Synthesis and crystal structure of La21Cr8-2a Al b Ge7-b C12 [a = 0.22 (2) and b = 0.758 (19)].

Single crystals of a new multinary chromium carbide, La21Cr8-2a Al b Ge7-b C12 (henicosa-lanthanum octa-chromium aluminium hexa-germanium dodeca-carbide), 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 tetra-hedra that are co-centered within regular C octa-hedra. These mutually separated Cr4-aC6 clusters are distributed throughout a three-dimensional framework of Al, Ge, and La. The title compound is isotypic with La21-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.

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 La21Mn8Ge6.2Al0.8C12, 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, La21Cr8−2AlbGe7−C12, [a = 0.22 (2), b = 0.758 (19)].

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. 1 ▸ a is a depiction of the unit cell from along the crystallographic a axis, and Fig. 1 ▸ b 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 Cr4−C6 unit (Fig. 1 ▸ c), an La9Ge6 unit (Fig. 1 ▸ d), and an La12AlGe1− unit (Fig. 1 ▸ e). 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 Cr4−C6 unit, (½, 0, 0) for the La9Ge6 unit, and (0, 0, 0) for the La12AlGe1- unit. Accordingly, La21Cr8−2AlGe7−C12 adopts a structure that is effectively a polyatomic analog of the Heusler structure (Graf et al., 2011 ▸) with composition X 2 YZ, where X = Cr4−C6, Y = La9Ge6, and Z = La12AlGe1− units. Taken together with the appropriate site occupancies, the title composition is thus obtained as X 2 YZ = La21Cr8−2aAlGe7−C12.

Figure 1

(a) A view of the crystal structure of La21Cr8−2AlbGe7−C12 along [100]. (b) The same crystal structure from an arbitrary view above the ab plane. (c) Cr-deficient Cr4−C6 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 Cr4−C6 unit shown in Fig. 1 ▸ c 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 SrCr8−Ga4+O19, a seminal example of a geometrically frustrated magnetic system (Broholm et al., 1990 ▸).

The remaining substructures, namely the La9Ge6 unit shown in Fig. 1 ▸ d and the La12AlGe1− unit shown in Fig. 1 ▸ e 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

La21Cr8−2AlGe7−C12 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.

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, ( ) and (00), required manual culling due to beamstop clipping.

Table 1

Experimental details

Crystal data
Chemical formula	La21Cr7.556Al0.758Ge6.242C12
M r	3927.6
Crystal system, space group	Cubic, F m 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
Δρmax, Δρmin (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 La21MnAlGe7−C12 (Zaikina et al., 2011 ▸) and somewhat lower than the reported ratio of 2.1:4.9 in La21FeAlGe7-C12 (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 La21FeAlGe7−C12. 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 La21Cr8−2AlGe7−C12 with the occupancy parameters a = 0.22 (2) and b = 0.758 (19).

Crystal structure: contains datablock(s) global, I. DOI: 10.1107/S2056989016015668/pk2592sup1.cif

Structure factors: contains datablock(s) global, I. DOI: 10.1107/S2056989016015668/pk2592Isup2.hkl

CCDC reference: 1508202

Additional supporting information: crystallographic information; 3D view; checkCIF report

La21Cr7.556Al0.758Ge6.242C12	Dx = 5.909 Mg m−3
Mr = 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

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

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	Δρmax = 1.07 e Å−3
328 reflections	Δρmin = −0.83 e Å−3
21 parameters	Extinction correction: B-C type 2 (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 810 (150)

