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Four dimensional crystallographic analysis of the incommensurate modulation in a Bi2Sr2CaCu2O8 single crystal

Authors:

Kan, X.B.; Moss, S.C.

Journal:

Acta Cryst. B 48 122-134 (1992)

DOI:

https://doi.org/10.1107/S0108768191011333

B-IncStrDB ID: 332EXVa1u Entry date: 2010-11-08 Last revision: 2021-12-30

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BiSr

Chemical data

Structural Formula Sum: Bi2.05 Ca0.75 Cu2 O8 Sr1.98 [ Help ]

Formula weight: 887 Da [ Help ]

Crystallographic data and experimental details

a: 5.415(2) Å [ Help ]

b: 5.421(2) Å [ Help ]

c: 30.88(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 906.5(8) Å3 [ Help ]

Z: 4 [ Help ]

μ: 58.982 mm-1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Crystal system: orthorhombic [ Help ]

Superspace group name (WJJ): N:B b 2 b:1 1 1 [ Help ]

Superspace group name: Bb2b(0β0)000 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

Space group name (H-M): B b 2 b [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0.212 1

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. WARNING: The published thermal displacement parameters, Biso, have been converted to Uiso. [ Help ]

Modulation functions description: Displacive modulation:Fourier series. Up to 2nd-order harmonircs. Modulation of Debye-Waller factors:Fourier series. Up to 2nd-order harmonics. [ Help ]

Structure factors calc. details: Gaussian integration [ Help ]

Nb. of observed reflections: 700 [ Help ]

wR(all): 0.073 [ Help ]

Structural Information

Average Structure: [ Help ]

Site description Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
Ca on Ca sites Ca/Ca Ca 4 0.75(5) 0.25 0 0.25 ? Uani
Sr on Ca sites Sr/Ca Sr 4 0.20(5) 0.25 0 0.25 ? Uani
Bi on Ca sites Bi/Ca Bi 4 0.05(3) 0.25 0 0.25 ? Uani
. Cu Cu 8 1 0.2501(8) 0.499(7) 0.1962(2) ? Uani
. Sr Sr 8 0.89(5) 0.2524(8) -0.003(7) 0.1395(2) ? Uani
. Bi Bi 8 1 0.2251(4) 0.483(6) 0.0514(1) ? Uani
. O1 O 8 1 -0.01(2) 0.75(2) 0.196(1) 0.013 Uiso
. O2 O 8 1 0.49(3) 0.27(3) 0.196(2) 0.013 Uiso
. O3 O 8 1 0.42(1) 0.56(2) 0.102(3) 0.013 Uiso
. O4 O 8 1 0.04(1) 0.21(2) 0.057(3) 0.013 Uiso

