Synthesis and crystal structure of La21Cr8−2aAlbGe7−bC12 [a = 0.22 (2) and b = 0.758 (19)]

The face-centered cubic crystal structure of a new multinary chromium carbide, La21Cr8−2aAlbGe7−bC12, is composed of isolated and geometrically frustrated regular Cr tetrahedra that are co-centered within regular C octahedra. These mutually separated Cr4−aC6 clusters are distributed throughout a three-dimensional framework of Al, Ge, and La.


Chemical context
Geometric frustration arises when crystallographic degeneracies lead to the near equalization of competing interatomic interactions. Often, such frustration results in the suppression to an arbitrarily low temperature of any eventual phase transition to an ordered ground state (Gilbert et al., 2016). In the simplest case, this phenomenon occurs when three antiferromagnetic exchange-coupled Ising spins are arranged on the vertices of an equilateral triangle, their counterbalanced interactions thereby precluding the transition to mutually energetically favorable magnetic order. The ability to tune the onset of order via geometric frustration has been shown to lead to a variety of intriguing properties, including magnetic monopoles (Pan et al., 2016), spin ice states (Hirschberger et al., 2015;Huang et al., 2016), tricritical phenomena (McNally et al., 2015), and quantum criticality (Miiller et al., 2016), with applications ranging from neural networks (Grass et al., 2016), to quantum computing (Katzgraber et al., 2015), to unconventional superconductivity (Glasbrenner et al., 2015). Over the last decades, a class of materials known as pyrochlores has provided a rich ground for studying magnetic frustration due to geometric degeneracies arising from their vertex-linked, regular tetrahedral building blocks (Gardner et al., 2010). The structure of the La 21 Fe 8 Sn 7 C 12 system also consists regular tetrahedra of Fe, but in this case they are mutually isolated from one another. Here too, geometric frustration has been observed to manifest itself in a spin glass ground state, as inferred from a frequency f-dependent cusp in the real part of measurements of ac magnetic susceptibility 0 near temperature T = 5 K (Benbow et al., 2009). On the other hand, if Fe is replaced with Mn as in isostructural La 21 Mn 8 Ge 6.2 Al 0.8 C 12 , ISSN 2056-9890 similar cusps occurring at T = 3 K and 6 K in 0 exhibit no such dependence, even over four orders of magnitude in f, suggesting that only local antiferromagnetic ordering within the Mn 4 C 6 cluster arises while the spin glass state remains absent down to T = 1.8 K (Zaikina et al., 2011). With the aim of unveiling a new avenue to explore frustrated states within this class of compounds, we present here the synthesis and crystal structure of a new Cr-based analog that is isostructural and likewise geometrically frustrated, La 21 Cr 8À2a Al b Ge 7Àb C 12 , [a = 0.22 (2), b = 0.758 (19)]. Fig. 1 shows a polyhedral representation of the crystal structure of the title compound, the geometrically frustrated substructure of which consists of a Cr-capped regular tetrahedron enclosed within a C-capped regular octahedron. Fig. 1a is a depiction of the unit cell from along the crystallographic a axis, and Fig. 1b shows the same from a generic angle above the ab plane. The structure can be thought to be composed of three building blocks -a geometrically frustrated and Crdeficient Cr 4Àa C 6 unit ( Fig. 1c), an La 9 Ge 6 unit ( Fig. 1d), and an La 12 Al b Ge 1Àb unit (Fig. 1e). These substructures are arranged on four interpenetrating face-centered cubic lattices that originate within the unit cell at ( 1 4 , 1 4 , 1 4 ) and ( 3 4 , 1 4 , 1 4 ) for the Cr 4Àa C 6 unit, ( 1 2 , 0, 0) for the La 9 Ge 6 unit, and (0, 0, 0) for the La 12 Al b Ge 1-b unit. Accordingly, La 21 Cr 8À2a Al b Ge 7Àb C 12 adopts a structure that is effectively a polyatomic analog of the Heusler structure (Graf et al., 2011) with composition X 2 YZ, where X = Cr 4Àa C 6 , Y = La 9 Ge 6 , and Z = La 12 Al b Ge 1Àb units. Taken together with the appropriate site occupancies, the title composition is thus obtained as X 2 YZ = La 21 Cr 8À2a Al b Ge 7Àb C 12 .

