Na3MgB37Si9: an icosa­hedral B12 cluster framework containing {Si8} units

Morito, H.; Ikeda, T.; Katsura, Y.; Yamane, H.

doi:10.1107/S2056989022000494

research communications

CRYSTALLOGRAPHIC
COMMUNICATIONS

ISSN: 2056-9890

Volume 78| Part 2| February 2022| Pages 203-206

https://doi.org/10.1107/S2056989022000494

Open

access

Na₃MgB₃₇Si₉: an icosahedral B₁₂ cluster framework containing {Si₈} units

Haruhiko Morito,^a ^* Takuji Ikeda,^b Yukari Katsura ^c and Hisanori Yamane ^d

^aInstitute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan, ^bResearch Institute for Chemical Process Technology, National Institute of Advanced Industrial Science and Technology, 4-2-1, Nigatake, Miyagino-ku, Sendai 983-8551, Japan, ^cNational Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki, 305-0047, Japan, and ^dInstitute of Multidisciplinary Research for Advanced Materials, Tohoku, University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
^*Correspondence e-mail: haruhiko.morito.b5@tohoku.ac.jp

Edited by W. T. A. Harrison, University of Aberdeen, Scotland (Received 20 December 2021; accepted 13 January 2022; online 18 January 2022)

Single crystals of a novel sodium–magnesium boride silicide, Na₃MgB₃₇Si₉ [a = 10.1630 (3) Å, c = 16.5742 (6) Å, space group R $[\overline{3}]$ m (No. 166)], were synthesized by heating a mixture of Na, Si and crystalline B with B₂O₃ flux in Mg vapor at 1373 K. The Mg atoms in the title compound are located at an interstitial site of the Dy_2.1B₃₇Si₉-type structure with an occupancy of 0.5. The (001) layers of B₁₂ icosahedra stack along the c-axis direction with shifting in the [–a/3, b/3, c/3] direction. A three-dimensional framework structure of the layers is formed via B—Si bonds and {Si₈} units of [Si]₃—Si—Si—[Si]₃.

Keywords: crystal structure; boron-rich boride; sodium; silicon; single-crystal; B₂O₃ flux; crystal structure; X-ray diffraction.

CCDC reference: 2141726

1. Chemical context

Boron-rich compounds composed of B₁₂ icosahedral clusters are attracting attention as thermoelectric materials because of their low thermal conductivity resulting from their complicated crystal structures (Cahill et al., 1977 ). In our previous study, a novel ternary borosilicide, Na₈B_74.5Si_17.5, was synthesized, and its crystal structure (Morito et al. 2010 ) and electronic structure measured using soft X-ray spectrometry (Terauchi et al. 2018 ), have been reported. This compound has a three-dimensional framework structure with layers composed of B₁₂ icosahedral clusters and Si chains in the channels of the B₁₂ clusters. During the investigation of this compound, a new crystalline phase was synthesized in which the stacking sequence of the B₁₂ cluster layers differed from that of Na₈B_74.5Si_17.5. The composition analysis revealed that the new phase contained a small amount of Mg derived from an impurity in the starting material of amorphous B powder. Single crystals of this phase were prepared in the present study by heating a starting mixture of Na, crystalline B, a flux of B₂O₃ with Mg vapor, and the crystal structure was determined using single-crystal X-ray diffraction.

2. Structural commentary

The crystal structure of the new phase of composition Na₃MgB₃₇Si₉ is trigonal (space group R $[\overline{3}]$ m, No. 166), and the hexagonal lattice constants are a = 10.1630 (3) Å and c = 16.5742 (6) Å. The structure is composed of B₁₂ icosahedral clusters: the B—B distances of the 30 distinct bonds in the cluster are in the range of 1.791 (3)–1.843 (5) Å and the average distance is 1.811 Å (Table 1). The B₁₂ icosahedral clusters are connected by a B2—B2 bond [1.761 (5) Å] on the (001) plane and form layers that stack along the c axis with a sequence of ABCABC by shifts of [–a/3, b/3, c/3] (Figs. 1 and 2).

Table 1
Selected geometric parameters (Å, °)

Na1—B2ⁱ	2.793 (2)	B2—B2^viii	1.761 (5)
Na1—B1	2.811 (2)	B3—B5ⁱ	1.689 (7)
Na1—Si2ⁱ	2.8621 (4)	B3—Si1ⁱ	1.888 (4)
Na1—B4ⁱ	2.9605 (16)	B4—Si2	2.082 (3)
Mg1—B2ⁱⁱ	2.333 (3)	B5—B3ⁱⁱⁱ	1.689 (7)
B1—B3ⁱⁱⁱ	1.791 (3)	B5—Si1^ix	1.96 (2)
B1—B2^iv	1.798 (3)	B5—B5^ix	2.47 (4)
B1—B1^v	1.806 (4)	Si1—Si1^ix	1.460 (10)
B1—B2^vi	1.813 (3)	Si2—Si3^x	2.3951 (9)
B1—B4^vii	1.815 (3)	Si3—Si3^xi	2.304 (3)
B1—Si2ⁱ	2.043 (2)

Si3^xi—Si3—Si2^x	104.62 (4)	Si2^x—Si3—Si2^xii	113.86 (3)
Symmetry codes: (i) $[-x+{\script{2\over 3}}, -y+{\script{1\over 3}}, -z+{\script{1\over 3}}]$ ; (ii) ; (iii) $[x-y-{\script{1\over 3}}, x-{\script{2\over 3}}, -z+{\script{1\over 3}}]$ ; (iv) $[x-y+{\script{2\over 3}}, -y+{\script{1\over 3}}, -z+{\script{1\over 3}}]$ ; (v) $[-x+{\script{2\over 3}}, -x+y+{\script{1\over 3}}, -z+{\script{1\over 3}}]$ ; (vi) ; (vii) $[-x+y+{\script{1\over 3}}, -x+{\script{2\over 3}}, z-{\script{1\over 3}}]$ ; (viii) ; (ix) ; (x) $[-x+{\script{1\over 3}}, -y+{\script{2\over 3}}, -z+{\script{2\over 3}}]$ ; (xi) ; (xii) $[y-{\script{2\over 3}}, -x+y-{\script{1\over 3}}, -z+{\script{2\over 3}}]$ .

Figure 1
Interconnection of B₁₂ clusters, Si1/B5—Si1/B5 bonds, {Si₈} units and Na and Mg atoms in Na₃MgB₃₇Si₉. Displacement ellipsoids are drawn at the 90% probability level. Symmetry codes: (i) x + $[{2\over 3}]$ , y + $[{1\over 3}]$ , z + $[{1\over 3}]$ ; (ii) −x + $[{2\over 3}]$ , −y + $[{1\over 3}]$ , −z + $[{1\over 3}]$ ; (iii) −x + y, 1 − x, z; (iv) 1 − y, 1 + x − y, z; (v) y − $[{1\over 3}]$ , −x + y + $[{1\over 3}]$ , −z + $[{1\over 3}]$ ; (vi) x − y + $[{2\over 3}]$ , x + $[{1\over 3}]$ , −z + $[{1\over 3}]$ ; (vii) −x + $[{2\over 3}]$ , −y − $[{2\over 3}]$ , −z + $[{1\over 3}]$ ; (viii) −x + $[{1\over 3}]$ , −y + $[{2\over 3}]$ , −z + $[{2\over 3}]$ ; (ix) x + $[{1\over 3}]$ , y + $[{2\over 3}]$ , z − $[{1\over 3}]$ ; (x) −y + $[{2\over 3}]$ , x − y + $[{1\over 3}]$ , z + $[{1\over 3}]$ ; (xi) x − $[{1\over 3}]$ , y + $[{1\over 3}]$ , z + $[{1\over 3}]$ ; (xii) −x + y + $[{2\over 3}]$ , −x + $[{4\over 3}]$ , z + $[{1\over 3}]$ ; (xiii) 1 − x + y, 1 − x, z; (xiv) x, 1 + y, z; (xv) −y, x − y, z; (xvi) x − y + $[{1\over 3}]$ , x − $[{1\over 3}]$ , −z + $[{2\over 3}]$ ; (xvii) y + $[{1\over 3}]$ , −x + y + $[{2\over 3}]$ , −z + $[{2\over 3}]$ ; (xviii) −x + $[{4\over 3}]$ , −y + $[{2\over 3}]$ , −z + $[{2\over 3}]$ .

Figure 2
[110] projection of the crystal structure of Na₃MgB₃₇Si₉.

Six B₁₂ units in the layers surround {Si₈} units of composition [Si2]₃—Si3—Si3—[Si2]₃. The bond lengths of 2.304 (3) Å for Si3—Si3 and 2.3951 (9) Å for Si2—Si3 are comparable with the bond length in crystalline silicon (2.35 Å). The bond angles of Si2—Si3—Si2 and Si2—Si3—Si3 are 113.86 (3)° and 104.61 (4)°, respectively, which are distorted from the regular tetrahedral bond angle of 109.47°. The Si2—B1 distance is 2.043 (2) Å, which is close to the Si—B distances (1.973–2.027 Å) found in β-silicon boride, SiB₃ (Salvador et al. 2003 ).

The framework structure of B₁₂ icosahedra and {Si₈} units of the title compound has also been reported in the structures of Mg₃B₃₆Si₉C (Ludwig et al. 2013 ), RE_1–xB₁₂Si_3.3–δ (RE = Y, Gd–Lu) (0 ≤ x ≤ 0.5, δ ∼ 0.3) (Zhang et al. 2003 ) and RE_1-xB₃₆Si₉C (RE = Y, Gd–Lu) (Ludwig et al. 2013) with the same space group of R $[\overline{3}]$ m. The {Si₈} units with Si2—B4 bonds [2.082 (3) Å] and Si1/B5—Si1/B5 pairs that bind to the B atoms at B3 connect the B₁₂ layers of Na₃MgB₃₇Si₉ (Fig. 1). Because the Si1—Si1 distance of 1.460 (10) Å is short for an Si—Si bond and the B5—B5 distance 2.47 (4) Å is long for a B—B bond, it was concluded that disordered pairs of Si1—B5 and B5—Si1 [B—Si = 1.96 (2) Å] are statistically present with equal occupancies. Similar disordered Si/B—Si/B pairs have been reported in Dy_0.7B_12.33Si₃ (Si/B occupancy 0.5/0.5, Si—B length = 1.838 Å; Zhang et al. 2003). Instead of Si/B—Si/B pairs (Ludwig et al. 2013), Mg₃B₃₆Si₉C contains Si/C—Si/C pairs (Si/C occupancy 0.507/0.493, Si—C length = 1.881 Å).

