High-temperature single-crystal X-ray diffraction study of tetragonal and cubic perovskite-type PbTiO₃ phases

A high-temperature single-crystal X-ray diffraction study of a synthetic PbTiO₃ perovskite was carried out over the wide temperature range 298–928 K. A transition from a tetragonal (P4mm) to a cubic () phase has been revealed near 753 K. In the non-centrosymmetric P4mm symmetry group, the difference in relative displacement between Pb and O along the c-axis is much larger than that between Ti and O. The Pb and Ti cations contribute sufficiently to polarization being shifted in the opposite direction compared with the shift of O atoms. Deviation from the linear changes in Debye–Waller factors and bonding distances in the tetragonal phases can be interpreted as a precursor phenomenon before the phase transition. Disturbance of the temperature factor U_eq for O is observed in the vicinity of the transition point, while U_eq values for Pb and Ti are continuously changing with increasing temperature. The O site includes the clear configurational disorder in the cubic phase. The polar local positional distortions remain in the cubic phase and are regarded as the cause of the paraelectricity. Estimated values of the Debye temperature Θ_D for Pb and Ti are 154 and 467 K in the tetragonal phase and decrease 22% in the high-temperature phase. Effective potentials for Pb and Ti change significantly and become soft after the phase transition.

Computing details

For all compounds, data collection: WinAFC Version 1.03 (Rigaku Corporation, 1999); cell refinement: WinAFC Version 1.03 (Rigaku Corporation, 1999); data reduction: RADY (Sasaki, 1987); program(s) used to refine structure: RADY (Sasaki, 1987); molecular graphics: ATOMS for Windows (Dowty, 2000).

(PbTiO3_298K)

Crystal data

O3PbTi	Dx = 7.979 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, P4mm	Cell parameters from 25 reflections
Hall symbol: P 4 -2	θ = 45.1–49.3°
a = 3.8992 (4) Å	µ = 69.66 mm^−1
c = 4.1499 (6) Å	T = 298 K
V = 63.09 (2) Å^3	Sphere, colourless
Z = 1	0.14 mm (radius)
F(000) = 128

Data collection

Rigaku AFC7R diffractometer	Rint = 0.076
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.007, Tmax = 0.054	k = 0→9
1164 measured reflections	l = −9→9
620 independent reflections	3 standard reflections every 100 reflections
602 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	14 parameters
R[F^2 > 2σ(F^2)] = 0.036	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.043	(Δ/σ)max = 0.0000033
S = 1.75	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
602 reflections	Extinction coefficient: 0.012 (2)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.00836 (10)
Ti	0.5000	0.5000	0.5382 (4)	0.0043 (4)
O1	0.5000	0.5000	0.113 (2)	0.0078 (16)
O2	0.5000	0.0000	0.615 (2)	0.007 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.008916 (2)	0.008916	0.00724 (10)	0.0	0.0	0.0
Ti	0.004178 (6)	0.004178	0.00452 (1)	0.0	0.0	0.0
O1	0.00915 (4)	0.00915	0.00512 (4)	0.0	0.0	0.0
O2	0.00859 (4)	0.00299 (3)	0.00981 (3)	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O1	2.7966 (17)	Ti—O1^ii	2.384 (10)
Pb—O2	3.211 (6)	Ti—O2	1.9754 (13)
Pb—O2^i	2.521 (5)	O1^ii—O2	2.841 (9)
Ti—O1	1.766 (10)	O1—O2	2.854 (10)
O1—Pb—O2	56.21 (13)	O1—Ti—O2	99.3 (2)
O1—Pb—O2^i	64.34 (13)	O1^ii—Ti—O2	80.7 (2)

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

(PbTiO3_373K)

Crystal data

O3PbTi	Dx = 7.976 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, P4mm	Cell parameters from 25 reflections
Hall symbol: P 4 -2	θ = 45.1–49.3°
a = 3.9043 (4) Å	µ = 69.63 mm^−1
c = 4.1407 (5) Å	T = 373 K
V = 63.12 (2) Å^3	Sphere, colourless
Z = 1	0.14 mm (radius)
F(000) = 128

