Lateral deformations of a crystal of potassium acid phthalate in an external electric field

The anisotropy of deformations in potassium acid phthalate crystals arising under the action of an external electric field up to 1 kV mm⁻¹ applied along the [001] polar axis was studied using X-ray diffraction methods at room temperature. Electrical conductivity was measured and rocking curves for reflections 400, 070 and 004 were obtained by time-resolved X-ray diffractometry in Laue and Bragg geometries. Two saturation processes were observed from the time dependences of the electrical conductivity. A shift in the diffraction peaks and a change in their intensity were found, which indicated a deformation of the crystal structure. Rapid piezoelectric deformation and reversible relaxation-like deformation, kinetically similar to the electrical conductivity of a crystal, were revealed. The deformation depended on the polarity and strength of the applied field. The deformation was more noticeable in the [100] direction and was practically absent in the [001] direction of the applied field. X-ray diffraction analysis revealed a disordered arrangement of potassium atoms, i.e. additional positions and vacancies. The heights of potential barriers between the positions of K⁺ ions and the paths of their possible migration in the crystal structure of potassium acid phthalate were determined. The data obtained by time-resolved X-ray diffractometry and X-ray structure analysis, along with additional electrophysical measurements, allow the conclusion that the migration of charge carriers (potassium cations) leads to lateral deformation of the crystal structure of potassium phthalate in an external electric field.

Computing details

Data collection: CrysAlis PRO 1.171.39.46 (Rigaku OD, 2018); cell refinement: CrysAlis PRO 1.171.39.46 (Rigaku OD, 2018); data reduction: CrysAlis PRO 1.171.39.46 (Rigaku OD, 2018).

(I)

Crystal data

C8H5K0.992O4	F(000) = 415
Mr = 203.91	Dx = 1.640 Mg m^−3
Orthorhombic, Pca21	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2c -2ac	Cell parameters from 7072 reflections
a = 9.6017 (2) Å	θ = 3.7–32.1°
b = 13.3049 (4) Å	µ = 0.61 mm^−1
c = 6.4665 (1) Å	T = 295 K
V = 826.09 (3) Å^3	Plate, colourless
Z = 4	0.39 × 0.23 × 0.05 mm

Data collection

Xcalibur, EosS2 with high theta cut diffractometer	2291 independent reflections
Radiation source: X-ray tube	1980 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.028
Detector resolution: 16.1745 pixels mm^-1	θmax = 29.8°, θmin = 3.7°
ω scans	h = −10→13
Absorption correction: analytical CrysAlisPro 1.171.39.46 (Rigaku Oxford Diffraction, 2018) Analytical numeric absorption correction using a multifaceted crystal model based on expressions derived by R.C. Clark & J.S. Reid. (Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	k = −18→18
Tmin = 0.879, Tmax = 0.971	l = −9→9
16577 measured reflections

Refinement

Refinement on F	All H-atom parameters refined
R[F^2 > 2σ(F^2)] = 0.024	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
wR(F^2) = 0.025	(Δ/σ)max = 0.009
S = 1.21	Δρmax = 0.12 e Å^−3
2291 reflections	Δρmin = −0.14 e Å^−3
152 parameters	Absolute structure: 1049 of Friedel pairs used in the refinement
0 restraints	Absolute structure parameter: −0.03 (3)
1 constraint

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
K1	0.40148 (9)	0.53893 (10)	0.8853 (12)	0.0287 (2)	0.757 (3)
K2	0.3974 (7)	0.5342 (5)	0.8899 (19)	0.088 (2)	0.212 (3)
K3	0.403 (2)	0.579 (2)	0.894 (4)	0.047 (7)*	0.023 (3)
O1	0.33875 (11)	0.37280 (8)	0.6170 (11)	0.0426 (3)
O2	0.20177 (11)	0.23701 (8)	0.6152 (12)	0.0389 (3)
O3	0.64490 (9)	0.40689 (7)	0.7932 (12)	0.0398 (3)
O4	0.49986 (9)	0.35611 (7)	1.0384 (11)	0.0348 (3)
C1	0.55798 (13)	0.24143 (10)	0.7703 (11)	0.0274 (4)
C2	0.44094 (13)	0.21074 (10)	0.6589 (12)	0.0296 (4)
C3	0.32245 (15)	0.28227 (11)	0.6288 (12)	0.0306 (4)
C4	0.66863 (15)	0.17485 (11)	0.7921 (12)	0.0349 (4)
C5	0.56862 (11)	0.34278 (9)	0.8736 (12)	0.0281 (4)
C6	0.43699 (16)	0.11544 (11)	0.5722 (12)	0.0369 (5)
C7	0.66267 (16)	0.07981 (11)	0.7084 (12)	0.0389 (5)
C8	0.54716 (18)	0.04983 (12)	0.5977 (12)	0.0412 (5)
H1	0.7484 (15)	0.1966 (9)	0.863 (3)	0.033 (3)*
H2	0.5412 (18)	−0.0161 (15)	0.544 (3)	0.053 (5)*
H3	0.125 (2)	0.2771 (15)	0.595 (3)	0.069 (7)*
H4	0.7388 (17)	0.0356 (10)	0.722 (3)	0.033 (4)*
H6	0.3557 (16)	0.0992 (11)	0.503 (3)	0.040 (4)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0290 (3)	0.0325 (5)	0.0246 (4)	0.0134 (3)	−0.0004 (4)	0.0006 (4)
K2	0.111 (4)	0.092 (5)	0.060 (4)	0.009 (3)	−0.013 (3)	−0.016 (4)
O1	0.0415 (6)	0.0336 (5)	0.0526 (7)	0.0004 (4)	−0.0112 (5)	−0.0009 (5)
O2	0.0305 (6)	0.0405 (6)	0.0456 (6)	−0.0018 (4)	−0.0081 (5)	0.0044 (5)
O3	0.0350 (5)	0.0424 (6)	0.0419 (6)	−0.0115 (4)	0.0016 (5)	0.0036 (5)
O4	0.0364 (5)	0.0396 (6)	0.0282 (5)	−0.0033 (4)	0.0036 (4)	−0.0052 (4)
C1	0.0279 (6)	0.0321 (7)	0.0220 (6)	−0.0010 (5)	0.0030 (6)	0.0026 (5)
C2	0.0306 (7)	0.0322 (7)	0.0259 (7)	−0.0017 (5)	0.0005 (6)	0.0025 (6)
C3	0.0314 (8)	0.0361 (8)	0.0243 (7)	−0.0018 (5)	−0.0044 (5)	−0.0019 (6)
C4	0.0317 (7)	0.0432 (8)	0.0297 (6)	0.0032 (6)	−0.0009 (6)	0.0049 (7)
C5	0.0212 (5)	0.0350 (6)	0.0279 (6)	−0.0002 (4)	−0.0042 (7)	0.0018 (7)
C6	0.0411 (8)	0.0374 (8)	0.0322 (7)	−0.0043 (6)	−0.0025 (7)	−0.0023 (6)
C7	0.0420 (9)	0.0394 (8)	0.0354 (8)	0.0131 (7)	0.0054 (6)	0.0049 (7)
C8	0.0554 (10)	0.0315 (8)	0.0368 (8)	0.0039 (7)	0.0047 (8)	−0.0022 (7)

