New phosphate langbeinites, K₂MTi(PO₄)₃ (M = Er, Yb or Y), and an alternative description of the langbeinite framework

Three new potassium rare-earth/titanium phosphate structures, K₂ErTi(PO₄)₃ (KErTP), K₂YbTi(PO₄)₃ (KYbTP) and K₂YTi(PO₄)₃ (KYTP), are presented, all of which are characterized by single-crystal X-ray diffraction studies. In addition, a fourth structure, K₂CrTi(PO₄)₃ (KCrTP), has been reinvestigated. All structures are isostructural to the langbeinite-type structure and result from changes made to the growth constituents in high-temperature flux-growth experiments intended to give structurally modified potassium titanyl phosphate (KTP). The two crystallographically independent octahedra sites (site symmetry 3) have a mixed Ti/M (M = Er, Yb, Y or Cr) population, although the rare-earth metals favour one site while chromium favours the other. An alternative approach for the description of the channels and cation cages in langbeinite and related structures is given using [M₅X₆O₃₉] units. The framework of langbeinite is compared with that of nasicon using these alternative building units. All of the investigated structures crystallize in space group P2₁3 with Z = 4; a = 10.1053 (2) Å, R = 0.023 (KErTP); a = 10.0939 (8) Å, R = 0.022 (KYbTP); a = 10.1318 (6) Å, R = 0.047 (KYTP); a = 9.8001 (2) Å, R = 0.016 (KCrTP).

Computing details

For all compounds, data collection: CAD-4 Software (Enraf-Nonius, 1989). Cell refinement: CAD-4 Software (Enraf-Nonius, 1989) for KErTP, KYbTP, KCrTP; Xtal3.71 (Hall et al., 2000) program: LATCON for KYTP. For all compounds, data reduction: Xtal3.71 (Hall et al., 2000) programs: DIFDAT; SORTRF; ADDREF; ABSORB; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: Xtal3.71 (Hall et al., 2000) program: CRYLSQ; software used to prepare material for publication: Xtal3.71 (Hall et al., 2000) programs: BONDLA; ATABLE; CIFIO.

Figures

(KErTP)

Crystal data

K2ErTiP3O12	Dx = 3.722 Mg m^−3
Mr = 578.25	Mo Kα radiation, λ = 0.71073 Å
Cubic, P213	Cell parameters from 20 reflections
Hall symbol: P 2ac 2ab 3	θ = 26.6–29.8°
a = 10.1053 (2) Å	µ = 10.19 mm^−1
V = 1031.92 (4) Å^3	T = 293 K
Z = 4	Tetrahedron, colourless
F(000) = 1076	0.06 × 0.06 × 0.05 mm

Data collection

Enraf-Nonius CAD-4 diffractometer	967 reflections with F^2 > 2σ(F^2)
Radiation source: Fine-focus sealed tube	Rint = 0.048
Graphite monochromator	θmax = 29.9°, θmin = 3.5°
ω–2θ scans	h = −14→0
Absorption correction: analytical (Alcock, 1974)	k = −14→0
Tmin = 0.567, Tmax = 0.650	l = −14→14
3285 measured reflections	3 standard reflections every 120 min
1008 independent reflections	intensity decay: none

Refinement

Refinement on F^2	w = 1/[σ^2(Fsqd) + 0.008(Fsqd)^2]
Least-squares matrix: full	(Δ/σ)max = 0.00018
R[F^2 > 2σ(F^2)] = 0.023	Δρmax = 0.60 e Å^−3
wR(F^2) = 0.077	Δρmin = −0.76 e Å^−3
S = 1.06	Extinction correction: Isotropic Gaussian, Zachariasen, 1967; Larson (1970), Eq22 p292 "Cryst. Comp." Munksgaard 1970
1008 reflections	Extinction coefficient: 90 (22) × 10^2
61 parameters	Absolute structure: Flack (1983) parameter refined
0 restraints	Absolute structure parameter: 0.04 (3)
9 constraints

Special details

Refinement. The following constraints were used during the refinement:

H-atom parameters constrained x(Ti1)=0.0 + 1.0*x(Er1) H-atom parameters constrained u11(Ti1)=0.0 + 1.0*u11(Er1) H-atom parameters constrained u12(Ti1)=0.0 + 1.0*u12(Er1) H-atom parameters constrained x(Ti2)=0.0 + 1.0*x(Er2) H-atom parameters constrained u11(Ti2)=0.0 + 1.0*u11(Er2) H-atom parameters constrained u12(Ti2)=0.0 + 1.0*u12(Er2) H-atom parameters constrained pop(Ti1)=1.0–1.0*pop(Er1) H-atom parameters constrained pop(Ti2)=0.0 + 1.0*pop(Er1) H-atom parameters constrained pop(Er2)=1.0–1.0*pop(Er1)

No restraints used.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0.04526 (18)	0.54526 (18)	−0.04526 (18)	0.0307 (6)
K2	−0.18088 (16)	0.31912 (16)	0.18088 (16)	0.0261 (5)
Er1	−0.16698 (4)	0.66698 (4)	0.33302 (4)	0.0131 (2)	0.583 (3)
Ti1	−0.16698 (4)	0.66698 (4)	0.33302 (4)	0.0131 (2)	0.417 (3)
Er2	0.39957 (4)	0.60043 (4)	0.10043 (4)	0.0129 (3)	0.417 (3)
Ti2	0.39957 (4)	0.60043 (4)	0.10043 (4)	0.0129 (3)	0.583 (3)
P	0.12640 (17)	0.48419 (18)	0.28844 (17)	0.0195 (7)
O1	0.0993 (8)	0.3452 (8)	0.2408 (7)	0.049 (4)
O2	0.0052 (8)	0.5669 (11)	0.2705 (9)	0.065 (5)
O3	0.1693 (7)	0.4850 (7)	0.4327 (7)	0.044 (4)
O4	0.2331 (8)	0.5476 (9)	0.2023 (10)	0.058 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0307 (6)	0.0307 (6)	0.0307 (6)	−0.0007 (6)	0.0007 (6)	0.0007 (6)
K2	0.0261 (5)	0.0261 (5)	0.0261 (5)	−0.0031 (5)	0.0031 (5)	0.0031 (5)
Er1	0.0131 (2)	0.0131 (2)	0.0131 (2)	0.0046 (4)	−0.0046 (4)	−0.0046 (4)
Ti1	0.0131 (2)	0.0131 (2)	0.0131 (2)	0.0046 (4)	−0.0046 (4)	−0.0046 (4)
Er2	0.0129 (3)	0.0129 (3)	0.0129 (3)	−0.0004 (5)	0.0004 (5)	0.0004 (5)
Ti2	0.0129 (3)	0.0129 (3)	0.0129 (3)	−0.0004 (5)	0.0004 (5)	0.0004 (5)
P	0.0158 (7)	0.0232 (8)	0.0196 (7)	0.0015 (6)	0.0019 (6)	−0.0004 (6)
O1	0.053 (4)	0.048 (4)	0.046 (4)	−0.022 (4)	0.002 (4)	−0.015 (3)
O2	0.044 (4)	0.086 (6)	0.064 (5)	0.038 (4)	0.009 (4)	0.028 (5)
O3	0.045 (4)	0.055 (4)	0.033 (3)	−0.001 (4)	−0.019 (3)	−0.011 (3)
O4	0.049 (4)	0.049 (4)	0.076 (6)	−0.017 (4)	0.034 (4)	−0.006 (4)

