Cation movement and phase transitions in KTP isostructures; X-ray study of sodium-doped KTP at 10.5 K

An accurate structure model of sodium-doped potassium titanyl phosphate, (Na_0.114K_0.886)K(TiO)₂(PO₄)₂, has been determined at 10.5 K by single-crystal X-ray diffraction. In addition to the low-temperature data, X-ray intensities have been collected at room temperature. When the temperature was decreased from room temperature to 10.5 K, both potassium cations moved 0.033 (2) Å along the c-axis, i.e. in the polar direction within the rigid Ti-O-P network. This alkaline metal ion displacement can be related to the Abrahams-Jamieson-Kurtz T_C criteria for oxygen framework ferroelectrics. Potassium titanyl phosphate (KTP) is a well known material for second harmonic generation (SHG), and the influence of sodium dopant on the TiO₆ octahedral geometry and SHG is discussed. The material studied crystallizes in the space group Pna2₁ with Z = 4, a = 12.7919 (5), b = 6.3798 (4), c = 10.5880 (7) Å, V = 864.08 (9) Å³, T = 10.5 (3) K and R = 0.023.

Computing details

For both compounds, data collection: Local diffractometer control software; cell refinement: Local diffractometer control software; data reduction: PROFIT (Streltsov & Zavodnik, 1989) and Xtal3.71 (Hall et al., 2000) programs: DIFDAT; SORTRF; ADDREF; ABSORB; program(s) used to solve structure: Atomic parameters from Norberg et al. (2000); program(s) used to refine structure: Xtal3.71 (Hall et al., 2000) program: CRYLSQ; molecular graphics: ORTEPIII for Windows (Farrugia, 1997), and Xtal3.71 (Hall et al., 2000) programs: FOURR; SLANT; CONTRS; software used to prepare material for publication: Xtal3.71 (Hall et al., 2000) programs: BONDLA; ATABLE; CIFIO.

(10K)

Crystal data

K1.886Na0.114O10P2Ti2	F(000) = 764.5
Mr = 394.06	Dx = 3.029 Mg m^−3
Orthorhombic, Pna21	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: p 2c -2n	Cell parameters from 28 reflections
a = 12.7919 (5) Å	θ = 19.5–38.3°
b = 6.3798 (4) Å	µ = 3.18 mm^−1
c = 10.5880 (7) Å	T = 11 K
V = 864.08 (9) Å^3	Prism, colourless
Z = 4	0.30 × 0.30 × 0.21 mm

Data collection

Huber 512 goniometer diffractometer	8961 reflections with F > 0σ(F)
Radiation source: normal-focus sealed tube	Rint = 0.017
None monochromator	θmax = 50.1°, θmin = 3.2°
ω–2θ scans	h = −15→27
Absorption correction: analytical (Alcock, 1974)	k = −11→13
Tmin = 0.389, Tmax = 0.521	l = −22→22
16753 measured reflections	3 standard reflections every 100 reflections
8961 independent reflections	intensity decay: 0.1%

Refinement

Refinement on F	w = 1/[σ^2(F) + 0.0015(F)^2]
Least-squares matrix: full	(Δ/σ)max = 0.001
R[F^2 > 2σ(F^2)] = 0.017	Δρmax = 1.67 e Å^−3
wR(F^2) = 0.037	Δρmin = −1.54 e Å^−3
S = 1.18	Extinction correction: Isotropic Gaussian (Zachariasen, 1967), Larson, 1970, Eq22 p292 "Cryst. Comp." Munksgaard 1970
8961 reflections	Extinction coefficient: 53E2 (2)
156 parameters	Absolute structure: Flack (1983) parameter refined
0 restraints	Absolute structure parameter: 0.508 (13)
1 constraint

Special details

Experimental. The correction for the absorption by the beryllium thermal shields was carried out with PROFIT (Streltsov & Zavodnik, 1989) program.

