The Ce₂Li_0.39Ni_1.61Si₂ structure as a new derivative of the AlB₂ family

A new quaternary dicerium lithium/nickel disilicide, Ce₂Li_0.39Ni_1.61Si₂, crystallizes as a new structure type of inter­metallic compounds closely related to the AlB₂ family. The crystal-chemical inter­relationships between parent AlB₂-type, BaLiSi, ZrBeSi and the title compound are discussed using the Bärnighausen formalism. Two Ce atoms occupy sites of 3m. symmetry. The remainder, i.e. Ni, mixed Ni/Li and Si atoms, occupy sites of m2 symmetry. The environment of the Ce atom is an 18-vertex polyhedron and the Ni, Ni/Li and Si atoms are enclosed in tricapped trigonal prisms. The title structure can be assigned to class No. 10 (trigonal prism and its derivatives) according to the Krypyakevich classification scheme [Krypyakevich (1977). In Structure Types of Inter­metallic Compounds. Moscow: Nauka]. The electronic structure of the title compound was calculated using the tight-binding linear muffin-tin orbital method in the atomic spheres approximation (TB-LMTO-ASA). Metallic bonding is dominant in this compound. The strongest inter­actions are Ni-Si and Ce-Si.

S1. Introduction

Ternary inter­metallic RE—T—Si compounds, based on rare earth (RE) elements and transition (T) metals (especially Mn, Fe, Co and Ni), are sufficiently well studied and described in the literature (Gladyshevskii et al., 1990). The equiatomic CeNiSi ternary compound crystallizes in the LaPtSi structure type with the noncentrosymmetric I4₁md space group (Lee et al., 1987). The CeLiSi ternary compound crystallizes in the α-ThSi₂ structure type with the centrosymmetric I4₁/amd space group (Pavlyuk et al., 1989). These compounds have a similar tetra­gonal structure because the LaPtSi structure type is a ternary substitutional variant of α-ThSi₂.

Earlier studies of four-component RE–T–Li–X alloys (X is a Group IV element, such as Si, Ge and Sn) show that quaternary phases can be formed in two ways, firstly, due to partial substitution of transition-metal atoms by Li atoms, and secondly, by the formation of ordered structures. The ability of Li atoms to partially substitute transition metal atoms was observed previously by us while studying solid solutions RELi_xCu_2–xSi₂ and RELi_xCu_2–xGe₂ (Pavlyuk et al., 1993), TbLi_1–xZn_xSn₂ (Stetskiv et al., 2012) and TmNi_1–xLi_xSn₂ (Stetskiv et al., 2013a), and ternary phases Li_2-xAg_1+xIn₃ (Chumak et al., 2013) and Li₁₈Cu₁₅Al₇ (Dmytriv et al., 2010). The ordered distribution of transition-metal and Li atoms in separate crystallographic sites was indicated for the TmLi₂Co₆Sn₂₀ phase which crystallizes as a derivative variant of the binary cubic Cr₂₃C₆ structure type (Stetskiv et al., 2013b). The Li atoms occupy the same crystallographic positions as the transition-metal atoms in previously studied ternary phases RELiGe with the ZrNiAl type (Pavlyuk et al., 1991; Pavlyuk & Bodak, 1992a) and RE₃Li₂Ge₃ with the Hf₃Ni₂Si₃ type (Pavlyuk & Bodak, 1992b).

S2. Experimental

S2.1. Synthesis and crystallization

Cerium, nickel, lithium and silicon, all with a nominal purity greater than 99.9 wt%, were used as starting elements for preparing the title alloy. First, pieces of the pure metals were pressed into pellets, 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. At this temperature, an alloy was held over 3 d and then the temperature was increased from 670 to 1070 K over a period 4 h. The alloy was annealed at this temperature for 8 h and cooled slowly to room temperature. After the melting and annealing procedures, the total weight loss was less than 2%. Small good-quality single crystals of the title compound were isolated from the alloy.

