Incommensurate crystal structure of PbHfO3

Bosak, A.; Svitlyk, V.; Arakcheeva, A.; Burkovsky, R.; Diadkin, V.; Roleder, K.; Chernyshov, D.

doi:10.1107/S205252061901494X

Incommensurate crystal structure of PbHfO₃

A. Bosak, V. Svitlyk, A. Arakcheeva, R. Burkovsky, V. Diadkin, K. Roleder and D. Chernyshov

Controversy in the description/identification of so-called intermediate phase(s) in PbHfO₃, stable in the range ∼420–480 K, has existed for a few decades. A synchrotron diffraction experiment on a partially detwinned crystal allowed the structure to be solved in the superspace group Imma(00γ)s00 (No. 74.2). In contrast to some previously published reports, in the pure compound only one distinct phase was observed between Pbam PbZrO₃-like antiferroelectric and Pm3m paraelectric phases. The modulation vector depends only slightly on temperature. The major structure modulation is associated with the displacement of lead ions, which is accompanied by a smaller amplitude modulation for the surrounding O atoms and tilting of HfO₆ octahedra. Tilting of the octahedra results in a doubling of the unit cell compared with the parent structure.

Keywords: perovskites; ferroic; diffraction; incommensurate.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S205252061901494X/dk5080sup1.cif Contains datablock I
	Structure factor file (CIF format) https://doi.org/10.1107/S205252061901494X/dk5080Isup2.hkl Contains datablock I
	Portable Document Format (PDF) file https://doi.org/10.1107/S205252061901494X/dk5080sup3.pdf Positional parameters, ADPs and difference maps

B-IncStrDB reference: 16122E0qAs3

CCDC reference: 1963876

Computing details top

Data collection: CrysAlis PRO, Agilent Technologies, Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET) (compiled Aug 13 2014,18:06:01); cell refinement: CrysAlis PRO, Agilent Technologies, Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET) (compiled Aug 13 2014,18:06:01); program(s) used to refine structure: Petricek, V., Dusek, M. & Palatinus L. (2014). Z. Kristallogr. 229 (5), 345-352; molecular graphics: Brandenburg, K. & Putz, H. (2005). DIAMOND Version 3. Crystal Impact GbR, Postfach 1251, D-53002 Bonn, Germany..

(I) top

Crystal data top

PbHfO₃	F(000) = 712
M_r = 433.7	D_x = 10.186 Mg m⁻³
Orthorhombic, Imma(00γ)s00†	Synchrotron radiation, λ = 0.77865 Å
q = 0.298200c*	Cell parameters from 3769 reflections
a = 5.8522 (8) Å	θ = 2.3–27.4°
b = 8.236 (3) Å	µ = 121.75 mm⁻¹
c = 5.867 (5) Å	T = 443 K
V = 282.8 (3) Å³	Rod
Z = 4	0.2 × 0.05 × 0.05 mm

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, −x₂+1/2, x₃, x₄+1/2; (3) −x₁, x₂+1/2, −x₃, −x₄; (4) x₁, −x₂, −x₃, −x₄+1/2; (5) −x₁, −x₂, −x₃, −x₄; (6) x₁, x₂+1/2, −x₃, −x₄+1/2; (7) x₁, −x₂+1/2, x₃, x₄; (8) −x₁, x₂, x₃, x₄+1/2; (9) x₁+1/2, x₂+1/2, x₃+1/2, x₄; (10) −x₁+1/2, −x₂, x₃+1/2, x₄+1/2; (11) −x₁+1/2, x₂, −x₃+1/2, −x₄; (12) x₁+1/2, −x₂+1/2, −x₃+1/2, −x₄+1/2; (13) −x₁+1/2, −x₂+1/2, −x₃+1/2, −x₄; (14) x₁+1/2, x₂, −x₃+1/2, −x₄+1/2; (15) x₁+1/2, −x₂, x₃+1/2, x₄; (16) −x₁+1/2, x₂+1/2, x₃+1/2, x₄+1/2.

