Probability density analyses of guest ions in hollandite A_xMg_x/2Ti_{8 − x/2}O₁₆ (A = K, Rb)

Probability density functions (PDFs) of mobile ions in one-dimensional ionic conductors of hollandite A_xMg_x/2Ti_{8 − x/2}O₁₆ (A = K, Rb) were examined by single-crystal X-ray diffraction. A conventional structure model was modified by imposing an additional constraint condition, which is based on microscopic description for the possible displacement of mobile ions adjacent to a vacancy in the tunnel. Joint PDFs and one-particle potentials for mobile ions were obtained from the structure models applying harmonic and anharmonic atomic displacement parameters (ADPs). Potential curves of the ion hopping between neighboring cavities were calculated from the joint PDF of the specific ions of the process. Energy barriers of the ion hopping were estimated at 52–60 meV from anharmonic ADP models of K-hollandite, while the values varied from 140 to 250 meV for Rb-hollandite.

Computing details

For all compounds, program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

(K-C22)

Crystal data

K1.56Mg0.78O16Ti7.22	Dx = 3.690 Mg m^−3
Mr = 681.5	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/m	Cell parameters from 24 reflections
Hall symbol: -I 4	θ = 20.1–24.1°
a = 10.1541 (11) Å	µ = 5.13 mm^−1
c = 2.9735 (14) Å	T = 298 K
V = 306.58 (15) Å^3	Prismatic, colorless
Z = 1	0.25 × 0.14 × 0.14 mm
F(000) = 326

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.027
Graphite monochromator	θmax = 50.0°, θmin = 2.8°
ω/2θ scans	h = −20→21
Absorption correction: analytical Tompa_analytical	k = −20→20
Tmin = 0.473, Tmax = 0.540	l = −5→0
2777 measured reflections	3 standard reflections every 200 reflections
835 independent reflections	intensity decay: 0.3%
785 reflections with I > 3σ(I)

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0001I^2)
R[F^2 > 2σ(F^2)] = 0.019	(Δ/σ)max = 0.030
wR(F^2) = 0.045	Δρmax = 0.76 e Å^−3
S = 2.03	Δρmin = −0.59 e Å^−3
835 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
27 parameters	Extinction coefficient: 0.0515 (11)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0	0	0.5	0.039 (2)	0.19 (2)
K2	0	0	0.305 (5)	0.050 (2)	0.294 (10)
Ti1	0.350895 (11)	0.167624 (11)	0	0.00768 (3)	0.9029 (6)
Mg1	0.350895	0.167624	0	0.00768 (3)	0.0970 (6)
O1	0.15533 (4)	0.20505 (4)	0	0.00686 (8)
O2	0.54050 (5)	0.16559 (5)	0	0.00827 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.041 (3)	0.041 (3)	0.035 (5)	0	0	0
K2	0.0172 (4)	0.0172 (4)	0.116 (6)	0	0	0
Ti1	0.00798 (5)	0.00865 (5)	0.00642 (6)	0.00100 (3)	0	0
Mg1	0.00798 (5)	0.00865 (5)	0.00642 (6)	0.00100 (3)	0	0
O1	0.00674 (14)	0.00677 (14)	0.00708 (16)	−0.00009 (11)	0	0
O2	0.00576 (14)	0.01080 (16)	0.00824 (18)	0.00024 (11)	0	0

Geometric parameters (Å, º)

K1—O1	3.0055 (4)	K2—O1^iii	3.331 (8)
K1—O1^i	3.0055 (4)	K2—O1^iv	2.765 (5)
K1—O1^ii	3.0055 (4)	K2—O1^v	3.331 (8)
K1—O1^iii	3.0055 (4)	K2—O1^vi	2.765 (5)
K1—O1^iv	3.0055 (4)	K2—O1^vii	3.331 (8)
K1—O1^v	3.0055 (4)	Ti1—O1	2.0218 (5)
K1—O1^vi	3.0055 (4)	Ti1—O1^viii	1.9713 (3)
K1—O1^vii	3.0055 (4)	Ti1—O1^ix	1.9713 (3)
K2—O1	2.765 (5)	Ti1—O2	1.9254 (5)
K2—O1^i	3.331 (8)	Ti1—O2^x	1.9760 (3)
K2—O1^ii	2.765 (5)	Ti1—O2^xi	1.9760 (3)
O1—K1—O1^i	59.296 (6)	O1^i—K2—O1^v	67.34 (19)
O1—K1—O1^ii	120.704 (6)	O1^i—K2—O1^vi	101.73 (11)
O1—K1—O1^iii	180	O1^i—K2—O1^vii	67.34 (19)
O1—K1—O1^iv	75.836 (11)	O1^ii—K2—O1	141.7 (5)
O1—K1—O1^v	104.164 (11)	O1^ii—K2—O1^i	160.8 (4)
O1—K1—O1^vi	75.836 (11)	O1^ii—K2—O1^iii	57.49 (8)
O1—K1—O1^vii	104.164 (11)	O1^ii—K2—O1^iv	83.84 (17)
O1^i—K1—O1	59.296 (6)	O1^ii—K2—O1^v	101.73 (11)
O1^i—K1—O1^ii	180	O1^ii—K2—O1^vi	83.84 (17)
O1^i—K1—O1^iii	120.704 (6)	O1^ii—K2—O1^vii	101.73 (11)
O1^i—K1—O1^iv	104.164 (11)	O1^iii—K2—O1	160.8 (4)
O1^i—K1—O1^v	75.836 (11)	O1^iii—K2—O1^i	103.3 (4)
O1^i—K1—O1^vi	104.164 (11)	O1^iii—K2—O1^ii	57.49 (8)
O1^i—K1—O1^vii	75.836 (11)	O1^iii—K2—O1^iv	101.73 (11)
O1^ii—K1—O1	120.704 (6)	O1^iii—K2—O1^v	67.34 (19)
O1^ii—K1—O1^i	180	O1^iii—K2—O1^vi	101.73 (11)
O1^ii—K1—O1^iii	59.296 (6)	O1^iii—K2—O1^vii	67.34 (19)
O1^ii—K1—O1^iv	75.836 (11)	O1^iv—K2—O1	83.84 (17)
O1^ii—K1—O1^v	104.164 (11)	O1^iv—K2—O1^i	101.73 (11)
O1^ii—K1—O1^vi	75.836 (11)	O1^iv—K2—O1^ii	83.84 (17)
O1^ii—K1—O1^vii	104.164 (11)	O1^iv—K2—O1^iii	101.73 (11)
O1^iii—K1—O1	180	O1^iv—K2—O1^v	57.49 (8)
O1^iii—K1—O1^i	120.704 (6)	O1^iv—K2—O1^vi	141.7 (5)
O1^iii—K1—O1^ii	59.296 (6)	O1^iv—K2—O1^vii	160.8 (4)
O1^iii—K1—O1^iv	104.164 (11)	O1^v—K2—O1	101.73 (11)
O1^iii—K1—O1^v	75.836 (11)	O1^v—K2—O1^i	67.34 (19)
O1^iii—K1—O1^vi	104.164 (11)	O1^v—K2—O1^ii	101.73 (11)
O1^iii—K1—O1^vii	75.836 (11)	O1^v—K2—O1^iii	67.34 (19)
O1^iv—K1—O1	75.836 (11)	O1^v—K2—O1^iv	57.49 (8)
O1^iv—K1—O1^i	104.164 (11)	O1^v—K2—O1^vi	160.8 (4)
O1^iv—K1—O1^ii	75.836 (11)	O1^v—K2—O1^vii	103.3 (4)
O1^iv—K1—O1^iii	104.164 (11)	O1^vi—K2—O1	83.84 (17)
O1^iv—K1—O1^v	59.296 (6)	O1^vi—K2—O1^i	101.73 (11)
O1^iv—K1—O1^vi	120.704 (6)	O1^vi—K2—O1^ii	83.84 (17)
O1^iv—K1—O1^vii	180	O1^vi—K2—O1^iii	101.73 (11)
O1^v—K1—O1	104.164 (11)	O1^vi—K2—O1^iv	141.7 (5)
O1^v—K1—O1^i	75.836 (11)	O1^vi—K2—O1^v	160.8 (4)
O1^v—K1—O1^ii	104.164 (11)	O1^vi—K2—O1^vii	57.49 (8)
O1^v—K1—O1^iii	75.836 (11)	O1^vii—K2—O1	101.73 (11)
O1^v—K1—O1^iv	59.296 (6)	O1^vii—K2—O1^i	67.34 (19)
O1^v—K1—O1^vi	180	O1^vii—K2—O1^ii	101.73 (11)
O1^v—K1—O1^vii	120.704 (6)	O1^vii—K2—O1^iii	67.34 (19)
O1^vi—K1—O1	75.836 (11)	O1^vii—K2—O1^iv	160.8 (4)
O1^vi—K1—O1^i	104.164 (11)	O1^vii—K2—O1^v	103.3 (4)
O1^vi—K1—O1^ii	75.836 (11)	O1^vii—K2—O1^vi	57.49 (8)
O1^vi—K1—O1^iii	104.164 (11)	O1—Ti1—O1^viii	81.095 (16)
O1^vi—K1—O1^iv	120.704 (6)	O1—Ti1—O1^ix	81.095 (16)
O1^vi—K1—O1^v	180	O1—Ti1—O2	169.78 (2)
O1^vi—K1—O1^vii	59.296 (6)	O1—Ti1—O2^x	92.269 (17)
O1^vii—K1—O1	104.164 (11)	O1—Ti1—O2^xi	92.269 (17)
O1^vii—K1—O1^i	75.836 (11)	O1^viii—Ti1—O1	81.095 (16)
O1^vii—K1—O1^ii	104.164 (11)	O1^viii—Ti1—O1^ix	97.910 (15)
O1^vii—K1—O1^iii	75.836 (11)	O1^viii—Ti1—O2	92.243 (17)
O1^vii—K1—O1^iv	180	O1^viii—Ti1—O2^x	81.853 (14)
O1^vii—K1—O1^v	120.704 (6)	O1^viii—Ti1—O2^xi	173.30 (2)
O1^vii—K1—O1^vi	59.296 (6)	O1^ix—Ti1—O1	81.095 (16)
O1—K2—O1^i	57.49 (8)	O1^ix—Ti1—O1^viii	97.910 (15)
O1—K2—O1^ii	141.7 (5)	O1^ix—Ti1—O2	92.243 (17)
O1—K2—O1^iii	160.8 (4)	O1^ix—Ti1—O2^x	173.30 (2)
O1—K2—O1^iv	83.84 (17)	O1^ix—Ti1—O2^xi	81.853 (14)
O1—K2—O1^v	101.73 (11)	O2—Ti1—O2^x	94.455 (18)
O1—K2—O1^vi	83.84 (17)	O2—Ti1—O2^xi	94.455 (18)
O1—K2—O1^vii	101.73 (11)	O2^x—Ti1—O2	94.455 (18)
O1^i—K2—O1	57.49 (8)	O2^x—Ti1—O2^xi	97.596 (15)
O1^i—K2—O1^ii	160.8 (4)	O2^xi—Ti1—O2	94.455 (18)
O1^i—K2—O1^iii	103.3 (4)	O2^xi—Ti1—O2^x	97.596 (15)
O1^i—K2—O1^iv	101.73 (11)

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

(K-C23)

Crystal data

K1.55Mg0.77O16Ti7.23	Dx = 3.687 Mg m^−3
Mr = 681.4	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/m	Cell parameters from 24 reflections
Hall symbol: -I 4	θ = 20.1–24.1°
a = 10.1541 (11) Å	µ = 5.13 mm^−1
c = 2.9735 (14) Å	T = 298 K
V = 306.58 (15) Å^3	Prismatic, colorless
Z = 1	0.25 × 0.14 × 0.14 mm
F(000) = 326

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.027
Graphite monochromator	θmax = 50.0°, θmin = 2.8°
ω/2θ scans	h = −20→21
Absorption correction: analytical Tompa_analytical	k = −20→20
Tmin = 0.473, Tmax = 0.540	l = −5→0
2777 measured reflections	3 standard reflections every 200 reflections
835 independent reflections	intensity decay: 0.3%
785 reflections with I > 3σ(I)

