Elaboration, structural study and validation of a new NASICON-type structure, Na0.72(Cr0.48,Al1.52)(Mo2.77,Al0.23)O12

Sonni, M.; Jendoubi, I.; Zid, M.F.

doi:10.1107/S2056989018003031

research communications

CRYSTALLOGRAPHIC
COMMUNICATIONS

ISSN: 2056-9890

Volume 74| Part 3| March 2018| Pages 406-409

https://doi.org/10.1107/S2056989018003031

Open

access

Elaboration, structural study and validation of a new NASICON-type structure, Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77,Al_0.23)O₁₂

Manel Sonni,^a Imen Jendoubi ^a and Mohamed Faouzi Zid ^a ^*

^aUniversity of Tunis El Manar, Faculty of Sciences of Tunis, Laboratory of Materials, Crystal Chemistry and Applied Thermodynamics, 2092 ElManar II, Tunis, Tunisia
^*Correspondence e-mail: medfaouzi.zid57@gmail.com

Edited by A. Van der Lee, Université de Montpellier II, France (Received 2 February 2018; accepted 21 February 2018; online 28 February 2018)

The title compound, sodium chromium/aluminium molybdenum/aluminium dodecaoxide, Na_0.72Cr_0.48Al_1.74Mo_2.77O₁₂, was prepared by solid-state reaction. Its crystal structure is related to NaSICON-type compounds. The framework is built up from M1O₆ (M1 = Cr/Al) octahedra and M2O₄ (M2 = Mo/Al) tetrahedra interconnected by corners. The three-dimensional framework contains cavities in which sodium cations are located. Two validation models (BVS and CHARDI) were used to confirm the proposed structural model. The mobility of Na⁺ ions in the structure has been investigated by theoretical means.

Keywords: NASICON structure; framework; crystal structure; BVS; CHARDI.

CCDC reference: 1824957

1. Chemical context

The search for new and better solid electrolyte materials has grown considerably in recent years because of their amazing properties and their diverse applications in the field of solid-state chemistry. Indeed, many new molybdate phases with high ionic conductivity have been synthesized and structurally characterized by X-ray diffraction. A large number belong to the NASICON (`Na super ionic conductor') family, e.g. phosphate (Tkachev et al., 1984 ; Catti et al., 2004 ), arsenate (Harrison & Phillips, 2001 ), sulfate (Slater & Greaves, 1994 ) and molybdate (Sun et al., 2012 ; Kozhevnikova & Imekhenova, 2006 ) based systems. The NASICON family groups together a set of phases of the same structural type with the general formula AM₂(XO₄)₃ (A = alkali, M = Ti, Fe, V, Co, Ni and X = P, As, Mo, W, S; Prabaharan et al., 2004 ). Apart from their superionic properties, a number of NASICON compounds have considerable potential for use in laser engineering, optics and electronics owing to their non-linear optical, electrical, magnetic and luminescent properties. It is in this context that we chose to explore A–Cr–Mo–O systems (A = monovalent ion). A new phase Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77,Al_0.23)O₁₂ was synthesized by solid-state reaction. We present here its crystal structure and its validation by the CHARDI (charge distribution) and BVS (bond-valence-sum) methods.

2. Structural commentary

The structural unit of Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77,Al_0.23)O₁₂ consists of one octahedron M1O₆ (M1 = Cr1/Al2) and one tetrahedron M2O₄ (M2 = Mo1/Al1) that share corners. The charge compensation is provided by Na⁺ cations (Fig. 1). The main construction unit in the anionic framework of the compound Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77,Al_0.23)O₁₂ is formed by two M1O₆ octahedra interconnected by three M2O₄ tetrahedra located along the c axis. Geometrical parameters are given in Table 1. This assembly forms M1₂M2₃O₁₈ units (Fig. 2). The junction between these units, provided by the formation of mixed bridges of the M1–O–M2 type, leads to a three-dimensional framework with cavities parallel to the [100] and [010] directions in which the Na⁺ cations are located (Fig. 3). Indeed, each M1O₆ octahedron share its six corners with different M2O₄ tetrahedra, leading to M1M2₆O₂₄ clusters (Fig. 4). The two validation models BVS (Brown & Altermatt, 1985 ; Brown, 2002 ; Adams, 2003 ) and CHARDI (Hoppe et al., 1989 ; Nespolo et al., 2001 ; Nespolo, 2001 ) confirm the proposed structural model, in particular the distribution at mixed sites. The calculated load values Q(i) and valences V(i) are in good agreement with the oxidation degrees weighted by the occupancy rates. The dispersion factor σ_cat, which measures the deviation of the calculated cationic charges, is equal to 0.3% (Table 2). The variation of the bond-valence sum of sodium as a function of the distance travelled in different directions shows that the [011] and [111] directions are the most favorable directions for the mobility of sodium. The paths along these directions have the same shape when the distance travelled is about 13.5 Å and the maximum valence is about 1.4 valence units (Fig. 5). The representation of the Na migration path in the direction [011] is shown in Fig. 6.

