B-IncStrDB

As Predicted and More: Modulated Channel Occupation in YZn_{5+x}

Authors:

Fredrickson, Rie T.; Fredrickson, Daniel C.

Journal:

Acta Crystallographica Section B 79 320-329 (2023)

DOI:

https://doi.org/10.1107/S2052520623005292

B-IncStrDB ID: uGPEM0uGBx9 Entry date: 2023-06-26 Last revision: 2024-02-25

I

Chemical data

Structural Formula: Y1 Zn5.217 [ Help ]

Formula analytical: Y1 Zn5.26(3) [ Help ]

Structural Formula Sum: Y1 Zn5.217 [ Help ]

Formula weight: 431 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: trigonal [ Help ]

Superspace group name: P-31c(1/31/3γ)00s [ Help ]

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

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x2,x1-x2,x3,-x2+x4
3	-x1+x2,-x1,x3,-x1+x4
4	-x2,-x1,-x3+1/2,-x4+1/2
5	-x1+x2,x2,-x3+1/2,x2-x4+1/2
6	x1,x1-x2,-x3+1/2,x1-x4+1/2
7	-x1,-x2,-x3,-x4
8	x2,-x1+x2,-x3,x2-x4
9	x1-x2,x1,-x3,x1-x4
10	x2,x1,x3+1/2,x4+1/2
11	x1-x2,-x2,x3+1/2,-x2+x4+1/2
12	-x1,-x1+x2,x3+1/2,-x1+x4+1/2

a: 8.88110(10) Å [ Help ]

b: 8.88110(10) Å [ Help ]

c: 9.20570(10) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 628.812(12) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.333333	0.333333	0.304100

Z: 6 [ Help ]

Cell determination reflection Nb.: 5676 [ Help ]

θ(min) for cell determination: 3.4420 ° [ Help ]

θ(max) for cell determination: 27.4200 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 42.899 mm^-1 [ Help ]

Absorption correction type: analytical [ Help ]

Absorption correction remarks: CrysAlisPro, Agilent Technologies, Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET) (compiled Aug 13 2014,18:06:01) Analytical numeric absorption correction using a multifaceted crystal model based on expressions derived by R.C. Clark & J.S. Reid. (Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.024 [ Help ]

Maximum transmission factor: 0.125 [ Help ]

Refinement details

Total nb. of reflections: 1450 [ Help ]

Nb. of observed reflections: 777 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(obs): 0.0272 [ Help ]

wR(obs): 0.0788 [ Help ]

R(all): 0.0560 [ Help ]

wR(all): 0.0876 [ Help ]

S(all): 1.53 [ Help ]

S(obs): 1.94 [ Help ]

Nb. of reflections: 1450 [ Help ]

Nb. of parameters: 91 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0141 [ Help ]

Δ/σ(mean): 0.0020 [ Help ]

Δρ(max): 4.73 e_Å^-3 [ Help ]

Δρ(min): -4.90 e_Å^-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 330(30) [ 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
Y1	Y	0.61475(10)	0.80738(5)	0.25	Uani	0.0107(3)	6	1	d	.	.	.
Zn1	Zn	0.86508(10)	0.43254(5)	0.25	Uani	0.0117(3)	6	1	d	.	.	.
Zn2	Zn	0.666667	0.333333	0.51174(10)	Uani	0.0122(3)	4	1	d	.	.	.
Zn3	Zn	1	0.5	0.5	Uani	0.0123(6)	6	1	d	.	.	.
Zn4	Zn	0.8383(2)	0.67858(8)	0.41030(6)	Uani	0.0139(5)	12	1	d	.	.	.
Zn5	Zn	1	1	0	Uani	0.0196(12)	2	0.988(4)	d	.	.	.
Zn6	Zn	1	1	0.25	Uani	0.0140(9)	2	0.664(4)	d	.	.	.

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

Atom site label	Atom site symbol	U11	U22	U33	U12	U13	U23
Y1	Y	0.0123(4)	0.0104(3)	0.0102(3)	0.00617(19)	0	0.0067(7)
Zn1	Zn	0.0118(4)	0.0130(3)	0.0099(4)	0.0059(2)	0	0.0002(12)
Zn2	Zn	0.0115(3)	0.0115(3)	0.0134(5)	0.00577(16)	0	0
Zn3	Zn	0.0115(4)	0.0122(9)	0.0108(4)	0.0040(9)	-0.0017(3)	0.0004(11)
Zn4	Zn	0.0162(8)	0.0147(4)	0.0140(3)	0.0102(7)	0.0002(8)	0.0006(2)
Zn5	Zn	0.0149(6)	0.0149(6)	0.029(3)	0.0074(3)	0	0
Zn6	Zn	0.0144(7)	0.0144(7)	0.013(2)	0.0072(4)	0	0

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

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

Atom site label	Center (x0)	Width
Zn5	0.5	0.988(4)
Zn6	0.75	0.664(4)

