Crystal and electronic structures of La₂LiGe_6-x (x = 0.21) and La₂LiGe₄Si₂

The synthesis and characterization of a new ternary di­lanthanum lithium hexa­germanide, La₂LiGe_6-x (x = 0.21), belonging to the Pr₂LiGe₆ structure type, and a quaternary dilanthanum lithium tetra­ger­man­ium disilicide, La₂LiGe₄Si₂, which crystallizes as an ordered variant of this type, are reported. In both structures, Li is on a site of mmm symmetry. All other atoms are on sites of m2m symmetry. These structures are new representatives of a homologous linear structure series based on structural fragments of the AlB₂, CaF₂ and ZrSi₂ structure types. The observed 17-vertex polyhedra are typical for La atoms and the environment of the Li atom is cubic. Two Ge atoms are enclosed in a tetra­gonal prism with one added atom (nine-vertex polyhedron). The trigonal prismatic coordination is typical for Ge or Si atoms. The metallic nature of the bonding is indicated by the inter­atomic distances and electronic structure calculations.

S1. Comment

The reaction of rare earth metals (RE) with lithium and the p-elements of group IV (Si, Ge and Sn) resulted in an isostructural series of compounds: RELiGe₂ (Pavlyuk et al., 1986), RE₂Li₂Ge₃ (Pavlyuk, Pecharskii, Bodak & Bruskov, 1988; Pavlyuk, Pecharskii & Bodak, 1989), RELiSn₂ (Pavlyuk, Bodak et al., 1989), RE₄LiGe₄ (Pavlyuk et al., 1990), RELiGe (Pavlyuk et al., 1991; Pavlyuk & Bodak, 1992a) and RE₃Li₂Ge₃ (Pavlyuk & Bodak, 1992b). A new ternary germanide, RE₂LiGe₆ (RE = Ce and Pr), which crystallizes in an orthorhombic structure with the space group Cmmm, was detected earlier during the systematic study of ternary germanium-rich alloys of Ce–Li–Ge and Pr–Li–Ge systems (Pavlyuk, Pecharskii & Bodak, 1988).

During a systematic study of ternary La–Li–Ge alloys synthesized with a high content of Ge, a new ternary phase was detected. The powder diffraction pattern of this compound was similar to that of the RE₂LiGe₆ (RE = Ce and Pr) ternary phases, but had added reflections which belonged to another phase. Substitution of some of the Ge atoms by Si in La₂LiGe_6-xSi_x quaternary alloys with x = 2.0 altered the unit-cell dimensions. [Please check rephrasing] Also at this composition, there was a significant decrease in the intensities of the [041], [151], [170] and [171] reflections and an increase in the intensities of the [001], [110] and other reflections. It appeared very likely that these changes were connected with an ordering process. It was decided to investigate these ternary and quaternary phases further using single-crystal methods.

The single-crystal data proved that both La₂LiGe₆, (I), and La₂LiGe₄Si₂, (II), crystallize in the same orthorhombic crystal system in the space group Cmmm, with 18 atoms per unit cell. The La atoms in both structures occupy the 4i site anf the Li atoms are located on the 2a site. In (I), all the Ge atoms occupy 4j sites, whereas in (II) one of these sites is fully occupied by Si atoms. Disorder in La₂LiGe_6-x occurs as the Ge atoms are partially displaced from a single site. The presence of these defects may lead to a limited homogeneity range for La₂LiGe_6-x. [Please check rephrasing]

Although (I) and (II) are very similar to the Pr₂LiGe₆ structure (Pavlyuk, Pecharskii & Bodak, 1988) in terms of having the same space group, the same Wyckoff positions and similar lattice parameters, quaternary (II) cannot be treated as being isostructural with it. According to the classification scheme of Krypyakevich (1977), an ordered variant must be treated as a new structure type.

A projection of the unit cell and the coordination polyhedra of the atoms for (II) are shown in Fig. 1. A detailed analysis shows that, in the case of (II), the Si atom has trigonal prismatic coordination with two additional capping atoms [coordination number (CN) = 8], i.e. Ge1 and Ge2 are enclosed in a tetragonal prism with one added atom (nine-vertex polyhedron). The 17-vertex polyhedron is typical for an La atom and the environment of the Li atom is cubic.

The title compounds may be viewed as the first intermetallic representatives of the novel homologous series based on the CaF₂, ZrSi₂ and AlB₂ structure types (Fig. 2). The general formula of the ternary series is R_m+nM_kX_2(k+m+n) and that of the quaternary series is R_m+nM_kX'_2(k+n)X''_{2 m} (m = number of blocks of AlB₂-type trigonal prisms, n = number of blocks of ZrSi₂-type empty tetragonal antiprisms and k = number of blocks of CaF₂-type filled and empty cubes). For the title compounds, m = n = k = 2 and the compositions of fragments are: LiGe₂ (for the CaF₂ block), LaGe₂ (for the ZrSi₂ block) and LaGe₂ in (I) or LaSi₂ in (II) (for the AlB₂ block). The combinations of these fragments in the unit cell gives the compositions of the title compounds as:

2LaSi₂ +2LaGe₂ + 2LiGe₂ = La₄Li₂Ge₈Si₄ = 2La₂LiGe₄Si₂

or

2LaGe₂ +2LaGe₂ + 2LiGe₂ = La₄Li₂Ge₁₂ = 2La₂LiGe₆.