The Na1 site in the title compound is located around the {Si₈} unit between the B₁₂ cluster layers. The Na1—Si2 distance is 2.8620 (4) Å and the Na1—B1 and Na1—B2 distances are 2.811 (2) and 2.793 (2) Å, respectively. These distances are almost the same as the Na—Si distance of Na₄Si₄ [2.878 (3) Å; Morito et al., 2015 ] and Na—B distance of NaB₁₅ (2.798 Å; Naslain & Kasper, 1970 ). The Mg1 atom is situated above and below the {Si₈} unit along the c-axis direction with an occupancy of 0.5. The Mg1—Si3 and Mg1—B2 distances are 2.403 (4) Å and 2.333 (3) Å, respectively, which are close to the Mg—Si (2.436 Å) and Mg—B distances (2.353 Å) in MgB₁₂Si₂ (Ludwig & Hillebrecht, 2006 ). The Na1—Mg1 distance in the title compound is 3.0389 (9) Å, which is close to the Na—Mg distance (3.120 Å) reported in Na₄Mg₄Sn₃ (Yamada et al. 2015 ). The site corresponding to the location of Mg1 in the title compound does not exist in Mg₃B₃₆Si₉C (Ludwig et al. 2013), RE_1-xB₁₂Si_3.3-δ (RE = Y, Gd–Lu) (0 ≤ x ≤ 0.5, δ ∼ 0.3) (Zhang et al. 2003) and RE_1-xB₃₆Si₉C (RE = Y, Gd–Lu) (Ludwig et al. 2013).

The number of electrons provided from Na and Mg to the framework of B₃₇Si₉ is five in Na₃MgB₃₇Si₉. In related compounds, the Mg atom in Mg₃B₃₆Si₉C and the Dy atom in Dy_0.7B_12.33Si₃ (Dy_2.1B₃₇Si₉) provide six and 6.3 electrons, respectively, and approximately six electrons are supplied from RE in RE_1–xB₁₂Si_3.3–δ (RE = Y, Gd–Lu) (0 ≤ x ≤ 0.5, δ ∼ 0.3) and RE_1–xB₃₆Si₉C (RE = Y, Gd–Lu). The lattice constants and unit-cell volume of Mg₃B₃₆Si₉C are a = 10.0793 Å, c = 16.372 Å, and V = 1440.4 Å³ (Ludwig et al. 2013), those of RE_1–xB₁₂Si_3.3–δ (RE = Y, Gd–Lu) (0 ≤ x ≤ 0.5, δ ∼ 0.3) are a = 10.046–10.095 Å, c = 16.298–16.467 Å, and V = 1429–1454 Å³ (Zhang et al. 2003) and those of RE_1–xB₃₆Si₉C (RE = Y, Gd–Lu) are a = 10.000–10.096 Å, c = 16.225–16.454 Å, and V = 1405–1452 Å³ (Ludwig et al. 2013). Thus, it may be seen that the lattice constants of Na₃MgB₃₇Si₉ are larger than those of related compounds and the unit-cell volume of Na₃MgB₃₇Si₉ is approximately 2% larger than the maximum unit-cell volume of 1454 Å³ for the RE_1–xB₁₂Si_3.3–δ series with RE = Yb (Zhang et al. 2003). This increase in the lattice constants could be related to the occupancy of the Mg1 site, which is not found in other compounds.

Table 2 compares the interatomic distances for Na₃MgB₃₇Si₉, Dy_2.1B₃₇Si₉ and Mg₃B₃₆Si₉C. The average B—B distances of B₁₂ icosahedra, B2—B2 distances between clusters, and Si2—B4 distances for Na₃MgB₃₇Si₉ are longer than those of other compounds. However, only the bond distance of Si3—Si3, in which Si3 only binds to Si, is specifically shorter. It is assumed that this bond became shorter because of an increase in the bond order from 1 because of a decrease in the number of electrons in the antibonding orbitals of the Si3—Si3 unit with a decrease in the electron count for the entire framework. Assuming that the main cause of the lattice expansion of Na₃MgB₃₇Si₉ is a decrease in the bonding force between B—B and B—Si atoms because of electron deficiency in the bonding orbitals of the B₃₇Si₉ framework, the lattice constant can be reduced by increasing the Mg occupancy, which can be attained by increasing the Mg vapor pressure during the synthesis.

Table 2
Cell parameters (Å), cell volumes (Å³) and selected bond lengths (Å) of Na₃MgB₃₇Si₉, Dy_2.1B₃₇Si₉^a and Mg₃B₃₆Si₉C

	Na₃MgB₃₇Si₉	Dy_2.1B₃₇Si₉	Mg₃B₃₆Si₉C
a	10.1630 (3)	10.078	10.079
c	16.5742 (6)	16.465	16.372
V	1482.54 (10)	1448.3	1440.4
B—B_av of B₁₂ icosahedron	1.811	1.805	1.798
B2—B2	1.761 (5)	1.738	1.738
Si1—B3	1.887 (4)	1.877	1.851
Si1—B5/C	1.96 (2)	1.84	1.88
Si2—B1	2.043 (2)	2.032	2.035
Si2—B4	2.082 (3)	2.053	2.038
Si3—Si2	2.3951 (9)	2.366	2.362
Si3—Si3	2.304 (3)	2.343	2.341
Na1—B1	2.811 (2)	2.794	2.792
Na1—B2	2.793 (2)	2.751	2.729
Na1—B4	2.9604 (16)	2.934	2.934
Na1—Si2	2.8620 (4)	2.835	2.832
Mg1—B2	2.333 (3)
Mg1—B4	2.568 (3)
Mg1—Si3	2.403 (4)
Notes: (a) Zhang et al. (2003); (b) Ludwig et al. (2013).

3. Database survey

In space group R $[\overline{3}]$ m, the framework structures of B₁₂ icosahedral clusters containing {Si₈} units similar to Na₃MgB₃₇Si₉ have been reported for Mg₃B₃₆Si₉C (Ludwig et al. 2013), RE_1–xB₁₂Si_3.3–δ (RE = Y, Gd–Lu) (0 ≤ x ≤ 0.5, δ ∼0.3) (Zhang et al. 2003) and RE_1–xB₃₆Si₉C (RE = Y, Gd–Lu) (Ludwig et al. 2013).

4. Synthesis and crystallization

Na metal pieces (purity 99.95%, Nippon Soda Co., Ltd.), crystalline B powder (99.9%, FUJIFILM Wako Pure Chemical Industries Co., Ltd.) and Si powder (99.999%, Kojundo Chemical Lab. Co., Ltd.) were weighed in a BN crucible (99.5%, Showa Denko K. K., outer diameter = 8.5 mm, inner diameter = 6.5 mm, depth = 18 mm), with a molar ratio of Na:B:Si = 5:4:3 (a total weight 280 mg) in a high-purity Ar-filled glove box (O₂ < 1 ppm, H₂O < 1 ppm). Then, 10 mg of B₂O₃ powder (90%, FUJIFILM Wako Pure Chemical Industries, Ltd.) were added to the crucible, which was stacked on another BN crucible containing 30 mg of Mg powder (99.9%, rare metallic), and these crucibles were encapsulated in a stainless steel container (SUS316, outer diameter = 12.7 mm, inner diameter = 10.75 mm, length 80 mm) with Ar gas. The container was heated at 1373 K for 24 h using an electric furnace. After cooling, the crucible was taken out from the reaction container, and any Na and NaSi remaining in the crucible were reacted and removed with 2-propanol and ethanol. Then, the sample was washed with pure water to remove water-soluble compounds such as sodium borate and alkoxide produced by the reaction of Na and alcohol to leave black plates of the title compound. An electron probe microanalyzer (EPMA; JEOL Ltd., JXA-8200) was used to analyze the composition of the obtained single crystal as Na 5.49 (8), Mg 2.37 (7), B 74.8 (7), Si 17.3 (4) atom %, which is nearly matched by Na₃MgB₃₇Si₉ (Na 6.0, Mg 2.0, B 74.0, Si 18.0 atom %). Other elements such as O were not found.

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 3. The occupancy of the Mg1 site in the analysis of the initial model was 0.506 (10), whereas the occupancy of the B5 and Si1 sites was 0.519 (15) and 0.481, respectively. These occupancies were fixed at 0.5, and the composition formula was determined to be Na₃MgB₃₇Si₉. The crystal structure was refined by considering (001) twinning, which reduced the R-value (all data) from 0.0651 to 0.0380.

Table 3
Experimental details

Crystal data
Chemical formula	Na₃MgB₃₇Si₉
M_r	746.06
Crystal system, space group	Trigonal, R $[\overline{3}]$ m
Temperature (K)	298
a, c (Å)	10.1630 (3), 16.5742 (6)
V (Å³)	1482.54 (10)
Z	3
Radiation type	Mo Kα
μ (mm⁻¹)	0.72
Crystal size (mm)	0.20 × 0.16 × 0.02

Data collection
Diffractometer	Burker, D8 QUEST
Absorption correction	Multi-scan (SADABS; Bruker, 2018 )
T_min, T_max	0.911, 1.000
No. of measured, independent and observed [I > 2σ(I)] reflections	8352, 562, 540
R_int	0.032
(sin θ/λ)_max (Å⁻¹)	0.703

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.035, 0.076, 1.31
No. of reflections	562
No. of parameters	57
Δρ_max, Δρ_min (e Å⁻³)	0.58, −0.53
Computer programs: APEX3 and SAINT (Bruker, 2018), SHELXT2014/5 (Sheldrick, 2015a ), SHELXL2014/7 (Sheldrick, 2015b ), VESTA (Momma & Izumi, 2011 ) and publCIF (Westrip, 2010 ).

Supporting information

CCDC reference: 2141726

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2056989022000494/hb8005sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989022000494/hb8005Isup2.hkl

checkCIF report

Computing details top

Data collection: Instrument Service (Bruker, 2018); cell refinement: APEX3 (Bruker, 2018); data reduction: SAINT (Bruker, 2018); program(s) used to solve structure: SHELXT2014/5 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2015b); molecular graphics: VESTA (Momma & Izumi, 2011); software used to prepare material for publication: publCIF (Westrip, 2010).

