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Simple and double modulation un Bi(2-x)PbxSr2CaCu2O8+δ

Authors:

Jakubowicz, N.; Grebille, D.; Hervieu, M.; Leligny, H.

Journal:

Physical Review B 63 214511 (2001)

DOI:

https://doi.org/10.1103/PhysRevB.63.214511

B-IncStrDB ID: 2742Es5N3I Entry date: 2021-10-26 Last revision: 2021-12-30

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mod1012466836_A

Chemical data

Structural Formula Sum: Bi1.69 Pb0.4 Sr2.0 Ca0.88 Cu2.05 O8.031 [ Help ]

Crystallographic data and experimental details

a: 5.4031(7) Å [ Help ]

b: 5.3759(5) Å [ Help ]

c: 30.779(5) Å [ Help ]

Z: 4 [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0.110(1) 0

Crystal system: orthorhombic [ Help ]

Superspace group name: Bbmb(0 β 1)00s [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4
2 -x1,x2+1/2,x3,x4
3 x1,-x2,x3,-x4+1/2
4 -x1,-x2+1/2,x3,-x4+1/2
5 -x1,-x2,-x3,-x4
6 x1,-x2+1/2,-x3,-x4
7 -x1,x2,-x3,x4+1/2
8 x1,x2+1/2,-x3,x4+1/2
9 x1+1/2,x2,x3+1/2,x4
10 -x1+1/2,x2+1/2,x3+1/2,x4
11 x1+1/2,-x2,x3+1/2,-x4+1/2
12 -x1+1/2,-x2+1/2,x3+1/2,-x4+1/2
13 -x1+1/2,-x2,-x3+1/2,-x4
14 x1+1/2,-x2+1/2,-x3+1/2,-x4
15 -x1+1/2,x2,-x3+1/2,x4+1/2
16 x1+1/2,x2+1/2,-x3+1/2,x4+1/2

Refinement details

Refinement remarks: Crystal A [ Help ]

Total nb. of reflections: 10170 [ Help ]

Nb. of observed reflections: 1193 [ Help ]

R(obs): 0.062 [ Help ]

wR(obs): 0.070 [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Occupancy x y z Uiso/equiv ADP type
Bi1 Bi 0.511(1) 0.2287(1) 0.5225(2) 0.05137(4) 0.0172(1) Uani
Sr Sr 0.488(2) 0.2528(2) 0.007(1) 0.13901(3) 0.0195(4) Uani
Ca Ca 0.864(2) 0.25 0 0.25 0.0168(5) Uani
Cu Cu 1 0.2506(3) 0.5 0.19597(4) 0.0139(4) Uani
OC1 O 1 0 0.25 0.1975(2) 0.023(1) Uiso
OC2 O 1 0.5 0.25 0.1989(2) 0.024(1) Uiso
OS O 0.52(1) 0.299(3) 0.452(4) 0.1163(2) 0.032(2) Uiso
OB O 0.44(1) 0.138(4) 0.113(4) 0.0547(3) 0.029(2) Uiso

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23
Bi1 0.0229(3) 0.0182(3) 0.0104(3) 0 -0.0005(2) 0
Sr 0.0136(6) 0.022(1) 0.0232(6) 0.003(2) 0.0034(6) -0.008(1)
Ca 0.011(1) 0.0141(9) 0.0249(7) 0 0 0
Cu 0.0111(9) 0.0071(7) 0.0235(6) 0 0 0

