Mode-crystallography analysis of the crystal structures and the low- and high-temperature phase transitions in Na_0.5K_0.5NbO₃

Na_0.5K_0.5NbO₃ has been synthesized by the conventional solid-state reaction process. The crystal structures and phase transitions, at low and high temperature, determined from the Rietveld refinements of X-ray and neutron powder diffraction data are reported. The structure evolution of Na_0.5K_0.5NbO₃ in the temperature range from 2 to 875 K shows the presence of three phase transitions. The first one, at ∼135 K, is discontinuous from the rhombohedral R3c (No. 161) space group to the room-temperature orthorhombic Amm2 (No. 38) space group; the second is discontinuous from the orthorhombic to the tetragonal P4mm space group (No. 99) at ∼465 K, and the third is continuous from the tetragonal to the cubic space group (No. 221) at ∼700 K. The obtained phase-transition sequence is R3c → Amm2 → P4mm → Pmm. No previous studies at low temperature have been carried out on the material with composition Na_0.5K_0.5NbO₃. In the course of the determination of the three experimentally found phases, a novel method of refinement is presented. This is a step forward in the use of the symmetry-adapted modes as degrees of freedom in the refinement process: the parameterization of a direction in the internal space of the, in this case, sole irreducible representation, GM₄⁻, responsible for the symmetry breaking from the parent cubic space group to the polar distorted low-symmetry phases. Eventually, this procedure enables the calculation of the spontaneous polarization.

Computing details

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

(I) Sodium Potassium Niobate oxide

Crystal data

K0.50Na0.50NbO3	V = 188.47 (2) Å^3
Mr = 171.94	Z = 3
Trigonal, R3m	Constant Wavelength Neutron Diffraction radiation, λ = 2.522769 Å
Hall symbol: R 3 -2"	T = 10 K
a = 5.6085 (3) Å	White
c = 6.9183 (6) Å	cylinder, 20 × 50 mm

Data collection

D1b, ILL Grenoble, France diffractometer	Data collection mode: transmission
Radiation source: nuclear reactor, D1b-ILL	Scan method: step
Specimen mounting: Vanadium can packed with powder	2θmin = 0.849°, 2θmax = 128.749°, 2θstep = 0.100°

Refinement

Rp = 4.648	Profile function: pseudo-Voigt
Rwp = 7.350	5 parameters
Rexp = 0.896	0 restraints
RBragg = 7.315
χ^2 = NOT FOUND	Background function: Set of experimental background points
1280 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Na1	0.00000	0.00000	0.0314 (5)	0.01092*	0.50000
K1	0.00000	0.00000	0.0314 (5)	0.01092*	0.50000
Nb1	0.00000	0.00000	0.5174 (5)	0.00759*
O1	0.1648 (2)	0.3296 (4)	0.3170 (3)	0.00665*

Geometric parameters (Å, º)

Na1—O1	2.5430 (4)	Nb1—O1	2.1178 (3)
Na1—O1	2.5430 (2)	Nb1—O1	2.1178 (2)
Na1—O1	2.5430 (4)	Nb1—O1	2.1178 (3)
Na1—O1	2.5430 (4)	Nb1—O1	2.1178 (3)
Na1—O1	2.5430 (2)	Nb1—O1	2.1178 (2)
Na1—O1	2.5430 (4)	Nb1—O1	2.1178 (3)
O1—Na1—O1	66.08 (11)	O1—Na1—O1	95.45 (11)
O1—Na1—O1	58.81 (8)	O1—Na1—O1	110.86 (13)
O1—Na1—O1	56.54 (10)	O1—Na1—O1	166.55 (10)
O1—Na1—O1	60.28 (7)	O1—Na1—O1	118.65 (12)
O1—Na1—O1	54.37 (10)	O1—Na1—O1	119.60 (14)
O1—Na1—O1	63.09 (11)	O1—Na1—O1	172.82 (16)
O1—Na1—O1	84.10 (11)	O1—Na1—O1	129.07 (15)
O1—Na1—O1	95.45 (13)	O1—Na1—O1	172.83 (14)

(II) Sodium Potassium Niobate oxide

Crystal data

K0.50Na0.50NbO3	c = 5.6763 (6) Å
Mr = 171.94	V = 126.33 (2) Å^3
Orthorhombic, Amm2	Z = 2
Hall symbol: A 2 -2	Cu Kα radiation, λ = 1.540560 Å
a = 3.9443 (3) Å	T = 295 K
b = 5.6425 (6) Å