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0001I^2)
R[F^2 > 2σ(F^2)] = 0.017	(Δ/σ)max = 0.049
wR(F^2) = 0.042	Δρmax = 0.69 e Å^−3
S = 1.92	Δρmin = −0.57 e Å^−3
835 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
29 parameters	Extinction coefficient: 0.0516 (10)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0	0	0.5	0.044 (5)	0.38 (3)
K2	0	0	0.250 (8)	0.0340 (11)	0.197 (17)
Ti1	0.350896 (10)	0.167627 (11)	0	0.00769 (3)	0.9039 (5)
Mg1	0.350896	0.167627	0	0.00769 (3)	0.0961 (5)
O1	0.15535 (4)	0.20504 (4)	0	0.00686 (8)
O2	0.54049 (4)	0.16558 (5)	0	0.00826 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0284 (8)	0.0284 (8)	0.076 (15)	0	0	0
K2	0.0152 (7)	0.0152 (7)	0.072 (3)	0	0	0
Ti1	0.00798 (5)	0.00865 (5)	0.00642 (6)	0.00101 (2)	0	0
Mg1	0.00798 (5)	0.00865 (5)	0.00642 (6)	0.00101 (2)	0	0
O1	0.00671 (13)	0.00677 (13)	0.00709 (15)	−0.00007 (10)	0	0
O2	0.00578 (13)	0.01074 (15)	0.00827 (17)	0.00021 (10)	0	0

Geometric parameters (Å, º)

K1—O1	3.0055 (4)	K2—O1^i	3.435 (15)
K1—O1^i	3.0055 (4)	K2—O1^ii	2.716 (6)
K1—O1^ii	3.0055 (4)	K2—O1^iii	3.435 (15)
K1—O1^iii	3.0055 (4)	K2—O1^iv	2.716 (6)
K1—O1^iv	3.0055 (4)	K2—O1^v	3.435 (15)
K1—O1^v	3.0055 (4)	K2—O1^vi	2.716 (6)
K1—O1^vi	3.0055 (4)	K2—O1^vii	3.435 (15)
K1—O1^vii	3.0055 (4)	Ti1—O1	2.0216 (4)
K1—O2^viii	3.4205 (5)	Ti1—O1^xii	1.9714 (3)
K1—O2^ix	3.4205 (5)	Ti1—O1^ix	1.9714 (3)
K1—O2^x	3.4205 (5)	Ti1—O2	1.9253 (4)
K1—O2^xi	3.4205 (5)	Ti1—O2^xiii	1.9761 (3)
K2—O1	2.716 (6)	Ti1—O2^x	1.9761 (3)
O1—K1—O1^i	59.296 (6)	O2^viii—K1—O2^x	90
O1—K1—O1^ii	120.704 (6)	O2^viii—K1—O2^xi	90
O1—K1—O1^iii	180	O2^ix—K1—O2^viii	180
O1—K1—O1^iv	75.836 (11)	O2^ix—K1—O2^x	90
O1—K1—O1^v	104.164 (11)	O2^ix—K1—O2^xi	90
O1—K1—O1^vi	75.836 (11)	O2^x—K1—O2^viii	90
O1—K1—O1^vii	104.164 (11)	O2^x—K1—O2^ix	90
O1—K1—O2^viii	128.653 (9)	O2^x—K1—O2^xi	180
O1—K1—O2^ix	51.347 (9)	O2^xi—K1—O2^viii	90
O1—K1—O2^x	52.822 (9)	O2^xi—K1—O2^ix	90
O1—K1—O2^xi	127.178 (9)	O2^xi—K1—O2^x	180
O1^i—K1—O1	59.296 (6)	O1—K2—O1^i	56.37 (18)
O1^i—K1—O1^ii	180	O1—K2—O1^ii	148.3 (9)
O1^i—K1—O1^iii	120.704 (6)	O1—K2—O1^iii	155.4 (8)
O1^i—K1—O1^iv	104.164 (11)	O1—K2—O1^iv	85.7 (2)
O1^i—K1—O1^v	75.836 (11)	O1—K2—O1^v	100.2 (2)
O1^i—K1—O1^vi	104.164 (11)	O1—K2—O1^vi	85.7 (2)
O1^i—K1—O1^vii	75.836 (11)	O1—K2—O1^vii	100.2 (2)
O1^i—K1—O2^viii	128.653 (9)	O1^i—K2—O1	56.37 (18)
O1^i—K1—O2^ix	51.347 (9)	O1^i—K2—O1^ii	155.4 (8)
O1^i—K1—O2^x	52.822 (9)	O1^i—K2—O1^iii	99.0 (6)
O1^i—K1—O2^xi	127.178 (9)	O1^i—K2—O1^iv	100.2 (2)
O1^ii—K1—O1	120.704 (6)	O1^i—K2—O1^v	65.1 (3)
O1^ii—K1—O1^i	180	O1^i—K2—O1^vi	100.2 (2)
O1^ii—K1—O1^iii	59.296 (6)	O1^i—K2—O1^vii	65.1 (3)
O1^ii—K1—O1^iv	75.836 (11)	O1^ii—K2—O1	148.3 (9)
O1^ii—K1—O1^v	104.164 (11)	O1^ii—K2—O1^i	155.4 (8)
O1^ii—K1—O1^vi	75.836 (11)	O1^ii—K2—O1^iii	56.37 (18)
O1^ii—K1—O1^vii	104.164 (11)	O1^ii—K2—O1^iv	85.7 (2)
O1^ii—K1—O2^viii	51.347 (9)	O1^ii—K2—O1^v	100.2 (2)
O1^ii—K1—O2^ix	128.653 (9)	O1^ii—K2—O1^vi	85.7 (2)
O1^ii—K1—O2^x	127.178 (9)	O1^ii—K2—O1^vii	100.2 (2)
O1^ii—K1—O2^xi	52.822 (9)	O1^iii—K2—O1	155.4 (8)
O1^iii—K1—O1	180	O1^iii—K2—O1^i	99.0 (6)
O1^iii—K1—O1^i	120.704 (6)	O1^iii—K2—O1^ii	56.37 (18)
O1^iii—K1—O1^ii	59.296 (6)	O1^iii—K2—O1^iv	100.2 (2)
O1^iii—K1—O1^iv	104.164 (11)	O1^iii—K2—O1^v	65.1 (3)
O1^iii—K1—O1^v	75.836 (11)	O1^iii—K2—O1^vi	100.2 (2)
O1^iii—K1—O1^vi	104.164 (11)	O1^iii—K2—O1^vii	65.1 (3)
O1^iii—K1—O1^vii	75.836 (11)	O1^iv—K2—O1	85.7 (2)
O1^iii—K1—O2^viii	51.347 (9)	O1^iv—K2—O1^i	100.2 (2)
O1^iii—K1—O2^ix	128.653 (9)	O1^iv—K2—O1^ii	85.7 (2)
O1^iii—K1—O2^x	127.178 (9)	O1^iv—K2—O1^iii	100.2 (2)
O1^iii—K1—O2^xi	52.822 (9)	O1^iv—K2—O1^v	56.37 (18)
O1^iv—K1—O1	75.836 (11)	O1^iv—K2—O1^vi	148.3 (9)
O1^iv—K1—O1^i	104.164 (11)	O1^iv—K2—O1^vii	155.4 (8)
O1^iv—K1—O1^ii	75.836 (11)	O1^v—K2—O1	100.2 (2)
O1^iv—K1—O1^iii	104.164 (11)	O1^v—K2—O1^i	65.1 (3)
O1^iv—K1—O1^v	59.296 (6)	O1^v—K2—O1^ii	100.2 (2)
O1^iv—K1—O1^vi	120.704 (6)	O1^v—K2—O1^iii	65.1 (3)
O1^iv—K1—O1^vii	180	O1^v—K2—O1^iv	56.37 (18)
O1^iv—K1—O2^viii	127.178 (9)	O1^v—K2—O1^vi	155.4 (8)
O1^iv—K1—O2^ix	52.822 (9)	O1^v—K2—O1^vii	99.0 (6)
O1^iv—K1—O2^x	128.653 (9)	O1^vi—K2—O1	85.7 (2)
O1^iv—K1—O2^xi	51.347 (9)	O1^vi—K2—O1^i	100.2 (2)
O1^v—K1—O1	104.164 (11)	O1^vi—K2—O1^ii	85.7 (2)
O1^v—K1—O1^i	75.836 (11)	O1^vi—K2—O1^iii	100.2 (2)
O1^v—K1—O1^ii	104.164 (11)	O1^vi—K2—O1^iv	148.3 (9)
O1^v—K1—O1^iii	75.836 (11)	O1^vi—K2—O1^v	155.4 (8)
O1^v—K1—O1^iv	59.296 (6)	O1^vi—K2—O1^vii	56.37 (18)
O1^v—K1—O1^vi	180	O1^vii—K2—O1	100.2 (2)
O1^v—K1—O1^vii	120.704 (6)	O1^vii—K2—O1^i	65.1 (3)
O1^v—K1—O2^viii	127.178 (9)	O1^vii—K2—O1^ii	100.2 (2)
O1^v—K1—O2^ix	52.822 (9)	O1^vii—K2—O1^iii	65.1 (3)
O1^v—K1—O2^x	128.653 (9)	O1^vii—K2—O1^iv	155.4 (8)
O1^v—K1—O2^xi	51.347 (9)	O1^vii—K2—O1^v	99.0 (6)
O1^vi—K1—O1	75.836 (11)	O1^vii—K2—O1^vi	56.37 (18)
O1^vi—K1—O1^i	104.164 (11)	O1—Ti1—O1^xii	81.093 (15)
O1^vi—K1—O1^ii	75.836 (11)	O1—Ti1—O1^ix	81.093 (15)
O1^vi—K1—O1^iii	104.164 (11)	O1—Ti1—O2	169.789 (19)
O1^vi—K1—O1^iv	120.704 (6)	O1—Ti1—O2^xiii	92.270 (16)
O1^vi—K1—O1^v	180	O1—Ti1—O2^x	92.270 (16)
O1^vi—K1—O1^vii	59.296 (6)	O1^xii—Ti1—O1	81.093 (15)
O1^vi—K1—O2^viii	52.822 (9)	O1^xii—Ti1—O1^ix	97.907 (14)
O1^vi—K1—O2^ix	127.178 (9)	O1^xii—Ti1—O2	92.249 (16)
O1^vi—K1—O2^x	51.347 (9)	O1^xii—Ti1—O2^xiii	81.855 (13)
O1^vi—K1—O2^xi	128.653 (9)	O1^xii—Ti1—O2^x	173.301 (19)
O1^vii—K1—O1	104.164 (11)	O1^ix—Ti1—O1	81.093 (15)
O1^vii—K1—O1^i	75.836 (11)	O1^ix—Ti1—O1^xii	97.907 (14)
O1^vii—K1—O1^ii	104.164 (11)	O1^ix—Ti1—O2	92.249 (16)
O1^vii—K1—O1^iii	75.836 (11)	O1^ix—Ti1—O2^xiii	173.301 (19)
O1^vii—K1—O1^iv	180	O1^ix—Ti1—O2^x	81.855 (13)
O1^vii—K1—O1^v	120.704 (6)	O2—Ti1—O2^xiii	94.450 (16)
O1^vii—K1—O1^vi	59.296 (6)	O2—Ti1—O2^x	94.450 (16)
O1^vii—K1—O2^viii	52.822 (9)	O2^xiii—Ti1—O2	94.450 (16)
O1^vii—K1—O2^ix	127.178 (9)	O2^xiii—Ti1—O2^x	97.593 (14)
O1^vii—K1—O2^x	51.347 (9)	O2^x—Ti1—O2	94.450 (16)
O1^vii—K1—O2^xi	128.653 (9)	O2^x—Ti1—O2^xiii	97.593 (14)
O2^viii—K1—O2^ix	180

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

(K-M22)

Crystal data

K1.53Mg0.77O16Ti7.23	Dx = 3.686 Mg m^−3
Mr = 680.7	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/m	Cell parameters from 24 reflections
Hall symbol: -I 4	θ = 20.1–24.1°
a = 10.1541 (11) Å	µ = 5.12 mm^−1
c = 2.9735 (14) Å	T = 298 K
V = 306.58 (15) Å^3	Prismatic, colorless
Z = 1	0.25 × 0.14 × 0.14 mm
F(000) = 325

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.027
Graphite monochromator	θmax = 50.0°, θmin = 2.8°
ω/2θ scans	h = −20→21
Absorption correction: analytical Tompa_analytical	k = −20→20
Tmin = 0.473, Tmax = 0.540	l = −5→0
2777 measured reflections	3 standard reflections every 200 reflections
835 independent reflections	intensity decay: 0.3%
785 reflections with I > 3σ(I)