Data collection top

Inhouse made diffractometer coupled to Pilatus2M detector at SNBL BM01/ESRF	490 reflections with I > 4σ(I)
Radiation source: synchrotron	R_int = 0.029
Absorption correction: multi-scan CrysAlisPro, Agilent Technologies, Version 1.171.37.34 (release 22-05-2014 CrysAlis171 .NET) (compiled May 22 2014,16:03:01) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	θ_max = 27.4°, θ_min = 2.3°
T_min = 0.643, T_max = 1.000	h = −6→6
3769 measured reflections	k = −6→6
679 independent reflections	l = −6→6

Refinement top

Refinement on F²	0 constraints
R[F² > 2σ(F²)] = 0.043	Weighting scheme based on measured s.u.'s w = 1/(σ²(I) + 0.0004I²)
wR(F²) = 0.133	(Δ/σ)_max = 0.026
S = 3.69	Δρ_max = 2.91 e Å⁻³
679 reflections	Δρ_min = −4.74 e Å⁻³
86 parameters	Extinction correction: SHELXL-2017/1 (Sheldrick, 2015), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.049 (5)

Special details top

Refinement. U33 for Hf shows negative value of -0.000811. This parameter is fixed for 0.000811. The positive U33 of 0.00145 is fixed for O1. X-harmonics in crenel interval are used for Pb1. Anharmonic ADPs are used for Hf1.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Hf1	0	0	0	0.012 (4)
Pb1	0.0292 (5)	0.75	0.50222 (6)	0.0220 (6)	0.5
O1	0	0.75	0.0467 (11)	0.009 (3)
O2	0.25	0.0227 (6)	0.25	0.0197 (19)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Hf1	0.004 (4)	0.031 (11)	0.000811	0	0	0.0035 (9)
Pb1	0.0168 (8)	0.0291 (14)	0.0201 (7)	0	−0.00184 (10)	0
O1	0.018 (3)	0.009 (9)	0.001445	0	0	0
O2	0.018 (3)	0.031 (4)	0.010 (3)	0	−0.000006	0

Geometric parameters (Å, º) top

	Average	Minimum	Maximum
Hf1—O1ⁱ	2.0815 (11)	2.0766 (13)	2.0883 (13)
Hf1—O1ⁱⁱ	2.0815 (11)	2.0766 (13)	2.0883 (13)
Hf1—O2	2.083 (5)	2.042 (8)	2.124 (8)
Hf1—O2ⁱⁱⁱ	2.083 (5)	2.042 (8)	2.124 (8)
Hf1—O2^iv	2.083 (5)	2.042 (8)	2.124 (8)
Hf1—O2^v	2.083 (5)	2.042 (8)	2.124 (8)
Pb1—O1	2.680 (8)	2.666 (9)	2.697 (9)
Pb1—O1^vi	3.207 (8)	3.180 (9)	3.241 (9)
Pb1—O1^vii	3.194 (12)	3.018 (13)	3.288 (13)
Pb1—O1^viii	2.686 (11)	2.592 (12)	2.860 (12)
Pb1—O2^ix	2.967 (7)	2.855 (8)	3.089 (8)
Pb1—O2^x	2.936 (7)	2.873 (8)	3.013 (8)
Pb1—O2^xi	3.169 (7)	3.053 (8)	3.268 (8)
Pb1—O2^xii	2.648 (7)	2.578 (7)	2.716 (7)
Pb1—O2^xiii	2.936 (7)	2.873 (8)	3.013 (8)
Pb1—O2^xiv	2.967 (7)	2.855 (8)	3.089 (8)
Pb1—O2^xv	2.648 (7)	2.578 (7)	2.716 (7)
Pb1—O2^xvi	3.169 (7)	3.053 (8)	3.268 (8)