Geometric parameters (Å, º)

K1—K1^i	3.887 (9)	K3—O3^ii	2.63 (3)
K1—K1^ii	3.887 (9)	K3—O3^iii	2.57 (2)
K1—K2	0.079 (8)	K3—O4^i	2.63 (3)
K1—K2^i	3.865 (13)	O1—C3	1.2170 (19)
K1—K2^ii	3.914 (13)	O2—C3	1.3088 (19)
K1—K3	0.54 (3)	O2—H3	0.92 (2)
K1—O1	2.874 (7)	O3—C5	1.239 (5)
K1—O3^ii	2.770 (10)	O4—C5	1.266 (9)
K1—O3^iii	2.635 (3)	C1—C2	1.396 (6)
K1—O4	2.791 (4)	C1—C4	1.391 (2)
K1—O4^i	2.807 (9)	C1—C5	1.509 (5)
K1—C5	3.0646 (17)	C2—C3	1.496 (2)
K2—K2^i	3.894 (16)	C2—C6	1.387 (5)
K2—K2^ii	3.894 (16)	C4—C7	1.376 (5)
K2—K3	0.60 (3)	C4—H1	0.939 (16)
K2—O1	2.836 (11)	C6—C8	1.381 (3)
K2—O3^ii	2.753 (14)	C6—H6	0.926 (16)
K2—O3^iii	2.623 (7)	C7—C8	1.379 (6)
K2—O4	2.740 (8)	C7—H4	0.942 (15)
K2—O4^i	2.876 (12)	C8—H2	0.94 (2)
K2—C5	3.034 (7)
K1^i—K1—K1^ii	112.59 (10)	K1^v—K2—O4^i	68.0 (2)
K1^i—K1—K1^iii	114.81 (16)	K1^v—K2—C5	110.1 (3)
K1^i—K1—K1^iv	57.86 (11)	K1^vi—K2—K2^i	163.6 (2)
K1^i—K1—K1^v	72.97 (16)	K1^vi—K2—K2^ii	73.9 (3)
K1^i—K1—K1^vi	160.73 (8)	K1^vi—K2—K2^iii	49.25 (18)
K1^i—K1—K2	110 (9)	K1^vi—K2—K2^iv	131.2 (3)
K1^i—K1—K2^i	1.13 (11)	K1^vi—K2—K2^v	96.9 (2)
K1^i—K1—K2^ii	112.77 (15)	K1^vi—K2—K2^vi	1.06 (12)
K1^i—K1—K2^iv	58.32 (16)	K1^vi—K2—K3	91 (3)
K1^i—K1—K2^v	72.62 (19)	K1^vi—K2—K3^i	156.3 (4)
K1^i—K1—K2^vi	160.42 (12)	K1^vi—K2—K3^ii	73.9 (4)
K1^i—K1—K3	110 (3)	K1^vi—K2—K3^v	96.0 (4)
K1^i—K1—K3^i	7.6 (4)	K1^vi—K2—K3^vi	7.0 (3)
K1^i—K1—K3^ii	110.1 (4)	K1^vi—K2—O1	110.0 (2)
K1^i—K1—K3^v	75.7 (4)	K1^vi—K2—O3^ii	36.10 (13)
K1^i—K1—K3^vi	166.0 (3)	K1^vi—K2—O3^iii	63.7 (3)
K1^i—K1—O1	52.76 (14)	K1^vi—K2—O4	89.5 (3)
K1^i—K1—O3^ii	159.99 (12)	K1^vi—K2—O4^i	144.1 (2)
K1^i—K1—O3^iii	109.9 (3)	K1^vi—K2—C5	113.5 (3)
K1^i—K1—O4	84.15 (17)	K2^i—K2—K2^ii	112.2 (2)
K1^i—K1—O4^i	45.85 (12)	K2^i—K2—K2^iii	117.0 (3)
K1^i—K1—C5	59.85 (17)	K2^i—K2—K2^iv	57.3 (2)
K1^ii—K1—K1^iii	114.81 (16)	K2^i—K2—K2^v	73.1 (3)
K1^ii—K1—K1^iv	57.86 (11)	K2^i—K2—K2^vi	163.3 (3)
K1^ii—K1—K1^v	160.73 (8)	K2^i—K2—K3	103 (3)
K1^ii—K1—K1^vi	72.97 (16)	K2^i—K2—K3^i	8.5 (4)
K1^ii—K1—K2	74 (9)	K2^i—K2—K3^ii	109.9 (4)
K1^ii—K1—K2^i	112.28 (15)	K2^i—K2—K3^v	75.9 (4)
K1^ii—K1—K2^ii	1.09 (10)	K2^i—K2—K3^vi	168.5 (4)
K1^ii—K1—K2^iv	57.63 (16)	K2^i—K2—O1	53.6 (2)
K1^ii—K1—K2^v	160.13 (13)	K2^i—K2—O3^ii	158.1 (3)
K1^ii—K1—K2^vi	72.12 (19)	K2^i—K2—O3^iii	109.8 (4)
K1^ii—K1—K3	99 (3)	K2^i—K2—O4	84.7 (3)
K1^ii—K1—K3^i	109.1 (4)	K2^i—K2—O4^i	44.7 (2)
K1^ii—K1—K3^ii	7.1 (4)	K2^i—K2—C5	60.0 (2)
