Atomic displacements in BiFeO₃ as a function of temperature: neutron diffraction study

The parameters of the crystal structure of BiFeO₃, described within the space group R3c, have been determined by high-resolution neutron powder diffraction for temperatures from 293 to 923 K. It was found that there is a local minimum for the rhombohedral angle α_rh, near the Néel temperature T_N ≃ 640 K, a gradual rotation of the FeO₆ octahedra and an increase of the Fe—O—Fe angle. The displacement of the Bi³⁺ ions from the FeO₆ octahedra which influence the electric polarization decreases with temperature. One of the Bi—Fe distances also has a local maximum near T_N. The atomic vibrations of Bi³⁺ and O²⁻ ions show a significant anisotropy.

Computing details

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

(BiFeO3_298K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 373.83 (1) Å^3
a = 5.57882 (5) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.86932 (16) Å	T = 298 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.238°, 2θmax = 160.088°, 2θstep = 0.050°

Refinement

Rp = 5.053	3198 data points
Rwp = 6.757	47 parameters
Rexp = 5.629	0 restraints
RBragg = 3.032

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0054 (8)
FE	0.00000	0.00000	0.22021 (10)	0.0047 (7)
O1	0.4469 (3)	0.0181 (4)	0.95183 (14)	0.0081 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0081 (7)	0.0081 (7)	0.0000 (9)	0.0040 (7)	0.00000	0.00000
FE	0.0044 (6)	0.0044 (6)	0.0053 (9)	0.0022 (6)	0.00000	0.00000
O1	0.0101 (3)	0.0079 (3)	0.0062 (2)	0.0034 (3)	0.0016 (3)	−0.0011 (3)

(BiFeO3_473K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 376.04 (1) Å^3
a = 5.58829 (5) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.90400 (17) Å	T = 473 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.237°, 2θmax = 160.087°, 2θstep = 0.050°

Refinement

Rp = 4.700	3198 data points
Rwp = 6.156	47 parameters
Rexp = 5.648	0 restraints
RBragg = 3.509

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0116 (8)
FE	0.00000	0.00000	0.22067 (10)	0.0083 (7)
O1	0.4477 (3)	0.0176 (4)	0.95256 (15)	0.0122 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0158 (8)	0.0158 (8)	0.0031 (9)	0.0079 (8)	0.00000	0.00000
FE	0.0069 (6)	0.0069 (6)	0.0111 (10)	0.0035 (6)	0.00000	0.00000
O1	0.0163 (3)	0.0120 (3)	0.0083 (2)	0.0055 (3)	0.0016 (3)	−0.0031 (3)

(BiFeO3_503K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 376.39 (1) Å^3
a = 5.58986 (5) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.90943 (17) Å	T = 503 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.237°, 2θmax = 160.087°, 2θstep = 0.050°

Refinement

Rp = 4.593	3198 data points
Rwp = 6.042	47 parameters
Rexp = 5.653	0 restraints
RBragg = 3.504

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0130 (9)
FE	0.00000	0.00000	0.22084 (10)	0.0083 (7)
O1	0.4474 (3)	0.0175 (4)	0.95279 (15)	0.0132 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0171 (8)	0.0171 (8)	0.0047 (9)	0.0085 (8)	0.00000	0.00000
FE	0.0078 (6)	0.0078 (6)	0.0094 (10)	0.0039 (6)	0.00000	0.00000
O1	0.0178 (3)	0.0120 (3)	0.0098 (2)	0.0055 (3)	0.0013 (3)	−0.0031 (3)

(BiFeO3_543K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 376.95 (1) Å^3
a = 5.59227 (5) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.91782 (17) Å	T = 543 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.239°, 2θmax = 160.089°, 2θstep = 0.050°

Refinement

Rp = 4.504	3198 data points
Rwp = 5.891	47 parameters
Rexp = 5.653	0 restraints
RBragg = 3.521

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0144 (9)
FE	0.00000	0.00000	0.22083 (10)	0.0091 (7)
O1	0.4482 (3)	0.0177 (4)	0.95266 (15)	0.0146 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0188 (8)	0.0188 (8)	0.0056 (9)	0.0094 (8)	0.00000	0.00000
FE	0.0082 (6)	0.0082 (6)	0.0109 (10)	0.0041 (6)	0.00000	0.00000
O1	0.0196 (3)	0.0136 (3)	0.0105 (3)	0.0064 (3)	0.0014 (3)	−0.0032 (3)

(BiFeO3_623K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 378.16 (1) Å^3
a = 5.59771 (6) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.93538 (18) Å	T = 623 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.239°, 2θmax = 160.089°, 2θstep = 0.050°

Refinement

Rp = 4.429	3198 data points
Rwp = 5.761	47 parameters
Rexp = 5.649	0 restraints
RBragg = 4.074

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0171 (9)
FE	0.00000	0.00000	0.22125 (11)	0.0106 (8)
O1	0.4481 (3)	0.0171 (4)	0.95308 (16)	0.0169 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0219 (9)	0.0219 (9)	0.0075 (10)	0.0110 (9)	0.00000	0.00000
FE	0.0099 (6)	0.0099 (6)	0.0121 (10)	0.0050 (6)	0.00000	0.00000
O1	0.0232 (3)	0.0149 (4)	0.0125 (3)	0.0079 (3)	0.0023 (3)	−0.0038 (3)

