The natural tiling approach to cation conductivity in KAlO₂ polymorphs

A detailed analysis of correlations between structural features and cation conductivity is performed for KAlO₂ polymorphs in a wide temperature range of 300-1023 K. To explore the migration maps of K⁺ cations we have used neutron diffraction data for low- and high-temperature KAlO₂ polymorphs and applied for the first time a novel algorithm based on the natural tiling concept and implemented it into the program package TOPOS. Five independent elementary channels for the K⁺ cation migration have been revealed whose cross-sections were found to be essentially different in the low-temperature form, indicating a high anisotropy of the cation conductivity. During the transition to the cubic high-temperature phase all five channels become equivalent with sharply increased cross-sections that account for the jump-like increase of the cation conductivity and gives rise to its three-dimensional character.

Computing details

For all compounds, program(s) used to refine structure: FULLPROF.

(KAlO2_300)

Crystal data

Al2O4·2(K)	c = 15.4564 (4) Å
Mr = 196.16	V = 918.26 (5) Å^3
Orthorhombic, PBCA	Z = 8
Hall symbol: -P 2ac 2ab	Dx = 2.838 Mg m^−3
a = 5.43867 (18) Å	Neutron radiation
b = 10.9236 (3) Å	T = 300 K

Data collection

HPRT neutron diffractometer	2θmin = 4.529°, 2θmax = 164.629°, 2θstep = 0.100°
Radiation source: nuclear reactor

Refinement

Rp = 1.263	Profile function: pseudo-Voigt
Rwp = 1.725	68 parameters
Rexp = 1.251	0 restraints
RBragg = 2.490	Background function: linear interpolation
1602 data points

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

	x	y	z	Uiso*/Ueq
Al1	0.2590 (10)	0.0104 (5)	0.1866 (7)	0.0059 (5)*
Al2	0.2811 (8)	0.2601 (5)	0.0656 (5)	0.0059 (5)*
K1	0.7534 (11)	0.0067 (6)	0.0611 (7)	0.021 (5)
K2	0.7916 (10)	0.2592 (5)	0.1863 (5)	0.014 (4)
O1	0.5673 (7)	0.2848 (4)	0.0162 (2)	0.018 (2)
O2	0.1777 (7)	0.4023 (3)	0.10588 (19)	0.0089 (19)
O3	0.2965 (6)	0.1555 (3)	0.1479 (2)	0.0164 (18)
O4	0.0526 (7)	0.4856 (3)	0.2776 (3)	0.012 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.020 (4)	0.018 (4)	0.026 (6)	0.00000	0.015 (4)	0.00000
K2	0.019 (3)	0.014 (3)	0.010 (5)	0.00000	−0.002 (3)	0.00000
O1	0.0104 (18)	0.029 (2)	0.014 (2)	0.00000	0.0093 (15)	0.00000
O2	0.014 (2)	0.0086 (18)	0.0037 (19)	0.00000	−0.0033 (13)	0.00000
O3	0.0044 (5)	0.018 (2)	0.027 (3)	0.00000	−0.0046 (16)	0.00000
O4	0.0103 (19)	0.012 (2)	0.015 (2)	0.00000	−0.0071 (17)	0.00000

Geometric parameters (Å, º)

Al1—O2^i	1.752 (9)	K1—O2^v	2.796 (11)
Al1—O3	1.706 (7)	K1—O2^i	2.698 (7)
Al1—O4^ii	1.803 (7)	K1—O4^vi	2.717 (11)
Al1—O4^i	1.761 (10)	K2—O1	2.912 (8)
Al2—O1	1.755 (6)	K2—O2^vii	2.898 (7)
Al2—O1^iii	1.786 (7)	K2—O3	2.981 (6)
Al2—O2	1.765 (7)	K2—O3^viii	2.802 (8)
Al2—O3	1.712 (8)	K2—O4^viii	2.849 (7)
K1—O1^iv	2.703 (8)
O2—Al1—O3	110.668	O1^viii—Al2—O1	108.160
O2—Al1—O4	107.574	O1^viii—Al2—O2	107.502
O2—Al1—O4	110.532	O1^viii—Al2—O3	103.672
O3—Al1—O4	111.067	O1—Al2—O2	106.489
O3—Al1—O4	110.690	O1—Al2—O3	111.993
O4—Al1—O4	106.177	O2—Al2—O3	109.926

