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The incommensurately modulated structure of the blue bronzes K0.3MoO3 and Rb0.3MoO3

Authors:

Schutte, W.J.; de Boer, J.L.

Journal:

Acta Cryst. B 49 579-591 (1993)

DOI:

https://doi.org/10.1107/S0108768192006578

B-IncStrDB ID: 752EUuIXZ Entry date: 2010-11-08 Last revision: 2021-12-30

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RbMo

Chemical data

Structural Formula Sum: Mo1 O3 Rb0.3 [ Help ]

Formula weight: 169.6 Da [ Help ]

Crystallographic data and experimental details

a: 18.536(2) Å [ Help ]

b: 7.556(1) Å [ Help ]

c: 20.07(1) Å [ Help ]

α: 90 ° [ Help ]

β: 118.52(1) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 2469.9(13) Å3 [ Help ]

Z: 40 [ Help ]

μ: 10.895 mm-1 [ Help ]

Cell measurement temperature: 100 K [ Help ]

Crystal system: monoclinic [ Help ]

Superspace group name (WJJ): C:C 2/m:s -1 [ Help ]

Superspace group name: X2/m(0β0)s0 [ 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,-x4
4 x1,-x2,x3,1/2-x4
5 1/2+x1,1/2+x2,x3,1/2+x4
6 1/2-x1,1/2+x2,-x3,x4
7 1/2-x1,1/2-x2,-x3,1/2-x4
8 1/2+x1,1/2-x2,x3,-x4
9 x1,x2,1/2+x3,1/2+x4
10 -x1,x2,1/2-x3,x4
11 -x1,-x2,1/2-x3,1/2-x4
12 x1,-x2,1/2+x3,-x4
13 1/2+x1,1/2+x2,1/2+x3,x4
14 1/2-x1,1/2+x2,1/2-x3,1/2+x4
15 1/2-x1,1/2-x2,1/2-x3,-x4
16 1/2+x1,1/2-x2,1/2+x3,1/2-x4

Space group name (H-M): C 1 2/m 1 [ Help ]

Symmetry operations of the space group: [ Help ]

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

Modulation dimension: 1 [ Help ]

Experimental remarks: Main reflections were measured from a small single crystal. Satellites were collected from a different larger single crystal. [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0.748 0

Refinement details

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

Structure factors calc. details: Gaussian integration [ Help ]

Nb. of observed reflections: 4458 [ Help ]

R(obs): 0.032 [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
Rb1 Rb 4 1 0.5 0 0.25 ? Uani
Rb2 Rb 8 1 0.31563(3) 0.5 0.14226(3) ? Uani
Mo1 Mo 8 1 0.22432(2) 0 0.08740(2) ? Uani
Mo2 Mo 16 1 0.07819(1) 0.25567(3) -0.02054(1) ? Uani
Mo3 Mo 16 1 -0.13937(1) 0.24995(3) -0.17181(1) ? Uani
O1 O 8 1 0.25 0.25 0.25 ? Uani
O2 O 8 1 0.2492(2) 0 0.0156(2) ? Uani
O3 O 8 1 0.3164(2) 0 0.1684(1) ? Uani
O4 O 8 1 0.0789(2) 0.5 -0.0037(2) ? Uani
O5 O 8 1 0.0884(2) 0 -0.0039(2) ? Uani
O6 O 8 1 -0.1561(2) 0 -0.1550(2) ? Uani
O7 O 8 1 -0.1422(2) 0.5 -0.1641(2) ? Uani
O8 O 16 1 0.0989(1) 0.2604(3) -0.0939(1) ? Uani
O9 O 16 1 0.1838(1) 0.2427(3) 0.0807(1) ? Uani
O10 O 16 1 -0.0889(1) 0.2198(3) -0.2223(1) ? Uani
O11 O 16 1 -0.0378(1) 0.2457(3) -0.0721(1) ? 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 0.748 0

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

Modulation code Atom site label Displacement axis Wave vector code
Rb1y1 Rb1 y 1
Rb2x1 Rb2 x 1
Rb2y1 Rb2 y 1
Rb2z1 Rb2 z 1
Mo1x1 Mo1 x 1
Mo1y2 Mo1 y 1
Mo1z1 Mo1 z 1
Mo2x1 Mo2 x 1
Mo2y2 Mo2 y 1
Mo2z1 Mo2 z 1
Mo3x1 Mo3 x 1
Mo3y2 Mo3 y 1
Mo3z1 Mo3 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
O11x1 O11 x 1
O11y1 O11 y 1
O11z1 O11 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Rb1y1 -0.0043(3) 0
Rb2x1 0 -0.0001(1)
Rb2y1 -0.0027(2) 0
Rb2z1 0 0.0001(1)
Mo1x1 0 0.00122(6)
Mo1y2 -0.0033(2) 0
Mo1z1 0 0.00145(7)
Mo2x1 0.00002(9) 0.00205(4)
Mo2y2 0.0010(1) -0.0019(1)
Mo2z1 -0.00053(8) 0.00072(4)
Mo3x1 0.00057(9) 0.00300(3)
Mo3y2 0.0004(1) 0.0002(1)
Mo3z1 -0.00041(9) 0.00216(4)
O1x1 0 -0.0002(4)
O1y1 0 -0.003(2)
O1z1 0 0.0019(5)
O2x1 0 -0.0006(6)
O2y1 -0.003(1) 0
O2z1 0 0.0006(6)
O3x1 0 0.0021(6)
O3y1 -0.005(1) 0
O3z1 0 0.001(7)
O4x1 0 -0.0014(7)
O4y1 -0.002(2) 0
O4z1 0 -0.0018(8)
O5x1 0 -0.0023(7)
O5y1 -0.000(2) 0
O5z1 0 -0.0019(8)
O6x1 0 0.0011(6)
O6y1 -0.002(1) 0
O6z1 0 -0.0001(6)
O7x1 0 0.0030(7)
O7y1 -0.003(2) 0
O7z1 0 -0.0002(7)
O8x1 -0.0003(7) 0.0022(3)
O8y1 -0.0007(9) -0.001(1)
O8z1 -0.0006(7) 0.0017(4)
O9x1 0.0007(7) 0.0012(3)
O9y1 0.0011(9) -0.002(1)
O9z1 0.0008(7) 0.0005(4)
O10x1 -0.0001(5) 0.0005(4)
O10y1 -0.003(1) 0.001(1)
O10z1 0.0002(5) -0.0004(4)
O11x1 0.0006(8) 0.0008(4)
O11y1 -0.0047(9) 0.001(1)
O11z1 -0.0011(7) -0.0001(4)