3 sodium 1 magnesium 37 boron 9 silicon top

Crystal data top

Na₃MgB₃₇Si₉	D_x = 2.507 Mg m⁻³
M_r = 746.06	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3m	Cell parameters from 6032 reflections
a = 10.1630 (3) Å	θ = 3.7–41.2°
c = 16.5742 (6) Å	µ = 0.72 mm⁻¹
V = 1482.54 (10) Å³	T = 298 K
Z = 3	Plate, black
F(000) = 1068	0.20 × 0.16 × 0.02 mm

Data collection top

Burker, D8 QUEST diffractometer	540 reflections with I > 2σ(I)
Detector resolution: 10 pixels mm^-1	R_int = 0.032
ω scans	θ_max = 30.0°, θ_min = 2.6°
Absorption correction: multi-scan (SADABS; Bruker, 2018)	h = −14→14
T_min = 0.911, T_max = 1.000	k = −14→14
8352 measured reflections	l = −23→22
562 independent reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + 11.3797P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.035	(Δ/σ)_max < 0.001
wR(F²) = 0.076	Δρ_max = 0.58 e Å⁻³
S = 1.31	Δρ_min = −0.53 e Å⁻³
562 reflections	Extinction correction: SHELXL2014/7 (Sheldrick 2015), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
57 parameters	Extinction coefficient: 0.0030 (6)

Special details top

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

Refinement. Refined as a 2-component inversion twin.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Na1	0.5000	0.0000	0.0000	0.0179 (5)
Mg1	0.0000	0.0000	0.2855 (2)	0.0074 (7)	0.5
B1	0.3002 (3)	0.0065 (2)	0.11511 (13)	0.0064 (4)
B2	0.0027 (3)	0.1787 (3)	0.19610 (13)	0.0072 (4)
B3	0.7591 (2)	0.2409 (2)	0.2315 (2)	0.0116 (7)
B4	0.47839 (19)	0.52161 (19)	0.39743 (19)	0.0079 (6)
B5	0.0000	0.0000	0.0744 (12)	0.026 (5)	0.5
Si1	0.0000	0.0000	0.0441 (3)	0.0103 (9)	0.5
Si2	0.46499 (5)	0.53501 (5)	0.27264 (5)	0.0056 (2)
Si3	0.0000	0.0000	0.43049 (10)	0.0120 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Na1	0.0137 (7)	0.0265 (11)	0.0178 (8)	0.0132 (6)	0.0027 (4)	0.0054 (8)
Mg1	0.0060 (9)	0.0060 (9)	0.0102 (15)	0.0030 (5)	0.000	0.000
B1	0.0064 (9)	0.0041 (9)	0.0080 (8)	0.0020 (8)	−0.0004 (7)	0.0001 (8)
B2	0.0054 (9)	0.0053 (9)	0.0102 (9)	0.0022 (8)	−0.0005 (8)	−0.0009 (8)
B3	0.0087 (10)	0.0087 (10)	0.0116 (13)	0.0001 (12)	0.0035 (7)	−0.0035 (7)
B4	0.0050 (9)	0.0050 (9)	0.0116 (13)	0.0009 (11)	−0.0004 (6)	0.0004 (6)
B5	0.033 (8)	0.033 (8)	0.012 (9)	0.017 (4)	0.000	0.000
Si1	0.0061 (11)	0.0061 (11)	0.019 (3)	0.0031 (5)	0.000	0.000
Si2	0.0044 (3)	0.0044 (3)	0.0073 (4)	0.0015 (3)	0.00040 (14)	−0.00040 (14)
Si3	0.0055 (4)	0.0055 (4)	0.0249 (8)	0.0028 (2)	0.000	0.000

Geometric parameters (Å, º) top

Na1—B2ⁱ	2.793 (2)	B3—Si1ⁱ	1.888 (4)
Na1—B2ⁱⁱ	2.793 (2)	B3—B5^xxx	3.343 (19)
Na1—B2ⁱⁱⁱ	2.793 (2)	B3—Na1^xxx	4.123 (3)
Na1—B2^iv	2.793 (2)	B3—Na1^xxxi	4.123 (3)
Na1—B1^v	2.811 (2)	B3—Na1^xxxii	4.605 (3)
Na1—B1^vi	2.811 (2)	B4—B3^xxviii	1.799 (5)
Na1—B1^vii	2.811 (2)	B4—B1^xxxiii	1.815 (3)
Na1—B1	2.811 (2)	B4—B1^xxxiv	1.815 (3)
Na1—Si2^viii	2.8620 (4)	B4—B2^xxxv	1.824 (4)
Na1—Si2^ix	2.8620 (4)	B4—B2^xv	1.824 (4)
Na1—Si2ⁱ	2.8621 (4)	B4—Si2	2.082 (3)
Na1—Si2ⁱⁱ	2.8621 (4)	B4—Mg1^xv	2.568 (3)
Na1—B4^viii	2.9604 (16)	B4—Na1^xxiv	2.9605 (16)
Na1—B4^ix	2.9604 (16)	B4—Na1^xxxiii	2.9605 (16)
Na1—B4ⁱ	2.9605 (16)	B4—B5^xxx	3.319 (3)
Na1—B4ⁱⁱ	2.9605 (16)	B4—B5ⁱ	4.031 (12)
Na1—Mg1ⁱ	3.0389 (9)	B4—B5^xv	4.117 (16)
Na1—Mg1ⁱⁱ	3.0389 (9)	B5—Si1	0.503 (18)
Mg1—B2^x	2.333 (3)	B5—B3^xviii	1.689 (7)
Mg1—B2^xi	2.333 (3)	B5—B3^xxxvi	1.689 (7)
Mg1—B2^xii	2.333 (3)	B5—B3ⁱ	1.689 (7)
Mg1—B2^xiii	2.333 (3)	B5—Si1^xxi	1.96 (2)
Mg1—B2^xiv	2.333 (3)	B5—B5^xxi	2.47 (4)
Mg1—B2	2.333 (3)	B5—B2^xiii	2.705 (16)
Mg1—Si3	2.403 (4)	B5—B2^xiv	2.705 (16)
Mg1—B4^xv	2.568 (3)	B5—B2^xi	2.705 (16)
Mg1—B4^xvi	2.568 (3)	B5—B2^xii	2.705 (16)
Mg1—B4^xvii	2.568 (3)	B5—B2^x	2.705 (16)
Mg1—Si2^xv	2.933 (2)	Si1—Si1^xxi	1.460 (10)
Mg1—Si2^xvii	2.933 (2)	Si1—B3^xviii	1.887 (4)
B1—B3^xviii	1.791 (3)	Si1—B3^xxxvi	1.887 (4)
B1—B2^iv	1.798 (3)	Si1—B3ⁱ	1.888 (4)
B1—B1^xix	1.806 (4)	Si1—B5^xxi	1.96 (2)
B1—B2^xiv	1.813 (3)	Si1—Na1^xiv	5.1337 (7)
B1—B4^ix	1.815 (3)	Si1—Na1^xxii	5.1337 (7)
B1—Si2ⁱ	2.043 (2)	Si1—Na1^xxxvii	5.1337 (7)
B1—B5	3.093 (5)	Si1—Na1^xxxviii	5.1337 (7)
B1—Na1^xx	3.954 (2)	Si1—Na1^x	5.1337 (7)
B1—B5ⁱ	4.268 (12)	Si2—B1ⁱ	2.043 (2)
B1—B5^xxi	4.356 (15)	Si2—B1^xxix	2.043 (2)
B1—Na1^xxii	4.768 (2)	Si2—Si3^xv	2.3951 (9)
B2—B2^xiii	1.761 (5)	Si2—Na1^xxxiii	2.8621 (4)
B2—B1^xxiii	1.798 (3)	Si2—Na1^xxiv	2.8621 (4)
B2—B1^x	1.813 (3)	Si2—Mg1^xv	2.933 (2)
B2—B3ⁱ	1.816 (4)	Si2—B5ⁱ	3.5572 (16)
B2—B4^xv	1.824 (4)	Si2—B5^xxx	4.197 (11)
B2—B2^xi	1.843 (5)	Si2—Na1^xxii	4.5605 (8)
B2—B5	2.705 (16)	Si2—Na1^xxxix	5.3470 (8)
B2—Na1^xxiv	2.793 (2)	Si3—Si3^xl	2.304 (3)
B2—Na1^xxv	4.143 (2)	Si3—Si2^xv	2.3951 (9)
B2—B5^xxvi	4.537 (5)	Si3—Si2^xvi	2.3952 (9)
B2—Na1^x	4.617 (2)	Si3—Si2^xvii	2.3952 (9)
B3—B5ⁱ	1.689 (7)	Si3—Na1^xx	3.3466 (8)
B3—B1^xxvii	1.791 (3)	Si3—Na1^xxv	3.3467 (8)
B3—B1^iv	1.791 (3)	Si3—Na1^xxiv	3.3467 (8)
B3—B4^xxviii	1.799 (5)	Si3—Na1^xli	4.8918 (14)
B3—B2ⁱ	1.816 (4)	Si3—Na1^xlii	4.8918 (14)
B3—B2^xxix	1.816 (4)	Si3—Na1^xliii	4.8918 (14)

