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Four-dimensional structure determination of the incommensurate modulated compound (Nd4Ca2)Ti6O20

Authors:

Grebille, D.; Berar, J.F.; Queyroux, F.; Nanot, M.; Gilles, J.C.; Bronsema, K.D.; van Smaalen, S.

Journal:

Materials Research Bulletin 22 253-260 (1987)

DOI:

https://doi.org/10.1016/0025-5408(87)90078-X

B-IncStrDB ID: qjmwo3MyGym Entry date: 2022-01-03 Last revision: 2022-01-03

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Nd4Ca2Ti6O20

Chemical data

Structural Formula Sum: Nd4 Ca2 Ti6 O20 [ Help ]

Crystallographic data and experimental details

a: 3.832 Å [ Help ]

b: 36.64 Å [ Help ]

c: 5.436 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 763.24 Å3 [ Help ]

Z: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.49 0 0

Crystal system: orthorhombic [ Help ]

Superspace group name (ITC): Cmc21(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,-x4
3 x1,-x2,x3+1/2,x4+1/2
4 -x1,-x2,x3+1/2,-x4+1/2
5 x1+1/2,x2+1/2,x3,x4
6 -x1+1/2,x2+1/2,x3,-x4
7 x1+1/2,-x2+1/2,x3+1/2,x4+1/2
8 -x1+1/2,-x2+1/2,x3+1/2,-x4+1/2

Refinement details

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

Nb. of observed reflections: 1699 [ Help ]

R(obs): 0.087 [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol x y z Uiso/equiv Symmetry multiplicity Occupancy
Ti1 Ti 0 0.1877(1) 0.255 0.003(1) 4 1
Ti2 Ti 0 0.1164(1) 0.723(1) 0.001(1) 4 1
Ti3 Ti 0 0.0375(1) 0.221(1) 0.003(1) 4 1
O1 O 0 0.6814(4) 0.233(5) 0.005(4) 4 1
O2 O 0 0.2259(4) 0.036(3) 0.004(3) 4 1
O3 O 0 0.2140(5) 0.529(4) 0.014(4) 4 1
O4 O 0 0.1540(5) 0.917(4) 0.005(4) 4 1
O5 O 0 0.1374(5) 0.407(4) 0.010(4) 4 1
O6 O 0 0.6080(5) 0.713(5) 0.005(4) 4 1
O7 O 0 0.0665(5) 0.496(4) 0.015(4) 4 1
O8 O 0 0.0794(5) 0.002(4) 0.013(4) 4 1
O9 O 0 0.5367(6) 0.288(5) 0.028(5) 4 1
O10 O 0 -0.0065(5) 0.415(4) 0.009(4) 4 1
Nd1 Nd 0 0.7176(1) 0.784(1) 0.0038(4) 4 0.823(8)
Ca1 Ca 0 0.7176(1) 0.784(1) 0.0038(4) 4 0.177(8)
Nd2 Nd 0 0.6138(1) 0.216(1) 0.0077(5) 4 0.719(8)
Ca2 Ca 0 0.6138(1) 0.216(1) 0.0077(5) 4 0.281(8)
Nd3 Nd 0 0.5388(1) 0.717(1) 0.0089(6) 4 0.457(11)
Ca3 Ca 0 0.5388(1) 0.717(1) 0.0089(6) 4 0.543(11)

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 0.49 0 0

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Nd1o1 Nd1 1
Ca1o1 Ca1 1
Nd2o1 Nd2 1
Ca2o1 Ca2 1
Nd3o1 Nd3 1
Ca3o1 Ca3 1

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Nd1o1 0.044(13) 0
Ca1o1 -0.044(13) 0
Nd2o1 0.061(11) 0
Ca2o1 -0.061(11) 0
Nd3o1 0.025(12) 0
Ca3o1 -0.025(12) 0

