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LiZn4-x (x= 0.825) as a (3 + 1)-dimensional modulated derivative of hexagonal close packing

Authors:

Pavlyuk, Volodymyr; Chumak, Ihor; Akselrud, Lev; Lidin, Sven; Ehrenberg, Helmut

Journal:

Acta Crystallographica, Section B 70 212-217 (2014)

DOI:

https://doi.org/10.1107/S2052520613030709

B-IncStrDB ID: 8692EytSde Entry date: 2014-06-12 Last revision: 2021-12-12

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Chemical data

Structural Formula Sum: Li Zn3.175 [ Help ]

Formula weight: 214.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Cmcm(α00)0s0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -x,-y,1/2+z
3 x,-y,-z
4 -x,y,1/2-z
5 -x,-y,-z
6 x,y,1/2-z
7 -x,y,z
8 x,-y,1/2+z
9 1/2+x,1/2+y,z
10 1/2-x,1/2-y,1/2+z
11 1/2+x,1/2-y,-z
12 1/2-x,1/2+y,1/2-z
13 1/2-x,1/2-y,-z
14 1/2+x,1/2+y,1/2-z
15 1/2-x,1/2+y,z
16 1/2+x,1/2-y,1/2+z

Space group name (H-M): C m c m [ Help ]

Space group name (Hall): -C 2c 2 [ Help ]

a: 2.7679 Å [ Help ]

b: 4.7942 Å [ Help ]

c: 4.3864 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 58.207 Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.571429 0.000000 0.000000

Z: 1 [ Help ]

Cell determination reflection Nb.: 10263 [ Help ]

θ(min) for cell determination: 1.21 ° [ Help ]

θ(max) for cell determination: 30.19 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 32.129 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: (SADABS; Bruker, 2004) [ Help ]

Minimum transmission factor: 0.365 [ Help ]

Maximum transmission factor: 0.560 [ Help ]

Refinement details

Total nb. of reflections: 378 [ Help ]

Nb. of observed reflections: 329 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0623 [ Help ]

wR(obs): 0.0875 [ Help ]

R(all): 0.0693 [ Help ]

wR(all): 0.0880 [ Help ]

S(all): 3.70 [ Help ]

S(obs): 3.96 [ Help ]

Nb. of reflections: 378 [ Help ]

Nb. of parameters: 12 [ Help ]

Number of constraints: 19 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]

Δ/σ(max): 0.0393 [ Help ]

Δ/σ(mean): 0.0168 [ Help ]

Δρ(max): 3.25 e_Å-3 [ Help ]

Δρ(min): -3.39 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ 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
Zn1 Zn 0.5 0.3365(7) 0.25 Uani 0.0083(5) 4 0.7605(14) d ? ? ?
Li1 Li 0.5 0.3365(7) 0.25 Uani 0.0083(5) 4 0.2395(14) d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Zn1 Zn 0.0076(8) 0.0098(8) 0.0076(7) 0 0 0
Li1 Li 0.0076(8) 0.0098(8) 0.0076(7) 0 0 0

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

Wave vector code q_1
1 1
2 2
3 3

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Zn1 0.25 0.7605(14)
Li1 0.75 0.2395(14)

Definition of the displacive (translational) Fourier series: [ Help ]

Modulation code Atom site label Displacement axis Wave vector code
Zn1x1 Zn1 x 1
Zn1y1 Zn1 y 1
Zn1z1 Zn1 z 1
Zn1x2 Zn1 x 2
Zn1y2 Zn1 y 2
Zn1z2 Zn1 z 2
Zn1x3 Zn1 x 3
Zn1y3 Zn1 y 3
Zn1z3 Zn1 z 3
Li1x1 Li1 x 1
Li1y1 Li1 y 1
Li1z1 Li1 z 1
Li1x2 Li1 x 2
Li1y2 Li1 y 2
Li1z2 Li1 z 2
Li1x3 Li1 x 3
Li1y3 Li1 y 3
Li1z3 Li1 z 3

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Zn1x1 0.0036(4) 0
Zn1y1 0 -0.0145(13)
Zn1z1 0 0
Zn1x2 0 0.0039(6)
Zn1y2 -0.0094(10) 0
Zn1z2 0 0
Zn1x3 -0.0021(6) 0
Zn1y3 0 0.0146(7)
Zn1z3 0 0
Li1x1 0.0036(4) 0
Li1y1 0 -0.0145(13)
Li1z1 0 0
Li1x2 0 0.0039(6)
Li1y2 -0.0094(10) 0
Li1z2 0 0
Li1x3 -0.0021(6) 0
Li1y3 0 0.0146(7)
Li1z3 0 0