Structural phase transition and hydrogen ordering of TlH2PO4 at low temperature

Oh, I.H.; Merz, M.; Mattauch, S.; Heger, G.

doi:10.1107/S0108768106018222

Structural phase transition and hydrogen ordering of TlH₂PO₄ at low temperature

I. H. Oh, M. Merz, S. Mattauch and G. Heger

The crystal structure of TlH₂PO₄ (TDP) has been studied at low temperature. The lattice parameters were derived from high-resolution X-ray powder diffraction in the temperature range between 8 and 300 K. A detailed crystal structure analysis of the antiferroelectric low-temperature phase TDP-III has been performed based on neutron diffraction data measured at 210 K on a twinned crystal consisting of two domain states. The structure model in the triclinic space group $P\bar 1$ is characterized by a complete ordering of all the H atoms in the asymmetric O—H

O hydrogen bonds. The phase transition from the ferroelastic TDP-II to the antiferroelectric TDP-III phase at 229.5 ± 0.5 K is only slightly of first order and shows no detectable hysteresis effects. Its mechanism is driven by the hydrogen ordering between the partially ordered TDP-II state and the completely ordered TDP-III state. The polymorphism of TDP and the fully deuterated TlD₂PO₄ (DTDP) is presented in the form of group–subgroup relations between the different space groups.

Keywords: phase transition; hydrogen ordering; low temperature; X-ray powder diffraction.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768106018222/lc5039sup1.cif Contains datablocks global, TDP298K, TDP240K, TDP210K
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768106018222/lc5039TDP210Ksup2.hkl Contains datablock trika
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768106018222/lc5039TDP240Ksup3.hkl Contains datablock tdp
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768106018222/lc5039TDP298Ksup4.hkl Contains datablock tdpii_split

Computing details top

For all compounds, data collection: pron; cell refinement: pron; data reduction: pron. Program(s) used to refine structure: PROMETHEUS(Zucker et al.,1983) for TDP298K, TDP240K; SHELXL97 (Sheldrick, 1997) for TDP210K. For all compounds, molecular graphics: drawxtal(Finger and Kroeker, 2004).

Figures top

(TDP298K) top

Crystal data top

H₂O₄PTl	F(000) = 119
M_r = 301.6	D_x = 4.753 Mg m⁻³
Monoclinic, P2₁/a	Neutron radiation, λ = 1.2413 Å
Hall symbol: -P 2yab	Cell parameters from 20 reflections
a = 14.331 (7) Å	θ = 17.5–22.5°
b = 4.535 (2) Å	µ = 0.04 mm⁻¹
c = 6.514 (3) Å	T = 298 K
β = 91.67 (2)°	Platelet, colourless
V = 423.2 (3) Å³	5 × 3 × 3 mm
Z = 4

Data collection top

Four circle diffractometer	R_int = 0.022
Radiation source: nuclear reactor, Ju¨lich SV28/2	θ_max = 51.0°, θ_min = 1.5°
Cu (200) monochromator	h = −17→17
ω scans	k = −5→4
2766 measured reflections	l = −8→6
814 independent reflections	3 standard reflections every 360 min
699 reflections with > 3σ(I)	intensity decay: 0.7%

Refinement top

Refinement on F²	All H-atom parameters refined
Least-squares matrix: full	w = 1/σ²(F_o²)
R[F² > 2σ(F²)] = 0.051	(Δ/σ)_max < 0.001
wR(F²) = 0.060	Δρ_max = 0.65 e Å⁻³
S = 3.90	Δρ_min = −0.42 e Å⁻³
699 reflections	Extinction correction: secondary Type I, isotropic, Gaussian (Zachariasen, 1967)
73 parameters	Extinction coefficient: 0.05425

Crystal data top

H₂O₄PTl	V = 423.2 (3) Å³
M_r = 301.6	Z = 4
Monoclinic, P2₁/a	Neutron radiation, λ = 1.2413 Å
a = 14.331 (7) Å	µ = 0.04 mm⁻¹
b = 4.535 (2) Å	T = 298 K
c = 6.514 (3) Å	5 × 3 × 3 mm
β = 91.67 (2)°

