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The determination of the incommensurately modulated structure of Niobium Tetratelluride

Authors:

van Smaalen, S.; Bronsema, K.D.; Mahy, J.

Journal:

Acta Cryst. B 42 43-50 (1986)

DOI:

https://doi.org/10.1107/S0108768186098609

B-IncStrDB ID: 682EJ32qI Entry date: 2010-11-08 Last revision: 2021-12-30

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NbTe_REFRNCE

Chemical data

Structural Formula Sum: Nb1 Te4 [ Help ]

Formula weight: 603.3 Da [ Help ]

Crystallographic data and experimental details

a: 9.191(3) Å [ Help ]

b: 9.191(3) Å [ Help ]

c: 6.837(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 577.6(3) Å3 [ Help ]

μ: 21.726 mm-1 [ Help ]

Z: 4 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Crystal system: tetragonal [ Help ]

Space group name (H-M): C4/mcc [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -y,x,z
3 -x,y,1/2+z
4 -x,-y,z
5 -y,-x,1/2+z
6 y,-x,z
7 x,-y,1/2+z
8 y,x,1/2+z
9 -x,-y,-z
10 y,-x,-z
11 x,-y,1/2-z
12 x,y,-z
13 y,x,1/2-z
14 -y,x,-z
15 -x,y,1/2-z
16 -y,-x,1/2-z
17 1/2+x,1/2+y,z
18 1/2-y,1/2+x,z
19 1/2-x,1/2+y,1/2+z
20 1/2-x,1/2-y,z
21 1/2-y,1/2-x,1/2+z
22 1/2+y,1/2-x,z
23 1/2+x,1/2-y,1/2+z
24 1/2+y,1/2+x,1/2+z
25 1/2-x,1/2-y,-z
26 1/2+y,1/2-x,-z
27 1/2+x,1/2-y,1/2-z
28 1/2+x,1/2+y,-z
29 1/2+y,1/2+x,1/2-z
30 1/2-y,1/2+x,-z
31 1/2-x,1/2+y,1/2-z
32 1/2-y,1/2-x,1/2-z

Refinement details

Refinement remarks: WARNING: The published thermal displacement parameters have been converted to U,s. The calculated standard uncertainties (s.u.) have been based uniquely on the published ones without considering the s.u. of any other quantity involved in such conversion. [ Help ]

Nb. of observed reflections: 923 [ Help ]

wR(all): 0.065 [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
Te Te 16 1 0.23599(9) 0.09193(8) 0 ? Uani
Nb Nb 4 1 0 0 0.25 ? Uani

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Te Te .0160(3) .0081(2) .0092(2) -.00466(17) 0 0
Nb Nb .0050(3) .0050(3) .068(2) 0 0 0

NbTe_MOD

Chemical data

Structural Formula: Nb Te4 [ Help ]

Crystallographic data and experimental details

a: 9.191(3) Å [ Help ]

b: 9.191(3) Å [ Help ]

c: 6.837(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 577.6(3) Å3 [ Help ]

Z: 4 [ Help ]

μ: 21.726 mm-1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Crystal system: tetragonal [ Help ]

Superspace group name (WJJ): W:P 4/m c c:1 -1 1 1 OS: 1/4 1/4 0 0 [ Help ]