Among the known structure types similar to the title compounds is Lu₂NiSn₆ (Skolozdra et al., 1985). The main diffrerence between that structure type and the present one is a difference in the location of the trigonal prism and the filled cubes.

The electronic structures of the title compounds were calculated using the tight-binding linear muffin-tin orbital (TB–LMTO) method in the atomic spheres approximation (TB–LMTO–ASA; Andersen, 1975; Andersen & Jepsen, 1984; Andersen et al., 1985, 1986), using the experimental crystallographic data reported here. The exchange and correlation were interpreted in the local density approximation (von Barth & Hedin, 1972).

The La and Li atoms donate their electrons to the Ge and Si atoms. Therefore, positive charge density can be observed around the rare earth and Li atoms, and negative charge density is present around the Ge atoms in phase (I) or the Ge and Si atoms in phase (II) (Fig. 3). The dominant type of bonding in this compound is metallic. However, Ge—Ge and Si—Si covalent dumb-bells are also observed. Similar covalent dumb-bells were observed in La₄Mg₅Ge₆ (Solokha et al., 2012), Tb₄Zn₅Ge₆ (Chumak et al., 2006) and Gd₄Zn₅Ge₆ (Kranenberg et al., 2001).

The total and partial density of states for La₂LiGe₆ and La₂LiGe₄Si₂ (Figs. 4a and 4b, respectively) in the region below E_F exhibit significant mixing between the La and Ge states in phase (I), and a decrease of this mixing in the case of phase (II). The region above E_F consists mostly of La 5d orbitals and Ge p orbitals. The Si and Ge s-type states are mainly close to the lower valence band (from -12.0 eV to <-7.5 eV). The higher occupation number of electronic states at the Fermi level for La₂LiGe₆ than for La₂LiGe₄Si₂ indicates a more metallic behaviour.

The crystal orbital Hamilton population (COHP) and integrated COHP (iCOHP) calculations were used to obtain a quantitative evaluation of the bonding strength between the different types of atoms. From the COHP curves for both phases (Fig. 5), it can be concluded that the strongest interactions are between Ge1—Ge1 atoms [δ = 2.451 Å and -iCOHP = 3.425 eV for (I), and δ = 2.381 Å and -iCOHP = 3.796 eV for (II)] and between Ge2—Ge2 atoms [δ = 2.423 Å and -iCOHP = 3.441 eV for (I), and δ = 2.389 Å and -iCOHP = 3.547 eV for (II)]. These atoms in both structures are enclosed by a tetragonal prism. The Si1···Si1 interaction in (II) (δ = 2.581 Å and -iCOHP = 2.162 eV) and the Ge3···Ge3 interaction in (I) (δ = 2.594 Å and -iCOHP = 2.060 eV), which are enclosed by a trigonal prism, are weak. These results indicate that the strength of Ge···Ge and Si···Si covalent interactions depends significantly on the type of coordination.

Related literature

For related literature, see: Andersen (1975); Andersen & Jepsen (1984); Andersen et al. (1985, 1986); Barth & Hedin (1972); Chumak et al. (2006); Kranenberg et al. (2001); Krypyakevich (1977); Pavlyuk & Bodak (1992a, 1992b); Pavlyuk et al. (1986, 1990, 1991); Pavlyuk, Bodak, Pecharskii, Skolozdra & Gladyshevskii (1989); Pavlyuk, Pecharskii & Bodak (1988, 1989); Pavlyuk, Pecharskii, Bodak & Bruskov (1988); Skolozdra et al. (1985); Solokha et al. (2012).

S2. Experimental

Lanthanum, lithium, germanium and silicon, all with a nominal purity greater than 99.9 wt.%, were used as starting materials. First, pieces of the pure metals with stoichiometries La₂₂Li₁₂Ge₆₆, La₂₂Li₁₂Ge₆₀Si₆ and La₂₂Li₁₂Ge₄₄Si₁₂ were pressed into pellets, then enclosed in a tantalum crucible and placed in a resistance furnace with a thermocouple controller. The heating rate from room temperature to 670 K was 5 K min^-1. The alloy was kept at this temperature for 2 d and then the temperature was increased from 670 to 1070 K over a period of 1 h. The alloy was then annealed at this temperature for 6 h and slowly cooled to room temperature. After these melting and annealing procedures, the total weight loss was less than 2%. Small good quality single crystals of (I) and (II) were isolated from the La₂₂Li₁₂Ge₆₆ and La₂₂Li₁₂Ge₄₄Si₁₂ alloys.