The crystal structure of the title compound was investigated by the single-crystal method. The synthesized bulk alloy was tested by powder diffraction to find how many phases contained this alloy. X-ray diffraction on powderized samples was performed by means of diffractometer Stoe Stadi P (Cu Kα radiation, step mode of scanning) in order to ensure phase analysis and check for phase purity. Rietveld matrix full-profile structure refinements were carried out and the XRD powder pattern of the compound conforms well to the powder pattern calculated on the basis of single-crystal models (Fig. 6). The powdered alloy is practically a single phase. The refined by powder method unit-cell dimensions are: a = 4.06054 (8), a = 8.3894 (2) Å, R_p = 4.78, R_wp = 6.85 and χ₂ = 5.78.

The content of lithium in the alloy were determined experimentally by means of a Flapho-4 flame photometer (Carl Zeiss Jena) using an inter­ference filter (671 nm) from a solution of the alloy (0.3 g) in HCl solution (25 ml, 1M). The evaluation of results is 74.4 mg l^-1 of lithium that corresponds to 6.7 at% in the alloy.

The density of the alloy was determined using the volumetric method. For quaternary phase Ce₂Li_0.39Ni_1.61Si₂, the measured density is 5.97 (5) Mg m^-3 a difference of less than 1% from the density calculated from X-ray data.

Summarizing the results of the study of a single crystal, and taking into account the results of flame photometry, the measurement of the density and the results of powder diffraction (single-phase alloy, added phases and reaction mixture contained pure Li was not observed), we can assume that Li and Ni form a statistical mixture in the structure.

S2.2. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. The analysis of extinction conditions give 16 trigonal and hexagonal space groups. Among these, only P6m2 fulfils simultaneously the requirements of an absence of systematic extinction conditions and a practically ordered distribution of atoms in separated sites. Consequently, the structure solution with direct methods was performed in this space group.

The initial refinement the model obtained by direct methods showed that the thermal displacement parameter of atom Ni3 was considerably different from those of the other Ni2 site, suggesting that this position is partially occupied by lithium. Take into account a statistical mixture Ni/Li in the Wyckoff 1f position, the structure model was successfully refined with anisotropic displacement parameters during the final refinement cycles. The Ni3/Li1 site occupancies were refined and summed to unity, yielding the reported approximate 0.61:0.39 ratio.

S3. Results and discussion

Structural studies of four-component alloys from CeLiSi–CeNiSi sections indicate the existence of a new Ce₂Li_0.39Ni_1.61Si₂ quaternary phase. The single-crystal data proves that the title compound crystallizes in the hexagonal crystal system in the space group P6m2, with six atoms per unit cell. The projection of the unit cell and the coordination polyhedra of the atoms are shown in Fig. 1. The Ce atoms in Wyckoff position 2g (site symmetry 3m.) are enclosed in an 18-vertex hexagonal prism in which all side faces are centred by six adjacent Ce atoms. The coordination polyhedra around the Ni, statistical mixtures of Ni/Li and Si atoms are tricapped trigonal prisms. For the Ni2 atom (Wyckoff position 1e, site symmetry 6m2) and statistical Ni/Li mixtures in Wyckoff position 1f (site symmetry 6m2), the tricapped trigonal prisms have compositions [Ni2Ce₆Si₃] and [(Ni/Li)3Ce₆Si₃]. The Si4 (Wyckoff position 1c, site symmetry 6m2) and Si5 (Wyckoff position 1d, site symmetry 6m2) atoms are enclosed in the tricapped trigonal prisms [Si4Ce₆Ni₃] and [Si5Ce₆(Ni/Li)₃], respectively. Taking into account the coordination polyhedra for the smallest atoms (Ni and Si), the title structure can be assigned to class No. 10 (trigonal prism and its derivatives) according to the classification scheme of Krypyakevich (1977).