(BiFeO3_643K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 378.50 (1) Å^3
a = 5.59922 (6) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.94046 (18) Å	T = 643 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.239°, 2θmax = 160.089°, 2θstep = 0.050°

Refinement

Rp = 4.321	3198 data points
Rwp = 5.646	47 parameters
Rexp = 5.645	0 restraints
RBragg = 4.085

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0182 (9)
FE	0.00000	0.00000	0.22155 (11)	0.0113 (8)
O1	0.4486 (3)	0.0175 (4)	0.95339 (16)	0.0172 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0236 (9)	0.0236 (9)	0.0075 (10)	0.0118 (9)	0.00000	0.00000
FE	0.0104 (6)	0.0104 (6)	0.0132 (10)	0.0052 (6)	0.00000	0.00000
O1	0.0234 (3)	0.0152 (4)	0.0130 (3)	0.0076 (3)	0.0017 (3)	−0.0043 (3)

(BiFeO3_663K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 378.81 (1) Å^3
a = 5.60065 (6) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.94476 (18) Å	T = 663 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.239°, 2θmax = 160.089°, 2θstep = 0.050°

Refinement

Rp = 4.228	3198 data points
Rwp = 5.582	47 parameters
Rexp = 5.653	0 restraints
RBragg = 3.612

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0191 (9)
FE	0.00000	0.00000	0.22153 (11)	0.0114 (8)
O1	0.4482 (3)	0.0172 (4)	0.95319 (16)	0.0183 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0245 (9)	0.0245 (9)	0.0081 (10)	0.0123 (9)	0.00000	0.00000
FE	0.0105 (6)	0.0105 (6)	0.0132 (11)	0.0053 (6)	0.00000	0.00000
O1	0.0246 (3)	0.0161 (4)	0.0141 (3)	0.0083 (3)	0.0032 (3)	−0.0040 (3)

(BiFeO3_723K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 379.63 (1) Å^3
a = 5.60456 (6) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.95570 (19) Å	T = 723 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.241°, 2θmax = 160.091°, 2θstep = 0.050°

Refinement

Rp = 4.274	3198 data points
Rwp = 5.588	43 parameters
Rexp = 5.653	0 restraints
RBragg = 4.142

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0210 (10)
FE	0.00000	0.00000	0.22182 (11)	0.0135 (8)
O1	0.4485 (3)	0.0172 (4)	0.95364 (17)	0.0197 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0272 (10)	0.0272 (10)	0.0085 (10)	0.0136 (10)	0.00000	0.00000
FE	0.0123 (7)	0.0123 (7)	0.0159 (11)	0.0062 (7)	0.00000	0.00000
O1	0.0266 (4)	0.0167 (4)	0.0159 (3)	0.0085 (3)	0.0021 (4)	−0.0051 (3)

(BiFeO3_823K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 380.97 (1) Å^3
a = 5.61135 (6) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.9708 (2) Å	T = 823 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.242°, 2θmax = 160.092°, 2θstep = 0.050°

Refinement

Rp = 4.099	3198 data points
Rwp = 5.324	43 parameters
Rexp = 5.657	0 restraints
RBragg = 4.244

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0261 (11)
FE	0.00000	0.00000	0.22236 (12)	0.0147 (8)
O1	0.4489 (3)	0.0168 (4)	0.95434 (18)	0.0235 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0320 (11)	0.0320 (11)	0.0144 (12)	0.0160 (11)	0.00000	0.00000
FE	0.0144 (7)	0.0144 (7)	0.0155 (11)	0.0072 (7)	0.00000	0.00000
O1	0.0322 (4)	0.0184 (4)	0.0200 (4)	0.0094 (4)	0.0019 (4)	−0.0061 (4)

(BiFeO3_923K) Bismuth ferrite

Crystal data

BiFeO3	α = 90°
Rhombohedral, R3C	γ = 120°
Hall symbol: R 3 -2"c	V = 382.26 (1) Å^3
a = 5.61853 (7) Å	Constant Wavelength Neutron Diffraction radiation
c = 13.9824 (2) Å	T = 923 K

Data collection

Radiation source: nuclear reactor

2θmin = 0.243°, 2θmax = 160.093°, 2θstep = 0.050°

Refinement

Rp = 3.981	3198 data points
Rwp = 5.126	43 parameters
Rexp = 5.649	0 restraints
RBragg = 4.453

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

	x	y	z	Uiso*/Ueq
BI	0.00000	0.00000	0.00000	0.0311 (12)
FE	0.00000	0.00000	0.22288 (13)	0.0171 (9)
O1	0.4502 (3)	0.0170 (4)	0.95544 (19)	0.0269 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
BI	0.0380 (11)	0.0380 (11)	0.0172 (12)	0.0190 (11)	0.00000	0.00000
FE	0.0161 (7)	0.0161 (7)	0.0190 (12)	0.0081 (7)	0.00000	0.00000
O1	0.0373 (5)	0.0200 (4)	0.0233 (4)	0.0097 (4)	0.0015 (5)	−0.0071 (4)