Table 1
Selected geometric parameters (Å, °)

Mo1—O2ⁱ	1.7358 (15)	Cr1—O2^v	1.9721 (16)
Mo1—O2	1.7359 (15)	Cr1—O2^vi	1.9721 (16)
Mo1—O1	1.7540 (16)	Na1—O1ⁱⁱ	2.4987 (15)
Mo1—O1ⁱ	1.7540 (15)	Na1—O1^vii	2.4987 (15)
Cr1—O1ⁱⁱ	1.9668 (16)	Na1—O1ⁱⁱⁱ	2.4987 (15)
Cr1—O1ⁱⁱⁱ	1.9668 (16)	Na1—O1^viii	2.4987 (15)
Cr1—O1^iv	1.9669 (16)	Na1—O1^iv	2.4987 (15)
Cr1—O2	1.9720 (16)	Na1—O1^ix	2.4987 (15)

O2ⁱ—Mo1—O2	109.56 (11)	O1^iv—Cr1—O2^vi	88.68 (7)
O2ⁱ—Mo1—O1	107.85 (8)	O2—Cr1—O2^vi	91.35 (7)
O2—Mo1—O1	111.40 (8)	O2^v—Cr1—O2^vi	91.35 (7)
O2ⁱ—Mo1—O1ⁱ	111.40 (8)	O1ⁱⁱ—Na1—O1^vii	180.0
O2—Mo1—O1ⁱ	107.86 (8)	O1ⁱⁱ—Na1—O1ⁱⁱⁱ	65.74 (6)
O1—Mo1—O1ⁱ	108.80 (11)	O1^vii—Na1—O1ⁱⁱⁱ	114.26 (6)
O1ⁱⁱ—Cr1—O1ⁱⁱⁱ	87.18 (7)	O1ⁱⁱ—Na1—O1^viii	114.26 (6)
O1ⁱⁱ—Cr1—O1^iv	87.18 (7)	O1^vii—Na1—O1^viii	65.74 (6)
O1ⁱⁱⁱ—Cr1—O1^iv	87.18 (7)	O1ⁱⁱⁱ—Na1—O1^viii	180.0
O1ⁱⁱ—Cr1—O2	92.79 (7)	O1ⁱⁱ—Na1—O1^iv	65.74 (6)
O1ⁱⁱⁱ—Cr1—O2	88.68 (7)	O1^vii—Na1—O1^iv	114.26 (6)
O1^iv—Cr1—O2	175.86 (7)	O1ⁱⁱⁱ—Na1—O1^iv	65.74 (6)
O1ⁱⁱ—Cr1—O2^v	88.68 (7)	O1^viii—Na1—O1^iv	114.26 (6)
O1ⁱⁱⁱ—Cr1—O2^v	175.86 (7)	O1ⁱⁱ—Na1—O1^ix	114.26 (6)
O1^iv—Cr1—O2^v	92.79 (7)	O1^vii—Na1—O1^ix	65.74 (6)
O2—Cr1—O2^v	91.35 (7)	O1ⁱⁱⁱ—Na1—O1^ix	114.26 (6)
O1ⁱⁱ—Cr1—O2^vi	175.85 (7)	O1^viii—Na1—O1^ix	65.74 (6)
O1ⁱⁱⁱ—Cr1—O2^vi	92.79 (7)	O1^iv—Na1—O1^ix	180.0
Symmetry codes: (i) $[x-y, -y, -z+{\script{3\over 2}}]$ ; (ii) $[x-y-{\script{1\over 3}}, x-{\script{2\over 3}}, -z+{\script{4\over 3}}]$ ; (iii) $[-x+{\script{2\over 3}}, -y+{\script{1\over 3}}, -z+{\script{4\over 3}}]$ ; (iv) $[y-{\script{1\over 3}}, -x+y+{\script{1\over 3}}, -z+{\script{4\over 3}}]$ ; (v) -x+y, -x, z; (vi) -y, x-y, z; (vii) $[-x+y+{\script{1\over 3}}, -x+{\script{2\over 3}}, z-{\script{1\over 3}}]$ ; (viii) $[x-{\script{2\over 3}}, y-{\script{1\over 3}}, z-{\script{1\over 3}}]$ ; (ix) $[-y+{\script{1\over 3}}, x-y-{\script{1\over 3}}, z-{\script{1\over 3}}]$ .

