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Combined X-ray single crystal and neutron powder refinement of modulated structures and application to the incommensurately modulated structure of Bi2Sr2CaCu2O8+y

Authors:

Gao, Y.; Coppens, P.; Cox, D.E.; Moodenbaugh, A.R.

Journal:

Acta Cryst. A 49 141-148 (1993)

DOI:

https://doi.org/10.1107/S010876739200552X

B-IncStrDB ID: 312EZB5Wy Entry date: 2010-11-08 Last revision: 2021-12-30

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Bi2Sr2CaCu2O8py

Chemical data

Structural Formula Sum: Bi1.98 Ca0.96 Cu2 O8.14 Sr1.75 [ Help ]

Formula weight: 862.9 Da [ Help ]

Crystallographic data and experimental details

a: 5.4150(3) Å [ Help ]

b: 5.4149(5) Å [ Help ]

c: 30.861(5) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 904.90(18) Å3 [ Help ]

Z: 4 [ Help ]

Crystal system: orthorhombic [ Help ]

Superspace group name (WJJ): M:A 2 a a:1 1 1 [ Help ]

Superspace group name: X2aa(α00)000 [ 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 1/2+x1,-x2,x3,x4
4 1/2+x1,x2,-x3,x4
5 x1,1/2+x2,1/2+x3,1/2+x4
6 x1,1/2-x2,1/2-x3,1/2+x4
7 1/2+x1,1/2-x2,1/2+x3,1/2+x4
8 1/2+x1,1/2+x2,1/2-x3,1/2+x4

Space group name (H-M): A 2 a a [ Help ]

Modulation dimension: 1 [ Help ]

Experimental remarks: Measured composition Bi2.12(10) Sr1.79(10) Ca0.92(5) Cu2 Superspace group taken from: Petricek, Gao, Lee & Coppens Phys. Rev. (1990) B42, 387-392 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.2095(5) 0 0

Refinement details

Refinement remarks: A combined refinement using single crystal X-ray and powder neutrons. WARNING: The published displacement parameters have been converted to relative units. 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. [ Help ]

Modulation functions description: Displacive modulation for Bi, Sr, Cu, Ca, O(1), O(2) and O(3) sites:Fourier series. Up to 2nd-order harmonics. Modulation of O(4) atoms described by a sawtooth function. Modulation of temperature factors for Bi sites:Fourier series. Up to 2nd-order harmonics. [ Help ]

Structure factors calc. details: Bessel functions [ Help ]

Nb. of observed reflections: 2001 [ Help ]

wR(all): 0.092 [ Help ]

Structural Information

Average Structure: [ Help ]

Site description Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
Bi on Bi sites Bi/Bi Bi 8 0.93(1) 0.504(2) 0.2333(4) 0.0523(1) ? Uani
Sr on Sr sites Sr/Sr Sr 8 0.875 0.00 0.2527(5) 0.1408(1) ? Uani
Bi on Sr sites Bi/Sr Bi 8 0.04(1) 0.00 0.2527(5) 0.1408(1) ? Uani
. Cu Cu 8 1 0.50 0.2502(6) 0.1966(1) ? Uani
Ca on Ca sites Ca/Ca Ca 4 0.96(4) 0.00 0.25 0.25 ? Uani
Sr on Ca sites Sr/Ca Sr 4 0.00 0.00 0.25 0.25 ? Uani
Bi on Ca sites Bi/Ca Bi 4 0.04 0.00 0.25 0.25 ? Uani
. O(1) O 8 1 0.75 0.00 0.1983(5) 0.002(5) Uiso
. O(2) O 8 1 0.25 0.50 0.1980(5) 0.004(6) Uiso
. O(3) O 8 1 0.51(1) 0.277(3) 0.1163(6) 0.004(7) Uiso
. O(4) O 8 1 0.03(1) 0.151(2) 0.0571(6) 0.018(7) 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 0.2095 0 0
2 0.419 0 0