Symmetry codes: (i) −x+1/2, y−1/2, z; (ii) −x, y−1/2, −z+1/2; (iii) x−1/2, −y+1/2, −z; (iv) −x+3/2, y−1/2, z; (v) x+1/2, −y+1/2, −z; (vi) −x+1, y−1/2, −z+1/2; (vii) x+1, y, z; (viii) x+1/2, y, −z+1/2.

(KAlO2_400)

Crystal data

Al2O4·2(K)	c = 15.4698 (9) Å
Mr = 196.16	V = 921.64 (10) Å^3
Orthorhombic, PBCA	Z = 8
Hall symbol: -P 2ac 2ab	Dx = 2.827 Mg m^−3
a = 5.4457 (3) Å	Neutron radiation
b = 10.9401 (7) Å	T = 400 K

Data collection

HPRT neutron diffractometer	2θmin = 4.531°, 2θmax = 164.831°, 2θstep = 0.100°
Radiation source: nuclear reactor

Refinement

Rp = 4.444	Profile function: pseudo-Voigt
Rwp = 5.756	70 parameters
Rexp = 4.851	0 restraints
RBragg = 3.196	Background function: linear interpolation
1604 data points

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

	x	y	z	Uiso*/Ueq
Al1	0.2579 (18)	0.0116 (9)	0.1864 (11)	0.0069 (10)*
Al2	0.2791 (14)	0.2596 (9)	0.0661 (9)	0.0069 (10)*
K1	0.752 (2)	0.0065 (10)	0.0625 (12)	0.024 (9)
K2	0.7901 (18)	0.2596 (9)	0.1875 (10)	0.021 (7)
O1	0.5651 (13)	0.2827 (7)	0.0165 (4)	0.021 (4)
O2	0.1799 (14)	0.4013 (6)	0.1066 (3)	0.011 (3)
O3	0.2965 (12)	0.1549 (7)	0.1477 (4)	0.020 (3)
O4	0.0527 (14)	0.4851 (6)	0.2775 (5)	0.014 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.027 (9)	0.010 (8)	0.034 (12)	0.00000	0.018 (8)	0.00000
K2	0.023 (6)	0.025 (7)	0.016 (9)	0.00000	0.006 (5)	0.00000
O1	0.013 (3)	0.028 (4)	0.020 (4)	0.00000	0.008 (3)	0.00000
O2	0.020 (4)	0.008 (3)	0.006 (3)	0.00000	−0.005 (2)	0.00000
O3	0.0081 (11)	0.033 (4)	0.021 (5)	0.00000	−0.003 (3)	0.00000
O4	0.007 (3)	0.022 (5)	0.015 (4)	0.00000	−0.002 (3)	0.00000

Geometric parameters (Å, º)

Al1—O2^i	1.759 (15)	K1—O2^v	2.831 (18)
Al1—O3	1.691 (13)	K1—O2^i	2.706 (14)
Al1—O4^ii	1.805 (13)	K1—O4^vi	2.704 (19)
Al1—O4^i	1.770 (17)	K2—O1	2.926 (16)
Al2—O1	1.755 (12)	K2—O2^vii	2.911 (13)
Al2—O1^iii	1.790 (13)	K2—O3	2.986 (12)
Al2—O2	1.757 (12)	K2—O3^viii	2.795 (16)
Al2—O3	1.707 (14)	K2—O4^viii	2.837 (12)
K1—O1^iv	2.737 (14)
O2—Al1—O3	111.315	O1^viii—Al2—O1	107.634
O2—Al1—O4	106.704	O1^viii—Al2—O2	107.564
O2—Al1—O4	109.519	O1^viii—Al2—O3	103.881
O3—Al1—O4	112.021	O1—Al2—O2	106.405
O3—Al1—O4	111.173	O1—Al2—O3	112.983
O4—Al1—O4	105.867	O2—Al2—O3	110.203

Symmetry codes: (i) −x+1/2, y−1/2, z; (ii) −x, y−1/2, −z+1/2; (iii) x−1/2, −y+1/2, −z; (iv) −x+3/2, y−1/2, z; (v) x+1/2, −y+1/2, −z; (vi) −x+1, y−1/2, −z+1/2; (vii) x+1, y, z; (viii) x+1/2, y, −z+1/2.

