Na
0.5K
0.5NbO
3 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
0.5NbO
3 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
R3
c (No. 161) space group to the room-temperature orthorhombic
Amm2 (No. 38) space group; the second is discontinuous from the orthorhombic to the tetragonal
P4
mm 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
R3
c →
Amm2 →
P4
mm →
Pm
m. No previous studies at low temperature have been carried out on the material with composition Na
0.5K
0.5NbO
3. 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, GM
4−, 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.
Supporting information
CCDC reference: 1043888
For both compounds, program(s) used to refine structure: FULLPROF.
(I) Sodium Potassium Niobate oxide
top
Crystal data top
K0.50Na0.50NbO3 | V = 188.47 (2) Å3 |
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 top
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 top
Rp = 4.648 | Profile function: pseudo-Voigt |
Rwp = 7.350 | 5 parameters |
Rexp = 0.896 | 0 restraints |
RBragg = 7.315 | |
χ2 = NOT FOUND | Background function: Set of experimental background points |
1280 data points | |
Crystal data top
K0.50Na0.50NbO3 | V = 188.47 (2) Å3 |
Mr = 171.94 | Z = 3 |
Trigonal, R3m | Constant Wavelength Neutron Diffraction radiation, λ = 2.522769 Å |
a = 5.6085 (3) Å | T = 10 K |
c = 6.9183 (6) Å | cylinder, 20 × 50 mm |
Data collection top
D1b, ILL Grenoble, France diffractometer | Scan method: step |
Specimen mounting: Vanadium can packed with powder | 2θmin = 0.849°, 2θmax = 128.749°, 2θstep = 0.100° |
Data collection mode: transmission | |
Refinement top
Rp = 4.648 | χ2 = NOT FOUND |
Rwp = 7.350 | 1280 data points |
Rexp = 0.896 | 5 parameters |
RBragg = 7.315 | 0 restraints |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | 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) top
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
top
Crystal data top
K0.50Na0.50NbO3 | c = 5.6763 (6) Å |
Mr = 171.94 | V = 126.33 (2) Å3 |
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 top
Scan method: step | 2θmin = 8.323°, 2θmax = 109.825°, 2θstep = 0.033° |
Refinement top
Rp = 14.719 | Profile function: pseudo-Voigt |
Rwp = 18.804 | 6 parameters |
Rexp = 6.032 | 0 restraints |
RBragg = 20.213 | |
χ2 = NOT FOUND | Background function: Set of experimental background points |
3046 data points | |
Crystal data top
K0.50Na0.50NbO3 | c = 5.6763 (6) Å |
Mr = 171.94 | V = 126.33 (2) Å3 |
Orthorhombic, Amm2 | Z = 2 |
a = 3.9443 (3) Å | Cu Kα radiation, λ = 1.540560 Å |
b = 5.6425 (6) Å | T = 295 K |
Data collection top
Scan method: step | 2θmin = 8.323°, 2θmax = 109.825°, 2θstep = 0.033° |
Refinement top
Rp = 14.719 | χ2 = NOT FOUND |
Rwp = 18.804 | 3046 data points |
Rexp = 6.032 | 6 parameters |
RBragg = 20.213 | 0 restraints |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | 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) top