Table 2
CHARDI and BVS analyses for the cations in the Na_0.72Cr_0.48Al_1.76Mo_2.77O₁₂ compound

q(i) = formal oxidation number; sof(i) = site occupancy; CN(i) = classical coordination number; Q(i) = calculated charge; V(i) = calculated valence; ECoN(i) = coordination number; d_mean(i) = mean distance; d_med(i) = median distance.

Cation	q(i)·sof(i)	Q(i)	V(i)	CN(i)	ECoN(i)	d_mean	d_med
Mo1/Al1	5.78	5.77	5.8426	4	4.00	1.7448	1.7443
M(Cr1/Al2)	3.000	2.99	2.9397	6	6.00	1.9694	1.9696
Na1	0.72	0.71	0.6893	6	6.00	2.4989	2.4989
σ_cat is the dispersion factor for cationic charges where σ_cat = [Σ_i(q_i − Q_i)²/N − 1]^1/2 = 0.025.

Figure 1
Structural unit of Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77,Al_0.23)O₁₂. Displacement ellipsoids are drawn at the 50% probability level. [Symmetry codes: (i) $[{2\over 3}]$ − x, $[{1\over 3}]$ − y, $[{1\over 3}]$ − z; (ii) − $[{1\over 3}]$ + x − y, − $[{2\over 3}]$ + x, $[{1\over 3}]$ − z; (iii) − $[{1\over 3}]$ + y, $[{1\over 3}]$ − x + y, $[{4\over 3}]$ − z; (iv) −x + y, −x, z; (v) −x, x − z, z; (vi) x − y, −y, $[{3\over 2}]$ − z.]

Figure 2
Projection of an M1₂M2₃O₁₈ unit along the a axis.

Figure 3
Projection of Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77,Al_0.23)O₁₂ along the a axis.

Figure 4
Projection of Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77,Al_0.23)O₁₂ along the c axis.

Figure 5
Ionic pathway valence curves of the title compound.

Figure 6
Modelling of the Na⁺ pathway in Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77, Al_0.23)O₁₂.

3. Database survey

A comparison between the structures of the title compound and those of other NASICON-type compounds reveals that other compounds also crystallize in the R $[\overline{3}]$ c space group with similar unit-cell parameters. When compared to NaZr₂(AsO₄)₃ (Coquerel et al., 1983 ) and Na₄Co₃Mo_22.33O₇₂ (Chakir et al., 2003 ), the only difference observed is the occupancy of the sites 6b, 12c and 18e. In NaZr₂(AsO₄)₃, the sites are fully occupied, whereas in Na₄Co₃Mo_22.33O₇₂, the 6b site is not totally occupied, and the 12c site is occupied by both Co and Mo. In the title compound, the 6b site is partially occupied and the 12c and 18e sites are mixed Cr/Al and Mo/Al sites, respectively.

4. Synthesis and crystallization

During the investigation of the A–Mo–Cr–O phase diagrams (A = Li, Na, Ag), the new compound Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77,Al_0.23)₁₂ was established. The crystals were obtained by grinding in an agate mortar the reagents NaNO₃, Cr(NO₃)₃·9H₂O and (NH₄)₆Mo₇O₂₄·4H₂O in a Na:Cr:Mo molar ratio of 1:1:4, respectively. The resulting mixture was calcined at 673 K to remove volatiles including NO₂, NH₃ and H₂O. The residual powder thus obtained was finely ground and then returned to the oven at a temperature close to the melting point at 973 K for three days to promote germination and crystal growth. After cooling, crystals of parallelepipedal shape and optimal size for data collection were obtained. A crystal of a good quality, selected under a polarizing microscope, was used for intensity measurements