B2ⁱ—Na1—B2ⁱⁱ	180.00 (5)	B1^iv—B3—B2^xxix	60.33 (12)
B2ⁱ—Na1—B2ⁱⁱⁱ	143.25 (9)	B4^xxviii—B3—B2^xxix	109.8 (2)
B2ⁱⁱ—Na1—B2ⁱⁱⁱ	36.75 (9)	B2ⁱ—B3—B2^xxix	60.99 (18)
B2ⁱ—Na1—B2^iv	36.75 (9)	B5ⁱ—B3—Si1ⁱ	14.9 (6)
B2ⁱⁱ—Na1—B2^iv	143.25 (9)	B1^xxvii—B3—Si1ⁱ	123.43 (12)
B2ⁱⁱⁱ—Na1—B2^iv	180.00 (11)	B1^iv—B3—Si1ⁱ	123.43 (12)
B2ⁱ—Na1—B1^v	109.34 (7)	B4^xxviii—B3—Si1ⁱ	129.2 (2)
B2ⁱⁱ—Na1—B1^v	70.66 (7)	B2ⁱ—B3—Si1ⁱ	113.5 (2)
B2ⁱⁱⁱ—Na1—B1^v	37.43 (6)	B2^xxix—B3—Si1ⁱ	113.5 (2)
B2^iv—Na1—B1^v	142.57 (6)	B5ⁱ—B3—B5^xxx	45.3 (8)
B2ⁱ—Na1—B1^vi	37.43 (6)	B1^xxvii—B3—B5^xxx	112.55 (16)
B2ⁱⁱ—Na1—B1^vi	142.57 (6)	B1^iv—B3—B5^xxx	112.55 (16)
B2ⁱⁱⁱ—Na1—B1^vi	109.34 (7)	B4^xxviii—B3—B5^xxx	98.8 (3)
B2^iv—Na1—B1^vi	70.66 (7)	B2ⁱ—B3—B5^xxx	136.96 (19)
B1^v—Na1—B1^vi	85.53 (9)	B2^xxix—B3—B5^xxx	136.96 (19)
B2ⁱ—Na1—B1^vii	142.57 (6)	Si1ⁱ—B3—B5^xxx	30.4 (3)
B2ⁱⁱ—Na1—B1^vii	37.43 (6)	B5ⁱ—B3—Na1^xxx	122.5 (5)
B2ⁱⁱⁱ—Na1—B1^vii	70.66 (7)	B1^xxvii—B3—Na1^xxx	99.85 (16)
B2^iv—Na1—B1^vii	109.34 (7)	B1^iv—B3—Na1^xxx	33.59 (11)
B1^v—Na1—B1^vii	94.47 (9)	B4^xxviii—B3—Na1^xxx	39.37 (5)
B1^vi—Na1—B1^vii	180.00 (6)	B2ⁱ—B3—Na1^xxx	133.94 (17)
B2ⁱ—Na1—B1	70.66 (7)	B2^xxix—B3—Na1^xxx	93.92 (11)
B2ⁱⁱ—Na1—B1	109.34 (7)	Si1ⁱ—B3—Na1^xxx	111.86 (14)
B2ⁱⁱⁱ—Na1—B1	142.57 (6)	B5^xxx—B3—Na1^xxx	88.28 (16)
B2^iv—Na1—B1	37.43 (6)	B5ⁱ—B3—Na1^xxxi	122.5 (5)
B1^v—Na1—B1	180.0	B1^xxvii—B3—Na1^xxxi	33.59 (11)
B1^vi—Na1—B1	94.47 (9)	B1^iv—B3—Na1^xxxi	99.85 (16)
B1^vii—Na1—B1	85.53 (9)	B4^xxviii—B3—Na1^xxxi	39.37 (5)
B2ⁱ—Na1—Si2^viii	78.17 (5)	B2ⁱ—B3—Na1^xxxi	93.92 (11)
B2ⁱⁱ—Na1—Si2^viii	101.83 (5)	B2^xxix—B3—Na1^xxxi	133.94 (17)
B2ⁱⁱⁱ—Na1—Si2^viii	76.28 (5)	Si1ⁱ—B3—Na1^xxxi	111.86 (14)
B2^iv—Na1—Si2^viii	103.72 (5)	B5^xxx—B3—Na1^xxxi	88.28 (16)
B1^v—Na1—Si2^viii	73.21 (5)	Na1^xxx—B3—Na1^xxxi	76.09 (7)
B1^vi—Na1—Si2^viii	42.21 (5)	B5ⁱ—B3—Na1	101.0 (6)
B1^vii—Na1—Si2^viii	137.79 (5)	B1^xxvii—B3—Na1	57.83 (11)
B1—Na1—Si2^viii	106.79 (5)	B1^iv—B3—Na1	111.50 (15)
B2ⁱ—Na1—Si2^ix	101.83 (5)	B4^xxviii—B3—Na1	108.78 (14)
B2ⁱⁱ—Na1—Si2^ix	78.17 (5)	B2ⁱ—B3—Na1	3.02 (8)
B2ⁱⁱⁱ—Na1—Si2^ix	103.72 (5)	B2^xxix—B3—Na1	63.98 (11)
B2^iv—Na1—Si2^ix	76.28 (5)	Si1ⁱ—B3—Na1	113.12 (15)
B1^v—Na1—Si2^ix	106.79 (5)	B5^xxx—B3—Na1	135.32 (13)
B1^vi—Na1—Si2^ix	137.79 (5)	Na1^xxx—B3—Na1	134.78 (8)
B1^vii—Na1—Si2^ix	42.21 (5)	Na1^xxxi—B3—Na1	91.40 (4)
B1—Na1—Si2^ix	73.21 (5)	B5ⁱ—B3—Na1^xxxii	101.0 (6)
Si2^viii—Na1—Si2^ix	180.00 (3)	B1^xxvii—B3—Na1^xxxii	111.50 (15)
B2ⁱ—Na1—Si2ⁱ	103.71 (5)	B1^iv—B3—Na1^xxxii	57.83 (11)
B2ⁱⁱ—Na1—Si2ⁱ	76.29 (5)	B4^xxviii—B3—Na1^xxxii	108.78 (14)
B2ⁱⁱⁱ—Na1—Si2ⁱ	101.83 (5)	B2ⁱ—B3—Na1^xxxii	63.98 (11)
B2^iv—Na1—Si2ⁱ	78.17 (5)	B2^xxix—B3—Na1^xxxii	3.02 (8)
B1^v—Na1—Si2ⁱ	137.79 (5)	Si1ⁱ—B3—Na1^xxxii	113.12 (15)
B1^vi—Na1—Si2ⁱ	106.80 (5)	B5^xxx—B3—Na1^xxxii	135.32 (13)
B1^vii—Na1—Si2ⁱ	73.20 (5)	Na1^xxx—B3—Na1^xxxii	91.40 (4)
B1—Na1—Si2ⁱ	42.21 (5)	Na1^xxxi—B3—Na1^xxxii	134.78 (8)
Si2^viii—Na1—Si2ⁱ	89.06 (3)	Na1—B3—Na1^xxxii	66.97 (5)
Si2^ix—Na1—Si2ⁱ	90.94 (3)	B3^xxviii—B4—B1^xxxiii	59.41 (12)
B2ⁱ—Na1—Si2ⁱⁱ	76.29 (5)	B3^xxviii—B4—B1^xxxiv	59.41 (12)
B2ⁱⁱ—Na1—Si2ⁱⁱ	103.71 (5)	B1^xxxiii—B4—B1^xxxiv	107.0 (2)
B2ⁱⁱⁱ—Na1—Si2ⁱⁱ	78.17 (5)	B3^xxviii—B4—B2^xxxv	106.60 (19)
B2^iv—Na1—Si2ⁱⁱ	101.83 (5)	B1^xxxiii—B4—B2^xxxv	59.22 (12)
B1^v—Na1—Si2ⁱⁱ	42.21 (5)	B1^xxxiv—B4—B2^xxxv	107.49 (19)
B1^vi—Na1—Si2ⁱⁱ	73.20 (5)	B3^xxviii—B4—B2^xv	106.60 (19)
B1^vii—Na1—Si2ⁱⁱ	106.80 (5)	B1^xxxiii—B4—B2^xv	107.49 (19)
B1—Na1—Si2ⁱⁱ	137.79 (5)	B1^xxxiv—B4—B2^xv	59.22 (12)
Si2^viii—Na1—Si2ⁱⁱ	90.94 (3)	B2^xxxv—B4—B2^xv	60.69 (17)
Si2^ix—Na1—Si2ⁱⁱ	89.06 (3)	B3^xxviii—B4—Si2	116.8 (2)
Si2ⁱ—Na1—Si2ⁱⁱ	180.00 (3)	B1^xxxiii—B4—Si2	120.31 (12)
B2ⁱ—Na1—B4^viii	109.24 (8)	B1^xxxiv—B4—Si2	120.31 (12)
B2ⁱⁱ—Na1—B4^viii	70.76 (8)	B2^xxxv—B4—Si2	126.71 (16)
B2ⁱⁱⁱ—Na1—B4^viii	36.82 (8)	B2^xv—B4—Si2	126.71 (16)
B2^iv—Na1—B4^viii	143.18 (8)	B3^xxviii—B4—Mg1^xv	165.7 (2)
B1^v—Na1—B4^viii	36.55 (7)	B1^xxxiii—B4—Mg1^xv	114.65 (14)
B1^vi—Na1—B4^viii	72.94 (8)	B1^xxxiv—B4—Mg1^xv	114.65 (14)
B1^vii—Na1—B4^viii	107.06 (8)	B2^xxxv—B4—Mg1^xv	61.46 (13)
B1—Na1—B4^viii	143.45 (7)	B2^xv—B4—Mg1^xv	61.46 (13)
Si2^viii—Na1—B4^viii	41.86 (6)	Si2—B4—Mg1^xv	77.46 (13)
Si2^ix—Na1—B4^viii	138.14 (6)	B3^xxviii—B4—Na1^xxiv	117.95 (7)
Si2ⁱ—Na1—B4^viii	107.63 (6)	B1^xxxiii—B4—Na1^xxiv	173.12 (16)
Si2ⁱⁱ—Na1—B4^viii	72.37 (6)	B1^xxxiv—B4—Na1^xxiv	67.24 (8)
B2ⁱ—Na1—B4^ix	70.76 (8)	B2^xxxv—B4—Na1^xxiv	118.03 (15)
B2ⁱⁱ—Na1—B4^ix	109.24 (8)	B2^xv—B4—Na1^xxiv	66.59 (8)
B2ⁱⁱⁱ—Na1—B4^ix	143.18 (8)	Si2—B4—Na1^xxiv	66.54 (6)
B2^iv—Na1—B4^ix	36.82 (8)	Mg1^xv—B4—Na1^xxiv	66.25 (7)
B1^v—Na1—B4^ix	143.45 (7)	B3^xxviii—B4—Na1^xxxiii	117.95 (7)
B1^vi—Na1—B4^ix	107.06 (8)	B1^xxxiii—B4—Na1^xxxiii	67.24 (8)
B1^vii—Na1—B4^ix	72.94 (8)	B1^xxxiv—B4—Na1^xxxiii	173.12 (16)
B1—Na1—B4^ix	36.55 (7)	B2^xxxv—B4—Na1^xxxiii	66.59 (8)
Si2^viii—Na1—B4^ix	138.14 (6)	B2^xv—B4—Na1^xxxiii	118.03 (15)
Si2^ix—Na1—B4^ix	41.86 (6)	Si2—B4—Na1^xxxiii	66.54 (6)
Si2ⁱ—Na1—B4^ix	72.37 (6)	Mg1^xv—B4—Na1^xxxiii	66.25 (7)
Si2ⁱⁱ—Na1—B4^ix	107.63 (6)	Na1^xxiv—B4—Na1^xxxiii	118.24 (11)
B4^viii—Na1—B4^ix	180.00 (18)	B3^xxviii—B4—B5^xxx	17.4 (4)
B2ⁱ—Na1—B4ⁱ	143.17 (8)	B1^xxxiii—B4—B5^xxx	66.8 (2)
B2ⁱⁱ—Na1—B4ⁱ	36.83 (8)	B1^xxxiv—B4—B5^xxx	66.8 (2)
B2ⁱⁱⁱ—Na1—B4ⁱ	70.76 (8)	B2^xxxv—B4—B5^xxx	121.1 (3)
B2^iv—Na1—B4ⁱ	109.24 (8)	B2^xv—B4—B5^xxx	121.1 (3)
B1^v—Na1—B4ⁱ	107.06 (8)	Si2—B4—B5^xxx	99.4 (4)
B1^vi—Na1—B4ⁱ	143.45 (7)	Mg1^xv—B4—B5^xxx	176.9 (4)
B1^vii—Na1—B4ⁱ	36.55 (7)	Na1^xxiv—B4—B5^xxx	112.64 (15)
B1—Na1—B4ⁱ	72.94 (8)	Na1^xxxiii—B4—B5^xxx	112.64 (15)
Si2^viii—Na1—B4ⁱ	107.63 (6)	B3^xxviii—B4—B5ⁱ	55.0 (3)
Si2^ix—Na1—B4ⁱ	72.37 (6)	B1^xxxiii—B4—B5ⁱ	87.8 (2)
Si2ⁱ—Na1—B4ⁱ	41.85 (6)	B1^xxxiv—B4—B5ⁱ	87.8 (2)
Si2ⁱⁱ—Na1—B4ⁱ	138.15 (6)	B2^xxxv—B4—B5ⁱ	146.20 (15)
B4^viii—Na1—B4ⁱ	96.65 (12)	B2^xv—B4—B5ⁱ	146.20 (15)
B4^ix—Na1—B4ⁱ	83.35 (12)	Si2—B4—B5ⁱ	61.8 (3)
B2ⁱ—Na1—B4ⁱⁱ	36.83 (8)	Mg1^xv—B4—B5ⁱ	139.3 (3)
B2ⁱⁱ—Na1—B4ⁱⁱ	143.17 (8)	Na1^xxiv—B4—B5ⁱ	95.59 (14)
B2ⁱⁱⁱ—Na1—B4ⁱⁱ	109.24 (8)	Na1^xxxiii—B4—B5ⁱ	95.59 (14)
B2^iv—Na1—B4ⁱⁱ	70.76 (8)	B5^xxx—B4—B5ⁱ	37.6 (6)
B1^v—Na1—B4ⁱⁱ	72.94 (8)	B3^xxviii—B4—B5^xv	108.0 (2)
B1^vi—Na1—B4ⁱⁱ	36.55 (7)	B1^xxxiii—B4—B5^xv	82.20 (16)
B1^vii—Na1—B4ⁱⁱ	143.45 (7)	B1^xxxiv—B4—B5^xv	82.20 (16)
B1—Na1—B4ⁱⁱ	107.06 (8)	B2^xxxv—B4—B5^xv	30.37 (9)
Si2^viii—Na1—B4ⁱⁱ	72.37 (6)	B2^xv—B4—B5^xv	30.37 (9)
Si2^ix—Na1—B4ⁱⁱ	107.63 (6)	Si2—B4—B5^xv	135.2 (2)
Si2ⁱ—Na1—B4ⁱⁱ	138.15 (6)	Mg1^xv—B4—B5^xv	57.7 (2)
Si2ⁱⁱ—Na1—B4ⁱⁱ	41.85 (6)	Na1^xxiv—B4—B5^xv	93.09 (12)
B4^viii—Na1—B4ⁱⁱ	83.35 (12)	Na1^xxxiii—B4—B5^xv	93.09 (12)
B4^ix—Na1—B4ⁱⁱ	96.65 (12)	B5^xxx—B4—B5^xv	125.4 (2)
B4ⁱ—Na1—B4ⁱⁱ	180.00 (13)	B5ⁱ—B4—B5^xv	163.0 (4)
B2ⁱ—Na1—Mg1ⁱ	46.93 (7)	Si1—B5—B3^xviii	105.6 (7)
B2ⁱⁱ—Na1—Mg1ⁱ	133.07 (7)	Si1—B5—B3^xxxvi	105.6 (7)
B2ⁱⁱⁱ—Na1—Mg1ⁱ	133.07 (7)	B3^xviii—B5—B3^xxxvi	113.0 (6)
B2^iv—Na1—Mg1ⁱ	46.93 (7)	Si1—B5—B3ⁱ	105.6 (7)
B1^v—Na1—Mg1ⁱ	101.34 (6)	B3^xviii—B5—B3ⁱ	113.0 (6)
B1^vi—Na1—Mg1ⁱ	78.66 (6)	B3^xxxvi—B5—B3ⁱ	113.0 (6)
B1^vii—Na1—Mg1ⁱ	101.34 (6)	Si1—B5—Si1^xxi	0.0
B1—Na1—Mg1ⁱ	78.65 (6)	B3^xviii—B5—Si1^xxi	105.6 (7)
Si2^viii—Na1—Mg1ⁱ	120.47 (4)	B3^xxxvi—B5—Si1^xxi	105.6 (7)
Si2^ix—Na1—Mg1ⁱ	59.53 (4)	B3ⁱ—B5—Si1^xxi	105.6 (7)
Si2ⁱ—Na1—Mg1ⁱ	120.47 (4)	Si1—B5—B5^xxi	0.000 (1)
Si2ⁱⁱ—Na1—Mg1ⁱ	59.53 (4)	B3^xviii—B5—B5^xxi	105.6 (7)
B4^viii—Na1—Mg1ⁱ	129.34 (6)	B3^xxxvi—B5—B5^xxi	105.6 (7)
B4^ix—Na1—Mg1ⁱ	50.66 (6)	B3ⁱ—B5—B5^xxi	105.6 (7)
B4ⁱ—Na1—Mg1ⁱ	129.34 (6)	Si1^xxi—B5—B5^xxi	0.0
B4ⁱⁱ—Na1—Mg1ⁱ	50.66 (6)	Si1—B5—B2	138.2 (3)
B2ⁱ—Na1—Mg1ⁱⁱ	133.07 (7)	B3^xviii—B5—B2	77.9 (5)
B2ⁱⁱ—Na1—Mg1ⁱⁱ	46.93 (7)	B3^xxxvi—B5—B2	111.0 (9)
B2ⁱⁱⁱ—Na1—Mg1ⁱⁱ	46.93 (7)	B3ⁱ—B5—B2	41.2 (4)
B2^iv—Na1—Mg1ⁱⁱ	133.07 (7)	Si1^xxi—B5—B2	138.2 (3)
B1^v—Na1—Mg1ⁱⁱ	78.66 (6)	B5^xxi—B5—B2	138.2 (3)
B1^vi—Na1—Mg1ⁱⁱ	101.34 (6)	Si1—B5—B2^xiii	138.2 (3)
B1^vii—Na1—Mg1ⁱⁱ	78.66 (6)	B3^xviii—B5—B2^xiii	41.2 (4)
B1—Na1—Mg1ⁱⁱ	101.35 (6)	B3^xxxvi—B5—B2^xiii	111.1 (9)
Si2^viii—Na1—Mg1ⁱⁱ	59.53 (4)	B3ⁱ—B5—B2^xiii	77.9 (5)
Si2^ix—Na1—Mg1ⁱⁱ	120.47 (4)	Si1^xxi—B5—B2^xiii	138.2 (3)
Si2ⁱ—Na1—Mg1ⁱⁱ	59.53 (4)	B5^xxi—B5—B2^xiii	138.2 (3)
Si2ⁱⁱ—Na1—Mg1ⁱⁱ	120.47 (4)	B2—B5—B2^xiii	38.0 (2)
B4^viii—Na1—Mg1ⁱⁱ	50.66 (6)	Si1—B5—B2^xiv	138.2 (3)
B4^ix—Na1—Mg1ⁱⁱ	129.34 (6)	B3^xviii—B5—B2^xiv	41.2 (4)
B4ⁱ—Na1—Mg1ⁱⁱ	50.66 (6)	B3^xxxvi—B5—B2^xiv	77.9 (5)
B4ⁱⁱ—Na1—Mg1ⁱⁱ	129.34 (6)	B3ⁱ—B5—B2^xiv	111.1 (9)
Mg1ⁱ—Na1—Mg1ⁱⁱ	180.00 (13)	Si1^xxi—B5—B2^xiv	138.2 (3)
B2^x—Mg1—B2^xi	44.34 (12)	B5^xxi—B5—B2^xiv	138.2 (3)
B2^x—Mg1—B2^xii	46.53 (12)	B2—B5—B2^xiv	70.5 (5)
B2^xi—Mg1—B2^xii	83.96 (13)	B2^xiii—B5—B2^xiv	39.8 (3)
B2^x—Mg1—B2^xiii	101.12 (17)	Si1—B5—B2^xi	138.2 (3)
B2^xi—Mg1—B2^xiii	83.96 (13)	B3^xviii—B5—B2^xi	111.0 (9)
B2^xii—Mg1—B2^xiii	83.96 (13)	B3^xxxvi—B5—B2^xi	77.9 (5)
B2^x—Mg1—B2^xiv	83.96 (13)	B3ⁱ—B5—B2^xi	41.2 (4)
B2^xi—Mg1—B2^xiv	101.12 (17)	Si1^xxi—B5—B2^xi	138.2 (3)
B2^xii—Mg1—B2^xiv	44.34 (12)	B5^xxi—B5—B2^xi	138.2 (3)
B2^xiii—Mg1—B2^xiv	46.53 (12)	B2—B5—B2^xi	39.8 (3)
B2^x—Mg1—B2	83.96 (13)	B2^xiii—B5—B2^xi	70.5 (5)
B2^xi—Mg1—B2	46.52 (12)	B2^xiv—B5—B2^xi	83.5 (6)
B2^xii—Mg1—B2	101.12 (17)	Si1—B5—B2^xii	138.2 (3)
B2^xiii—Mg1—B2	44.34 (12)	B3^xviii—B5—B2^xii	77.9 (5)
B2^xiv—Mg1—B2	83.96 (13)	B3^xxxvi—B5—B2^xii	41.2 (4)
B2^x—Mg1—Si3	129.43 (9)	B3ⁱ—B5—B2^xii	111.1 (9)
B2^xi—Mg1—Si3	129.43 (9)	Si1^xxi—B5—B2^xii	138.2 (3)
B2^xii—Mg1—Si3	129.43 (9)	B5^xxi—B5—B2^xii	138.2 (3)
B2^xiii—Mg1—Si3	129.43 (9)	B2—B5—B2^xii	83.5 (6)
B2^xiv—Mg1—Si3	129.43 (9)	B2^xiii—B5—B2^xii	70.5 (5)
B2—Mg1—Si3	129.43 (9)	B2^xiv—B5—B2^xii	38.0 (2)
B2^x—Mg1—B4^xv	85.59 (9)	B2^xi—B5—B2^xii	70.5 (5)
B2^xi—Mg1—B4^xv	43.37 (9)	Si1—B5—B2^x	138.2 (3)
B2^xii—Mg1—B4^xv	127.11 (15)	B3^xviii—B5—B2^x	111.1 (9)
B2^xiii—Mg1—B4^xv	85.59 (9)	B3^xxxvi—B5—B2^x	41.2 (4)
B2^xiv—Mg1—B4^xv	127.11 (15)	B3ⁱ—B5—B2^x	77.9 (5)
B2—Mg1—B4^xv	43.37 (9)	Si1^xxi—B5—B2^x	138.2 (3)
Si3—Mg1—B4^xv	96.04 (11)	B5^xxi—B5—B2^x	138.2 (3)
B2^x—Mg1—B4^xvi	43.37 (9)	B2—B5—B2^x	70.5 (5)
B2^xi—Mg1—B4^xvi	85.59 (9)	B2^xiii—B5—B2^x	83.5 (6)
B2^xii—Mg1—B4^xvi	43.37 (9)	B2^xiv—B5—B2^x	70.5 (5)
B2^xiii—Mg1—B4^xvi	127.11 (15)	B2^xi—B5—B2^x	38.0 (2)
B2^xiv—Mg1—B4^xvi	85.59 (9)	B2^xii—B5—B2^x	39.8 (3)
B2—Mg1—B4^xvi	127.11 (15)	B5—Si1—Si1^xxi	180.0