The title quaternary compound is derived from the well-known simple aristotype AlB₂ (Hofmann & Jäniche, 1935). Many previously studied compounds which belong to this family are described by Hoffmann & Pöttgen (2001). In the base AlB₂ structure type, the smallest atoms (B) form 6³ nets and the largest atom (Al) forms well-known triangular 3⁶ nets which are typical for closest packing of atoms. In the title compound, the Ni, Ni/Li and Si atoms form a two-dimensional graphite-like nets. Along the [001] direction (z axis), these hexagonal layers are separated by Ce-atom layers (Fig. 2). The composition of the two-dimensional graphite-like nets and the way they pack it clearly explained by a doubling of unit-cell dimension c and the noncentrosymmetric nature of the title quaternary phase relative to the parent AlB₂ type. The honeycomb arrangement of graphite-like nets in the AlB₂ type consist of six B atoms. In the title phase at z = 0, the honeycomb contains three Ni2 atoms and three Si4 atoms, while at z = 1/2, the honeycomb contains three Ni3/Li3 atoms and three Si5 atoms.

The Bärnighausen scheme (Bärnighausen, 1980), including the atomic site development from AlB₂ to ternary phases BaLiSi and ZrBeSi, and quaternary phase Ce₂Li_0.39Ni_1.61Si₂, is shown in Fig. 3. The BaLiSi type (Axel et al., 1968), space group P6m2, derives from AlB₂ via translationengleiche symmetry reduction of index 2. The ZrBeSi type (Nielsen & Baenziger, 1954) can be transformed from AlB₂ via klassengleiche symmetry reduction of index 2. The Ce₂Li_0.39Ni_1.61Si₂ hexagonal phase derives from the BaLiSi type via isomorphic transition or from ZrBeSi via translationengleiche symmetry reduction of index 2.

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

Around the Ce, Ni and Li atoms, the minimum electron localization function (ELF) are observed and the maximum ELF > 0.80 is around the Si atoms (Fig. 4). The total and partial density of states (DOS) for the title compound (Fig. 5a) in the region below E_F exhibits significant mixing between the Ce, Ni and Si states. For the region above E_F, the contributions are mostly from Ce 4f and 5d orbitals and Si p orbitals. The Si s-type states and Ni d-type states are mainly close to the lower valence band. The visible occupation number for electronic states at the Fermi level indicate a 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, both phases (Fig. 5b-d) can be concluded that the strongest inter­actions are between Ni—Si atoms (d = 2.344 Å and -iCOHP = 3.004 eV) and Ce—Si atoms (d = 3.147 Å and -iCOHP = 1.378 eV). The Ce—Ni inter­action is weak (d = 3.147 Å and -iCOHP= 0.477 eV).

Related literature

For general background, see: Chumak et al. (2013); Dmytriv et al. (2010); Gladyshevskii et al. (1990); Pavlyuk & Bodak (1992a, 1992b); Pavlyuk et al. (1989, 1991, 1993); Stetskiv et al. (2012). For related structures, see: Bärnighausen (1980); Hoffmann & Pöttgen (2001); Hofmann & Jäniche (1935); Krypyakevich (1977); Lee et al. (1987); Nielsen & Baenziger (1954). For other related literature, see: Andersen (1975); Andersen et al. (1985, 1986); Barth & Hedin (1972).

Computing details

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)/publCIF (Westrip, 2010).

Figures

Fig. 1. The projection of the unit cell and coordination polyhedra of the atoms of Ce₂Li_0.39Ni_1.61Si₂.

Fig. 2. Packing of the hexagonal layers in the related structures of the AlB₂ family.

Fig. 3. Group–subgroup scheme on the basis of Bärnighausen formalism for AlB₂, BaLiSi, ZrBeSi and quaternary phase Ce₂Li_0.39Ni_1.61Si₂.

Fig. 4. (a–c) The electron localization function and (d) isosurface from electronic structure calculations for ordered structure models Ce₂NiLiSi₂.

