B-IncStrDB

Incommensurate crystal structure of PbHfO₃

Authors:

Bosak, Alexei; Svitlyk, Volodymir; Arakcheeva, Alla; Burkovskiy, Roman; Diadkin, Vadim; Roleder, Krystian; Chernyshov, Dmitry

Journal:

Acta Crystallographica, Section B 76 7-12 (2020)

DOI:

https://doi.org/10.1107/S205252061901494X

B-IncStrDB ID: 16122E0qAs3 Entry date: 2019-11-25 Last revision: 2021-12-12

I

Chemical data

Structural Formula Sum: Pb Hf O3 [ Help ]

Formula weight: 433.7 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Imma(00γ)s00 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
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

a: 5.8522(8) Å [ Help ]

b: 8.236(3) Å [ Help ]

c: 5.867(5) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 282.8(3) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.298200

Z: 4 [ Help ]

Cell determination reflection Nb.: 3769 [ Help ]

θ(min) for cell determination: 2.27 ° [ Help ]

θ(max) for cell determination: 27.39 ° [ Help ]

Cell measurement temperature: 443 K [ Help ]

μ: 121.752 mm^-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: 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. [ Help ]

Minimum transmission factor: 0.64256 [ Help ]

Maximum transmission factor: 1.00000 [ Help ]

Refinement details

Refinement remarks: 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. [ Help ]

Total nb. of reflections: 679 [ Help ]

Nb. of observed reflections: 490 [ Help ]

Intense reflections threshold: I>4σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(obs): 0.0432 [ Help ]

wR(obs): 0.1305 [ Help ]

R(all): 0.0456 [ Help ]

wR(all): 0.1326 [ Help ]

S(all): 3.69 [ Help ]

S(obs): 4.40 [ Help ]

Nb. of reflections: 679 [ Help ]

Nb. of parameters: 86 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.0004I²) [ Help ]

Δ/σ(max): 0.0259 [ Help ]

Δ/σ(mean): 0.0048 [ Help ]

Δρ(max): 2.91 e_Å^-3 [ Help ]

Δρ(min): -4.74 e_Å^-3 [ Help ]

Extinction method: SHELXL-2017/1 (Sheldrick, 2015) [ Help ]

Extinction coefficient: 0.049(5) [ Help ]

Extinction expression: Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4 [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	x	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Hf1	Hf	0	0	0	Uani	0.012(4)	4	1	d	?	?	?
Pb1	Pb	0.0292(5)	0.75	0.50222(6)	Uani	0.0220(6)	8	0.5	d	?	?	?
O1	O	0	0.75	0.0467(11)	Uani	0.009(3)	4	1	d	?	?	?
O2	O	0.25	0.0227(6)	0.25	Uani	0.0197(19)	8	1	d	?	?	?

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U13	U23
Hf1	Hf	0.004(4)	0.031(11)	0.000811	0	0.0035(9)
Pb1	Pb	0.0168(8)	0.0291(14)	0.0201(7)	-0.00184(10)	0
O1	O	0.018(3)	0.009(9)	0.001445	0	0
O2	O	0.018(3)	0.031(4)	0.010(3)	-0.000006	0

Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]

Atom site label	Atom symbol	C111	C112	C113	C122	C123	C133	C222	C223	C233	C333
Hf1	Hf	0	0	0	0	0	0	0	0	0	0

Anharmonic ADPs (D coefficients): (Show/hide table) [ Help ]

Atom site label	Atom symbol	D1111	D1112	D1113	D1122	D1123	D1133	D1222	D1223	D1233	D1333	D2222	D2223	D2233	D2333	D3333
Hf1	Hf	0.07(3)	0	0	0.015(8)	-0.0009(8)	-0.002(9)	0	0	0	0	0.07(4)	0.027(3)	0.008(6)	0.002(2)	0.055(10)

Anharmonic ADPs (E coefficients): (Show/hide table) [ Help ]

Atom site label	Atom symbol	E11111	E11112	E11113	E11122	E11123	E11133	E11222	E11223	E11233	E11333	E12222	E12223	E12233	E12333	E13333	E22222	E22223	E22233	E22333	E23333	E33333
Hf1	Hf	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Anharmonic ADPs (F coefficients): (Show/hide table) [ Help ]

Atom site label	Atom symbol	F111111	F111112	F111113	F111122	F111123	F111133	F111222	F111223	F111233	F111333	F112222	F112223	F112233	F112333	F113333	F122222	F122223	F122233	F122333	F123333	F133333	F222222	F222223	F222233	F222333	F223333	F233333	F333333
Hf1	Hf	0.13(5)	0	0	0.005(5)	-0.0012(6)	-0.007(8)	0	0	0	0	0.018(8)	0.0000(3)	0.0002(15)	0.0000(4)	0.003(8)	0	0	0	0	0	0	0.08(6)	0.045(5)	0.004(4)	0.0003(8)	0.005(5)	0.003(2)	0.09(2)