Geometric parameters (Å, º)

K1—K2	3.958 (2)	Er1—O2	2.109 (9)
K1—O2	3.224 (9)	Ti1—O2	2.109 (9)
K1—O4	3.141 (9)	Ti1—O1^ii	2.065 (8)
K1—O3	2.909 (8)	Ti1—O2	2.109 (9)
K1—O3	2.909 (8)	Ti1—O1^iii	2.065 (8)
K1—O2	3.224 (9)	Ti1—O1^i	2.065 (8)
K1—O4	3.141 (9)	Ti1—O2	2.109 (9)
K1—O2^i	3.224 (9)	Er2—O4	2.043 (9)
K1—O4^i	3.141 (9)	Er2—O3	2.026 (7)
K1—O3	2.909 (8)	Er2—O3^iv	2.026 (7)
K2—O1	2.907 (8)	Er2—O4	2.043 (9)
K2—O2	3.145 (11)	Er2—O3	2.026 (7)
K2—O4	3.033 (9)	Er2—O4	2.043 (9)
K2—O2	3.145 (11)	Ti2—O4	2.043 (9)
K2—O4	3.033 (9)	Ti2—O3	2.026 (7)
K2—O1	2.907 (8)	Ti2—O3^iv	2.026 (7)
K2—O1^i	2.907 (8)	Ti2—O4	2.043 (9)
K2—O2	3.145 (11)	Ti2—O3	2.026 (7)
K2—O4	3.033 (9)	Ti2—O4	2.043 (9)
Er1—O2	2.109 (9)	P—O1	1.510 (8)
Er1—O1^ii	2.065 (8)	P—O2	1.494 (10)
Er1—O2	2.109 (9)	P—O3	1.521 (7)
Er1—O1^iii	2.065 (8)	P—O4	1.527 (9)
Er1—O1^i	2.065 (8)
O2—K1—O4	44.5 (2)	O1^i—K2—O2	59.4 (2)
O2—K1—O3	102.0 (2)	O1^i—K2—O4	99.8 (2)
O2—K1—O3	164.4 (2)	O2—K2—O4	45.9 (2)
O2—K1—O2	87.2 (3)	O2—Er1—O1^ii	92.1 (4)
O2—K1—O4	130.8 (3)	O2—Er1—O2	89.7 (4)
O2—K1—O2^i	87.2 (3)	O2—Er1—O1^iii	172.5 (4)
O2—K1—O4^i	82.3 (2)	O2—Er1—O1^i	83.0 (3)
O2—K1—O3	80.7 (3)	O2—Er1—O2	89.7 (4)
O4—K1—O3	57.5 (2)	O1^ii—Er1—O2	83.0 (3)
O4—K1—O3	148.5 (2)	O1^ii—Er1—O1^iii	95.4 (3)
O4—K1—O2	82.3 (2)	O1^ii—Er1—O1^i	95.4 (3)
O4—K1—O4	118.9 (2)	O1^ii—Er1—O2	172.5 (4)
O4—K1—O2^i	130.8 (3)	O2—Er1—O1^iii	92.1 (4)
O4—K1—O4^i	118.9 (2)	O2—Er1—O1^i	172.5 (4)
O4—K1—O3	82.1 (2)	O2—Er1—O2	89.7 (4)
O3—K1—O3	92.1 (2)	O1^iii—Er1—O1^i	95.4 (3)
O3—K1—O2	80.7 (3)	O1^iii—Er1—O2	83.0 (3)
O3—K1—O4	82.1 (2)	O1^i—Er1—O2	92.1 (4)
O3—K1—O2^i	164.4 (2)	O2—Ti1—O1^ii	92.1 (4)
O3—K1—O4^i	148.5 (2)	O2—Ti1—O2	89.7 (4)
O3—K1—O3	92.1 (2)	O2—Ti1—O1^iii	172.5 (4)
O3—K1—O2	102.0 (2)	O2—Ti1—O1^i	83.0 (3)
O3—K1—O4	57.5 (2)	O2—Ti1—O2	89.7 (4)
O3—K1—O2^i	80.7 (3)	O1^ii—Ti1—O2	83.0 (3)
O3—K1—O4^i	82.1 (2)	O1^ii—Ti1—O1^iii	95.4 (3)
O3—K1—O3	92.1 (2)	O1^ii—Ti1—O1^i	95.4 (3)
O2—K1—O4	44.5 (2)	O1^ii—Ti1—O2	172.5 (4)
O2—K1—O2^i	87.2 (3)	O2—Ti1—O1^iii	92.1 (4)
O2—K1—O4^i	130.8 (3)	O2—Ti1—O1^i	172.5 (4)
O2—K1—O3	164.4 (2)	O2—Ti1—O2	89.7 (4)
O4—K1—O2^i	82.3 (2)	O1^iii—Ti1—O1^i	95.4 (3)
O4—K1—O4^i	118.9 (2)	O1^iii—Ti1—O2	83.0 (3)
O4—K1—O3	148.5 (2)	O1^i—Ti1—O2	92.1 (4)
O2^i—K1—O4^i	44.5 (2)	O4—Er2—O3	91.6 (3)
O2^i—K1—O3	102.0 (2)	O4—Er2—O3^iv	87.7 (3)
O4^i—K1—O3	57.5 (2)	O4—Er2—O4	86.1 (4)
O1—K2—O2	59.4 (2)	O4—Er2—O3	173.5 (3)
O1—K2—O4	99.8 (2)	O4—Er2—O4	86.1 (4)
O1—K2—O2	157.1 (2)	O3—Er2—O3^iv	94.4 (3)
O1—K2—O4	151.6 (2)	O3—Er2—O4	173.5 (3)
O1—K2—O1	97.7 (2)	O3—Er2—O3	94.4 (3)
O1—K2—O1^i	97.7 (2)	O3—Er2—O4	87.7 (3)
O1—K2—O2	86.1 (2)	O3^iv—Er2—O4	91.6 (3)
O1—K2—O4	101.9 (2)	O3^iv—Er2—O3	94.4 (3)
O2—K2—O4	45.9 (2)	O3^iv—Er2—O4	173.5 (3)
O2—K2—O2	114.8 (2)	O4—Er2—O3	87.7 (3)
O2—K2—O4	99.7 (3)	O4—Er2—O4	86.1 (4)
O2—K2—O1	86.1 (2)	O3—Er2—O4	91.6 (3)
O2—K2—O1^i	157.1 (2)	O4—Ti2—O3	91.6 (3)
O2—K2—O2	114.8 (2)	O4—Ti2—O3^iv	87.7 (3)
O2—K2—O4	86.4 (2)	O4—Ti2—O4	86.1 (4)
O4—K2—O2	86.4 (2)	O4—Ti2—O3	173.5 (3)
O4—K2—O4	54.7 (2)	O4—Ti2—O4	86.1 (4)
O4—K2—O1	101.9 (2)	O3—Ti2—O3^iv	94.4 (3)
O4—K2—O1^i	151.6 (2)	O3—Ti2—O4	173.5 (3)
O4—K2—O2	99.7 (3)	O3—Ti2—O3	94.4 (3)
O4—K2—O4	54.7 (2)	O3—Ti2—O4	87.7 (3)
O2—K2—O4	45.9 (2)	O3^iv—Ti2—O4	91.6 (3)
O2—K2—O1	59.4 (2)	O3^iv—Ti2—O3	94.4 (3)
O2—K2—O1^i	86.1 (2)	O3^iv—Ti2—O4	173.5 (3)
O2—K2—O2	114.8 (2)	O4—Ti2—O3	87.7 (3)
O2—K2—O4	99.7 (3)	O4—Ti2—O4	86.1 (4)
O4—K2—O1	99.8 (2)	O3—Ti2—O4	91.6 (3)
O4—K2—O1^i	101.9 (2)	O1—P—O2	109.5 (5)
O4—K2—O2	86.4 (2)	O1—P—O3	111.3 (4)
O4—K2—O4	54.7 (2)	O1—P—O4	109.7 (5)
O1—K2—O1^i	97.7 (2)	O2—P—O3	110.3 (5)
O1—K2—O2	157.1 (2)	O2—P—O4	106.0 (5)
O1—K2—O4	151.6 (2)	O3—P—O4	110.0 (5)