Data collection

Rigaku AFC7R diffractometer	Rint = 0.075
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.054	k = 0→9
1159 measured reflections	l = −9→9
618 independent reflections	3 standard reflections every 100 reflections
599 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	14 parameters
R[F^2 > 2σ(F^2)] = 0.039	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.043	(Δ/σ)max = 0.000065
S = 1.74	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
599 reflections	Extinction coefficient: 0.042 (5)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.01074 (11)
Ti	0.5000	0.5000	0.5368 (4)	0.0054 (4)
O1	0.5000	0.5000	0.110 (2)	0.0101 (18)
O2	0.5000	0.0000	0.609 (2)	0.009 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.011343 (2)	0.011343	0.00953 (13)	0.0	0.0	0.0
Ti	0.005233 (6)	0.005233	0.00558 (1)	0.0	0.0	0.0
O1	0.01228 (4)	0.01228	0.00575 (4)	0.0	0.0	0.0
O2	0.00963 (4)	0.00267 (3)	0.01366 (4)	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O1	2.7983 (17)	Ti—O1^ii	2.375 (11)
Pb—O2	3.190 (7)	Ti—O2	1.9752 (13)
Pb—O2^i	2.535 (6)	O1^ii—O2	2.843 (10)
Ti—O1	1.766 (11)	O1—O2	2.848 (10)
O1—Pb—O2	56.22 (13)	O1—Ti—O2	98.8 (2)
O1—Pb—O2^i	64.34 (14)	O1^ii—Ti—O2	81.2 (2)

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

(PbTiO3_473K)

Crystal data

O3PbTi	Dx = 7.977 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, P4mm	Cell parameters from 25 reflections
Hall symbol: P 4 -2	θ = 45.1–49.3°
a = 3.9117 (4) Å	µ = 69.64 mm^−1
c = 4.1243 (6) Å	T = 473 K
V = 63.10 (2) Å^3	Sphere, colourless
Z = 1	0.14 mm (radius)
F(000) = 128

Data collection

Rigaku AFC7R diffractometer	Rint = 0.079
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.054	k = 0→9
1166 measured reflections	l = −9→9
620 independent reflections	3 standard reflections every 100 reflections
576 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	14 parameters
R[F^2 > 2σ(F^2)] = 0.046	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.050	(Δ/σ)max = 0.000025
S = 1.78	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
576 reflections	Extinction coefficient: 0.039 (6)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.01416 (15)
Ti	0.5000	0.5000	0.5347 (5)	0.0068 (5)
O1	0.5000	0.5000	0.102 (2)	0.011 (2)
O2	0.5000	0.0000	0.605 (2)	0.010 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.014984 (3)	0.014984	0.0125 (2)	0.0	0.0	0.0
Ti	0.006957 (8)	0.006957	0.00636 (1)	0.0	0.0	0.0
O1	0.01318 (5)	0.01318	0.00525 (4)	0.0	0.0	0.0
O2	0.01071 (5)	0.00394 (4)	0.01488 (4)	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O1	2.7979 (16)	Ti—O1^ii	2.340 (11)
Pb—O2	3.171 (7)	Ti—O2	1.9773 (14)
Pb—O2^i	2.545 (6)	O1^ii—O2	2.833 (10)
Ti—O1	1.784 (11)	O1—O2	2.851 (10)
O1—Pb—O2	56.65 (13)	O1—Ti—O2	98.4 (3)
O1—Pb—O2^i	63.84 (14)	O1^ii—Ti—O2	81.6 (3)

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

(PbTiO3_573K)

Crystal data

O3PbTi	Dx = 7.981 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, P4mm	Cell parameters from 25 reflections
Hall symbol: P 4 -2	θ = 45.1–49.3°
a = 3.9211 (5) Å	µ = 69.67 mm^−1
c = 4.1025 (7) Å	T = 573 K
V = 63.08 (2) Å^3	Sphere, colourless
Z = 1	0.14 mm (radius)
F(000) = 128

Data collection

Rigaku AFC7R diffractometer	Rint = 0.076
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.054	k = 0→9
1165 measured reflections	l = −9→9
614 independent reflections	3 standard reflections every 100 reflections
526 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	14 parameters
R[F^2 > 2σ(F^2)] = 0.044	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.047	(Δ/σ)max = 0.0000016
S = 1.76	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
526 reflections	Extinction coefficient: 0.055 (7)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.0180 (2)
Ti	0.5000	0.5000	0.5325 (5)	0.0081 (5)
O1	0.5000	0.5000	0.096 (3)	0.014 (2)
O2	0.5000	0.0000	0.596 (2)	0.013 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.019102 (4)	0.019102	0.0157 (2)	0.0	0.0	0.0
Ti	0.008804 (9)	0.008804	0.00663 (2)	0.0	0.0	0.0
O1	0.01602 (6)	0.01602	0.00952 (5)	0.0	0.0	0.0
O2	0.01767 (7)	0.00164 (4)	0.01843 (5)	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O1	2.8005 (16)	Ti—O1^ii	2.312 (12)
Pb—O2	3.133 (7)	Ti—O2	1.9775 (12)
Pb—O2^i	2.568 (6)	O1^ii—O2	2.836 (11)
Ti—O1	1.791 (12)	O1—O2	2.839 (11)
O1—Pb—O2	56.78 (14)	O1—Ti—O2	97.5 (3)
O1—Pb—O2^i	63.67 (14)	O1^ii—Ti—O2	82.5 (3)