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0001I^2)
R[F^2 > 2σ(F^2)] = 0.019	(Δ/σ)max = 0.045
wR(F^2) = 0.045	Δρmax = 0.95 e Å^−3
S = 2.05	Δρmin = −0.59 e Å^−3
835 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
26 parameters	Extinction coefficient: 0.0515 (11)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0	0	0.5	0.0445 (15)	0.297 (11)
K2	0	0	0.282 (3)	0.0415 (10)	0.234 (4)
Ti1	0.350895 (11)	0.167625 (12)	0	0.00769 (3)	0.9043 (5)
Mg1	0.350895	0.167625	0	0.00769 (3)	0.0957 (5)
O1	0.15533 (4)	0.20504 (5)	0	0.00687 (8)
O2	0.54050 (5)	0.16557 (5)	0	0.00823 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0328 (10)	0.0328 (10)	0.068 (4)	0	0	0
K2	0.0154 (4)	0.0154 (4)	0.094 (3)	0	0	0
Ti1	0.00798 (5)	0.00866 (5)	0.00642 (6)	0.00101 (3)	0	0
Mg1	0.00798 (5)	0.00866 (5)	0.00642 (6)	0.00101 (3)	0	0
O1	0.00674 (14)	0.00679 (14)	0.00707 (16)	−0.00011 (11)	0	0
O2	0.00573 (14)	0.01079 (16)	0.00818 (18)	0.00026 (11)	0	0

Geometric parameters (Å, º)

K1—O1	3.0054 (4)	K2—O1^iii	3.374 (5)
K1—O1^i	3.0054 (4)	K2—O1^iv	2.743 (2)
K1—O1^ii	3.0054 (4)	K2—O1^v	3.374 (5)
K1—O1^iii	3.0054 (4)	K2—O1^vi	2.743 (2)
K1—O1^iv	3.0054 (4)	K2—O1^vii	3.374 (5)
K1—O1^v	3.0054 (4)	Ti1—O1	2.0218 (5)
K1—O1^vi	3.0054 (4)	Ti1—O1^viii	1.9714 (3)
K1—O1^vii	3.0054 (4)	Ti1—O1^ix	1.9714 (3)
K2—O1	2.743 (2)	Ti1—O2	1.9254 (5)
K2—O1^i	3.374 (5)	Ti1—O2^x	1.9760 (3)
K2—O1^ii	2.743 (2)	Ti1—O2^xi	1.9760 (3)
O1—K1—O1^i	59.298 (6)	O1^i—K2—O1^v	66.37 (11)
O1—K1—O1^ii	120.702 (6)	O1^i—K2—O1^vi	101.14 (7)
O1—K1—O1^iii	180	O1^i—K2—O1^vii	66.37 (11)
O1—K1—O1^iv	75.835 (11)	O1^ii—K2—O1	144.5 (3)
O1—K1—O1^v	104.165 (11)	O1^ii—K2—O1^i	158.5 (2)
O1—K1—O1^vi	75.835 (11)	O1^ii—K2—O1^iii	57.05 (5)
O1—K1—O1^vii	104.165 (11)	O1^ii—K2—O1^iv	84.65 (9)
O1^i—K1—O1	59.298 (6)	O1^ii—K2—O1^v	101.14 (7)
O1^i—K1—O1^ii	180	O1^ii—K2—O1^vi	84.65 (9)
O1^i—K1—O1^iii	120.702 (6)	O1^ii—K2—O1^vii	101.14 (7)
O1^i—K1—O1^iv	104.165 (11)	O1^iii—K2—O1	158.5 (2)
O1^i—K1—O1^v	75.835 (11)	O1^iii—K2—O1^i	101.4 (2)
O1^i—K1—O1^vi	104.165 (11)	O1^iii—K2—O1^ii	57.05 (5)
O1^i—K1—O1^vii	75.835 (11)	O1^iii—K2—O1^iv	101.14 (7)
O1^ii—K1—O1	120.702 (6)	O1^iii—K2—O1^v	66.37 (11)
O1^ii—K1—O1^i	180	O1^iii—K2—O1^vi	101.14 (7)
O1^ii—K1—O1^iii	59.298 (6)	O1^iii—K2—O1^vii	66.37 (11)
O1^ii—K1—O1^iv	75.835 (11)	O1^iv—K2—O1	84.65 (9)
O1^ii—K1—O1^v	104.165 (11)	O1^iv—K2—O1^i	101.14 (7)
O1^ii—K1—O1^vi	75.835 (11)	O1^iv—K2—O1^ii	84.65 (9)
O1^ii—K1—O1^vii	104.165 (11)	O1^iv—K2—O1^iii	101.14 (7)
O1^iii—K1—O1	180	O1^iv—K2—O1^v	57.05 (5)
O1^iii—K1—O1^i	120.702 (6)	O1^iv—K2—O1^vi	144.5 (3)
O1^iii—K1—O1^ii	59.298 (6)	O1^iv—K2—O1^vii	158.5 (2)
O1^iii—K1—O1^iv	104.165 (11)	O1^v—K2—O1	101.14 (7)
O1^iii—K1—O1^v	75.835 (11)	O1^v—K2—O1^i	66.37 (11)
O1^iii—K1—O1^vi	104.165 (11)	O1^v—K2—O1^ii	101.14 (7)
O1^iii—K1—O1^vii	75.835 (11)	O1^v—K2—O1^iii	66.37 (11)
O1^iv—K1—O1	75.835 (11)	O1^v—K2—O1^iv	57.05 (5)
O1^iv—K1—O1^i	104.165 (11)	O1^v—K2—O1^vi	158.5 (2)
O1^iv—K1—O1^ii	75.835 (11)	O1^v—K2—O1^vii	101.4 (2)
O1^iv—K1—O1^iii	104.165 (11)	O1^vi—K2—O1	84.65 (9)
O1^iv—K1—O1^v	59.298 (6)	O1^vi—K2—O1^i	101.14 (7)
O1^iv—K1—O1^vi	120.702 (6)	O1^vi—K2—O1^ii	84.65 (9)
O1^iv—K1—O1^vii	180	O1^vi—K2—O1^iii	101.14 (7)
O1^v—K1—O1	104.165 (11)	O1^vi—K2—O1^iv	144.5 (3)
O1^v—K1—O1^i	75.835 (11)	O1^vi—K2—O1^v	158.5 (2)
O1^v—K1—O1^ii	104.165 (11)	O1^vi—K2—O1^vii	57.05 (5)
O1^v—K1—O1^iii	75.835 (11)	O1^vii—K2—O1	101.14 (7)
O1^v—K1—O1^iv	59.298 (6)	O1^vii—K2—O1^i	66.37 (11)
O1^v—K1—O1^vi	180	O1^vii—K2—O1^ii	101.14 (7)
O1^v—K1—O1^vii	120.702 (6)	O1^vii—K2—O1^iii	66.37 (11)
O1^vi—K1—O1	75.835 (11)	O1^vii—K2—O1^iv	158.5 (2)
O1^vi—K1—O1^i	104.165 (11)	O1^vii—K2—O1^v	101.4 (2)
O1^vi—K1—O1^ii	75.835 (11)	O1^vii—K2—O1^vi	57.05 (5)
O1^vi—K1—O1^iii	104.165 (11)	O1—Ti1—O1^viii	81.099 (16)
O1^vi—K1—O1^iv	120.702 (6)	O1—Ti1—O1^ix	81.099 (16)
O1^vi—K1—O1^v	180	O1—Ti1—O2	169.79 (2)
O1^vi—K1—O1^vii	59.298 (6)	O1—Ti1—O2^x	92.271 (17)
O1^vii—K1—O1	104.165 (11)	O1—Ti1—O2^xi	92.271 (17)
O1^vii—K1—O1^i	75.835 (11)	O1^viii—Ti1—O1	81.099 (16)
O1^vii—K1—O1^ii	104.165 (11)	O1^viii—Ti1—O1^ix	97.907 (15)
O1^vii—K1—O1^iii	75.835 (11)	O1^viii—Ti1—O2	92.243 (17)
O1^vii—K1—O1^iv	180	O1^viii—Ti1—O2^x	81.855 (14)
O1^vii—K1—O1^v	120.702 (6)	O1^viii—Ti1—O2^xi	173.31 (2)
O1^vii—K1—O1^vi	59.298 (6)	O1^ix—Ti1—O1	81.099 (16)
O1—K2—O1^i	57.05 (5)	O1^ix—Ti1—O1^viii	97.907 (15)
O1—K2—O1^ii	144.5 (3)	O1^ix—Ti1—O2	92.243 (17)
O1—K2—O1^iii	158.5 (2)	O1^ix—Ti1—O2^x	173.31 (2)
O1—K2—O1^iv	84.65 (9)	O1^ix—Ti1—O2^xi	81.855 (14)
O1—K2—O1^v	101.14 (7)	O2—Ti1—O2^x	94.449 (18)
O1—K2—O1^vi	84.65 (9)	O2—Ti1—O2^xi	94.449 (18)
O1—K2—O1^vii	101.14 (7)	O2^x—Ti1—O2	94.449 (18)
O1^i—K2—O1	57.05 (5)	O2^x—Ti1—O2^xi	97.596 (15)
O1^i—K2—O1^ii	158.5 (2)	O2^xi—Ti1—O2	94.449 (18)
O1^i—K2—O1^iii	101.4 (2)	O2^xi—Ti1—O2^x	97.596 (15)
O1^i—K2—O1^iv	101.14 (7)

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

(K-M23)

Crystal data

K1.54Mg0.77O16Ti7.23	Dx = 3.688 Mg m^−3
Mr = 681.1	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/m	Cell parameters from 24 reflections
Hall symbol: -I 4	θ = 20.1–24.1°
a = 10.1541 (11) Å	µ = 5.12 mm^−1
c = 2.9735 (14) Å	T = 298 K
V = 306.58 (15) Å^3	Prismatic, colorless
Z = 1	0.25 × 0.14 × 0.14 mm
F(000) = 326

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.027
Graphite monochromator	θmax = 50.0°, θmin = 2.8°
ω/2θ scans	h = −20→21
Absorption correction: analytical Tompa_analytical	k = −20→20
Tmin = 0.473, Tmax = 0.540	l = −5→0
2777 measured reflections	3 standard reflections every 200 reflections
835 independent reflections	intensity decay: 0.3%
785 reflections with I > 3σ(I)

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0001I^2)
R[F^2 > 2σ(F^2)] = 0.018	(Δ/σ)max = 0.039
wR(F^2) = 0.042	Δρmax = 0.68 e Å^−3
S = 1.93	Δρmin = −0.58 e Å^−3
835 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
28 parameters	Extinction coefficient: 0.0515 (10)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0	0	0.5	0.0363 (14)	0.310 (13)
K2	0	0	0.266 (4)	0.0371 (7)	0.230 (4)
Ti1	0.350896 (10)	0.167626 (11)	0	0.00768 (3)	0.9038 (5)
Mg1	0.350896	0.167626	0	0.00768 (3)	0.0962 (5)
O1	0.15535 (4)	0.20504 (4)	0	0.00686 (8)
O2	0.54050 (4)	0.16558 (5)	0	0.00827 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0292 (8)	0.0292 (8)	0.051 (4)	0	0	0
K2	0.0164 (4)	0.0164 (4)	0.079 (2)	0	0	0
Ti1	0.00798 (5)	0.00865 (5)	0.00642 (6)	0.00101 (2)	0	0
Mg1	0.00798 (5)	0.00865 (5)	0.00642 (6)	0.00101 (2)	0	0
O1	0.00671 (13)	0.00676 (13)	0.00709 (15)	−0.00007 (10)	0	0
O2	0.00577 (13)	0.01073 (15)	0.00829 (17)	0.00021 (10)	0	0

Geometric parameters (Å, º)