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

(KYbTP)

Crystal data

K2YbTiP3O12	Dx = 3.772 Mg m^−3
Mr = 584.03	Mo Kα radiation, λ = 0.71073 Å
Cubic, P213	Cell parameters from 24 reflections
Hall symbol: P 2ac 2ab 3	θ = 24.0–29.8°
a = 10.0939 (8) Å	µ = 11.16 mm^−1
V = 1028.4 (2) Å^3	T = 293 K
Z = 4	Tetrahedron, colourless
F(000) = 1084	0.04 × 0.03 × 0.03 mm

Data collection

Enraf-Nonius CAD-4 diffractometer	904 reflections with F^2 > 2σ(F^2)
Radiation source: Fine-focus sealed tube	Rint = 0.063
Graphite monochromator	θmax = 29.9°, θmin = 3.5°
ω–2θ scans	h = −14→0
Absorption correction: analytical (Alcock, 1974)	k = −14→14
Tmin = 0.687, Tmax = 0.753	l = −14→14
6213 measured reflections	3 standard reflections every 120 min
1008 independent reflections	intensity decay: none

Refinement

Refinement on F^2	9 constraints
Least-squares matrix: full	w = 1/[σ^2(Fsqd) + 0.045(Fsqd)^2]
R[F^2 > 2σ(F^2)] = 0.022	(Δ/σ)max = 0.000041
wR(F^2) = 0.066	Δρmax = 1.28 e Å^−3
S = 1.08	Δρmin = −0.93 e Å^−3
1008 reflections	Absolute structure: Flack (1983) parameter refined
60 parameters	Absolute structure parameter: 0.00 (3)
0 restraints

Special details

Refinement. The following constraints were used during the refinement:

H-atom parameters constrained x(Ti1)=0.0 + 1.0*x(Yb1) H-atom parameters constrained u11(Ti1)=0.0 + 1.0*u11(Yb1) H-atom parameters constrained u12(Ti1)=0.0 + 1.0*u12(Yb1) H-atom parameters constrained x(Ti2)=0.0 + 1.0*x(Yb2) H-atom parameters constrained u11(Ti2)=0.0 + 1.0*u11(Yb2) H-atom parameters constrained u12(Ti2)=0.0 + 1.0*u12(Yb2) H-atom parameters constrained pop(Ti1)=1.0–1.0*pop(Yb1) H-atom parameters constrained pop(Ti2)=0.0 + 1.0*pop(Yb1) H-atom parameters constrained pop(Yb2)=1.0–1.0*pop(Yb1)

No restraints used.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0.0454 (2)	0.5454 (2)	−0.0454 (2)	0.0315 (7)
K2	−0.18045 (16)	0.31955 (16)	0.18045 (16)	0.0250 (5)
Yb1	−0.16699 (3)	0.66699 (3)	0.33301 (3)	0.0116 (2)	0.643 (3)
Ti1	−0.16699 (3)	0.66699 (3)	0.33301 (3)	0.0116 (2)	0.357 (3)
Yb2	0.39847 (5)	0.60153 (5)	0.10153 (5)	0.0106 (3)	0.357 (3)
Ti2	0.39847 (5)	0.60153 (5)	0.10153 (5)	0.0106 (3)	0.643 (3)
P	0.12740 (17)	0.48538 (19)	0.28995 (18)	0.0178 (8)
O1	0.0972 (7)	0.3469 (7)	0.2412 (7)	0.041 (4)
O2	0.0051 (8)	0.5704 (10)	0.2720 (8)	0.056 (5)
O3	0.1694 (7)	0.4856 (7)	0.4354 (7)	0.038 (3)
O4	0.2364 (8)	0.5474 (9)	0.2076 (9)	0.057 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0315 (7)	0.0315 (7)	0.0315 (7)	−0.0010 (7)	0.0010 (7)	0.0010 (7)
K2	0.0250 (5)	0.0250 (5)	0.0250 (5)	−0.0021 (6)	0.0021 (6)	0.0021 (6)
Yb1	0.0116 (2)	0.0116 (2)	0.0116 (2)	0.0052 (4)	−0.0052 (4)	−0.0052 (4)
Ti1	0.0116 (2)	0.0116 (2)	0.0116 (2)	0.0052 (4)	−0.0052 (4)	−0.0052 (4)
Yb2	0.0106 (3)	0.0106 (3)	0.0106 (3)	−0.0006 (5)	0.0006 (5)	0.0006 (5)
Ti2	0.0106 (3)	0.0106 (3)	0.0106 (3)	−0.0006 (5)	0.0006 (5)	0.0006 (5)
P	0.0144 (7)	0.0201 (8)	0.0188 (8)	0.0016 (6)	0.0030 (6)	0.0005 (6)
O1	0.042 (4)	0.042 (4)	0.040 (3)	−0.012 (3)	0.004 (3)	−0.018 (3)
O2	0.041 (4)	0.075 (6)	0.051 (4)	0.036 (4)	0.005 (4)	0.017 (5)
O3	0.037 (3)	0.050 (4)	0.028 (3)	−0.005 (4)	−0.013 (3)	−0.007 (3)
O4	0.048 (5)	0.054 (5)	0.069 (6)	−0.011 (4)	0.037 (4)	−0.004 (4)

Geometric parameters (Å, º)