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 3. After processing the data, the structure was solved successfully in the R $[\overline{3}]$ c space group, using direct methods implemented in the SHELXS97 program (Sheldrick, 2008 ). The molybdenum, chromium and oxygen atoms were located first. At this stage, an empirical ψ-scan correction (North et al., 1968 ) was applied. Difference-Fourier syntheses using the program SHELXL97 (Sheldrick, 2008), allowed the rest of the atoms in the cell to be localized. We obtained intense peaks close to Cr and Mo; the liberation of the occupancy factors led to values different from the full site occupancy (0.62530 for Mo and 0.24035 for Cr). The EDX analysis (Fig. 7) of the sample confirmed the presence of aluminium and we then used EADP and EXYZ constraints as well as SUMP to refine Al1 with the Mo1 site and Al2 with the Cr1 site. After refinement and verification of the electrical neutrality, the final formula was Na_0.72 (1)(Cr_0.48 (1),Al_1.52 (2))(Mo_2.77 (3),Al_0.23 (2))O₁₂. The remaining maximum and minimum electron densities in the difference-Fourier map are acceptable and are at 0.78 Å from the Mo1 site and at 0.89 Å from the Mo2, respectively.

Table 3
Experimental details

Crystal data
Chemical formula	Na_0.72(Cr_0.48·Al_1.52)(Mo_2.77·Al_0.23)O₁₂
M_r	546.34
Crystal system, space group	Trigonal, R $[\overline{3}]$ c
Temperature (K)	298
a, c (Å)	9.217 (2), 22.646 (2)
V (Å³)	1666.1 (7)
Z	6
Radiation type	Mo Kα
μ (mm⁻¹)	3.74
Crystal size (mm)	0.24 × 0.21 × 0.18

Data collection
Diffractometer	Enraf–Nonius CAD-4
Absorption correction	ψ scan (North et al., 1968)
T_min, T_max	0.491, 0.599
No. of measured, independent and observed [I > 2σ(I)] reflections	2878, 414, 401
R_int	0.026
(sin θ/λ)_max (Å⁻¹)	0.637

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.013, 0.024, 1.25
No. of reflections	414
No. of parameters	35
No. of restraints	2
Δρ_max, Δρ_min (e Å⁻³)	0.23, −0.43
Computer programs: CAD-4 EXPRESS (Duisenberg, 1992 ; Macíček & Yordanov, 1992 ), XCAD4 (Harms & Wocadlo, 1995 ), SHELXS97 (Sheldrick, 2008), SHELXL2014 (Sheldrick, 2015 ), DIAMOND (Brandenburg, 2006 ), WinGX (Farrugia, 2012 ) and publCIF (Westrip, 2010 ).

Figure 7
EDX analysis of the sample confirming the presence of aluminium in Na_0.72(Cr_0.48,Al_1.52)(Mo_2.77, Al_0.23)O₁₂.

Supporting information

CCDC reference: 1824957

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2056989018003031/vn2134sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989018003031/vn2134Isup2.hkl

checkCIF report

Computing details top

Data collection: CAD-4 EXPRESS (Duisenberg, 1992; Macíček & Yordanov, 1992); cell refinement: CAD-4 EXPRESS (Duisenberg, 1992; Macíček & Yordanov, 1992); data reduction: XCAD4 (Harms & Wocadlo, 1995); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg, 2006); software used to prepare material for publication: WinGX (Farrugia, 2012) and publCIF (Westrip, 2010).

Sodium chromium/aluminium molybdenum/aluminium dodecaoxide top

Crystal data top

Na_0.72(Cr_0.48·Al_1.52)(Mo_2.77·Al_0.23)O₁₂	D_x = 3.267 Mg m⁻³
M_r = 546.34	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3c	Cell parameters from 25 reflections
a = 9.217 (2) Å	θ = 12.1–14.8°
c = 22.646 (2) Å	µ = 3.74 mm⁻¹
V = 1666.1 (7) Å³	T = 298 K
Z = 6	Prism, red
F(000) = 1526	0.24 × 0.21 × 0.18 mm

Data collection top

Enraf–Nonius CAD-4 diffractometer	R_int = 0.026
Radiation source: fine-focus sealed tube	θ_max = 26.9°, θ_min = 3.1°
ω/2θ scans	h = −11→11
Absorption correction: ψ scan (North et al., 1968)	k = −2→11
T_min = 0.491, T_max = 0.599	l = −28→28
2878 measured reflections	2 standard reflections every 120 reflections
414 independent reflections	intensity decay: 0.8%
401 reflections with I > 2σ(I)