Refinement. The following constraints were used during the refinement:

H-atom parameters constrained pop(Na1)=1.0–1.0*pop(K1)

No restraints used.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0.37665 (3)	0.22060 (4)	0.30013 (4)	0.00501 (10)	0.886 (3)
Na1	0.3435 (6)	0.2317 (7)	0.2723 (6)	0.0067 (18)	0.114 (3)
K2	0.104799 (18)	0.30202 (4)	0.05454 (4)	0.00607 (7)
Ti1	0.373144 (12)	0.50094 (2)	−0.00824 (4)	0.00264 (5)
Ti2	0.246260 (12)	0.73089 (3)	0.24322 (4)	0.00265 (5)
P1	0.49765 (2)	0.66341 (4)	0.25211 (5)	0.00294 (8)
P2	0.18144 (2)	0.49851 (4)	0.50443 (5)	0.00284 (9)
O1	0.48538 (7)	0.51197 (12)	0.14237 (9)	0.0047 (2)
O2	0.50893 (6)	0.53385 (13)	0.37516 (9)	0.0046 (2)
O3	0.39995 (6)	0.80223 (13)	0.27100 (9)	0.0046 (2)
O4	0.59339 (6)	0.80653 (12)	0.23296 (9)	0.0047 (2)
O11	0.27502 (6)	0.53280 (13)	0.13510 (8)	0.0045 (2)
O12	0.22370 (6)	0.96044 (13)	0.38101 (8)	0.0046 (2)
O5	0.11282 (6)	0.69039 (12)	0.53248 (9)	0.0042 (2)
O6	0.11135 (6)	0.30862 (12)	0.47983 (9)	0.0047 (2)
O7	0.25356 (6)	0.46234 (14)	0.61972 (9)	0.0046 (2)
O8	0.25368 (6)	0.53840 (15)	0.3910 (6)	0.0048 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.00598 (12)	0.00376 (8)	0.00530 (11)	−0.00074 (5)	0.00085 (8)	−0.00008 (6)
Na1	0.010 (2)	0.0036 (14)	0.0066 (17)	0.0002 (12)	−0.0021 (18)	−0.0018 (12)
K2	0.00511 (6)	0.00640 (6)	0.00670 (8)	−0.00123 (5)	0.00005 (5)	−0.00003 (6)
Ti1	0.00294 (5)	0.00232 (5)	0.00266 (6)	0.00003 (3)	−0.00010 (4)	−0.00010 (4)
Ti2	0.00290 (5)	0.00257 (5)	0.00248 (5)	0.00006 (3)	0.00005 (4)	−0.00013 (4)
P1	0.00296 (7)	0.00304 (7)	0.00282 (9)	0.00004 (6)	−0.00011 (6)	−0.00019 (7)
P2	0.00368 (8)	0.00220 (8)	0.00262 (10)	0.00010 (5)	0.00005 (7)	0.00017 (5)
O1	0.0048 (2)	0.0050 (2)	0.0043 (3)	0.00094 (17)	−0.00069 (19)	−0.00161 (18)
O2	0.0049 (2)	0.0053 (2)	0.0036 (2)	−0.00009 (18)	−0.00063 (17)	0.0012 (2)
O3	0.0036 (2)	0.0044 (2)	0.0059 (2)	0.00048 (16)	−0.00007 (18)	−0.0007 (2)
O4	0.0038 (2)	0.0043 (2)	0.0061 (3)	−0.00028 (15)	−0.00008 (18)	0.0001 (2)
O11	0.0054 (2)	0.0045 (2)	0.0037 (2)	0.00012 (18)	0.00098 (18)	−0.0007 (2)
O12	0.0041 (2)	0.0050 (2)	0.0047 (2)	0.00008 (17)	0.00096 (17)	−0.0006 (2)
O5	0.0050 (2)	0.0025 (2)	0.0051 (2)	0.00030 (16)	0.00069 (18)	−0.00018 (18)
O6	0.0054 (2)	0.0027 (2)	0.0059 (3)	−0.00112 (16)	−0.00034 (18)	−0.0004 (2)
O7	0.0049 (2)	0.0049 (2)	0.0040 (3)	−0.00052 (17)	−0.00083 (16)	0.0003 (2)
O8	0.0053 (2)	0.0058 (2)	0.0034 (2)	0.00012 (17)	0.00126 (16)	0.0011 (2)

Geometric parameters (Å, º)