K1—K2	3.949 (3)	Yb1—O2	2.085 (8)
K1—O2	3.240 (9)	Ti1—O2	2.085 (8)
K1—O4	3.199 (9)	Ti1—O1^ii	2.087 (7)
K1—O3	2.902 (7)	Ti1—O2	2.085 (8)
K1—O3	2.902 (7)	Ti1—O1^iii	2.087 (7)
K1—O2	3.240 (9)	Ti1—O1^i	2.087 (7)
K1—O4	3.199 (9)	Ti1—O2	2.085 (8)
K1—O2^i	3.240 (9)	Yb2—O4	2.030 (8)
K1—O4^i	3.199 (9)	Yb2—O3	2.014 (7)
K1—O3	2.902 (7)	Yb2—O3^iv	2.014 (7)
K2—O1	2.882 (8)	Yb2—O4	2.030 (8)
K2—O2	3.112 (9)	Yb2—O3	2.014 (7)
K2—O4	3.023 (9)	Yb2—O4	2.030 (8)
K2—O2	3.112 (9)	Ti2—O4	2.030 (8)
K2—O4	3.023 (9)	Ti2—O3	2.014 (7)
K2—O1	2.882 (8)	Ti2—O3^iv	2.014 (7)
K2—O1^i	2.882 (8)	Ti2—O4	2.030 (8)
K2—O2	3.112 (9)	Ti2—O3	2.014 (7)
K2—O4	3.023 (9)	Ti2—O4	2.030 (8)
Yb1—O2	2.085 (8)	P—O1	1.513 (8)
Yb1—O1^ii	2.087 (7)	P—O2	1.515 (9)
Yb1—O2	2.085 (8)	P—O3	1.528 (7)
Yb1—O1^iii	2.087 (7)	P—O4	1.514 (9)
Yb1—O1^i	2.087 (7)
O2—K1—O4	44.4 (2)	O1^i—K2—O2	59.4 (2)
O2—K1—O3	101.5 (2)	O1^i—K2—O4	100.9 (2)
O2—K1—O3	164.2 (2)	O2—K2—O4	46.7 (2)
O2—K1—O2	87.9 (2)	O2—Yb1—O1^ii	91.1 (3)
O2—K1—O4	131.2 (2)	O2—Yb1—O2	89.7 (3)
O2—K1—O2^i	87.9 (2)	O2—Yb1—O1^iii	173.0 (3)
O2—K1—O4^i	81.9 (2)	O2—Yb1—O1^i	83.4 (3)
O2—K1—O3	79.9 (2)	O2—Yb1—O2	89.7 (3)
O4—K1—O3	57.1 (2)	O1^ii—Yb1—O2	83.4 (3)
O4—K1—O3	148.9 (2)	O1^ii—Yb1—O1^iii	95.9 (3)
O4—K1—O2	81.9 (2)	O1^ii—Yb1—O1^i	95.9 (3)
O4—K1—O4	118.8 (2)	O1^ii—Yb1—O2	173.0 (3)
O4—K1—O2^i	131.2 (2)	O2—Yb1—O1^iii	91.1 (3)
O4—K1—O4^i	118.8 (2)	O2—Yb1—O1^i	173.0 (3)
O4—K1—O3	82.4 (2)	O2—Yb1—O2	89.7 (3)
O3—K1—O3	92.8 (2)	O1^iii—Yb1—O1^i	95.9 (3)
O3—K1—O2	79.9 (2)	O1^iii—Yb1—O2	83.4 (3)
O3—K1—O4	82.4 (2)	O1^i—Yb1—O2	91.1 (3)
O3—K1—O2^i	164.2 (2)	O2—Ti1—O1^ii	91.1 (3)
O3—K1—O4^i	148.9 (2)	O2—Ti1—O2	89.7 (3)
O3—K1—O3	92.8 (2)	O2—Ti1—O1^iii	173.0 (3)
O3—K1—O2	101.5 (2)	O2—Ti1—O1^i	83.4 (3)
O3—K1—O4	57.1 (2)	O2—Ti1—O2	89.7 (3)
O3—K1—O2^i	79.9 (2)	O1^ii—Ti1—O2	83.4 (3)
O3—K1—O4^i	82.4 (2)	O1^ii—Ti1—O1^iii	95.9 (3)
O3—K1—O3	92.8 (2)	O1^ii—Ti1—O1^i	95.9 (3)
O2—K1—O4	44.4 (2)	O1^ii—Ti1—O2	173.0 (3)
O2—K1—O2^i	87.9 (2)	O2—Ti1—O1^iii	91.1 (3)
O2—K1—O4^i	131.2 (2)	O2—Ti1—O1^i	173.0 (3)
O2—K1—O3	164.2 (2)	O2—Ti1—O2	89.7 (3)
O4—K1—O2^i	81.9 (2)	O1^iii—Ti1—O1^i	95.9 (3)
O4—K1—O4^i	118.8 (2)	O1^iii—Ti1—O2	83.4 (3)
O4—K1—O3	148.9 (2)	O1^i—Ti1—O2	91.1 (3)
O2^i—K1—O4^i	44.4 (2)	O4—Yb2—O3	92.7 (3)
O2^i—K1—O3	101.5 (2)	O4—Yb2—O3^iv	87.1 (3)
O4^i—K1—O3	57.1 (2)	O4—Yb2—O4	86.2 (4)
O1—K2—O2	59.4 (2)	O4—Yb2—O3	173.2 (3)
O1—K2—O4	100.9 (2)	O4—Yb2—O4	86.2 (4)
O1—K2—O2	157.1 (2)	O3—Yb2—O3^iv	93.9 (3)
O1—K2—O4	151.6 (2)	O3—Yb2—O4	173.2 (3)
O1—K2—O1	97.7 (2)	O3—Yb2—O3	93.9 (3)
O1—K2—O1^i	97.7 (2)	O3—Yb2—O4	87.1 (3)
O1—K2—O2	85.6 (2)	O3^iv—Yb2—O4	92.7 (3)
O1—K2—O4	100.8 (2)	O3^iv—Yb2—O3	93.9 (3)
O2—K2—O4	46.7 (2)	O3^iv—Yb2—O4	173.2 (3)
O2—K2—O2	115.0 (2)	O4—Yb2—O3	87.1 (3)
O2—K2—O4	100.7 (2)	O4—Yb2—O4	86.2 (4)
O2—K2—O1	85.6 (2)	O3—Yb2—O4	92.7 (3)
O2—K2—O1^i	157.1 (2)	O4—Ti2—O3	92.7 (3)
O2—K2—O2	115.0 (2)	O4—Ti2—O3^iv	87.1 (3)
O2—K2—O4	85.5 (2)	O4—Ti2—O4	86.2 (4)
O4—K2—O2	85.5 (2)	O4—Ti2—O3	173.2 (3)
O4—K2—O4	54.6 (2)	O4—Ti2—O4	86.2 (4)
O4—K2—O1	100.8 (2)	O3—Ti2—O3^iv	93.9 (3)
O4—K2—O1^i	151.6 (2)	O3—Ti2—O4	173.2 (3)
O4—K2—O2	100.7 (2)	O3—Ti2—O3	93.9 (3)
O4—K2—O4	54.6 (2)	O3—Ti2—O4	87.1 (3)
O2—K2—O4	46.7 (2)	O3^iv—Ti2—O4	92.7 (3)
O2—K2—O1	59.4 (2)	O3^iv—Ti2—O3	93.9 (3)
O2—K2—O1^i	85.6 (2)	O3^iv—Ti2—O4	173.2 (3)
O2—K2—O2	115.0 (2)	O4—Ti2—O3	87.1 (3)
O2—K2—O4	100.7 (2)	O4—Ti2—O4	86.2 (4)
O4—K2—O1	100.9 (2)	O3—Ti2—O4	92.7 (3)
O4—K2—O1^i	100.8 (2)	O1—P—O2	108.7 (5)
O4—K2—O2	85.5 (2)	O1—P—O3	111.7 (4)
O4—K2—O4	54.6 (2)	O1—P—O4	110.5 (5)
O1—K2—O1^i	97.7 (2)	O2—P—O3	109.9 (4)
O1—K2—O2	157.1 (2)	O2—P—O4	107.0 (5)
O1—K2—O4	151.6 (2)	O3—P—O4	109.0 (4)

