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Incommensurate modulated structure of BaMnF4 with monoclinic symmetry at 100 and 210K

Authors:

Sciau, Ph.; Lapasset, J.; Grebille, D.; Berar, J.F.

Journal:

Acta Crystallographica Section B 44 108-116 (1988)

DOI:

https://doi.org/10.1107/S0108768187010280

B-IncStrDB ID: 182EHLnvm Entry date: 2010-11-08 Last revision: 2021-12-30

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BaMn100

Chemical data

Structural Formula Sum: Ba1 F4 Mn1 [ Help ]

Formula weight: 268.3 Da [ Help ]

Crystallographic data and experimental details

a: 6.01 Å [ Help ]

b: 30.26(6) Å [ Help ]

c: 8.44(2) Å [ Help ]

α: 90.0 ° [ Help ]

β: 90.0 ° [ Help ]

γ: 90.0 ° [ Help ]

Volume: 1535.0(5) Å3 [ Help ]

Z: 4 [ Help ]

μ: 6.711 mm-1 [ Help ]

Cell measurement temperature: 100.0 K [ Help ]

Crystal system: monoclinic [ Help ]

Superspace group name (WJJ): U:A 21 1 1:1 1 1 [ Help ]

Superspace group name: X21(α00)0 [ Help ]

Space group name (H-M): A 21 1 1 [ Help ]

Modulation dimension: 1 [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4
2 1/2+x1,-x2,-x3,x4
3 x1,1/2+x2,1/2+x3,x4
4 1/2+x1,1/2-x2,1/2-x3,x4
5 x1,1/2+x2,x3,1/2+x4
6 1/2+x1,1/2-x2,-x3,1/2+x4
7 x1,x2,1/2+x3,1/2+x4
8 1/2+x1,-x2,1/2-x3,1/2+x4

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 1/2+x,-y,-z
3 x,1/2+y,1/2+z
4 1/2+x,1/2-y,1/2-z
5 x,1/2+y,z
6 1/2+x,1/2-y,-z
7 x,y,1/2+z
8 1/2+x,-y,1/2-z

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.399 0.0 0.0

Refinement details

Refinement remarks: Anisotropic temperature factors refined for reflections with 0.38 [ 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: 4321 [ Help ]

R(obs): 0.0451 [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
Ba Ba 8 1.0 0.448 0.17246(1) 0.2503(1) 0.0058(1) Uani
Mn Mn 8 1.0 -0.0051(2) 0.20808(3) 0.0042(3) 0.0043(3) Uani
F1 F 8 1.0 0.1962(7) 0.1497(2) 0.0031(10) 0.007(9) Uani
F2 F 8 1.0 0.7195(7) 0.1685(2) -0.0016(9) 0.0092(9) Uani
F3 F 8 1.0 0.3346(7) 0.232(2) -0.0027(11) 0.0094(9) Uani
F4 F 8 1.0 0.0214(8) 0.2111(2) 0.2487(9) 0.014(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 0.399 0.0 0.0
2 0.798 0.0 0.0

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

Modulation code Atom site label Displacement axis Wave vector code
Bax1 Ba x 1
Bax2 Ba x 2
Bay1 Ba y 1
Bay2 Ba y 2
Baz1 Ba z 1
Baz2 Ba z 2
Mnx1 Mn x 1
Mnx2 Mn x 2
Mny1 Mn y 1
Mny2 Mn y 2
Mnz1 Mn z 1
Mnz2 Mn z 2
F1x1 F1 x 1
F1x2 F1 x 2
F1y1 F1 y 1
F1y2 F1 y 2
F1z1 F1 z 1
F1z2 F1 z 2
F2x1 F2 x 1
F2x2 F2 x 2
F2y1 F2 y 1
F2y2 F2 y 2
F2z1 F2 z 1
F2z2 F2 z 2
F3x1 F3 x 1
F3x2 F3 x 2
F3y1 F3 y 1
F3y2 F3 y 2
F3z1 F3 z 1
F3z2 F3 z 2
F4x1 F4 x 1
F4x2 F4 x 2
F4y1 F4 y 1
F4y2 F4 y 2
F4z1 F4 z 1
F4z2 F4 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Bax1 0.0128 0.0211(1)
Bax2 -0.0023(1) 0.0046(2)
Bay1 0.00383(3) 0.00495(3)
Bay2 0.00027(4) 0.00253(2)
Baz1 -0.0009(1) -0.0004(1)
Baz2 0.0013(2) -0.0009(2)
Mnx1 -0.0021(3) -0.0017(3)
Mnx2 -0.0004(3) 0.0026(3)
Mny1 0.00035(5) -0.00053(5)
Mny2 0.00173(5) 0.0002(5)
Mnz1 0.004(2) 0.0017(2)
Mnz2 0.0002(5) -0.0011(4)
F1x1 0.0007(10) -0.0031(11)
F1x2 -0.0007(12) 0.0049(12)
F1y1 0.0011(2) -0.0007(2)
F1y2 0.0016(2) 0.0005(2)
F1z1 0.0095(8) 0.0205(7)
F1z2 0.0036(14) -0.0033(16)
F2x1 -0.0089(11) 0.0026(10)
F2x2 -0.0028(11) 0.0043(12)
F2y1 0.0043(2) -0.001(2)
F2y2 0.002(2) 0.0004(3)
F2z1 -0.0062(8) -0.0139(8)
F2z2 -0.0018(15) 0.0003(15)
F3x1 -0.0087(11) -0.0018(10)
F3x2 -0.0037(12) 0.0021(12)
F3y1 0.0013(3) -0.0005(2)
F3y2 0.0021(2) 0.0007(2)
F3z1 -0.0269(8) -0.0124(8)
F3z2 -0.0025(18) 0.0044(18)
F4x1 0.0322(12) 0.0114(12)
F4x2 -0.0046(14) 0.0043(16)
F4y1 0.0043(3) 0.0106(2)
F4y2 0.002(3) -0.0008(3)
F4z1 0.0026(9) 0.0008(9)
F4z2 -0.0003(15) -0.0002(14)