Si3—Mg1—B4^xvi	96.04 (11)	B5—Si1—B3^xviii	59.53 (17)
B4^xv—Mg1—B4^xvi	118.91 (4)	Si1^xxi—Si1—B3^xviii	120.47 (17)
B2^x—Mg1—B4^xvii	127.11 (15)	B5—Si1—B3^xxxvi	59.53 (17)
B2^xi—Mg1—B4^xvii	127.11 (15)	Si1^xxi—Si1—B3^xxxvi	120.47 (17)
B2^xii—Mg1—B4^xvii	85.59 (9)	B3^xviii—Si1—B3^xxxvi	96.6 (2)
B2^xiii—Mg1—B4^xvii	43.37 (9)	B5—Si1—B3ⁱ	59.53 (17)
B2^xiv—Mg1—B4^xvii	43.37 (9)	Si1^xxi—Si1—B3ⁱ	120.47 (17)
B2—Mg1—B4^xvii	85.59 (9)	B3^xviii—Si1—B3ⁱ	96.6 (2)
Si3—Mg1—B4^xvii	96.04 (11)	B3^xxxvi—Si1—B3ⁱ	96.6 (2)
B4^xv—Mg1—B4^xvii	118.91 (4)	B5—Si1—B5^xxi	180.0
B4^xvi—Mg1—B4^xvii	118.91 (4)	Si1^xxi—Si1—B5^xxi	0.0
B2^x—Mg1—Si2^xv	112.42 (6)	B3^xviii—Si1—B5^xxi	120.47 (17)
B2^xi—Mg1—Si2^xv	82.24 (6)	B3^xxxvi—Si1—B5^xxi	120.47 (17)
B2^xii—Mg1—Si2^xv	157.19 (6)	B3ⁱ—Si1—B5^xxi	120.47 (17)
B2^xiii—Mg1—Si2^xv	112.42 (6)	B5—Si1—Na1^xiv	98.18 (5)
B2^xiv—Mg1—Si2^xv	157.19 (6)	Si1^xxi—Si1—Na1^xiv	81.82 (5)
B2—Mg1—Si2^xv	82.24 (6)	B3^xviii—Si1—Na1^xiv	144.19 (12)
Si3—Mg1—Si2^xv	52.19 (6)	B3^xxxvi—Si1—Na1^xiv	48.18 (10)
B4^xv—Mg1—Si2^xv	43.85 (8)	B3ⁱ—Si1—Na1^xiv	94.136 (18)
B4^xvi—Mg1—Si2^xv	117.22 (8)	B5^xxi—Si1—Na1^xiv	81.82 (5)
B4^xvii—Mg1—Si2^xv	117.22 (8)	B5—Si1—Na1^xxii	98.18 (5)
B2^x—Mg1—Si2^xvii	157.19 (6)	Si1^xxi—Si1—Na1^xxii	81.82 (5)
B2^xi—Mg1—Si2^xvii	157.19 (6)	B3^xviii—Si1—Na1^xxii	48.18 (10)
B2^xii—Mg1—Si2^xvii	112.42 (6)	B3^xxxvi—Si1—Na1^xxii	144.19 (12)
B2^xiii—Mg1—Si2^xvii	82.24 (6)	B3ⁱ—Si1—Na1^xxii	94.136 (18)
B2^xiv—Mg1—Si2^xvii	82.24 (6)	B5^xxi—Si1—Na1^xxii	81.82 (5)
B2—Mg1—Si2^xvii	112.42 (6)	Na1^xiv—Si1—Na1^xxii	163.65 (11)
Si3—Mg1—Si2^xvii	52.19 (6)	B5—Si1—Na1^xxxvii	98.18 (5)
B4^xv—Mg1—Si2^xvii	117.22 (8)	Si1^xxi—Si1—Na1^xxxvii	81.82 (5)
B4^xvi—Mg1—Si2^xvii	117.21 (8)	B3^xviii—Si1—Na1^xxxvii	144.19 (12)
B4^xvii—Mg1—Si2^xvii	43.85 (8)	B3^xxxvi—Si1—Na1^xxxvii	94.135 (18)
Si2^xv—Mg1—Si2^xvii	86.35 (8)	B3ⁱ—Si1—Na1^xxxvii	48.18 (10)
B3^xviii—B1—B2^iv	108.06 (16)	B5^xxi—Si1—Na1^xxxvii	81.82 (5)
B3^xviii—B1—B1^xix	107.43 (15)	Na1^xiv—Si1—Na1^xxxvii	59.328 (9)
B2^iv—B1—B1^xix	60.40 (13)	Na1^xxii—Si1—Na1^xxxvii	118.01 (3)
B3^xviii—B1—B2^xiv	60.52 (15)	B5—Si1—Na1^xxxviii	98.18 (5)
B2^iv—B1—B2^xiv	108.83 (15)	Si1^xxi—Si1—Na1^xxxviii	81.82 (5)
B1^xix—B1—B2^xiv	59.60 (13)	B3^xviii—Si1—Na1^xxxviii	94.137 (18)
B3^xviii—B1—B4^ix	59.85 (16)	B3^xxxvi—Si1—Na1^xxxviii	48.19 (10)
B2^iv—B1—B4^ix	60.63 (15)	B3ⁱ—Si1—Na1^xxxviii	144.19 (12)
B1^xix—B1—B4^ix	108.74 (15)	B5^xxi—Si1—Na1^xxxviii	81.82 (5)
B2^xiv—B1—B4^ix	109.26 (16)	Na1^xiv—Si1—Na1^xxxviii	59.328 (9)
B3^xviii—B1—Si2ⁱ	110.42 (15)	Na1^xxii—Si1—Na1^xxxviii	118.01 (3)
B2^iv—B1—Si2ⁱ	136.22 (14)	Na1^xxxvii—Si1—Na1^xxxviii	118.01 (3)
B1^xix—B1—Si2ⁱ	123.70 (8)	B5—Si1—Na1	98.18 (5)
B2^xiv—B1—Si2ⁱ	107.77 (13)	Si1^xxi—Si1—Na1	81.82 (5)
B4^ix—B1—Si2ⁱ	125.94 (15)	B3^xviii—Si1—Na1	48.19 (10)
B3^xviii—B1—Na1	125.76 (15)	B3^xxxvi—Si1—Na1	94.137 (18)
B2^iv—B1—Na1	70.74 (10)	B3ⁱ—Si1—Na1	144.19 (12)
B1^xix—B1—Na1	116.13 (15)	B5^xxi—Si1—Na1	81.82 (5)
B2^xiv—B1—Na1	173.69 (13)	Na1^xiv—Si1—Na1	118.01 (3)
B4^ix—B1—Na1	76.20 (11)	Na1^xxii—Si1—Na1	59.328 (9)
Si2ⁱ—B1—Na1	70.23 (6)	Na1^xxxvii—Si1—Na1	163.65 (11)
B3^xviii—B1—B5	26.44 (12)	Na1^xxxviii—Si1—Na1	59.329 (9)
B2^iv—B1—B5	134.42 (13)	B5—Si1—Na1^x	98.18 (5)
B1^xix—B1—B5	118.8 (4)	Si1^xxi—Si1—Na1^x	81.82 (5)
B2^xiv—B1—B5	60.4 (4)	B3^xviii—Si1—Na1^x	94.135 (18)
B4^ix—B1—B5	80.5 (2)	B3^xxxvi—Si1—Na1^x	144.19 (12)
Si2ⁱ—B1—B5	85.06 (18)	B3ⁱ—Si1—Na1^x	48.18 (10)
Na1—B1—B5	124.6 (4)	B5^xxi—Si1—Na1^x	81.82 (5)
B3^xviii—B1—Na1^xx	99.62 (14)	Na1^xiv—Si1—Na1^x	118.01 (3)
B2^iv—B1—Na1^xx	99.93 (10)	Na1^xxii—Si1—Na1^x	59.328 (9)
B1^xix—B1—Na1^xx	39.67 (11)	Na1^xxxvii—Si1—Na1^x	59.328 (9)
B2^xiv—B1—Na1^xx	39.15 (8)	Na1^xxxviii—Si1—Na1^x	163.65 (11)
B4^ix—B1—Na1^xx	139.11 (13)	Na1—Si1—Na1^x	118.01 (3)
Si2ⁱ—B1—Na1^xx	93.52 (7)	B1ⁱ—Si2—B1^xxix	99.44 (13)
Na1—B1—Na1^xx	134.55 (7)	B1ⁱ—Si2—B4	112.65 (8)
B5—B1—Na1^xx	94.3 (3)	B1^xxix—Si2—B4	112.65 (8)
B3^xviii—B1—B5ⁱ	102.63 (12)	B1ⁱ—Si2—Si3^xv	110.23 (7)
B2^iv—B1—B5ⁱ	23.0 (2)	B1^xxix—Si2—Si3^xv	110.23 (7)
B1^xix—B1—B5ⁱ	39.4 (2)	B4—Si2—Si3^xv	111.12 (10)
B2^xiv—B1—B5ⁱ	86.6 (2)	B1ⁱ—Si2—Na1^xxxiii	166.61 (7)
B4^ix—B1—B5ⁱ	72.9 (2)	B1^xxix—Si2—Na1^xxxiii	67.56 (6)
Si2ⁱ—B1—B5ⁱ	146.89 (9)	B4—Si2—Na1^xxxiii	71.60 (4)
Na1—B1—B5ⁱ	92.17 (19)	Si3^xv—Si2—Na1^xxxiii	78.52 (2)
B5—B1—B5ⁱ	127.32 (17)	B1ⁱ—Si2—Na1^xxiv	67.56 (6)
Na1^xx—B1—B5ⁱ	78.9 (2)	B1^xxix—Si2—Na1^xxiv	166.61 (7)
B3^xviii—B1—B5^xxi	45.13 (19)	B4—Si2—Na1^xxiv	71.60 (4)
B2^iv—B1—B5^xxi	127.76 (14)	Si3^xv—Si2—Na1^xxiv	78.52 (2)
B1^xix—B1—B5^xxi	151.4 (2)	Na1^xxxiii—Si2—Na1^xxiv	125.18 (3)
B2^xiv—B1—B5^xxi	93.9 (2)	B1ⁱ—Si2—Mg1^xv	130.08 (7)
B4^ix—B1—B5^xxi	67.63 (14)	B1^xxix—Si2—Mg1^xv	130.08 (6)
Si2ⁱ—B1—B5^xxi	71.88 (9)	B4—Si2—Mg1^xv	58.69 (11)
Na1—B1—B5^xxi	91.1 (2)	Si3^xv—Si2—Mg1^xv	52.42 (7)
B5—B1—B5^xxi	33.5 (6)	Na1^xxxiii—Si2—Mg1^xv	63.235 (15)
Na1^xx—B1—B5^xxi	124.81 (18)	Na1^xxiv—Si2—Mg1^xv	63.235 (15)
B5ⁱ—B1—B5^xxi	138.30 (13)	B1ⁱ—Si2—B5ⁱ	60.03 (17)
B3^xviii—B1—Na1^xxii	58.43 (12)	B1^xxix—Si2—B5ⁱ	60.03 (17)
B2^iv—B1—Na1^xxii	59.13 (9)	B4—Si2—B5ⁱ	87.2 (3)
B1^xix—B1—Na1^xxii	105.05 (8)	Si3^xv—Si2—B5ⁱ	161.7 (3)
B2^xiv—B1—Na1^xxii	105.67 (11)	Na1^xxxiii—Si2—B5ⁱ	108.61 (12)
B4^ix—B1—Na1^xxii	4.27 (10)	Na1^xxiv—Si2—B5ⁱ	108.61 (12)
Si2ⁱ—B1—Na1^xxii	130.03 (8)	Mg1^xv—Si2—B5ⁱ	145.8 (3)
Na1—B1—Na1^xxii	79.66 (5)	B1ⁱ—Si2—B5^xxx	80.55 (17)
B5—B1—Na1^xxii	80.33 (15)	B1^xxix—Si2—B5^xxx	80.55 (17)
Na1^xx—B1—Na1^xxii	134.85 (5)	B4—Si2—B5^xxx	51.3 (3)
B5ⁱ—B1—Na1^xxii	70.00 (18)	Si3^xv—Si2—B5^xxx	162.4 (2)
B5^xxi—B1—Na1^xxii	69.77 (5)	Na1^xxxiii—Si2—B5^xxx	93.66 (11)
B2^xiii—B2—B1^xxiii	131.14 (10)	Na1^xxiv—Si2—B5^xxx	93.66 (11)
B2^xiii—B2—B1^x	111.97 (10)	Mg1^xv—Si2—B5^xxx	110.0 (2)
B1^xxiii—B2—B1^x	60.00 (14)	B5ⁱ—Si2—B5^xxx	35.9 (6)
B2^xiii—B2—B3ⁱ	106.92 (13)	B1ⁱ—Si2—Na1^xxii	59.92 (6)
B1^xxiii—B2—B3ⁱ	106.68 (18)	B1^xxix—Si2—Na1^xxii	59.92 (6)
B1^x—B2—B3ⁱ	59.15 (14)	B4—Si2—Na1^xxii	165.73 (10)
B2^xiii—B2—B4^xv	136.84 (12)	Si3^xv—Si2—Na1^xxii	83.15 (4)
B1^xxiii—B2—B4^xv	60.14 (13)	Na1^xxxiii—Si2—Na1^xxii	112.858 (15)
B1^x—B2—B4^xv	108.04 (17)	Na1^xxiv—Si2—Na1^xxii	112.858 (15)
B3ⁱ—B2—B4^xv	106.97 (16)	Mg1^xv—Si2—Na1^xxii	135.57 (6)
B2^xiii—B2—B2^xi	120.000 (1)	B5ⁱ—Si2—Na1^xxii	78.6 (3)
B1^xxiii—B2—B2^xi	107.39 (10)	B5^xxx—Si2—Na1^xxii	114.5 (2)
B1^x—B2—B2^xi	107.25 (10)	B1ⁱ—Si2—Na1^xxxix	123.16 (7)
B3ⁱ—B2—B2^xi	59.51 (9)	B1^xxix—Si2—Na1^xxxix	123.16 (7)
B4^xv—B2—B2^xi	59.65 (9)	B4—Si2—Na1^xxxix	85.66 (9)
B2^xiii—B2—Mg1	67.83 (6)	Si3^xv—Si2—Na1^xxxix	25.46 (4)
B1^xxiii—B2—Mg1	127.40 (14)	Na1^xxxiii—Si2—Na1^xxxix	69.017 (15)
B1^x—B2—Mg1	171.03 (15)	Na1^xxiv—Si2—Na1^xxxix	69.017 (15)
B3ⁱ—B2—Mg1	112.01 (15)	Mg1^xv—Si2—Na1^xxxix	26.96 (6)
B4^xv—B2—Mg1	75.16 (13)	B5ⁱ—Si2—Na1^xxxix	172.8 (3)
B2^xi—B2—Mg1	66.74 (6)	B5^xxx—Si2—Na1^xxxix	136.9 (2)
B2^xiii—B2—B5	71.01 (12)	Na1^xxii—Si2—Na1^xxxix	108.610 (15)
B1^xxiii—B2—B5	142.0 (3)	Si3^xl—Si3—Si2^xv	104.62 (4)
B1^x—B2—B5	83.9 (3)	Si3^xl—Si3—Si2^xvi	104.61 (4)
B3ⁱ—B2—B5	37.8 (2)	Si2^xv—Si3—Si2^xvi	113.86 (3)
B4^xv—B2—B5	129.70 (16)	Si3^xl—Si3—Si2^xvii	104.61 (4)
B2^xi—B2—B5	70.08 (13)	Si2^xv—Si3—Si2^xvii	113.86 (3)
Mg1—B2—B5	87.7 (3)	Si2^xvi—Si3—Si2^xvii	113.86 (3)
B2^xiii—B2—Na1^xxiv	71.62 (5)	Si3^xl—Si3—Mg1	180.0
B1^xxiii—B2—Na1^xxiv	71.82 (10)	Si2^xv—Si3—Mg1	75.38 (4)
B1^x—B2—Na1^xxiv	116.66 (12)	Si2^xvi—Si3—Mg1	75.39 (4)
B3ⁱ—B2—Na1^xxiv	175.02 (13)	Si2^xvii—Si3—Mg1	75.39 (4)
B4^xv—B2—Na1^xxiv	76.58 (10)	Si3^xl—Si3—Na1^xx	118.76 (3)
B2^xi—B2—Na1^xxiv	125.43 (5)	Si2^xv—Si3—Na1^xx	136.62 (7)
Mg1—B2—Na1^xxiv	72.08 (8)	Si2^xvi—Si3—Na1^xx	56.938 (18)
B5—B2—Na1^xxiv	142.00 (18)	Si2^xvii—Si3—Na1^xx	56.938 (18)
B2^xiii—B2—Na1^xxv	113.62 (3)	Mg1—Si3—Na1^xx	61.24 (3)
B1^xxiii—B2—Na1^xxv	98.99 (11)	Si3^xl—Si3—Na1^xxv	118.76 (3)
B1^x—B2—Na1^xxv	131.77 (12)	Si2^xv—Si3—Na1^xxv	56.938 (18)
B3ⁱ—B2—Na1^xxv	92.82 (10)	Si2^xvi—Si3—Na1^xxv	56.940 (18)
B4^xv—B2—Na1^xxv	39.10 (9)	Si2^xvii—Si3—Na1^xxv	136.62 (7)
B2^xi—B2—Na1^xxv	33.32 (3)	Mg1—Si3—Na1^xxv	61.24 (3)
Mg1—B2—Na1^xxv	46.23 (4)	Na1^xx—Si3—Na1^xxv	98.79 (3)
B5—B2—Na1^xxv	96.5 (2)	Si3^xl—Si3—Na1^xxiv	118.76 (3)
Na1^xxiv—B2—Na1^xxv	92.11 (5)	Si2^xv—Si3—Na1^xxiv	56.938 (18)
B2^xiii—B2—B5^xxvi	157.80 (15)	Si2^xvi—Si3—Na1^xxiv	136.62 (7)
B1^xxiii—B2—B5^xxvi	29.13 (9)	Si2^xvii—Si3—Na1^xxiv	56.940 (18)
B1^x—B2—B5^xxvi	69.9 (2)	Mg1—Si3—Na1^xxiv	61.24 (3)
B3ⁱ—B2—B5^xxvi	93.1 (3)	Na1^xx—Si3—Na1^xxiv	98.79 (3)
B4^xv—B2—B5^xxvi	38.8 (2)	Na1^xxv—Si3—Na1^xxiv	98.78 (3)
B2^xi—B2—B5^xxvi	78.28 (3)	Si3^xl—Si3—Na1^xli	36.851 (12)
Mg1—B2—B5^xxvi	113.9 (2)	Si2^xv—Si3—Na1^xli	67.76 (3)
B5—B2—B5^xxvi	130.32 (9)	Si2^xvi—Si3—Na1^xli	119.48 (4)
Na1^xxiv—B2—B5^xxvi	87.6 (2)	Si2^xvii—Si3—Na1^xli	119.48 (4)
Na1^xxv—B2—B5^xxvi	73.92 (14)	Mg1—Si3—Na1^xli	143.149 (12)
B2^xiii—B2—Na1^x	111.07 (3)	Na1^xx—Si3—Na1^xli	155.61 (4)
B1^xxiii—B2—Na1^x	57.51 (9)	Na1^xxv—Si3—Na1^xli	97.015 (14)
B1^x—B2—Na1^x	3.84 (8)	Na1^xxiv—Si3—Na1^xli	97.015 (14)
B3ⁱ—B2—Na1^x	62.97 (11)	Si3^xl—Si3—Na1^xlii	36.852 (12)
B4^xv—B2—Na1^x	107.75 (13)	Si2^xv—Si3—Na1^xlii	119.48 (4)
B2^xi—B2—Na1^x	110.53 (3)	Si2^xvi—Si3—Na1^xlii	119.48 (4)
Mg1—B2—Na1^x	174.62 (10)	Si2^xvii—Si3—Na1^xlii	67.76 (3)
B5—B2—Na1^x	87.0 (3)	Mg1—Si3—Na1^xlii	143.148 (12)
Na1^xxiv—B2—Na1^x	112.83 (6)	Na1^xx—Si3—Na1^xlii	97.015 (14)
Na1^xxv—B2—Na1^x	133.76 (6)	Na1^xxv—Si3—Na1^xlii	155.61 (4)
B5^xxvi—B2—Na1^x	69.2 (2)	Na1^xxiv—Si3—Na1^xlii	97.016 (14)
B5ⁱ—B3—B1^xxvii	125.38 (12)	Na1^xli—Si3—Na1^xlii	62.58 (2)
B5ⁱ—B3—B1^iv	125.38 (12)	Si3^xl—Si3—Na1^xliii	36.852 (12)
B1^xxvii—B3—B1^iv	109.1 (2)	Si2^xv—Si3—Na1^xliii	119.48 (4)
B5ⁱ—B3—B4^xxviii	144.1 (7)	Si2^xvi—Si3—Na1^xliii	67.76 (3)
B1^xxvii—B3—B4^xxviii	60.74 (14)	Si2^xvii—Si3—Na1^xliii	119.48 (4)
B1^iv—B3—B4^xxviii	60.74 (14)	Mg1—Si3—Na1^xliii	143.148 (12)
B5ⁱ—B3—B2ⁱ	101.0 (6)	Na1^xx—Si3—Na1^xliii	97.015 (14)
B1^xxvii—B3—B2ⁱ	60.33 (12)	Na1^xxv—Si3—Na1^xliii	97.016 (14)
B1^iv—B3—B2ⁱ	109.4 (2)	Na1^xxiv—Si3—Na1^xliii	155.61 (4)
B4^xxviii—B3—B2ⁱ	109.8 (2)	Na1^xli—Si3—Na1^xliii	62.58 (2)
B5ⁱ—B3—B2^xxix	101.0 (6)	Na1^xlii—Si3—Na1^xliii	62.58 (2)
B1^xxvii—B3—B2^xxix	109.4 (2)