Refinement top

Refinement on F²	2 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + 4.1215P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.013	(Δ/σ)_max = 0.001
wR(F²) = 0.024	Δρ_max = 0.23 e Å⁻³
S = 1.25	Δρ_min = −0.42 e Å⁻³
414 reflections	Extinction correction: SHELXL2014 (Sheldrick, 2015), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
35 parameters	Extinction coefficient: 0.00046 (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. 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 > 2sigma(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 (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Mo1	0.28488 (2)	0.0000	0.7500	0.01214 (9)	0.921 (6)
Al1	0.28488 (2)	0.0000	0.7500	0.01214 (9)	0.080 (10)
Cr1	0.0000	0.0000	0.63854 (3)	0.0109 (2)	0.238 (11)
Al2	0.0000	0.0000	0.63854 (3)	0.0109 (2)	0.761 (19)
Na1	0.0000	0.0000	0.5000	0.0259 (9)	0.724 (8)
O1	0.48491 (19)	0.17851 (19)	0.74736 (7)	0.0326 (4)
O2	0.1686 (2)	−0.0152 (2)	0.68761 (6)	0.0376 (5)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Mo1	0.01265 (11)	0.01229 (13)	0.01137 (12)	0.00614 (6)	0.00085 (4)	0.00169 (8)
Al1	0.01265 (11)	0.01229 (13)	0.01137 (12)	0.00614 (6)	0.00085 (4)	0.00169 (8)
Cr1	0.0117 (3)	0.0117 (3)	0.0092 (3)	0.00587 (14)	0.000	0.000
Al2	0.0117 (3)	0.0117 (3)	0.0092 (3)	0.00587 (14)	0.000	0.000
Na1	0.0322 (11)	0.0322 (11)	0.0132 (12)	0.0161 (6)	0.000	0.000
O1	0.0254 (8)	0.0218 (8)	0.0442 (9)	0.0071 (7)	−0.0038 (6)	0.0003 (7)
O2	0.0364 (9)	0.0446 (11)	0.0278 (8)	0.0172 (8)	−0.0093 (7)	0.0015 (7)

Geometric parameters (Å, º) top

Mo1—O2ⁱ	1.7358 (15)	Na1—O1ⁱⁱ	2.4987 (15)
Mo1—O2	1.7359 (15)	Na1—O1^vii	2.4987 (15)
Mo1—O1	1.7540 (16)	Na1—O1ⁱⁱⁱ	2.4987 (15)
Mo1—O1ⁱ	1.7540 (15)	Na1—O1^viii	2.4987 (15)
Cr1—O1ⁱⁱ	1.9668 (16)	Na1—O1^iv	2.4987 (15)
Cr1—O1ⁱⁱⁱ	1.9668 (16)	Na1—O1^ix	2.4987 (15)
Cr1—O1^iv	1.9669 (16)	Na1—Al2^x	3.1373 (7)
Cr1—O2	1.9720 (16)	Na1—Cr1^x	3.1373 (7)
Cr1—O2^v	1.9721 (16)	O1—Al2ⁱⁱⁱ	1.9668 (16)
Cr1—O2^vi	1.9721 (16)	O1—Cr1ⁱⁱⁱ	1.9668 (16)
Cr1—Na1	3.1374 (7)	O1—Na1^xi	2.4987 (15)