S3. Refinement

The structures of (I) and (II) were solved after applying an analytical absorption correction. In the first stage of the structure solution, the positions of the La, Ge and Si atoms were obtained correctly by direct methods. For (I), the residual factor R1 = 0.030 after refinement of the La and Ge atoms and the highest difference peak was 6.54 e Å^-3. For (II), R1 = 0.032 after refinement of the La, Ge and Si atoms and the highest difference peak was 7.58 e Å^-3. The remaining Li atoms were located in subsequent difference Fourier syntheses and, after refinement of their parameters, R1 reduced to 0.024 for (I) and 0.020 for (II), and the highest difference peaks decreased to 1.20 e Å^-3 for (I) and 1.15 e Å^-3 for (II). However, in (I), the Ge1 position showed a displacement parameter considerably different from those of the other Ge atoms, suggesting that this position is only partially occupied by the Ge atom.

Computing details

For both compounds, data collection: CrysAlis CCD (Oxford Diffraction, 2008); cell refinement: CrysAlis CCD (Oxford Diffraction, 2008); data reduction: CrysAlis RED (Oxford Diffraction, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2006); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures

	Fig. 1. A projection of the unit cell and coordination polyhedra of the atoms for La2LiGe4Si2, (II).
	Fig. 2. The packing of the AlB2, ZrSi2 and CaF2 fragments in the unit cell of La2LiGe4Si2, (II).
	Fig. 3. (a) The electron localization function (ELF) mapping and (b) isosurfaces of the ELF around the atoms for La2LiGe6, (I), and La2LiGe4Si2, (II).
	Fig. 4. The total and partial density of states for (a) La2LiGe6, (I), and (b) La2LiGe4Si2, (II).
	Fig. 5. -COHP curves for: (a) and (b) La2LiGe6, (I); and (c), (d) and (e) La2LiGe4Si2, (II).

(I) dilanthanum lithium hexagermanide

Crystal data

La2LiGe5.79	F(000) = 605.2
Mr = 1410.11	Dx = 6.032 Mg m^−3
Orthorhombic, Cmmm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2 2	Cell parameters from 289 reflections
a = 4.1871 (1) Å	θ = 3.9–27.6°
b = 21.1132 (6) Å	µ = 32.73 mm^−1
c = 4.3912 (1) Å	T = 293 K
V = 388.20 (2) Å^3	Plate, metallic dark grey
Z = 1	0.14 × 0.12 × 0.02 mm

Data collection

Oxford Xcalibur3 CCD area-detector diffractometer	290 independent reflections
Radiation source: fine-focus sealed tube	289 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.034
Detector resolution: 0 pixels mm^-1	θmax = 27.6°, θmin = 3.9°
ω scans	h = −5→5
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2008)	k = −27→27
Tmin = 0.015, Tmax = 0.528	l = −5→5
1770 measured reflections

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.024	Secondary atom site location: difference Fourier map
wR(F^2) = 0.059	w = 1/[σ^2(Fo^2) + (0.P)^2 + 14.9101P] where P = (Fo^2 + 2Fc^2)/3
S = 1.20	(Δ/σ)max < 0.001
290 reflections	Δρmax = 1.20 e Å^−3
21 parameters	Δρmin = −0.98 e Å^−3

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
La1	0.0000	0.16551 (3)	0.0000	0.0114 (2)
Ge1	0.0000	0.05806 (7)	0.5000	0.0179 (5)	0.896 (8)
Ge2	0.0000	0.44262 (6)	0.0000	0.0152 (3)
Ge3	0.0000	0.28626 (6)	0.5000	0.0155 (3)
Li1	0.0000	0.0000	0.0000	0.018 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
La1	0.0096 (3)	0.0127 (3)	0.0118 (3)	0.000	0.000	0.000
Ge1	0.0164 (8)	0.0201 (8)	0.0171 (8)	0.000	0.000	0.000
Ge2	0.0131 (6)	0.0185 (6)	0.0140 (6)	0.000	0.000	0.000
Ge3	0.0132 (6)	0.0194 (6)	0.0139 (6)	0.000	0.000	0.000
Li1	0.022 (15)	0.015 (13)	0.018 (15)	0.000	0.000	0.000

Geometric parameters (Å, º)

