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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.
Supporting information
B-IncStrDB reference: 16122E0qAs3
CCDC reference: 1963876
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..
Crystal data top
PbHfO3 | F(000) = 712 |
Mr = 433.7 | Dx = 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 | Rint = 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. | θmax = 27.4°, θmin = 2.3° |
Tmin = 0.643, Tmax = 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 | Δρmax = 2.91 e Å−3 |
679 reflections | Δρmin = −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 | Uiso*/Ueq | 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—O2iv | 2.083 (5) | 2.042 (8) | 2.124 (8) |
Hf1—O2v | 2.083 (5) | 2.042 (8) | 2.124 (8) |
Pb1—O1 | 2.680 (8) | 2.666 (9) | 2.697 (9) |
Pb1—O1vi | 3.207 (8) | 3.180 (9) | 3.241 (9) |
Pb1—O1vii | 3.194 (12) | 3.018 (13) | 3.288 (13) |
Pb1—O1viii | 2.686 (11) | 2.592 (12) | 2.860 (12) |
Pb1—O2ix | 2.967 (7) | 2.855 (8) | 3.089 (8) |
Pb1—O2x | 2.936 (7) | 2.873 (8) | 3.013 (8) |
Pb1—O2xi | 3.169 (7) | 3.053 (8) | 3.268 (8) |
Pb1—O2xii | 2.648 (7) | 2.578 (7) | 2.716 (7) |
Pb1—O2xiii | 2.936 (7) | 2.873 (8) | 3.013 (8) |
Pb1—O2xiv | 2.967 (7) | 2.855 (8) | 3.089 (8) |
Pb1—O2xv | 2.648 (7) | 2.578 (7) | 2.716 (7) |
Pb1—O2xvi | 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—O2iv | 90.1 (2) | 86.3 (3) | 93.8 (2) |
O1i—Hf1—O2v | 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—O2iv | 89.7 (2) | 87.8 (2) | 91.7 (3) |
O1ii—Hf1—O2v | 90.1 (2) | 86.3 (3) | 93.8 (2) |
O2—Hf1—O2iii | 90.6 (3) | 86.1 (3) | 95.3 (3) |
O2—Hf1—O2iv | 176.2 (3) | 175.0 (3) | 180 |
O2—Hf1—O2v | 89.4 (3) | 89.3 (3) | 89.5 (3) |
O2iii—Hf1—O2iv | 89.4 (3) | 89.3 (3) | 89.5 (3) |
O2iii—Hf1—O2v | 176.2 (3) | 175.0 (3) | 180 |
O2iv—Hf1—O2v | 90.6 (3) | 86.1 (3) | 95.3 (3) |
O1—Pb1—O1vi | 171.8 (3) | 166.7 (3) | 176.7 (3) |
O1—Pb1—O1vii | 81.4 (2) | 77.1 (3) | 85.5 (2) |
O1—Pb1—O1viii | 87.3 (3) | 82.7 (3) | 92.1 (3) |
O1—Pb1—O2ix | 62.4 (2) | 60.29 (19) | 64.3 (2) |
O1—Pb1—O2x | 118.0 (2) | 114.4 (3) | 121.5 (2) |
O1—Pb1—O2xi | 59.6 (2) | 57.83 (19) | 61.6 (2) |
O1—Pb1—O2xii | 124.5 (2) | 121.1 (2) | 128.4 (2) |
O1—Pb1—O2xiii | 118.0 (2) | 114.4 (3) | 121.5 (2) |
O1—Pb1—O2xiv | 62.4 (2) | 60.29 (19) | 64.3 (2) |
O1—Pb1—O2xv | 124.5 (2) | 121.1 (2) | 128.4 (2) |
O1—Pb1—O2xvi | 59.6 (2) | 57.83 (19) | 61.6 (2) |
O1vi—Pb1—O1vii | 90.4 (2) | 87.3 (2) | 92.8 (2) |
O1vi—Pb1—O1viii | 100.9 (3) | 98.0 (3) | 103.8 (3) |
O1vi—Pb1—O2ix | 121.45 (19) | 120.40 (19) | 122.8 (2) |
O1vi—Pb1—O2x | 56.6 (2) | 55.1 (2) | 59.2 (2) |
O1vi—Pb1—O2xi | 115.5 (2) | 113.1 (2) | 116.7 (2) |