	x	y	z	Uiso*/Ueq	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)*

	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

La1—La1i	3.8282 (4)	La2—Ge1xiii	3.2864 (5)
La1—La1ii	3.8859 (3)	La2—Ge1xiv	3.2864 (5)
La1—La1iii	3.8859 (3)	La2—Cr1vi	3.2216 (7)
La1—La1iv	3.8859 (3)	La2—Cr1vii	3.2216 (7)
La1—La1v	3.8859 (3)	La2—Cr1i	3.2216 (7)
La1—La2vi	3.9907 (4)	La2—C1vi	2.8015 (9)
La1—La2vii	3.9907 (4)	La2—C1xv	2.8015 (9)
La1—La2viii	3.9907 (4)	La2—C1xvi	2.8015 (9)
La1—La2ix	3.9907 (4)	Cr1—Cr1vi	2.4821 (9)
La1—Cr1	3.2932 (7)	Cr1—Cr1vii	2.4821 (9)
La1—Cr1x	3.2932 (7)	Cr1—Cr1i	2.4821 (9)
La1—C1	2.574 (4)	Cr1—C1	1.949 (5)
La1—C1xi	2.574 (4)	Cr1—C1ii	1.949 (5)
La2—La3	3.7115 (3)	Cr1—C1iv	1.949 (5)
La2—Ge1xii	3.2864 (5)
La1i—La1—La1ii	120.000 (6)	La3—La2—Cr1vii	153.589 (14)
La1i—La1—La1iii	120.000 (6)	La3—La2—Cr1i	153.589 (14)
La1i—La1—La1iv	120.000 (6)	La3—La2—C1vi	136.07 (12)
La1i—La1—La1v	120.000 (6)	La3—La2—C1xv	136.07 (12)
La1i—La1—La2vi	61.339 (6)	La3—La2—C1xvi	136.07 (12)
La1i—La1—La2vii	61.339 (6)	Ge1xii—La2—Ge1xiii	94.557 (15)
La1i—La1—La2viii	61.339 (6)	Ge1xii—La2—Ge1xiv	94.557 (15)
La1i—La1—La2ix	61.339 (6)	Ge1xii—La2—Cr1vi	131.521 (19)
La1i—La1—Cr1	78.207 (12)	Ge1xii—La2—Cr1vii	131.521 (19)
La1i—La1—Cr1x	78.207 (12)	Ge1xii—La2—Cr1i	95.56 (2)
La1i—La1—C1	41.96 (10)	Ge1xii—La2—C1vi	165.90 (12)
La1i—La1—C1xi	41.96 (10)	Ge1xii—La2—C1xv	95.00 (8)
La1ii—La1—La1iii	90.000 (7)	Ge1xii—La2—C1xvi	95.00 (8)
La1ii—La1—La1iv	60.000 (5)	Ge1xiii—La2—Ge1xiv	94.557 (15)
La1ii—La1—La1v	120.000 (7)	Ge1xiii—La2—Cr1vi	131.521 (19)
La1ii—La1—La2vi	60.865 (6)	Ge1xiii—La2—Cr1vii	95.56 (2)
La1ii—La1—La2vii	101.955 (5)	Ge1xiii—La2—Cr1i	131.521 (19)
La1ii—La1—La2viii	165.127 (7)	Ge1xiii—La2—C1vi	95.00 (8)
La1ii—La1—La2ix	105.813 (7)	Ge1xiii—La2—C1xv	165.90 (12)
La1ii—La1—Cr1	53.844 (12)	Ge1xiii—La2—C1xvi	95.00 (8)
La1ii—La1—Cr1x	142.596 (13)	Ge1xiv—La2—Cr1vi	95.56 (2)
La1ii—La1—C1	84.21 (8)	Ge1xiv—La2—Cr1vii	131.521 (19)
La1ii—La1—C1xi	147.63 (4)	Ge1xiv—La2—Cr1i	131.521 (19)
La1iii—La1—La1iv	120.000 (7)	Ge1xiv—La2—C1vi	95.00 (8)
La1iii—La1—La1v	60.000 (5)	Ge1xiv—La2—C1xv	95.00 (8)
La1iii—La1—La2vi	105.813 (7)	Ge1xiv—La2—C1xvi	165.90 (12)
La1iii—La1—La2vii	165.127 (7)	Cr1vi—La2—Cr1vii	45.314 (17)
La1iii—La1—La2viii	101.955 (5)	Cr1vi—La2—Cr1i	45.314 (17)
La1iii—La1—La2ix	60.865 (6)	Cr1vi—La2—C1vi	36.93 (9)