(KAlO2_500)

Crystal data

Al2O4·2(K)	c = 15.4893 (12) Å
Mr = 196.16	V = 926.38 (12) Å^3
Orthorhombic, PBCA	Z = 8
Hall symbol: -P 2ac 2ab	Dx = 2.813 Mg m^−3
a = 5.4560 (4) Å	Neutron radiation
b = 10.9617 (8) Å	T = 500 K

Data collection

HPRT neutron diffractometer	2θmin = 4.534°, 2θmax = 164.834°, 2θstep = 0.100°
Radiation source: nuclear reactor

Refinement

Rp = 4.701	Profile function: pseudo-Voigt
Rwp = 6.056	70 parameters
Rexp = 4.863	0 restraints
RBragg = 3.861	Background function: linear interpolation
1604 data points

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

	x	y	z	Uiso*/Ueq
Al1	0.260 (2)	0.0095 (11)	0.1845 (11)	0.0097 (12)*
Al2	0.2793 (16)	0.2607 (10)	0.0671 (10)	0.0097 (12)*
K1	0.744 (2)	0.0060 (11)	0.0606 (14)	0.029 (11)
K2	0.787 (2)	0.2603 (10)	0.1868 (12)	0.025 (9)
O1	0.5661 (15)	0.2814 (8)	0.0161 (4)	0.026 (4)
O2	0.1817 (15)	0.4001 (7)	0.1067 (4)	0.015 (4)
O3	0.2935 (14)	0.1529 (8)	0.1464 (5)	0.026 (4)
O4	0.0539 (16)	0.4877 (7)	0.2771 (6)	0.023 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.026 (10)	0.011 (9)	0.051 (15)	0.00000	0.020 (9)	0.00000
K2	0.024 (7)	0.024 (9)	0.028 (11)	0.00000	−0.002 (6)	0.00000
O1	0.021 (4)	0.044 (5)	0.012 (4)	0.00000	0.012 (3)	0.00000
O2	0.018 (4)	0.009 (4)	0.019 (4)	0.00000	−0.002 (3)	0.00000
O3	0.0081 (13)	0.033 (5)	0.038 (6)	0.00000	−0.002 (3)	0.00000
O4	0.006 (4)	0.042 (7)	0.022 (5)	0.00000	−0.004 (4)	0.00000

Geometric parameters (Å, º)

Al1—O2^i	1.730 (16)	K1—O1^iv	2.759 (15)
Al1—O3	1.689 (15)	K1—O2^v	2.81 (2)
Al1—O4^ii	1.829 (15)	K1—O2^i	2.693 (15)
Al1—O4^i	1.774 (18)	K1—O4^vi	2.75 (2)
Al2—O1	1.768 (13)	K2—O1	2.915 (19)
Al2—O1^iii	1.796 (15)	K2—O2^vii	2.920 (15)
Al2—O2	1.731 (14)	K2—O3^viii	2.839 (19)
Al2—O3	1.706 (16)	K2—O4^viii	2.854 (14)
O2—Al1—O3	112.454	O1^viii—Al2—O1	106.596
O2—Al1—O4	107.954	O1^viii—Al2—O2	108.510
O2—Al1—O4	111.393	O1^viii—Al2—O3	109.870
O3—Al1—O4	109.671	O1—Al2—O2	106.372
O3—Al1—O4	107.613	O1—Al2—O3	111.744
O4—Al1—O4	110.245	O2—Al2—O3	111.589

Symmetry codes: (i) −x+1/2, y−1/2, z; (ii) −x, y−1/2, −z+1/2; (iii) x−1/2, −y+1/2, −z; (iv) −x+3/2, y−1/2, z; (v) x+1/2, −y+1/2, −z; (vi) −x+1, y−1/2, −z+1/2; (vii) x+1, y, z; (viii) x+1/2, y, −z+1/2.