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

(PbTiO3_673K)

Crystal data

O3PbTi	Dx = 7.996 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, P4mm	Cell parameters from 25 reflections
Hall symbol: P 4 -2	θ = 45.1–49.3°
a = 3.9339 (9) Å	µ = 69.80 mm^−1
c = 4.0683 (12) Å	T = 673 K
V = 62.95 (3) Å^3	Sphere, colourless
Z = 1	0.14 mm (radius)
F(000) = 128

Data collection

Rigaku AFC7R diffractometer	Rint = 0.080
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.054	k = 0→9
1170 measured reflections	l = −9→9
612 independent reflections	3 standard reflections every 100 reflections
432 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	14 parameters
R[F^2 > 2σ(F^2)] = 0.048	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.049	(Δ/σ)max = 0.000023
S = 1.79	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
432 reflections	Extinction coefficient: 0.053 (9)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.0228 (3)
Ti	0.5000	0.5000	0.5284 (8)	0.0095 (7)
O1	0.5000	0.5000	0.084 (3)	0.019 (3)
O2	0.5000	0.0000	0.582 (2)	0.014 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.024199 (7)	0.024199	0.0201 (3)	0.0	0.0	0.0
Ti	0.01096 (1)	0.01096	0.00652 (2)	0.0	0.0	0.0
O1	0.02333 (9)	0.02333	0.01049 (7)	0.0	0.0	0.0
O2	0.01914 (8)	0.00501 (5)	0.01722 (6)	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O1	2.8027 (18)	Ti—O1^ii	2.261 (15)
Pb—O2	3.080 (8)	Ti—O2	1.9793 (13)
Pb—O2^i	2.599 (7)	O1^ii—O2	2.825 (13)
Ti—O1	1.808 (15)	O1—O2	2.834 (13)
O1—Pb—O2	57.17 (15)	O1—Ti—O2	96.4 (3)
O1—Pb—O2^i	63.16 (16)	O1^ii—Ti—O2	83.6 (3)

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

(PbTiO3_723K)

Crystal data

O3PbTi	Dx = 8.013 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, P4mm	Cell parameters from 25 reflections
Hall symbol: P 4 -2	θ = 45.1–49.3°
a = 3.9435 (7) Å	µ = 69.95 mm^−1
c = 4.0401 (10) Å	T = 723 K
V = 62.83 (3) Å^3	Sphere, colourless
Z = 1	0.14 mm (radius)
F(000) = 128

Data collection

Rigaku AFC7R diffractometer	Rint = 0.077
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.054	k = 0→9
1150 measured reflections	l = −9→9
605 independent reflections	3 standard reflections every 100 reflections
368 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	14 parameters
R[F^2 > 2σ(F^2)] = 0.046	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.047	(Δ/σ)max = 0.0000043
S = 1.70	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
368 reflections	Extinction coefficient: 0.046 (9)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.0264 (4)
Ti	0.5000	0.5000	0.5250 (13)	0.01115 (8)
O1	0.5000	0.5000	0.072 (3)	0.020 (4)
O2	0.5000	0.0000	0.572 (2)	0.017 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.027447 (8)	0.027447	0.0244 (4)	0.0	0.0	0.0
Ti	0.01257 (1)	0.01257	0.00830 (3)	0.0	0.0	0.0
O1	0.02490 (9)	0.02490	0.00881 (8)	0.0	0.0	0.0
O2	0.02703 (10)	0.00343 (5)	0.02170 (9)	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O1	2.8038 (15)	Ti—O1^ii	2.211 (15)
Pb—O2	3.038 (8)	Ti—O2	1.9808 (12)
Pb—O2^i	2.623 (7)	O1^ii—O2	2.821 (13)
Ti—O1	1.829 (15)	O1—O2	2.824 (13)
O1—Pb—O2	57.59 (15)	O1—Ti—O2	95.5 (3)
O1—Pb—O2^i	62.63 (16)	O1^ii—Ti—O2	84.5 (3)