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

(KYTP)

Crystal data

K2YTiP3O12	Dx = 3.192 Mg m^−3
Mr = 499.89	Mo Kα radiation, λ = 0.71073 Å
Cubic, P213	Cell parameters from 18 reflections
Hall symbol: P 2ac 2ab 3	θ = 7.5–17.3°
a = 10.1318 (6) Å	µ = 7.65 mm^−1
V = 1040.06 (11) Å^3	T = 293 K
Z = 4	Tetrahedron, colourless
F(000) = 960	0.02 × 0.01 × 0.01 mm

Data collection

Enraf-Nonius CAD-4 diffractometer	701 reflections with F^2 > 2σ(F^2)
Radiation source: Fine-focus sealed tube	Rint = 0.107
Graphite monochromator	θmax = 29.9°, θmin = 3.5°
ω–2θ scans	h = −14→0
Absorption correction: analytical (Alcock, 1974)	k = −14→0
Tmin = 0.917, Tmax = 0.933	l = −14→14
3303 measured reflections	3 standard reflections every 120 min
1014 independent reflections	intensity decay: none

Refinement

Refinement on F^2	9 constraints
Least-squares matrix: full	w = 1/[σ^2(Fsqd) + 0.025(Fsqd)^2]
R[F^2 > 2σ(F^2)] = 0.047	(Δ/σ)max = 0.000038
wR(F^2) = 0.180	Δρmax = 1.65 e Å^−3
S = 1.19	Δρmin = −2.22 e Å^−3
1014 reflections	Absolute structure: Flack (1983) parameter refined
60 parameters	Absolute structure parameter: −0.10 (5)
0 restraints

Special details

Refinement. The following constraints were used during the refinement:

H-atom parameters constrained x(Ti1)=0.0 + 1.0*x(Y1) H-atom parameters constrained u11(Ti1)=0.0 + 1.0*u11(Y1) H-atom parameters constrained u12(Ti1)=0.0 + 1.0*u12(Y1) H-atom parameters constrained x(Ti2)=0.0 + 1.0*x(Y2) H-atom parameters constrained u11(Ti2)=0.0 + 1.0*u11(Y2) H-atom parameters constrained u12(Ti2)=0.0 + 1.0*u12(Y2) H-atom parameters constrained pop(Ti1)=1.0–1.0*pop(Y1) H-atom parameters constrained pop(Ti2)=0.0 + 1.0*pop(Y1) H-atom parameters constrained pop(Y2)=1.0–1.0*pop(Y1)

No restraints used.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0.2048 (4)	0.7048 (4)	0.7952 (4)	0.0317 (13)
K2	0.4309 (3)	0.9309 (3)	0.5691 (3)	0.0266 (11)
Y1	0.08346 (14)	0.91654 (14)	0.41654 (14)	0.0141 (8)	0.614 (18)
Ti1	0.08346 (14)	0.91654 (14)	0.41654 (14)	0.0141 (8)	0.386 (18)
Y2	0.14820 (15)	0.35180 (15)	0.64820 (15)	0.0127 (9)	0.386 (18)
Ti2	0.14820 (15)	0.35180 (15)	0.64820 (15)	0.0127 (9)	0.614 (18)
P	0.2659 (4)	0.6239 (3)	0.4618 (4)	0.0209 (17)
O1	0.4027 (15)	0.6537 (16)	0.5101 (15)	0.052 (8)
O2	0.182 (2)	0.7454 (15)	0.4782 (16)	0.062 (10)
O3	0.2653 (14)	0.5810 (13)	0.3180 (13)	0.042 (7)
O4	0.2050 (18)	0.5188 (18)	0.546 (2)	0.067 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0317 (13)	0.0317 (13)	0.0317 (13)	−0.0008 (14)	0.0008 (14)	0.0008 (14)
K2	0.0266 (11)	0.0266 (11)	0.0266 (11)	−0.0034 (12)	0.0034 (12)	0.0034 (12)
Y1	0.0141 (8)	0.0141 (8)	0.0141 (8)	0.0044 (17)	−0.0044 (17)	−0.0044 (17)
Ti1	0.0141 (8)	0.0141 (8)	0.0141 (8)	0.0044 (17)	−0.0044 (17)	−0.0044 (17)
Y2	0.0127 (9)	0.0127 (9)	0.0127 (9)	−0.0006 (18)	0.0006 (18)	0.0006 (18)
Ti2	0.0127 (9)	0.0127 (9)	0.0127 (9)	−0.0006 (18)	0.0006 (18)	0.0006 (18)
P	0.0248 (18)	0.0168 (16)	0.0211 (17)	0.0011 (13)	0.0007 (13)	0.0013 (13)
O1	0.045 (8)	0.061 (9)	0.049 (8)	−0.022 (7)	−0.018 (6)	0.005 (7)
O2	0.090 (13)	0.031 (7)	0.063 (10)	0.031 (8)	0.020 (9)	−0.000 (7)
O3	0.050 (8)	0.040 (7)	0.037 (7)	−0.006 (6)	−0.011 (5)	−0.014 (6)
O4	0.064 (11)	0.057 (10)	0.080 (12)	−0.015 (9)	−0.012 (9)	0.044 (9)

Geometric parameters (Å, º)