(KAlO2_600)

Crystal data

Al2O4·2(K)	c = 15.5103 (14) Å
Mr = 196.16	V = 931.53 (14) Å^3
Orthorhombic, PBCA	Z = 8
Hall symbol: -P 2ac 2ab	Dx = 2.797 Mg m^−3
a = 5.4668 (4) Å	Neutron radiation
b = 10.9862 (9) Å	T = 600 K

Data collection

HPRT neutron diffractometer	2θmin = 4.542°, 2θmax = 164.842°, 2θstep = 0.100°
Radiation source: nuclear reactor

Refinement

Rp = 4.565	Profile function: pseudo-Voigt
Rwp = 5.776	70 parameters
Rexp = 4.869	0 restraints
RBragg = 4.455	Background function: linear interpolation
1604 data points

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

	x	y	z	Uiso*/Ueq
Al1	0.256 (2)	0.0108 (11)	0.1870 (11)	0.0127 (12)*
Al2	0.2795 (17)	0.2589 (11)	0.0656 (11)	0.0127 (12)*
K1	0.749 (3)	0.0050 (12)	0.0635 (15)	0.037 (13)
K2	0.782 (2)	0.2574 (11)	0.1888 (13)	0.033 (10)
O1	0.5636 (16)	0.2803 (9)	0.0158 (5)	0.032 (5)
O2	0.1885 (16)	0.3986 (7)	0.1076 (5)	0.020 (4)
O3	0.2938 (15)	0.1508 (9)	0.1450 (6)	0.037 (5)
O4	0.0510 (17)	0.4873 (8)	0.2767 (7)	0.031 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.037 (12)	0.017 (10)	0.057 (17)	0.00000	0.023 (12)	0.00000
K2	0.021 (8)	0.034 (10)	0.043 (14)	0.00000	−0.001 (6)	0.00000
O1	0.022 (4)	0.051 (6)	0.022 (5)	0.00000	0.003 (4)	0.00000
O2	0.027 (5)	0.003 (4)	0.029 (5)	0.00000	−0.004 (3)	0.00000
O3	0.0132 (15)	0.053 (6)	0.044 (7)	0.00000	−0.006 (4)	0.00000
O4	0.006 (4)	0.062 (9)	0.024 (5)	0.00000	−0.004 (4)	0.00000

Geometric parameters (Å, º)

Al1—O2^i	1.769 (17)	K1—O2^v	2.88 (2)
Al1—O3	1.683 (16)	K1—O2^i	2.749 (18)
Al1—O4^ii	1.789 (15)	K1—O4^vi	2.72 (2)
Al1—O4^i	1.765 (18)	K2—O1	2.95 (2)
Al2—O1	1.750 (14)	K2—O2^vii	2.988 (16)
Al2—O1^iii	1.781 (16)	K2—O3	2.993 (15)
Al2—O2	1.740 (15)	K2—O3^viii	2.83 (2)
Al2—O3	1.713 (18)	K2—O4^viii	2.874 (15)
K1—O1^iv	2.773 (17)
O2—Al1—O3	110.263	O1^viii—Al2—O1	107.917
O2—Al1—O4	106.230	O1^viii—Al2—O2	107.483
O2—Al1—O4	110.142	O1^viii—Al2—O3	109.870
O3—Al1—O4	111.647	O1—Al2—O2	106.810
O3—Al1—O4	111.429	O1—Al2—O3	111.712
O4—Al1—O4	106.954	O2—Al2—O3	111.857

Symmetry codes: (i) −x+1/2, y−1/2, z; (ii) −x, y−1/2, −z+1/2; (iii) x−1/2, −y+1/2, −z; (iv) −x+3/2, y−1/2, z; (v) x+1/2, −y+1/2, −z; (vi) −x+1, y−1/2, −z+1/2; (vii) x+1, y, z; (viii) x+1/2, y, −z+1/2.