Structural commentary
The geometrically frustrated Cr-deficient Cr 4Àa C 6 unit shown in Fig. 1c is composed of a single inequivalent Cr position and a single C position. Accordingly, nearest neighbor Cr-C distances are uniformly 1.949 (5) Å , in good agreement with nearest neighbor distances in binary Cr carbides. Like-wise, all Cr-Cr distances within the substructure are similarly identical at 2.4821 (9) Å , only slightly smaller than the 2.512 Å nearest neighbor distance observed in Cr metal (Gorbunoff et al., 2009). Perhaps more interesting, however, is this relative proximity when compared with the 2.878 Å that separates neighboring Cr in the frustrated Kagomé planes of SrCr 8Àx Ga 4+x O 19 , a seminal example of a geometrically frustrated magnetic system (Broholm et al., 1990).
The remaining substructures, namely the La 9 Ge 6 unit shown in Fig. 1d and the La 12 Al b Ge 1Àb unit shown in Fig. 1e form cages about their central La3 and Al2/Ge2 sites respectively. The cage-like nature of this configuration is clear from the large anisotropic displacement parameters U eq corresponding to these two central sites, as has been previously observed in isostructural materials (Benbow et al., 2009;Zaikina et al., 2011). These sites are likely characterized by strong rattling modes of the central loosely bound atom, such as is observed in skutterudite compounds (Sergueev et al., 2015). Not surprisingly, the distance between central La3 and its nearest neighbor Ge1 is a rather long, 3.41450 (13) Å . The central Al2/Ge2 site is even further -3.8858 (2) Å from its nearest neighbor La1. A brief review of the crystallographic literature finds nearest neighbor bond lengths in La-Ge binaries to be typically on the order of only 3.0 to 3.2 Å , far smaller than either of these distances, which lends credence to the emerging picture of a stuffed, skutterudite-like arrangement.

Synthesis and crystallization
La 21 Cr 8À2a Al b Ge 7Àb C 12 crystals were grown from a self flux of excess La (Alfa Aesar, 00175) and the following chemicals: Cr (Alfa Aesar, 38494), Ge (Strategic Metal, SM1301-B), and graphite (McMaster-Carr 9121K71) in an La:Cr:Ge:C atomic ratio of 561:214:76:149. The growth process was carried out in Al 2 O 3 crucibles sealed within fused quartz ampoules under high purity Ar gas. Ampoules were heated to 1423 K over a period of four h, left to soak at that temperature for an additional four h, and cooled to 1173 K over 50 h to induce nucleation and to promote crystal growth. The ampoule was then quickly centrifuged at 2000 r.p.m. for several seconds to separate the solid crystals from the liquid La-rich solution. Crystals took the form of well-faceted tablets with metallic luster.

Refinement details
Details regarding the crystal itself, as well as data collection and structural refinement are presented in Table 1. No evidence for twin domains was observed, and all sites with the exception of C were refined with anisotropic displacement parameters. Here permitting anisotropic displacement parameters did not appreciably improve the refinement. Two reflections, (111) and (002), required manual culling due to beamstop clipping.
The refinement was improved when the Ge2 site was permitted to be mixed with Al. In this case, Al and Ge coordinates and displacement parameters were constrained to be equal, and the sum of the Al and Ge occupancies was constrained to unity. The refined Al:Ge ratio 0.758 (19):6.242 (19) is in excellent agreement with observed ratios of 0.83 (2):6.17 (2) in La 21 MnAl b Ge 7Àb C 12 (Zaikina et al., 2011) and somewhat lower than the reported ratio of 2.1:4.9 in La 21 FeAl b Ge 7-b C 12 (Benbow et al., 2009). Like the Mn-based analog, however, we observe no evidence to suggest that the Ge1 site is mixed, as was the case with the more Alrich La 21 FeAl b Ge 7Àb C 12 . Regardless of any quantitative differences, the potential for Al -apparently extracted by an La-rich flux from Al 2 O 3 growth crucibles -to mix with Ge appears to be a universal phenomenon in this class of compounds. It remains unclear if Al is required to stabilize the Ge-containing examples of these phases, which have not been reported in its absence.
In addition to mixing on the Al2/Ge2 site, excess charge was observed in Fourier maps when the Cr site was constrained to full occupancy, and the refinement was substantially improved when this parameter was subsequently freed. Permitting instead partial occupancy of Al on the Cr site did not appreciably improve the refinement. No evidence for mixed or nonunity occupancy was found for any of the La sites, despite previously published density functional theory calculations that found a composition of La 20 Mn 8 Te 7 C 12 to be stabilized by the shift of the Fermi energy to a pseudogap in the density of states (Zaikina et al., 2011) Data collection: APEX2 (Bruker, 2007) and SAINT (Bruker, 2007); cell refinement: APEX2 (Bruker, 2007) and SAINT (Bruker, 2007); data reduction: APEX2 (Bruker, 2007) and SAINT (Bruker, 2007); program(s) used to solve structure: SUPERFLIP (Palatinus & Chapuis, 2007); program(s) used to refine structure: JANA2006 (Petřìček et al., 2014); molecular graphics: VESTA (Momma & Izumi, 2011); software used to prepare material for publication: publCIF (Westrip, 2010).