La1iii—La1—Cr1	142.596 (13)	Cr1vi—La2—C1xv	36.93 (9)
La1iii—La1—Cr1x	53.844 (12)	Cr1vi—La2—C1xvi	70.34 (12)
La1iii—La1—C1	147.63 (4)	Cr1vii—La2—Cr1i	45.314 (17)
La1iii—La1—C1xi	84.21 (8)	Cr1vii—La2—C1vi	36.93 (9)
La1iv—La1—La1v	90.000 (7)	Cr1vii—La2—C1xv	70.34 (12)
La1iv—La1—La2vi	101.955 (5)	Cr1vii—La2—C1xvi	36.93 (9)
La1iv—La1—La2vii	60.865 (6)	Cr1i—La2—C1vi	70.34 (12)
La1iv—La1—La2viii	105.813 (7)	Cr1i—La2—C1xv	36.93 (9)
La1iv—La1—La2ix	165.127 (7)	Cr1i—La2—C1xvi	36.93 (9)
La1iv—La1—Cr1	53.844 (12)	C1vi—La2—C1xv	73.86 (13)
La1iv—La1—Cr1x	142.596 (13)	C1vi—La2—C1xvi	73.86 (13)
La1iv—La1—C1	84.21 (8)	C1xv—La2—C1xvi	73.86 (13)
La1iv—La1—C1xi	147.63 (4)	La2—La3—La2xix	109.471 (6)
La1v—La1—La2vi	165.127 (7)	La2—La3—La2xx	109.471 (6)
La1v—La1—La2vii	105.813 (7)	La2—La3—La2xxi	109.471 (6)
La1v—La1—La2viii	60.865 (6)	La2—La3—La2xxii	70.529 (6)
La1v—La1—La2ix	101.955 (5)	La2—La3—La2xxiii	180.0 (5)
La1v—La1—Cr1	142.596 (13)	La2—La3—La2xxiv	70.529 (6)
La1v—La1—Cr1x	53.844 (12)	La2—La3—La2xxv	70.529 (6)
La1v—La1—C1	147.63 (4)	La2xix—La3—La2xx	109.471 (6)
La1v—La1—C1xi	84.21 (8)	La2xix—La3—La2xxi	109.471 (6)
La2vi—La1—La2vii	87.896 (6)	La2xix—La3—La2xxii	180.0 (5)
La2vi—La1—La2viii	122.677 (8)	La2xix—La3—La2xxiii	70.529 (6)
La2vi—La1—La2ix	64.952 (7)	La2xix—La3—La2xxiv	70.529 (6)
La2vi—La1—Cr1	51.418 (12)	La2xix—La3—La2xxv	70.529 (6)
La2vi—La1—Cr1x	115.315 (13)	La2xx—La3—La2xxi	109.471 (6)
La2vi—La1—C1	44.302 (12)	La2xx—La3—La2xxii	70.529 (6)
La2vi—La1—C1xi	90.13 (7)	La2xx—La3—La2xxiii	70.529 (6)
La2vii—La1—La2viii	64.952 (7)	La2xx—La3—La2xxiv	180.0 (5)
La2vii—La1—La2ix	122.677 (8)	La2xx—La3—La2xxv	70.529 (6)
La2vii—La1—Cr1	51.418 (12)	La2xxi—La3—La2xxii	70.529 (6)
La2vii—La1—Cr1x	115.315 (13)	La2xxi—La3—La2xxiii	70.529 (6)
La2vii—La1—C1	44.302 (12)	La2xxi—La3—La2xxiv	70.529 (6)
La2vii—La1—C1xi	90.13 (7)	La2xxi—La3—La2xxv	180.0 (5)
La2viii—La1—La2ix	87.896 (6)	La2xxii—La3—La2xxiii	109.471 (6)
La2viii—La1—Cr1	115.314 (13)	La2xxii—La3—La2xxiv	109.471 (6)
La2viii—La1—Cr1x	51.418 (12)	La2xxii—La3—La2xxv	109.471 (6)
La2viii—La1—C1	90.13 (7)	La2xxiii—La3—La2xxiv	109.471 (6)
La2viii—La1—C1xi	44.302 (12)	La2xxiii—La3—La2xxv	109.471 (6)
La2ix—La1—Cr1	115.314 (13)	La2xxiv—La3—La2xxv	109.471 (6)
La2ix—La1—Cr1x	51.418 (12)	La2xxvi—Ge1—La2i	134.47 (3)
La2ix—La1—C1	90.13 (7)	La2xxvi—Ge1—La2xxvii	81.389 (12)
