Mg5TiO4(BO3)2

Kawano, T.; Yamane, H.

doi:10.1107/S0108270110036577

Mg₅TiO₄(BO₃)₂

Single crystals of pentamagnesium titanium(IV) tetraoxide bis(borate), Mg₅TiO₄(BO₃)₂, were prepared by slow cooling of the melt from 1623 K in air. The crystal is isostructural with the mineral ludwigite (Mg₂FeO₂BO₃). The Mg and Ti atoms are coordinated by six O atoms and the B atom is coordinated by three O atoms. There are three Mg sites and one mixed site statistically occupied by Mg and Ti atoms. Atoms are at the following special positions: 2a (0, 0, 0) and 2d (0, $1 \over 2$ , $1 \over 2$ ) for two Mg atoms, 4g (x, y, 0) for the mixed Ti/Mg site and the BO₃ group, and 4h (x, y, $1 \over 2$ ) for a third Mg and two oxide O atoms. MgO₆ and (Ti/Mg)O₆ octahedra are connected by sharing of edges to form zigzag folding layers along the c axis. Triangular prismatic tunnels are formed between the folding layers by sharing apical O atoms of the MgO₆ and (Ti/Mg)O₆ octahedra.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270110036577/ku3033sup1.cif Contains datablocks I, global
	Structure factor file (CIF format) https://doi.org/10.1107/S0108270110036577/ku3033Isup2.hkl Contains datablock I

Comment top

Some oxyborates with a structural chemical formula of M^II₅M^IVO₄(BO₃)₂ have been reported. The title compound, Mg₅TiO₄(BO₃)_2, and Mg₅SnO₄(BO₃)₂ were synthesized by Konijnendijk & Blasse (1985). They presumed that Mg₅TiO₄(BO₃)₂ and Mg₅SnO₄(BO₃)₂ were isostructural with ludwigite [Mg₂FeO₂BO₃ or Mg₄Fe₂O₄(BO₃)₂] (Takéuchi et al., 1950) and orthopinakiolite [Mg₃Mn₃O₄(BO₃)₂] (Randmets, 1960; Takéuchi, 1978), respectively. They also synthesized solid solutions of Mg₅Sn_1–_xTi_xO₄(BO₃)₂ (0 ≤ x ≤ 1) and reported their photoluminescence properties. Crystal structure analysis of these compounds, however, was not carried out. Recently, the crystal structure of Mg₅SnO₄(BO₃)₂ has been found to be a novel ludwigite-type superstructure [triclinic, space group F1, a = 6.1295 (8), b = 18.714 (3), c = 24.719 (3) Å, α = 90.021 (5)°, β = 90.032 (4)° and γ = 90.041 (5)°] by single-crystal X-ray diffraction (Kawano & Yamane, 2010). On the other hand, no information on the crystal structure of Mg₅TiO₄(BO₃)₂ has been reported. In the present study, we confirmed Mg₅TiO₄(BO₃)₂ as isostructural with the mineral ludwigite (Mg₂FeO₂BO₃, orthorhombic, space group Pbam) and analysed its crystal structure. Synthetic oxyborates having the ludwigite structure are, for example, Ni₅M^IVO₄(BO₃)₂ [M^IV = Ti (Stenger et al., 1973; Armbruster & Lager, 1985), V (Bluhm & Müller-Buschbaum, 1989a), Mn (Bluhm & Müller-Buschbaum, 1989a), Ge (Bluhm & Müller-Buschbaum, 1989b) and Zr (Bluhm & Müller-Buschbaum, 1989b)], Co₅M^IVO₄(BO₃)₂ [M^IV = Ti (Stenger et al., 1973), Mn (Utzolino & Bluhm, 1996) and Sn (Utzolino & Bluhm, 1996)] and Zn₅MnO₄(BO₃)₂ (Busche & Bluhm, 1995).

Figs. 1 and 2 show the coordination environments for Mg, Ti, B and O atoms, and the crystal structure of Mg₅TiO₄(BO₃)₂, respectively. Atoms in the crystal structure are at the following special positions: 2a (0, 0, 0) for Mg3, 2d (0, 1/2, 1/2) for Mg4, 4g (x, y, 0) for Ti1/Mg1, B1, O1, O2 and O3, and 4h (x, y, 1/2) for Mg2, O4 and O5. In the asymmetric unit, there are three Mg sites and one mixed site statistically occupied by Mg and Ti atoms with an occupancy of 0.5. The formula of Mg₄(MgTi)O₄(BO₃)₂ is obtained by replacing two Fe atoms in Mg₄Fe₂O₄(BO₃)₂ (Takéuchi et al., 1950) by Mg and Ti atoms, i.e. 2Fe³⁺ → Mg²⁺ + Ti⁴⁺.