Fig. 5. The electronic density of states (DOS) and crystal orbital Hamilton population (COHP) for Ce₂NiLiSi₂.

Fig. 6. The powder diffraction pattern of the Ce₂Li_0.39Ni_1.61Si₂ alloy.

Dicerium di(lithium/nickel) disilicide

Crystal data

Ce2Li0.39Ni1.61Si2	Dx = 6.002 Mg m^−3 Dm = 5.97 Mg m^−3 Dm measured by not measured
Mr = 433.38	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P6m2	Cell parameters from 136 reflections
Hall symbol: P -6 2	θ = 2.4–27.3°
a = 4.0596 (3) Å	µ = 25.16 mm^−1
c = 8.4011 (17) Å	T = 293 K
V = 119.90 (3) Å^3	Plate, grey
Z = 1	0.07 × 0.06 × 0.01 mm
F(000) = 190.1

Data collection

Oxford Diffraction Xcalibur3 CCD diffractometer	141 independent reflections
Radiation source: fine-focus sealed tube	133 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.119
Detector resolution: 0 pixels mm^-1	θmax = 27.3°, θmin = 2.4°
ω scans	h = −5→5
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2008)	k = −5→5
Tmin = 0.228, Tmax = 0.787	l = −10→10
1089 measured reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.025	w = 1/[σ^2(Fo^2) + (0.0328P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.099	(Δ/σ)max = 0.055
S = 1.30	Δρmax = 1.08 e Å^−3
141 reflections	Δρmin = −1.43 e Å^−3
13 parameters	Absolute structure: Flack (1983), 56 Friedel pairs
0 restraints	Absolute structure parameter: 0.4 (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)
Ce1	0.0000	0.0000	0.24999 (12)	0.0102 (6)
Ni2	0.6667	0.3333	0.0000	0.008 (3)
Ni3	0.6667	0.3333	0.5000	0.015 (5)	0.606 (15)
Li3	0.6667	0.3333	0.5000	0.015 (5)	0.394 (15)
Si4	0.3333	0.6667	0.0000	0.022 (8)
Si5	0.3333	0.6667	0.5000	0.021 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ce1	0.0121 (8)	0.0121 (8)	0.0064 (7)	0.0061 (4)	0.000	0.000
Ni2	0.008 (4)	0.008 (4)	0.010 (6)	0.0038 (18)	0.000	0.000
Ni3	0.013 (7)	0.013 (7)	0.019 (11)	0.006 (3)	0.000	0.000
Li3	0.013 (7)	0.013 (7)	0.019 (11)	0.006 (3)	0.000	0.000
Si4	0.026 (11)	0.026 (11)	0.013 (15)	0.013 (6)	0.000	0.000
Si5	0.029 (12)	0.029 (12)	0.005 (13)	0.015 (6)	0.000	0.000

Geometric parameters (Å, º)