K1—O1	2.8601 (10)	K2—O5	2.7940 (8)
K1—O2	2.7365 (9)	K2—O7	2.9078 (9)
K1—O3	2.7034 (9)	K2—O8	3.017 (4)
K1—O11	2.9513 (9)	Ti1—O1	2.1469 (10)
K1—O12	2.7048 (9)	Ti1—O2	1.9619 (9)
K1—O5	2.8437 (10)	Ti1—O11	1.9800 (9)
K1—O7	3.0229 (9)	Ti1—O12	1.7253 (9)
K1—O8	2.741 (2)	Ti1—O5	2.0356 (8)
K1—Na1	0.521 (7)	Ti1—O6	1.9769 (8)
Na1—O1	2.896 (6)	Ti2—O3	2.0393 (8)
Na1—O2	3.063 (7)	Ti2—O4	1.9730 (8)
Na1—O3	2.833 (5)	Ti2—O11	1.7444 (9)
Na1—O11	2.563 (6)	Ti2—O12	2.0872 (9)
Na1—O12	2.582 (6)	Ti2—O7	1.9723 (10)
Na1—O5	2.613 (6)	Ti2—O8	1.992 (5)
Na1—O7	2.665 (6)	P1—O1	1.5193 (10)
Na1—O8	2.594 (7)	P1—O2	1.5497 (10)
K2—O1	2.6854 (9)	P1—O3	1.5447 (8)
K2—O2	2.9412 (9)	P1—O4	1.5410 (8)
K2—O3	3.0027 (11)	P2—O5	1.5354 (8)
K2—O4	3.1348 (9)	P2—O6	1.5296 (8)
K2—O11	2.7635 (9)	P2—O7	1.5474 (10)
K2—O12	3.0348 (9)	P2—O8	1.536 (5)
O1—K1—O2	52.71 (3)	O5—K2—O7	130.81 (2)
O1—K1—O11	55.24 (2)	O5—K2—O8	124.02 (7)
O1—K1—O8	90.19 (8)	O5—K2—O1	58.34 (3)
O1—K1—O3	121.43 (3)	O5—K2—O4	89.44 (2)
O1—K1—O12	159.31 (3)	O2—K2—O3	49.05 (2)
O1—K1—O5	55.87 (3)	O2—K2—O12	99.23 (3)
O1—K1—O7	104.66 (3)	O2—K2—O7	91.60 (3)
O2—K1—O11	87.21 (2)	O2—K2—O8	66.55 (6)
O2—K1—O8	73.30 (4)	O2—K2—O1	60.55 (3)
O2—K1—O3	133.31 (3)	O2—K2—O4	146.05 (2)
O2—K1—O12	143.47 (3)	O3—K2—O12	53.79 (2)
O2—K1—O5	108.03 (3)	O3—K2—O7	104.49 (3)
O2—K1—O7	157.25 (3)	O3—K2—O8	55.85 (10)
O11—K1—O8	57.03 (13)	O3—K2—O1	109.57 (3)
O11—K1—O3	130.34 (3)	O3—K2—O4	126.96 (2)
O11—K1—O12	106.44 (3)	O12—K2—O7	86.64 (2)
O11—K1—O5	58.44 (2)	O12—K2—O8	53.45 (5)
O11—K1—O7	75.58 (3)	O12—K2—O1	150.38 (3)
O8—K1—O3	146.49 (5)	O12—K2—O4	97.65 (2)
O8—K1—O12	85.85 (5)	O7—K2—O8	49.22 (10)
O8—K1—O5	115.30 (13)	O7—K2—O1	73.52 (3)
O8—K1—O7	107.99 (8)	O7—K2—O4	118.67 (3)
O3—K1—O12	60.66 (3)	O8—K2—O1	97.13 (4)
O3—K1—O5	79.29 (3)	O8—K2—O4	144.87 (4)