Symmetry codes: (i) −x+2/3, −y+1/3, −z+1/3; (ii) x+1/3, y−1/3, z−1/3; (iii) −x+y+1/3, y−1/3, z−1/3; (iv) x−y+2/3, −y+1/3, −z+1/3; (v) −x+1, −y, −z; (vi) −x+y+1, y, z; (vii) x−y, −y, −z; (viii) x−y+2/3, x−2/3, −z+1/3; (ix) −x+y+1/3, −x+2/3, z−1/3; (x) −y, x−y, z; (xi) −y, −x, z; (xii) x, x−y, z; (xiii) −x+y, y, z; (xiv) −x+y, −x, z; (xv) −x+1/3, −y+2/3, −z+2/3; (xvi) y−2/3, −x+y−1/3, −z+2/3; (xvii) x−y+1/3, x−1/3, −z+2/3; (xviii) x−y−1/3, x−2/3, −z+1/3; (xix) −x+2/3, −x+y+1/3, −z+1/3; (xx) −x+y+2/3, −x+1/3, z+1/3; (xxi) −x, −y, −z; (xxii) −x+y+1, −x+1, z; (xxiii) x−y−1/3, −y+1/3, −z+1/3; (xxiv) x−1/3, y+1/3, z+1/3; (xxv) −y−1/3, x−y−2/3, z+1/3; (xxvi) −x−1/3, −y+1/3, −z+1/3; (xxvii) y+2/3, −x+y+1/3, −z+1/3; (xxviii) −x+4/3, −y+2/3, −z+2/3; (xxix) y+2/3, x+1/3, −z+1/3; (xxx) x+2/3, y+1/3, z+1/3; (xxxi) −y+2/3, x−y−2/3, z+1/3; (xxxii) −y+1, x−y, z; (xxxiii) −y+2/3, x−y+1/3, z+1/3; (xxxiv) −x+y+2/3, y+1/3, z+1/3; (xxxv) y+1/3, x+2/3, −z+2/3; (xxxvi) y−1/3, −x+y+1/3, −z+1/3; (xxxvii) x−1, y, z; (xxxviii) −y, x−y−1, z; (xxxix) −x+y+2/3, −x+4/3, z+1/3; (xl) −x, −y, −z+1; (xli) −x+y+1/3, −x+2/3, z+2/3; (xlii) −y+1/3, x−y−1/3, z+2/3; (xliii) x−2/3, y−1/3, z+2/3.