O2ⁱ—Mo1—O2	109.56 (11)	O1ⁱⁱⁱ—Na1—O1^iv	65.74 (6)
O2ⁱ—Mo1—O1	107.85 (8)	O1^viii—Na1—O1^iv	114.26 (6)
O2—Mo1—O1	111.40 (8)	O1ⁱⁱ—Na1—O1^ix	114.26 (6)
O2ⁱ—Mo1—O1ⁱ	111.40 (8)	O1^vii—Na1—O1^ix	65.74 (6)
O2—Mo1—O1ⁱ	107.86 (8)	O1ⁱⁱⁱ—Na1—O1^ix	114.26 (6)
O1—Mo1—O1ⁱ	108.80 (11)	O1^viii—Na1—O1^ix	65.74 (6)
O1ⁱⁱ—Cr1—O1ⁱⁱⁱ	87.18 (7)	O1^iv—Na1—O1^ix	180.0
O1ⁱⁱ—Cr1—O1^iv	87.18 (7)	O1ⁱⁱ—Na1—Al2^x	141.20 (4)
O1ⁱⁱⁱ—Cr1—O1^iv	87.18 (7)	O1^vii—Na1—Al2^x	38.80 (4)
O1ⁱⁱ—Cr1—O2	92.79 (7)	O1ⁱⁱⁱ—Na1—Al2^x	141.19 (4)
O1ⁱⁱⁱ—Cr1—O2	88.68 (7)	O1^viii—Na1—Al2^x	38.81 (4)
O1^iv—Cr1—O2	175.86 (7)	O1^iv—Na1—Al2^x	141.19 (4)
O1ⁱⁱ—Cr1—O2^v	88.68 (7)	O1^ix—Na1—Al2^x	38.81 (4)
O1ⁱⁱⁱ—Cr1—O2^v	175.86 (7)	O1ⁱⁱ—Na1—Cr1^x	141.20 (4)
O1^iv—Cr1—O2^v	92.79 (7)	O1^vii—Na1—Cr1^x	38.80 (4)
O2—Cr1—O2^v	91.35 (7)	O1ⁱⁱⁱ—Na1—Cr1^x	141.19 (4)
O1ⁱⁱ—Cr1—O2^vi	175.85 (7)	O1^viii—Na1—Cr1^x	38.81 (4)
O1ⁱⁱⁱ—Cr1—O2^vi	92.79 (7)	O1^iv—Na1—Cr1^x	141.19 (4)
O1^iv—Cr1—O2^vi	88.68 (7)	O1^ix—Na1—Cr1^x	38.81 (4)
O2—Cr1—O2^vi	91.35 (7)	Al2^x—Na1—Cr1^x	0.0
O2^v—Cr1—O2^vi	91.35 (7)	O1ⁱⁱ—Na1—Cr1	38.80 (4)
O1ⁱⁱ—Cr1—Na1	52.76 (5)	O1^vii—Na1—Cr1	141.20 (4)
O1ⁱⁱⁱ—Cr1—Na1	52.76 (5)	O1ⁱⁱⁱ—Na1—Cr1	38.81 (4)
O1^iv—Cr1—Na1	52.76 (5)	O1^viii—Na1—Cr1	141.19 (4)
O2—Cr1—Na1	124.30 (5)	O1^iv—Na1—Cr1	38.81 (4)
O2^v—Cr1—Na1	124.30 (5)	O1^ix—Na1—Cr1	141.19 (4)
O2^vi—Cr1—Na1	124.30 (5)	Al2^x—Na1—Cr1	180.0
O1ⁱⁱ—Na1—O1^vii	180.0	Cr1^x—Na1—Cr1	180.0
O1ⁱⁱ—Na1—O1ⁱⁱⁱ	65.74 (6)	Mo1—O1—Al2ⁱⁱⁱ	144.66 (9)
O1^vii—Na1—O1ⁱⁱⁱ	114.26 (6)	Mo1—O1—Cr1ⁱⁱⁱ	144.66 (9)
O1ⁱⁱ—Na1—O1^viii	114.26 (6)	Al2ⁱⁱⁱ—O1—Cr1ⁱⁱⁱ	0.0
O1^vii—Na1—O1^viii	65.74 (6)	Mo1—O1—Na1^xi	126.81 (8)
O1ⁱⁱⁱ—Na1—O1^viii	180.0	Al2ⁱⁱⁱ—O1—Na1^xi	88.43 (6)
O1ⁱⁱ—Na1—O1^iv	65.74 (6)	Cr1ⁱⁱⁱ—O1—Na1^xi	88.43 (6)
O1^vii—Na1—O1^iv	114.26 (6)	Mo1—O2—Cr1	158.35 (10)

Symmetry codes: (i) x−y, −y, −z+3/2; (ii) x−y−1/3, x−2/3, −z+4/3; (iii) −x+2/3, −y+1/3, −z+4/3; (iv) y−1/3, −x+y+1/3, −z+4/3; (v) −x+y, −x, z; (vi) −y, x−y, z; (vii) −x+y+1/3, −x+2/3, z−1/3; (viii) x−2/3, y−1/3, z−1/3; (ix) −y+1/3, x−y−1/3, z−1/3; (x) −x, −y, −z+1; (xi) x+2/3, y+1/3, z+1/3.