(KAlO2_700)

Crystal data

Al2O4·2(K)	c = 15.5359 (18) Å
Mr = 196.16	V = 937.35 (17) Å^3
Orthorhombic, PBCA	Z = 8
Hall symbol: -P 2ac 2ab	Dx = 2.780 Mg m^−3
a = 5.4788 (5) Å	Neutron radiation
b = 11.0123 (11) Å	T = 700 K

Data collection

HPRT neutron diffractometer	2θmin = 4.547°, 2θmax = 164.847°, 2θstep = 0.100°
Radiation source: nuclear reactor

Refinement

Rp = 4.701	Profile function: pseudo-Voigt
Rwp = 5.915	70 parameters
Rexp = 4.863	0 restraints
RBragg = 5.940	Background function: linear interpolation
1604 data points

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

	x	y	z	Uiso*/Ueq
Al1	0.255 (2)	0.0106 (14)	0.1849 (12)	0.0164 (13)*
Al2	0.2783 (19)	0.2600 (12)	0.0632 (12)	0.0164 (13)*
K1	0.749 (3)	0.0045 (15)	0.067 (2)	0.054 (12)
K2	0.774 (2)	0.2593 (12)	0.1897 (14)	0.030 (8)
O1	0.5622 (19)	0.2773 (11)	0.0163 (6)	0.042 (5)
O2	0.1872 (18)	0.3957 (9)	0.1095 (6)	0.029 (4)
O3	0.2938 (16)	0.1493 (10)	0.1444 (7)	0.042 (6)
O4	0.048 (2)	0.4878 (10)	0.2750 (9)	0.043 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.022 (5)	0.031 (6)	0.11 (2)	0.00000	0.024 (14)	0.00000
K2	0.022 (5)	0.031 (6)	0.038 (13)	0.00000	−0.010 (6)	0.00000
O1	0.028 (4)	0.074 (8)	0.025 (6)	0.00000	0.0003 (4)	0.00000
O2	0.0053 (11)	0.021 (5)	0.061 (7)	0.00000	−0.006 (5)	0.00000
O3	0.0138 (17)	0.056 (7)	0.057 (8)	0.00000	−0.008 (5)	0.00000
O4	0.021 (5)	0.068 (10)	0.040 (8)	0.00000	0.013 (5)	0.00000

Geometric parameters (Å, º)

Al1—O2^i	1.753 (19)	K1—O2^v	2.98 (3)
Al1—O3	1.666 (19)	K1—O2^i	2.75 (2)
Al1—O4^ii	1.791 (17)	K1—O4^vi	2.70 (3)
Al1—O4^i	1.79 (2)	K2—O1	2.94 (2)
Al2—O1	1.728 (16)	K2—O2^vii	2.991 (17)
Al2—O1^iii	1.760 (18)	K2—O3	2.978 (15)
Al2—O2	1.732 (17)	K2—O3^viii	2.85 (2)
Al2—O3	1.76 (2)	K2—O4^viii	2.856 (17)
K1—O1^iv	2.82 (2)
O2—Al1—O3	112.731	O1^viii—Al2—O1	109.597
O2—Al1—O4	107.380	O1^viii—Al2—O2	108.421
O2—Al1—O4	108.251	O1^viii—Al2—O3	109.623
O3—Al1—O4	112.229	O1—Al2—O2	107.400
O3—Al1—O4	110.365	O1—Al2—O3	112.005
O4—Al1—O4	105.542	O2—Al2—O3	108.331

Symmetry codes: (i) −x+1/2, y−1/2, z; (ii) −x, y−1/2, −z+1/2; (iii) x−1/2, −y+1/2, −z; (iv) −x+3/2, y−1/2, z; (v) x+1/2, −y+1/2, −z; (vi) −x+1, y−1/2, −z+1/2; (vii) x+1, y, z; (viii) x+1/2, y, −z+1/2.