K1^ii—K1—K3^v	165.3 (3)	K2^ii—K2—K2^iii	117.0 (3)
K1^ii—K1—K3^vi	74.7 (4)	K2^ii—K2—K2^iv	57.3 (2)
K1^ii—K1—O1	113.53 (13)	K2^ii—K2—K2^v	163.3 (3)
K1^ii—K1—O3^ii	49.88 (14)	K2^ii—K2—K2^vi	73.1 (3)
K1^ii—K1—O3^iii	135.7 (3)	K2^ii—K2—K3	98 (3)
K1^ii—K1—O4	46.20 (16)	K2^ii—K2—K3^i	109.4 (4)
K1^ii—K1—O4^i	129.28 (9)	K2^ii—K2—K3^ii	8.3 (4)
K1^ii—K1—C5	62.52 (17)	K2^ii—K2—K3^v	168.1 (4)
K1^iii—K1—K1^iv	155.65 (4)	K2^ii—K2—K3^vi	75.4 (4)
K1^iii—K1—K1^v	49.17 (12)	K2^ii—K2—O1	116.1 (3)
K1^iii—K1—K1^vi	49.17 (12)	K2^ii—K2—O3^ii	49.8 (2)
K1^iii—K1—K2	50 (6)	K2^ii—K2—O3^iii	137.3 (4)
K1^iii—K1—K2^i	115.8 (2)	K2^ii—K2—O4	47.5 (2)
K1^iii—K1—K2^ii	115.5 (2)	K2^ii—K2—O4^i	127.0 (2)
K1^iii—K1—K2^iv	156.27 (9)	K2^ii—K2—C5	63.8 (2)
K1^iii—K1—K2^v	49.06 (16)	K2^iii—K2—K2^iv	158.5 (2)
K1^iii—K1—K2^vi	49.57 (16)	K2^iii—K2—K2^v	49.7 (2)
K1^iii—K1—K3	104 (2)	K2^iii—K2—K2^vi	49.7 (2)
K1^iii—K1—K3^i	112.0 (4)	K2^iii—K2—K3	106 (2)
K1^iii—K1—K3^ii	111.5 (4)	K2^iii—K2—K3^i	113.4 (4)
K1^iii—K1—K3^v	50.9 (3)	K2^iii—K2—K3^ii	113.2 (4)
K1^iii—K1—K3^vi	51.7 (3)	K2^iii—K2—K3^v	51.3 (4)
K1^iii—K1—O1	68.46 (8)	K2^iii—K2—K3^vi	51.7 (4)
K1^iii—K1—O3^ii	84.13 (12)	K2^iii—K2—O1	70.35 (18)
K1^iii—K1—O3^iii	31.11 (8)	K2^iii—K2—O3^ii	84.7 (2)
K1^iii—K1—O4	98.46 (7)	K2^iii—K2—O3^iii	31.54 (15)
K1^iii—K1—O4^i	115.77 (18)	K2^iii—K2—O4	101.0 (2)
K1^iii—K1—C5	109.41 (4)	K2^iii—K2—O4^i	115.6 (3)
K1^iv—K1—K1^v	130.83 (19)	K2^iii—K2—C5	112.08 (19)
K1^iv—K1—K1^vi	130.83 (19)	K2^iv—K2—K2^v	130.3 (3)
K1^iv—K1—K2	109 (5)	K2^iv—K2—K2^vi	130.3 (3)
K1^iv—K1—K2^i	57.21 (16)	K2^iv—K2—K3	95 (2)
K1^iv—K1—K2^ii	57.68 (16)	K2^iv—K2—K3^i	57.5 (4)
K1^iv—K1—K2^iv	0.71 (11)	K2^iv—K2—K3^ii	57.9 (4)
K1^iv—K1—K2^v	130.5 (2)	K2^iv—K2—K3^v	132.6 (4)
K1^iv—K1—K2^vi	130.0 (2)	K2^iv—K2—K3^vi	132.1 (4)
K1^iv—K1—K3	100 (2)	K2^iv—K2—O1	93.1 (2)
K1^iv—K1—K3^i	57.3 (3)	K2^iv—K2—O3^ii	101.4 (3)
K1^iv—K1—K3^ii	58.1 (3)	K2^iv—K2—O3^iii	164.5 (4)
K1^iv—K1—K3^v	133.1 (4)	K2^iv—K2—O4	59.07 (16)
K1^iv—K1—K3^vi	132.1 (4)	K2^iv—K2—O4^i	76.0 (2)
K1^iv—K1—O1	92.45 (9)	K2^iv—K2—C5	46.45 (12)
K1^iv—K1—O3^ii	102.24 (16)	K2^v—K2—K2^vi	97.6 (2)
K1^iv—K1—O3^iii	166.3 (3)	K2^v—K2—K3	95 (3)
K1^iv—K1—O4	59.02 (6)	K2^v—K2—K3^i	73.4 (4)
K1^iv—K1—O4^i	77.00 (10)	K2^v—K2—K3^ii	155.9 (4)
K1^iv—K1—C5	46.25 (3)	K2^v—K2—K3^v	7.9 (4)
K1^v—K1—K1^vi	96.04 (10)	K2^v—K2—K3^vi	97.2 (4)
K1^v—K1—K2	87 (9)	K2^v—K2—O1	53.2 (2)
K1^v—K1—K2^i	73.6 (2)	K2^v—K2—O3^ii	128.0 (2)
