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A superspace-group description of the commensurately modulated structure of TaTe4

Authors:

Budkowski, A.; Prodan, A.; Marinkovic, V.; Kucharczyk, D.; Uszynski, I.; Boswell, F.W.

Journal:

Acta Cryst. B 45 529-534 (1989)

DOI:

https://doi.org/10.1107/S0108768189007743

B-IncStrDB ID: 902E2DnqZ Entry date: 2010-11-08 Last revision: 2021-12-30

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TaTe

Chemical data

Structural Formula Sum: Ta1 Te4 [ Help ]

Formula weight: 691.3 Da [ Help ]

Crystallographic data and experimental details

a: 13.0308(10) Å [ Help ]

b: 13.0308(10) Å [ Help ]

c: 6.8118(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1156.66(13) Å3 [ Help ]

Z: 8 [ Help ]

μ: 38.622 mm-1 [ Help ]

Crystal system: tetragonal [ Help ]

Superspace group name (WJJ): P:P 4/n c c:1 -1 1 1 [ Help ]

Superspace group name: P4/ncc(00γ)0000 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

Space group name (H-M): P 4/n c c [ Help ]

Symmetry operations of the space group: [ Help ]

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

Modulation dimension: 1 [ Help ]

Experimental remarks: Experimental data taken from: Bronsema, van Smaalen, de Boer, Wiegers, Jellinek & Mahy Acta Cryst. (1987) B43, 305-313 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0 0.666666

Refinement details

Refinement remarks: Commensurate struture described within the superspace formalism. Global phase fixed at t=0. Reflections with |F|<3σ(F) and θ>47.7o were excluded. [ Help ]

Modulation functions description: Displacive modulation:Fourier series. 1st-order harmonics. [ Help ]

Structure factors calc. details: Bessel functions [ Help ]

Nb. of observed reflections: 3998 [ Help ]

R(obs): 0.059 [ Help ]

Structural Information

Average Structure: [ Help ]

Site description Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
Ta of columns A and B TaAB Ta 4 1 0.75 0.25 0.25 ? Uani
Ta of columns C and D TaCD Ta 4 1 0.25 0.25 0.24806(2) ? Uani
Te of columns A and B TeAB Te 16 1 0.82139(6) 0.41336(7) 0.00016(3) ? Uani
Te of columns C and D TeCD Te 16 1 0.32182(6) 0.41343(7) -0.00215(2) ? 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 0.666666

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

Modulation code Atom site label Displacement axis Wave vector code
TaABz1 TaAB z 1
TaCDz1 TaCD z 1
TeABx1 TeAB x 1
TeABy1 TeAB y 1
TeABz1 TeAB z 1
TeCDx1 TeCD x 1
TeCDy1 TeCD y 1
TeCDz1 TeCD z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
TaABz1 0 0.04553(14)
TaCDz1 0.03862(15) -0.02574(16)
TeABx1 -0.01054(8) -0.00253(6)
TeABy1 -0.00544(7) 0.00036(6)
TeABz1 -0.00162(13) 0.00860(12)
TeCDx1 0.00859(7) 0.00289(6)
TeCDy1 0.00211(6) 0.00748(8)
TeCDz1 0.00798(13) -0.00462(11)

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
TaAB Ta 0.0064(3) 0.0064(3) 0.0061(2) -0.0004(3) 0 0
TaCD Ta 0.0065(3) 0.0065(3) 0.0063(2) 0 0 0
TeAB Te 0.0091(3) 0.0079(3) 0.0092(3) -0.0005(2) -0.0001(2) -0.0006(2)
TeCD Te 0.0090(3) 0.0086(3) 0.0090(3) -0.0006(2) -0.0001(1) 0.0003(1)