O3—K1—O7	56.67 (3)	O1—K2—O4	111.05 (3)
O12—K1—O5	107.95 (3)	O1—Ti1—O11	81.44 (4)
O12—K1—O7	57.79 (3)	O1—Ti1—O2	87.53 (4)
O5—K1—O7	50.16 (2)	O1—Ti1—O12	171.87 (4)
O1—Na1—O2	49.24 (11)	O1—Ti1—O5	79.37 (3)
O1—Na1—O11	58.80 (12)	O1—Ti1—O6	87.01 (3)
O1—Na1—O8	92.40 (16)	O11—Ti1—O2	168.94 (4)
O1—Na1—O3	115.8 (2)	O11—Ti1—O12	94.66 (4)
O1—Na1—O12	176.1 (2)	O11—Ti1—O5	89.63 (4)
O1—Na1—O5	57.76 (13)	O11—Ti1—O6	90.61 (4)
O1—Na1—O7	113.7 (2)	O2—Ti1—O12	96.17 (4)
O2—Na1—O11	88.04 (15)	O2—Ti1—O5	87.44 (4)
O2—Na1—O8	70.05 (13)	O2—Ti1—O6	89.71 (4)
O2—Na1—O3	115.7 (2)	O12—Ti1—O5	93.53 (4)
O2—Na1—O12	132.3 (2)	O12—Ti1—O6	100.22 (4)
O2—Na1—O5	105.1 (2)	O5—Ti1—O6	166.19 (4)
O2—Na1—O7	160.6 (3)	O3—Ti2—O11	93.04 (4)
O11—Na1—O8	63.76 (18)	O3—Ti2—O12	82.87 (3)
O11—Na1—O3	144.0 (2)	O3—Ti2—O8	88.76 (4)
O11—Na1—O12	123.5 (3)	O3—Ti2—O7	85.84 (3)
O11—Na1—O5	66.29 (14)	O3—Ti2—O4	172.07 (4)
O11—Na1—O7	88.9 (2)	O11—Ti2—O12	174.99 (4)
O8—Na1—O3	147.6 (3)	O11—Ti2—O8	93.38 (12)
O8—Na1—O12	91.5 (2)	O11—Ti2—O7	96.15 (4)
O8—Na1—O5	129.9 (3)	O11—Ti2—O4	94.89 (4)
O8—Na1—O7	125.0 (3)	O12—Ti2—O8	83.68 (12)
O3—Na1—O12	60.36 (11)	O12—Ti2—O7	86.46 (4)
O3—Na1—O5	80.99 (15)	O12—Ti2—O4	89.22 (3)
O3—Na1—O7	59.50 (11)	O8—Ti2—O7	169.28 (12)
O12—Na1—O5	119.5 (2)	O8—Ti2—O4	90.91 (4)
O12—Na1—O7	64.01 (14)	O7—Ti2—O4	93.17 (3)
O5—Na1—O7	56.34 (12)	O1—P1—O2	108.27 (5)
O11—K2—O5	143.29 (3)	O1—P1—O3	112.34 (5)
O11—K2—O2	154.02 (3)	O1—P1—O4	111.00 (5)
O11—K2—O3	108.92 (3)	O2—P1—O3	105.80 (5)
O11—K2—O12	55.93 (2)	O2—P1—O4	110.65 (5)
O11—K2—O7	80.38 (3)	O3—P1—O4	108.68 (4)
O11—K2—O8	90.08 (5)	O5—P2—O6	109.22 (5)
O11—K2—O1	137.63 (3)	O5—P2—O7	107.89 (5)
O11—K2—O4	54.99 (2)	O5—P2—O8	111.29 (6)
O5—K2—O2	57.54 (2)	O6—P2—O7	111.45 (5)
O5—K2—O3	84.04 (3)	O6—P2—O8	110.53 (13)
O5—K2—O12	131.59 (3)	O7—P2—O8	106.42 (15)

