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

Pabla, J.; Janssen, Y.; Simonson, J.W.

doi:10.1107/S2056989016015668

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Volume 72| Part 11| November 2016| Pages 1565-1568

https://doi.org/10.1107/S2056989016015668

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Synthesis and crystal structure of La₂₁Cr_8−2aAl_bGe_7−bC₁₂ [a = 0.22 (2) and b = 0.758 (19)]

Jaskarun Pabla,^a Yuri Janssen ^a and Jack W. Simonson ^a ^*

^aDepartment of Physics, Farmingdale State College, Farmingdale, NY 11735, USA
^*Correspondence e-mail: jack.simonson@farmingdale.edu

Edited by S. Parkin, University of Kentucky, USA (Received 9 September 2016; accepted 4 October 2016; online 11 October 2016)

Single crystals of a new multinary chromium carbide, La₂₁Cr_8−2aAl_bGe_7−bC₁₂ (henicosalanthanum octachromium aluminium hexagermanium dodecacarbide), were grown from an La-rich self flux and were characterized by single-crystal X-ray diffraction. The face-centered cubic crystal structure is composed of isolated and geometrically frustrated regular Cr tetrahedra that are co-centered within regular C octahedra. These mutually separated Cr_4−aC₆ clusters are distributed throughout a three-dimensional framework of Al, Ge, and La. The title compound is isotypic with La_21−δMn₈X₇C₁₂ and R₂₁Fe₈X₇C₁₂ (R = La, Ce, Pr; X = Al, Bi, Ge, Sn, Sb, Te) and represents the first example of a Cr-based compound with this structure-type.

Keywords: crystal structure; geometric frustration; multinary chromium carbides.

CCDC reference: 1508202

1. 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 La₂₁Fe₈Sn₇C₁₂ 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 χ′ near temperature T = 5 K (Benbow et al., 2009 ). On the other hand, if Fe is replaced with Mn as in isostructural La₂₁Mn₈Ge_6.2Al_0.8C₁₂, similar cusps occurring at T = 3 K and 6 K in χ′ exhibit no such dependence, even over four orders of magnitude in f, suggesting that only local antiferromagnetic ordering within the Mn₄C₆ 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, La₂₁Cr_8−2aAl_bGe_7−bC₁₂, [a = 0.22 (2), b = 0.758 (19)].

2. Structural commentary

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 Cr-deficient Cr_4−aC₆ unit (Fig. 1c), an La₉Ge₆ unit (Fig. 1d), and an La₁₂Al_bGe_1−b unit (Fig. 1e). These substructures are arranged on four interpenetrating face-centered cubic lattices that originate within the unit cell at (¼, ¼, ¼) and (¾, ¼, ¼) for the Cr_4−aC₆ unit, (½, 0, 0) for the La₉Ge₆ unit, and (0, 0, 0) for the La₁₂Al_bGe_1-b unit. Accordingly, La₂₁Cr_8−2aAl_bGe_7−bC₁₂ adopts a structure that is effectively a polyatomic analog of the Heusler structure (Graf et al., 2011 ) with composition X₂YZ, where X = Cr_4−aC₆, Y = La₉Ge₆, and Z = La₁₂Al_bGe_1−b units. Taken together with the appropriate site occupancies, the title composition is thus obtained as X₂YZ = La₂₁Cr_8−2aAl_bGe_7−bC₁₂.

Figure 1
(a) A view of the crystal structure of La₂₁Cr_8−2aAl_bGe_7−bC₁₂ along [100]. (b) The same crystal structure from an arbitrary view above the ab plane. (c) Cr-deficient Cr_4−aC₆ substructure depicted as four tetrahedrally arranged and vertex-linked CrC₃ plaquettes. (d) La3 coordination polyhedron. (e) Al2/Ge2 coordination polyhedron. In all sub-figures, colors are as follows: La (white), Cr (red), Al (green), Ge (blue), and C (black). Polyhedra are colored according to the central element. In c–e, the ellipsoids correspond to 99% probability.

The geometrically frustrated Cr-deficient Cr_4−aC₆ 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. Likewise, 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_8−xGa_4+xO₁₉, a seminal example of a geometrically frustrated magnetic system (Broholm et al., 1990 ).