Cell parameters (Å), cell volumes (Å³) and selected bond lengths (Å) of Na₃MgB₃₇Si₉, Dy_2.1B₃₇Si₉^a and Mg₃B₃₆Si₉C top

	Na₃MgB₃₇Si₉	Dy_2.1B₃₇Si₉	Mg₃B₃₆Si₉C
a	10.1630 (3)	10.078	10.079
c	16.5742 (6)	16.465	16.372
V	1482.54 (10)	1448.3	1440.4
B—B_av of B₁₂ icosahedron	1.811	1.805	1.798
B2—B2	1.761 (5)	1.738	1.738
Si1—B3	1.887 (4)	1.877	1.851
Si1—B5/C	1.96 (2)	1.84	1.88
Si2—B1	2.043 (2)	2.032	2.035
Si2—B4	2.082 (3)	2.053	2.038
Si3—Si2	2.3951 (9)	2.366	2.362
Si3—Si3	2.304 (3)	2.343	2.341
Na1—B1	2.811 (2)	2.794	2.792
Na1—B2	2.793 (2)	2.751	2.729
Na1—B4	2.9604 (16)	2.934	2.934
Na1—Si2	2.8620 (4)	2.835	2.832
Mg1—B2	2.333 (3)
Mg1—B4	2.568 (3)
Mg1—Si3	2.403 (4)