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 0.110 0
2 0 0.220 0

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

Modulation code Atom site label Displacement axis Wave vector code
Bi1x2 Bi1 x 2
Bi1y1 Bi1 y 1
Bi1y2 Bi1 y 2
Bi1z1 Bi1 z 1
Bi1z2 Bi1 z 2
Sry1 Sr y 1
Sry2 Sr y 2
Srz1 Sr z 1
Srz2 Sr z 2
Caz1 Ca z 1
Cuy1 Cu y 1
Cuy2 Cu y 2
Cuz1 Cu z 1
Cuz2 Cu z 2
OC1y1 OC1 y 1
OC1z1 OC1 z 1
OC2y1 OC2 y 1
OC2z1 OC2 z 1
OSx1 OS x 1
OSy1 OS y 1
OSz1 OS z 1
OBx1 OB x 1
OBy1 OB y 1
OBz1 OB z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Bi1x2 0.0007(2) 0.0023(2)
Bi1y1 -0.0183(3) 0.0372(6)
Bi1y2 -0.0141(2) -0.0039(5)
Bi1z1 0.00860(3) 0.00242(6)
Bi1z2 0.00282(4) 0.00099(4)
Sry1 -0.007(9) 0.023(1)
Sry2 -0.0033(6) -0.011(1)
Srz1 0.00871(7) 0
Srz2 -0.0009(2) 0.00032(5)
Caz1 0.0093(1) 0
Cuy1 0 0.0087(2)
Cuy2 -0.0020(4) 0
Cuz1 0.00869(7) 0
Cuz2 0 0.00029(8)
OC1y1 0 0.010(2)
OC1z1 0.0095(4) 0
OC2y1 0 0.010(2)
OC2z1 0.0089(4) 0
OSx1 -0.025(2) 0.035(6)
OSy1 0.026(2) -0.005(5)
OSz1 0.0068(3) 0
OBx1 0.004(3) 0.022(5)
OBy1 -0.038(3) 0
OBz1 0.0104(5) 0

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Bi1o1 Bi1 1
Sro1 Sr 1
Cao2 Ca 2
OSo1 OS 1
OBo1 OB 1

Occupation Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Bi1o1 -0.327(9) 0
Sro1 0 0.21(1)
Cao2 0 -0.026(4)
OSo1 0.05(1) -0.43(3)
OBo1 0.11(2) 0.38(1)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Bi1U111 Bi1 U11 1
Bi1U221 Bi1 U22 1
Bi1U331 Bi1 U33 1
Bi1U121 Bi1 U12 1
Bi1U131 Bi1 U13 1
Bi1U231 Bi1 U23 1
SrU111 Sr U11 1
SrU221 Sr U22 1
SrU331 Sr U33 1
SrU121 Sr U12 1
SrU131 Sr U13 1
SrU231 Sr U23 1
CuU221 Cu U22 1
CuU331 Cu U33 1
CuU131 Cu U13 1
CuU231 Cu U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Bi1U111 -0.0036(3) -0.006(1)
Bi1U221 0 -0.0093(6)
Bi1U331 -0.0040(2) -0.0053(5)
Bi1U121 0.0031(7) 0
Bi1U131 0 -0.0020(7)
Bi1U231 -0.0027(3) -0.0013(1)
SrU111 -0.0015(6) 0
SrU221 -0.0154(7) -0.010(2)
SrU331 -0.0027(7) -0.009(2)
SrU121 0 -0.002(1)
SrU131 0 -0.006(2)
SrU231 0 0.007(1)
CuU221 -0.0031(7) 0
CuU331 -0.002(1) 0
CuU131 0.0023(9) 0
CuU231 0 0.0041(5)

mod1012466836_B

Chemical data

Structural Formula Sum: Bi1.8 Pb0.2 Sr2.0 Ca0.9 Cu2.0 O8.1 [ Help ]

Crystallographic data and experimental details

a: 5.395(1) Å [ Help ]

b: 5.405(1) Å [ Help ]

c: 30.772(5) Å [ Help ]

Z: 4 [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0.200(3) 1
2 0 0.150(2) 0

Crystal system: orthorhombic [ Help ]