(RT)

Crystal data

K1.886Na0.114O10P2Ti2	F(000) = 764.5
Mr = 394.06	Dx = 3.021 Mg m^−3
Orthorhombic, Pna21	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: p 2c -2n	Cell parameters from 14 reflections
a = 12.806 (1) Å	θ = 19.5–23.7°
b = 6.3889 (6) Å	µ = 3.17 mm^−1
c = 10.588 (1) Å	T = 293 K
V = 866.27 (13) Å^3	Prism, colourless
Z = 4	0.30 × 0.30 × 0.21 mm

Data collection

Huber 512 goniometer diffractometer	1539 reflections with F > 0σ(F)
Radiation source: normal-focus sealed tube	Rint = 0.018
None monochromator	θmax = 25.1°, θmin = 3.2°
ω–2θ scans	h = −15→15
Absorption correction: analytical (Alcock, 1974)	k = −7→7
Tmin = 0.428, Tmax = 0.513	l = −12→12
5704 measured reflections	3 standard reflections every 100 reflections
1539 independent reflections	intensity decay: 0.1%

Refinement

Refinement on F	w = 1/[σ^2(F) + 0.001(F)^2]
Least-squares matrix: full	(Δ/σ)max = 0.00023
R[F^2 > 2σ(F^2)] = 0.016	Δρmax = 0.52 e Å^−3
wR(F^2) = 0.024	Δρmin = −0.34 e Å^−3
S = 1.12	Extinction correction: Isotropic Gaussian (Zachariasen, 1967), Larson, 1970, Eq22 p292 "Cryst. Comp." Munksgaard 1970
1539 reflections	Extinction coefficient: 41E2 (3)
150 parameters	Absolute structure: Flack (1983) parameter refined
0 restraints	Absolute structure parameter: 0.55 (3)
1 constraint

Special details

Experimental. The correction for the absorption by the beryllium thermal shields was carried out with PROFIT (Streltsov & Zavodnik, 1989) program.

Refinement. The following constraints were used during the refinement:

H-atom parameters constrained pop(Na1)=1.0–1.0*pop(K1)

The population of Na1 was constrained to be the same as determined for the more extended low temperature data. Refinement with a non-constrained population parameter for Na1 resulted in an enlarged U_eq of 0.043 (10) Ų and a population parameter of 0.079 (7).

No restraints used.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0.37854 (13)	0.21969 (16)	0.3025 (2)	0.0186 (6)	0.886 (3)
Na1	0.3478 (14)	0.223 (3)	0.284 (2)	0.024 (7)*	0.114 (3)
K2	0.10443 (6)	0.30340 (12)	0.05659 (14)	0.0210 (4)
Ti1	0.37298 (4)	0.50080 (6)	−0.00944 (15)	0.0053 (3)
Ti2	0.24661 (3)	0.73115 (7)	0.24212 (15)	0.0052 (3)
P1	0.49783 (4)	0.66329 (11)	0.25090 (15)	0.0059 (4)
P2	0.18138 (6)	0.49843 (8)	0.50313 (15)	0.0062 (4)
O1	0.4856 (2)	0.5134 (4)	0.1409 (3)	0.0106 (11)
O2	0.50984 (19)	0.5344 (4)	0.3738 (2)	0.0104 (11)
O3	0.40038 (17)	0.8024 (3)	0.2705 (2)	0.0088 (10)
O4	0.59358 (15)	0.8069 (3)	0.2318 (2)	0.0090 (10)
O11	0.2750 (2)	0.5344 (4)	0.1339 (2)	0.0084 (10)
O12	0.2234 (2)	0.9602 (4)	0.3803 (2)	0.0089 (10)
O5	0.11302 (16)	0.6893 (3)	0.5316 (2)	0.0089 (10)
O6	0.11145 (16)	0.3093 (3)	0.4779 (2)	0.0096 (10)
O7	0.25309 (18)	0.4611 (4)	0.6184 (2)	0.0089 (11)
O8	0.25372 (18)	0.5397 (4)	0.390 (2)	0.0088 (12)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0223 (6)	0.0096 (5)	0.0239 (6)	−0.0042 (4)	0.0068 (6)	−0.0012 (4)
K2	0.0146 (3)	0.0211 (4)	0.0273 (4)	−0.0065 (3)	−0.0000 (3)	0.0004 (4)
Ti1	0.0068 (3)	0.0045 (3)	0.0045 (3)	0.00009 (13)	−0.0005 (2)	−0.00077 (18)
Ti2	0.0061 (3)	0.0051 (3)	0.0045 (3)	0.00063 (15)	0.00038 (15)	−0.0001 (2)
P1	0.0053 (4)	0.0067 (4)	0.0056 (4)	−0.0003 (2)	−0.0004 (2)	−0.0009 (4)
P2	0.0086 (4)	0.0045 (4)	0.0057 (4)	0.0003 (2)	0.0010 (3)	0.0006 (2)
O1	0.0092 (12)	0.0120 (11)	0.0105 (10)	0.0035 (7)	−0.0027 (9)	−0.0040 (9)
O2	0.0118 (13)	0.0097 (10)	0.0096 (12)	−0.0014 (8)	−0.0013 (8)	0.0009 (10)
O3	0.0069 (9)	0.0084 (10)	0.0110 (11)	−0.0011 (6)	0.0001 (8)	0.0002 (8)
O4	0.0082 (10)	0.0090 (10)	0.0099 (9)	0.0001 (6)	0.0010 (9)	0.0011 (8)
O11	0.0100 (10)	0.0072 (9)	0.0079 (9)	−0.0006 (9)	0.0016 (9)	−0.0001 (8)
O12	0.0095 (11)	0.0078 (9)	0.0093 (10)	−0.0023 (10)	0.0024 (9)	−0.0016 (8)
O5	0.0118 (10)	0.0051 (10)	0.0098 (12)	0.0014 (8)	0.0027 (8)	−0.0012 (8)
O6	0.0121 (10)	0.0064 (10)	0.0104 (11)	0.0007 (6)	−0.0028 (8)	0.0027 (9)
O7	0.0118 (12)	0.0086 (11)	0.0064 (11)	−0.0031 (7)	−0.0011 (7)	0.0028 (9)
O8	0.0110 (14)	0.0085 (11)	0.0071 (10)	0.0034 (8)	0.0022 (8)	0.0044 (9)