K1^v—K1—K2^ii	161.74 (13)	K2^v—K2—O3^iii	38.0 (3)
K1^v—K1—K2^iv	131.3 (2)	K2^v—K2—O4	120.0 (3)
K1^v—K1—K2^v	0.84 (10)	K2^v—K2—O4^i	68.4 (3)
K1^v—K1—K2^vi	96.69 (15)	K2^v—K2—C5	109.3 (3)
K1^v—K1—K3	96 (3)	K2^vi—K2—K3	91 (3)
K1^v—K1—K3^i	74.0 (4)	K2^vi—K2—K3^i	155.8 (4)
K1^v—K1—K3^ii	154.5 (4)	K2^vi—K2—K3^ii	73.0 (4)
K1^v—K1—K3^v	7.1 (4)	K2^vi—K2—K3^v	96.7 (4)
K1^v—K1—K3^vi	96.3 (3)	K2^vi—K2—K3^vi	7.8 (4)
K1^v—K1—O1	53.91 (12)	K2^vi—K2—O1	109.7 (2)
K1^v—K1—O3^ii	126.89 (9)	K2^vi—K2—O3^ii	35.91 (17)
K1^v—K1—O3^iii	37.50 (19)	K2^vi—K2—O3^iii	64.6 (3)
K1^v—K1—O4	119.34 (15)	K2^vi—K2—O4	88.4 (3)
K1^v—K1—O4^i	68.38 (17)	K2^vi—K2—O4^i	145.2 (2)
K1^v—K1—C5	109.39 (19)	K2^vi—K2—C5	112.5 (3)
K1^vi—K1—K2	53 (8)	K3—K2—K3^i	111 (3)
K1^vi—K1—K2^i	161.86 (13)	K3—K2—K3^ii	107 (3)
K1^vi—K1—K2^ii	73.16 (19)	K3—K2—K3^v	88 (3)
K1^vi—K1—K2^iv	130.6 (2)	K3—K2—K3^vi	84 (3)
K1^vi—K1—K2^v	96.17 (15)	K3—K2—O1	143 (3)
K1^vi—K1—K2^vi	1.05 (12)	K3—K2—O3^ii	72 (3)
K1^vi—K1—K3	87 (3)	K3—K2—O3^iii	78 (2)
K1^vi—K1—K3^i	154.4 (4)	K3—K2—O4	144 (3)
K1^vi—K1—K3^ii	73.1 (4)	K3—K2—O4^i	60 (3)
K1^vi—K1—K3^v	95.3 (3)	K3—K2—C5	142 (2)
K1^vi—K1—K3^vi	6.9 (3)	K3^i—K2—K3^ii	106.0 (5)
K1^vi—K1—O1	107.98 (11)	K3^i—K2—K3^v	77.3 (5)
K1^vi—K1—O3^ii	35.38 (9)	K3^i—K2—K3^vi	162.5 (5)
K1^vi—K1—O3^iii	62.8 (2)	K3^i—K2—O1	46.8 (4)
K1^vi—K1—O4	87.86 (19)	K3^i—K2—O3^ii	158.5 (4)
K1^vi—K1—O4^i	145.06 (6)	K3^i—K2—O3^iii	111.2 (5)
K1^vi—K1—C5	111.62 (19)	K3^i—K2—O4	77.5 (4)
K2—K1—K2^i	111 (9)	K3^i—K2—O4^i	53.0 (4)
K2—K1—K2^ii	75 (9)	K3^i—K2—C5	53.2 (4)
K2—K1—K2^iv	109 (5)	K3^ii—K2—K3^v	162.2 (5)
K2—K1—K2^v	86 (9)	K3^ii—K2—K3^vi	76.4 (5)
K2—K1—K2^vi	52 (8)	K3^ii—K2—O1	108.1 (4)
K2—K1—K3	139 (8)	K3^ii—K2—O3^ii	54.3 (4)
K2—K1—K3^i	103 (8)	K3^ii—K2—O3^iii	137.4 (5)
K2—K1—K3^ii	68 (8)	K3^ii—K2—O4	39.7 (4)
K2—K1—K3^v	92 (8)	K3^ii—K2—O4^i	131.3 (4)
K2—K1—K3^vi	59 (8)	K3^ii—K2—C5	57.4 (4)
K2—K1—O1	61 (10)	K3^v—K2—K3^vi	95.3 (5)
K2—K1—O3^ii	77 (10)	K3^v—K2—O1	60.9 (4)
K2—K1—O3^iii	81 (6)	K3^v—K2—O3^ii	124.1 (4)
K2—K1—O4	49 (5)	K3^v—K2—O3^iii	34.0 (4)
K2—K1—O4^i	149 (10)	K3^v—K2—O4	127.9 (5)
K2—K1—C5	66 (5)	K3^v—K2—O4^i	64.9 (4)
K2^i—K1—K2^ii	112.44 (19)	K3^v—K2—C5	116.7 (5)
K2^i—K1—K2^iv	57.7 (2)	K3^vi—K2—O1	115.7 (4)
K2^i—K1—K2^v	73.3 (2)	K3^vi—K2—O3^ii	33.0 (3)
K2^i—K1—K2^vi	161.55 (16)	K3^vi—K2—O3^iii	61.9 (4)
K2^i—K1—K3	109 (3)	K3^vi—K2—O4	95.3 (5)
K2^i—K1—K3^i	8.5 (4)	K3^vi—K2—O4^i	138.0 (4)
K2^i—K1—K3^ii	109.9 (4)	K3^vi—K2—C5	119.7 (5)