Notes: (a) Zhang et al. (2003); (b) Ludwig et al. (2013).

Acknowledgements

We thank T. Kamaya for his help with the EPMA analysis.

Funding information

Funding for this research was provided by: the Japan Science and Technology Agency (JST) CREST (grant No. JPMJCR19J1).

References

Bruker (2018). APEX3, SAINT and SADABS. Bruker AXS inc., Madison, Wisconsin, USA. Google Scholar
Cahill, D. G., Fischer, H. E., Watson, S. K., Pohl, R. O. & Slack, G. A. (1989). Phys. Rev. B, 40, 3254–3260. CrossRef CAS Google Scholar
Ludwig, T. & Hillebrecht, H. (2006). J. Solid State Chem. 179, 1623–1629. CrossRef ICSD CAS Google Scholar
Ludwig, T., Pediaditakis, A., Sagawe, V. & Hillebrecht, H. (2013). J. Solid State Chem. 204, 113–122. CrossRef ICSD CAS Google Scholar
Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272–1276. Web of Science CrossRef CAS IUCr Journals Google Scholar
Morito, H., Eck, B., Dronskowski, R. & Yamane, H. (2010). Dalton Trans. 39, 10197–10202. CrossRef ICSD CAS PubMed Google Scholar
Morito, H., Momma, K. & Yamane, H. (2015). J. Alloys Compd. 623, 473–479. CrossRef ICSD CAS Google Scholar
Naslain, R. & Kasper, J. S. (1970). J. Solid State Chem. 1, 150–151. CrossRef ICSD CAS Google Scholar
Salvador, J. R., Bilc, D., Mahanti, S. D. & Kanatzidis, M. G. (2003). Angew. Chem. Int. Ed. 42, 1929–1932. CrossRef ICSD CAS Google Scholar
Sheldrick, G. M. (2015a). Acta Cryst. A71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Sheldrick, G. M. (2015b). Acta Cryst. C71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Terauchi, M., Morito, H., Yamane, H., Koshiya, S. & Kimoto, K. (2018). Microscopy, 67, i72–i77. CrossRef CAS PubMed Google Scholar
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar
Yamada, T., Ishiyama, R. & Yamane, H. (2015). Jpn. J. Appl. Phys. 54, 07J, C04. Google Scholar
Zhang, F. X., Xu, F. F., Mori, T., Liu, Q. L. & Tanaka, T. (2003). J. Solid State Chem. 170, 75–81. CrossRef ICSD CAS Google Scholar