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]

Wave vector code	q_1
1	1
2	2
3	3

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Pb1	0.75	0.5

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Hf1x1	Hf1	x	1
Hf1y1	Hf1	y	1
Hf1z1	Hf1	z	1
Hf1x2	Hf1	x	2
Hf1y2	Hf1	y	2
Hf1z2	Hf1	z	2
Hf1x3	Hf1	x	3
Hf1y3	Hf1	y	3
Hf1z3	Hf1	z	3
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1x2	O1	x	2
O1y2	O1	y	2
O1z2	O1	z	2
O1x3	O1	x	3
O1y3	O1	y	3
O1z3	O1	z	3
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O2x2	O2	x	2
O2y2	O2	y	2
O2z2	O2	z	2
O2x3	O2	x	3
O2y3	O2	y	3
O2z3	O2	z	3

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Hf1x1	0	-0.00464(13)
Hf1y1	0	0
Hf1z1	0	0
Hf1x2	0	0
Hf1y2	0	0.00005(2)
Hf1z2	0	-0.00022(3)
Hf1x3	0	-0.00097(3)
Hf1y3	0	0
Hf1z3	0	0
O1x1	-0.0197(8)	0.0200(9)
O1y1	0	0
O1z1	0	0
O1x2	0	0
O1y2	0	0
O1z2	0.0005(5)	-0.0019(5)
O1x3	-0.0018(6)	0.0043(6)
O1y3	0	0
O1z3	0	0
O2x1	0	0.0137(9)
O2y1	-0.0097(4)	0
O2z1	0	-0.0078(7)
O2x2	0	-0.0001(4)
O2y2	-0.0001(3)	0
O2z2	0	-0.0004(4)
O2x3	0	0.0066(4)
O2y3	-0.0007(3)	0
O2z3	0	-0.0062(4)

Displacive (translational) XHarm coefficients: (Show/hide table) [ Help ]

Atom site label	Displacement axis	XHarm order	XHarm coefficient
Pb1	x	1	-0.00084(6)
Pb1	y	1	0
Pb1	z	1	-0.0004(4)
Pb1	x	2	0.0042(4)
Pb1	y	2	0
Pb1	z	2	-0.00068(5)
Pb1	x	3	0.00016(8)
Pb1	y	3	0
Pb1	z	3	0.0012(5)
Pb1	x	4	0.0082(6)
Pb1	y	4	0
Pb1	z	4	-0.0004(6)

ADP XHarm coefficients: (Show/hide table) [ Help ]

Atom site label	Tensor element	XHarm order	XHarm coefficient
Pb1	U11	1	0.00308(15)
Pb1	U22	1	-0.0008(4)
Pb1	U33	1	0.0002(3)
Pb1	U12	1	0
Pb1	U13	1	-0.0017(5)
Pb1	U23	1	0
Pb1	U11	2	0.0000(9)
Pb1	U22	2	-0.0007(2)
Pb1	U33	2	-0.00087(15)
Pb1	U12	2	0
Pb1	U13	2	-0.00013(19)
Pb1	U23	2	0
Pb1	U11	3	0.0012(2)
Pb1	U22	3	0.0000(5)
Pb1	U33	3	-0.0005(3)
Pb1	U12	3	0
Pb1	U13	3	-0.0003(7)
Pb1	U23	3	0
Pb1	U11	4	-0.0111(18)
Pb1	U22	4	0.0002(12)
Pb1	U33	4	0.0014(7)
Pb1	U12	4	0
Pb1	U13	4	-0.0007(6)
Pb1	U23	4	0

Incommensurate crystal structure of PbHfO₃

Bosak, Alexei; Svitlyk, Volodymir; Arakcheeva, Alla; Burkovskiy, Roman; Diadkin, Vadim; Roleder, Krystian; Chernyshov, Dmitry

Acta Crystallographica, Section B 76 7-12 (2020)

https://doi.org/10.1107/S205252061901494X

Download CIF

Open in JSmol

I

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Incommensurate crystal structure of PbHfO3

Bosak, Alexei; Svitlyk, Volodymir; Arakcheeva, Alla; Burkovskiy, Roman; Diadkin, Vadim; Roleder, Krystian; Chernyshov, Dmitry

Acta Crystallographica, Section B 76 7-12 (2020)

https://doi.org/10.1107/S205252061901494X

Download CIF

Open in JSmol

I

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Incommensurate crystal structure of PbHfO₃