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

(PbTiO3_743K)

Crystal data

O3PbTi	Dx = 8.023 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, P4mm	Cell parameters from 25 reflections
Hall symbol: P 4 -2	θ = 45.1–49.3°
a = 3.9474 (8) Å	µ = 70.05 mm^−1
c = 4.0263 (10) Å	T = 743 K
V = 62.74 (3) Å^3	Sphere, colourless
Z = 1	0.14 mm (radius)
F(000) = 128

Data collection

Rigaku AFC7R diffractometer	Rint = 0.070
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.051	k = 0→9
1150 measured reflections	l = −9→9
608 independent reflections	3 standard reflections every 100 reflections
325 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	14 parameters
R[F^2 > 2σ(F^2)] = 0.047	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.056	(Δ/σ)max = 0.0000056
S = 1.65	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
325 reflections	Extinction coefficient: 0.060 (12)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.0284 (5)
Ti	0.5000	0.5000	0.523 (2)	0.01189 (10)
O1	0.5000	0.5000	0.066 (5)	0.030 (7)
O2	0.5000	0.0000	0.567 (3)	0.019 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.02910 (1)	0.02910	0.0269 (4)	0.0	0.0	0.0
Ti	0.01375 (2)	0.01375	0.00820 (3)	0.0	0.0	0.0
O1	0.0379 (1)	0.0379	0.0128 (1)	0.0	0.0	0.0
O2	0.02696 (13)	0.00368 (7)	0.0275 (1)	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O1	2.8038 (19)	Ti—O1^ii	2.19 (3)
Pb—O2	3.019 (11)	Ti—O2	1.9820 (16)
Pb—O2^i	2.632 (10)	O1^ii—O2	2.824 (18)
Ti—O1	1.84 (3)	O1—O2	2.815 (18)
O1—Pb—O2	57.88 (18)	O1—Ti—O2	95.2 (3)
O1—Pb—O2^i	62.27 (18)	O1^ii—Ti—O2	84.8 (3)

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

(PbTiO3_753K)

Crystal data

O3PbTi	Dx = 8.033 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Tetragonal, P4mm	Cell parameters from 25 reflections
Hall symbol: P 4 -2	θ = 45.1–49.3°
a = 3.9503 (9) Å	µ = 70.13 mm^−1
c = 4.0161 (12) Å	T = 753 K
V = 62.67 (4) Å^3	Sphere, colourless
Z = 1	0.14 mm (radius)
F(000) = 128

Data collection

Rigaku AFC7R diffractometer	Rint = 0.073
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.050	k = 0→9
1150 measured reflections	l = −9→9
605 independent reflections	3 standard reflections every 100 reflections
299 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	14 parameters
R[F^2 > 2σ(F^2)] = 0.049	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.055	(Δ/σ)max = 0.0000058
S = 1.70	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
299 reflections	Extinction coefficient: 0.071 (14)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.0303 (6)
Ti	0.5000	0.5000	0.523 (2)	0.01230 (11)
O1	0.5000	0.5000	0.061 (4)	0.025 (6)
O2	0.5000	0.0000	0.563 (3)	0.017 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.03128 (1)	0.03128	0.0282 (4)	0.0	0.0	0.0
Ti	0.01428 (2)	0.01428	0.00832 (3)	0.0	0.0	0.0
O1	0.0353 (1)	0.0353	0.0034 (1)	0.0	0.0	0.0
O2	0.02945 (13)	0.00408 (7)	0.0164 (1)	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O1	2.8039 (15)	Ti—O1^ii	2.162 (18)
Pb—O2	3.002 (10)	Ti—O2	1.9818 (13)
Pb—O2^i	2.643 (9)	O1^ii—O2	2.822 (15)
Ti—O1	1.854 (18)	O1—O2	2.811 (15)
O1—Pb—O2	58.05 (16)	O1—Ti—O2	94.7 (3)
O1—Pb—O2^i	62.06 (17)	O1^ii—Ti—O2	85.3 (3)

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

(PbTiO3_758K)

Crystal data

O3PbTi	Dx = 8.084 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 25 reflections
Hall symbol: -P 4 2 3	θ = 45.1–49.3°
a = 3.9637 (7) Å	µ = 70.58 mm^−1
V = 62.27 (3) Å^3	T = 758 K
Z = 1	Sphere, colourless
F(000) = 128	0.14 mm (radius)