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

Modulation code Atom site label Displacement axis Wave vector code
Bi/Bix1 Bi/Bi x 1
Bi/Bix2 Bi/Bi x 2
Bi/Biy1 Bi/Bi y 1
Bi/Biy2 Bi/Bi y 2
Bi/Biz1 Bi/Bi z 1
Bi/Biz2 Bi/Bi z 2
Sr/Srx1 Sr/Sr x 1
Sr/Srx2 Sr/Sr x 2
Sr/Sry1 Sr/Sr y 1
Sr/Sry2 Sr/Sr y 2
Sr/Srz1 Sr/Sr z 1
Sr/Srz2 Sr/Sr z 2
Bi/Srx1 Bi/Sr x 1
Bi/Srx2 Bi/Sr x 2
Bi/Sry1 Bi/Sr y 1
Bi/Sry2 Bi/Sr y 2
Bi/Srz1 Bi/Sr z 1
Bi/Srz2 Bi/Sr 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
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
O(1)x1 O(1) x 1
O(1)x2 O(1) x 2
O(1)y1 O(1) y 1
O(1)y2 O(1) y 2
O(1)z1 O(1) z 1
O(1)z2 O(1) z 2
O(2)x1 O(2) x 1
O(2)x2 O(2) x 2
O(2)y1 O(2) y 1
O(2)y2 O(2) y 2
O(2)z1 O(2) z 1
O(2)z2 O(2) z 2
O(3)x1 O(3) x 1
O(3)x2 O(3) x 2
O(3)y1 O(3) y 1
O(3)y2 O(3) y 2
O(3)z1 O(3) z 1
O(3)z2 O(3) z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Bi/Bix1 .0591(18) .013(4)
Bi/Bix2 .0148(18) -.0037(18)
Bi/Biy1 .0129(18) -.0074(18)
Bi/Biy2 .000(4) -.0203(18)
Bi/Biz1 -.0006(3) -.0052(3)
Bi/Biz2 -.0023(3) -.0016(3)
Sr/Srx1 .0425(18) 0
Sr/Srx2 .0203(18) 0
Sr/Sry1 0 .006(4)
Sr/Sry2 0 .000(6)
Sr/Srz1 0 -.0068(3)
Sr/Srz2 0 -.0019(3)
Bi/Srx1 .0425(18) 0
Bi/Srx2 .0203(18) 0
Bi/Sry1 0 .006(4)
Bi/Sry2 0 .000(6)
Bi/Srz1 0 -.0068(3)
Bi/Srz2 0 -.0019(3)
Cux1 .0111(18) 0
Cux2 -.0018(18) 0
Cuy1 0 -.006(4)
Cuy2 0 .018(4)
Cuz1 0 -.0087(3)
Cuz2 0 -.0026(3)
Ca/Cax1 0 0
Ca/Cax2 -.0055(18) 0
Ca/Cay1 0 -.004(6)
Ca/Cay2 0 0
Ca/Caz1 0 -.0087(3)
Ca/Caz2 0 0
Sr/Cax1 0 0
Sr/Cax2 -.0055(18) 0
Sr/Cay1 0 -.004(6)
Sr/Cay2 0 0
Sr/Caz1 0 -.0087(3)
Sr/Caz2 0 0
Bi/Cax1 0 0
Bi/Cax2 -.0055(18) 0
Bi/Cay1 0 -.004(6)
Bi/Cay2 0 0
Bi/Caz1 0 -.0087(3)
Bi/Caz2 0 0
O(1)x1 .013(7) 0
O(1)x2 -.028(7) 0
O(1)y1 -.002(11) 0
O(1)y2 -.002(11) 0
O(1)z1 0 -.0130(13)
O(1)z2 0 -.0023(16)
O(2)x1 .007(6) 0
O(2)x2 .028(9) 0
O(2)y1 .011(11) 0
O(2)y2 .006(11) 0
O(2)z1 0 -.0026(16)
O(2)z2 0 .0087(16)
O(3)x1 .096(7) .039(13)
O(3)x2 .039(11) .033(15)
O(3)y1 .013(11) .042(11)
O(3)y2 .044(11) .018(17)
O(3)z1 -.0100(19) -.0075(13)
O(3)z2 -.0084(19) .002(2)

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
O(4) -0.270(6) 0.022(9) 0.014(2) 0.42(2) 1.07(2)

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Bi/Bi Bi 0.072(3) 0.021(2) 0.012(2) -0.006(3) 0.009(3) -0.004(2)
Sr/Sr Sr 0.025(3) 0.006(1) 0.023(2) 0 0 0.005(3)
Bi/Sr Bi 0.025(3) 0.006(1) 0.023(2) 0 0 0.005(3)
Cu Cu 0.013(2) -0.001(3) 0.029(3) 0 0 -0.003(3)
Ca/Ca Ca 0.007(3) 0.004(2) 0.019(5) 0 0 -0.006(6)
Sr/Ca Sr 0.007(3) 0.004(2) 0.019(5) 0 0 -0.006(6)
Bi/Ca Bi 0.007(3) 0.004(2) 0.019(5) 0 0 -0.006(6)

Definition of the ADP Fourier series: [ Help ]

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

ADP Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Bi/BiU111 -0.032(4) 0.053(5)
Bi/BiU112 -0.013(8) 0.055(4)
Bi/BiU221 0.025(4) -0.001(4)
Bi/BiU222 0.004(5) -0.013(3)
Bi/BiU331 0.004(4) -0.006(2)
Bi/BiU332 -0.002(5) -0.009(4)
Bi/BiU121 -0.007(3) 0.024(5)
Bi/BiU122 0.025(5) 0.020(6)
Bi/BiU131 -0.002(2) 0.003(4)
Bi/BiU132 0.026(3) -0.008(5)
Bi/BiU231 -0.004(5) -0.005(2)
Bi/BiU232 -0.028(3) 0.001(5)