K2^i—K1—K3^v	76.2 (4)	O1—K2—O3^ii	140.9 (3)
K2^i—K1—K3^vi	167.1 (4)	O1—K2—O3^iii	83.9 (3)
K2^i—K1—O1	53.89 (17)	O1—K2—O4	68.5 (2)
K2^i—K1—O3^ii	159.22 (16)	O1—K2—O4^i	87.7 (4)
K2^i—K1—O3^iii	110.4 (3)	O1—K2—C5	56.64 (19)
K2^i—K1—O4	84.6 (2)	O3^ii—K2—O3^iii	90.3 (3)
K2^i—K1—O4^i	45.12 (16)	O3^ii—K2—O4	88.1 (4)
K2^i—K1—C5	60.2 (2)	O3^ii—K2—O4^i	130.9 (3)
K2^ii—K1—K2^iv	57.4 (2)	O3^ii—K2—C5	110.6 (4)
K2^ii—K1—K2^v	161.14 (16)	O3^iii—K2—O4	132.4 (3)
K2^ii—K1—K2^vi	72.3 (2)	O3^iii—K2—O4^i	88.7 (3)
K2^ii—K1—K3	98 (3)	O3^iii—K2—C5	138.0 (3)
K2^ii—K1—K3^i	109.4 (4)	O4—K2—O4^i	126.3 (3)
K2^ii—K1—K3^ii	8.2 (4)	O4—K2—C5	24.66 (19)
K2^ii—K1—K3^v	166.1 (4)	O4^i—K2—C5	102.3 (3)
K2^ii—K1—K3^vi	74.7 (4)	K1—K3—K1^i	63 (3)
K2^ii—K1—O1	114.54 (16)	K1—K3—K1^ii	73 (3)
K2^ii—K1—O3^ii	49.49 (18)	K1—K3—K1^v	77 (3)
K2^ii—K1—O3^iii	135.9 (3)	K1—K3—K1^vi	86 (3)
K2^ii—K1—O4	47.21 (19)	K1—K3—K2	5.0 (12)
K2^ii—K1—O4^i	128.56 (14)	K1—K3—K2^i	64 (3)
K2^ii—K1—C5	63.3 (2)	K1—K3—K2^ii	74 (3)
K2^iv—K1—K2^v	130.9 (3)	K1—K3—K2^v	76 (3)
K2^iv—K1—K2^vi	129.8 (2)	K1—K3—K2^vi	86 (3)
K2^iv—K1—K3	100 (2)	K1—K3—K3^i	56 (3)
K2^iv—K1—K3^i	57.9 (4)	K1—K3—K3^ii	67 (3)
K2^iv—K1—K3^ii	58.0 (4)	K1—K3—K3^v	84 (3)
K2^iv—K1—K3^v	133.5 (4)	K1—K3—K3^vi	93 (3)
K2^iv—K1—K3^vi	131.7 (4)	K1—K3—O3^ii	100 (3)
K2^iv—K1—O1	93.15 (13)	K1—K3—O3^iii	91 (3)
K2^iv—K1—O3^ii	101.8 (2)	K1—K3—O4^i	104 (3)
K2^iv—K1—O3^iii	166.4 (3)	K1^i—K3—K1^ii	105.8 (6)
K2^iv—K1—O4	59.45 (10)	K1^i—K3—K1^v	70.1 (4)
K2^iv—K1—O4^i	76.93 (14)	K1^i—K3—K1^vi	147.8 (7)
K2^iv—K1—C5	46.89 (8)	K1^i—K3—K2	68 (3)
K2^v—K1—K2^vi	96.80 (18)	K1^i—K3—K2^i	1.04 (10)
K2^v—K1—K3	97 (3)	K1^i—K3—K2^ii	106.1 (6)
K2^v—K1—K3^i	73.5 (4)	K1^i—K3—K2^v	69.7 (4)
K2^v—K1—K3^ii	153.8 (4)	K1^i—K3—K2^vi	147.3 (7)
K2^v—K1—K3^v	7.9 (4)	K1^i—K3—K3^i	6.9 (4)
K2^v—K1—K3^vi	96.6 (3)	K1^i—K3—K3^ii	102.7 (6)
K2^v—K1—O1	53.08 (15)	K1^i—K3—K3^v	73.4 (5)
K2^v—K1—O3^ii	127.27 (14)	K1^i—K3—K3^vi	154.4 (8)
K2^v—K1—O3^iii	38.0 (2)	K1^i—K3—O3^ii	153.6 (9)
K2^v—K1—O4	118.51 (18)	K1^i—K3—O3^iii	105.4 (8)
K2^v—K1—O4^i	68.7 (2)	K1^i—K3—O4^i	42.3 (4)
K2^v—K1—C5	108.6 (2)	K1^ii—K3—K1^v	148.1 (7)
K2^vi—K1—K3	87 (3)	K1^ii—K3—K1^vi	71.8 (4)
K2^vi—K1—K3^i	153.9 (4)	K1^ii—K3—K2	72 (3)
K2^vi—K1—K3^ii	72.2 (4)	K1^ii—K3—K2^i	105.6 (6)
K2^vi—K1—K3^v	96.1 (3)	K1^ii—K3—K2^ii	1.10 (11)
K2^vi—K1—K3^vi	7.7 (4)	K1^ii—K3—K2^v	147.3 (7)
K2^vi—K1—O1	107.69 (15)	K1^ii—K3—K2^vi	70.9 (4)
K2^vi—K1—O3^ii	35.19 (13)	K1^ii—K3—K3^i	101.7 (6)