Geometric parameters (Å, º)

K1—O1	2.887 (3)	K2—O5	2.798 (2)
K1—O2	2.727 (3)	K2—O7	2.922 (3)
K1—O3	2.702 (2)	K2—O8	3.042 (14)
K1—O11	2.998 (3)	Ti1—O1	2.150 (3)
K1—O12	2.715 (3)	Ti1—O2	1.957 (3)
K1—O5	2.877 (3)	Ti1—O11	1.981 (3)
K1—O7	3.061 (3)	Ti1—O12	1.719 (3)
K1—O8	2.755 (8)	Ti1—O5	2.045 (2)
K1—Na1	0.438 (19)	Ti1—O6	1.985 (2)
Na1—O1	2.98 (2)	Ti2—O3	2.043 (2)
Na1—O2	3.02 (2)	Ti2—O4	1.978 (2)
Na1—O3	2.78 (2)	Ti2—O11	1.739 (3)
Na1—O11	2.71 (2)	Ti2—O12	2.091 (3)
Na1—O12	2.53 (2)	Ti2—O7	1.969 (3)
Na1—O5	2.73 (2)	Ti2—O8	1.988 (18)
Na1—O7	2.75 (2)	P1—O1	1.516 (3)
Na1—O8	2.60 (2)	P1—O2	1.547 (3)
K2—O1	2.685 (3)	P1—O3	1.546 (2)
K2—O2	2.974 (3)	P1—O4	1.545 (2)
K2—O3	3.030 (3)	P2—O5	1.531 (2)
K2—O4	3.108 (2)	P2—O6	1.528 (2)
K2—O11	2.760 (3)	P2—O7	1.546 (3)
K2—O12	3.057 (3)	P2—O8	1.539 (18)
O1—K1—O2	52.54 (8)	O5—K2—O7	130.93 (7)
O1—K1—O11	54.61 (8)	O5—K2—O8	123.3 (2)
O1—K1—O8	89.5 (3)	O5—K2—O1	58.66 (7)
O1—K1—O3	121.19 (10)	O5—K2—O4	89.92 (6)
O1—K1—O12	157.57 (11)	O2—K2—O3	48.54 (7)
O1—K1—O5	55.59 (8)	O2—K2—O12	98.44 (8)
O1—K1—O7	103.58 (10)	O2—K2—O7	91.17 (7)
O2—K1—O11	86.73 (8)	O2—K2—O8	66.2 (2)
O2—K1—O8	73.61 (12)	O2—K2—O1	60.12 (8)
O2—K1—O3	134.28 (9)	O2—K2—O4	146.06 (7)
O2—K1—O12	144.81 (12)	O3—K2—O12	53.49 (6)
O2—K1—O5	107.59 (9)	O3—K2—O7	103.59 (7)
O2—K1—O7	155.98 (11)	O3—K2—O8	55.3 (4)
O11—K1—O8	56.3 (5)	O3—K2—O1	108.62 (8)
O11—K1—O3	129.25 (11)	O3—K2—O4	126.70 (7)
O11—K1—O12	105.46 (9)	O12—K2—O7	86.08 (7)
O11—K1—O5	57.86 (8)	O12—K2—O8	52.89 (16)
O11—K1—O7	74.88 (8)	O12—K2—O1	149.16 (8)
O8—K1—O3	146.56 (17)	O12—K2—O4	97.71 (7)
O8—K1—O12	85.81 (16)	O7—K2—O8	48.9 (4)
O8—K1—O5	114.0 (5)	O7—K2—O1	73.45 (8)
O8—K1—O7	107.1 (3)	O7—K2—O4	119.58 (7)
O3—K1—O12	60.75 (8)	O8—K2—O1	96.53 (14)
O3—K1—O5	78.72 (9)	O8—K2—O4	144.76 (11)
