Investigation of the structure and phase transitions in the novel A-site substituted distorted perovskite compound Na_0.5Bi_0.5TiO₃

Rietveld neutron powder profile analysis of the compound Na_0.5Bi_0.5TiO₃ (NBT) is reported over the temperature range 5–873 K. The sequence of phase transitions from the high-temperature prototypic cubic structure (above 813 K), to one of tetragonal (673–773 K) and then rhombohedral structures (5–528 K) has been established. Coexisting tetragonal/cubic (773–813 K) and rhombohedral/tetragonal (with an upper temperature limit of 145 K between 528 and 673 K) phases have also been observed. Refinements have revealed that the rhombohedral phase, space group R3c, with a_H = 5.4887 (2), c_H = 13.5048 (8) Å, V = 352.33 (3) ų, Z = 6 and D_x = 5.99 Mg m⁻³, exhibits an antiphase, a⁻a⁻a⁻ oxygen tilt system, ω = 8.24 (4)°, with parallel cation displacements at room temperature. The tetragonal phase, space group P4bm, with a_T = 5.5179 (2), c_T = 3.9073 (2) Å, V = 118.96 (1) ų, Z = 2 and D_x = 5.91 Mg m⁻³, possesses an unusual combination of in-phase, a⁰a⁰c⁺ oxygen octahedra tilts, ω = 3.06 (2)°, and antiparallel cation displacements along the polar axis. General trends of cation displacements and the various deviations of the octahedral network from the prototypic cubic perovskite structure have been established and their systematic behaviour with temperature is reported. An investigation of phase transition behaviour using second harmonic generation (SHG) to establish the centrosymmetric or non-centrosymmetric nature of the various phases is also reported.

Computing details

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

(293K) sodium bismuth titanate

Crystal data

Na0.5Bi0.5TiO3	V = 352.33 (3) Å^3
Mr = 211.88	Z = 6
Trigonal, R3c	Neutron radiation
a = 5.4887 (2) Å	T = 273 K
c = 13.5048 (8) Å

Data collection

2θmin = 18.015°, 2θmax = 143.965°, 2θstep = 0.05°

Refinement

Rp = 0.059	42 parameters
Rwp = 0.078	Background function: linear
Profile function: pseudo-Voigt	Preferred orientation correction: none

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Na1	0.0	0.0	0.2627 (6)	0.02672	.5
Bi2	0.0	0.0	0.2627 (6)	0.05411	.5
Ti3	0.0	0.0	0.0063 (6)	0.01032
O4	0.126 (1)	0.336 (1)	0.0833 (1)	0.0266

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.022 (3)	0.011 (2)	0.0	0.022 (3)	0.036 (9)	0.0
Bi2	0.036 (2)	0.018 (1)	0.0	0.036 (2)	0.091 (6)	0.0
Ti3	0.011 (2)	0.006 (1)	0.0	0.011 (2)	0.009 (3)	0.0
O4	0.031 (3)	0.014 (3)	−0.011 (1)	0.006 (1)	0.048 (1)	−0.004 (3)

Geometric parameters (Å, º)

Na1—O	2.9105 (1)	Na1—Ti	3.4624 (2)
Na1—O	2.5203 (1)	Na1—Ti	3.2900 (2)
Na1—O	2.9792 (1)	Na1—Ti	3.3926 (1)
Na1—O	2.6168 (1)	Na1—Ti	3.3349 (1)
Ti—Na1—Ti	71.843 (1)	Ti—Na1—O	36.681 (1)
Ti—Na1—Ti	110.753 (1)	Ti—Na1—O	147.138 (1)
Ti—Na1—O	71.843 (1)	Ti—Na1—O	35.057 (1)
Ti—Na1—O	93.911 (5)	Ti—Na1—O	88.031 (2)
Ti—Na1—O	37.396 (1)	Ti—Na1—O	96.329 (2)
Ti—Na1—O	91.476 (1)

(673K) sodium bismuth titanate

Crystal data

Na0.5Bi0.5TiO3	V = 118.96 (1) Å^3
Mr = 211.88	Z = 2
Tetragonal, P4bm	Neutron radiation
a = 5.5179 (2) Å	T = 673 K
c = 3.9073 (2) Å

Data collection

2θmax = 148.715°

Refinement

Rp = 0.044	43 parameters
Rwp = 0.056	Background function: linear
3000 data points	Preferred orientation correction: none

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Na1	0.0	0.5	0.545 (2)	0.04709	.5
Bi2	0.0	0.5	0.545 (2)	0.05936	.5
Ti3	0.0	0.0	0.0	0.01408
O4	0.0	0.0	0.510 (3)	0.04866
O5	0.271 (1)	0.229 (1)	0.015 (4)	0.03532

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.051 (6)	0.051 (6)	0.039 (2)	0.001 (1)	0.0	0.0
Bi2	0.071 (3)	0.071 (3)	0.037 (6)	−0.002 (4)	0.0	0.0
Ti3	0.014 (2)	0.014 (2)	0.014 (4)	0.0	0.0	0.0
O4	0.063 (2)	0.063 (2)	0.020 (3)	0.0	0.0	0.0
O5	0.024 (1)	0.024 (1)	0.056 (2)	−0.013 (1)	0.001 (3)	−0.001 (3)

Geometric parameters (Å, º)

Na1—O(1)	2.7622 (1)	Na1—O(2)	2.5629 (1)
Na1—O(2)	2.9593 (1)	Na1—Ti	3.4842 (1)
Na1—O(2)	2.8032 (1)	Na1—Ti	3.2828 (1)
Na1—O(2)	2.7327 (1)
Ti—Na1—Ti	114.363 (5)	Ti—Na1—O(2)	91.540 (2)
Ti—Na1—Ti	72.918 (2)	Ti—Na1—O(2)	91.262 (3)
Ti—Na1—O(1)	35.660 (2)	Ti—Na1—O(2)	36.601 (1)
Ti—Na1—O(1)	150.023 (3)	Ti—Na1—O(2)	142.994 (1)
Ti—Na1—O(1)	91.540 (1)	Ti—Na1—O(2)	91.444 (4)

(873K) sodium bismuth titanate

Crystal data

Na0.5Bi0.5TiO3	V = 59.95 (1) Å^3
Mr = 211.88	Z = 1
Cubic, Pm3m	Neutron radiation
a = 3.91368 (3) Å	T = 873 K

Data collection

2θmin = 22.015°, 2θmax = 139.965°, 2θstep = 0.05°

Refinement

Rp = 0.045	39 parameters
Rwp = 0.053	Background function: linear
3000 data points	Preferred orientation correction: none
Profile function: pseudo_Voigt

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Na1	0.0	0.0	0.0	0.07687	.5
Bi2	0.0	0.0	0.0	0.07676	.5
Ti3	0.5	0.5	0.5	0.02185
O4	0.5	0.5	0.0	0.04542

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.077 (4)	0.0	0.0	0.077 (4)	0.077 (4)	0.0
Bi2	0.077 (2)	0.0	0.0	0.077 (2)	0.077 (2)	0.0
Ti3	0.022 (1)	0.0	0.0	0.022 (1)	0.022 (1)	0.0
O4	0.062 (1)	0.0	0.0	0.062 (1)	0.012 (1)	0.0

Geometric parameters (Å, º)

Na1—O	2.7674	Na1—Ti	3.3894 (1)
O—Na1—O	90.000 (1)	O—Na1—O	60.000 (1)
O—Na1—O	180.000 (1)	O—Ti—O	179.980 (1)
O—Na1—O	120.000 (1)	O—Ti—O	90.000 (1)