The remaining substructures, namely the La₉Ge₆ unit shown in Fig. 1d and the La₁₂Al_bGe_1−b 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.

3. Synthesis and crystallization

La₂₁Cr_8−2aAl_bGe_7−bC₁₂ 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 Al₂O₃ 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.

4. 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, ( $[\overline{1}]$ $[\overline{1}]$ $[\overline{1}]$ ) and (00 $[\overline{2}]$ ), required manual culling due to beamstop clipping.

Table 1
Experimental details

Crystal data
Chemical formula	La₂₁Cr_7.556Al_0.758Ge_6.242C₁₂
M_r	3927.6
Crystal system, space group	Cubic, Fm $[\overline{3}]$ m
Temperature (K)	294
a (Å)	16.4048 (6)
V (Å³)	4414.8 (5)
Z	4
Radiation type	Mo Kα
μ (mm⁻¹)	25.76
Crystal size (mm)	0.12 × 0.11 × 0.07

Data collection
Diffractometer	Bruker APEXII CCD
Absorption correction	Numerical (SADABS; Bruker, 2008 )
T_min, T_max	0.342, 0.527
No. of measured, independent and observed [I > 3σ(I)] reflections	40979, 328, 321
R_int	0.041
(sin θ/λ)_max (Å⁻¹)	0.670

Refinement
R[F > 3σ(F)], wR(F), S	0.012, 0.045, 1.91
No. of reflections	328
No. of parameters	21
Δρ_max, Δρ_min (e Å⁻³)	1.07, −0.83
Computer programs: APEX2 and SAINT (Bruker, 2007 ), SUPERFLIP (Palatinus & Chapuis, 2007 ), JANA2006 (Petřìček et al., 2014 ), VESTA (Momma & Izumi, 2011 ) and publCIF (Westrip, 2010 ).

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 La₂₁MnAl_bGe_7−bC₁₂ (Zaikina et al., 2011) and somewhat lower than the reported ratio of 2.1:4.9 in La₂₁FeAl_bGe_7-bC₁₂ (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 Al-rich La₂₁FeAl_bGe_7−bC₁₂. Regardless of any quantitative differences, the potential for Al – apparently extracted by an La-rich flux from Al₂O₃ 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 non-unity occupancy was found for any of the La sites, despite previously published density functional theory calculations that found a composition of La₂₀Mn₈Te₇C₁₂ to be stabilized by the shift of the Fermi energy to a pseudogap in the density of states (Zaikina et al., 2011). Our final refined composition is then La₂₁Cr_8−2aAl_bGe_7−bC₁₂ with the occupancy parameters a = 0.22 (2) and b = 0.758 (19).

Supporting information

CCDC reference: 1508202

Crystal structure: contains datablocks global, I. DOI: https://doi.org/10.1107/S2056989016015668/pk2592sup1.cif

Structure factors: contains datablocks global, I. DOI: https://doi.org/10.1107/S2056989016015668/pk2592Isup2.hkl

checkCIF report

Computing details top

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).

Henicosalanthanum octachromium alumimium hexagermanium dodecacarbide top

Crystal data top

La₂₁Cr_7.556Al_0.758Ge_6.242C₁₂	D_x = 5.909 Mg m⁻³
M_r = 3927.6	Mo Kα radiation, λ = 0.71073 Å
Cubic, Fm3m	Cell parameters from 9327 reflections
Hall symbol: -F 4 2 3	θ = 5.0–56.7°
a = 16.4048 (6) Å	µ = 25.76 mm⁻¹
V = 4414.8 (5) Å³	T = 294 K
Z = 4	Plate, metallic_black
F(000) = 6639.4	0.12 × 0.11 × 0.07 mm

Data collection top

Bruker APEXII CCD diffractometer	328 independent reflections
Radiation source: X-ray tube	321 reflections with I > 3σ(I)
Graphite monochromator	R_int = 0.041
ω and φ scans	θ_max = 28.4°, θ_min = 2.2°
Absorption correction: numerical (SADABS; Bruker, 2008)	h = −21→21
T_min = 0.342, T_max = 0.527	k = −21→21
40979 measured reflections	l = −21→21