Mg and Ti atoms are situated in six-coordinated oxygen octahedra. MgO₆ and (Ti/Mg)O₆ octahedra are connected by sharing the edges to form zigzag folding layers along the c axis. As shown in Fig. 2, a repeating unit of the folding layers is composed of Mg2O₆–Mg3O₆–Mg2O₆ stacking along the b axis and (Ti1/Mg1)O₆–Mg4O₆–(Ti1/Mg1)O₆ stacking along the a axis. The folding layers are connected by sharing the apical O4 atoms of the Mg2O₆, Mg4O₆ and (Ti1/Mg1)O₆ octahedra. Triangular prismatic tunnels are formed between the folding layers. The B1 atoms in the tunnels are coordinated by the O1, O2 and O3 atoms, forming isolated triangular borate groups of B1O₃. The O4 and O5 belonging to the Mg2O₆, Mg4O₆ and (Ti1/Mg1)O₆ octahedra make no bond with the B1 atoms.

Bond valence sums (BVS) (Brown & Altermatt, 1985) of the Mg, Ti and B atoms were calculated with the bond valence parameters of l₀(Mg²⁺) = 1.693, l₀(Ti⁴⁺) = 1.815 and l₀(B³⁺) = 1.371 Å (Brese & O'Keeffe, 1991). The BVS values of the Mg2, Mg3 and Mg4 atoms were 2.1, 2.0 and 2.1, respectively. Those of the Ti1 and Mg1 atoms at the Ti1/Mg1 site were 3.33 and 2.39, respectively. The average of these values was 2.86 and close to the mean valence (+3) of Mg²⁺ and Ti⁴⁺. The B1—O distances are in the range 1.377 (4)–1.388 (4) Å, and these values are consistent with those of M^II₅M^IVO₄(BO₃)₂ [1.32 (3)–1.43 (3) Å] mentioned above (Stenger et al., 1973; Armbruster & Lager, 1985; Bluhm & Müller-Buschbaum, 1989a,b; Stenger et al., 1973; Utzolino & Bluhm, 1996; Busche & Bluhm, 1995). The O—B1—O angles of 119.0 (3)–121.9 (3)° indicate an almost planar triangle of B1O₃.

Related literature top

For related literature, see: Armbruster & Lager (1985); Bluhm & Müller-Buschbaum (1989a, 1989b); Brese & O'Keeffe (1991); Brown & Altermatt (1985); Busche & Bluhm (1995); Kawano & Yamane (2010); Konijnendijk & Blasse (1985); Randmets (1960); Stenger et al. (1973); Takéuchi (1978); Takéuchi et al. (1950); Utzolino & Bluhm (1996).

Experimental top

The starting materials were powders of MgO (99.9%, Rare Metallic), TiO₂ (99.9%, Rare Metallic) and H₃BO₃ (99.99%, Sigma-Aldrich). MgO was heated at 1173–1273 K for 6–12 h in air before weighing. The powders were weighed with a molar ratio of MgO: TiO₂: H₃BO₃ = 5: 1: 2.7 and mixed in an agate mortar with a pestle. The mixture was pressed into a pellet, placed in a platinum boat and heated at 1623 K for 6 h in air. Heating and cooling rates were 200 and 15 K h^-1, respectively. The pellet partially melted, and single crystals were formed on its edge. A colourless and transparent single crystal showing blue emission under 254 nm ultraviolet excitation was selected.

Computing details top

Data collection: PROCESS-AUTO (Rigaku/MSC, 2005); cell refinement: PROCESS-AUTO (Rigaku/MSC, 2005); data reduction: CrystalStructure (Rigaku/MSC, 2005); program(s) used to solve structure: SIR2004 (Burla et al., 2005); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: VESTA (Momma & Izumi, 2008); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top

Fig. 1. The atomic arrangement around Mg, Ti, B and O atoms in the structure of Mg₅TiO₄(BO₃)₂. Displacement ellipsoids are drawn at the 90% probability level. [Symmetry codes: (i) x, y, z-1; (ii) -x+1/2, y+1/2, z; (iii) x-1/2, -y+1/2, -z+1; (iv) x, y, z+1; (v) x-1/2, -y+1/2, -z; (vi) -x+1/2, y-1/2, z; (vii) -x+1/2, y-1/2, z-1; (viii) -x, -y, -z; (ix) -x, -y+1, -z+1; (x) -x+1/2, y+1/2, z+1.]