Data collection top

Four circle diffractometer	R_int = 0.022
2766 measured reflections	3 standard reflections every 360 min
814 independent reflections	intensity decay: 0.7%
699 reflections with > 3σ(I)

Refinement top

R[F² > 2σ(F²)] = 0.051	73 parameters
wR(F²) = 0.060	All H-atom parameters refined
S = 3.90	Δρ_max = 0.65 e Å⁻³
699 reflections	Δρ_min = −0.42 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Tl	0.12833 (5)	−0.0049 (2)	0.2585 (1)	0.0389 (3)
P	0.12455 (8)	0.5207 (3)	0.7608 (2)	0.0237 (4)
O1	0.07470 (10)	0.3996 (4)	0.9468 (2)	0.0526 (7)
O2	0.05391 (10)	0.6547 (3)	0.6063 (2)	0.0417 (6)
O3	0.19149 (10)	0.7704 (3)	0.8299 (2)	0.0353 (6)
O4	0.18173 (10)	0.2726 (3)	0.6680 (2)	0.0340 (5)
H1	−0.0088 (5)	0.5245 (18)	0.0161 (11)	0.0419 (7)*	0.50
H2	0.0078 (4)	0.5308 (15)	0.5232 (9)	0.0382 (6)*	0.50
H3	0.1845 (2)	0.0052 (7)	0.7544 (4)	0.0516 (7)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Tl	0.0392 (2)	0.0397 (3)	0.0379 (3)			0.0083 (2)
P	0.0230 (3)	0.0219 (5)	0.0265 (4)			0.0051 (3)
O1	0.0402 (6)	0.0623 (7)	0.0553 (6)	0.0244 (5)	0.0259 (4)	0.0359 (5)
O2	0.0410 (5)	0.0359 (5)	0.0469 (5)	−0.0097 (4)	−0.0200 (4)	0.0139 (4)
O3	0.0391 (5)	0.0239 (5)	0.0423 (5)	−0.0148 (3)	0.0024 (3)	−0.0037 (4)
O4	0.0421 (5)	0.0240 (5)	0.0366 (5)	−0.0028 (3)	0.0113 (3)	−0.0044 (4)
H3	0.0408 (7)	0.068 (1)	0.0460 (9)	−0.0062 (8)		−0.015 (1)

Geometric parameters (Å, º) top

P—O1	1.527 (2)	Tl—O3	2.939 (7)
P—O2	1.532 (2)	Tl—O2	2.965 (3)
P—O3	1.543 (2)	Tl—O4	3.028 (5)
P—O4	1.527 (2)	Tl—O3	3.133 (5)
Tl—O1	2.828 (5)	Tl—O2	3.201 (5)
Tl—O4	2.931 (2)

O1—P—O2	110.39 (3)	O2—P—O3	107.08 (2)
O1—P—O3	109.50 (2)	O2—P—O4	112.60 (4)
O1—P—O4	108.55 (2)	O3—P—O4	108.67 (3)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O1—H1···O1	1.040 (7)	1.409 (7)	2.445 (7)	172.8 (4)
O2—H2···O2	1.012 (6)	1.469 (6)	2.480 (6)	176.2 (5)
O3—H3···O4	1.176 (3)	1.337 (3)	2.512 (3)	176.9 (5)

(TDP240K) top

Crystal data top

H₂O₄PTl	F(000) = 118.6
M_r = 301.6	D_x = 4.753 Mg m⁻³
Monoclinic, P2₁/a	Neutron radiation, λ = 0.8724 Å
Hall symbol: -P 2yab	Cell parameters from 12 reflections
a = 14.26 (2) Å	θ = 17.5–22.5°
b = 4.517 (9) Å	µ = 0.04 mm⁻¹
c = 6.497 (10) Å	T = 240 K
β = 92.19 (13)°	Platelet, colourless
V = 418.2 (11) Å³	5 × 3 × 3 mm
Z = 4