K1—O1	3.0055 (4)	K2—O1^iii	3.404 (7)
K1—O1^i	3.0055 (4)	K2—O1^iv	2.729 (3)
K1—O1^ii	3.0055 (4)	K2—O1^v	3.404 (7)
K1—O1^iii	3.0055 (4)	K2—O1^vi	2.729 (3)
K1—O1^iv	3.0055 (4)	K2—O1^vii	3.404 (7)
K1—O1^v	3.0055 (4)	Ti1—O1	2.0216 (4)
K1—O1^vi	3.0055 (4)	Ti1—O1^viii	1.9714 (3)
K1—O1^vii	3.0055 (4)	Ti1—O1^ix	1.9714 (3)
K2—O1	2.729 (3)	Ti1—O2	1.9253 (4)
K2—O1^i	3.404 (7)	Ti1—O2^x	1.9761 (3)
K2—O1^ii	2.729 (3)	Ti1—O2^xi	1.9761 (3)
O1—K1—O1^i	59.296 (6)	O1^i—K2—O1^v	65.73 (15)
O1—K1—O1^ii	120.704 (6)	O1^i—K2—O1^vi	100.71 (10)
O1—K1—O1^iii	180	O1^i—K2—O1^vii	65.73 (15)
O1—K1—O1^iv	75.836 (11)	O1^ii—K2—O1	146.3 (4)
O1—K1—O1^v	104.164 (11)	O1^ii—K2—O1^i	157.0 (3)
O1—K1—O1^vi	75.836 (11)	O1^ii—K2—O1^iii	56.73 (7)
O1—K1—O1^vii	104.164 (11)	O1^ii—K2—O1^iv	85.18 (12)
O1^i—K1—O1	59.296 (6)	O1^ii—K2—O1^v	100.71 (10)
O1^i—K1—O1^ii	180	O1^ii—K2—O1^vi	85.18 (12)
O1^i—K1—O1^iii	120.704 (6)	O1^ii—K2—O1^vii	100.71 (10)
O1^i—K1—O1^iv	104.164 (11)	O1^iii—K2—O1	157.0 (3)
O1^i—K1—O1^v	75.836 (11)	O1^iii—K2—O1^i	100.2 (3)
O1^i—K1—O1^vi	104.164 (11)	O1^iii—K2—O1^ii	56.73 (7)
O1^i—K1—O1^vii	75.836 (11)	O1^iii—K2—O1^iv	100.71 (10)
O1^ii—K1—O1	120.704 (6)	O1^iii—K2—O1^v	65.73 (15)
O1^ii—K1—O1^i	180	O1^iii—K2—O1^vi	100.71 (10)
O1^ii—K1—O1^iii	59.296 (6)	O1^iii—K2—O1^vii	65.73 (15)
O1^ii—K1—O1^iv	75.836 (11)	O1^iv—K2—O1	85.18 (12)
O1^ii—K1—O1^v	104.164 (11)	O1^iv—K2—O1^i	100.71 (10)
O1^ii—K1—O1^vi	75.836 (11)	O1^iv—K2—O1^ii	85.18 (12)
O1^ii—K1—O1^vii	104.164 (11)	O1^iv—K2—O1^iii	100.71 (10)
O1^iii—K1—O1	180	O1^iv—K2—O1^v	56.73 (7)
O1^iii—K1—O1^i	120.704 (6)	O1^iv—K2—O1^vi	146.3 (4)
O1^iii—K1—O1^ii	59.296 (6)	O1^iv—K2—O1^vii	157.0 (3)
O1^iii—K1—O1^iv	104.164 (11)	O1^v—K2—O1	100.71 (10)
O1^iii—K1—O1^v	75.836 (11)	O1^v—K2—O1^i	65.73 (15)
O1^iii—K1—O1^vi	104.164 (11)	O1^v—K2—O1^ii	100.71 (10)
O1^iii—K1—O1^vii	75.836 (11)	O1^v—K2—O1^iii	65.73 (15)
O1^iv—K1—O1	75.836 (11)	O1^v—K2—O1^iv	56.73 (7)
O1^iv—K1—O1^i	104.164 (11)	O1^v—K2—O1^vi	157.0 (3)
O1^iv—K1—O1^ii	75.836 (11)	O1^v—K2—O1^vii	100.2 (3)
O1^iv—K1—O1^iii	104.164 (11)	O1^vi—K2—O1	85.18 (12)
O1^iv—K1—O1^v	59.296 (6)	O1^vi—K2—O1^i	100.71 (10)
O1^iv—K1—O1^vi	120.704 (6)	O1^vi—K2—O1^ii	85.18 (12)
O1^iv—K1—O1^vii	180	O1^vi—K2—O1^iii	100.71 (10)
O1^v—K1—O1	104.164 (11)	O1^vi—K2—O1^iv	146.3 (4)
O1^v—K1—O1^i	75.836 (11)	O1^vi—K2—O1^v	157.0 (3)
O1^v—K1—O1^ii	104.164 (11)	O1^vi—K2—O1^vii	56.73 (7)
O1^v—K1—O1^iii	75.836 (11)	O1^vii—K2—O1	100.71 (10)
O1^v—K1—O1^iv	59.296 (6)	O1^vii—K2—O1^i	65.73 (15)
O1^v—K1—O1^vi	180	O1^vii—K2—O1^ii	100.71 (10)
O1^v—K1—O1^vii	120.704 (6)	O1^vii—K2—O1^iii	65.73 (15)
O1^vi—K1—O1	75.836 (11)	O1^vii—K2—O1^iv	157.0 (3)
O1^vi—K1—O1^i	104.164 (11)	O1^vii—K2—O1^v	100.2 (3)
O1^vi—K1—O1^ii	75.836 (11)	O1^vii—K2—O1^vi	56.73 (7)
O1^vi—K1—O1^iii	104.164 (11)	O1—Ti1—O1^viii	81.093 (15)
O1^vi—K1—O1^iv	120.704 (6)	O1—Ti1—O1^ix	81.093 (15)
O1^vi—K1—O1^v	180	O1—Ti1—O2	169.79 (2)
O1^vi—K1—O1^vii	59.296 (6)	O1—Ti1—O2^x	92.269 (16)
O1^vii—K1—O1	104.164 (11)	O1—Ti1—O2^xi	92.269 (16)
O1^vii—K1—O1^i	75.836 (11)	O1^viii—Ti1—O1	81.093 (15)
O1^vii—K1—O1^ii	104.164 (11)	O1^viii—Ti1—O1^ix	97.907 (14)
O1^vii—K1—O1^iii	75.836 (11)	O1^viii—Ti1—O2	92.248 (16)
O1^vii—K1—O1^iv	180	O1^viii—Ti1—O2^x	81.855 (13)
O1^vii—K1—O1^v	120.704 (6)	O1^viii—Ti1—O2^xi	173.300 (19)
O1^vii—K1—O1^vi	59.296 (6)	O1^ix—Ti1—O1	81.093 (15)
O1—K2—O1^i	56.73 (7)	O1^ix—Ti1—O1^viii	97.907 (14)
O1—K2—O1^ii	146.3 (4)	O1^ix—Ti1—O2	92.248 (16)
O1—K2—O1^iii	157.0 (3)	O1^ix—Ti1—O2^x	173.300 (19)
O1—K2—O1^iv	85.18 (12)	O1^ix—Ti1—O2^xi	81.855 (13)
O1—K2—O1^v	100.71 (10)	O2—Ti1—O2^x	94.452 (17)
O1—K2—O1^vi	85.18 (12)	O2—Ti1—O2^xi	94.452 (17)
O1—K2—O1^vii	100.71 (10)	O2^x—Ti1—O2	94.452 (17)
O1^i—K2—O1	56.73 (7)	O2^x—Ti1—O2^xi	97.594 (14)
O1^i—K2—O1^ii	157.0 (3)	O2^xi—Ti1—O2	94.452 (17)
O1^i—K2—O1^iii	100.2 (3)	O2^xi—Ti1—O2^x	97.594 (14)
O1^i—K2—O1^iv	100.71 (10)

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

(Rb-C22)

Crystal data

Mg0.75O16Rb1.51Ti7.25	Dx = 4.024 Mg m^−3
Mr = 750.1	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/m	Cell parameters from 25 reflections
Hall symbol: -I 4	θ = 20.1–24.0°
a = 10.2052 (7) Å	µ = 10.46 mm^−1
c = 2.9717 (6) Å	T = 298 K
V = 309.49 (7) Å^3	Prismatic, colorless
Z = 1	0.15 × 0.05 × 0.05 mm
F(000) = 352

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.069
Graphite monochromator	θmax = 49.9°, θmin = 2.8°
ω/2θ scans	h = −21→21
Absorption correction: analytical Tompa_analytical	k = −21→21
Tmin = 0.418, Tmax = 0.637	l = 0→6
3639 measured reflections	3 standard reflections every 200 reflections
912 independent reflections	intensity decay: 4.7%
623 reflections with I > 3σ(I)

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0001I^2)
R[F^2 > 2σ(F^2)] = 0.022	(Δ/σ)max = 0.022
wR(F^2) = 0.051	Δρmax = 0.84 e Å^−3
S = 1.18	Δρmin = −0.66 e Å^−3
912 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
27 parameters	Extinction coefficient: 0.0490 (11)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Rb1	0	0	0.5	0.074 (2)	0.592 (10)
Rb2	0	0	0.3020 (12)	0.0089 (8)	0.081 (5)
Ti1	0.34990 (2)	0.16657 (2)	0	0.00742 (5)	0.9057 (3)
Mg1	0.349898	0.166572	0	0.00742 (5)	0.0943 (3)
O1	0.15622 (9)	0.20689 (9)	0	0.00665 (18)
O2	0.53972 (9)	0.16623 (10)	0	0.00819 (19)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0164 (3)	0.0164 (3)	0.188 (6)	0	0	0
Rb2	0.0071 (8)	0.0071 (8)	0.012 (2)	0	0	0
Ti1	0.00775 (9)	0.00868 (9)	0.00584 (7)	0.00091 (7)	0	0
Mg1	0.00775 (9)	0.00868 (9)	0.00584 (7)	0.00091 (7)	0	0
O1	0.0066 (3)	0.0068 (3)	0.0065 (3)	−0.0001 (2)	0	0
O2	0.0057 (3)	0.0106 (3)	0.0083 (3)	0.0002 (2)	0	0

Geometric parameters (Å, º)