La1—Ge2^i	3.0975 (10)	Ge2—La1^i	3.0975 (10)
La1—Ge2^ii	3.0975 (10)	Ge2—La1^ii	3.0975 (10)
La1—Ge1^iii	3.1571 (12)	Ge3—Ge3^v	2.5936 (16)
La1—Ge1	3.1571 (12)	Ge3—Ge3^iv	2.5936 (16)
La1—Ge3^iv	3.2001 (5)	Ge3—La1^iv	3.2001 (5)
La1—Ge3^i	3.2001 (5)	Ge3—La1^i	3.2001 (5)
La1—Ge3^v	3.2001 (5)	Ge3—La1^ii	3.2001 (5)
La1—Ge3^ii	3.2001 (5)	Ge3—La1^v	3.2001 (5)
La1—Ge3	3.3646 (11)	Ge3—La1^vii	3.3646 (11)
La1—Ge3^iii	3.3646 (11)	Li1—Ge2^ii	2.4188 (6)
La1—Li1	3.4944 (6)	Li1—Ge2^xi	2.4188 (6)
Ge1—Ge1^vi	2.451 (3)	Li1—Ge2^i	2.4188 (6)
Ge1—Li1	2.5146 (7)	Li1—Ge2^xii	2.4188 (6)
Ge1—Li1^vii	2.5146 (7)	Li1—Ge1^xiii	2.5146 (7)
Ge1—La1^vii	3.1571 (12)	Li1—Ge1^vi	2.5146 (7)
Ge2—Li1^viii	2.4188 (6)	Li1—Ge1^iii	2.5146 (7)
Ge2—Li1^ix	2.4188 (6)	Li1—La1^xiii	3.4944 (6)
Ge2—Ge2^x	2.423 (3)
Ge2^i—La1—Ge2^ii	85.04 (3)	Li1^ix—Ge2—La1^i	77.534 (14)
Ge2^i—La1—Ge1^iii	58.022 (17)	Ge2^x—Ge2—La1^i	137.478 (17)
Ge2^ii—La1—Ge1^iii	58.022 (17)	Li1^viii—Ge2—La1^ii	77.534 (14)
Ge2^i—La1—Ge1	58.022 (17)	Li1^ix—Ge2—La1^ii	162.58 (4)
Ge2^ii—La1—Ge1	58.022 (17)	Ge2^x—Ge2—La1^ii	137.478 (17)
Ge1^iii—La1—Ge1	88.13 (4)	La1^i—Ge2—La1^ii	85.04 (3)
Ge2^i—La1—Ge3^iv	132.59 (2)	Ge3^v—Ge3—Ge3^iv	107.64 (9)
Ge2^ii—La1—Ge3^iv	78.02 (2)	Ge3^v—Ge3—La1^iv	135.72 (2)
Ge1^iii—La1—Ge3^iv	134.90 (2)	Ge3^iv—Ge3—La1^iv	70.111 (17)
Ge1—La1—Ge3^iv	75.61 (2)	Ge3^v—Ge3—La1^i	70.111 (17)
Ge2^i—La1—Ge3^i	78.02 (2)	Ge3^iv—Ge3—La1^i	135.72 (2)
Ge2^ii—La1—Ge3^i	132.59 (2)	La1^iv—Ge3—La1^i	142.89 (5)
Ge1^iii—La1—Ge3^i	75.61 (2)	Ge3^v—Ge3—La1^ii	135.72 (2)
Ge1—La1—Ge3^i	134.90 (2)	Ge3^iv—Ge3—La1^ii	70.111 (17)
Ge3^iv—La1—Ge3^i	142.89 (5)	La1^iv—Ge3—La1^ii	86.644 (16)
Ge2^i—La1—Ge3^v	78.02 (2)	La1^i—Ge3—La1^ii	81.719 (14)
Ge2^ii—La1—Ge3^v	132.59 (2)	Ge3^v—Ge3—La1^v	70.111 (17)
Ge1^iii—La1—Ge3^v	134.90 (2)	Ge3^iv—Ge3—La1^v	135.72 (2)
Ge1—La1—Ge3^v	75.61 (2)	La1^iv—Ge3—La1^v	81.719 (14)
Ge3^iv—La1—Ge3^v	81.719 (14)	La1^i—Ge3—La1^v	86.644 (16)
Ge3^i—La1—Ge3^v	86.644 (16)	La1^ii—Ge3—La1^v	142.89 (5)
Ge2^i—La1—Ge3^ii	132.59 (2)	Ge3^v—Ge3—La1	63.43 (4)
Ge2^ii—La1—Ge3^ii	78.02 (2)	Ge3^iv—Ge3—La1	63.43 (4)
Ge1^iii—La1—Ge3^ii	75.61 (2)	La1^iv—Ge3—La1	133.54 (2)
Ge1—La1—Ge3^ii	134.90 (2)	La1^i—Ge3—La1	78.078 (17)
Ge3^iv—La1—Ge3^ii	86.644 (16)	La1^ii—Ge3—La1	78.078 (17)
Ge3^i—La1—Ge3^ii	81.719 (14)	La1^v—Ge3—La1	133.54 (2)
Ge3^v—La1—Ge3^ii	142.89 (5)	Ge3^v—Ge3—La1^vii	63.43 (4)
Ge2^i—La1—Ge3	123.949 (13)	Ge3^iv—Ge3—La1^vii	63.43 (4)
Ge2^ii—La1—Ge3	123.949 (13)	La1^iv—Ge3—La1^vii	78.078 (17)
Ge1^iii—La1—Ge3	176.67 (3)	La1^i—Ge3—La1^vii	133.54 (2)
Ge1—La1—Ge3	95.20 (2)	La1^ii—Ge3—La1^vii	133.54 (2)
Ge3^iv—La1—Ge3	46.46 (2)	La1^v—Ge3—La1^vii	78.078 (17)