K2^vi—K1—O3^iii	63.7 (2)	K1^ii—K3—K3^ii	6.4 (4)
K2^vi—K1—O4	86.8 (2)	K1^ii—K3—K3^v	154.3 (8)
K2^vi—K1—O4^i	146.10 (11)	K1^ii—K3—K3^vi	74.3 (6)
K2^vi—K1—C5	110.6 (2)	K1^ii—K3—O3^ii	48.1 (4)
K3—K1—K3^i	117 (3)	K1^ii—K3—O3^iii	132.9 (9)
K3—K1—K3^ii	106 (3)	K1^ii—K3—O4^i	131.0 (7)
K3—K1—K3^v	89 (3)	K1^v—K3—K1^vi	94.8 (4)
K3—K1—K3^vi	80 (3)	K1^v—K3—K2	78 (3)
K3—K1—O1	147 (3)	K1^v—K3—K2^i	70.8 (4)
K3—K1—O3^ii	69 (3)	K1^v—K3—K2^ii	149.2 (7)
K3—K1—O3^iii	77 (2)	K1^v—K3—K2^v	0.89 (9)
K3—K1—O4	145 (3)	K1^v—K3—K2^vi	95.3 (5)
K3—K1—O4^i	65 (3)	K1^v—K3—K3^i	70.6 (5)
K3—K1—C5	146 (2)	K1^v—K3—K3^ii	141.9 (7)
K3^i—K1—K3^ii	105.8 (5)	K1^v—K3—K3^v	6.9 (4)
K3^i—K1—K3^v	77.5 (5)	K1^v—K3—K3^vi	96.0 (5)
K3^i—K1—K3^vi	160.7 (5)	K1^v—K3—O3^ii	128.4 (7)
K3^i—K1—O1	47.0 (4)	K1^v—K3—O3^iii	35.3 (4)
K3^i—K1—O3^ii	158.7 (4)	K1^v—K3—O4^i	67.9 (5)
K3^i—K1—O3^iii	111.4 (4)	K1^vi—K3—K2	81 (3)
K3^i—K1—O4	77.4 (4)	K1^vi—K3—K2^i	148.8 (7)
K3^i—K1—O4^i	53.4 (4)	K1^vi—K3—K2^ii	72.1 (5)
K3^i—K1—C5	53.3 (4)	K1^vi—K3—K2^v	94.8 (5)
K3^ii—K1—K3^v	160.1 (5)	K1^vi—K3—K2^vi	1.05 (11)
K3^ii—K1—K3^vi	75.7 (5)	K1^vi—K3—K3^i	141.5 (7)
K3^ii—K1—O1	106.6 (4)	K1^vi—K3—K3^ii	71.4 (5)
K3^ii—K1—O3^ii	53.8 (4)	K1^vi—K3—K3^v	95.0 (5)
K3^ii—K1—O3^iii	135.6 (4)	K1^vi—K3—K3^vi	7.1 (4)
K3^ii—K1—O4	39.4 (4)	K1^vi—K3—O3^ii	34.3 (3)
K3^ii—K1—O4^i	132.6 (3)	K1^vi—K3—O3^iii	63.0 (5)
K3^ii—K1—C5	56.9 (4)	K1^vi—K3—O4^i	156.6 (8)
K3^v—K1—K3^vi	94.8 (5)	K2—K3—K2^i	69 (3)
K3^v—K1—O1	60.8 (4)	K2—K3—K2^ii	73 (3)
K3^v—K1—O3^ii	123.7 (3)	K2—K3—K2^v	77 (3)
K3^v—K1—O3^iii	34.2 (4)	K2—K3—K2^vi	81 (3)
K3^v—K1—O4	126.4 (4)	K2—K3—K3^i	61 (3)
K3^v—K1—O4^i	65.3 (4)	K2—K3—K3^ii	66 (3)
K3^v—K1—C5	116.0 (4)	K2—K3—K3^v	84 (3)
K3^vi—K1—O1	113.7 (3)	K2—K3—K3^vi	88 (3)
K3^vi—K1—O3^ii	32.5 (3)	K2—K3—O3^ii	96 (3)
K3^vi—K1—O3^iii	61.2 (4)	K2—K3—O3^iii	88 (2)
K3^vi—K1—O4	93.7 (4)	K2—K3—O4^i	109 (3)
K3^vi—K1—O4^i	139.1 (3)	K2^i—K3—K2^ii	106.0 (6)
K3^vi—K1—C5	117.8 (4)	K2^i—K3—K2^v	70.4 (5)
O1—K1—O3^ii	137.84 (19)	K2^i—K3—K2^vi	148.3 (7)
O1—K1—O3^iii	82.99 (16)	K2^i—K3—K3^i	7.7 (4)
O1—K1—O4	67.34 (16)	K2^i—K3—K3^ii	102.6 (6)
O1—K1—O4^i	88.3 (3)	K2^i—K3—K3^v	74.0 (6)
O1—K1—C5	55.94 (13)	K2^i—K3—K3^vi	155.4 (8)
O3^ii—K1—O3^iii	89.6 (2)	K2^i—K3—O3^ii	153.6 (9)
O3^ii—K1—O4	86.8 (3)	K2^i—K3—O3^iii	106.1 (8)
O3^ii—K1—O4^i	133.29 (12)	K2^i—K3—O4^i	41.7 (4)
O3^ii—K1—C5	109.2 (2)	K2^ii—K3—K2^v	148.4 (7)
O3^iii—K1—O4	129.42 (8)	K2^ii—K3—K2^vi	71.2 (5)