Refinement top

Refinement on F²	1 constraint
R[F > 3σ(F)] = 0.012	Weighting scheme based on measured s.u.'s w = 1/(σ²(I) + 0.0004I²)
wR(F) = 0.045	(Δ/σ)_max = 0.015
S = 1.91	Δρ_max = 1.07 e Å⁻³
328 reflections	Δρ_min = −0.83 e Å⁻³
21 parameters	Extinction correction: B-C type 2 (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 810 (150)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
La1	0	0.167496 (14)	0.167496 (14)	0.01125 (10)
La2	0.369379 (15)	0.369379 (15)	0.369379 (15)	0.00984 (9)
La3	0.5	0.5	0.5	0.0384 (3)
Ge1	0.29186 (6)	0	0	0.0121 (2)
Cr1	0.19651 (4)	0.19651 (4)	0.19651 (4)	0.0068 (2)	0.944 (5)
Ge2	0	0	0	0.0323 (12)	0.242 (19)
Al2	0	0	0	0.0323 (12)	0.758 (19)
C1	0.1049 (4)	0.25	0.25	0.0127 (11)*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
La1	0.0074 (2)	0.01315 (17)	0.01315 (17)	0	0	0.00046 (13)
La2	0.00984 (15)	0.00984 (15)	0.00984 (15)	−0.00052 (8)	−0.00052 (8)	−0.00052 (8)
La3	0.0384 (4)	0.0384 (4)	0.0384 (4)	0	0	0
Ge1	0.0139 (5)	0.0112 (3)	0.0112 (3)	0	0	0
Cr1	0.0068 (3)	0.0068 (3)	0.0068 (3)	0.0008 (2)	0.0008 (2)	0.0008 (2)
Ge2	0.032 (2)	0.032 (2)	0.032 (2)	0	0	0
Al2	0.032 (2)	0.032 (2)	0.032 (2)	0	0	0

Geometric parameters (Å, º) top

La1—La1ⁱ	3.8282 (4)	La2—Ge1^xiii	3.2864 (5)
La1—La1ⁱⁱ	3.8859 (3)	La2—Ge1^xiv	3.2864 (5)
La1—La1ⁱⁱⁱ	3.8859 (3)	La2—Cr1^vi	3.2216 (7)
La1—La1^iv	3.8859 (3)	La2—Cr1^vii	3.2216 (7)
La1—La1^v	3.8859 (3)	La2—Cr1ⁱ	3.2216 (7)
La1—La2^vi	3.9907 (4)	La2—C1^vi	2.8015 (9)
La1—La2^vii	3.9907 (4)	La2—C1^xv	2.8015 (9)
La1—La2^viii	3.9907 (4)	La2—C1^xvi	2.8015 (9)
La1—La2^ix	3.9907 (4)	Cr1—Cr1^vi	2.4821 (9)
La1—Cr1	3.2932 (7)	Cr1—Cr1^vii	2.4821 (9)
La1—Cr1^x	3.2932 (7)	Cr1—Cr1ⁱ	2.4821 (9)
La1—C1	2.574 (4)	Cr1—C1	1.949 (5)
La1—C1^xi	2.574 (4)	Cr1—C1ⁱⁱ	1.949 (5)
La2—La3	3.7115 (3)	Cr1—C1^iv	1.949 (5)
La2—Ge1^xii	3.2864 (5)