O3—K1—O7	56.26 (7)	O1—K2—O4	112.34 (8)
O12—K1—O5	106.78 (9)	O1—Ti1—O11	81.58 (12)
O12—K1—O7	57.37 (7)	O1—Ti1—O2	87.57 (10)
O5—K1—O7	49.41 (7)	O1—Ti1—O12	172.14 (12)
O1—Na1—O2	49.0 (3)	O1—Ti1—O5	79.65 (10)
O1—Na1—O11	56.5 (4)	O1—Ti1—O6	86.87 (10)
O1—Na1—O8	90.6 (6)	O11—Ti1—O2	169.13 (12)
O1—Na1—O3	115.6 (6)	O11—Ti1—O12	94.69 (11)
O1—Na1—O12	172.9 (9)	O11—Ti1—O5	89.89 (10)
O1—Na1—O5	56.0 (4)	O11—Ti1—O6	90.44 (10)
O1—Na1—O7	109.3 (7)	O2—Ti1—O12	95.98 (13)
O2—Na1—O11	86.5 (5)	O2—Ti1—O5	87.45 (10)
O2—Na1—O8	71.0 (5)	O2—Ti1—O6	89.67 (10)
O2—Na1—O3	119.1 (6)	O12—Ti1—O5	93.47 (11)
O2—Na1—O12	138.0 (8)	O12—Ti1—O6	100.14 (12)
O2—Na1—O5	103.4 (6)	O5—Ti1—O6	166.31 (11)
O2—Na1—O7	157.2 (8)	O3—Ti2—O11	93.23 (11)
O11—Na1—O8	61.6 (6)	O3—Ti2—O12	83.00 (10)
O11—Na1—O3	139.6 (8)	O3—Ti2—O8	88.69 (13)
O11—Na1—O12	120.4 (7)	O3—Ti2—O7	85.97 (10)
O11—Na1—O5	63.0 (5)	O3—Ti2—O4	172.06 (11)
O11—Na1—O7	84.8 (6)	O11—Ti2—O12	175.31 (12)
O8—Na1—O3	152.5 (9)	O11—Ti2—O8	93.7 (4)
O8—Na1—O12	93.0 (7)	O11—Ti2—O7	95.77 (13)
O8—Na1—O5	124.5 (9)	O11—Ti2—O4	94.71 (11)
O8—Na1—O7	122.0 (7)	O12—Ti2—O8	83.5 (4)
O3—Na1—O12	62.0 (4)	O12—Ti2—O7	86.76 (10)
O3—Na1—O5	80.0 (5)	O12—Ti2—O4	89.07 (10)
O3—Na1—O7	59.3 (4)	O8—Ti2—O7	169.4 (4)
O12—Na1—O5	117.1 (7)	O8—Ti2—O4	90.75 (11)
O12—Na1—O7	63.6 (4)	O7—Ti2—O4	93.28 (10)
O5—Na1—O7	53.9 (4)	O1—P1—O2	108.66 (14)
O11—K2—O5	143.79 (8)	O1—P1—O3	112.52 (15)
O11—K2—O2	153.06 (8)	O1—P1—O4	110.89 (16)
O11—K2—O3	108.28 (7)	O2—P1—O3	105.87 (15)
O11—K2—O12	55.61 (7)	O2—P1—O4	110.31 (14)
O11—K2—O7	80.77 (7)	O3—P1—O4	108.47 (11)
O11—K2—O8	89.75 (15)	O5—P2—O6	109.23 (12)
O11—K2—O1	138.84 (9)	O5—P2—O7	107.87 (15)
O11—K2—O4	55.26 (6)	O5—P2—O8	111.19 (16)
O5—K2—O2	57.20 (7)	O6—P2—O7	111.38 (14)
O5—K2—O3	83.42 (7)	O6—P2—O8	110.6 (4)
O5—K2—O12	130.89 (8)	O7—P2—O8	106.5 (5)