Fig. 2. Crystal structure of Mg₅TiO₄(BO₃)₂ in a representation using cation-centred oxygen polyhedra. The area surrounded by a dashed line indicates the repeating unit of the zigzag folding layers.

pentamagnesium titanium(IV) tetraoxide bis(borate) top

Crystal data top

Mg₅TiO₄(BO₃)₂	F(000) = 344
M_r = 351.07	D_x = 3.396 Mg m⁻³
Orthorhombic, Pbam	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2 2ab	Cell parameters from 2730 reflections
a = 9.2636 (5) Å	θ = 3.3–27.5°
b = 12.2989 (5) Å	µ = 1.76 mm⁻¹
c = 3.01309 (15) Å	T = 298 K
V = 343.29 (3) Å³	Block, colourless
Z = 2	0.13 × 0.09 × 0.08 mm

Data collection top

Rigaku R-AXIS RAPID II diffractometer	463 independent reflections
Radiation source: fine-focus sealed tube	413 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.027
Detector resolution: 10 pixels mm^-1	θ_max = 27.5°, θ_min = 3.3°
ω scans	h = −12→12
Absorption correction: numerical (NUMABS; Higashi, 1999)	k = −15→15
T_min = 0.864, T_max = 0.925	l = −3→3
3166 measured reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F² > 2σ(F²)] = 0.020	Secondary atom site location: difference Fourier map
wR(F²) = 0.070	w = 1/[σ²(F_o²) + (0.0422P)² + 0.0192P] where P = (F_o² + 2F_c²)/3
S = 1.29	(Δ/σ)_max < 0.001
463 reflections	Δρ_max = 0.41 e Å⁻³
54 parameters	Δρ_min = −0.42 e Å⁻³

Crystal data top

Mg₅TiO₄(BO₃)₂	V = 343.29 (3) Å³
M_r = 351.07	Z = 2
Orthorhombic, Pbam	Mo Kα radiation
a = 9.2636 (5) Å	µ = 1.76 mm⁻¹
b = 12.2989 (5) Å	T = 298 K
c = 3.01309 (15) Å	0.13 × 0.09 × 0.08 mm

Data collection top

Rigaku R-AXIS RAPID II diffractometer	463 independent reflections
Absorption correction: numerical (NUMABS; Higashi, 1999)	413 reflections with I > 2σ(I)
T_min = 0.864, T_max = 0.925	R_int = 0.027
3166 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.020	54 parameters
wR(F²) = 0.070	0 restraints
S = 1.29	Δρ_max = 0.41 e Å⁻³
463 reflections	Δρ_min = −0.42 e Å⁻³

Special details top

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 > 2σ(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)
Ti1	0.23863 (5)	0.38402 (4)	0.0000	0.0043 (2)	0.50
Mg1	0.23863 (5)	0.38402 (4)	0.0000	0.0043 (2)	0.50
Mg2	0.00149 (7)	0.21804 (6)	0.5000	0.0060 (3)
Mg3	0.0000	0.0000	0.0000	0.0083 (3)
Mg4	0.0000	0.5000	0.5000	0.0061 (3)
O1	0.12572 (18)	0.14254 (11)	0.0000	0.0071 (4)
O2	0.35021 (16)	0.04263 (12)	0.0000	0.0068 (4)
O3	0.35034 (16)	0.23704 (13)	0.0000	0.0070 (4)
O4	0.10946 (19)	0.35677 (11)	0.5000	0.0090 (4)
O5	0.38167 (17)	0.42350 (12)	0.5000	0.0080 (4)
B1	0.2745 (3)	0.1398 (2)	0.0000	0.0065 (6)*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ti1/Mg1	0.0035 (3)	0.0052 (3)	0.0042 (4)	0.0006 (2)	0.000	0.000
Mg2	0.0060 (5)	0.0054 (5)	0.0065 (5)	−0.0007 (2)	0.000	0.000
Mg3	0.0110 (6)	0.0066 (6)	0.0072 (6)	0.0009 (4)	0.000	0.000
Mg4	0.0057 (6)	0.0049 (6)	0.0077 (7)	0.0007 (4)	0.000	0.000
O1	0.0065 (8)	0.0091 (8)	0.0057 (9)	0.0007 (6)	0.000	0.000
O2	0.0072 (8)	0.0063 (8)	0.0070 (9)	0.0005 (6)	0.000	0.000
O3	0.0077 (8)	0.0070 (8)	0.0064 (8)	0.0001 (6)	0.000	0.000
O4	0.0061 (9)	0.0029 (8)	0.0179 (11)	0.0001 (6)	0.000	0.000
O5	0.0050 (8)	0.0059 (8)	0.0132 (10)	0.0002 (6)	0.000	0.000