Ge3^i—La1—Ge3	101.922 (17)	La1—Ge3—La1^vii	81.47 (3)
Ge3^v—La1—Ge3	46.46 (2)	Ge2^ii—Li1—Ge2^xi	180.00 (5)
Ge3^ii—La1—Ge3	101.922 (17)	Ge2^ii—Li1—Ge2^i	119.89 (5)
Ge2^i—La1—Ge3^iii	123.949 (13)	Ge2^xi—Li1—Ge2^i	60.11 (5)
Ge2^ii—La1—Ge3^iii	123.949 (13)	Ge2^ii—Li1—Ge2^xii	60.11 (5)
Ge1^iii—La1—Ge3^iii	95.20 (2)	Ge2^xi—Li1—Ge2^xii	119.89 (5)
Ge1—La1—Ge3^iii	176.67 (3)	Ge2^i—Li1—Ge2^xii	180.00 (5)
Ge3^iv—La1—Ge3^iii	101.922 (17)	Ge2^ii—Li1—Ge1^xiii	104.131 (17)
Ge3^i—La1—Ge3^iii	46.46 (2)	Ge2^xi—Li1—Ge1^xiii	75.869 (17)
Ge3^v—La1—Ge3^iii	101.922 (17)	Ge2^i—Li1—Ge1^xiii	104.131 (17)
Ge3^ii—La1—Ge3^iii	46.46 (2)	Ge2^xii—Li1—Ge1^xiii	75.869 (17)
Ge3—La1—Ge3^iii	81.47 (3)	Ge2^ii—Li1—Ge1	75.869 (17)
Ge2^i—La1—Li1	42.522 (17)	Ge2^xi—Li1—Ge1	104.131 (17)
Ge2^ii—La1—Li1	42.522 (17)	Ge2^i—Li1—Ge1	75.869 (17)
Ge1^iii—La1—Li1	44.06 (2)	Ge2^xii—Li1—Ge1	104.131 (17)
Ge1—La1—Li1	44.06 (2)	Ge1^xiii—Li1—Ge1	180.00 (6)
Ge3^iv—La1—Li1	108.56 (2)	Ge2^ii—Li1—Ge1^vi	104.131 (17)
Ge3^i—La1—Li1	108.56 (2)	Ge2^xi—Li1—Ge1^vi	75.869 (17)
Ge3^v—La1—Li1	108.56 (2)	Ge2^i—Li1—Ge1^vi	104.131 (17)
Ge3^ii—La1—Li1	108.56 (2)	Ge2^xii—Li1—Ge1^vi	75.869 (17)
Ge3—La1—Li1	139.265 (16)	Ge1^xiii—Li1—Ge1^vi	121.65 (6)
Ge3^iii—La1—Li1	139.265 (16)	Ge1—Li1—Ge1^vi	58.35 (6)
Ge2^i—La1—La1^ii	167.88 (2)	Ge2^ii—Li1—Ge1^iii	75.869 (17)
Ge2^ii—La1—La1^ii	107.074 (16)	Ge2^xi—Li1—Ge1^iii	104.131 (17)
Ge1^iii—La1—La1^ii	128.299 (15)	Ge2^i—Li1—Ge1^iii	75.869 (17)
Ge1—La1—La1^ii	128.299 (15)	Ge2^xii—Li1—Ge1^iii	104.131 (17)
Ge3^iv—La1—La1^ii	52.73 (2)	Ge1^xiii—Li1—Ge1^iii	58.35 (6)
Ge3^i—La1—La1^ii	93.24 (3)	Ge1—Li1—Ge1^iii	121.65 (6)
Ge3^v—La1—La1^ii	93.24 (3)	Ge1^vi—Li1—Ge1^iii	180.00 (6)
Ge3^ii—La1—La1^ii	52.73 (2)	Ge2^ii—Li1—La1^xiii	120.06 (3)
Ge3—La1—La1^ii	49.191 (15)	Ge2^xi—Li1—La1^xiii	59.94 (3)
Ge3^iii—La1—La1^ii	49.191 (15)	Ge2^i—Li1—La1^xiii	120.06 (3)
Li1—La1—La1^ii	149.597 (9)	Ge2^xii—Li1—La1^xiii	59.94 (3)
Ge1^vi—Ge1—Li1	60.83 (3)	Ge1^xiii—Li1—La1^xiii	60.83 (3)
Ge1^vi—Ge1—Li1^vii	60.83 (3)	Ge1—Li1—La1^xiii	119.17 (3)
Li1—Ge1—Li1^vii	121.65 (6)	Ge1^vi—Li1—La1^xiii	60.83 (3)
Ge1^vi—Ge1—La1^vii	135.94 (2)	Ge1^iii—Li1—La1^xiii	119.17 (3)
Li1—Ge1—La1^vii	163.24 (5)	Ge2^ii—Li1—La1	59.94 (3)
Li1^vii—Ge1—La1^vii	75.110 (14)	Ge2^xi—Li1—La1	120.06 (3)
Ge1^vi—Ge1—La1	135.94 (2)	Ge2^i—Li1—La1	59.94 (3)
Li1—Ge1—La1	75.110 (14)	Ge2^xii—Li1—La1	120.06 (3)
Li1^vii—Ge1—La1	163.24 (5)	Ge1^xiii—Li1—La1	119.17 (3)
La1^vii—Ge1—La1	88.13 (4)	Ge1—Li1—La1	60.83 (3)
Li1^viii—Ge2—Li1^ix	119.89 (5)	Ge1^vi—Li1—La1	119.17 (3)
Li1^viii—Ge2—Ge2^x	59.94 (3)	Ge1^iii—Li1—La1	60.83 (3)
Li1^ix—Ge2—Ge2^x	59.94 (3)	La1^xiii—Li1—La1	180.0
Li1^viii—Ge2—La1^i	162.58 (4)