Data collection

Scan method: step

2θmin = 8.323°, 2θmax = 109.825°, 2θstep = 0.033°

Refinement

Rp = 14.719	Profile function: pseudo-Voigt
Rwp = 18.804	6 parameters
Rexp = 6.032	0 restraints
RBragg = 20.213
χ^2 = NOT FOUND	Background function: Set of experimental background points
3046 data points

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Na1	0.00000	0.00000	0.0453 (11)	0.01092*	0.50000
K1	0.00000	0.00000	0.0453 (11)	0.01092*	0.50000
Nb1	0.50000	0.00000	0.5251 (11)	0.00758*
O1	0.00000	0.00000	0.4727 (11)	0.00665*
O1_2	0.50000	0.7535 (8)	0.2285 (8)	0.00665*

Geometric parameters (Å, º)

Na1—O1^i	2.8512 (13)	Nb1—O1_2^vii	1.838 (6)
Na1—O1^ii	2.8512 (13)	Nb1—O1_2^vii	1.838 (6)
Na1—O1_2^iii	2.628 (4)	Nb1—O1_2^iv	2.184 (7)
Na1—O1_2^iv	2.628 (4)	K1—O1^i	2.8512 (13)
Na1—O1_2^v	3.028 (5)	K1—O1^ii	2.8512 (13)
Na1—O1_2^i	3.028 (5)	K1—O1_2^iii	2.628 (4)
Nb1—O1	1.9945 (13)	K1—O1_2^iv	2.628 (4)
Nb1—O1^vi	1.9945 (13)	K1—O1_2^v	3.028 (5)
Nb1—O1_2^iv	2.184 (7)	K1—O1_2^i	3.028 (5)
O1—Na1—O1^i	98.3 (3)	O1—K1—O1_2^v	126.4 (3)
O1—Na1—O1^ii	98.3 (3)	O1—K1—O1_2^i	126.4 (3)
O1—Na1—O1_2^iii	66.7 (3)	O1^i—K1—O1^ii	163.38 (4)
O1—Na1—O1_2^iv	66.7 (3)	O1^i—K1—O1_2^iii	62.19 (13)
O1—Na1—O1_2^v	126.4 (3)	O1^i—K1—O1_2^iv	62.19 (13)
O1—Na1—O1_2^i	126.4 (3)	O1^ii—K1—O1_2^iii	125.52 (19)
O1^i—Na1—O1^ii	163.38 (4)	O1^ii—K1—O1_2^iv	125.52 (19)
O1^i—Na1—O1_2^iii	62.19 (13)	O1^ii—K1—O1_2^v	56.41 (13)
O1^i—Na1—O1_2^iv	62.19 (13)	O1^ii—K1—O1_2^i	56.41 (13)
O1^ii—Na1—O1_2^iii	125.52 (19)	O1_2^iii—K1—O1_2^iv	97.27 (12)
O1^ii—Na1—O1_2^iv	125.52 (19)	O1_2^iii—K1—O1_2^v	89.8 (2)
O1^ii—Na1—O1_2^v	56.41 (13)	O1_2^iii—K1—O1_2^i	166.9 (2)
O1^ii—Na1—O1_2^i	56.41 (13)	O1_2^iv—K1—O1_2^v	166.9 (2)
O1_2^iii—Na1—O1_2^iv	97.27 (12)	O1_2^iv—K1—O1_2^i	89.8 (2)
O1_2^iii—Na1—O1_2^v	89.8 (2)	O1_2^v—K1—O1_2^i	81.28 (14)
O1_2^iii—Na1—O1_2^i	166.9 (2)	O1—Nb1—O1^vi	162.85 (6)
O1_2^iv—Na1—O1_2^v	166.9 (2)	O1—Nb1—O1_2^iv	83.4 (2)
O1_2^iv—Na1—O1_2^i	89.8 (2)	O1—Nb1—O1_2^vii	95.4 (3)
O1_2^v—Na1—O1_2^i	81.28 (14)	O1^vi—Nb1—O1_2^iv	83.4 (2)
O1—K1—O1^i	98.3 (3)	O1^vi—Nb1—O1_2^vii	95.4 (3)
O1—K1—O1^ii	98.3 (3)	O1_2^iv—Nb1—O1_2^vii	168.5 (4)
O1—K1—O1_2^iii	66.7 (3)	O1—Nb1—O1_2^iv	83.4 (2)
O1—K1—O1_2^iv	66.7 (3)	O1—Nb1—O1_2^vii	95.4 (3)

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