Ce1—Si4^i	3.1471 (7)	Ni3—Ce1^iv	3.1472 (7)
Ce1—Ni2^i	3.1471 (7)	Ni3—Ce1^ix	3.1472 (7)
Ce1—Si4^ii	3.1471 (7)	Ni3—Ce1^x	3.1472 (7)
Ce1—Ni2^iii	3.1471 (7)	Ni3—Ce1^vii	3.1472 (7)
Ce1—Ni2	3.1471 (7)	Ni3—Ce1^xi	3.1472 (7)
Ce1—Si4	3.1471 (7)	Si4—Ni2^xii	2.3438 (2)
Ce1—Si5	3.1472 (7)	Si4—Ni2^iii	2.3438 (2)
Ce1—Ni3	3.1472 (7)	Si4—Ce1^v	3.1471 (7)
Ce1—Si5^ii	3.1472 (7)	Si4—Ce1^xiii	3.1471 (7)
Ce1—Li3^iii	3.1472 (7)	Si4—Ce1^vii	3.1471 (7)
Ce1—Ni3^iii	3.1472 (7)	Si4—Ce1^xii	3.1471 (7)
Ni2—Si4^iv	2.3438 (2)	Si4—Ce1^viii	3.1471 (7)
Ni2—Si4^ii	2.3438 (2)	Si5—Li3^xii	2.3438 (2)
Ni2—Si4	2.3438 (2)	Si5—Li3^iii	2.3438 (2)
Ni2—Ce1^v	3.1471 (7)	Si5—Ni3^xii	2.3438 (2)
Ni2—Ce1^vi	3.1471 (7)	Si5—Ni3^iii	2.3438 (2)
Ni2—Ce1^vii	3.1471 (7)	Si5—Ce1^xii	3.1472 (7)
Ni2—Ce1^iv	3.1471 (7)	Si5—Ce1^ix	3.1472 (7)
Ni2—Ce1^viii	3.1471 (7)	Si5—Ce1^xiv	3.1472 (7)
Ni3—Si5^iv	2.3438 (2)	Si5—Ce1^vii	3.1472 (7)
Ni3—Si5^ii	2.3438 (2)	Si5—Ce1^xi	3.1472 (7)
Ni3—Si5	2.3438 (2)
Si4^i—Ce1—Ni2^i	43.724 (11)	Ce1—Ni3—Ce1^x	136.277 (11)
Si4^i—Ce1—Si4^ii	80.33 (2)	Ce1^iv—Ni3—Ce1^x	83.73 (3)
Ni2^i—Ce1—Si4^ii	43.724 (11)	Ce1^ix—Ni3—Ce1^x	80.32 (2)
Si4^i—Ce1—Ni2^iii	43.724 (11)	Si5^iv—Ni3—Ce1^vii	68.139 (5)
Ni2^i—Ce1—Ni2^iii	80.33 (2)	Si5^ii—Ni3—Ce1^vii	138.136 (15)
Si4^ii—Ce1—Ni2^iii	96.28 (3)	Si5—Ni3—Ce1^vii	68.139 (5)
Si4^i—Ce1—Ni2	96.28 (3)	Ce1—Ni3—Ce1^vii	80.32 (2)
Ni2^i—Ce1—Ni2	80.33 (2)	Ce1^iv—Ni3—Ce1^vii	80.32 (2)
Si4^ii—Ce1—Ni2	43.724 (11)	Ce1^ix—Ni3—Ce1^vii	83.73 (3)
Ni2^iii—Ce1—Ni2	80.33 (2)	Ce1^x—Ni3—Ce1^vii	136.277 (11)
Si4^i—Ce1—Si4	80.33 (2)	Si5^iv—Ni3—Ce1^xi	138.136 (15)
Ni2^i—Ce1—Si4	96.28 (3)	Si5^ii—Ni3—Ce1^xi	68.139 (5)
Si4^ii—Ce1—Si4	80.33 (2)	Si5—Ni3—Ce1^xi	68.139 (5)
Ni2^iii—Ce1—Si4	43.724 (11)	Ce1—Ni3—Ce1^xi	83.73 (3)
Ni2—Ce1—Si4	43.724 (11)	Ce1^iv—Ni3—Ce1^xi	136.277 (11)