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

Modulation code Atom site label Displacement axis Wave vector code
Ti1x1 Ti1 x 1
Ti1y1 Ti1 y 1
Ti1z1 Ti1 z 1
Ti2x1 Ti2 x 1
Ti2y1 Ti2 y 1
Ti2z1 Ti2 z 1
Ti3x1 Ti3 x 1
Ti3y1 Ti3 y 1
Ti3z1 Ti3 z 1
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1
O5x1 O5 x 1
O5y1 O5 y 1
O5z1 O5 z 1
O6x1 O6 x 1
O6y1 O6 y 1
O6z1 O6 z 1
O7x1 O7 x 1
O7y1 O7 y 1
O7z1 O7 z 1
O8x1 O8 x 1
O8y1 O8 y 1
O8z1 O8 z 1
O9x1 O9 x 1
O9y1 O9 y 1
O9z1 O9 z 1
O10x1 O10 x 1
O10y1 O10 y 1
O10z1 O10 z 1
Nd1x1 Nd1 x 1
Nd1y1 Nd1 y 1
Nd1z1 Nd1 z 1
Ca1x1 Ca1 x 1
Ca1y1 Ca1 y 1
Ca1z1 Ca1 z 1
Nd2x1 Nd2 x 1
Nd2y1 Nd2 y 1
Nd2z1 Nd2 z 1
Ca2x1 Ca3 x 1
Ca2y1 Ca3 y 1
Ca2z1 Ca3 z 1
Nd3x1 Nd3 x 1
Nd3y1 Nd3 y 1
Nd3z1 Nd3 z 1
Ca3x1 Ca3 x 1
Ca3y1 Ca3 y 1
Ca3z1 Ca3 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ti1x1 0 0.010
Ti1y1 -0.0007(2) 0
Ti1z1 -0.000(1) 0
Ti2x1 0 -0.003(2)
Ti2y1 -0.0006(2) 0
Ti2z1 0.002(1) 0
Ti3x1 0 0.005(2)
Ti3y1 0.0002(2) 0
Ti3z1 -0.001(1) 0
O1x1 0 -0.000(7)
O1y1 0.0006(7) 0
O1z1 0.093(6) 0
O2x1 0 -0.045(7)
O2y1 -0.0023(7) 0
O2z1 -0.013(6) 0
O3x1 0 0.064(9)
O3y1 0.0026(8) 0
O3z1 -0.010(8) 0
O4x1 0 -0.138(8)
O4y1 0.0005(9) 0
O4z1 -0.001(6) 0
O5x1 0 0.053(8)
O5y1 0.0009(8) 0
O5z1 0.012(6) 0
O6x1 0 -0.001(7)
O6y1 -0.0043(7) 0
O6z1 -0.091(5) 0
O7x1 0 0.098(9)
O7y1 -0.0003(9) 0
O7z1 0.006(7) 0
O8x1 0 -0.089(8)
O8y1 -0.0001(9) 0
O8z1 0.002(6) 0
O9x1 0 0.003(10)
O9y1 -0.0022(10) 0
O9z1 -0.009(7) 0
O10x1 0 0.097(8)
O10y1 0.0002(9) 0
O10z1 -0.006(6) 0
Nd1x1 0 0.005(1)
Nd1y1 -0.0092(1) 0
Nd1z1 -0.0425(4) 0
Ca1x1 0 0.005(1)
Ca1y1 -0.0092(1) 0
Ca1z1 -0.0425(4) 0
Nd2x1 0 0.003(1)
Nd2y1 0.0050(1) 0
Nd2z1 -0.0033(6) 0
Ca2x1 0 0.003(1)
Ca2y1 0.0050(1) 0
Ca2z1 -0.0033(6) 0
Nd3x1 0 0.001(1)
Nd3y1 0.0052(1) 0
Nd3z1 0.0064(7) 0
Ca3x1 0 0.001(1)
Ca3y1 0.0052(1) 0
Ca3z1 0.0064(7) 0