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Y1x1	Y1	x	1
Y1y1	Y1	y	1
Y1z1	Y1	z	1
Zn1x1	Zn1	x	1
Zn1y1	Zn1	y	1
Zn1z1	Zn1	z	1
Zn2x1	Zn2	x	1
Zn2y1	Zn2	y	1
Zn2z1	Zn2	z	1
Zn3x1	Zn3	x	1
Zn3y1	Zn3	y	1
Zn3z1	Zn3	z	1
Zn4x1	Zn4	x	1
Zn4y1	Zn4	y	1
Zn4z1	Zn4	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Y1x1	0.0102(3)	0.00386(10)
Y1y1	0.00417(17)	0.0044(2)
Y1z1	0.00062(7)	-0.00165(19)
Zn1x1	-0.00096(12)	-0.0021(3)
Zn1y1	-0.0035(5)	0.00028(17)
Zn1z1	-0.0008(2)	0.00036(10)
Zn2x1	-0.0048(3)	-0.0014(2)
Zn2y1	-0.0036(3)	0.0035(3)
Zn2z1	0	0
Zn3x1	0	-0.0039(3)
Zn3y1	0	-0.0020(3)
Zn3z1	0	0.0014(2)
Zn4x1	-0.0039(2)	-0.0035(2)
Zn4y1	-0.0094(2)	-0.0043(2)
Zn4z1	-0.00357(19)	0.00202(19)

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

Atom site label	Displacement axis	Polynomial order	Polynomial coeff.
Zn5	x	1	0
Zn5	y	1	0
Zn5	z	1	-0.0996(9)
Zn5	x	2	0
Zn5	y	2	0
Zn5	z	2	0
Zn6	x	1	0
Zn6	y	1	0
Zn6	z	1	-0.0447(8)
Zn6	x	2	0
Zn6	y	2	0
Zn6	z	2	0

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

Modulation code	Atom site label	Tensor element	Wave vector code
Y1U111	Y1	U11	1
Y1U221	Y1	U22	1
Y1U331	Y1	U33	1
Y1U121	Y1	U12	1
Y1U131	Y1	U13	1
Y1U231	Y1	U23	1
Zn1U111	Zn1	U11	1
Zn1U221	Zn1	U22	1
Zn1U331	Zn1	U33	1
Zn1U121	Zn1	U12	1
Zn1U131	Zn1	U13	1
Zn1U231	Zn1	U23	1
Zn2U111	Zn2	U11	1
Zn2U221	Zn2	U22	1
Zn2U331	Zn2	U33	1
Zn2U121	Zn2	U12	1
Zn2U131	Zn2	U13	1
Zn2U231	Zn2	U23	1
Zn3U111	Zn3	U11	1
Zn3U221	Zn3	U22	1
Zn3U331	Zn3	U33	1
Zn3U121	Zn3	U12	1
Zn3U131	Zn3	U13	1
Zn3U231	Zn3	U23	1
Zn4U111	Zn4	U11	1
Zn4U221	Zn4	U22	1
Zn4U331	Zn4	U33	1
Zn4U121	Zn4	U12	1
Zn4U131	Zn4	U13	1
Zn4U231	Zn4	U23	1

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

Modulation code	Cosine coefficient	Sine coefficient
Y1U111	0.0036(9)	0.0014(4)
Y1U221	0.001(3)	-0.0005(7)
Y1U331	0.0006(10)	0.0002(4)
Y1U121	0.0022(6)	-0.0002(7)
Y1U131	0.0001(3)	-0.0004(8)
Y1U231	-0.0013(18)	-0.0007(5)
Zn1U111	-0.0001(5)	-0.0002(12)
Zn1U221	0.002(2)	-0.0011(9)
Zn1U331	0.0002(5)	0.0003(12)
Zn1U121	0.002(2)	-0.0010(7)
Zn1U131	-0.0002(9)	0.0001(4)
Zn1U231	0.0000(7)	0.0004(8)
Zn2U111	0.0011(12)	-0.0007(9)
Zn2U221	0.0001(11)	0.0013(9)
Zn2U331	0	0
Zn2U121	0.0011(7)	0.0006(13)
Zn2U131	-0.0008(12)	0.0004(11)
Zn2U231	-0.0001(14)	0.0009(9)
Zn3U111	0.0025(13)	0
Zn3U221	0.0004(13)	0
Zn3U331	-0.0042(12)	0
Zn3U121	0.0016(11)	0
Zn3U131	0.0000(12)	0
Zn3U231	-0.0008(11)	0
Zn4U111	-0.0019(10)	0.0001(10)
Zn4U221	-0.0017(9)	0.0035(10)
Zn4U331	0.0005(9)	-0.0039(10)
Zn4U121	-0.0012(8)	0.0015(8)
Zn4U131	-0.0003(8)	0.0001(8)
Zn4U231	-0.0012(7)	0.0014(7)

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

Atom site label	Tensor element	Polynomial order	Polynomial coeff.
Zn5	U11	1	0
Zn5	U22	1	0
Zn5	U33	1	0
Zn5	U12	1	0
Zn5	U13	1	0
Zn5	U23	1	0
Zn5	U11	2	-0.008(3)
Zn5	U22	2	-0.008(3)
Zn5	U33	2	-0.016(6)
Zn5	U12	2	-0.0038(13)
Zn5	U13	2	0
Zn5	U23	2	0