Data collection top

Four circle diffractometer	R_int = 0.021
Radiation source: nuclear reactor, Ju¨lich SV28/1	θ_max = 37.5°, θ_min = 3.5°
Cu (220) monochromator	h = −19→19
ω scans	k = −6→4
1695 measured reflections	l = −9→8
845 independent reflections	2 standard reflections every 540 min
630 reflections with > 3σ(I)	intensity decay: 0.7%

Refinement top

Refinement on F²	All H-atom parameters refined
Least-squares matrix: full	w = 1/σ²(F_o²)
R[F² > 2σ(F²)] = 0.046	(Δ/σ)_max < 0.001
wR(F²) = 0.054	Δρ_max = 0.51 e Å⁻³
S = 2.21	Δρ_min = −0.48 e Å⁻³
699 reflections	Extinction correction: secondary Type I, isotropic, Gaussian (Zachariasen, 1967)
73 parameters	Extinction coefficient: 0.05425

Crystal data top

H₂O₄PTl	V = 418.2 (11) Å³
M_r = 301.6	Z = 4
Monoclinic, P2₁/a	Neutron radiation, λ = 0.8724 Å
a = 14.26 (2) Å	µ = 0.04 mm⁻¹
b = 4.517 (9) Å	T = 240 K
c = 6.497 (10) Å	5 × 3 × 3 mm
β = 92.19 (13)°

Data collection top

Four circle diffractometer	R_int = 0.021
1695 measured reflections	2 standard reflections every 540 min
845 independent reflections	intensity decay: 0.7%
630 reflections with > 3σ(I)

Refinement top

R[F² > 2σ(F²)] = 0.046	73 parameters
wR(F²) = 0.054	All H-atom parameters refined
S = 2.21	Δρ_max = 0.51 e Å⁻³
699 reflections	Δρ_min = −0.48 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Tl	0.12833 (7)	−0.0075 (4)	0.2603 (2)	0.0309 (3)
P	0.12432 (10)	0.5238 (5)	0.7633 (2)	0.0178 (5)
O1	0.0764 (1)	0.4034 (6)	0.9526 (3)	0.0392 (7)
O2	0.0516 (1)	0.6604 (5)	0.6104 (3)	0.0304 (7)
O3	0.1925 (1)	0.7757 (6)	0.8310 (3)	0.0284 (7)
O4	0.1802 (1)	0.2764 (5)	0.6662 (3)	0.0262 (7)
H1	−0.0097 (5)	0.526 (2)	0.0162 (11)	0.031 (1)*	0.50
H2	0.0067 (5)	0.534 (2)	0.5249 (9)	0.032 (1)*	0.50
H3	0.1847 (2)	0.0057 (13)	0.7562 (5)	0.042 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Tl	0.0314 (4)	0.0283 (12)	0.0334 (5)			0.0066 (6)
P	0.0179 (5)	0.0141 (15)	0.0216 (6)		0.0011 (4)	0.0031 (7)
O1	0.0292 (7)	0.050 (2)	0.0403 (8)	0.0175 (7)	0.0179 (6)	0.0268 (8)
O2	0.0289 (7)	0.0270 (19)	0.0339 (8)	−0.0046 (7)	−0.0120 (5)	0.0093 (8)
O3	0.0307 (8)	0.018 (2)	0.0355 (8)		−0.0122 (5)	−0.0034 (7)
O4	0.0313 (7)	0.0169 (18)	0.0307 (7)		0.0083 (5)	−0.0036 (7)
H3	0.034 (1)	0.048 (4)	0.042 (1)			−0.013 (1)

Geometric parameters (Å, º) top

P—O1	1.529 (3)	Tl—O3	2.936 (2)
P—O2	1.538 (3)	Tl—O2	2.970 (7)
P—O3	1.549 (3)	Tl—O4	2.999 (5)
P—O4	1.523 (3)	Tl—O3	3.127 (8)
Tl—O1	2.806 (7)	Tl—O2	3.146 (2)
Tl—O4	2.920 (4)