Na1—O1i | 2.8512 (13) | Nb1—O1_2vii | 1.838 (6) |
Na1—O1ii | 2.8512 (13) | Nb1—O1_2vii | 1.838 (6) |
Na1—O1_2iii | 2.628 (4) | Nb1—O1_2iv | 2.184 (7) |
Na1—O1_2iv | 2.628 (4) | K1—O1i | 2.8512 (13) |
Na1—O1_2v | 3.028 (5) | K1—O1ii | 2.8512 (13) |
Na1—O1_2i | 3.028 (5) | K1—O1_2iii | 2.628 (4) |
Nb1—O1 | 1.9945 (13) | K1—O1_2iv | 2.628 (4) |
Nb1—O1vi | 1.9945 (13) | K1—O1_2v | 3.028 (5) |
Nb1—O1_2iv | 2.184 (7) | K1—O1_2i | 3.028 (5) |
| | | |
O1—Na1—O1i | 98.3 (3) | O1—K1—O1_2v | 126.4 (3) |
O1—Na1—O1ii | 98.3 (3) | O1—K1—O1_2i | 126.4 (3) |
O1—Na1—O1_2iii | 66.7 (3) | O1i—K1—O1ii | 163.38 (4) |
O1—Na1—O1_2iv | 66.7 (3) | O1i—K1—O1_2iii | 62.19 (13) |
O1—Na1—O1_2v | 126.4 (3) | O1i—K1—O1_2iv | 62.19 (13) |
O1—Na1—O1_2i | 126.4 (3) | O1ii—K1—O1_2iii | 125.52 (19) |
O1i—Na1—O1ii | 163.38 (4) | O1ii—K1—O1_2iv | 125.52 (19) |
O1i—Na1—O1_2iii | 62.19 (13) | O1ii—K1—O1_2v | 56.41 (13) |
O1i—Na1—O1_2iv | 62.19 (13) | O1ii—K1—O1_2i | 56.41 (13) |
O1ii—Na1—O1_2iii | 125.52 (19) | O1_2iii—K1—O1_2iv | 97.27 (12) |
O1ii—Na1—O1_2iv | 125.52 (19) | O1_2iii—K1—O1_2v | 89.8 (2) |
O1ii—Na1—O1_2v | 56.41 (13) | O1_2iii—K1—O1_2i | 166.9 (2) |
O1ii—Na1—O1_2i | 56.41 (13) | O1_2iv—K1—O1_2v | 166.9 (2) |
O1_2iii—Na1—O1_2iv | 97.27 (12) | O1_2iv—K1—O1_2i | 89.8 (2) |
O1_2iii—Na1—O1_2v | 89.8 (2) | O1_2v—K1—O1_2i | 81.28 (14) |
O1_2iii—Na1—O1_2i | 166.9 (2) | O1—Nb1—O1vi | 162.85 (6) |
O1_2iv—Na1—O1_2v | 166.9 (2) | O1—Nb1—O1_2iv | 83.4 (2) |
O1_2iv—Na1—O1_2i | 89.8 (2) | O1—Nb1—O1_2vii | 95.4 (3) |
O1_2v—Na1—O1_2i | 81.28 (14) | O1vi—Nb1—O1_2iv | 83.4 (2) |
O1—K1—O1i | 98.3 (3) | O1vi—Nb1—O1_2vii | 95.4 (3) |
O1—K1—O1ii | 98.3 (3) | O1_2iv—Nb1—O1_2vii | 168.5 (4) |
O1—K1—O1_2iii | 66.7 (3) | O1—Nb1—O1_2iv | 83.4 (2) |
O1—K1—O1_2iv | 66.7 (3) | O1—Nb1—O1_2vii | 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. |
Experimental details
| (I) | (II) |
Crystal data |
Chemical formula | K0.50Na0.50NbO3 | K0.50Na0.50NbO3 |
Mr | 171.94 | 171.94 |
Crystal system, space group | Trigonal, R3m | Orthorhombic, Amm2 |
Temperature (K) | 10 | 295 |
a, b, c (Å) | 5.6085 (3), 5.6085 (3), 6.9183 (6) | 3.9443 (3), 5.6425 (6), 5.6763 (6) |
α, β, γ (°) | 90, 90, 120 | 90, 90, 90 |
V (Å3) | 188.47 (2) | 126.33 (2) |
Z | 3 | 2 |
Radiation type | Constant Wavelength Neutron Diffraction, λ = 2.522769 Å | Cu Kα, λ = 1.540560 Å |
µ (mm−1) | ? | – |
Specimen shape, size (mm) | Cylinder, 20 × 50 | ?, ? × ? × ? |
|
Data collection |
Data collection method | D1b, ILL Grenoble, France | ? |
Specimen mounting | Vanadium can packed with powder | ? |
Data collection mode | Transmission | ? |
Scan method | Step | Step |
2θ values (°) | 2θmin = 0.849 2θmax = 128.749 2θstep = 0.100 | 2θmin = 8.323 2θmax = 109.825 2θstep = 0.033 |
|
Refinement |
R factors and goodness of fit | Rp = 4.648, Rwp = 7.350, Rexp = 0.896, RBragg = 7.315, χ2 = NOT FOUND | Rp = 14.719, Rwp = 18.804, Rexp = 6.032, RBragg = 20.213, χ2 = NOT FOUND |
No. of data points | 1280 | 3046 |
No. of parameters | 5 | 6 |