Rb1—O1	3.0344 (8)	Rb2—O1^iii	3.362 (2)
Rb1—O1^i	3.0344 (8)	Rb2—O1^iv	2.7937 (15)
Rb1—O1^ii	3.0344 (8)	Rb2—O1^v	3.362 (2)
Rb1—O1^iii	3.0344 (8)	Rb2—O1^vi	2.7937 (15)
Rb1—O1^iv	3.0344 (8)	Rb2—O1^vii	3.362 (2)
Rb1—O1^v	3.0344 (8)	Ti1—O1	2.0188 (9)
Rb1—O1^vi	3.0344 (8)	Ti1—O1^viii	1.9696 (6)
Rb1—O1^vii	3.0344 (8)	Ti1—O1^ix	1.9696 (6)
Rb2—O1	2.7937 (15)	Ti1—O2	1.9371 (9)
Rb2—O1^i	3.362 (2)	Ti1—O2^x	1.9776 (6)
Rb2—O1^ii	2.7937 (15)	Ti1—O2^xi	1.9776 (6)
O1—Rb1—O1^i	58.639 (12)	O1^i—Rb2—O1^v	67.62 (6)
O1—Rb1—O1^ii	121.361 (12)	O1^i—Rb2—O1^vi	101.43 (4)
O1—Rb1—O1^iii	180	O1^i—Rb2—O1^vii	67.62 (6)
O1—Rb1—O1^iv	76.13 (2)	O1^ii—Rb2—O1	142.53 (14)
O1—Rb1—O1^v	103.87 (2)	O1^ii—Rb2—O1^i	160.64 (12)
O1—Rb1—O1^vi	76.13 (2)	O1^ii—Rb2—O1^iii	56.83 (2)
O1—Rb1—O1^vii	103.87 (2)	O1^ii—Rb2—O1^iv	84.08 (5)
O1^i—Rb1—O1	58.639 (12)	O1^ii—Rb2—O1^v	101.43 (4)
O1^i—Rb1—O1^ii	180	O1^ii—Rb2—O1^vi	84.08 (5)
O1^i—Rb1—O1^iii	121.361 (12)	O1^ii—Rb2—O1^vii	101.43 (4)
O1^i—Rb1—O1^iv	103.87 (2)	O1^iii—Rb2—O1	160.64 (12)
O1^i—Rb1—O1^v	76.13 (2)	O1^iii—Rb2—O1^i	103.80 (10)
O1^i—Rb1—O1^vi	103.87 (2)	O1^iii—Rb2—O1^ii	56.83 (2)
O1^i—Rb1—O1^vii	76.13 (2)	O1^iii—Rb2—O1^iv	101.43 (4)
O1^ii—Rb1—O1	121.361 (12)	O1^iii—Rb2—O1^v	67.62 (6)
O1^ii—Rb1—O1^i	180	O1^iii—Rb2—O1^vi	101.43 (4)
O1^ii—Rb1—O1^iii	58.639 (12)	O1^iii—Rb2—O1^vii	67.62 (6)
O1^ii—Rb1—O1^iv	76.13 (2)	O1^iv—Rb2—O1	84.08 (5)
O1^ii—Rb1—O1^v	103.87 (2)	O1^iv—Rb2—O1^i	101.43 (4)
O1^ii—Rb1—O1^vi	76.13 (2)	O1^iv—Rb2—O1^ii	84.08 (5)
O1^ii—Rb1—O1^vii	103.87 (2)	O1^iv—Rb2—O1^iii	101.43 (4)
O1^iii—Rb1—O1	180	O1^iv—Rb2—O1^v	56.83 (2)
O1^iii—Rb1—O1^i	121.361 (12)	O1^iv—Rb2—O1^vi	142.53 (14)
O1^iii—Rb1—O1^ii	58.639 (12)	O1^iv—Rb2—O1^vii	160.64 (12)
O1^iii—Rb1—O1^iv	103.87 (2)	O1^v—Rb2—O1	101.43 (4)
O1^iii—Rb1—O1^v	76.13 (2)	O1^v—Rb2—O1^i	67.62 (6)
O1^iii—Rb1—O1^vi	103.87 (2)	O1^v—Rb2—O1^ii	101.43 (4)
O1^iii—Rb1—O1^vii	76.13 (2)	O1^v—Rb2—O1^iii	67.62 (6)
O1^iv—Rb1—O1	76.13 (2)	O1^v—Rb2—O1^iv	56.83 (2)
O1^iv—Rb1—O1^i	103.87 (2)	O1^v—Rb2—O1^vi	160.64 (12)
O1^iv—Rb1—O1^ii	76.13 (2)	O1^v—Rb2—O1^vii	103.80 (10)
O1^iv—Rb1—O1^iii	103.87 (2)	O1^vi—Rb2—O1	84.08 (5)
O1^iv—Rb1—O1^v	58.639 (12)	O1^vi—Rb2—O1^i	101.43 (4)
O1^iv—Rb1—O1^vi	121.361 (12)	O1^vi—Rb2—O1^ii	84.08 (5)
O1^iv—Rb1—O1^vii	180	O1^vi—Rb2—O1^iii	101.43 (4)
O1^v—Rb1—O1	103.87 (2)	O1^vi—Rb2—O1^iv	142.53 (14)
O1^v—Rb1—O1^i	76.13 (2)	O1^vi—Rb2—O1^v	160.64 (12)
O1^v—Rb1—O1^ii	103.87 (2)	O1^vi—Rb2—O1^vii	56.83 (2)
O1^v—Rb1—O1^iii	76.13 (2)	O1^vii—Rb2—O1	101.43 (4)
O1^v—Rb1—O1^iv	58.639 (12)	O1^vii—Rb2—O1^i	67.62 (6)
O1^v—Rb1—O1^vi	180	O1^vii—Rb2—O1^ii	101.43 (4)
O1^v—Rb1—O1^vii	121.361 (12)	O1^vii—Rb2—O1^iii	67.62 (6)
O1^vi—Rb1—O1	76.13 (2)	O1^vii—Rb2—O1^iv	160.64 (12)
O1^vi—Rb1—O1^i	103.87 (2)	O1^vii—Rb2—O1^v	103.80 (10)
O1^vi—Rb1—O1^ii	76.13 (2)	O1^vii—Rb2—O1^vi	56.83 (2)
O1^vi—Rb1—O1^iii	103.87 (2)	O1—Ti1—O1^viii	80.52 (3)
O1^vi—Rb1—O1^iv	121.361 (12)	O1—Ti1—O1^ix	80.52 (3)
O1^vi—Rb1—O1^v	180	O1—Ti1—O2	168.34 (4)
O1^vi—Rb1—O1^vii	58.639 (12)	O1—Ti1—O2^x	92.98 (3)
O1^vii—Rb1—O1	103.87 (2)	O1—Ti1—O2^xi	92.98 (3)
O1^vii—Rb1—O1^i	76.13 (2)	O1^viii—Ti1—O1	80.52 (3)
O1^vii—Rb1—O1^ii	103.87 (2)	O1^viii—Ti1—O1^ix	97.95 (3)
O1^vii—Rb1—O1^iii	76.13 (2)	O1^viii—Ti1—O2	91.89 (3)
O1^vii—Rb1—O1^iv	180	O1^viii—Ti1—O2^x	81.94 (3)
O1^vii—Rb1—O1^v	121.361 (12)	O1^viii—Ti1—O2^xi	173.41 (4)
O1^vii—Rb1—O1^vi	58.639 (12)	O1^ix—Ti1—O1	80.52 (3)
O1—Rb2—O1^i	56.83 (2)	O1^ix—Ti1—O1^viii	97.95 (3)
O1—Rb2—O1^ii	142.53 (14)	O1^ix—Ti1—O2	91.89 (3)
O1—Rb2—O1^iii	160.64 (12)	O1^ix—Ti1—O2^x	173.41 (4)
O1—Rb2—O1^iv	84.08 (5)	O1^ix—Ti1—O2^xi	81.94 (3)
O1—Rb2—O1^v	101.43 (4)	O2—Ti1—O2^x	94.71 (3)
O1—Rb2—O1^vi	84.08 (5)	O2—Ti1—O2^xi	94.71 (3)
O1—Rb2—O1^vii	101.43 (4)	O2^x—Ti1—O2	94.71 (3)
O1^i—Rb2—O1	56.83 (2)	O2^x—Ti1—O2^xi	97.42 (3)
O1^i—Rb2—O1^ii	160.64 (12)	O2^xi—Ti1—O2	94.71 (3)
O1^i—Rb2—O1^iii	103.80 (10)	O2^xi—Ti1—O2^x	97.42 (3)
O1^i—Rb2—O1^iv	101.43 (4)

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

(Rb-C23)

Crystal data

Mg0.75O16Rb1.51Ti7.25	Dx = 4.024 Mg m^−3
Mr = 750.1	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/m	Cell parameters from 25 reflections
Hall symbol: -I 4	θ = 20.1–24.0°
a = 10.2052 (7) Å	µ = 10.46 mm^−1
c = 2.9717 (6) Å	T = 298 K
V = 309.49 (7) Å^3	Prismatic, colorless
Z = 1	0.15 × 0.05 × 0.05 mm
F(000) = 352

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.069
Graphite monochromator	θmax = 49.9°, θmin = 2.8°
ω/2θ scans	h = −21→21
Absorption correction: analytical Tompa_analytical	k = −21→21
Tmin = 0.418, Tmax = 0.637	l = 0→6
3639 measured reflections	3 standard reflections every 200 reflections
912 independent reflections	intensity decay: 4.7%
623 reflections with I > 3σ(I)

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0001I^2)
R[F^2 > 2σ(F^2)] = 0.022	(Δ/σ)max = 0.041
wR(F^2) = 0.050	Δρmax = 0.88 e Å^−3
S = 1.19	Δρmin = −0.66 e Å^−3
912 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
29 parameters	Extinction coefficient: 0.0490 (11)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Rb1	0	0	0.5	0.072 (3)	0.588 (13)
Rb2	0	0	0.299 (4)	0.0091 (9)	0.083 (7)
Ti1	0.34990 (2)	0.16657 (2)	0	0.00742 (5)	0.9057 (3)
Mg1	0.349899	0.166573	0	0.00742 (5)	0.0943 (3)
O1	0.15623 (9)	0.20688 (9)	0	0.00665 (18)
O2	0.53972 (9)	0.16623 (10)	0	0.00820 (19)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0165 (4)	0.0165 (4)	0.182 (10)	0	0	0
Rb2	0.0072 (9)	0.0072 (9)	0.013 (2)	0	0	0
Ti1	0.00774 (9)	0.00868 (9)	0.00584 (7)	0.00091 (7)	0	0
Mg1	0.00774 (9)	0.00868 (9)	0.00584 (7)	0.00091 (7)	0	0
O1	0.0066 (3)	0.0068 (3)	0.0065 (3)	−0.0001 (2)	0	0
O2	0.0057 (3)	0.0106 (3)	0.0083 (3)	0.0002 (2)	0	0

Geometric parameters (Å, º)