La1ⁱ—La1—La1ⁱⁱ	120.000 (6)	La3—La2—Cr1^vii	153.589 (14)
La1ⁱ—La1—La1ⁱⁱⁱ	120.000 (6)	La3—La2—Cr1ⁱ	153.589 (14)
La1ⁱ—La1—La1^iv	120.000 (6)	La3—La2—C1^vi	136.07 (12)
La1ⁱ—La1—La1^v	120.000 (6)	La3—La2—C1^xv	136.07 (12)
La1ⁱ—La1—La2^vi	61.339 (6)	La3—La2—C1^xvi	136.07 (12)
La1ⁱ—La1—La2^vii	61.339 (6)	Ge1^xii—La2—Ge1^xiii	94.557 (15)
La1ⁱ—La1—La2^viii	61.339 (6)	Ge1^xii—La2—Ge1^xiv	94.557 (15)
La1ⁱ—La1—La2^ix	61.339 (6)	Ge1^xii—La2—Cr1^vi	131.521 (19)
La1ⁱ—La1—Cr1	78.207 (12)	Ge1^xii—La2—Cr1^vii	131.521 (19)
La1ⁱ—La1—Cr1^x	78.207 (12)	Ge1^xii—La2—Cr1ⁱ	95.56 (2)
La1ⁱ—La1—C1	41.96 (10)	Ge1^xii—La2—C1^vi	165.90 (12)
La1ⁱ—La1—C1^xi	41.96 (10)	Ge1^xii—La2—C1^xv	95.00 (8)
La1ⁱⁱ—La1—La1ⁱⁱⁱ	90.000 (7)	Ge1^xii—La2—C1^xvi	95.00 (8)
La1ⁱⁱ—La1—La1^iv	60.000 (5)	Ge1^xiii—La2—Ge1^xiv	94.557 (15)
La1ⁱⁱ—La1—La1^v	120.000 (7)	Ge1^xiii—La2—Cr1^vi	131.521 (19)
La1ⁱⁱ—La1—La2^vi	60.865 (6)	Ge1^xiii—La2—Cr1^vii	95.56 (2)
La1ⁱⁱ—La1—La2^vii	101.955 (5)	Ge1^xiii—La2—Cr1ⁱ	131.521 (19)
La1ⁱⁱ—La1—La2^viii	165.127 (7)	Ge1^xiii—La2—C1^vi	95.00 (8)
La1ⁱⁱ—La1—La2^ix	105.813 (7)	Ge1^xiii—La2—C1^xv	165.90 (12)
La1ⁱⁱ—La1—Cr1	53.844 (12)	Ge1^xiii—La2—C1^xvi	95.00 (8)
La1ⁱⁱ—La1—Cr1^x	142.596 (13)	Ge1^xiv—La2—Cr1^vi	95.56 (2)
La1ⁱⁱ—La1—C1	84.21 (8)	Ge1^xiv—La2—Cr1^vii	131.521 (19)
La1ⁱⁱ—La1—C1^xi	147.63 (4)	Ge1^xiv—La2—Cr1ⁱ	131.521 (19)
La1ⁱⁱⁱ—La1—La1^iv	120.000 (7)	Ge1^xiv—La2—C1^vi	95.00 (8)
La1ⁱⁱⁱ—La1—La1^v	60.000 (5)	Ge1^xiv—La2—C1^xv	95.00 (8)
La1ⁱⁱⁱ—La1—La2^vi	105.813 (7)	Ge1^xiv—La2—C1^xvi	165.90 (12)
La1ⁱⁱⁱ—La1—La2^vii	165.127 (7)	Cr1^vi—La2—Cr1^vii	45.314 (17)
La1ⁱⁱⁱ—La1—La2^viii	101.955 (5)	Cr1^vi—La2—Cr1ⁱ	45.314 (17)
La1ⁱⁱⁱ—La1—La2^ix	60.865 (6)	Cr1^vi—La2—C1^vi	36.93 (9)
La1ⁱⁱⁱ—La1—Cr1	142.596 (13)	Cr1^vi—La2—C1^xv	36.93 (9)
La1ⁱⁱⁱ—La1—Cr1^x	53.844 (12)	Cr1^vi—La2—C1^xvi	70.34 (12)
La1ⁱⁱⁱ—La1—C1	147.63 (4)	Cr1^vii—La2—Cr1ⁱ	45.314 (17)
La1ⁱⁱⁱ—La1—C1^xi	84.21 (8)	Cr1^vii—La2—C1^vi	36.93 (9)
La1^iv—La1—La1^v	90.000 (7)	Cr1^vii—La2—C1^xv	70.34 (12)
La1^iv—La1—La2^vi	101.955 (5)	Cr1^vii—La2—C1^xvi	36.93 (9)
La1^iv—La1—La2^vii	60.865 (6)	Cr1ⁱ—La2—C1^vi	70.34 (12)
La1^iv—La1—La2^viii	105.813 (7)	Cr1ⁱ—La2—C1^xv	36.93 (9)
La1^iv—La1—La2^ix	165.127 (7)	Cr1ⁱ—La2—C1^xvi	36.93 (9)
La1^iv—La1—Cr1	53.844 (12)	C1^vi—La2—C1^xv	73.86 (13)