Geometric parameters (Å, º) top

Ti1/Mg1—O4ⁱ	1.9528 (11)	Mg3—Ti1/Mg1^vi	2.8102 (5)
Ti1/Mg1—O4	1.9528 (11)	Mg3—Mg3ⁱ	3.0131 (2)
Ti1/Mg1—O5	2.0643 (11)	Mg3—Mg3^iv	3.0131 (2)
Ti1/Mg1—O5ⁱ	2.0643 (11)	Mg4—O4	2.0326 (15)
Ti1/Mg1—O3	2.0829 (16)	Mg4—O4^x	2.0326 (15)
Ti1/Mg1—O2ⁱⁱ	2.1172 (16)	Mg4—O2^xi	2.1142 (11)
Ti1/Mg1—Mg3ⁱⁱⁱ	2.8102 (5)	Mg4—O2^vi	2.1142 (11)
Ti1/Mg1—Ti1/Mg1ⁱ	3.0131 (2)	Mg4—O2ⁱⁱ	2.1142 (11)
Ti1/Mg1—Ti1/Mg1^iv	3.0131 (2)	Mg4—O2^v	2.1142 (11)
Ti1/Mg1—Mg4ⁱ	3.0316 (4)	Mg4—Mg4^iv	3.0131 (2)
Mg2—O4	1.9778 (16)	Mg4—Mg4ⁱ	3.0131 (2)
Mg2—O5^v	2.0645 (17)	Mg4—Ti1/Mg1^xii	3.0316 (4)
Mg2—O1^iv	2.1110 (12)	Mg4—Ti1/Mg1^x	3.0316 (4)
Mg2—O1	2.1110 (12)	O1—B1	1.379 (3)
Mg2—O3^vi	2.1296 (12)	O1—Mg2ⁱ	2.1110 (12)
Mg2—O3^v	2.1296 (12)	O2—B1	1.385 (3)
Mg2—Mg2^iv	3.0131 (2)	O2—Mg4^xiii	2.1142 (11)
Mg2—Mg2ⁱ	3.0131 (2)	O2—Mg4ⁱⁱⁱ	2.1142 (11)
Mg2—Mg3	3.0759 (7)	O2—Ti1/Mg1^vii	2.1172 (16)
Mg2—Mg3^iv	3.0759 (7)	O3—B1	1.387 (3)
Mg2—Ti1/Mg1^vi	3.1264 (7)	O3—Mg2^xiii	2.1296 (12)
Mg3—O5^vii	2.0872 (11)	O3—Mg2ⁱⁱⁱ	2.1296 (12)
Mg3—O5^vi	2.0872 (11)	O4—Ti1/Mg1^iv	1.9528 (11)
Mg3—O5^viii	2.0872 (11)	O5—Ti1/Mg1^iv	2.0643 (11)
Mg3—O5^v	2.0872 (11)	O5—Mg2^xiii	2.0645 (17)
Mg3—O1	2.1047 (15)	O5—Mg3^xiii	2.0872 (11)
Mg3—O1^ix	2.1047 (15)	O5—Mg3ⁱⁱⁱ	2.0872 (11)
Mg3—Ti1/Mg1^vii	2.8102 (5)