O1—P—O2	110.55 (5)	O2—P—O3	106.79 (3)
O1—P—O3	109.13 (3)	O2—P—O4	112.18 (5)
O1—P—O4	109.21 (3)	O3—P—O4	108.88 (4)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O1—H1···O1	1.032 (7)	1.422 (7)	2.448 (7)	172.3 (4)
O2—H2···O2	1.010 (8)	1.475 (9)	2.483 (8)	174.9 (6)
O3—H3···O4	1.150 (6)	1.356 (6)	2.506 (6)	177.2 (4)

(TDP210K) top

Crystal data top

H₈O₁₆P₄Tl₄	Z = 16
M_r = 1206.4	F(000) = 474.3
Triclinic, C1	D_x = 4.820 Mg m⁻³
Hall symbol: -C 1	Neutron radiation, λ = 0.8724 Å
a = 28.483 (12) Å	Cell parameters from 12 reflections
b = 9.016 (5) Å	θ = 17.5–22.5°
c = 6.502 (3) Å	µ = 0.04 mm⁻¹
α = 90.09 (5)°	T = 210 K
β = 92.21 (3)°	Platelet, colourless
γ = 90.49 (3)°	5 × 3 × 3 mm
V = 1668.4 (14) Å³

Data collection top

Four circle diffractometer	R_int = 0.062
Radiation source: nuclear reactor, Ju¨lich SV28/1	θ_max = 37.8°, θ_min = 3.5°
Cu (220) monochromator	h = −40→38
ω scans	k = −12→8
3170 measured reflections	l = −8→9
2982 independent reflections	2 standard reflections every 540 min
1428 reflections with I > 2σ(I)	intensity decay: 2.5%

Refinement top

Refinement on F²	All H-atom parameters refined
Least-squares matrix: full	w = 1/σ²(F_o²)'
R[F² > 2σ(F²)] = 0.046	(Δ/σ)_max < 0.001
wR(F²) = 0.054	Δρ_max = 3.03 e Å⁻³
S = 1.93	Δρ_min = −2.28 e Å⁻³
2982 reflections	Extinction correction: SHELXL
131 parameters	Extinction coefficient: 0.00300 (15)

Crystal data top

H₈O₁₆P₄Tl₄	γ = 90.49 (3)°
M_r = 1206.4	V = 1668.4 (14) Å³
Triclinic, C1	Z = 16
a = 28.483 (12) Å	Neutron radiation, λ = 0.8724 Å
b = 9.016 (5) Å	µ = 0.04 mm⁻¹
c = 6.502 (3) Å	T = 210 K
α = 90.09 (5)°	5 × 3 × 3 mm
β = 92.21 (3)°

Data collection top

Four circle diffractometer	R_int = 0.062
3170 measured reflections	2 standard reflections every 540 min
2982 independent reflections	intensity decay: 2.5%
1428 reflections with I > 2σ(I)