La1^iv—La1—Cr1^x	142.596 (13)	C1^vi—La2—C1^xvi	73.86 (13)
La1^iv—La1—C1	84.21 (8)	C1^xv—La2—C1^xvi	73.86 (13)
La1^iv—La1—C1^xi	147.63 (4)	La2—La3—La2^xix	109.471 (6)
La1^v—La1—La2^vi	165.127 (7)	La2—La3—La2^xx	109.471 (6)
La1^v—La1—La2^vii	105.813 (7)	La2—La3—La2^xxi	109.471 (6)
La1^v—La1—La2^viii	60.865 (6)	La2—La3—La2^xxii	70.529 (6)
La1^v—La1—La2^ix	101.955 (5)	La2—La3—La2^xxiii	180.0 (5)
La1^v—La1—Cr1	142.596 (13)	La2—La3—La2^xxiv	70.529 (6)
La1^v—La1—Cr1^x	53.844 (12)	La2—La3—La2^xxv	70.529 (6)
La1^v—La1—C1	147.63 (4)	La2^xix—La3—La2^xx	109.471 (6)
La1^v—La1—C1^xi	84.21 (8)	La2^xix—La3—La2^xxi	109.471 (6)
La2^vi—La1—La2^vii	87.896 (6)	La2^xix—La3—La2^xxii	180.0 (5)
La2^vi—La1—La2^viii	122.677 (8)	La2^xix—La3—La2^xxiii	70.529 (6)
La2^vi—La1—La2^ix	64.952 (7)	La2^xix—La3—La2^xxiv	70.529 (6)
La2^vi—La1—Cr1	51.418 (12)	La2^xix—La3—La2^xxv	70.529 (6)
La2^vi—La1—Cr1^x	115.315 (13)	La2^xx—La3—La2^xxi	109.471 (6)
La2^vi—La1—C1	44.302 (12)	La2^xx—La3—La2^xxii	70.529 (6)
La2^vi—La1—C1^xi	90.13 (7)	La2^xx—La3—La2^xxiii	70.529 (6)
La2^vii—La1—La2^viii	64.952 (7)	La2^xx—La3—La2^xxiv	180.0 (5)
La2^vii—La1—La2^ix	122.677 (8)	La2^xx—La3—La2^xxv	70.529 (6)
La2^vii—La1—Cr1	51.418 (12)	La2^xxi—La3—La2^xxii	70.529 (6)
La2^vii—La1—Cr1^x	115.315 (13)	La2^xxi—La3—La2^xxiii	70.529 (6)
La2^vii—La1—C1	44.302 (12)	La2^xxi—La3—La2^xxiv	70.529 (6)
La2^vii—La1—C1^xi	90.13 (7)	La2^xxi—La3—La2^xxv	180.0 (5)
La2^viii—La1—La2^ix	87.896 (6)	La2^xxii—La3—La2^xxiii	109.471 (6)
La2^viii—La1—Cr1	115.314 (13)	La2^xxii—La3—La2^xxiv	109.471 (6)
La2^viii—La1—Cr1^x	51.418 (12)	La2^xxii—La3—La2^xxv	109.471 (6)
La2^viii—La1—C1	90.13 (7)	La2^xxiii—La3—La2^xxiv	109.471 (6)
La2^viii—La1—C1^xi	44.302 (12)	La2^xxiii—La3—La2^xxv	109.471 (6)
La2^ix—La1—Cr1	115.314 (13)	La2^xxiv—La3—La2^xxv	109.471 (6)
La2^ix—La1—Cr1^x	51.418 (12)	La2^xxvi—Ge1—La2ⁱ	134.47 (3)
La2^ix—La1—C1	90.13 (7)	La2^xxvi—Ge1—La2^xxvii	81.389 (12)
La2^ix—La1—C1^xi	44.302 (12)	La2^xxvi—Ge1—La2^xxviii	81.389 (12)
Cr1—La1—Cr1^x	156.414 (18)	La2ⁱ—Ge1—La2^xxvii	81.389 (12)
Cr1—La1—C1	36.25 (10)	La2ⁱ—Ge1—La2^xxviii	81.389 (12)
Cr1—La1—C1^xi	120.16 (10)	La2^xxvii—Ge1—La2^xxviii	134.47 (3)
Cr1^x—La1—C1	120.16 (10)	La1—Cr1—La1ⁱⁱ	72.313 (15)
Cr1^x—La1—C1^xi	36.25 (10)	La1—Cr1—La1^iv	72.313 (15)
C1—La1—C1^xi	83.91 (14)	La1—Cr1—La2^vi	75.541 (15)