O4ⁱ—Ti1/Mg1—O4	100.97 (8)	O1—Mg3—O1^ix	180.00 (4)
O4ⁱ—Ti1/Mg1—O5	175.33 (5)	O5^vii—Mg3—Ti1/Mg1^vii	47.05 (3)
O4—Ti1/Mg1—O5	82.57 (5)	O5^vi—Mg3—Ti1/Mg1^vii	132.95 (3)
O4ⁱ—Ti1/Mg1—O5ⁱ	82.57 (5)	O5^viii—Mg3—Ti1/Mg1^vii	47.05 (3)
O4—Ti1/Mg1—O5ⁱ	175.33 (5)	O5^v—Mg3—Ti1/Mg1^vii	132.95 (3)
O5—Ti1/Mg1—O5ⁱ	93.74 (7)	O1—Mg3—Ti1/Mg1^vii	86.91 (5)
O4ⁱ—Ti1/Mg1—O3	98.94 (5)	O1^ix—Mg3—Ti1/Mg1^vii	93.09 (5)
O4—Ti1/Mg1—O3	98.94 (5)	O5^vii—Mg3—Ti1/Mg1^vi	132.95 (3)
O5—Ti1/Mg1—O3	83.41 (5)	O5^vi—Mg3—Ti1/Mg1^vi	47.05 (3)
O5ⁱ—Ti1/Mg1—O3	83.41 (5)	O5^viii—Mg3—Ti1/Mg1^vi	132.95 (3)
O4ⁱ—Ti1/Mg1—O2ⁱⁱ	85.41 (5)	O5^v—Mg3—Ti1/Mg1^vi	47.05 (3)
O4—Ti1/Mg1—O2ⁱⁱ	85.41 (5)	O1—Mg3—Ti1/Mg1^vi	93.09 (4)
O5—Ti1/Mg1—O2ⁱⁱ	91.88 (5)	O1^ix—Mg3—Ti1/Mg1^vi	86.91 (5)
O5ⁱ—Ti1/Mg1—O2ⁱⁱ	91.88 (5)	Ti1/Mg1^vii—Mg3—Ti1/Mg1^vi	180.00 (2)
O3—Ti1/Mg1—O2ⁱⁱ	173.08 (6)	O5^vii—Mg3—Mg3ⁱ	136.20 (3)
O4ⁱ—Ti1/Mg1—Mg3ⁱⁱⁱ	127.95 (4)	O5^vi—Mg3—Mg3ⁱ	43.80 (3)
O4—Ti1/Mg1—Mg3ⁱⁱⁱ	127.95 (4)	O5^viii—Mg3—Mg3ⁱ	43.80 (3)
O5—Ti1/Mg1—Mg3ⁱⁱⁱ	47.74 (3)	O5^v—Mg3—Mg3ⁱ	136.20 (3)
O5ⁱ—Ti1/Mg1—Mg3ⁱⁱⁱ	47.74 (3)	O1—Mg3—Mg3ⁱ	90
O3—Ti1/Mg1—Mg3ⁱⁱⁱ	90.71 (4)	O1^ix—Mg3—Mg3ⁱ	90
O2ⁱⁱ—Ti1/Mg1—Mg3ⁱⁱⁱ	82.37 (4)	Ti1/Mg1^vii—Mg3—Mg3ⁱ	90
O4ⁱ—Ti1/Mg1—Ti1/Mg1ⁱ	39.51 (4)	Ti1/Mg1^vi—Mg3—Mg3ⁱ	90
O4—Ti1/Mg1—Ti1/Mg1ⁱ	140.49 (4)	O5^vii—Mg3—Mg3^iv	43.80 (3)
O5—Ti1/Mg1—Ti1/Mg1ⁱ	136.87 (3)	O5^vi—Mg3—Mg3^iv	136.20 (3)
O5ⁱ—Ti1/Mg1—Ti1/Mg1ⁱ	43.13 (3)	O5^viii—Mg3—Mg3^iv	136.20 (3)
O3—Ti1/Mg1—Ti1/Mg1ⁱ	90	O5^v—Mg3—Mg3^iv	43.80 (3)
O2ⁱⁱ—Ti1/Mg1—Ti1/Mg1ⁱ	90	O1—Mg3—Mg3^iv	90
Mg3ⁱⁱⁱ—Ti1/Mg1—Ti1/Mg1ⁱ	90	O1^ix—Mg3—Mg3^iv	90
O4ⁱ—Ti1/Mg1—Ti1/Mg1^iv	140.49 (4)	Ti1/Mg1^vii—Mg3—Mg3^iv	90
O4—Ti1/Mg1—Ti1/Mg1^iv	39.51 (4)	Ti1/Mg1^vi—Mg3—Mg3^iv	90
O5—Ti1/Mg1—Ti1/Mg1^iv	43.13 (3)	Mg3ⁱ—Mg3—Mg3^iv	180
O5ⁱ—Ti1/Mg1—Ti1/Mg1^iv	136.87 (3)	O4—Mg4—O4^x	180
O3—Ti1/Mg1—Ti1/Mg1^iv	90	O4—Mg4—O2^xi	83.54 (5)
O2ⁱⁱ—Ti1/Mg1—Ti1/Mg1^iv	90	O4^x—Mg4—O2^xi	96.46 (5)
Mg3ⁱⁱⁱ—Ti1/Mg1—Ti1/Mg1^iv	90	O4—Mg4—O2^vi	96.46 (5)
Ti1/Mg1ⁱ—Ti1/Mg1—Ti1/Mg1^iv	180.00 (4)	O4^x—Mg4—O2^vi	83.54 (5)
O4ⁱ—Ti1/Mg1—Mg4ⁱ	41.46 (4)	O2^xi—Mg4—O2^vi	180