O1ⁱ—Hf1—O1ⁱⁱ	174.3 (3)	172.6 (3)	180
O1ⁱ—Hf1—O2	89.7 (2)	87.8 (2)	91.7 (3)
O1ⁱ—Hf1—O2ⁱⁱⁱ	90.1 (2)	86.3 (3)	93.8 (2)
O1ⁱ—Hf1—O2^iv	90.1 (2)	86.3 (3)	93.8 (2)
O1ⁱ—Hf1—O2^v	89.7 (2)	87.8 (2)	91.7 (3)
O1ⁱⁱ—Hf1—O2	90.1 (2)	86.3 (3)	93.8 (2)
O1ⁱⁱ—Hf1—O2ⁱⁱⁱ	89.7 (2)	87.8 (2)	91.7 (3)
O1ⁱⁱ—Hf1—O2^iv	89.7 (2)	87.8 (2)	91.7 (3)
O1ⁱⁱ—Hf1—O2^v	90.1 (2)	86.3 (3)	93.8 (2)
O2—Hf1—O2ⁱⁱⁱ	90.6 (3)	86.1 (3)	95.3 (3)
O2—Hf1—O2^iv	176.2 (3)	175.0 (3)	180
O2—Hf1—O2^v	89.4 (3)	89.3 (3)	89.5 (3)
O2ⁱⁱⁱ—Hf1—O2^iv	89.4 (3)	89.3 (3)	89.5 (3)
O2ⁱⁱⁱ—Hf1—O2^v	176.2 (3)	175.0 (3)	180
O2^iv—Hf1—O2^v	90.6 (3)	86.1 (3)	95.3 (3)
O1—Pb1—O1^vi	171.8 (3)	166.7 (3)	176.7 (3)
O1—Pb1—O1^vii	81.4 (2)	77.1 (3)	85.5 (2)
O1—Pb1—O1^viii	87.3 (3)	82.7 (3)	92.1 (3)
O1—Pb1—O2^ix	62.4 (2)	60.29 (19)	64.3 (2)
O1—Pb1—O2^x	118.0 (2)	114.4 (3)	121.5 (2)
O1—Pb1—O2^xi	59.6 (2)	57.83 (19)	61.6 (2)
O1—Pb1—O2^xii	124.5 (2)	121.1 (2)	128.4 (2)
O1—Pb1—O2^xiii	118.0 (2)	114.4 (3)	121.5 (2)
O1—Pb1—O2^xiv	62.4 (2)	60.29 (19)	64.3 (2)
O1—Pb1—O2^xv	124.5 (2)	121.1 (2)	128.4 (2)
O1—Pb1—O2^xvi	59.6 (2)	57.83 (19)	61.6 (2)
O1^vi—Pb1—O1^vii	90.4 (2)	87.3 (2)	92.8 (2)
O1^vi—Pb1—O1^viii	100.9 (3)	98.0 (3)	103.8 (3)
O1^vi—Pb1—O2^ix	121.45 (19)	120.40 (19)	122.8 (2)
O1^vi—Pb1—O2^x	56.6 (2)	55.1 (2)	59.2 (2)
O1^vi—Pb1—O2^xi	115.5 (2)	113.1 (2)	116.7 (2)
O1^vi—Pb1—O2^xii	60.1 (2)	57.4 (2)	61.3 (2)
O1^vi—Pb1—O2^xiii	56.6 (2)	55.1 (2)	59.2 (2)
O1^vi—Pb1—O2^xiv	121.45 (19)	120.40 (19)	122.8 (2)
O1^vi—Pb1—O2^xv	60.1 (2)	57.4 (2)	61.3 (2)
O1^vi—Pb1—O2^xvi	115.5 (2)	113.1 (2)	116.7 (2)
O1^vii—Pb1—O1^viii	168.7 (3)	168.1 (2)	169.2 (2)
O1^vii—Pb1—O2^ix	111.9 (2)	110.4 (2)	112.9 (2)
O1^vii—Pb1—O2^x	58.4 (2)	56.9 (2)	59.9 (2)
O1^vii—Pb1—O2^xi	55.17 (19)	53.80 (18)	56.19 (18)
O1^vii—Pb1—O2^xii	121.2 (2)	119.3 (3)	123.1 (2)
O1^vii—Pb1—O2^xiii	58.4 (2)	56.9 (2)	59.9 (2)
O1^vii—Pb1—O2^xiv	111.9 (2)	110.4 (2)	112.9 (2)
O1^vii—Pb1—O2^xv	121.2 (2)	119.3 (3)	123.1 (2)
O1^vii—Pb1—O2^xvi	55.17 (19)	53.80 (18)	56.19 (18)
O1^viii—Pb1—O2^ix	62.0 (2)	60.9 (2)	63.7 (2)
O1^viii—Pb1—O2^x	128.5 (2)	126.4 (2)	130.7 (2)
O1^viii—Pb1—O2^xi	118.5 (2)	117.7 (2)	119.9 (2)