Superspace group name: Bbmb(0 β 1,0 γ 0)000,00s [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4,x5
2 -x1,x2+1/2,x3,x4,x5
3 x1,-x2,x3,-x4,-x5+1/2
4 -x1,-x2+1/2,x3,-x4,-x5+1/2
5 -x1,-x2,-x3,-x4,-x5
6 x1,-x2+1/2,-x3,-x4,-x5
7 -x1,x2,-x3,x4,x5+1/2
8 x1,x2+1/2,-x3,x4,x5+1/2
9 x1+1/2,x2,x3+1/2,x4+1/2,x5
10 -x1+1/2,x2+1/2,x3+1/2,x4+1/2,x5
11 x1+1/2,-x2,x3+1/2,-x4+1/2,-x5+1/2
12 -x1+1/2,-x2+1/2,x3+1/2,-x4+1/2,-x5+1/2
13 -x1+1/2,-x2,-x3+1/2,-x4+1/2,-x5
14 x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-x5
15 -x1+1/2,x2,-x3+1/2,x4+1/2,x5+1/2
16 x1+1/2,x2+1/2,-x3+1/2,x4+1/2,x5+1/2

Refinement details

Refinement remarks: Crystal B [ Help ]

Total nb. of reflections: 7284 [ Help ]

Nb. of observed reflections: 1752 [ Help ]

R(obs): 0.063 [ Help ]

wR(obs): 0.061 [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Occupancy x y z Uiso/equiv ADP type
Bi1 Bi 0.5131(9) 0.2267(1) 0.5169(5) 0.051492(9) 0.0105(2) Uani
Sr Sr 1 0.25259(9) 0 0.14017(1) 0.0085(3) Uani
Ca Ca 0.894(1) 0.25 0 0.25 0.0124(2) Uani
Cu Cu 1 0.2498(1) 0.5 0.19657(3) 0.0123(1) Uani
OC1 O 1 0 0.25 0.1974(1) 0.0056(9) Uiso
OC2 O 1 0.5 0.25 0.1994(1) 0.0089(9) Uiso
OS O 1 0.2737(8) 0.5 0.1184(1) 0.015(1) Uiso
OB O 0.522(7) 0.145(3) 0.103(4) 0.0575(6) 0.021(1) Uiso

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23
Bi1 0.0160(1) 0.0077(1) 0.0078(1) 0 0 0.0050(4)
Sr 0.0087(2) 0.0089(3) 0.0079(2) 0 0.0024(2) 0
Ca 0.0083(5) 0.0176(7) 0.0119(6) 0 0 0
Cu 0.0015(3) 0.0087(4) 0.0047(4) 0 -0.0006(3) 0

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 0.200 1
2 0 0.150 0
3 0 0.400 2
4 0 0.350 1
5 0 0.050 1