Rb1—O1	3.0343 (8)	Rb2—O1^iii	3.368 (7)
Rb1—O1^i	3.0343 (8)	Rb2—O1^iv	2.790 (4)
Rb1—O1^ii	3.0343 (8)	Rb2—O1^v	3.368 (7)
Rb1—O1^iii	3.0343 (8)	Rb2—O1^vi	2.790 (4)
Rb1—O1^iv	3.0343 (8)	Rb2—O1^vii	3.368 (7)
Rb1—O1^v	3.0343 (8)	Ti1—O1	2.0188 (9)
Rb1—O1^vi	3.0343 (8)	Ti1—O1^viii	1.9696 (6)
Rb1—O1^vii	3.0343 (8)	Ti1—O1^ix	1.9696 (6)
Rb2—O1	2.790 (4)	Ti1—O2	1.9372 (9)
Rb2—O1^i	3.368 (7)	Ti1—O2^x	1.9776 (6)
Rb2—O1^ii	2.790 (4)	Ti1—O2^xi	1.9776 (6)
O1—Rb1—O1^i	58.639 (12)	O1^i—Rb2—O1^v	67.48 (17)
O1—Rb1—O1^ii	121.361 (12)	O1^i—Rb2—O1^vi	101.35 (10)
O1—Rb1—O1^iii	180	O1^i—Rb2—O1^vii	67.48 (17)
O1—Rb1—O1^iv	76.13 (2)	O1^ii—Rb2—O1	142.9 (5)
O1—Rb1—O1^v	103.87 (2)	O1^ii—Rb2—O1^i	160.3 (4)
O1—Rb1—O1^vi	76.13 (2)	O1^ii—Rb2—O1^iii	56.77 (7)
O1—Rb1—O1^vii	103.87 (2)	O1^ii—Rb2—O1^iv	84.20 (14)
O1^i—Rb1—O1	58.639 (12)	O1^ii—Rb2—O1^v	101.35 (10)
O1^i—Rb1—O1^ii	180	O1^ii—Rb2—O1^vi	84.20 (14)
O1^i—Rb1—O1^iii	121.361 (12)	O1^ii—Rb2—O1^vii	101.35 (10)
O1^i—Rb1—O1^iv	103.87 (2)	O1^iii—Rb2—O1	160.3 (4)
O1^i—Rb1—O1^v	76.13 (2)	O1^iii—Rb2—O1^i	103.5 (3)
O1^i—Rb1—O1^vi	103.87 (2)	O1^iii—Rb2—O1^ii	56.77 (7)
O1^i—Rb1—O1^vii	76.13 (2)	O1^iii—Rb2—O1^iv	101.35 (10)
O1^ii—Rb1—O1	121.361 (12)	O1^iii—Rb2—O1^v	67.48 (17)
O1^ii—Rb1—O1^i	180	O1^iii—Rb2—O1^vi	101.35 (10)
O1^ii—Rb1—O1^iii	58.639 (12)	O1^iii—Rb2—O1^vii	67.48 (17)
O1^ii—Rb1—O1^iv	76.13 (2)	O1^iv—Rb2—O1	84.20 (14)
O1^ii—Rb1—O1^v	103.87 (2)	O1^iv—Rb2—O1^i	101.35 (10)
O1^ii—Rb1—O1^vi	76.13 (2)	O1^iv—Rb2—O1^ii	84.20 (14)
O1^ii—Rb1—O1^vii	103.87 (2)	O1^iv—Rb2—O1^iii	101.35 (10)
O1^iii—Rb1—O1	180	O1^iv—Rb2—O1^v	56.77 (7)
O1^iii—Rb1—O1^i	121.361 (12)	O1^iv—Rb2—O1^vi	142.9 (5)
O1^iii—Rb1—O1^ii	58.639 (12)	O1^iv—Rb2—O1^vii	160.3 (4)
O1^iii—Rb1—O1^iv	103.87 (2)	O1^v—Rb2—O1	101.35 (10)
O1^iii—Rb1—O1^v	76.13 (2)	O1^v—Rb2—O1^i	67.48 (17)
O1^iii—Rb1—O1^vi	103.87 (2)	O1^v—Rb2—O1^ii	101.35 (10)
O1^iii—Rb1—O1^vii	76.13 (2)	O1^v—Rb2—O1^iii	67.48 (17)
O1^iv—Rb1—O1	76.13 (2)	O1^v—Rb2—O1^iv	56.77 (7)
O1^iv—Rb1—O1^i	103.87 (2)	O1^v—Rb2—O1^vi	160.3 (4)
O1^iv—Rb1—O1^ii	76.13 (2)	O1^v—Rb2—O1^vii	103.5 (3)
O1^iv—Rb1—O1^iii	103.87 (2)	O1^vi—Rb2—O1	84.20 (14)
O1^iv—Rb1—O1^v	58.639 (12)	O1^vi—Rb2—O1^i	101.35 (10)
O1^iv—Rb1—O1^vi	121.361 (12)	O1^vi—Rb2—O1^ii	84.20 (14)
O1^iv—Rb1—O1^vii	180	O1^vi—Rb2—O1^iii	101.35 (10)
O1^v—Rb1—O1	103.87 (2)	O1^vi—Rb2—O1^iv	142.9 (5)
O1^v—Rb1—O1^i	76.13 (2)	O1^vi—Rb2—O1^v	160.3 (4)
O1^v—Rb1—O1^ii	103.87 (2)	O1^vi—Rb2—O1^vii	56.77 (7)
O1^v—Rb1—O1^iii	76.13 (2)	O1^vii—Rb2—O1	101.35 (10)
O1^v—Rb1—O1^iv	58.639 (12)	O1^vii—Rb2—O1^i	67.48 (17)
O1^v—Rb1—O1^vi	180	O1^vii—Rb2—O1^ii	101.35 (10)
O1^v—Rb1—O1^vii	121.361 (12)	O1^vii—Rb2—O1^iii	67.48 (17)
O1^vi—Rb1—O1	76.13 (2)	O1^vii—Rb2—O1^iv	160.3 (4)
O1^vi—Rb1—O1^i	103.87 (2)	O1^vii—Rb2—O1^v	103.5 (3)
O1^vi—Rb1—O1^ii	76.13 (2)	O1^vii—Rb2—O1^vi	56.77 (7)
O1^vi—Rb1—O1^iii	103.87 (2)	O1—Ti1—O1^viii	80.52 (3)
O1^vi—Rb1—O1^iv	121.361 (12)	O1—Ti1—O1^ix	80.52 (3)
O1^vi—Rb1—O1^v	180	O1—Ti1—O2	168.35 (4)
O1^vi—Rb1—O1^vii	58.639 (12)	O1—Ti1—O2^x	92.98 (3)
O1^vii—Rb1—O1	103.87 (2)	O1—Ti1—O2^xi	92.98 (3)
O1^vii—Rb1—O1^i	76.13 (2)	O1^viii—Ti1—O1	80.52 (3)
O1^vii—Rb1—O1^ii	103.87 (2)	O1^viii—Ti1—O1^ix	97.94 (3)
O1^vii—Rb1—O1^iii	76.13 (2)	O1^viii—Ti1—O2	91.89 (3)
O1^vii—Rb1—O1^iv	180	O1^viii—Ti1—O2^x	81.94 (3)
O1^vii—Rb1—O1^v	121.361 (12)	O1^viii—Ti1—O2^xi	173.41 (4)
O1^vii—Rb1—O1^vi	58.639 (12)	O1^ix—Ti1—O1	80.52 (3)
O1—Rb2—O1^i	56.77 (7)	O1^ix—Ti1—O1^viii	97.94 (3)
O1—Rb2—O1^ii	142.9 (5)	O1^ix—Ti1—O2	91.89 (3)
O1—Rb2—O1^iii	160.3 (4)	O1^ix—Ti1—O2^x	173.41 (4)
O1—Rb2—O1^iv	84.20 (14)	O1^ix—Ti1—O2^xi	81.94 (3)
O1—Rb2—O1^v	101.35 (10)	O2—Ti1—O2^x	94.70 (3)
O1—Rb2—O1^vi	84.20 (14)	O2—Ti1—O2^xi	94.70 (3)
O1—Rb2—O1^vii	101.35 (10)	O2^x—Ti1—O2	94.70 (3)
O1^i—Rb2—O1	56.77 (7)	O2^x—Ti1—O2^xi	97.42 (3)
O1^i—Rb2—O1^ii	160.3 (4)	O2^xi—Ti1—O2	94.70 (3)
O1^i—Rb2—O1^iii	103.5 (3)	O2^xi—Ti1—O2^x	97.42 (3)
O1^i—Rb2—O1^iv	101.35 (10)

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

(Rb-M22)

Crystal data

Mg0.75O16Rb1.50Ti7.25	Dx = 4.021 Mg m^−3
Mr = 749.6	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/m	Cell parameters from 25 reflections
Hall symbol: -I 4	θ = 20.1–24.0°
a = 10.2052 (7) Å	µ = 10.43 mm^−1
c = 2.9717 (6) Å	T = 298 K
V = 309.49 (7) Å^3	Prismatic, colorless
Z = 1	0.15 × 0.05 × 0.05 mm
F(000) = 352

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.069
Graphite monochromator	θmax = 49.9°, θmin = 2.8°
ω/2θ scans	h = −21→21
Absorption correction: analytical Tompa_analytical	k = −21→21
Tmin = 0.418, Tmax = 0.637	l = 0→6
3639 measured reflections	3 standard reflections every 200 reflections
912 independent reflections	intensity decay: 4.7%
623 reflections with I > 3σ(I)

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0001I^2)
R[F^2 > 2σ(F^2)] = 0.022	(Δ/σ)max = 0.048
wR(F^2) = 0.051	Δρmax = 1.10 e Å^−3
S = 1.20	Δρmin = −0.67 e Å^−3
912 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
26 parameters	Extinction coefficient: 0.0485 (11)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Rb1	0	0	0.5	0.0229 (7)	0.251 (6)
Rb2	0	0	0.3266 (11)	0.0218 (4)	0.250 (2)
Ti1	0.34990 (2)	0.16657 (2)	0	0.00739 (5)	0.9062 (3)
Mg1	0.349903	0.166575	0	0.00739 (5)	0.0938 (3)
O1	0.15623 (9)	0.20686 (9)	0	0.00663 (18)
O2	0.53975 (9)	0.16621 (10)	0	0.00818 (19)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0184 (6)	0.0184 (6)	0.032 (2)	0	0	0
Rb2	0.0120 (3)	0.0120 (3)	0.0412 (11)	0	0	0
Ti1	0.00773 (9)	0.00865 (9)	0.00581 (7)	0.00090 (7)	0	0
Mg1	0.00773 (9)	0.00865 (9)	0.00581 (7)	0.00090 (7)	0	0
O1	0.0066 (3)	0.0068 (3)	0.0065 (3)	−0.0001 (2)	0	0
O2	0.0056 (3)	0.0106 (3)	0.0083 (4)	0.0002 (2)	0	0

Geometric parameters (Å, º)

Rb1—O1	3.0342 (8)	Rb2—O1^iii	3.317 (2)
Rb1—O1^i	3.0342 (8)	Rb2—O1^iv	2.8180 (14)
Rb1—O1^ii	3.0342 (8)	Rb2—O1^v	3.317 (2)
Rb1—O1^iii	3.0342 (8)	Rb2—O1^vi	2.8180 (14)
Rb1—O1^iv	3.0342 (8)	Rb2—O1^vii	3.317 (2)
Rb1—O1^v	3.0342 (8)	Ti1—O1	2.0188 (9)
Rb1—O1^vi	3.0342 (8)	Ti1—O1^viii	1.9697 (6)
Rb1—O1^vii	3.0342 (8)	Ti1—O1^ix	1.9697 (6)
Rb2—O1	2.8180 (14)	Ti1—O2	1.9374 (10)
Rb2—O1^i	3.317 (2)	Ti1—O2^x	1.9774 (6)
Rb2—O1^ii	2.8180 (14)	Ti1—O2^xi	1.9774 (6)
O1—Rb1—O1^i	58.641 (12)	O1^i—Rb2—O1^v	68.66 (5)
O1—Rb1—O1^ii	121.359 (12)	O1^i—Rb2—O1^vi	101.99 (3)
O1—Rb1—O1^iii	180	O1^i—Rb2—O1^vii	68.66 (5)
O1—Rb1—O1^iv	76.13 (2)	O1^ii—Rb2—O1	139.70 (13)
O1—Rb1—O1^v	103.87 (2)	O1^ii—Rb2—O1^i	163.05 (11)
O1—Rb1—O1^vi	76.13 (2)	O1^ii—Rb2—O1^iii	57.25 (2)
O1—Rb1—O1^vii	103.87 (2)	O1^ii—Rb2—O1^iv	83.19 (5)
O1^i—Rb1—O1	58.641 (12)	O1^ii—Rb2—O1^v	101.99 (3)
O1^i—Rb1—O1^ii	180	O1^ii—Rb2—O1^vi	83.19 (5)
O1^i—Rb1—O1^iii	121.359 (12)	O1^ii—Rb2—O1^vii	101.99 (3)
O1^i—Rb1—O1^iv	103.87 (2)	O1^iii—Rb2—O1	163.05 (11)
O1^i—Rb1—O1^v	76.13 (2)	O1^iii—Rb2—O1^i	105.79 (9)
O1^i—Rb1—O1^vi	103.87 (2)	O1^iii—Rb2—O1^ii	57.25 (2)
O1^i—Rb1—O1^vii	76.13 (2)	O1^iii—Rb2—O1^iv	101.99 (3)
O1^ii—Rb1—O1	121.359 (12)	O1^iii—Rb2—O1^v	68.66 (5)
O1^ii—Rb1—O1^i	180	O1^iii—Rb2—O1^vi	101.99 (3)
O1^ii—Rb1—O1^iii	58.641 (12)	O1^iii—Rb2—O1^vii	68.66 (5)
O1^ii—Rb1—O1^iv	76.13 (2)	O1^iv—Rb2—O1	83.19 (5)
O1^ii—Rb1—O1^v	103.87 (2)	O1^iv—Rb2—O1^i	101.99 (3)
O1^ii—Rb1—O1^vi	76.13 (2)	O1^iv—Rb2—O1^ii	83.19 (5)
O1^ii—Rb1—O1^vii	103.87 (2)	O1^iv—Rb2—O1^iii	101.99 (3)
O1^iii—Rb1—O1	180	O1^iv—Rb2—O1^v	57.25 (2)
O1^iii—Rb1—O1^i	121.359 (12)	O1^iv—Rb2—O1^vi	139.70 (13)
O1^iii—Rb1—O1^ii	58.641 (12)	O1^iv—Rb2—O1^vii	163.05 (11)
O1^iii—Rb1—O1^iv	103.87 (2)	O1^v—Rb2—O1	101.99 (3)
O1^iii—Rb1—O1^v	76.13 (2)	O1^v—Rb2—O1^i	68.66 (5)
O1^iii—Rb1—O1^vi	103.87 (2)	O1^v—Rb2—O1^ii	101.99 (3)
O1^iii—Rb1—O1^vii	76.13 (2)	O1^v—Rb2—O1^iii	68.66 (5)
O1^iv—Rb1—O1	76.13 (2)	O1^v—Rb2—O1^iv	57.25 (2)
O1^iv—Rb1—O1^i	103.87 (2)	O1^v—Rb2—O1^vi	163.05 (11)
O1^iv—Rb1—O1^ii	76.13 (2)	O1^v—Rb2—O1^vii	105.79 (9)
O1^iv—Rb1—O1^iii	103.87 (2)	O1^vi—Rb2—O1	83.19 (5)
O1^iv—Rb1—O1^v	58.641 (12)	O1^vi—Rb2—O1^i	101.99 (3)
O1^iv—Rb1—O1^vi	121.359 (12)	O1^vi—Rb2—O1^ii	83.19 (5)
O1^iv—Rb1—O1^vii	180	O1^vi—Rb2—O1^iii	101.99 (3)
O1^v—Rb1—O1	103.87 (2)	O1^vi—Rb2—O1^iv	139.70 (13)
O1^v—Rb1—O1^i	76.13 (2)	O1^vi—Rb2—O1^v	163.05 (11)
O1^v—Rb1—O1^ii	103.87 (2)	O1^vi—Rb2—O1^vii	57.25 (2)
O1^v—Rb1—O1^iii	76.13 (2)	O1^vii—Rb2—O1	101.99 (3)
O1^v—Rb1—O1^iv	58.641 (12)	O1^vii—Rb2—O1^i	68.66 (5)
O1^v—Rb1—O1^vi	180	O1^vii—Rb2—O1^ii	101.99 (3)
O1^v—Rb1—O1^vii	121.359 (12)	O1^vii—Rb2—O1^iii	68.66 (5)
O1^vi—Rb1—O1	76.13 (2)	O1^vii—Rb2—O1^iv	163.05 (11)
O1^vi—Rb1—O1^i	103.87 (2)	O1^vii—Rb2—O1^v	105.79 (9)
O1^vi—Rb1—O1^ii	76.13 (2)	O1^vii—Rb2—O1^vi	57.25 (2)
O1^vi—Rb1—O1^iii	103.87 (2)	O1—Ti1—O1^viii	80.52 (3)
O1^vi—Rb1—O1^iv	121.359 (12)	O1—Ti1—O1^ix	80.52 (3)
O1^vi—Rb1—O1^v	180	O1—Ti1—O2	168.36 (4)
O1^vi—Rb1—O1^vii	58.641 (12)	O1—Ti1—O2^x	92.97 (3)
O1^vii—Rb1—O1	103.87 (2)	O1—Ti1—O2^xi	92.97 (3)
O1^vii—Rb1—O1^i	76.13 (2)	O1^viii—Ti1—O1	80.52 (3)
O1^vii—Rb1—O1^ii	103.87 (2)	O1^viii—Ti1—O1^ix	97.94 (3)
O1^vii—Rb1—O1^iii	76.13 (2)	O1^viii—Ti1—O2	91.89 (3)
O1^vii—Rb1—O1^iv	180	O1^viii—Ti1—O2^x	81.94 (3)
O1^vii—Rb1—O1^v	121.359 (12)	O1^viii—Ti1—O2^xi	173.41 (4)
O1^vii—Rb1—O1^vi	58.641 (12)	O1^ix—Ti1—O1	80.52 (3)
O1—Rb2—O1^i	57.25 (2)	O1^ix—Ti1—O1^viii	97.94 (3)
O1—Rb2—O1^ii	139.70 (13)	O1^ix—Ti1—O2	91.89 (3)
O1—Rb2—O1^iii	163.05 (11)	O1^ix—Ti1—O2^x	173.41 (4)
O1—Rb2—O1^iv	83.19 (5)	O1^ix—Ti1—O2^xi	81.94 (3)
O1—Rb2—O1^v	101.99 (3)	O2—Ti1—O2^x	94.70 (4)
O1—Rb2—O1^vi	83.19 (5)	O2—Ti1—O2^xi	94.70 (4)
O1—Rb2—O1^vii	101.99 (3)	O2^x—Ti1—O2	94.70 (4)
O1^i—Rb2—O1	57.25 (2)	O2^x—Ti1—O2^xi	97.43 (3)
O1^i—Rb2—O1^ii	163.05 (11)	O2^xi—Ti1—O2	94.70 (4)
O1^i—Rb2—O1^iii	105.79 (9)	O2^xi—Ti1—O2^x	97.43 (3)
O1^i—Rb2—O1^iv	101.99 (3)