Si4^i—Ce1—Si5	136.276 (4)	Ce1^ix—Ni3—Ce1^xi	80.32 (2)
Ni2^i—Ce1—Si5	180.00 (3)	Ce1^x—Ni3—Ce1^xi	80.32 (2)
Si4^ii—Ce1—Si5	136.276 (4)	Ce1^vii—Ni3—Ce1^xi	136.277 (11)
Ni2^iii—Ce1—Si5	99.674 (9)	Ni2^xii—Si4—Ni2^iii	120.0
Ni2—Ce1—Si5	99.674 (9)	Ni2^xii—Si4—Ni2	120.0
Si4—Ce1—Si5	83.727 (12)	Ni2^iii—Si4—Ni2	120.0
Si4^i—Ce1—Ni3	180.00 (3)	Ni2^xii—Si4—Ce1^v	138.138 (15)
Ni2^i—Ce1—Ni3	136.276 (4)	Ni2^iii—Si4—Ce1^v	68.138 (5)
Si4^ii—Ce1—Ni3	99.674 (9)	Ni2—Si4—Ce1^v	68.138 (5)
Ni2^iii—Ce1—Ni3	136.276 (4)	Ni2^xii—Si4—Ce1^xiii	68.138 (5)
Ni2—Ce1—Ni3	83.727 (12)	Ni2^iii—Si4—Ce1^xiii	68.138 (5)
Si4—Ce1—Ni3	99.674 (9)	Ni2—Si4—Ce1^xiii	138.138 (15)
Si5—Ce1—Ni3	43.723 (11)	Ce1^v—Si4—Ce1^xiii	80.33 (2)
Si4^i—Ce1—Si5^ii	136.276 (4)	Ni2^xii—Si4—Ce1^vii	68.138 (5)
Ni2^i—Ce1—Si5^ii	99.674 (9)	Ni2^iii—Si4—Ce1^vii	138.138 (15)
Si4^ii—Ce1—Si5^ii	83.727 (12)	Ni2—Si4—Ce1^vii	68.138 (5)
Ni2^iii—Ce1—Si5^ii	180.00 (3)	Ce1^v—Si4—Ce1^vii	136.276 (11)
Ni2—Ce1—Si5^ii	99.674 (9)	Ce1^xiii—Si4—Ce1^vii	136.276 (11)
Si4—Ce1—Si5^ii	136.276 (4)	Ni2^xii—Si4—Ce1^xii	68.138 (5)
Si5—Ce1—Si5^ii	80.32 (2)	Ni2^iii—Si4—Ce1^xii	68.138 (5)
Ni3—Ce1—Si5^ii	43.723 (11)	Ni2—Si4—Ce1^xii	138.138 (15)
Si4^i—Ce1—Li3^iii	99.674 (9)	Ce1^v—Si4—Ce1^xii	136.276 (11)
Ni2^i—Ce1—Li3^iii	136.276 (4)	Ce1^xiii—Si4—Ce1^xii	83.72 (3)
Si4^ii—Ce1—Li3^iii	180.00 (3)	Ce1^vii—Si4—Ce1^xii	80.33 (2)
Ni2^iii—Ce1—Li3^iii	83.727 (12)	Ni2^xii—Si4—Ce1^viii	68.138 (5)
Ni2—Ce1—Li3^iii	136.276 (4)	Ni2^iii—Si4—Ce1^viii	138.138 (15)
Si4—Ce1—Li3^iii	99.674 (9)	Ni2—Si4—Ce1^viii	68.138 (5)
Si5—Ce1—Li3^iii	43.723 (11)	Ce1^v—Si4—Ce1^viii	80.33 (2)
Ni3—Ce1—Li3^iii	80.32 (2)	Ce1^xiii—Si4—Ce1^viii	80.33 (2)
Si5^ii—Ce1—Li3^iii	96.27 (3)	Ce1^vii—Si4—Ce1^viii	83.72 (3)
Si4^i—Ce1—Ni3^iii	99.674 (9)	Ce1^xii—Si4—Ce1^viii	136.276 (11)
Ni2^i—Ce1—Ni3^iii	136.276 (4)	Ni2^xii—Si4—Ce1	138.138 (15)