La1^vi—La2—La1^vii	57.323 (6)	La1—Cr1—La2^vii	75.541 (15)
La1^vi—La2—La1^xv	113.653 (7)	La1—Cr1—La2ⁱ	139.88 (2)
La1^vi—La2—La1^xvii	58.269 (6)	La1—Cr1—Cr1^vi	142.60 (3)
La1^vi—La2—La1^xvi	113.653 (7)	La1—Cr1—Cr1^vii	142.60 (3)
La1^vi—La2—La1^xviii	150.254 (8)	La1—Cr1—Cr1ⁱ	101.79 (3)
La1^vi—La2—La3	104.871 (7)	La1—Cr1—C1	51.34 (11)
La1^vi—La2—Ge1^xii	147.964 (10)	La1—Cr1—C1ⁱⁱ	113.23 (9)
La1^vi—La2—Ge1^xiii	97.605 (8)	La1—Cr1—C1^iv	113.23 (9)
La1^vi—La2—Ge1^xiv	55.083 (13)	La1ⁱⁱ—Cr1—La1^iv	72.313 (15)
La1^vi—La2—Cr1^vi	53.041 (13)	La1ⁱⁱ—Cr1—La2^vi	75.541 (15)
La1^vi—La2—Cr1^vii	76.602 (13)	La1ⁱⁱ—Cr1—La2^vii	139.88 (2)
La1^vi—La2—Cr1ⁱ	98.244 (13)	La1ⁱⁱ—Cr1—La2ⁱ	75.541 (15)
La1^vi—La2—C1^vi	39.92 (8)	La1ⁱⁱ—Cr1—Cr1^vi	142.60 (3)
La1^vi—La2—C1^xv	79.52 (2)	La1ⁱⁱ—Cr1—Cr1^vii	101.79 (3)
La1^vi—La2—C1^xvi	113.23 (10)	La1ⁱⁱ—Cr1—Cr1ⁱ	142.60 (3)
La1^vii—La2—La1^xv	150.254 (8)	La1ⁱⁱ—Cr1—C1	113.23 (9)
La1^vii—La2—La1^xvii	113.653 (7)	La1ⁱⁱ—Cr1—C1ⁱⁱ	51.34 (11)
La1^vii—La2—La1^xvi	58.269 (6)	La1ⁱⁱ—Cr1—C1^iv	113.23 (9)
La1^vii—La2—La1^xviii	113.653 (7)	La1^iv—Cr1—La2^vi	139.88 (2)
La1^vii—La2—La3	104.871 (7)	La1^iv—Cr1—La2^vii	75.541 (15)
La1^vii—La2—Ge1^xii	147.964 (10)	La1^iv—Cr1—La2ⁱ	75.541 (15)
La1^vii—La2—Ge1^xiii	55.083 (13)	La1^iv—Cr1—Cr1^vi	101.79 (3)
La1^vii—La2—Ge1^xiv	97.605 (8)	La1^iv—Cr1—Cr1^vii	142.60 (3)
La1^vii—La2—Cr1^vi	76.602 (13)	La1^iv—Cr1—Cr1ⁱ	142.60 (3)
La1^vii—La2—Cr1^vii	53.041 (13)	La1^iv—Cr1—C1	113.23 (9)
La1^vii—La2—Cr1ⁱ	98.244 (13)	La1^iv—Cr1—C1ⁱⁱ	113.23 (9)
La1^vii—La2—C1^vi	39.92 (8)	La1^iv—Cr1—C1^iv	51.34 (11)
La1^vii—La2—C1^xv	113.23 (10)	La2^vi—Cr1—La2^vii	118.56 (2)
La1^vii—La2—C1^xvi	79.52 (2)	La2^vi—Cr1—La2ⁱ	118.56 (2)
La1^xv—La2—La1^xvii	57.323 (6)	La2^vi—Cr1—Cr1^vi	118.32 (3)
La1^xv—La2—La1^xvi	113.653 (7)	La2^vi—Cr1—Cr1^vii	67.34 (2)
La1^xv—La2—La1^xviii	58.269 (6)	La2^vi—Cr1—Cr1ⁱ	67.34 (2)
La1^xv—La2—La3	104.871 (7)	La2^vi—Cr1—C1	59.74 (2)
La1^xv—La2—Ge1^xii	55.083 (13)	La2^vi—Cr1—C1ⁱⁱ	59.74 (2)
La1^xv—La2—Ge1^xiii	147.964 (10)	La2^vi—Cr1—C1^iv	168.77 (11)
La1^xv—La2—Ge1^xiv	97.605 (8)	La2^vii—Cr1—La2ⁱ	118.56 (2)
La1^xv—La2—Cr1^vi	76.602 (13)	La2^vii—Cr1—Cr1^vi	67.34 (2)
La1^xv—La2—Cr1^vii	98.244 (13)	La2^vii—Cr1—Cr1^vii	118.32 (3)
La1^xv—La2—Cr1ⁱ	53.041 (13)	La2^vii—Cr1—Cr1ⁱ	67.34 (2)