CHARDI and BVS analyses for the cations in the Na_0.72Cr_0.48Al_1.76Mo_2.77O₁₂ compound top

q(i) = formal oxidation number; sof(i) = site occupancy; CN(i) = classical coordination number; Q(i) = calculated charge; V(i) = calculated valence; ECoN(i)= coordination number; d_mean(i) = mean distance; d_med(i) = median distance.

Cation	q(i)·sof(i)	Q(i)	V(i)	CN(i)	ECoN(i)	d_mean	d_med
Mo1/Al1	5.78	5.77	5.8426	4	4.00	1.7448	1.7443
M(Cr1/Al2)	3.000	2.99	2.9397	6	6.00	1.9694	1.9696
Na1	0.72	0.71	0.6893	6	6.00	2.4989	2.4989

σ_cat is the dispersion factor for cationic charges where σ_cat = [Σ_i(q_i - Q_i)²/N - 1]^1/2 = 0.025.

Acknowledgements

The authors wish to thank the Ministry of Higher Education and Scientific Research of Tunisia for the funding of the laboratory LMCTA LR15ES01.

References

Adams, S. (2003). softBV. University of Göttingen, Germany. Google Scholar
Brandenburg, K. (2006). DIAMOND. Crystal Impact GbR, Bonn, Germany. Google Scholar
Brown, I. D. (2002). The Chemical Bond in Inorganic Chemistry – The Bond Valence Model. Oxford University Press. Google Scholar
Brown, I. D. & Altermatt, D. (1985). Acta Cryst. B41, 244–247. CrossRef CAS Web of Science IUCr Journals Google Scholar
Catti, M., Comotti, A., Di Blas, S. & Ibberson, R. M. (2004). J. Mater. Chem. 14, 835–839. CrossRef CAS Google Scholar
Chakir, M., Jazouli, A. E. & de Waal, D. (2003). Mater. Res. Bull. 38, 1773–1779. CrossRef CAS Google Scholar
Coquerel, G., Gicquel-Mayer, C., Mayer, M. & Perez, G. (1983). Acta Cryst. C39, 1602–1604. CrossRef CAS IUCr Journals Google Scholar
Duisenberg, A. J. M. (1992). J. Appl. Cryst. 25, 92–96. CrossRef CAS Web of Science IUCr Journals Google Scholar
Farrugia, L. J. (2012). J. Appl. Cryst. 45, 849–854. Web of Science CrossRef CAS IUCr Journals Google Scholar
Harms, K. & Wocadlo, S. (1995). XCAD4. University of Marburg, Germany. Google Scholar
Harrison, W. T. A. & Phillips, M. L. F. (2001). Acta Cryst. C57, 2–3. CrossRef CAS IUCr Journals Google Scholar
Hoppe, R., Voigt, S., Glaum, H., Kissel, J., Müller, H. P. & Bernet, K. (1989). J. Less-Common Met. 156, 105–122. CrossRef CAS Web of Science Google Scholar
Kozhevnikova, N. M. & Imekhenova, A. V. (2006). Zh. Neorg. Khim. 51, 4, 589–592. Google Scholar
Macíček, J. & Yordanov, A. (1992). J. Appl. Cryst. 25, 73–80. CrossRef Web of Science IUCr Journals Google Scholar
Nespolo, M. (2001). CHARDI-IT. Laboratoire CRM², Université de Lorraine, Nancy, France. Google Scholar
Nespolo, M., Ferraris, G., Ivaldi, G. & Hoppe, R. (2001). Acta Cryst. B57, 652–664. Web of Science CrossRef CAS IUCr Journals Google Scholar
North, A. C. T., Phillips, D. C. & Mathews, F. S. (1968). Acta Cryst. A24, 351–359. CrossRef IUCr Journals Web of Science Google Scholar
Prabaharan, S. R. S., Fauzi, A., Michael, M. S. & Begam, K. M. (2004). Solid State Ionics, 171, 157–165. CrossRef CAS Google Scholar
Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122. Web of Science CrossRef CAS IUCr Journals Google Scholar
Sheldrick, G. M. (2015). Acta Cryst. C71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Slater, P. R. & Greaves, C. (1994). J. Mater. Chem. 4, 1463–1467. CrossRef CAS Google Scholar
Sun, Q., Ren, Q. Q. & Fu, Z. W. (2012). Electrochem. Commun. 23, 145–148. CrossRef CAS Google Scholar
Tkachev, V. V., Ponomarev, V. I. & Atovmyan, L. O. (1984). Zh. Strukt. Khim. 25, 128–134. CAS Google Scholar
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.