O3^iii—K1—O4^i	89.9 (2)	K2^ii—K3—K3^i	102.2 (6)
O3^iii—K1—C5	135.81 (13)	K2^ii—K3—K3^ii	7.5 (4)
O4—K1—O4^i	127.07 (19)	K2^ii—K3—K3^v	155.4 (8)
O4—K1—C5	24.39 (18)	K2^ii—K3—K3^vi	74.4 (6)
O4^i—K1—C5	103.1 (2)	K2^ii—K3—O3^ii	47.8 (4)
K1—K2—K1^i	69 (9)	K2^ii—K3—O3^iii	133.5 (9)
K1—K2—K1^ii	105 (9)	K2^ii—K3—O4^i	130.6 (7)
K1—K2—K1^iii	130 (6)	K2^v—K3—K2^vi	95.3 (5)
K1—K2—K1^v	92 (9)	K2^v—K3—K3^i	70.0 (5)
K1—K2—K1^vi	127 (8)	K2^v—K3—K3^ii	141.1 (7)
K1—K2—K2^i	68 (9)	K2^v—K3—K3^v	7.8 (4)
K1—K2—K2^ii	104 (9)	K2^v—K3—K3^vi	96.1 (6)
K1—K2—K2^iii	129 (6)	K2^v—K3—O3^ii	128.5 (7)
K1—K2—K2^iv	70 (5)	K2^v—K3—O3^iii	35.7 (4)
K1—K2—K2^v	93 (9)	K2^v—K3—O4^i	68.1 (6)
K1—K2—K2^vi	127 (8)	K2^vi—K3—K3^i	140.9 (7)
K1—K2—K3	36 (7)	K2^vi—K3—K3^ii	70.4 (5)
K1—K2—K3^i	76 (9)	K2^vi—K3—K3^v	95.7 (6)
K1—K2—K3^ii	111 (8)	K2^vi—K3—K3^vi	7.9 (4)
K1—K2—K3^v	87 (8)	K2^vi—K3—O3^ii	34.0 (3)
K1—K2—K3^vi	120 (8)	K2^vi—K3—O3^iii	63.8 (5)
K1—K2—O1	117 (10)	K2^vi—K3—O4^i	157.6 (8)
K1—K2—O3^ii	102 (10)	K3^i—K3—K3^ii	98.0 (7)
K1—K2—O3^iii	98 (6)	K3^i—K3—K3^v	74.6 (6)
K1—K2—O4	129 (5)	K3^i—K3—K3^vi	148.3 (8)
K1—K2—O4^i	30 (10)	K3^i—K3—O3^ii	148.5 (9)
K1—K2—C5	112 (5)	K3^i—K3—O3^iii	105.2 (8)
K1^i—K2—K1^ii	112.44 (19)	K3^i—K3—O4^i	49.2 (6)
K1^i—K2—K1^iii	115.4 (3)	K3^ii—K3—K3^v	148.3 (8)
K1^i—K2—K1^v	72.8 (2)	K3^ii—K3—K3^vi	74.6 (6)
K1^i—K2—K1^vi	162.5 (2)	K3^ii—K3—O3^ii	50.9 (6)
K1^i—K2—K2^i	1.13 (11)	K3^ii—K3—O3^iii	130.3 (9)
K1^i—K2—K2^ii	112.6 (2)	K3^ii—K3—O4^i	131.9 (8)
K1^i—K2—K2^iii	116.0 (3)	K3^v—K3—K3^vi	95.4 (6)
K1^i—K2—K2^iv	57.92 (18)	K3^v—K3—O3^ii	127.5 (8)
K1^i—K2—K2^v	72.4 (2)	K3^v—K3—O3^iii	33.2 (5)
K1^i—K2—K2^vi	162.2 (2)	K3^v—K3—O4^i	65.8 (6)
K1^i—K2—K3	104 (3)	K3^vi—K3—O3^ii	32.4 (4)
K1^i—K2—K3^i	7.6 (4)	K3^vi—K3—O3^iii	62.5 (6)
K1^i—K2—K3^ii	110.1 (4)	K3^vi—K3—O4^i	152.4 (9)
K1^i—K2—K3^v	75.4 (4)	O3^ii—K3—O3^iii	94.3 (8)
K1^i—K2—K3^vi	167.4 (4)	O3^ii—K3—O4^i	154.0 (11)
K1^i—K2—O1	52.5 (2)	O3^iii—K3—O4^i	95.5 (9)
K1^i—K2—O3^ii	158.9 (3)	K1—O1—C3	138.6 (6)
K1^i—K2—O3^iii	109.4 (4)	K2—O1—C3	137.4 (6)
K1^i—K2—O4	84.3 (3)	C3—O2—H3	116.9 (13)
K1^i—K2—O4^i	45.41 (17)	K1^i—O3—K1^iv	107.1 (2)
K1^i—K2—C5	59.7 (2)	K1^i—O3—K2^iv	107.3 (3)
K1^ii—K2—K1^iii	116.4 (3)	K1^i—O3—K3^iv	112.2 (6)
K1^ii—K2—K1^v	162.9 (2)	K1^i—O3—C5	119.0 (4)
K1^ii—K2—K1^vi	73.7 (2)	K1^iv—O3—K2^i	105.9 (3)
K1^ii—K2—K2^i	112.1 (2)	K1^iv—O3—K3^i	111.5 (6)
K1^ii—K2—K2^ii	1.09 (10)	K1^iv—O3—C5	130.2 (4)