Si4^ii—Ce1—Ni3^iii	180.00 (3)	Ni2^iii—Si4—Ce1	68.138 (5)
Ni2^iii—Ce1—Ni3^iii	83.727 (12)	Ni2—Si4—Ce1	68.138 (5)
Ni2—Ce1—Ni3^iii	136.276 (4)	Ce1^v—Si4—Ce1	83.72 (3)
Si4—Ce1—Ni3^iii	99.674 (9)	Ce1^xiii—Si4—Ce1	136.276 (11)
Si5—Ce1—Ni3^iii	43.723 (11)	Ce1^vii—Si4—Ce1	80.33 (2)
Ni3—Ce1—Ni3^iii	80.32 (2)	Ce1^xii—Si4—Ce1	80.33 (2)
Si5^ii—Ce1—Ni3^iii	96.27 (3)	Ce1^viii—Si4—Ce1	136.276 (11)
Li3^iii—Ce1—Ni3^iii	0.0	Li3^xii—Si5—Li3^iii	120.0
Si4^iv—Ni2—Si4^ii	120.0	Li3^xii—Si5—Ni3^xii	0.0
Si4^iv—Ni2—Si4	120.0	Li3^iii—Si5—Ni3^xii	120.0
Si4^ii—Ni2—Si4	120.0	Li3^xii—Si5—Ni3^iii	120.0
Si4^iv—Ni2—Ce1^v	138.138 (15)	Li3^iii—Si5—Ni3^iii	0.0
Si4^ii—Ni2—Ce1^v	68.138 (5)	Ni3^xii—Si5—Ni3^iii	120.0
Si4—Ni2—Ce1^v	68.138 (5)	Li3^xii—Si5—Ni3	120.0
Si4^iv—Ni2—Ce1^vi	68.138 (5)	Li3^iii—Si5—Ni3	120.0
Si4^ii—Ni2—Ce1^vi	68.138 (5)	Ni3^xii—Si5—Ni3	120.0
Si4—Ni2—Ce1^vi	138.138 (15)	Ni3^iii—Si5—Ni3	120.0
Ce1^v—Ni2—Ce1^vi	80.33 (2)	Li3^xii—Si5—Ce1	138.136 (15)
Si4^iv—Ni2—Ce1^vii	68.138 (5)	Li3^iii—Si5—Ce1	68.139 (5)
Si4^ii—Ni2—Ce1^vii	138.138 (15)	Ni3^xii—Si5—Ce1	138.136 (15)
Si4—Ni2—Ce1^vii	68.138 (5)	Ni3^iii—Si5—Ce1	68.139 (5)
Ce1^v—Ni2—Ce1^vii	136.276 (11)	Ni3—Si5—Ce1	68.139 (5)
Ce1^vi—Ni2—Ce1^vii	136.276 (11)	Li3^xii—Si5—Ce1^xii	68.139 (5)
Si4^iv—Ni2—Ce1^iv	68.138 (5)	Li3^iii—Si5—Ce1^xii	68.139 (5)
Si4^ii—Ni2—Ce1^iv	68.138 (5)	Ni3^xii—Si5—Ce1^xii	68.139 (5)
Si4—Ni2—Ce1^iv	138.138 (15)	Ni3^iii—Si5—Ce1^xii	68.139 (5)
Ce1^v—Ni2—Ce1^iv	136.276 (11)	Ni3—Si5—Ce1^xii	138.136 (15)
Ce1^vi—Ni2—Ce1^iv	83.72 (3)	Ce1—Si5—Ce1^xii	80.32 (2)
Ce1^vii—Ni2—Ce1^iv	80.33 (2)	Li3^xii—Si5—Ce1^ix	68.139 (5)
Si4^iv—Ni2—Ce1^viii	68.138 (5)	Li3^iii—Si5—Ce1^ix	138.136 (15)
Si4^ii—Ni2—Ce1^viii	138.138 (15)	Ni3^xii—Si5—Ce1^ix	68.139 (5)
Si4—Ni2—Ce1^viii	68.138 (5)	Ni3^iii—Si5—Ce1^ix	138.136 (15)