O4—Ti1/Mg1—Mg4ⁱ	91.00 (5)	O4—Mg4—O2ⁱⁱ	83.54 (5)
O5—Ti1/Mg1—Mg4ⁱ	136.06 (5)	O4^x—Mg4—O2ⁱⁱ	96.46 (5)
O5ⁱ—Ti1/Mg1—Mg4ⁱ	89.70 (4)	O2^xi—Mg4—O2ⁱⁱ	90.89 (6)
O3—Ti1/Mg1—Mg4ⁱ	140.41 (3)	O2^vi—Mg4—O2ⁱⁱ	89.11 (6)
O2ⁱⁱ—Ti1/Mg1—Mg4ⁱ	44.20 (3)	O4—Mg4—O2^v	96.46 (5)
Mg3ⁱⁱⁱ—Ti1/Mg1—Mg4ⁱ	112.918 (15)	O4^x—Mg4—O2^v	83.54 (5)
Ti1/Mg1ⁱ—Ti1/Mg1—Mg4ⁱ	60.202 (5)	O2^xi—Mg4—O2^v	89.11 (6)
Ti1/Mg1^iv—Ti1/Mg1—Mg4ⁱ	119.798 (5)	O2^vi—Mg4—O2^v	90.89 (6)
O4—Mg2—O5^v	177.86 (7)	O2ⁱⁱ—Mg4—O2^v	180.00 (8)
O4—Mg2—O1^iv	95.95 (6)	O4—Mg4—Mg4^iv	90
O5^v—Mg2—O1^iv	85.54 (6)	O4^x—Mg4—Mg4^iv	90
O4—Mg2—O1	95.95 (6)	O2^xi—Mg4—Mg4^iv	44.56 (3)
O5^v—Mg2—O1	85.54 (6)	O2^vi—Mg4—Mg4^iv	135.44 (3)
O1^iv—Mg2—O1	91.07 (7)	O2ⁱⁱ—Mg4—Mg4^iv	135.44 (3)
O4—Mg2—O3^vi	96.24 (6)	O2^v—Mg4—Mg4^iv	44.56 (3)
O5^v—Mg2—O3^vi	82.26 (5)	O4—Mg4—Mg4ⁱ	90
O1^iv—Mg2—O3^vi	167.79 (7)	O4^x—Mg4—Mg4ⁱ	90
O1—Mg2—O3^vi	88.15 (4)	O2^xi—Mg4—Mg4ⁱ	135.44 (3)
O4—Mg2—O3^v	96.24 (6)	O2^vi—Mg4—Mg4ⁱ	44.56 (3)
O5^v—Mg2—O3^v	82.26 (5)	O2ⁱⁱ—Mg4—Mg4ⁱ	44.56 (3)
O1^iv—Mg2—O3^v	88.15 (4)	O2^v—Mg4—Mg4ⁱ	135.44 (3)
O1—Mg2—O3^v	167.79 (7)	Mg4^iv—Mg4—Mg4ⁱ	180
O3^vi—Mg2—O3^v	90.05 (6)	O4—Mg4—Ti1/Mg1^xii	140.49 (3)
O4—Mg2—Mg2^iv	90	O4^x—Mg4—Ti1/Mg1^xii	39.51 (3)
O5^v—Mg2—Mg2^iv	90	O2^xi—Mg4—Ti1/Mg1^xii	135.72 (4)
O1^iv—Mg2—Mg2^iv	44.47 (3)	O2^vi—Mg4—Ti1/Mg1^xii	44.28 (4)
O1—Mg2—Mg2^iv	135.53 (3)	O2ⁱⁱ—Mg4—Ti1/Mg1^xii	90.45 (4)
O3^vi—Mg2—Mg2^iv	135.03 (3)	O2^v—Mg4—Ti1/Mg1^xii	89.55 (4)
O3^v—Mg2—Mg2^iv	44.97 (3)	Mg4^iv—Mg4—Ti1/Mg1^xii	119.798 (5)
O4—Mg2—Mg2ⁱ	90	Mg4ⁱ—Mg4—Ti1/Mg1^xii	60.202 (5)
O5^v—Mg2—Mg2ⁱ	90	O4—Mg4—Ti1/Mg1^x	140.49 (3)
O1^iv—Mg2—Mg2ⁱ	135.53 (3)	O4^x—Mg4—Ti1/Mg1^x	39.51 (3)
O1—Mg2—Mg2ⁱ	44.47 (3)	O2^xi—Mg4—Ti1/Mg1^x	90.45 (4)
O3^vi—Mg2—Mg2ⁱ	44.97 (3)	O2^vi—Mg4—Ti1/Mg1^x	89.55 (4)
O3^v—Mg2—Mg2ⁱ	135.03 (3)	O2ⁱⁱ—Mg4—Ti1/Mg1^x	135.72 (4)
Mg2^iv—Mg2—Mg2ⁱ	180	O2^v—Mg4—Ti1/Mg1^x	44.28 (4)
O4—Mg2—Mg3	138.97 (4)	Mg4^iv—Mg4—Ti1/Mg1^x	60.202 (5)
O5^v—Mg2—Mg3	42.48 (3)	Mg4ⁱ—Mg4—Ti1/Mg1^x	119.798 (5)
O1^iv—Mg2—Mg3	88.20 (4)	Ti1/Mg1^xii—Mg4—Ti1/Mg1^x	59.596 (10)