La1^xv—La2—C1^vi	113.23 (10)	La2^vii—Cr1—C1	59.74 (2)
La1^xv—La2—C1^xv	39.92 (8)	La2^vii—Cr1—C1ⁱⁱ	168.77 (11)
La1^xv—La2—C1^xvi	79.52 (2)	La2^vii—Cr1—C1^iv	59.74 (2)
La1^xvii—La2—La1^xvi	150.254 (8)	La2ⁱ—Cr1—Cr1^vi	67.34 (2)
La1^xvii—La2—La1^xviii	113.653 (7)	La2ⁱ—Cr1—Cr1^vii	67.34 (2)
La1^xvii—La2—La3	104.871 (7)	La2ⁱ—Cr1—Cr1ⁱ	118.32 (3)
La1^xvii—La2—Ge1^xii	97.605 (8)	La2ⁱ—Cr1—C1	168.77 (11)
La1^xvii—La2—Ge1^xiii	147.964 (10)	La2ⁱ—Cr1—C1ⁱⁱ	59.74 (2)
La1^xvii—La2—Ge1^xiv	55.083 (13)	La2ⁱ—Cr1—C1^iv	59.74 (2)
La1^xvii—La2—Cr1^vi	53.041 (13)	Cr1^vi—Cr1—Cr1^vii	60.00 (3)
La1^xvii—La2—Cr1^vii	98.244 (13)	Cr1^vi—Cr1—Cr1ⁱ	60.00 (3)
La1^xvii—La2—Cr1ⁱ	76.602 (13)	Cr1^vi—Cr1—C1	103.11 (10)
La1^xvii—La2—C1^vi	79.52 (2)	Cr1^vi—Cr1—C1ⁱⁱ	103.11 (10)
La1^xvii—La2—C1^xv	39.92 (8)	Cr1^vi—Cr1—C1^iv	50.45 (11)
La1^xvii—La2—C1^xvi	113.23 (10)	Cr1^vii—Cr1—Cr1ⁱ	60.00 (3)
La1^xvi—La2—La1^xviii	57.323 (6)	Cr1^vii—Cr1—C1	103.11 (10)
La1^xvi—La2—La3	104.871 (7)	Cr1^vii—Cr1—C1ⁱⁱ	50.45 (11)
La1^xvi—La2—Ge1^xii	97.605 (8)	Cr1^vii—Cr1—C1^iv	103.11 (10)
La1^xvi—La2—Ge1^xiii	55.083 (13)	Cr1ⁱ—Cr1—C1	50.45 (11)
La1^xvi—La2—Ge1^xiv	147.964 (10)	Cr1ⁱ—Cr1—C1ⁱⁱ	103.11 (10)
La1^xvi—La2—Cr1^vi	98.244 (13)	Cr1ⁱ—Cr1—C1^iv	103.11 (10)
La1^xvi—La2—Cr1^vii	53.041 (13)	C1—Cr1—C1ⁱⁱ	119.45 (4)
La1^xvi—La2—Cr1ⁱ	76.602 (13)	C1—Cr1—C1^iv	119.45 (4)
La1^xvi—La2—C1^vi	79.52 (2)	C1ⁱⁱ—Cr1—C1^iv	119.45 (4)
La1^xvi—La2—C1^xv	113.23 (10)	La1—C1—La1ⁱ	96.09 (19)
La1^xvi—La2—C1^xvi	39.92 (8)	La1—C1—La2^vi	95.78 (7)
La1^xviii—La2—La3	104.871 (7)	La1—C1—La2^vii	95.78 (7)
La1^xviii—La2—Ge1^xii	55.083 (13)	La1—C1—Cr1	92.41 (2)
La1^xviii—La2—Ge1^xiii	97.605 (8)	La1—C1—Cr1ⁱ	171.5 (2)
La1^xviii—La2—Ge1^xiv	147.964 (10)	La1ⁱ—C1—La2^vi	95.78 (7)
La1^xviii—La2—Cr1^vi	98.244 (13)	La1ⁱ—C1—La2^vii	95.78 (7)
La1^xviii—La2—Cr1^vii	76.602 (13)	La1ⁱ—C1—Cr1	171.5 (2)
La1^xviii—La2—Cr1ⁱ	53.041 (13)	La1ⁱ—C1—Cr1ⁱ	92.41 (2)
La1^xviii—La2—C1^vi	113.23 (10)	La2^vi—C1—La2^vii	162.7 (2)
La1^xviii—La2—C1^xv	79.52 (2)	La2^vi—C1—Cr1	83.33 (10)
La1^xviii—La2—C1^xvi	39.92 (8)	La2^vi—C1—Cr1ⁱ	83.33 (10)
La3—La2—Ge1^xii	58.029 (15)	La2^vii—C1—Cr1	83.33 (10)
La3—La2—Ge1^xiii	58.029 (15)	La2^vii—C1—Cr1ⁱ	83.33 (10)
La3—La2—Ge1^xiv	58.029 (15)	Cr1—C1—Cr1ⁱ	79.1 (2)
La3—La2—Cr1^vi	153.589 (14)