La2ix—La1—C1xi	44.302 (12)	La2xxvi—Ge1—La2xxviii	81.389 (12)
Cr1—La1—Cr1x	156.414 (18)	La2i—Ge1—La2xxvii	81.389 (12)
Cr1—La1—C1	36.25 (10)	La2i—Ge1—La2xxviii	81.389 (12)
Cr1—La1—C1xi	120.16 (10)	La2xxvii—Ge1—La2xxviii	134.47 (3)
Cr1x—La1—C1	120.16 (10)	La1—Cr1—La1ii	72.313 (15)
Cr1x—La1—C1xi	36.25 (10)	La1—Cr1—La1iv	72.313 (15)
C1—La1—C1xi	83.91 (14)	La1—Cr1—La2vi	75.541 (15)
La1vi—La2—La1vii	57.323 (6)	La1—Cr1—La2vii	75.541 (15)
La1vi—La2—La1xv	113.653 (7)	La1—Cr1—La2i	139.88 (2)
La1vi—La2—La1xvii	58.269 (6)	La1—Cr1—Cr1vi	142.60 (3)
La1vi—La2—La1xvi	113.653 (7)	La1—Cr1—Cr1vii	142.60 (3)
La1vi—La2—La1xviii	150.254 (8)	La1—Cr1—Cr1i	101.79 (3)
La1vi—La2—La3	104.871 (7)	La1—Cr1—C1	51.34 (11)
La1vi—La2—Ge1xii	147.964 (10)	La1—Cr1—C1ii	113.23 (9)
La1vi—La2—Ge1xiii	97.605 (8)	La1—Cr1—C1iv	113.23 (9)
La1vi—La2—Ge1xiv	55.083 (13)	La1ii—Cr1—La1iv	72.313 (15)
La1vi—La2—Cr1vi	53.041 (13)	La1ii—Cr1—La2vi	75.541 (15)
La1vi—La2—Cr1vii	76.602 (13)	La1ii—Cr1—La2vii	139.88 (2)
La1vi—La2—Cr1i	98.244 (13)	La1ii—Cr1—La2i	75.541 (15)
La1vi—La2—C1vi	39.92 (8)	La1ii—Cr1—Cr1vi	142.60 (3)
La1vi—La2—C1xv	79.52 (2)	La1ii—Cr1—Cr1vii	101.79 (3)
La1vi—La2—C1xvi	113.23 (10)	La1ii—Cr1—Cr1i	142.60 (3)
La1vii—La2—La1xv	150.254 (8)	La1ii—Cr1—C1	113.23 (9)
La1vii—La2—La1xvii	113.653 (7)	La1ii—Cr1—C1ii	51.34 (11)
La1vii—La2—La1xvi	58.269 (6)	La1ii—Cr1—C1iv	113.23 (9)
La1vii—La2—La1xviii	113.653 (7)	La1iv—Cr1—La2vi	139.88 (2)
La1vii—La2—La3	104.871 (7)	La1iv—Cr1—La2vii	75.541 (15)
La1vii—La2—Ge1xii	147.964 (10)	La1iv—Cr1—La2i	75.541 (15)
La1vii—La2—Ge1xiii	55.083 (13)	La1iv—Cr1—Cr1vi	101.79 (3)
La1vii—La2—Ge1xiv	97.605 (8)	La1iv—Cr1—Cr1vii	142.60 (3)
La1vii—La2—Cr1vi	76.602 (13)	La1iv—Cr1—Cr1i	142.60 (3)
La1vii—La2—Cr1vii	53.041 (13)	La1iv—Cr1—C1	113.23 (9)
La1vii—La2—Cr1i	98.244 (13)	La1iv—Cr1—C1ii	113.23 (9)
La1vii—La2—C1vi	39.92 (8)	La1iv—Cr1—C1iv	51.34 (11)
La1vii—La2—C1xv	113.23 (10)	La2vi—Cr1—La2vii	118.56 (2)
La1vii—La2—C1xvi	79.52 (2)	La2vi—Cr1—La2i	118.56 (2)
La1xv—La2—La1xvii	57.323 (6)	La2vi—Cr1—Cr1vi	118.32 (3)
La1xv—La2—La1xvi	113.653 (7)	La2vi—Cr1—Cr1vii	67.34 (2)
La1xv—La2—La1xviii	58.269 (6)	La2vi—Cr1—Cr1i	67.34 (2)
La1xv—La2—La3	104.871 (7)	La2vi—Cr1—C1	59.74 (2)
La1xv—La2—Ge1xii	55.083 (13)	La2vi—Cr1—C1ii	59.74 (2)
La1xv—La2—Ge1xiii	147.964 (10)	La2vi—Cr1—C1iv	168.77 (11)
La1xv—La2—Ge1xiv	97.605 (8)	La2vii—Cr1—La2i	118.56 (2)