Superspace group name: X4/mcc(00γ)0000 [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4
2 -x2,x1,x3,x4
3 -x1,x2,1/2+x3,x4
4 -x1,-x2,x3,x4
5 -x2,-x1,1/2+x3,x4
6 x2,-x1,x3,x4
7 x1,-x2,1/2+x3,x4
8 x2,x1,1/2+x3,x4
9 -x1,-x2,-x3,-x4
10 x2,-x1,-x3,-x4
11 x1,-x2,1/2-x3,-x4
12 x1,x2,-x3,-x4
13 x2,x1,1/2-x3,-x4
14 -x2,x1,-x3,-x4
15 -x1,x2,1/2-x3,-x4
16 -x2,-x1,1/2-x3,-x4
17 1/2+x1,1/2+x2,x3,1/2+x4
18 1/2-x2,1/2+x1,x3,1/2+x4
19 1/2-x1,1/2+x2,1/2+x3,1/2+x4
20 1/2-x1,1/2-x2,x3,1/2+x4
21 1/2-x2,1/2-x1,1/2+x3,1/2+x4
22 1/2+x2,1/2-x1,x3,1/2+x4
23 1/2+x1,1/2-x2,1/2+x3,1/2+x4
24 1/2+x2,1/2+x1,1/2+x3,1/2+x4
25 1/2-x1,1/2-x2,-x3,1/2-x4
26 1/2+x2,1/2-x1,-x3,1/2-x4
27 1/2+x1,1/2-x2,1/2-x3,1/2-x4
28 1/2+x1,1/2+x2,-x3,1/2-x4
29 1/2+x2,1/2+x1,1/2-x3,1/2-x4
30 1/2-x2,1/2+x1,-x3,1/2-x4
31 1/2-x1,1/2+x2,1/2-x3,1/2-x4
32 1/2-x2,1/2-x1,1/2-x3,1/2-x4

Space group name (H-M): C4/mcc [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -y,x,z
3 -x,y,1/2+z
4 -x,-y,z
5 -y,-x,1/2+z
6 y,-x,z
7 x,-y,1/2+z
8 y,x,1/2+z
9 -x,-y,-z
10 y,-x,-z
11 x,-y,1/2-z
12 x,y,-z
13 y,x,1/2-z
14 -y,x,-z
15 -x,y,1/2-z
16 -y,-x,1/2-z
17 1/2+x,1/2+y,z
18 1/2-y,1/2+x,z
19 1/2-x,1/2+y,1/2+z
20 1/2-x,1/2-y,z
21 1/2-y,1/2-x,1/2+z
22 1/2+y,1/2-x,z
23 1/2+x,1/2-y,1/2+z
24 1/2+y,1/2+x,1/2+z
25 1/2-x,1/2-y,-z
26 1/2+y,1/2-x,-z
27 1/2+x,1/2-y,1/2-z
28 1/2+x,1/2+y,-z
29 1/2+y,1/2+x,1/2-z
30 1/2-y,1/2+x,-z
31 1/2-x,1/2+y,1/2-z
32 1/2-y,1/2-x,1/2-z

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0 0.691

Refinement details

Refinement remarks: WARNING: The published thermal displacement parameters have been converted to U,s. The calculated standard uncertainties (s.u.) have been based uniquely on the published ones without considering the s.u. of any other quantity involved in such conversion. Fourier term Nb z 1: sign probably incorrect in the paper (table 8) [ Help ]

Modulation functions description: Displacive modulation:Fourier series. Up to 2nd-order harmonics. [ Help ]

Structure factors calc. details: Gaussian integration [ Help ]

Nb. of observed reflections: 3894 [ Help ]

R(obs): 0.106 [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
Te Te 16 1 0.23589(4) 0.09195(4) 0 ? Uani
Nb Nb 4 1 0 0 0.25 ? Uani

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

Wave vector code q_x q_y q_z
1 0 0 0.691
2 0 0 1.382

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

Modulation code Atom site label Displacement axis Wave vector code
Nbz1 Nb z 1
Nbz2 Nb z 2
Tex1 Te x 1
Tex2 Te x 2
Tey1 Te y 1
Tey2 Te y 2
Tez1 Te z 1
Tez2 Te z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Nbz1 0 -0.03899(22)
Nbz2 0 0.01640(24)
Tex1 0.01389(5) 0
Tex2 -0.00386(6) 0
Tey1 -0.00669(5) 0
Tey2 -0.00103(6) 0
Tez1 0 -0.00637(8)
Tez2 0 -0.00236(7)

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Te Te .00822(13) .00800(13) .00966(9) -.00034(9) 0 0
Nb Nb .00805(17) .00805(17) .0110(3) 0 0 0