K1—K2	3.969 (5)	Y1—O1	2.100 (15)
K1—O2	3.246 (17)	Ti1—O2	2.097 (16)
K1—O4	3.15 (2)	Ti1—O1	2.100 (15)
K1—O3	2.921 (14)	Ti1—O1	2.100 (15)
K1—O3	2.921 (14)	Ti1—O2	2.097 (16)
K1—O2	3.246 (17)	Ti1—O2	2.097 (16)
K1—O4	3.15 (2)	Ti1—O1	2.100 (15)
K1—O2	3.246 (17)	Y2—O4	2.066 (18)
K1—O4	3.15 (2)	Y2—O3	2.047 (14)
K1—O3	2.921 (14)	Y2—O4	2.066 (18)
K2—O1	2.886 (17)	Y2—O3	2.047 (14)
K2—O2	3.146 (19)	Y2—O3^i	2.047 (14)
K2—O4	3.054 (19)	Y2—O4	2.066 (18)
K2—O1	2.886 (17)	Ti2—O4	2.066 (18)
K2—O2	3.146 (19)	Ti2—O3	2.047 (14)
K2—O4	3.054 (19)	Ti2—O4	2.066 (18)
K2—O2	3.146 (19)	Ti2—O3	2.047 (14)
K2—O4	3.054 (19)	Ti2—O3^i	2.047 (14)
K2—O1	2.886 (17)	Ti2—O4	2.066 (18)
Y1—O2	2.097 (16)	P—O1	1.501 (16)
Y1—O1	2.100 (15)	P—O2	1.504 (17)
Y1—O1	2.100 (15)	P—O3	1.520 (14)
Y1—O2	2.097 (16)	P—O4	1.497 (19)
Y1—O2	2.097 (16)
O2—K1—O4	44.2 (4)	O2—K2—O4	45.7 (5)
O2—K1—O3	102.2 (4)	O2—K2—O1	59.7 (4)
O2—K1—O3	80.6 (5)	O4—K2—O1	100.0 (5)
O2—K1—O2	87.3 (4)	O2—Y1—O1	91.7 (7)
O2—K1—O4	81.7 (5)	O2—Y1—O1	82.6 (6)
O2—K1—O2	87.3 (5)	O2—Y1—O2	89.7 (7)
O2—K1—O4	130.4 (5)	O2—Y1—O2	89.7 (7)
O2—K1—O3	164.2 (4)	O2—Y1—O1	172.2 (7)
O4—K1—O3	58.0 (4)	O1—Y1—O1	96.1 (6)
O4—K1—O3	82.5 (4)	O1—Y1—O2	172.2 (7)
O4—K1—O2	130.4 (5)	O1—Y1—O2	82.6 (6)
O4—K1—O4	118.6 (5)	O1—Y1—O1	96.1 (6)
O4—K1—O2	81.7 (5)	O1—Y1—O2	91.7 (7)
O4—K1—O4	118.6 (5)	O1—Y1—O2	172.2 (7)
O4—K1—O3	149.0 (5)	O1—Y1—O1	96.1 (6)
O3—K1—O3	91.9 (4)	O2—Y1—O2	89.7 (7)
O3—K1—O2	164.2 (4)	O2—Y1—O1	82.6 (6)
O3—K1—O4	149.0 (5)	O2—Y1—O1	91.7 (7)
O3—K1—O2	80.6 (5)	O2—Ti1—O1	91.7 (7)
O3—K1—O4	82.5 (4)	O2—Ti1—O1	82.6 (6)
O3—K1—O3	91.9 (4)	O2—Ti1—O2	89.7 (7)
O3—K1—O2	102.2 (4)	O2—Ti1—O2	89.7 (7)
O3—K1—O4	58.0 (4)	O2—Ti1—O1	172.2 (7)
O3—K1—O2	164.2 (4)	O1—Ti1—O1	96.1 (6)
O3—K1—O4	149.0 (5)	O1—Ti1—O2	172.2 (7)
O3—K1—O3	91.9 (4)	O1—Ti1—O2	82.6 (6)
O2—K1—O4	44.2 (4)	O1—Ti1—O1	96.1 (6)
O2—K1—O2	87.3 (4)	O1—Ti1—O2	91.7 (7)
O2—K1—O4	81.7 (5)	O1—Ti1—O2	172.2 (7)
O2—K1—O3	80.6 (5)	O1—Ti1—O1	96.1 (6)
O4—K1—O2	130.4 (5)	O2—Ti1—O2	89.7 (7)
O4—K1—O4	118.6 (5)	O2—Ti1—O1	82.6 (6)
O4—K1—O3	82.5 (4)	O2—Ti1—O1	91.7 (7)
O2—K1—O4	44.2 (4)	O4—Y2—O3	91.7 (7)
O2—K1—O3	102.2 (4)	O4—Y2—O4	87.5 (7)
O4—K1—O3	58.0 (4)	O4—Y2—O3	174.6 (7)
O1—K2—O2	59.7 (4)	O4—Y2—O3^i	87.1 (6)
O1—K2—O4	100.0 (5)	O4—Y2—O4	87.5 (7)
O1—K2—O1	97.2 (4)	O3—Y2—O4	87.1 (6)
O1—K2—O2	85.7 (4)	O3—Y2—O3	93.6 (5)
O1—K2—O4	101.5 (5)	O3—Y2—O3^i	93.6 (5)
O1—K2—O2	156.9 (4)	O3—Y2—O4	174.6 (7)
O1—K2—O4	152.7 (5)	O4—Y2—O3	91.7 (7)
O1—K2—O1	97.2 (4)	O4—Y2—O3^i	174.6 (7)
O2—K2—O4	45.7 (5)	O4—Y2—O4	87.5 (7)
O2—K2—O1	156.9 (4)	O3—Y2—O3^i	93.6 (5)
O2—K2—O2	115.0 (4)	O3—Y2—O4	87.1 (6)
O2—K2—O4	86.7 (5)	O3^i—Y2—O4	91.7 (7)
O2—K2—O2	115.0 (4)	O4—Ti2—O3	91.7 (7)
O2—K2—O4	100.5 (5)	O4—Ti2—O4	87.5 (7)
O2—K2—O1	85.7 (4)	O4—Ti2—O3	174.6 (7)
O4—K2—O1	152.7 (5)	O4—Ti2—O3^i	87.1 (6)
O4—K2—O2	100.5 (5)	O4—Ti2—O4	87.5 (7)
O4—K2—O4	55.8 (5)	O3—Ti2—O4	87.1 (6)
O4—K2—O2	86.7 (5)	O3—Ti2—O3	93.6 (5)
O4—K2—O4	55.8 (5)	O3—Ti2—O3^i	93.6 (5)
O4—K2—O1	101.5 (5)	O3—Ti2—O4	174.6 (7)
O1—K2—O2	59.7 (4)	O4—Ti2—O3	91.7 (7)
O1—K2—O4	100.0 (5)	O4—Ti2—O3^i	174.6 (7)
O1—K2—O2	85.7 (4)	O4—Ti2—O4	87.5 (7)
O1—K2—O4	101.5 (5)	O3—Ti2—O3^i	93.6 (5)
O1—K2—O1	97.2 (4)	O3—Ti2—O4	87.1 (6)
O2—K2—O4	45.7 (5)	O3^i—Ti2—O4	91.7 (7)
O2—K2—O2	115.0 (4)	O1—P—O2	108.7 (10)
O2—K2—O4	86.7 (5)	O1—P—O3	112.0 (8)
O2—K2—O1	156.9 (4)	O1—P—O4	109.7 (10)
O4—K2—O2	100.5 (5)	O2—P—O3	109.7 (9)
O4—K2—O4	55.8 (5)	O2—P—O4	106.6 (10)
O4—K2—O1	152.7 (5)	O3—P—O4	109.9 (9)

Symmetry code: (i) z, x, y.