O1—Mg2—Mg3	43.06 (4)	B1—O1—Mg3	122.18 (14)
O3^vi—Mg2—Mg3	82.92 (4)	B1—O1—Mg2ⁱ	123.77 (8)
O3^v—Mg2—Mg3	124.73 (5)	Mg3—O1—Mg2ⁱ	93.71 (6)
Mg2^iv—Mg2—Mg3	119.327 (7)	B1—O1—Mg2	123.77 (8)
Mg2ⁱ—Mg2—Mg3	60.673 (7)	Mg3—O1—Mg2	93.71 (6)
O4—Mg2—Mg3^iv	138.97 (4)	Mg2ⁱ—O1—Mg2	91.07 (7)
O5^v—Mg2—Mg3^iv	42.48 (3)	B1—O2—Mg4^xiii	123.09 (8)
O1^iv—Mg2—Mg3^iv	43.06 (4)	B1—O2—Mg4ⁱⁱⁱ	123.09 (8)
O1—Mg2—Mg3^iv	88.19 (4)	Mg4^xiii—O2—Mg4ⁱⁱⁱ	90.89 (6)
O3^vi—Mg2—Mg3^iv	124.73 (5)	B1—O2—Ti1/Mg1^vii	126.73 (15)
O3^v—Mg2—Mg3^iv	82.92 (4)	Mg4^xiii—O2—Ti1/Mg1^vii	91.53 (5)
Mg2^iv—Mg2—Mg3^iv	60.673 (7)	Mg4ⁱⁱⁱ—O2—Ti1/Mg1^vii	91.52 (5)
Mg2ⁱ—Mg2—Mg3^iv	119.327 (7)	B1—O3—Ti1/Mg1	119.79 (14)
Mg3—Mg2—Mg3^iv	58.653 (15)	B1—O3—Mg2^xiii	123.82 (8)
O4—Mg2—Ti1/Mg1^vi	137.75 (4)	Ti1/Mg1—O3—Mg2^xiii	95.83 (6)
O5^v—Mg2—Ti1/Mg1^vi	40.78 (3)	B1—O3—Mg2ⁱⁱⁱ	123.82 (8)
O1^iv—Mg2—Ti1/Mg1^vi	126.29 (5)	Ti1/Mg1—O3—Mg2ⁱⁱⁱ	95.83 (6)
O1—Mg2—Ti1/Mg1^vi	84.50 (4)	Mg2^xiii—O3—Mg2ⁱⁱⁱ	90.05 (6)
O3^vi—Mg2—Ti1/Mg1^vi	41.51 (4)	Ti1/Mg1^iv—O4—Ti1/Mg1	100.97 (8)
O3^v—Mg2—Ti1/Mg1^vi	86.16 (4)	Ti1/Mg1^iv—O4—Mg2	117.25 (5)
Mg2^iv—Mg2—Ti1/Mg1^vi	118.808 (8)	Ti1/Mg1—O4—Mg2	117.25 (5)
Mg2ⁱ—Mg2—Ti1/Mg1^vi	61.192 (8)	Ti1/Mg1^iv—O4—Mg4	99.03 (5)
Mg3—Mg2—Ti1/Mg1^vi	53.876 (13)	Ti1/Mg1—O4—Mg4	99.03 (5)
Mg3^iv—Mg2—Ti1/Mg1^vi	83.25 (2)	Mg2—O4—Mg4	119.69 (9)
O5^vii—Mg3—O5^vi	180.00 (10)	Ti1/Mg1—O5—Ti1/Mg1^iv	93.74 (7)
O5^vii—Mg3—O5^viii	92.41 (6)	Ti1/Mg1—O5—Mg2^xiii	98.44 (6)
O5^vi—Mg3—O5^viii	87.59 (6)	Ti1/Mg1^iv—O5—Mg2^xiii	98.44 (6)
O5^vii—Mg3—O5^v	87.59 (6)	Ti1/Mg1—O5—Mg3^xiii	165.91 (9)
O5^vi—Mg3—O5^v	92.41 (6)	Ti1/Mg1^iv—O5—Mg3^xiii	85.203 (14)
O5^viii—Mg3—O5^v	180.00 (10)	Mg2^xiii—O5—Mg3^xiii	95.61 (6)
O5^vii—Mg3—O1	94.87 (5)	Ti1/Mg1—O5—Mg3ⁱⁱⁱ	85.203 (14)
O5^vi—Mg3—O1	85.13 (5)	Ti1/Mg1^iv—O5—Mg3ⁱⁱⁱ	165.91 (9)
O5^viii—Mg3—O1	94.87 (5)	Mg2^xiii—O5—Mg3ⁱⁱⁱ	95.61 (6)
O5^v—Mg3—O1	85.13 (5)	Mg3^xiii—O5—Mg3ⁱⁱⁱ	92.41 (6)
O5^vii—Mg3—O1^ix	85.13 (5)	O1—B1—O2	121.8 (2)
O5^vi—Mg3—O1^ix	94.87 (5)	O1—B1—O3	119.00 (19)
O5^viii—Mg3—O1^ix	85.13 (5)	O2—B1—O3	119.2 (2)
O5^v—Mg3—O1^ix	94.87 (5)