O1vi—Pb1—O2xii | 60.1 (2) | 57.4 (2) | 61.3 (2) |
O1vi—Pb1—O2xiii | 56.6 (2) | 55.1 (2) | 59.2 (2) |
O1vi—Pb1—O2xiv | 121.45 (19) | 120.40 (19) | 122.8 (2) |
O1vi—Pb1—O2xv | 60.1 (2) | 57.4 (2) | 61.3 (2) |
O1vi—Pb1—O2xvi | 115.5 (2) | 113.1 (2) | 116.7 (2) |
O1vii—Pb1—O1viii | 168.7 (3) | 168.1 (2) | 169.2 (2) |
O1vii—Pb1—O2ix | 111.9 (2) | 110.4 (2) | 112.9 (2) |
O1vii—Pb1—O2x | 58.4 (2) | 56.9 (2) | 59.9 (2) |
O1vii—Pb1—O2xi | 55.17 (19) | 53.80 (18) | 56.19 (18) |
O1vii—Pb1—O2xii | 121.2 (2) | 119.3 (3) | 123.1 (2) |
O1vii—Pb1—O2xiii | 58.4 (2) | 56.9 (2) | 59.9 (2) |
O1vii—Pb1—O2xiv | 111.9 (2) | 110.4 (2) | 112.9 (2) |
O1vii—Pb1—O2xv | 121.2 (2) | 119.3 (3) | 123.1 (2) |
O1vii—Pb1—O2xvi | 55.17 (19) | 53.80 (18) | 56.19 (18) |
O1viii—Pb1—O2ix | 62.0 (2) | 60.9 (2) | 63.7 (2) |
O1viii—Pb1—O2x | 128.5 (2) | 126.4 (2) | 130.7 (2) |
O1viii—Pb1—O2xi | 118.5 (2) | 117.7 (2) | 119.9 (2) |
O1viii—Pb1—O2xii | 65.8 (2) | 63.8 (2) | 67.5 (3) |
O1viii—Pb1—O2xiii | 128.5 (2) | 126.4 (2) | 130.7 (2) |
O1viii—Pb1—O2xiv | 62.0 (2) | 60.9 (2) | 63.7 (2) |
O1viii—Pb1—O2xv | 65.8 (2) | 63.8 (2) | 67.5 (3) |
O1viii—Pb1—O2xvi | 118.5 (2) | 117.7 (2) | 119.9 (2) |
O2ix—Pb1—O2x | 168.9 (2) | 165.9 (2) | 171.7 (2) |
O2ix—Pb1—O2xi | 121.7 (2) | 121.4 (3) | 122.1 (2) |
O2ix—Pb1—O2xii | 62.1 (2) | 60.52 (19) | 64.1 (2) |
O2ix—Pb1—O2xiii | 89.54 (18) | 87.48 (18) | 92.86 (17) |
O2ix—Pb1—O2xiv | 99.8 (2) | 97.4 (2) | 102.7 (2) |
O2ix—Pb1—O2xv | 126.9 (3) | 124.2 (3) | 130.2 (3) |
O2ix—Pb1—O2xvi | 56.9 (2) | 56.7 (2) | 57.08 (18) |
O2x—Pb1—O2xi | 58.86 (19) | 57.18 (19) | 60.3 (2) |
O2x—Pb1—O2xii | 116.6 (3) | 115.9 (3) | 117.1 (3) |
O2x—Pb1—O2xiii | 80.6 (2) | 76.3 (2) | 85.3 (2) |
O2x—Pb1—O2xiv | 89.54 (19) | 87.48 (19) | 92.86 (18) |
O2x—Pb1—O2xv | 63.0 (2) | 62.5 (2) | 63.3 (2) |
O2x—Pb1—O2xvi | 113.0 (2) | 110.2 (2) | 115.4 (2) |
O2xi—Pb1—O2xii | 174.6 (3) | 172.3 (3) | 176.3 (3) |
O2xi—Pb1—O2xiii | 113.0 (2) | 110.2 (2) | 115.4 (2) |
O2xi—Pb1—O2xiv | 56.9 (2) | 56.7 (2) | 57.1 (2) |
O2xi—Pb1—O2xv | 90.97 (19) | 87.60 (19) | 93.11 (18) |
O2xi—Pb1—O2xvi | 89.1 (2) | 86.6 (2) | 91.0 (2) |
O2xii—Pb1—O2xiii | 63.0 (2) | 62.5 (2) | 63.3 (2) |
O2xii—Pb1—O2xiv | 126.9 (3) | 124.2 (2) | 130.2 (3) |
O2xii—Pb1—O2xv | 88.5 (2) | 83.0 (2) | 93.8 (3) |
O2xii—Pb1—O2xvi | 90.97 (19) | 87.60 (18) | 93.11 (17) |
O2xiii—Pb1—O2xiv | 168.9 (2) | 165.9 (3) | 171.7 (2) |
O2xiii—Pb1—O2xv | 116.6 (3) | 115.9 (3) | 117.1 (3) |
O2xiii—Pb1—O2xvi | 58.86 (19) | 57.18 (19) | 60.3 (2) |
O2xiv—Pb1—O2xv | 62.1 (2) | 60.52 (19) | 64.1 (2) |
O2xiv—Pb1—O2xvi | 121.7 (2) | 121.4 (3) | 122.1 (2) |
O2xv—Pb1—O2xvi | 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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