K1^ii—K2—K2^iii	116.4 (3)	K2^i—O3—K2^iv	106.1 (3)
K1^ii—K2—K2^iv	57.47 (18)	K2^i—O3—K3^iv	111.2 (6)
K1^ii—K2—K2^v	162.3 (2)	K2^i—O3—C5	120.4 (5)
K1^ii—K2—K2^vi	72.9 (2)	K2^iv—O3—K3^i	112.0 (6)
K1^ii—K2—K3	100 (3)	K2^iv—O3—C5	130.7 (5)
K1^ii—K2—K3^i	109.1 (4)	K3^i—O3—K3^iv	114.4 (8)
K1^ii—K2—K3^ii	7.2 (4)	K3^i—O3—C5	111.0 (7)
K1^ii—K2—K3^v	167.4 (4)	K3^iv—O3—C5	120.9 (7)
K1^ii—K2—K3^vi	75.4 (4)	K1—O4—K1^ii	87.94 (16)
K1^ii—K2—O1	115.1 (2)	K1—O4—K2^ii	87.4 (2)
K1^ii—K2—O3^ii	50.2 (2)	K1—O4—K3^ii	98.3 (6)
K1^ii—K2—O3^iii	137.3 (4)	K1—O4—C5	90.0 (3)
K1^ii—K2—O4	46.6 (2)	K1^ii—O4—K2	88.3 (2)
K1^ii—K2—O4^i	127.7 (2)	K1^ii—O4—C5	124.49 (18)
K1^ii—K2—C5	63.0 (2)	K2—O4—K2^ii	87.8 (3)
K1^iii—K2—K1^v	49.56 (14)	K2—O4—K3^ii	98.6 (6)
K1^iii—K2—K1^vi	49.75 (14)	K2—O4—C5	90.8 (4)
K1^iii—K2—K2^i	116.3 (3)	K2^ii—O4—C5	123.9 (2)
K1^iii—K2—K2^ii	117.0 (3)	K3^ii—O4—C5	126.7 (5)
K1^iii—K2—K2^iii	0.88 (10)	C2—C1—C4	118.8 (3)
K1^iii—K2—K2^iv	157.70 (18)	C2—C1—C5	123.00 (16)
K1^iii—K2—K2^v	49.47 (17)	C4—C1—C5	118.2 (3)
K1^iii—K2—K2^vi	50.15 (17)	C1—C2—C3	119.6 (3)
K1^iii—K2—K3	107 (2)	C1—C2—C6	119.86 (18)
K1^iii—K2—K3^i	112.7 (4)	C3—C2—C6	120.5 (4)
K1^iii—K2—K3^ii	113.1 (4)	O1—C3—O2	124.40 (17)
K1^iii—K2—K3^v	51.2 (3)	O1—C3—C2	122.68 (14)
K1^iii—K2—K3^vi	52.3 (3)	O2—C3—C2	112.91 (13)
K1^iii—K2—O1	69.51 (15)	C1—C4—C7	120.9 (4)
K1^iii—K2—O3^ii	85.3 (2)	C1—C4—H1	118.5 (8)
K1^iii—K2—O3^iii	32.11 (12)	C7—C4—H1	120.6 (8)
K1^iii—K2—O4	100.41 (19)	K1—C5—O3	74.55 (11)
K1^iii—K2—O4^i	115.7 (3)	K1—C5—O4	65.60 (19)
K1^iii—K2—C5	111.26 (18)	K1—C5—C1	137.4 (3)
K1^v—K2—K1^vi	96.80 (16)	K2—C5—O3	75.93 (18)
K1^v—K2—K2^i	73.4 (3)	K2—C5—O4	64.6 (3)
K1^v—K2—K2^ii	163.9 (2)	K2—C5—C1	136.8 (3)
K1^v—K2—K2^iii	49.75 (18)	O3—C5—O4	124.4 (4)
K1^v—K2—K2^iv	130.7 (3)	O3—C5—C1	118.0 (6)
K1^v—K2—K2^v	0.83 (10)	O4—C5—C1	117.6 (3)
K1^v—K2—K2^vi	97.5 (2)	C2—C6—C8	120.6 (4)
K1^v—K2—K3	95 (3)	C2—C6—H6	115.6 (10)
K1^v—K2—K3^i	73.8 (4)	C8—C6—H6	123.7 (10)
K1^v—K2—K3^ii	156.5 (4)	C4—C7—C8	120.2 (2)
K1^v—K2—K3^v	7.1 (4)	C4—C7—H4	120.3 (10)
K1^v—K2—K3^vi	97.0 (4)	C8—C7—H4	119.4 (10)
K1^v—K2—O1	54.03 (19)	C6—C8—C7	119.7 (3)
K1^v—K2—O3^ii	127.6 (2)	C6—C8—H2	119.8 (12)
K1^v—K2—O3^iii	37.5 (2)	C7—C8—H2	120.4 (11)
K1^v—K2—O4	120.8 (3)

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O2—H3···O4^v	0.92 (2)	1.64 (2)	2.551 (2)	173 (2)
C6—H6···O2	0.926 (16)	2.465 (15)	2.792 (2)	100.9 (11)

Symmetry code: (v) −x+1/2, y, z−1/2.