(KCrTP)

Crystal data

K2CrTiP3O12	Dx = 3.267 Mg m^−3
Mr = 462.98	Mo Kα radiation, λ = 0.71073 Å
Cubic, P213	Cell parameters from 23 reflections
Hall symbol: P 2ac 2ab 3	θ = 31.3–34.9°
a = 9.8001 (2) Å	µ = 3.47 mm^−1
V = 941.22 (4) Å^3	T = 293 K
Z = 4	Tetrahedron, green
F(000) = 900	0.09 × 0.09 × 0.07 mm

Data collection

Enraf-Nonius CAD-4 diffractometer	1346 reflections with F^2 > 2σ(F^2)
Radiation source: Fine-focus sealed tube	Rint = 0.027
Graphite monochromator	θmax = 35.0°, θmin = 3.6°
ω–2θ scans	h = −15→0
Absorption correction: analytical (Alcock, 1974)	k = −15→0
Tmin = 0.759, Tmax = 0.813	l = −15→15
4496 measured reflections	3 standard reflections every 120 min
1394 independent reflections	intensity decay: none

Refinement

Refinement on F^2	w = 1/[σ^2(Fsqd) + 0.0035(Fsqd)^2]
Least-squares matrix: full	(Δ/σ)max = 0.00016
R[F^2 > 2σ(F^2)] = 0.016	Δρmax = 0.42 e Å^−3
wR(F^2) = 0.052	Δρmin = −0.47 e Å^−3
S = 1.05	Extinction correction: Isotropic Gaussian, Zachariasen, 1967; Larson (1970), Eq22 p292 "Cryst. Comp." Munksgaard 1970
1394 reflections	Extinction coefficient: 114 (19) × 10^2
61 parameters	Absolute structure: Flack (1983) parameter refined
0 restraints	Absolute structure parameter: 0.02 (2)
9 constraints

Special details

Refinement. The following constraints were used during the refinement:

H-atom parameters constrained x(Ti1)=0.0 + 1.0*x(Cr1) H-atom parameters constrained u11(Ti1)=0.0 + 1.0*u11(Cr1) H-atom parameters constrained u12(Ti1)=0.0 + 1.0*u12(Cr1) H-atom parameters constrained x(Ti2)=0.0 + 1.0*x(Cr2) H-atom parameters constrained u11(Ti2)=0.0 + 1.0*u11(Cr2) H-atom parameters constrained u12(Ti2)=0.0 + 1.0*u12(Cr2) H-atom parameters constrained pop(Ti1)=1.0–1.0*pop(Cr1) H-atom parameters constrained pop(Ti2)=0.0 + 1.0*pop(Cr1) H-atom parameters constrained pop(Cr2)=1.0–1.0*pop(Cr1)

No restraints used.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0.04267 (6)	0.54267 (6)	−0.04267 (6)	0.02127 (17)
K2	−0.18241 (5)	0.31759 (5)	0.18241 (5)	0.01717 (15)
Cr1	−0.16346 (3)	0.66346 (3)	0.33654 (3)	0.00506 (11)	0.388 (17)
Ti1	−0.16346 (3)	0.66346 (3)	0.33654 (3)	0.00506 (11)	0.612 (17)
Cr2	0.39336 (3)	0.60664 (3)	0.10664 (3)	0.00519 (11)	0.612 (17)
Ti2	0.39336 (3)	0.60664 (3)	0.10664 (3)	0.00519 (11)	0.388 (17)
P	0.12393 (4)	0.47720 (4)	0.29292 (4)	0.00488 (17)
O1	0.10088 (16)	0.32849 (14)	0.25110 (16)	0.0121 (5)
O2	−0.01088 (15)	0.55333 (16)	0.27003 (17)	0.0136 (6)
O3	0.17127 (15)	0.48624 (14)	0.44146 (14)	0.0106 (5)
O4	0.22865 (15)	0.54768 (15)	0.20204 (15)	0.0131 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.02127 (17)	0.02127 (17)	0.02127 (17)	0.00006 (17)	−0.00006 (17)	−0.00006 (17)
K2	0.01717 (15)	0.01717 (15)	0.01717 (15)	−0.00182 (13)	0.00182 (13)	0.00182 (13)
Cr1	0.00506 (11)	0.00506 (11)	0.00506 (11)	0.0002 (2)	−0.0002 (2)	−0.0002 (2)
Ti1	0.00506 (11)	0.00506 (11)	0.00506 (11)	0.0002 (2)	−0.0002 (2)	−0.0002 (2)
Cr2	0.00519 (11)	0.00519 (11)	0.00519 (11)	−0.0006 (2)	0.0006 (2)	0.0006 (2)
Ti2	0.00519 (11)	0.00519 (11)	0.00519 (11)	−0.0006 (2)	0.0006 (2)	0.0006 (2)
P	0.00481 (16)	0.00516 (16)	0.00468 (17)	0.00033 (12)	0.00082 (12)	−0.00012 (12)
O1	0.0163 (6)	0.0066 (5)	0.0134 (5)	0.0002 (5)	0.0022 (5)	−0.0042 (4)
O2	0.0102 (5)	0.0151 (6)	0.0157 (6)	0.0079 (5)	0.0002 (5)	−0.0002 (5)
O3	0.0134 (5)	0.0131 (6)	0.0051 (5)	−0.0037 (5)	−0.0010 (4)	0.0005 (4)
O4	0.0130 (6)	0.0154 (6)	0.0109 (5)	−0.0055 (5)	0.0060 (4)	0.0008 (5)

Geometric parameters (Å, º)