(KAlO2_773)

Crystal data

Al2O4·2(K)	c = 15.5598 (5) Å
Mr = 196.16	V = 942.40 (6) Å^3
Orthorhombic, PBCA	Z = 8
Hall symbol: -P 2ac 2ab	Dx = 2.765 Mg m^−3
a = 5.4888 (2) Å	Neutron radiation
b = 11.0346 (4) Å	T = 773 K

Data collection

HPRT neutron diffractometer	2θmin = 4.538°, 2θmax = 164.838°, 2θstep = 0.100°
Radiation source: nuclear reactor

Refinement

Rp = 2.984	Profile function: pseudo-Voigt
Rwp = 3.859	66 parameters
Rexp = 1.577	0 restraints
RBragg = 5.993	Background function: linear interpolation
1604 data points

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

	x	y	z	Uiso*/Ueq
Al1	0.249 (3)	0.0060 (18)	0.1853 (15)	0.020 (4)*
Al2	0.272 (2)	0.2554 (11)	0.0647 (15)	0.020 (4)*
K1	0.761 (6)	0.0022 (19)	0.0604 (19)	0.07 (2)
K2	0.782 (3)	0.2559 (14)	0.1888 (16)	0.050 (16)
O1	0.553 (2)	0.2729 (14)	0.0141 (7)	0.070 (10)
O2	0.192 (3)	0.3933 (13)	0.1115 (8)	0.063 (10)
O3	0.2922 (16)	0.1482 (10)	0.1417 (7)	0.029 (6)
O4	0.045 (2)	0.4910 (9)	0.2758 (8)	0.039 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.088 (19)	0.09 (2)	0.025 (17)	0.00000	−0.01103	0.00000
K2	0.042 (11)	0.08 (2)	0.025 (16)	0.00000	−0.001 (7)	0.00000
O1	0.026 (6)	0.128 (15)	0.054 (9)	0.00000	0.026 (5)	0.00000
O2	0.105 (12)	0.031 (8)	0.052 (9)	0.00000	−0.004 (7)	0.00000
O3	0.011 (4)	0.027 (7)	0.049 (7)	0.00000	0.003 (5)	0.00000
O4	0.018 (6)	0.078 (10)	0.022 (5)	0.00000	0.005 (6)	0.00000

Geometric parameters (Å, º)

Al1—O2^i	1.72 (2)	K1—O2^v	3.33 (3)
Al1—O3	1.72 (2)	K1—O3	3.29 (3)
Al1—O4^ii	1.73 (2)	K1—O4^vi	2.77 (3)
Al1—O4^i	1.82 (2)	K2—O1	3.00 (2)
Al2—O1	1.743 (16)	K2—O2^vii	2.961 (17)
Al2—O1^iii	1.745 (18)	K2—O2^viii	3.49 (2)
Al2—O2	1.744 (16)	K2—O3	3.036 (16)
Al2—O3	1.69 (2)	K2—O3^vii	3.124 (16)
K1—O1	3.28 (2)	K2—O3^viii	2.89 (2)
K1—O1^iv	3.17 (2)	K2—O4^vii	3.259 (17)
K1—O1^v	2.82 (2)	K2—O4^vi	3.122 (16)
K1—O2^iv	2.94 (3)	K2—O4^viii	2.958 (16)
K1—O2^i	2.87 (3)
O2—Al1—O3	111.579	O1^viii—Al2—O1	108.178
O2—Al1—O4	109.951	O1^viii—Al2—O2	108.421
O2—Al1—O4	109.404	O1^viii—Al2—O3	109.870
O3—Al1—O4	110.626	O1—Al2—O2	105.984
O3—Al1—O4	107.613	O1—Al2—O3	114.750
O4—Al1—O4	107.548	O2—Al2—O3	109.413

Symmetry codes: (i) −x+1/2, y−1/2, z; (ii) −x, y−1/2, −z+1/2; (iii) x−1/2, −y+1/2, −z; (iv) x+1/2, −y+1/2, −z; (v) −x+3/2, y−1/2, z; (vi) −x+1, y−1/2, −z+1/2; (vii) x+1, y, z; (viii) x+1/2, y, −z+1/2.