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

(Rb-M23)

Crystal data

Mg0.75O16Rb1.50Ti7.25	Dx = 4.021 Mg m^−3
Mr = 749.6	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/m	Cell parameters from 25 reflections
Hall symbol: -I 4	θ = 20.1–24.0°
a = 10.2052 (7) Å	µ = 10.44 mm^−1
c = 2.9717 (6) Å	T = 298 K
V = 309.49 (7) Å^3	Prismatic, colorless
Z = 1	0.15 × 0.05 × 0.05 mm
F(000) = 352

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.069
Graphite monochromator	θmax = 49.9°, θmin = 2.8°
ω/2θ scans	h = −21→21
Absorption correction: analytical Tompa_analytical	k = −21→21
Tmin = 0.418, Tmax = 0.637	l = 0→6
3639 measured reflections	3 standard reflections every 200 reflections
912 independent reflections	intensity decay: 4.7%
623 reflections with I > 3σ(I)

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0001I^2)
R[F^2 > 2σ(F^2)] = 0.022	(Δ/σ)max = 0.034
wR(F^2) = 0.051	Δρmax = 1.11 e Å^−3
S = 1.19	Δρmin = −0.68 e Å^−3
912 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
28 parameters	Extinction coefficient: 0.0487 (11)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Rb1	0	0	0.5	0.0210 (9)	0.255 (7)
Rb2	0	0	0.3230 (19)	0.0208 (5)	0.248 (2)
Ti1	0.34990 (2)	0.16657 (2)	0	0.00740 (5)	0.9061 (3)
Mg1	0.349902	0.166575	0	0.00740 (5)	0.0939 (3)
O1	0.15623 (9)	0.20687 (9)	0	0.00664 (18)
O2	0.53975 (9)	0.16622 (10)	0	0.00818 (19)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0178 (8)	0.0178 (8)	0.028 (2)	0	0	0
Rb2	0.0123 (3)	0.0123 (3)	0.0380 (14)	0	0	0
Ti1	0.00773 (9)	0.00866 (9)	0.00581 (7)	0.00090 (7)	0	0
Mg1	0.00773 (9)	0.00866 (9)	0.00581 (7)	0.00090 (7)	0	0
O1	0.0066 (3)	0.0068 (3)	0.0065 (3)	−0.0001 (2)	0	0
O2	0.0056 (3)	0.0106 (3)	0.0084 (4)	0.0002 (2)	0	0

Geometric parameters (Å, º)

Rb1—O1	3.0342 (8)	Rb2—O1^iii	3.324 (4)
Rb1—O1^i	3.0342 (8)	Rb2—O1^iv	2.814 (2)
Rb1—O1^ii	3.0342 (8)	Rb2—O1^v	3.324 (4)
Rb1—O1^iii	3.0342 (8)	Rb2—O1^vi	2.814 (2)
Rb1—O1^iv	3.0342 (8)	Rb2—O1^vii	3.324 (4)
Rb1—O1^v	3.0342 (8)	Ti1—O1	2.0188 (9)
Rb1—O1^vi	3.0342 (8)	Ti1—O1^viii	1.9697 (6)
Rb1—O1^vii	3.0342 (8)	Ti1—O1^ix	1.9697 (6)
Rb2—O1	2.814 (2)	Ti1—O2	1.9374 (10)
Rb2—O1^i	3.324 (4)	Ti1—O2^x	1.9774 (6)
Rb2—O1^ii	2.814 (2)	Ti1—O2^xi	1.9774 (6)
O1—Rb1—O1^i	58.641 (12)	O1^i—Rb2—O1^v	68.50 (8)
O1—Rb1—O1^ii	121.359 (12)	O1^i—Rb2—O1^vi	101.91 (5)
O1—Rb1—O1^iii	180	O1^i—Rb2—O1^vii	68.50 (8)
O1—Rb1—O1^iv	76.13 (2)	O1^ii—Rb2—O1	140.1 (2)
O1—Rb1—O1^v	103.87 (2)	O1^ii—Rb2—O1^i	162.69 (19)
O1—Rb1—O1^vi	76.13 (2)	O1^ii—Rb2—O1^iii	57.19 (3)
O1—Rb1—O1^vii	103.87 (2)	O1^ii—Rb2—O1^iv	83.32 (7)
O1^i—Rb1—O1	58.641 (12)	O1^ii—Rb2—O1^v	101.91 (5)
O1^i—Rb1—O1^ii	180	O1^ii—Rb2—O1^vi	83.32 (7)
O1^i—Rb1—O1^iii	121.359 (12)	O1^ii—Rb2—O1^vii	101.91 (5)
O1^i—Rb1—O1^iv	103.87 (2)	O1^iii—Rb2—O1	162.69 (19)
O1^i—Rb1—O1^v	76.13 (2)	O1^iii—Rb2—O1^i	105.49 (16)
O1^i—Rb1—O1^vi	103.87 (2)	O1^iii—Rb2—O1^ii	57.19 (3)
O1^i—Rb1—O1^vii	76.13 (2)	O1^iii—Rb2—O1^iv	101.91 (5)
O1^ii—Rb1—O1	121.359 (12)	O1^iii—Rb2—O1^v	68.50 (8)
O1^ii—Rb1—O1^i	180	O1^iii—Rb2—O1^vi	101.91 (5)
O1^ii—Rb1—O1^iii	58.641 (12)	O1^iii—Rb2—O1^vii	68.50 (8)
O1^ii—Rb1—O1^iv	76.13 (2)	O1^iv—Rb2—O1	83.32 (7)
O1^ii—Rb1—O1^v	103.87 (2)	O1^iv—Rb2—O1^i	101.91 (5)
O1^ii—Rb1—O1^vi	76.13 (2)	O1^iv—Rb2—O1^ii	83.32 (7)
O1^ii—Rb1—O1^vii	103.87 (2)	O1^iv—Rb2—O1^iii	101.91 (5)
O1^iii—Rb1—O1	180	O1^iv—Rb2—O1^v	57.19 (3)
O1^iii—Rb1—O1^i	121.359 (12)	O1^iv—Rb2—O1^vi	140.1 (2)
O1^iii—Rb1—O1^ii	58.641 (12)	O1^iv—Rb2—O1^vii	162.69 (19)
O1^iii—Rb1—O1^iv	103.87 (2)	O1^v—Rb2—O1	101.91 (5)
O1^iii—Rb1—O1^v	76.13 (2)	O1^v—Rb2—O1^i	68.50 (8)
O1^iii—Rb1—O1^vi	103.87 (2)	O1^v—Rb2—O1^ii	101.91 (5)
O1^iii—Rb1—O1^vii	76.13 (2)	O1^v—Rb2—O1^iii	68.50 (8)
O1^iv—Rb1—O1	76.13 (2)	O1^v—Rb2—O1^iv	57.19 (3)
O1^iv—Rb1—O1^i	103.87 (2)	O1^v—Rb2—O1^vi	162.69 (19)
O1^iv—Rb1—O1^ii	76.13 (2)	O1^v—Rb2—O1^vii	105.49 (16)
O1^iv—Rb1—O1^iii	103.87 (2)	O1^vi—Rb2—O1	83.32 (7)
O1^iv—Rb1—O1^v	58.641 (12)	O1^vi—Rb2—O1^i	101.91 (5)
O1^iv—Rb1—O1^vi	121.359 (12)	O1^vi—Rb2—O1^ii	83.32 (7)
O1^iv—Rb1—O1^vii	180	O1^vi—Rb2—O1^iii	101.91 (5)
O1^v—Rb1—O1	103.87 (2)	O1^vi—Rb2—O1^iv	140.1 (2)
O1^v—Rb1—O1^i	76.13 (2)	O1^vi—Rb2—O1^v	162.69 (19)
O1^v—Rb1—O1^ii	103.87 (2)	O1^vi—Rb2—O1^vii	57.19 (3)
O1^v—Rb1—O1^iii	76.13 (2)	O1^vii—Rb2—O1	101.91 (5)
O1^v—Rb1—O1^iv	58.641 (12)	O1^vii—Rb2—O1^i	68.50 (8)
O1^v—Rb1—O1^vi	180	O1^vii—Rb2—O1^ii	101.91 (5)
O1^v—Rb1—O1^vii	121.359 (12)	O1^vii—Rb2—O1^iii	68.50 (8)
O1^vi—Rb1—O1	76.13 (2)	O1^vii—Rb2—O1^iv	162.69 (19)
O1^vi—Rb1—O1^i	103.87 (2)	O1^vii—Rb2—O1^v	105.49 (16)
O1^vi—Rb1—O1^ii	76.13 (2)	O1^vii—Rb2—O1^vi	57.19 (3)
O1^vi—Rb1—O1^iii	103.87 (2)	O1—Ti1—O1^viii	80.52 (3)
O1^vi—Rb1—O1^iv	121.359 (12)	O1—Ti1—O1^ix	80.52 (3)
O1^vi—Rb1—O1^v	180	O1—Ti1—O2	168.35 (4)
O1^vi—Rb1—O1^vii	58.641 (12)	O1—Ti1—O2^x	92.97 (3)
O1^vii—Rb1—O1	103.87 (2)	O1—Ti1—O2^xi	92.97 (3)
O1^vii—Rb1—O1^i	76.13 (2)	O1^viii—Ti1—O1	80.52 (3)
O1^vii—Rb1—O1^ii	103.87 (2)	O1^viii—Ti1—O1^ix	97.94 (3)
O1^vii—Rb1—O1^iii	76.13 (2)	O1^viii—Ti1—O2	91.89 (3)
O1^vii—Rb1—O1^iv	180	O1^viii—Ti1—O2^x	81.94 (3)
O1^vii—Rb1—O1^v	121.359 (12)	O1^viii—Ti1—O2^xi	173.41 (4)
O1^vii—Rb1—O1^vi	58.641 (12)	O1^ix—Ti1—O1	80.52 (3)
O1—Rb2—O1^i	57.19 (3)	O1^ix—Ti1—O1^viii	97.94 (3)
O1—Rb2—O1^ii	140.1 (2)	O1^ix—Ti1—O2	91.89 (3)
O1—Rb2—O1^iii	162.69 (19)	O1^ix—Ti1—O2^x	173.41 (4)
O1—Rb2—O1^iv	83.32 (7)	O1^ix—Ti1—O2^xi	81.94 (3)
O1—Rb2—O1^v	101.91 (5)	O2—Ti1—O2^x	94.70 (3)
O1—Rb2—O1^vi	83.32 (7)	O2—Ti1—O2^xi	94.70 (3)
O1—Rb2—O1^vii	101.91 (5)	O2^x—Ti1—O2	94.70 (3)
O1^i—Rb2—O1	57.19 (3)	O2^x—Ti1—O2^xi	97.43 (3)
O1^i—Rb2—O1^ii	162.69 (19)	O2^xi—Ti1—O2	94.70 (3)
O1^i—Rb2—O1^iii	105.49 (16)	O2^xi—Ti1—O2^x	97.43 (3)
O1^i—Rb2—O1^iv	101.91 (5)