Symmetry codes: (i) −x−1/2, −y+1/2, −z; (ii) −x+1/2, −y+1/2, −z; (iii) x, y, z−1; (iv) −x+1/2, −y+1/2, −z+1; (v) −x−1/2, −y+1/2, −z+1; (vi) −x, −y, −z+1; (vii) x, y, z+1; (viii) x+1/2, y+1/2, z; (ix) x−1/2, y+1/2, z; (x) −x, −y+1, −z; (xi) x−1/2, y−1/2, z; (xii) x+1/2, y−1/2, z; (xiii) −x, −y, −z.

(II) dilanthanum lithium tetragermanium disilicide

Crystal data

La2LiGe4Si2	F(000) = 546
Mr = 631.38	Dx = 5.493 Mg m^−3
Orthorhombic, Cmmm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2 2	Cell parameters from 289 reflections
a = 4.1462 (1) Å	θ = 3.9–27.8°
b = 21.0674 (6) Å	µ = 26.69 mm^−1
c = 4.3704 (1) Å	T = 293 K
V = 381.75 (2) Å^3	Plate, metallic dark grey
Z = 2	0.12 × 0.09 × 0.03 mm

Data collection

Oxford Xcalibur3 CCD area-detector diffractometer	290 independent reflections
Radiation source: fine-focus sealed tube	289 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.073
Detector resolution: 0 pixels mm^-1	θmax = 27.8°, θmin = 3.9°
ω scans	h = −5→5
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2008)	k = −27→27
Tmin = 0.074, Tmax = 0.451	l = −5→5
1770 measured reflections

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.020	Secondary atom site location: difference Fourier map
wR(F^2) = 0.045	w = 1/[σ^2(Fo^2) + (0.P)^2 + 0.5539P] where P = (Fo^2 + 2Fc^2)/3
S = 1.20	(Δ/σ)max < 0.001
290 reflections	Δρmax = 1.15 e Å^−3
18 parameters	Δρmin = −1.62 e Å^−3

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
La1	0.0000	0.165371 (18)	0.0000	0.01556 (16)
Ge1	0.0000	0.05651 (3)	0.5000	0.0146 (2)
Ge2	0.0000	0.44330 (3)	0.0000	0.0140 (2)
Si1	0.0000	0.28647 (10)	0.5000	0.0159 (4)
Li1	0.0000	0.0000	0.0000	0.011 (3)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
La1	0.01094 (19)	0.0230 (2)	0.0128 (3)	0.000	0.000	0.000
Ge1	0.0125 (3)	0.0203 (4)	0.0112 (5)	0.000	0.000	0.000
Ge2	0.0122 (3)	0.0193 (4)	0.0105 (4)	0.000	0.000	0.000
Si1	0.0131 (7)	0.0249 (9)	0.0099 (12)	0.000	0.000	0.000

Geometric parameters (Å, º)