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

Modulation code Atom site label Displacement axis Wave vector code
Bi1x1 Bi1 x 1
Bi1x3 Bi1 x 3
Bi1x4 Bi1 x 4
Bi1x5 Bi1 x 5
Bi1y1 Bi1 y 1
Bi1y2 Bi1 y 2
Bi1y3 Bi1 y 3
Bi1y4 Bi1 y 4
Bi1y5 Bi1 y 5
Bi1z1 Bi1 z 1
Bi1z2 Bi1 z 2
Bi1z3 Bi1 z 3
Bi1z4 Bi1 z 4
Bi1z5 Bi1 z 5
Srx5 Sr x 5
Sry1 Sr y 1
Sry2 Sr y 2
Sry3 Sr y 3
Sry4 Sr y 4
Sry5 Sr y 5
Srz1 Sr z 1
Srz2 Sr z 2
Srz4 Sr z 4
Cax2 Ca x 2
Cay3 Ca y 3
Cay4 Ca y 4
Cay5 Ca y 5
Caz1 Ca z 1
Caz2 Ca z 2
Cuy1 Cu y 1
Cuy2 Cu y 2
Cuy3 Cu y 3
Cuy4 Cu y 4
Cuy5 Cu y 5
Cuz1 Cu z 1
Cuz2 Cu z 2
Cuz3 Cu z 3
Cuz4 Cu z 4
OC1y1 OC1 y 1
OC1z1 OC1 z 1
OC1z2 OC1 z 2
OC2y1 OC2 y 1
OC2y2 OC2 y 2
OC2z1 OC2 z 1
OC2z2 OC2 z 2
OSx3 OS x 3
OSy1 OS y 1
OSy3 OS y 3
OSz1 OS z 1
OSz2 OS z 2
OBx1 OB x 1
OBx2 OB x 2
OBy1 OB y 1
OBy2 OB y 2
OBz1 OB z 1
OBz2 OB z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Bi1x1 0 -0.00450(9)
Bi1x3 0 -0.0024(2)
Bi1x4 0.005(3) 0.0021(3)
Bi1x5 0 0.0035(3)
Bi1y1 0.0302(8) -0.0049(4)
Bi1y2 -0.04420(7) 0.02698(9)
Bi1y3 0.0105(2) -0.0248(5)
Bi1y4 -0.0070(2) -0.0177(2)
Bi1y5 0 0.0175(3)
Bi1z1 0 0.00350(1)
Bi1z2 0.00607(2) 0.01061(1)
Bi1z3 -0.0077(3) 0
Bi1z4 -0.00653(2) 0
Bi1z5 -0.00681(3) 0
Srx5 -0.0020(4) 0
Sry1 0.0415(1) 0
Sry2 0 0.0241(3)
Sry3 0.0105(3) 0
Sry4 0 0.0115(3)
Sry5 0 0
Srz1 0 -0.00685(3)
Srz2 0.0063(3) 0
Srz4 0.00079(4) 0
Cax2 0.0010(6) 0
Cay3 -0.0029(7) 0
Cay4 0 0
Cay5 0 -0.007(1)
Caz1 0 -0.00782(8)
Caz2 0.00616(9) 0
Cuy1 0.0118(2) 0
Cuy2 0 0.0073(4)
Cuy3 0 0
Cuy4 0 0.0012(5)
Cuy5 0 -0.0058(6)
Cuz1 0 -0.00862(4)
Cuz2 0.00715(5) 0
Cuz3 0 -0.00066(8)
Cuz4 0.00079(7) 0
OC1y1 0.013(1) 0
OC1z1 0 -0.0083(2)
OC1z2 0.0074(3) 0
OC2y1 0.012(1) 0
OC2y2 0 0.023(2)
OC2z1 0 -0.0075(2)
OC2z2 0.0071(3) 0
OSx3 0 0.009(3)
OSy1 0.076(1) 0
OSy3 0.034(2) 0
OSz1 0 -0.0051(2)
OSz2 0.0052(3) 0
OBx1 0.008(1) -0.011(2)
OBx2 -0.006(3) 0.005(3)
OBy1 0.029(2) 0.062(2)
OBy2 -0.037(3) 0.038(4)
OBz1 0.023(3) -0.0050(3)
OBz2 0.0058(3) 0.0011(6)

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Bi1o1 Bi1 1
Bi1o2 Bi1 2
Bi1o3 Bi1 3
Bi1o4 Bi1 4
Bi1o5 Bi1 5
Cao4 Ca 4
Cao5 Ca 5
OBo1 OB 1
OBo2 OB 2

Occupation Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Bi1o1 0.564(2) 0
Bi1o2 0 0.0468(2)
Bi1o3 -0.033(2) 0
Bi1o4 0.023(2) -0.219(2)
Bi1o5 0.057(2) -0.207(2)
Cao4 0.021(6) 0
Cao5 -0.056(7) 0
OBo1 0.54(1) -0.14(1)
OBo2 0 0.15(2)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Bi1U111 Bi1 U11 1
Bi1U221 Bi1 U22 1
Bi1U331 Bi1 U33 1
Bi1U121 Bi1 U12 1
Bi1U131 Bi1 U13 1

ADP Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Bi1U111 0 0.0064(1)
Bi1U221 0.0133(2) 0.0242(2)
Bi1U331 -0.0193(1) 0
Bi1U121 0 0.0013(3)
Bi1U131 0 -0.0022(1)