K1—K2	3.8205 (7)	Cr1—O2	1.9559 (15)
K1—O2	3.1108 (17)	Ti1—O2	1.9559 (15)
K1—O4	3.0126 (16)	Ti1—O1^ii	1.9312 (14)
K1—O3	2.8220 (15)	Ti1—O2	1.9559 (15)
K1—O3	2.8220 (15)	Ti1—O1^iii	1.9312 (14)
K1—O2	3.1108 (17)	Ti1—O1^i	1.9312 (14)
K1—O4	3.0126 (16)	Ti1—O2	1.9559 (15)
K1—O2^i	3.1108 (17)	Cr2—O4	1.9528 (15)
K1—O4^i	3.0126 (16)	Cr2—O3	1.9622 (14)
K1—O3	2.8220 (15)	Cr2—O3^iv	1.9622 (14)
K2—O1	2.8588 (16)	Cr2—O4	1.9528 (15)
K2—O2	2.9834 (16)	Cr2—O3	1.9622 (14)
K2—O4	2.9128 (16)	Cr2—O4	1.9528 (15)
K2—O4	2.9128 (16)	Ti2—O4	1.9528 (15)
K2—O1	2.8588 (16)	Ti2—O3	1.9622 (14)
K2—O2	2.9834 (16)	Ti2—O3^iv	1.9622 (14)
K2—O1^i	2.8588 (16)	Ti2—O4	1.9528 (15)
K2—O2^i	2.9834 (16)	Ti2—O3	1.9622 (14)
K2—O4	2.9128 (16)	Ti2—O4	1.9528 (15)
Cr1—O2	1.9559 (15)	P—O1	1.5307 (14)
Cr1—O1^ii	1.9312 (14)	P—O2	1.5338 (15)
Cr1—O2	1.9559 (15)	P—O3	1.5304 (14)
Cr1—O1^iii	1.9312 (14)	P—O4	1.5244 (16)
Cr1—O1^i	1.9312 (14)
O2—K1—O4	46.95 (4)	O1^i—K2—O2^i	49.92 (4)
O2—K1—O3	103.02 (4)	O1^i—K2—O4	95.36 (4)
O2—K1—O3	163.71 (5)	O2^i—K2—O4	132.77 (5)
O2—K1—O2	82.68 (4)	O2—Cr1—O1^ii	94.08 (6)
O2—K1—O4	128.72 (4)	O2—Cr1—O2	90.96 (7)
O2—K1—O2^i	82.68 (4)	O2—Cr1—O1^iii	172.52 (7)
O2—K1—O4^i	82.04 (4)	O2—Cr1—O1^i	83.44 (7)
O2—K1—O3	82.94 (4)	O2—Cr1—O2	90.96 (7)
O4—K1—O3	56.25 (4)	O1^ii—Cr1—O2	83.44 (7)
O4—K1—O3	148.28 (5)	O1^ii—Cr1—O1^iii	91.99 (6)
O4—K1—O2	82.04 (4)	O1^ii—Cr1—O1^i	91.99 (6)
O4—K1—O4	118.99 (4)	O1^ii—Cr1—O2	172.52 (7)
O4—K1—O2^i	128.72 (4)	O2—Cr1—O1^iii	94.08 (7)
O4—K1—O4^i	118.99 (4)	O2—Cr1—O1^i	172.52 (6)
O4—K1—O3	82.56 (4)	O2—Cr1—O2	90.96 (7)
O3—K1—O3	92.89 (4)	O1^iii—Cr1—O1^i	91.99 (6)
O3—K1—O2	82.94 (4)	O1^iii—Cr1—O2	83.44 (7)
O3—K1—O4	82.56 (4)	O1^i—Cr1—O2	94.08 (7)
O3—K1—O2^i	163.71 (4)	O2—Ti1—O1^ii	94.08 (6)
O3—K1—O4^i	148.28 (5)	O2—Ti1—O2	90.96 (7)
O3—K1—O3	92.89 (4)	O2—Ti1—O1^iii	172.52 (7)
O3—K1—O2	103.02 (4)	O2—Ti1—O1^i	83.44 (7)
O3—K1—O4	56.25 (4)	O2—Ti1—O2	90.96 (7)
O3—K1—O2^i	82.94 (4)	O1^ii—Ti1—O2	83.44 (7)
O3—K1—O4^i	82.56 (4)	O1^ii—Ti1—O1^iii	91.99 (6)
O3—K1—O3	92.89 (4)	O1^ii—Ti1—O1^i	91.99 (6)
O2—K1—O4	46.95 (4)	O1^ii—Ti1—O2	172.52 (7)
O2—K1—O2^i	82.68 (4)	O2—Ti1—O1^iii	94.08 (7)
O2—K1—O4^i	128.72 (4)	O2—Ti1—O1^i	172.52 (6)
O2—K1—O3	163.71 (4)	O2—Ti1—O2	90.96 (7)
O4—K1—O2^i	82.04 (4)	O1^iii—Ti1—O1^i	91.99 (6)
O4—K1—O4^i	118.99 (4)	O1^iii—Ti1—O2	83.44 (7)
O4—K1—O3	148.28 (5)	O1^i—Ti1—O2	94.08 (7)
O2^i—K1—O4^i	46.95 (4)	O4—Cr2—O3	89.48 (6)
O2^i—K1—O3	103.02 (4)	O4—Cr2—O3^iv	89.13 (6)
O4^i—K1—O3	56.25 (4)	O4—Cr2—O4	89.46 (6)
O1—K2—O2	49.92 (4)	O4—Cr2—O3	178.24 (7)
O1—K2—O4	95.36 (4)	O4—Cr2—O4	89.46 (6)
O1—K2—O4	149.29 (5)	O3—Cr2—O3^iv	91.91 (6)
O1—K2—O1	101.61 (4)	O3—Cr2—O4	178.24 (6)
O1—K2—O2	52.51 (4)	O3—Cr2—O3	91.91 (6)
O1—K2—O1^i	101.61 (4)	O3—Cr2—O4	89.13 (6)
O1—K2—O2^i	116.16 (5)	O3^iv—Cr2—O4	89.48 (6)
O1—K2—O4	99.76 (4)	O3^iv—Cr2—O3	91.91 (6)
O2—K2—O4	132.77 (5)	O3^iv—Cr2—O4	178.24 (7)
O2—K2—O4	140.17 (4)	O4—Cr2—O3	89.13 (6)
O2—K2—O1	116.16 (5)	O4—Cr2—O4	89.46 (6)
O2—K2—O2	87.06 (4)	O3—Cr2—O4	89.48 (6)
O2—K2—O1^i	52.51 (4)	O4—Ti2—O3	89.48 (6)
O2—K2—O2^i	87.06 (4)	O4—Ti2—O3^iv	89.13 (6)
O2—K2—O4	94.48 (4)	O4—Ti2—O4	89.46 (6)
O4—K2—O4	56.30 (4)	O4—Ti2—O3	178.24 (7)
O4—K2—O1	99.76 (4)	O4—Ti2—O4	89.46 (6)
O4—K2—O2	94.48 (4)	O3—Ti2—O3^iv	91.91 (6)
O4—K2—O1^i	149.29 (5)	O3—Ti2—O4	178.24 (6)
O4—K2—O2^i	140.17 (4)	O3—Ti2—O3	91.91 (6)
O4—K2—O4	56.30 (4)	O3—Ti2—O4	89.13 (6)
O4—K2—O1	95.36 (4)	O3^iv—Ti2—O4	89.48 (6)
O4—K2—O2	132.77 (5)	O3^iv—Ti2—O3	91.91 (6)
O4—K2—O1^i	99.76 (4)	O3^iv—Ti2—O4	178.24 (7)
O4—K2—O2^i	94.48 (4)	O4—Ti2—O3	89.13 (6)
O4—K2—O4	56.30 (4)	O4—Ti2—O4	89.46 (6)
O1—K2—O2	49.92 (4)	O3—Ti2—O4	89.48 (6)
O1—K2—O1^i	101.61 (4)	O1—P—O2	107.27 (9)
O1—K2—O2^i	52.51 (4)	O1—P—O3	110.76 (8)
O1—K2—O4	149.29 (4)	O1—P—O4	111.98 (8)
O2—K2—O1^i	116.16 (5)	O2—P—O3	111.85 (8)
O2—K2—O2^i	87.06 (4)	O2—P—O4	105.90 (9)
O2—K2—O4	140.17 (4)	O3—P—O4	108.99 (8)

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