La1xv—La2—Cr1vi	76.602 (13)	La2vii—Cr1—Cr1vi	67.34 (2)
La1xv—La2—Cr1vii	98.244 (13)	La2vii—Cr1—Cr1vii	118.32 (3)
La1xv—La2—Cr1i	53.041 (13)	La2vii—Cr1—Cr1i	67.34 (2)
La1xv—La2—C1vi	113.23 (10)	La2vii—Cr1—C1	59.74 (2)
La1xv—La2—C1xv	39.92 (8)	La2vii—Cr1—C1ii	168.77 (11)
La1xv—La2—C1xvi	79.52 (2)	La2vii—Cr1—C1iv	59.74 (2)
La1xvii—La2—La1xvi	150.254 (8)	La2i—Cr1—Cr1vi	67.34 (2)
La1xvii—La2—La1xviii	113.653 (7)	La2i—Cr1—Cr1vii	67.34 (2)
La1xvii—La2—La3	104.871 (7)	La2i—Cr1—Cr1i	118.32 (3)
La1xvii—La2—Ge1xii	97.605 (8)	La2i—Cr1—C1	168.77 (11)
La1xvii—La2—Ge1xiii	147.964 (10)	La2i—Cr1—C1ii	59.74 (2)
La1xvii—La2—Ge1xiv	55.083 (13)	La2i—Cr1—C1iv	59.74 (2)
La1xvii—La2—Cr1vi	53.041 (13)	Cr1vi—Cr1—Cr1vii	60.00 (3)
La1xvii—La2—Cr1vii	98.244 (13)	Cr1vi—Cr1—Cr1i	60.00 (3)
La1xvii—La2—Cr1i	76.602 (13)	Cr1vi—Cr1—C1	103.11 (10)
La1xvii—La2—C1vi	79.52 (2)	Cr1vi—Cr1—C1ii	103.11 (10)
La1xvii—La2—C1xv	39.92 (8)	Cr1vi—Cr1—C1iv	50.45 (11)
La1xvii—La2—C1xvi	113.23 (10)	Cr1vii—Cr1—Cr1i	60.00 (3)
La1xvi—La2—La1xviii	57.323 (6)	Cr1vii—Cr1—C1	103.11 (10)
La1xvi—La2—La3	104.871 (7)	Cr1vii—Cr1—C1ii	50.45 (11)
La1xvi—La2—Ge1xii	97.605 (8)	Cr1vii—Cr1—C1iv	103.11 (10)
La1xvi—La2—Ge1xiii	55.083 (13)	Cr1i—Cr1—C1	50.45 (11)
La1xvi—La2—Ge1xiv	147.964 (10)	Cr1i—Cr1—C1ii	103.11 (10)
La1xvi—La2—Cr1vi	98.244 (13)	Cr1i—Cr1—C1iv	103.11 (10)
La1xvi—La2—Cr1vii	53.041 (13)	C1—Cr1—C1ii	119.45 (4)
La1xvi—La2—Cr1i	76.602 (13)	C1—Cr1—C1iv	119.45 (4)
La1xvi—La2—C1vi	79.52 (2)	C1ii—Cr1—C1iv	119.45 (4)
La1xvi—La2—C1xv	113.23 (10)	La1—C1—La1i	96.09 (19)
La1xvi—La2—C1xvi	39.92 (8)	La1—C1—La2vi	95.78 (7)
La1xviii—La2—La3	104.871 (7)	La1—C1—La2vii	95.78 (7)
La1xviii—La2—Ge1xii	55.083 (13)	La1—C1—Cr1	92.41 (2)
La1xviii—La2—Ge1xiii	97.605 (8)	La1—C1—Cr1i	171.5 (2)
La1xviii—La2—Ge1xiv	147.964 (10)	La1i—C1—La2vi	95.78 (7)
La1xviii—La2—Cr1vi	98.244 (13)	La1i—C1—La2vii	95.78 (7)
La1xviii—La2—Cr1vii	76.602 (13)	La1i—C1—Cr1	171.5 (2)
La1xviii—La2—Cr1i	53.041 (13)	La1i—C1—Cr1i	92.41 (2)
La1xviii—La2—C1vi	113.23 (10)	La2vi—C1—La2vii	162.7 (2)
La1xviii—La2—C1xv	79.52 (2)	La2vi—C1—Cr1	83.33 (10)
La1xviii—La2—C1xvi	39.92 (8)	La2vi—C1—Cr1i	83.33 (10)
La3—La2—Ge1xii	58.029 (15)	La2vii—C1—Cr1	83.33 (10)
La3—La2—Ge1xiii	58.029 (15)	La2vii—C1—Cr1i	83.33 (10)
La3—La2—Ge1xiv	58.029 (15)	Cr1—C1—Cr1i	79.1 (2)
La3—La2—Cr1vi	153.589 (14)