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 0.212 1
2 0 0.414 2

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

Modulation code Atom site label Displacement axis Wave vector code
Ca/Cax1 Ca/Ca x 1
Ca/Cax2 Ca/Ca x 2
Ca/Cay1 Ca/Ca y 1
Ca/Cay2 Ca/Ca y 2
Ca/Caz1 Ca/Ca z 1
Ca/Caz2 Ca/Ca z 2
Sr/Cax1 Sr/Ca x 1
Sr/Cax2 Sr/Ca x 2
Sr/Cay1 Sr/Ca y 1
Sr/Cay2 Sr/Ca y 2
Sr/Caz1 Sr/Ca z 1
Sr/Caz2 Sr/Ca z 2
Bi/Cax1 Bi/Ca x 1
Bi/Cax2 Bi/Ca x 2
Bi/Cay1 Bi/Ca y 1
Bi/Cay2 Bi/Ca y 2
Bi/Caz1 Bi/Ca z 1
Bi/Caz2 Bi/Ca z 2
Cux1 Cu x 1
Cux2 Cu x 2
Cuy1 Cu y 1
Cuy2 Cu y 2
Cuz1 Cu z 1
Cuz2 Cu z 2
Srx1 Sr x 1
Srx2 Sr x 2
Sry1 Sr y 1
Sry2 Sr y 2
Srz1 Sr z 1
Srz2 Sr z 2
Bix1 Bi x 1
Bix2 Bi x 2
Biy1 Bi y 1
Biy2 Bi y 2
Biz1 Bi z 1
Biz2 Bi z 2
O1x1 O1 x 1
O1x2 O1 x 2
O1y1 O1 y 1
O1y2 O1 y 2
O1z1 O1 z 1
O1z2 O1 z 2
O2x1 O2 x 1
O2x2 O2 x 2
O2y1 O2 y 1
O2y2 O2 y 2
O2z1 O2 z 1
O2z2 O2 z 2
O3x1 O3 x 1
O3x2 O3 x 2
O3y1 O3 y 1
O3y2 O3 y 2
O3z1 O3 z 1
O3z2 O3 z 2
O4x1 O4 x 1
O4x2 O4 x 2
O4y1 O4 y 1
O4y2 O4 y 2
O4z1 O4 z 1
O4z2 O4 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ca/Cax1 0.000(4) -0.005(7)
Ca/Cax2 -0.004(17) -0.042(8)
Ca/Cay1 0.000(5) -0.006(8)
Ca/Cay2 -0.004(7) -0.007(8)
Ca/Caz1 0.008(1) 0.007(2)
Ca/Caz2 -0.002(2) -0.004(2)
Sr/Cax1 0.000(4) -0.005(7)
Sr/Cax2 -0.004(17) -0.042(8)
Sr/Cay1 0.000(5) -0.006(8)
Sr/Cay2 -0.004(7) -0.007(8)
Sr/Caz1 0.008(1) 0.007(2)
Sr/Caz2 -0.002(2) -0.004(2)
Bi/Cax1 0.000(4) -0.005(7)
Bi/Cax2 -0.004(17) -0.042(8)
Bi/Cay1 0.000(5) -0.006(8)
Bi/Cay2 -0.004(7) -0.007(8)
Bi/Caz1 0.008(1) 0.007(2)
Bi/Caz2 -0.002(2) -0.004(2)
Cux1 0.002(5) -0.001(9)
Cux2 -0.004(14) 0.014(7)
Cuy1 -0.006(6) -0.016(2)
Cuy2 0.002(7) -0.002(4)
Cuz1 0.0094(5) 0.002(2)
Cuz2 -0.003(1) 0.003(2)
Srx1 -0.002(5) 0.005(11)
Srx2 -0.009(11) 0.007(9)
Sry1 -0.029(5) -0.047(3)
Sry2 0.013(5) 0.012(4)
Srz1 0.0086(4) -0.004(1)
Srz2 -0.0015(6) -0.000(1)
Bix1 0.004(3) -0.003(3)
Bix2 0.003(5) 0.002(6)
Biy1 -0.043(5) -0.059(3)
Biy2 0.008(2) 0.010(4)
Biz1 0.0040(5) -0.0042(5)
Biz2 -0.0058(7) -0.002(1)
O1x1 0.030(40) 0.010(20)
O1x2 -0.006(48) -0.031(39)
O1y1 0.003(40) -0.006(20)
O1y2 -0.038(36) 0.012(45)
O1z1 0.010(4) -0.011(8)
O1z2 0.002(6) 0.002(10)
O2x1 0.024(43) -0.012(21)
O2x2 0.005(44) 0.006(29)
O2y1 0.041(48) -0.011(19)
O2y2 0.011(10) -0.016(42)
O2z1 0.009(6) 0.016(7)
O2z2 -0.001(6) 0.002(14)
O3x1 -0.018(19) -0.008(24)
O3x2 0.080(18) 0.091(21)
O3y1 -0.101(23) -0.146(26)
O3y2 0.027(26) -0.012(24)
O3z1 0.009(4) 0.013(5)
O3z2 0.016(4) -0.007(4)
O4x1 0.053(17) -0.132(15)
O4x2 -0.023(18) -0.041(20)
O4y1 0.073(21) 0.098(18)
O4y2 0.133(19) -0.030(23)
O4z1 -0.002(5) 0.008(5)
O4z2 -0.024(4) -0.004(5)

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Ca/Ca Ca 0.000(13) 0.000(9) 0.000(14) -0.003(6) -0.008(8) -0.008(8)
Sr/Ca Sr 0.000(13) 0.000(9) 0.000(14) -0.003(6) -0.008(8) -0.008(8)
Bi/Ca Bi 0.000(13) 0.000(9) 0.000(14) -0.003(6) -0.008(8) -0.008(8)
Cu Cu 0.007(4) 0.010(4) 0.010(5) -0.006(9) -0.006(7) 0.017(8)
Sr Sr 0.001(3) 0.003(4) 0.000(5) -0.006(10) 0.000(5) 0.014(5)
Bi Bi 0.0163(15) 0.045(3) 0.000(5) -0.010(6) 0.003(3) 0.014(5)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
BiU111 Bi U11 1
BiU221 Bi U22 1
BiU331 Bi U33 1
BiU121 Bi U12 1
BiU131 Bi U13 1
BiU231 Bi U23 1
BiU112 Bi U11 2
BiU222 Bi U22 2
BiU332 Bi U33 2
BiU122 Bi U12 2
BiU132 Bi U13 2
BiU232 Bi U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
BiU111 -0.003(3) 0.006(6)
BiU221 -0.039(7) 0.018(7)
BiU331 0.000(5) 0.004831
BiU121 0.016(7) -0.013(4)
BiU131 0.001(4) 0.003(4)
BiU231 -0.017(7) 0.005(4)
BiU112 0.004(6) -0.003(7)
BiU222 0.022(9) -0.021(6)
BiU332 0.005(5) 0.000(5)
BiU122 0.004(4) 0.000(9)
BiU132 0.002(3) -0.004(4)
BiU232 0.013(4) -0.007(7)