Data collection

Rigaku AFC7R diffractometer	Rint = 0.060
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.046	k = 0→9
1100 measured reflections	l = −9→9
129 independent reflections	3 standard reflections every 100 reflections
64 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	6 parameters
R[F^2 > 2σ(F^2)] = 0.038	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.033	(Δ/σ)max = 0.00000843
S = 1.52	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
64 reflections	Extinction coefficient: 0.30 (8)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.00362 (3)
Ti	0.5000	0.5000	0.5000	0.01643 (3)
O	0.0000	0.5000	0.5000	0.026 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.00362 (3)	0.00362	0.00362	0.0	0.0	0.0
Ti	0.01643 (3)	0.01643	0.01643	0.0	0.0	0.0
O	0.01384 (9)	0.03224 (8)	0.03224	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O	2.8027 (4)	O—O^i	2.8027 (4)
Ti—O	1.9818 (4)
O—Pb—O^i	60 (11)	O—Ti—O^i	90 (4)

Symmetry code: (i) y, z, x.

(PbTiO3_763K)

Crystal data

O3PbTi	Dx = 8.083 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 25 reflections
Hall symbol: -P 4 2 3	θ = 45.1–49.3°
a = 3.9639 (8) Å	µ = 70.56 mm^−1
V = 62.28 (3) Å^3	T = 763 K
Z = 1	Sphere, colourless
F(000) = 128	0.14 mm (radius)

Data collection

Rigaku AFC7R diffractometer	Rint = 0.062
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.044	k = 0→9
1099 measured reflections	l = −9→9
129 independent reflections	3 standard reflections every 100 reflections
62 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	6 parameters
R[F^2 > 2σ(F^2)] = 0.033	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.030	(Δ/σ)max = 0.000000153
S = 1.59	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
62 reflections	Extinction coefficient: 0.35 (8)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.00369 (3)
Ti	0.5000	0.5000	0.5000	0.01759 (3)
O	0.0000	0.5000	0.5000	0.024 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.00369 (3)	0.00369	0.00369	0.0	0.0	0.0
Ti	0.01759 (3)	0.01759	0.01759	0.0	0.0	0.0
O	0.01085 (7)	0.03114 (7)	0.03114	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O	2.8029 (4)	O—O^i	2.8029 (4)
Ti—O	1.9819 (4)
O—Pb—O^i	60 (11)	O—Ti—O^i	90 (4)

Symmetry code: (i) y, z, x.

(PbTiO3_773K)

Crystal data

O3PbTi	Dx = 8.078 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 25 reflections
Hall symbol: -P 4 2 3	θ = 45.1–49.3°
a = 3.9646 (9) Å	µ = 70.52 mm^−1
V = 62.32 (4) Å^3	T = 773 K
Z = 1	Sphere, colourless
F(000) = 128	0.14 mm (radius)

Data collection

Rigaku AFC7R diffractometer	Rint = 0.076
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.046	k = 0→9
590 measured reflections	l = −9→9
129 independent reflections	3 standard reflections every 100 reflections
59 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	6 parameters
R[F^2 > 2σ(F^2)] = 0.036	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.032	(Δ/σ)max = 0.00000408
S = 1.61	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
59 reflections	Extinction coefficient: 0.43 (9)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.00379 (4)
Ti	0.5000	0.5000	0.5000	0.01682 (3)
O	0.0000	0.5000	0.5000	0.022 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.00379 (4)	0.00379	0.00379	0.0	0.0	0.0
Ti	0.01682 (3)	0.01682	0.01682	0.0	0.0	0.0
O	0.01368 (8)	0.02544 (6)	0.02544	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O	2.8034 (5)	O—O^i	2.8034 (5)
Ti—O	1.9823 (5)
O—Pb—O^i	60 (11)	O—Ti—O^i	90 (4)

Symmetry code: (i) y, z, x.