Ce1^v—Ni2—Ce1^viii	80.33 (2)	Ni3—Si5—Ce1^ix	68.139 (5)
Ce1^vi—Ni2—Ce1^viii	80.33 (2)	Ce1—Si5—Ce1^ix	136.277 (11)
Ce1^vii—Ni2—Ce1^viii	83.72 (3)	Ce1^xii—Si5—Ce1^ix	136.277 (11)
Ce1^iv—Ni2—Ce1^viii	136.276 (11)	Li3^xii—Si5—Ce1^xiv	68.139 (5)
Si4^iv—Ni2—Ce1	138.138 (15)	Li3^iii—Si5—Ce1^xiv	68.139 (5)
Si4^ii—Ni2—Ce1	68.138 (5)	Ni3^xii—Si5—Ce1^xiv	68.139 (5)
Si4—Ni2—Ce1	68.138 (5)	Ni3^iii—Si5—Ce1^xiv	68.139 (5)
Ce1^v—Ni2—Ce1	83.72 (3)	Ni3—Si5—Ce1^xiv	138.136 (15)
Ce1^vi—Ni2—Ce1	136.276 (11)	Ce1—Si5—Ce1^xiv	136.277 (11)
Ce1^vii—Ni2—Ce1	80.33 (2)	Ce1^xii—Si5—Ce1^xiv	83.73 (3)
Ce1^iv—Ni2—Ce1	80.33 (2)	Ce1^ix—Si5—Ce1^xiv	80.32 (2)
Ce1^viii—Ni2—Ce1	136.276 (11)	Li3^xii—Si5—Ce1^vii	68.139 (5)
Si5^iv—Ni3—Si5^ii	120.0	Li3^iii—Si5—Ce1^vii	138.136 (15)
Si5^iv—Ni3—Si5	120.0	Ni3^xii—Si5—Ce1^vii	68.139 (5)
Si5^ii—Ni3—Si5	120.0	Ni3^iii—Si5—Ce1^vii	138.136 (15)
Si5^iv—Ni3—Ce1	138.136 (15)	Ni3—Si5—Ce1^vii	68.139 (5)
Si5^ii—Ni3—Ce1	68.139 (5)	Ce1—Si5—Ce1^vii	80.32 (2)
Si5—Ni3—Ce1	68.139 (5)	Ce1^xii—Si5—Ce1^vii	80.32 (2)
Si5^iv—Ni3—Ce1^iv	68.139 (5)	Ce1^ix—Si5—Ce1^vii	83.73 (3)
Si5^ii—Ni3—Ce1^iv	68.139 (5)	Ce1^xiv—Si5—Ce1^vii	136.277 (11)
Si5—Ni3—Ce1^iv	138.136 (15)	Li3^xii—Si5—Ce1^xi	138.136 (15)
Ce1—Ni3—Ce1^iv	80.32 (2)	Li3^iii—Si5—Ce1^xi	68.139 (5)
Si5^iv—Ni3—Ce1^ix	68.139 (5)	Ni3^xii—Si5—Ce1^xi	138.136 (15)
Si5^ii—Ni3—Ce1^ix	138.136 (15)	Ni3^iii—Si5—Ce1^xi	68.139 (5)
Si5—Ni3—Ce1^ix	68.139 (5)	Ni3—Si5—Ce1^xi	68.139 (5)
Ce1—Ni3—Ce1^ix	136.277 (11)	Ce1—Si5—Ce1^xi	83.73 (3)
Ce1^iv—Ni3—Ce1^ix	136.277 (11)	Ce1^xii—Si5—Ce1^xi	136.277 (11)
Si5^iv—Ni3—Ce1^x	68.139 (5)	Ce1^ix—Si5—Ce1^xi	80.32 (2)
Si5^ii—Ni3—Ce1^x	68.139 (5)	Ce1^xiv—Si5—Ce1^xi	80.32 (2)
Si5—Ni3—Ce1^x	138.136 (15)	Ce1^vii—Si5—Ce1^xi	136.277 (11)

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