O1^viii—Pb1—O2^xii	65.8 (2)	63.8 (2)	67.5 (3)
O1^viii—Pb1—O2^xiii	128.5 (2)	126.4 (2)	130.7 (2)
O1^viii—Pb1—O2^xiv	62.0 (2)	60.9 (2)	63.7 (2)
O1^viii—Pb1—O2^xv	65.8 (2)	63.8 (2)	67.5 (3)
O1^viii—Pb1—O2^xvi	118.5 (2)	117.7 (2)	119.9 (2)
O2^ix—Pb1—O2^x	168.9 (2)	165.9 (2)	171.7 (2)
O2^ix—Pb1—O2^xi	121.7 (2)	121.4 (3)	122.1 (2)
O2^ix—Pb1—O2^xii	62.1 (2)	60.52 (19)	64.1 (2)
O2^ix—Pb1—O2^xiii	89.54 (18)	87.48 (18)	92.86 (17)
O2^ix—Pb1—O2^xiv	99.8 (2)	97.4 (2)	102.7 (2)
O2^ix—Pb1—O2^xv	126.9 (3)	124.2 (3)	130.2 (3)
O2^ix—Pb1—O2^xvi	56.9 (2)	56.7 (2)	57.08 (18)
O2^x—Pb1—O2^xi	58.86 (19)	57.18 (19)	60.3 (2)
O2^x—Pb1—O2^xii	116.6 (3)	115.9 (3)	117.1 (3)
O2^x—Pb1—O2^xiii	80.6 (2)	76.3 (2)	85.3 (2)
O2^x—Pb1—O2^xiv	89.54 (19)	87.48 (19)	92.86 (18)
O2^x—Pb1—O2^xv	63.0 (2)	62.5 (2)	63.3 (2)
O2^x—Pb1—O2^xvi	113.0 (2)	110.2 (2)	115.4 (2)
O2^xi—Pb1—O2^xii	174.6 (3)	172.3 (3)	176.3 (3)
O2^xi—Pb1—O2^xiii	113.0 (2)	110.2 (2)	115.4 (2)
O2^xi—Pb1—O2^xiv	56.9 (2)	56.7 (2)	57.1 (2)
O2^xi—Pb1—O2^xv	90.97 (19)	87.60 (19)	93.11 (18)
O2^xi—Pb1—O2^xvi	89.1 (2)	86.6 (2)	91.0 (2)
O2^xii—Pb1—O2^xiii	63.0 (2)	62.5 (2)	63.3 (2)
O2^xii—Pb1—O2^xiv	126.9 (3)	124.2 (2)	130.2 (3)
O2^xii—Pb1—O2^xv	88.5 (2)	83.0 (2)	93.8 (3)
O2^xii—Pb1—O2^xvi	90.97 (19)	87.60 (18)	93.11 (17)
O2^xiii—Pb1—O2^xiv	168.9 (2)	165.9 (3)	171.7 (2)
O2^xiii—Pb1—O2^xv	116.6 (3)	115.9 (3)	117.1 (3)
O2^xiii—Pb1—O2^xvi	58.86 (19)	57.18 (19)	60.3 (2)
O2^xiv—Pb1—O2^xv	62.1 (2)	60.52 (19)	64.1 (2)
O2^xiv—Pb1—O2^xvi	121.7 (2)	121.4 (3)	122.1 (2)
O2^xv—Pb1—O2^xvi	174.6 (3)	172.3 (3)	176.3 (3)

Symmetry codes: (i) x₁, x₂−1, x₃, x₄; (ii) −x₁, x₂−1/2, −x₃, −x₄; (iii) −x₁+1/2, −x₂, x₃−1/2, x₄+1/2; (iv) −x₁, −x₂, −x₃, −x₄; (v) x₁−1/2, x₂, −x₃+1/2, −x₄+1/2; (vi) x₁, x₂, x₃+1, x₄; (vii) −x₁−1/2, x₂, −x₃+1/2, −x₄; (viii) −x₁+1/2, x₂, −x₃+1/2, −x₄; (ix) x₁, x₂+1, x₃, x₄; (x) x₁−1/2, x₂+1/2, x₃+1/2, x₄; (xi) −x₁, −x₂+1/2, x₃, x₄+1/2; (xii) −x₁+1/2, −x₂+1, x₃+1/2, x₄+1/2; (xiii) −x₁, −x₂+1, −x₃+1, −x₄; (xiv) −x₁+1/2, −x₂+1/2, −x₃+1/2, −x₄; (xv) x₁, x₂+1/2, −x₃+1, −x₄+1/2; (xvi) x₁−1/2, x₂+1, −x₃+1/2, −x₄+1/2.

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