Refinement top

R[F² > 2σ(F²)] = 0.046	131 parameters
wR(F²) = 0.054	All H-atom parameters refined
S = 1.93	Δρ_max = 3.03 e Å⁻³
2982 reflections	Δρ_min = −2.28 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Tl1	0.0644 (3)	0.499 (1)	0.265 (1)	0.027 (2)*
Tl2	0.1883 (2)	0.249 (1)	0.727 (1)	0.029 (2)*
Tl3	0.0639 (3)	0.995 (1)	0.253 (1)	0.027 (2)*
Tl4	0.1838 (2)	0.744 (1)	0.749 (2)	0.029 (2)*
P1	0.0620 (4)	0.261 (2)	0.762 (2)	0.016 (2)*
P2	0.1881 (4)	0.013 (2)	0.231 (2)	0.020 (3)*
P3	0.0625 (3)	0.761 (2)	0.756 (2)	0.013 (2)*
P4	0.1876 (4)	0.512 (2)	0.231 (2)	0.015 (2)*
O1	0.0410 (3)	0.216 (1)	0.973 (1)	0.019 (2)*
O2	0.2148 (4)	0.438 (2)	0.064 (2)	0.025 (2)*
O3	0.0348 (3)	0.686 (2)	0.934 (2)	0.020 (2)*
O4	0.2092 (3)	0.961 (2)	0.032 (2)	0.018 (2)*
O5	0.0290 (4)	0.323 (2)	0.594 (2)	0.022 (2)*
O6	0.2263 (4)	0.085 (2)	0374 (2)	0.021 (2)*
O7	0.0266 (4)	0.828 (2)	0.603 (2)	0.023 (3)*
O8	0.2266 (4)	0.589 (2)	0.375 (2)	0.017 (2)*
O9	0.0999 (3)	0.388 (2)	0.812 (2)	0.021 (2)*
O10	0.1509 (4)	0.138 (2)	0.181 (2)	0.014 (2)*
O11	0.0936 (4)	0.886 (2)	0.845 (2)	0.024 (2)*
O12	0.1571 (3)	0.636 (1)	0.154 (1)	0.014 (2)*
O13	0.0890 (4)	0.138 (2)	0.658 (2)	0.014 (2)*
O14	0.1591 (4)	0.389 (2)	0.332 (2)	0.022 (3)*
O15	0.0878 (4)	0.640 (2)	0.657 (2)	0.019 (2)*
O16	0.1559 (3)	0.888 (2)	0.317 (2)	0.025 (2)*
H1	0.9920 (6)	0.267 (3)	0.018 (3)	0.048 (4)*
H2	0.2509 (9)	1.001 (4)	−0.010 (3)	0.010 (3)*
H3	0.9992 (6)	0.254 (3)	0.516 (3)	0.023 (2)*
H4	0.2567 (5)	−0.018 (2)	0.538 (2)	0.037 (4)*
H5	0.1585 (6)	0.775 (2)	0.258 (2)	0.030 (4)*
H6	0.4065 (7)	0.507 (3)	0.223 (3)	0.038 (5)*
H7	0.3413 (8)	0.243 (4)	0.755 (3)	0.038 (4)*
H8	0.4066 (6)	0.012 (3)	0.243 (3)	0.029 (4)*

Geometric parameters (Å, º) top

P1—O1	1.57 (2)	Tl1—O1	3.23 (2)
P1—O5	1.53 (2)	Tl2—O2	2.85 (2)
P1—O9	1.59 (2)	Tl2—O9	2.90 (1)
P1—O13	1.52 (2)	Tl2—O6	2.94 (2)
P2—O4	1.53 (2)	Tl2—O14	2.96 (2)
P2—O6	1.54 (2)	Tl2—O6	2.97 (2)
P2—O10	1.58 (2)	Tl2—O13	3.01 (1)
P2—O16	1.57 (2)	Tl3—O1	2.76 (3)
P3—O3	1.58 (2)	Tl3—O16	2.82 (1)
P3—O7	1.53 (2)	Tl3—O10	2.84 (1)
P3—O11	1.53 (2)	Tl3—O7	2.96 (2)
P3—O15	1.47 (2)	Tl3—O11	2.99 (2)
P4—O2	1.52 (2)	Tl3—O13	2.99 (2)
P4—O8	1.58 (2)	Tl3—O7	3.21 (2)
P4—O12	1.50 (2)	Tl4—O4	2.75 (2)
P4—O14	1.53 (2)	Tl4—O15	2.93 (1)
Tl1—O3	2.85 (1)	Tl4—O12	2.94 (1)
Tl1—O5	2.87 (1)	Tl4—O11	2.97 (2)
Tl1—O14	2.90 (2)	Tl4—O8	3.09 (1)
Tl1—O15	2.90 (2)	Tl4—O8	3.10 (1)
Tl1—O12	3.02 (1)	Tl4—O16	3.17 (1)