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

Experimental details

Crystal data
Chemical formula	Mg₅TiO₄(BO₃)₂
M_r	351.07
Crystal system, space group	Orthorhombic, Pbam
Temperature (K)	298
a, b, c (Å)	9.2636 (5), 12.2989 (5), 3.01309 (15)
V (Å³)	343.29 (3)
Z	2
Radiation type	Mo Kα
µ (mm⁻¹)	1.76
Crystal size (mm)	0.13 × 0.09 × 0.08

Data collection
Diffractometer	Rigaku R-AXIS RAPID II diffractometer
Absorption correction	Numerical (NUMABS; Higashi, 1999)
T_min, T_max	0.864, 0.925
No. of measured, independent and observed [I > 2σ(I)] reflections	3166, 463, 413
R_int	0.027
(sin θ/λ)_max (Å⁻¹)	0.649

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.020, 0.070, 1.29
No. of reflections	463
No. of parameters	54
Δρ_max, Δρ_min (e Å⁻³)	0.41, −0.42

Computer programs: PROCESS-AUTO (Rigaku/MSC, 2005), CrystalStructure (Rigaku/MSC, 2005), SIR2004 (Burla et al., 2005), SHELXL97 (Sheldrick, 2008), VESTA (Momma & Izumi, 2008).

Selected geometric parameters (Å, º) top

Ti1/Mg1—O4	1.9528 (11)	Mg3—O5ⁱⁱ	2.0872 (11)
Ti1/Mg1—O5	2.0643 (11)	Mg3—O1	2.1047 (15)
Ti1/Mg1—O3	2.0829 (16)	Mg4—O4	2.0326 (15)
Ti1/Mg1—O2ⁱ	2.1172 (16)	Mg4—O2ⁱ	2.1142 (11)
Mg2—O4	1.9778 (16)	O1—B1	1.379 (3)
Mg2—O5ⁱⁱ	2.0645 (17)	O2—B1	1.385 (3)
Mg2—O1	2.1110 (12)	O3—B1	1.387 (3)
Mg2—O3ⁱⁱ	2.1296 (12)

O1—B1—O2	121.8 (2)	O2—B1—O3	119.2 (2)
O1—B1—O3	119.00 (19)

Symmetry codes: (i) −x+1/2, y+1/2, z; (ii) x−1/2, −y+1/2, −z+1.

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