are listed in the Pearson Data Base [5]. This structure type allows for a broad range of element combinations, variations of the valence electron count and certain differences in the atomic radii. Especially the cerium [6], [7], ytterbium [7], [8], and uranium [9], [10], [11] containing phases have been studied with respect to their greatly varying magnetic ground states and valence changes. If the geometrical requests for a given element combination cannot be fulfilled, superstructure formation along with small distortions (and thinning of the subcell symmetry) is a way out [12], [13].

Besides distortions, the ZrNiAl structure also allows for coloring on the four crystallographically independent sites, leading to other ordering variants with distinctly different bonding patterns. Typical compositions are Ni₆BSi₂, Zr₆CoGa₂, Lu₃CoGa₅, Zr₃Cu₄Si₂, or Y₃NiAl₃Ge₂ [14], all keeping the subcell structure, space group P6̅2m. This is different for the structures of Ti₄Ni₂Ga₃ [15] and the series RE₃Co₂In₄ (RE=Ho, Er, Tm, Lu) with the Lu₃Co₂In₄ type [16]. The Ti₄Ni₂Ga₃ type shows a doubling of the subcell c axis and substantial shifts of several atoms off the subcell mirror planes. The 1:1 Co/In coloring within the trigonal rare earth prisms in the Lu₃Co₂In₄ type series deserves a symmetry reduction to space group P6̅. Phase analytical studies in the gadolinium–rhodium–indium systems led to the isotypic compound Gd₃Rh_1.94In₄ [17]. As an example we present the coloring variants for HoRhIn [18] and Ho₃Rh₂In₄ in Fig. 1.

Fig. 1:

Projection of the HoRhIn [18] and Ho₃Rh₂In₄ structures onto the crystallographic xy planes. Holmium, rhodium and indium atoms are drawn as medium grey, blue, and magenta circles, respectively. The trigonal prismatic units and the two-dimensional [RhIn], respectively [Rh₂In₄] networks are emphasized. Atom designations and relevant interatomic distances are given.

The ordering pattern is even more complex for the scandium compounds Sc₃Ni_2.10In_3.60, Sc₃Ni_2.14In_3.76, ScPd_0.981In and Sc₃Rh_1.594In₄ [19]. The palladium compound crystallizes with the subcell structure with small defects on the transition metal site. The coloring in the nickel compounds deserves the same symmetry reduction as reported for the Lu₃Co₂In₄ series and Gd₃Rh_1.94In₄. The ordering variant with the lowest space group symmetry is Sc₃Rh_1.594In₄, which crystallizes with a translationengleiche subgroup of Ti₄Ni₂Ga₃.

In continuation of our studies on coloring variants of the ZrNiAl type [3], [6], [12], [13], [17], [19] we systematically investigated the existence range for the Lu₃Co₂In₄ type. These phases are formed only with the smaller (late) rare earth elements. Herein we report on the synthesis, the solid solution behavior and the crystal chemistry of the three series RE₃T₂In₄ with RE=Y, Gd–Tm, Lu and T=Ni, Ru, Rh.

2 Experimental

3 Crystal chemistry

The indides RE₃T₂In₄ (RE=Y, Gd–Tm, Lu; T=Ni, Ru, Rh) crystallize with the hexagonal Lu₃Co₂In₄ structure [16] and extend significantly the number of representatives for this type. The four series (with T=Co, Ni, Ru, Rh) only exist for the smaller (late) rare earth elements. The cell volumes decrease from the gadolinium to the lutetium compound (Fig. 2) as a consequence of the lanthanide contraction. The three yttrium compounds fit in these series in between the volumes of the terbium and dysprosium compounds, similar to many other series of rare earth-transition metal-indides [26]. Small deviations in the volume plot are a consequence of the solid solutions.

Fig. 2:

Course of the cell volumes of the series of hexagonal RE₃T₂In₄ compounds.

Interestingly no ytterbium-based compound was obtained for any of these series. This seems to correlate with the existence range of the equiatomic compounds RETIn. With cobalt and ruthenium no equiatomic RETIn phases exist and within the RENiIn series no ytterbium compound has been reported [26], whereas YbRhIn [18] adopts the orthorhombic TiNiSi type with completely different crystal chemistry. This might be a consequence of the ytterbium valence (tendency towards divalent ytterbium).

In the following discussion we exemplarily focus on the three indides HoRhIn [18], Ho₃Rh₂In₄ and Ho₃Rh_2.39In_3.61. The complete list of interatomic distances is given in Table 5. The striking difference between HoRhIn (a=747.21(6), c=385.72(3) pm, c/a=0.516) and Ho₃Rh₂In₄ (a=780.5(2), c=373.6(1) pm, c/a=0.479) is the course of the lattice parameters influenced by the Rh/In substitution. Since the covalent radius [27] of indium (150 pm) is significantly larger than that of rhodium (125 pm), we observe a drastic widening of those trigonal holmium prisms that are filled with indium. This leads to the strong increase of the lattice parameter a. In parallel, for keeping the overall bonding, the c parameter decreases. This anisotropic behavior occurs for all 3-2-4 phases that have a 1-1-1 counterpart. The cell parameters of the mixed occupied phase Ho₃Rh_2.39In_3.61 fit in between the data for HoRhIn and Ho₃Rh₂In₄.

The ordered Rh/In substitution has consequences on the individual atom coordinations. First of all one observes a lowering of the space group symmetry from P6̅2m to P6̅ (translationengleiche symmetry reduction of index 2; splitting of the 2c subcell site into two one-fold sites). The corresponding group-subgroup relation has been published in [17]. The changes of the interatomic distances are readily visible from Table 5 and Fig. 1. The distances for the partially substituted phase Ho₃Rh_2.38In_3.62 are between those of HoRhIn and Ho₃Rh₂In₄. The Rh/In ordering leads to Ho₆ prisms with smaller (378 pm; filled with rhodium) and longer edges (451 pm, filled with indium).

The shortest interatomic distances in the three phases occur for Rh–In (272–275 pm), in close agreement with the sum of the covalent radii [27] for Rh+In of 275 pm. This underlines the importance of Rh–In bonding as a stabilizing parameter. Similar ranges of Rh–In distances occur in many ternary alkaline earth and rare earth based indides [28], [29]. Filling half of the Ho₆ prisms with indium (this is the situation in Ho₃Rh₂In₄) leads to substantial In–In bonding. Each of these indium atoms binds to three In₃ triangles (349 pm In–In) with In–In distances of 294 pm, somewhat shorter than the In–In distances in indium metal (4×325 and 8×338 pm) [30].

A final question concerns the stability range for these hexagonal RETIn (≡RE₃T₃In₃) and RE₃T₂In₄ phases. A first approach might be the valence electron count (VEC). Since the 3-2-4 phases exist with Ru, Rh, and Ni as transition metal component, the VEC ranges from 37 to 41 per formula unit. Equiatomic hexagonal indides are known with T=Rh, Ni, Pd, Pt, Cu, Au. This corresponds to a VEC range from 45 to 51 (three formula units are calculated for better comparison with the 3-2-4 phases). Increasing or decreasing the VEC out of these small ranges may destabilize such a structural arrangement. This might be the reason for the non-existence of RERuIn phases. However, VEC cannot be the only determining parameter since also no RECoIn phases exist that would formally be isotypic with the RERhIn series. More detailed phase analytical studies along with electronic structure calculations are needed in future in order to fully understand this structural family.