La1—Ge2^i	3.0885 (6)	Ge2—La1^i	3.0885 (6)
La1—Ge2^ii	3.0885 (6)	Ge2—La1^ii	3.0885 (6)
La1—Ge1^iii	3.1679 (6)	Si1—Si1^v	2.581 (2)
La1—Ge1	3.1679 (6)	Si1—Si1^iv	2.581 (2)
La1—Si1^iv	3.1784 (7)	Si1—La1^iv	3.1784 (7)
La1—Si1^i	3.1784 (7)	Si1—La1^i	3.1784 (7)
La1—Si1^v	3.1784 (7)	Si1—La1^v	3.1784 (7)
La1—Si1^ii	3.1784 (7)	Si1—La1^ii	3.1784 (7)
La1—Si1	3.3592 (16)	Si1—La1^vii	3.3592 (16)
La1—Si1^iii	3.3592 (16)	Li1—Ge2^ii	2.3926 (3)
La1—Li1	3.4839 (4)	Li1—Ge2^xi	2.3926 (3)
Ge1—Ge1^vi	2.3808 (14)	Li1—Ge2^i	2.3926 (3)
Ge1—Li1	2.4884 (3)	Li1—Ge2^xii	2.3926 (3)
Ge1—Li1^vii	2.4884 (3)	Li1—Ge1^xiii	2.4884 (3)
Ge1—La1^vii	3.1679 (6)	Li1—Ge1^iii	2.4884 (3)
Ge2—Ge2^viii	2.3891 (14)	Li1—Ge1^vi	2.4884 (3)
Ge2—Li1^ix	2.3926 (3)	Li1—La1^xiii	3.4839 (4)
Ge2—Li1^x	2.3926 (3)
Ge2^i—La1—Ge2^ii	84.32 (2)	Li1^ix—Ge2—La1^i	162.11 (2)
Ge2^i—La1—Ge1^iii	57.543 (9)	Li1^x—Ge2—La1^i	77.789 (8)
Ge2^ii—La1—Ge1^iii	57.543 (9)	Ge2^viii—Ge2—La1^ii	137.838 (10)
Ge2^i—La1—Ge1	57.543 (9)	Li1^ix—Ge2—La1^ii	77.789 (8)
Ge2^ii—La1—Ge1	57.543 (9)	Li1^x—Ge2—La1^ii	162.11 (2)
Ge1^iii—La1—Ge1	87.23 (2)	La1^i—Ge2—La1^ii	84.32 (2)
Ge2^i—La1—Si1^iv	132.41 (3)	Si1^v—Si1—Si1^iv	106.90 (15)
Ge2^ii—La1—Si1^iv	78.39 (3)	Si1^v—Si1—La1^iv	135.57 (3)
Ge1^iii—La1—Si1^iv	134.86 (3)	Si1^iv—Si1—La1^iv	70.49 (2)
Ge1—La1—Si1^iv	75.93 (3)	Si1^v—Si1—La1^i	70.49 (2)
Ge2^i—La1—Si1^i	78.39 (3)	Si1^iv—Si1—La1^i	135.57 (3)
Ge2^ii—La1—Si1^i	132.41 (3)	La1^iv—Si1—La1^i	142.77 (7)
Ge1^iii—La1—Si1^i	75.93 (3)	Si1^v—Si1—La1^v	70.49 (2)
Ge1—La1—Si1^i	134.86 (3)	Si1^iv—Si1—La1^v	135.57 (3)
Si1^iv—La1—Si1^i	142.77 (7)	La1^iv—Si1—La1^v	81.42 (2)
Ge2^i—La1—Si1^v	78.39 (3)	La1^i—Si1—La1^v	86.87 (2)
Ge2^ii—La1—Si1^v	132.41 (3)	Si1^v—Si1—La1^ii	135.57 (3)
Ge1^iii—La1—Si1^v	134.86 (3)	Si1^iv—Si1—La1^ii	70.49 (2)
Ge1—La1—Si1^v	75.93 (3)	La1^iv—Si1—La1^ii	86.87 (2)
Si1^iv—La1—Si1^v	81.42 (2)	La1^i—Si1—La1^ii	81.42 (2)
Si1^i—La1—Si1^v	86.87 (2)	La1^v—Si1—La1^ii	142.77 (7)
Ge2^i—La1—Si1^ii	132.41 (3)	Si1^v—Si1—La1	63.11 (6)
Ge2^ii—La1—Si1^ii	78.39 (3)	Si1^iv—Si1—La1	63.11 (6)
Ge1^iii—La1—Si1^ii	75.93 (3)	La1^iv—Si1—La1	133.60 (4)
Ge1—La1—Si1^ii	134.86 (3)	La1^i—Si1—La1	78.182 (18)
Si1^iv—La1—Si1^ii	86.87 (2)	La1^v—Si1—La1	133.60 (4)
Si1^i—La1—Si1^ii	81.42 (2)	La1^ii—Si1—La1	78.182 (18)
Si1^v—La1—Si1^ii	142.77 (7)	Si1^v—Si1—La1^vii	63.11 (6)
Ge2^i—La1—Si1	124.262 (14)	Si1^iv—Si1—La1^vii	63.11 (6)
Ge2^ii—La1—Si1	124.262 (14)	La1^iv—Si1—La1^vii	78.182 (18)
Ge1^iii—La1—Si1	176.97 (3)	La1^i—Si1—La1^vii	133.60 (4)
Ge1—La1—Si1	95.81 (2)	La1^v—Si1—La1^vii	78.182 (18)
Si1^iv—La1—Si1	46.40 (4)	La1^ii—Si1—La1^vii	133.60 (4)
Si1^i—La1—Si1	101.818 (17)	La1—Si1—La1^vii	81.16 (5)
Si1^v—La1—Si1	46.40 (4)	Ge2^ii—Li1—Ge2^xi	180.00 (3)
Si1^ii—La1—Si1	101.818 (18)	Ge2^ii—Li1—Ge2^i	120.10 (3)
Ge2^i—La1—Si1^iii	124.262 (14)	Ge2^xi—Li1—Ge2^i	59.90 (3)