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

(Rb-M24)

Crystal data

Mg0.76O16Rb1.51Ti7.24	Dx = 4.026 Mg m^−3
Mr = 750.3	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/m	Cell parameters from 25 reflections
Hall symbol: -I 4	θ = 20.1–24.0°
a = 10.2052 (7) Å	µ = 10.48 mm^−1
c = 2.9717 (6) Å	T = 298 K
V = 309.49 (7) Å^3	Prismatic, colorless
Z = 1	0.15 × 0.05 × 0.05 mm
F(000) = 352

Data collection

Rigaku AFC-7R diffractometer	Rint = 0.069
Graphite monochromator	θmax = 49.9°, θmin = 2.8°
ω/2θ scans	h = −21→21
Absorption correction: analytical Tompa_analytical	k = −21→21
Tmin = 0.418, Tmax = 0.637	l = 0→6
3639 measured reflections	3 standard reflections every 200 reflections
912 independent reflections	intensity decay: 4.7%
623 reflections with I > 3σ(I)

Refinement

Refinement on F^2	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.0001I^2)
R[F^2 > 2σ(F^2)] = 0.022	(Δ/σ)max = 0.030
wR(F^2) = 0.050	Δρmax = 0.78 e Å^−3
S = 1.18	Δρmin = −0.67 e Å^−3
912 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
31 parameters	Extinction coefficient: 0.049174

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Rb1	0	0	0.5	0.0232 (14)	0.270 (9)
Rb2	0	0	0.326 (3)	0.031 (3)	0.243 (3)
Ti1	0.34990 (2)	0.16657 (2)	0	0.00743 (5)	0.9054 (4)
Mg1	0.349897	0.166572	0	0.00743 (5)	0.0946 (4)
O1	0.15622 (9)	0.20689 (9)	0	0.00669 (18)
O2	0.53972 (9)	0.16622 (10)	0	0.00821 (19)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.013 (2)	0.013 (2)	0.044 (3)	0	0	0
Rb2	0.0160 (15)	0.0160 (15)	0.062 (8)	0	0	0
Ti1	0.00776 (9)	0.00869 (9)	0.00584 (7)	0.00090 (7)	0	0
Mg1	0.00776 (9)	0.00869 (9)	0.00584 (7)	0.00090 (7)	0	0
O1	0.0067 (3)	0.0069 (3)	0.0065 (3)	−0.0001 (2)	0	0
O2	0.0057 (3)	0.0107 (3)	0.0083 (3)	0.0002 (2)	0	0

Geometric parameters (Å, º)

Rb1—O1	3.0344 (8)	Rb2—O1^iii	3.318 (6)
Rb1—O1^i	3.0344 (8)	Rb2—O1^iv	2.818 (3)
Rb1—O1^ii	3.0344 (8)	Rb2—O1^v	3.318 (6)
Rb1—O1^iii	3.0344 (8)	Rb2—O1^vi	2.818 (3)
Rb1—O1^iv	3.0344 (8)	Rb2—O1^vii	3.318 (6)
Rb1—O1^v	3.0344 (8)	Ti1—O1	2.0189 (9)
Rb1—O1^vi	3.0344 (8)	Ti1—O1^viii	1.9695 (6)
Rb1—O1^vii	3.0344 (8)	Ti1—O1^ix	1.9695 (6)
Rb2—O1	2.818 (3)	Ti1—O2	1.9371 (9)
Rb2—O1^i	3.318 (6)	Ti1—O2^x	1.9776 (6)
Rb2—O1^ii	2.818 (3)	Ti1—O2^xi	1.9776 (6)
O1—Rb1—O1^i	58.638 (12)	O1^i—Rb2—O1^v	68.65 (14)
O1—Rb1—O1^ii	121.362 (12)	O1^i—Rb2—O1^vi	101.99 (7)
O1—Rb1—O1^iii	180	O1^i—Rb2—O1^vii	68.65 (14)
O1—Rb1—O1^iv	76.13 (2)	O1^ii—Rb2—O1	139.7 (4)
O1—Rb1—O1^v	103.87 (2)	O1^ii—Rb2—O1^i	163.0 (3)
O1—Rb1—O1^vi	76.13 (2)	O1^ii—Rb2—O1^iii	57.25 (5)
O1—Rb1—O1^vii	103.87 (2)	O1^ii—Rb2—O1^iv	83.19 (12)
O1^i—Rb1—O1	58.638 (12)	O1^ii—Rb2—O1^v	101.99 (7)
O1^i—Rb1—O1^ii	180	O1^ii—Rb2—O1^vi	83.19 (12)
O1^i—Rb1—O1^iii	121.362 (12)	O1^ii—Rb2—O1^vii	101.99 (7)
O1^i—Rb1—O1^iv	103.87 (2)	O1^iii—Rb2—O1	163.0 (3)
O1^i—Rb1—O1^v	76.13 (2)	O1^iii—Rb2—O1^i	105.8 (3)
O1^i—Rb1—O1^vi	103.87 (2)	O1^iii—Rb2—O1^ii	57.25 (5)
O1^i—Rb1—O1^vii	76.13 (2)	O1^iii—Rb2—O1^iv	101.99 (7)
O1^ii—Rb1—O1	121.362 (12)	O1^iii—Rb2—O1^v	68.65 (14)
O1^ii—Rb1—O1^i	180	O1^iii—Rb2—O1^vi	101.99 (7)
O1^ii—Rb1—O1^iii	58.638 (12)	O1^iii—Rb2—O1^vii	68.65 (14)
O1^ii—Rb1—O1^iv	76.13 (2)	O1^iv—Rb2—O1	83.19 (12)
O1^ii—Rb1—O1^v	103.87 (2)	O1^iv—Rb2—O1^i	101.99 (7)
O1^ii—Rb1—O1^vi	76.13 (2)	O1^iv—Rb2—O1^ii	83.19 (12)
O1^ii—Rb1—O1^vii	103.87 (2)	O1^iv—Rb2—O1^iii	101.99 (7)
O1^iii—Rb1—O1	180	O1^iv—Rb2—O1^v	57.25 (5)
O1^iii—Rb1—O1^i	121.362 (12)	O1^iv—Rb2—O1^vi	139.7 (4)
O1^iii—Rb1—O1^ii	58.638 (12)	O1^iv—Rb2—O1^vii	163.0 (3)
O1^iii—Rb1—O1^iv	103.87 (2)	O1^v—Rb2—O1	101.99 (7)
O1^iii—Rb1—O1^v	76.13 (2)	O1^v—Rb2—O1^i	68.65 (14)
O1^iii—Rb1—O1^vi	103.87 (2)	O1^v—Rb2—O1^ii	101.99 (7)
O1^iii—Rb1—O1^vii	76.13 (2)	O1^v—Rb2—O1^iii	68.65 (14)
O1^iv—Rb1—O1	76.13 (2)	O1^v—Rb2—O1^iv	57.25 (5)
O1^iv—Rb1—O1^i	103.87 (2)	O1^v—Rb2—O1^vi	163.0 (3)
O1^iv—Rb1—O1^ii	76.13 (2)	O1^v—Rb2—O1^vii	105.8 (3)
O1^iv—Rb1—O1^iii	103.87 (2)	O1^vi—Rb2—O1	83.19 (12)
O1^iv—Rb1—O1^v	58.638 (12)	O1^vi—Rb2—O1^i	101.99 (7)
O1^iv—Rb1—O1^vi	121.362 (12)	O1^vi—Rb2—O1^ii	83.19 (12)
O1^iv—Rb1—O1^vii	180	O1^vi—Rb2—O1^iii	101.99 (7)
O1^v—Rb1—O1	103.87 (2)	O1^vi—Rb2—O1^iv	139.7 (4)
O1^v—Rb1—O1^i	76.13 (2)	O1^vi—Rb2—O1^v	163.0 (3)
O1^v—Rb1—O1^ii	103.87 (2)	O1^vi—Rb2—O1^vii	57.25 (5)
O1^v—Rb1—O1^iii	76.13 (2)	O1^vii—Rb2—O1	101.99 (7)
O1^v—Rb1—O1^iv	58.638 (12)	O1^vii—Rb2—O1^i	68.65 (14)
O1^v—Rb1—O1^vi	180	O1^vii—Rb2—O1^ii	101.99 (7)
O1^v—Rb1—O1^vii	121.362 (12)	O1^vii—Rb2—O1^iii	68.65 (14)
O1^vi—Rb1—O1	76.13 (2)	O1^vii—Rb2—O1^iv	163.0 (3)
O1^vi—Rb1—O1^i	103.87 (2)	O1^vii—Rb2—O1^v	105.8 (3)
O1^vi—Rb1—O1^ii	76.13 (2)	O1^vii—Rb2—O1^vi	57.25 (5)
O1^vi—Rb1—O1^iii	103.87 (2)	O1—Ti1—O1^viii	80.52 (3)
O1^vi—Rb1—O1^iv	121.362 (12)	O1—Ti1—O1^ix	80.52 (3)
O1^vi—Rb1—O1^v	180	O1—Ti1—O2	168.34 (4)
O1^vi—Rb1—O1^vii	58.638 (12)	O1—Ti1—O2^x	92.98 (3)
O1^vii—Rb1—O1	103.87 (2)	O1—Ti1—O2^xi	92.98 (3)
O1^vii—Rb1—O1^i	76.13 (2)	O1^viii—Ti1—O1	80.52 (3)
O1^vii—Rb1—O1^ii	103.87 (2)	O1^viii—Ti1—O1^ix	97.95 (3)
O1^vii—Rb1—O1^iii	76.13 (2)	O1^viii—Ti1—O2	91.89 (3)
O1^vii—Rb1—O1^iv	180	O1^viii—Ti1—O2^x	81.94 (3)
O1^vii—Rb1—O1^v	121.362 (12)	O1^viii—Ti1—O2^xi	173.41 (4)
O1^vii—Rb1—O1^vi	58.638 (12)	O1^ix—Ti1—O1	80.52 (3)
O1—Rb2—O1^i	57.25 (5)	O1^ix—Ti1—O1^viii	97.95 (3)
O1—Rb2—O1^ii	139.7 (4)	O1^ix—Ti1—O2	91.89 (3)
O1—Rb2—O1^iii	163.0 (3)	O1^ix—Ti1—O2^x	173.41 (4)
O1—Rb2—O1^iv	83.19 (12)	O1^ix—Ti1—O2^xi	81.94 (3)
O1—Rb2—O1^v	101.99 (7)	O2—Ti1—O2^x	94.70 (3)
O1—Rb2—O1^vi	83.19 (12)	O2—Ti1—O2^xi	94.70 (3)
O1—Rb2—O1^vii	101.99 (7)	O2^x—Ti1—O2	94.70 (3)
O1^i—Rb2—O1	57.25 (5)	O2^x—Ti1—O2^xi	97.42 (3)
O1^i—Rb2—O1^ii	163.0 (3)	O2^xi—Ti1—O2	94.70 (3)
O1^i—Rb2—O1^iii	105.8 (3)	O2^xi—Ti1—O2^x	97.42 (3)
O1^i—Rb2—O1^iv	101.99 (7)

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