O1—P1—O9	105.7 (9)	O3—P3—O15	106.0 (9)
O1—P1—O5	118.3 (9)	O7—P3—O11	107.9 (9)
O1—P1—O13	114.7 (9)	O7—P3—O15	109.9 (9)
O5—P1—O9	106.5 (9)	O11—P3—O15	115.2 (9)
O5—P1—O13	105.1 (9)	O2—P4—O8	104.5 (9)
O4—P2—O6	104.4 (9)	O2—P4—O12	113.8 (9
O4—P2—O10	111.7 (1)	O2—P4—O14	106.3 (9)
O4—P2—O16	106.6 (1)	O8—P4—O12	105.9 (9)
O3—P3—O7	107.8 (9)	O8—P4—O14	115.2 (9)
O3—P3—O11	109.4 (9)	O12—P4—O14	111.8 (9)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O3—H1···O1	0.94 (2)	1.51 (2)	2.44 (3)	167.5 (2)
O2—H2···O4	1.18 (3)	1.28 (3)	2.45 (1)	167.4 (9)
O5—H3···O7	1.12 (2)	1.30 (3)	2.41 (1)	169.3 (9)
O8—H4···O6	0.97 (2)	1.64 (2)	2.606 (9)	173.1 (9)
O16—H5···O12	1.09 (3)	1.42 (3)	2.50 (2)	170.9 (9)
O11—H6···O13	1.06 (3)	1.52 (3)	2.58 (2)	172.6 (3)
O10—H7···O14	1.17 (3)	1.32 (2)	2.48 (2)	168.8 (6)
O9—H8···O15	0.99 (3)	1.53 (3)	2.51 (2)	173.9 (2)

Experimental details

	(TDP298K)	(TDP240K)	(TDP210K)
Crystal data
Chemical formula	H₂O₄PTl	H₂O₄PTl	H₈O₁₆P₄Tl₄
M_r	301.6	301.6	1206.4
Crystal system, space group	Monoclinic, P2₁/a	Monoclinic, P2₁/a	Triclinic, C1
Temperature (K)	298	240	210
a, b, c (Å)	14.331 (7), 4.535 (2), 6.514 (3)	14.26 (2), 4.517 (9), 6.497 (10)	28.483 (12), 9.016 (5), 6.502 (3)
α, β, γ (°)	90, 91.67 (2), 90	90, 92.19 (13), 90	90.09 (5), 92.21 (3), 90.49 (3)
V (Å³)	423.2 (3)	418.2 (11)	1668.4 (14)
Z	4	4	16
Radiation type	Neutron, λ = 1.2413 Å	Neutron, λ = 0.8724 Å	Neutron, λ = 0.8724 Å
µ (mm⁻¹)	0.04	0.04	0.04
Crystal size (mm)	5 × 3 × 3	5 × 3 × 3	5 × 3 × 3

Data collection
Diffractometer	Four circle diffractometer	Four circle diffractometer	Four circle diffractometer
Absorption correction	–	–	–
No. of measured, independent and observed reflections	2766, 814, 699 [ > 3σ(I)]	1695, 845, 630 [ > 3σ(I)]	3170, 2982, 1428 [I > 2σ(I)]
R_int	0.022	0.021	0.062
(sin θ/λ)_max (Å⁻¹)	0.626	0.697	0.703

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.051, 0.060, 3.90	0.046, 0.054, 2.21	0.046, 0.054, 1.93
No. of reflections	699	699	2982
No. of parameters	73	73	131
No. of restraints	?	?	?
H-atom treatment	All H-atom parameters refined	All H-atom parameters refined	All H-atom parameters refined
Δρ_max, Δρ_min (e Å⁻³)	0.65, −0.42	0.51, −0.48	3.03, −2.28

Computer programs: pron, PROMETHEUS(Zucker et al.,1983), SHELXL97 (Sheldrick, 1997), drawxtal(Finger and Kroeker, 2004).

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