(PbTiO3_823K)

Crystal data

O3PbTi	Dx = 8.061 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 25 reflections
Hall symbol: -P 4 2 3	θ = 45.1–49.3°
a = 3.9674 (8) Å	µ = 70.37 mm^−1
V = 62.45 (4) Å^3	T = 823 K
Z = 1	Sphere, colourless
F(000) = 128	0.14 mm (radius)

Data collection

Rigaku AFC7R diffractometer	Rint = 0.063
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.043	k = 0→9
590 measured reflections	l = −9→9
129 independent reflections	3 standard reflections every 100 reflections
58 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	6 parameters
R[F^2 > 2σ(F^2)] = 0.039	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.034	(Δ/σ)max = 0.00000557
S = 1.57	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
58 reflections	Extinction coefficient: 0.54 (10)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.00402 (4)
Ti	0.5000	0.5000	0.5000	0.01873 (4)
O	0.0000	0.5000	0.5000	0.023 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.00402 (4)	0.00402	0.00402	0.0	0.0	0.0
Ti	0.01873 (4)	0.01873	0.01873	0.0	0.0	0.0
O	0.01493 (9)	0.02718 (7)	0.02718	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O	2.8054 (4)	O—O^i	2.8054 (4)
Ti—O	1.9837 (4)
O—Pb—O^i	60 (11)	O—Ti—O^i	90 (4)

Symmetry code: (i) y, z, x.

(PbTiO3_873K)

Crystal data

O3PbTi	Dx = 8.044 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 25 reflections
Hall symbol: -P 4 2 3	θ = 45.1–49.3°
a = 3.9702 (9) Å	µ = 70.22 mm^−1
V = 62.58 (4) Å^3	T = 873 K
Z = 1	Sphere, colourless
F(000) = 128	0.14 mm (radius)

Data collection

Rigaku AFC7R diffractometer	Rint = 0.063
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.042	k = 0→9
590 measured reflections	l = −9→9
129 independent reflections	3 standard reflections every 100 reflections
54 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	6 parameters
R[F^2 > 2σ(F^2)] = 0.041	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.036	(Δ/σ)max = 0.0000105
S = 1.52	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
54 reflections	Extinction coefficient: 0.54 (13)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.00423 (5)
Ti	0.5000	0.5000	0.5000	0.01962 (5)
O	0.0000	0.5000	0.5000	0.023 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.00423 (5)	0.00423	0.00423	0.0	0.0	0.0
Ti	0.01962 (5)	0.01962	0.01962	0.0	0.0	0.0
O	0.02012 (12)	0.02421 (8)	0.02421	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O	2.8074 (5)	O—O^i	2.8074 (5)
Ti—O	1.9851 (5)
O—Pb—O^i	60 (11)	O—Ti—O^i	90 (4)

Symmetry code: (i) y, z, x.

(PbTiO3_923K)

Crystal data

O3PbTi	Dx = 8.024 Mg m^−3
Mr = 303.06	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 25 reflections
Hall symbol: -P 4 2 3	θ = 45.1–49.3°
a = 3.9734 (9) Å	µ = 70.55 mm^−1
V = 62.73 (4) Å^3	T = 923 K
Z = 1	Sphere, colourless
F(000) = 128	0.14 mm (radius)

Data collection

Rigaku AFC7R diffractometer	Rint = 0.075
ω–2θ scans	θmax = 60.0°
Absorption correction: ψ scan (North, Phillips & Mathews, 1968)	h = 0→9
Tmin = 0.010, Tmax = 0.040	k = 0→9
590 measured reflections	l = −9→9
129 independent reflections	3 standard reflections every 100 reflections
44 reflections with F_ > _3.0_σ(F)	intensity decay: none

Refinement

Refinement on F	6 parameters
R[F^2 > 2σ(F^2)] = 0.057	Weighting scheme based on measured s.u.'s w = 1/σ^2(F)
wR(F^2) = 0.050	(Δ/σ)max = 0.0000037
S = 1.65	Extinction correction: isotropic Type I (Becker & Coppens, 1974a and 1974b)
44 reflections	Extinction coefficient: 0.6 (2)×10^4

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

	x	y	z	Uiso*/Ueq
Pb	0.0000	0.0000	0.0000	0.00445 (8)
Ti	0.5000	0.5000	0.5000	0.02105 (8)
O	0.0000	0.5000	0.5000	0.024 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb	0.00445 (8)	0.00445	0.00445	0.0	0.0	0.0
Ti	0.02105 (8)	0.02105	0.02105	0.0	0.0	0.0
O	0.01926 (18)	0.02571 (12)	0.02571	0.0	0.0	0.0

Geometric parameters (Å, º)

Pb—O	2.8097 (5)	O—O^i	2.8097 (5)
Ti—O	1.9867 (5)
O—Pb—O^i	60 (11)	O—Ti—O^i	90 (4)

Symmetry code: (i) y, z, x.