Ge2^ii—La1—Si1^iii	124.262 (14)	Ge2^ii—Li1—Ge2^xii	59.90 (3)
Ge1^iii—La1—Si1^iii	95.81 (2)	Ge2^xi—Li1—Ge2^xii	120.10 (3)
Ge1—La1—Si1^iii	176.97 (3)	Ge2^i—Li1—Ge2^xii	180.00 (3)
Si1^iv—La1—Si1^iii	101.818 (18)	Ge2^ii—Li1—Ge1^xiii	103.818 (9)
Si1^i—La1—Si1^iii	46.40 (4)	Ge2^xi—Li1—Ge1^xiii	76.182 (9)
Si1^v—La1—Si1^iii	101.818 (18)	Ge2^i—Li1—Ge1^xiii	103.818 (9)
Si1^ii—La1—Si1^iii	46.40 (4)	Ge2^xii—Li1—Ge1^xiii	76.182 (9)
Si1—La1—Si1^iii	81.16 (5)	Ge2^ii—Li1—Ge1	76.182 (9)
Ge2^i—La1—Li1	42.161 (10)	Ge2^xi—Li1—Ge1	103.818 (9)
Ge2^ii—La1—Li1	42.161 (10)	Ge2^i—Li1—Ge1	76.182 (9)
Ge1^iii—La1—Li1	43.615 (10)	Ge2^xii—Li1—Ge1	103.818 (9)
Ge1—La1—Li1	43.615 (10)	Ge1^xiii—Li1—Ge1	180.00 (3)
Si1^iv—La1—Li1	108.61 (4)	Ge2^ii—Li1—Ge1^iii	76.182 (9)
Si1^i—La1—Li1	108.61 (4)	Ge2^xi—Li1—Ge1^iii	103.818 (9)
Si1^v—La1—Li1	108.61 (4)	Ge2^i—Li1—Ge1^iii	76.182 (9)
Si1^ii—La1—Li1	108.61 (4)	Ge2^xii—Li1—Ge1^iii	103.818 (9)
Si1—La1—Li1	139.42 (2)	Ge1^xiii—Li1—Ge1^iii	57.16 (3)
Si1^iii—La1—Li1	139.42 (2)	Ge1—Li1—Ge1^iii	122.84 (3)
Ge2^i—La1—La1^ii	168.011 (13)	Ge2^ii—Li1—Ge1^vi	103.818 (9)
Ge2^ii—La1—La1^ii	107.666 (9)	Ge2^xi—Li1—Ge1^vi	76.182 (9)
Ge1^iii—La1—La1^ii	128.749 (7)	Ge2^i—Li1—Ge1^vi	103.818 (9)
Ge1—La1—La1^ii	128.749 (7)	Ge2^xii—Li1—Ge1^vi	76.182 (9)
Si1^iv—La1—La1^ii	52.86 (3)	Ge1^xiii—Li1—Ge1^vi	122.84 (3)
Si1^i—La1—La1^ii	92.97 (4)	Ge1—Li1—Ge1^vi	57.16 (3)
Si1^v—La1—La1^ii	92.97 (4)	Ge1^iii—Li1—Ge1^vi	180.00 (3)
Si1^ii—La1—La1^ii	52.86 (3)	Ge2^ii—Li1—La1^xiii	119.951 (14)
Si1—La1—La1^ii	48.959 (18)	Ge2^xi—Li1—La1^xiii	60.049 (14)
Si1^iii—La1—La1^ii	48.959 (18)	Ge2^i—Li1—La1^xiii	119.951 (14)
Li1—La1—La1^ii	149.827 (5)	Ge2^xii—Li1—La1^xiii	60.049 (14)
Ge1^vi—Ge1—Li1	61.420 (14)	Ge1^xiii—Li1—La1^xiii	61.420 (14)
Ge1^vi—Ge1—Li1^vii	61.420 (14)	Ge1—Li1—La1^xiii	118.580 (14)
Li1—Ge1—Li1^vii	122.84 (3)	Ge1^iii—Li1—La1^xiii	118.580 (14)
Ge1^vi—Ge1—La1^vii	136.385 (10)	Ge1^vi—Li1—La1^xiii	61.420 (14)
Li1—Ge1—La1^vii	162.19 (2)	Ge2^ii—Li1—La1	60.049 (14)
Li1^vii—Ge1—La1^vii	74.965 (7)	Ge2^xi—Li1—La1	119.951 (14)
Ge1^vi—Ge1—La1	136.385 (10)	Ge2^i—Li1—La1	60.049 (14)
Li1—Ge1—La1	74.965 (8)	Ge2^xii—Li1—La1	119.951 (14)
Li1^vii—Ge1—La1	162.19 (2)	Ge1^xiii—Li1—La1	118.580 (14)
La1^vii—Ge1—La1	87.23 (2)	Ge1—Li1—La1	61.420 (14)
Ge2^viii—Ge2—Li1^ix	60.049 (14)	Ge1^iii—Li1—La1	61.420 (14)
Ge2^viii—Ge2—Li1^x	60.049 (14)	Ge1^vi—Li1—La1	118.580 (14)
Li1^ix—Ge2—Li1^x	120.10 (3)	La1^xiii—Li1—La1	180.0
Ge2^viii—Ge2—La1^i	137.838 (10)

Symmetry codes: (i) −x−1/2, −y+1/2, −z; (ii) −x+1/2, −y+1/2, −z; (iii) x, y, z−1; (iv) −x+1/2, −y+1/2, −z+1; (v) −x−1/2, −y+1/2, −z+1; (vi) −x, −y, −z+1; (vii) x, y, z+1; (viii) −x, −y+1, −z; (ix) x+1/2, y+1/2, z; (x) x−1/2, y+1/2, z; (xi) x−1/2, y−1/2, z; (xii) x+1/2, y−1/2, z; (xiii) −x, −y, −z.