(KAlO2_833)

Crystal data

Al8O16·8(K)	V = 475.16 (7) Å^3
Mr = 783.62	Z = 1
Cubic, FD3M	Dx = 2.739 Mg m^−3
Hall symbol: -F 4vw 2vw 3	Neutron radiation
a = 7.8033 (6) Å	T = 833 K

Data collection

HPRT neutron diffractometer	2θmin = 4.520°, 2θmax = 164.820°, 2θstep = 0.100°
Radiation source: nuclear reactor

Refinement

Rp = 5.985	Profile function: pseudo-Voigt
Rwp = 7.808	26 parameters
Rexp = 4.914	0 restraints
RBragg = 11.546	Background function: linear interpolation
1604 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Al1	0.12500	0.12500	0.12500	0.0272 (13)*
K1	0.37500	0.37500	0.37500	0.065 (2)*
O2	0.05 (2)	−0.04 (2)	−0.01 (7)	0.037 (6)*	0.08333

Geometric parameters (Å, º)

Al1—O2	1.8 (3)	K1—O2^ii	2.8 (2)
Al1—O2^i	1.8 (3)	K1—O2^iii	2.8 (2)
O2—Al1—O2^i	29

Symmetry codes: (i) z, x, y; (ii) x, −y+1/4, −z+1/4; (iii) −y+1/4, −z+1/4, x.

(KAlO2_923)

Crystal data

Al8O16·8(K)	V = 477.83 (5) Å^3
Mr = 783.62	Z = 1
Cubic, FD3M	Dx = 2.723 Mg m^−3
Hall symbol: -F 4vw 2vw 3	Neutron radiation
a = 7.8179 (5) Å	T = 923 K

Data collection

HPRT neutron diffractometer	2θmin = 4.540°, 2θmax = 164.840°, 2θstep = 0.100°
Radiation source: nuclear reactor

Refinement

Rp = 4.625	Profile function: pseudo-Voigt
Rwp = 6.153	32 parameters
Rexp = 4.898	0 restraints
RBragg = 3.186	Background function: linear interpolation
1604 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Al1	0.12500	0.12500	0.12500	0.0293 (11)*
K1	0.37500	0.37500	0.37500	0.0677 (18)*
O2	0.036 (10)	−0.048 (4)	0.01 (3)	0.035 (5)*	0.08333

Geometric parameters (Å, º)

Al1—O2	1.77 (13)	K1—O2^ii	2.92 (11)
Al1—O2^i	1.75 (15)	K1—O2^iii	2.9 (2)
O2—Al1—O2^i	31

Symmetry codes: (i) −x, −y, −z; (ii) x, −y+1/4, −z+1/4; (iii) −y+1/4, −z+1/4, x.

(KAlO2_1023)

Crystal data

Al8O16·8(K)	V = 480.58 (4) Å^3
Mr = 783.62	Z = 1
Cubic, FD3M	Dx = 2.715 Mg m^−3
Hall symbol: -F 4vw 2vw 3	Neutron radiation
a = 7.8329 (3) Å	T = 1023 K

Data collection

HPRT neutron diffractometer	2θmin = 4.546°, 2θmax = 164.846°, 2θstep = 0.100°
Radiation source: nuclear reactor

Refinement

Rp = 2.564	Profile function: pseudo-Voigt
Rwp = 3.541	32 parameters
Rexp = 1.611	0 restraints
RBragg = 4.334	Background function: linear interpolation
1604 data points

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

	x	y	z	Uiso*/Ueq
Al1	0.12500	0.12500	0.12500	0.0486 (9)*
K1	0.37500	0.37500	0.37500	0.0921 (13)*
O2	0.00000	0.00000	0.00000	0.197 (6)*

Geometric parameters (Å, º)

Al1—O2	1.6959 (1)	K1—O2^i	3.2474 (1)
O2—Al1—O2^i	109.471

Symmetry code: (i) x, −y+1/4, −z+1/4.