Symmetry codes: (i) x, −y+1/2, −z+1/2; (ii) z, x, y; (iii) −z, −x, y; (iv) y, z, x; (v) −y, z, −x; (vi) −x+1/2, −y+1/2, z; (vii) −x+1/2, y, −z+1/2; (viii) y−1/2, x, −z+1/2; (ix) y−1/2, −x+1/2, z; (x) −y, x, z; (xi) −x, z, y; (xii) x, y+1/2, z+1/2; (xiii) z+1/2, x, y+1/2; (xiv) y+1/2, z+1/2, x; (xv) z, −x+1/2, −y+1/2; (xvi) −y+1/2, z, −x+1/2; (xvii) −z+1/2, −x+1/2, y; (xviii) y, −z+1/2, −x+1/2; (xix) −x+1, −y+1, z; (xx) −x+1, y, −z+1; (xxi) x, −y+1, −z+1; (xxii) y, x, −z+1; (xxiii) −y+1, −x+1, −z+1; (xxiv) y, −x+1, z; (xxv) −y+1, x, z; (xxvi) x, y−1/2, z−1/2; (xxvii) y, x−1/2, −z+1/2; (xxviii) y, −x+1/2, z−1/2.

Acknowledgements

Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for support of this research under contract 56764-UNI10. We are likewise grateful to M. C. Aronson for providing access to the Bruker APEXII single-crystal diffractometer at Brookhaven National Laboratory. JWS was supported in part by a Provost's Research Fellowship from Farmingdale State College.

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