All the Disorder Mechanisms in the 13:58 Phases Come Together. Out of the Modulated Confusion Rises the Remarkable Phase Ce12.60Cd58.68(2)

Authors:

Ying Piao, Shu; Palatinus, Lukas; Lidin, Sven

Journal:

Inorganic Chemistry 47 1079-1086 (2008)

DOI:

https://dx.doi.org/10.1021/ic701962b

B-IncStrDB ID: MlNyLHhwteR Entry date: 2022-01-10 Last revision: 2022-01-10

(I)

Chemical data


Structural Formula Sum: Cd58.682 Ce12.599 [ Help ]

Formula weight: 8361.8 Da [ Help ]

Crystallographic data and experimental details


Crystal system: orthorhombic [ Help ]

Superspace group name: Ccmm(α00)00s [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 27.2789(14) Å [ Help ]

b: 15.75920(10) Å [ Help ]

c: 15.5816(4) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 6698.4(4) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.66670 0.00000 0.00000

Z: 4 [ Help ]

μ: 26.503 mm-1 [ Help ]

Absorption correction type: none [ Help ]

Minimum transmission factor: 0.35 [ Help ]

Maximum transmission factor: 1.26 [ Help ]

Experimental remarks: The maximum transmission factor is outside the bounds (>1) [ Help ]

Refinement details


Total nb. of reflections: 19149 [ Help ]

Nb. of observed reflections: 10494 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: F [ Help ]

R(obs): 0.0554 [ Help ]

wR(obs): 0.0574 [ Help ]

R(all): 0.0554 [ Help ]

wR(all): 0.0574 [ Help ]

S(all): 2.65 [ Help ]

S(obs): 2.65 [ Help ]

Nb. of reflections: 10494 [ Help ]

Nb. of parameters: 404 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]

Δ/σ(max): 0.0475 [ Help ]

Δ/σ(mean): 0.0013 [ Help ]

Δρ(max): 5.67 e_Å-3 [ Help ]

Δρ(min): -4.89 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information


Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated Coords restraints or constraints Disordered cluster Disordered group
Ce1a Ce -0.02061(3) 0.43447(5) -0.25 Uani 0.0137(3) 8 1 d . . .
Ce1b Ce 0.29458(4) -0.25 -0.25 Uani 0.0124(4) 4 1 d . . .
Ce2a Ce 0.14714(2) -0.06154(3) -0.05258(4) Uani 0.01186(18) 16 1 d . . .
Ce2b Ce 0.45511(3) 0.25 -0.05447(6) Uani 0.0116(2) 8 1 d . . .
Ce3a Ce -0.18734(4) -0.06062(6) -0.23197(13) Uani 0.0206(6) 16 0.5 d . . .
Ce3b Ce 0.6267(3) -0.25 -0.2821(7) Uani 0.0179(5) 8 0.5 d . . .
Ce4 Ce 0.25 0.25 0 Uani 0.0142(6) 4 0.5987(14) d . . .
Cd1a Cd 0.56620(4) 0.90216(6) -0.09580(7) Uani 0.0205(4) 16 0.976(4) d . . .
Cd1b Cd 0.26811(5) -0.0861(2) -0.10207(10) Uani 0.0390(6) 16 0.5987(14) d . . .
Cd1b2 Cd 0.26795(5) -0.11022(15) -0.09900(11) Uani 0.0192(6) 16 0.4013(14) d . . .
Cd1c Cd 0.0726(4) 0.4636(7) 1.0908(12) Uani 0.0277(8) 16 0.4013(14) d . . .
Cd1c2 Cd 0.0889(2) 0.4471(3) 1.1017(4) Uani 0.0213(5) 16 0.5987(14) d . . .
Cd2 Cd 0.08202(6) 0.75 -0.75 Uani 0.0181(5) 4 1 d . . .
Cd3 Cd 0.08248(4) 0.75 -0.09481(8) Uani 0.0146(3) 8 1 d . . .
Cd4a Cd 0.20114(4) 0.10194(6) -0.15644(7) Uani 0.0254(3) 16 1 d . . .
Cd4b Cd 0.34777(5) 0.25 -0.15864(9) Uani 0.0220(5) 8 1 d . . .
Cd5a Cd 0.15510(13) 0.3457(2) 0.9992(3) Uani 0.0244(5) 16 0.5987(14) d . . .
Cd5a2 Cd 0.1654(5) 0.3854(9) 1.0582(13) Uani 0.0505(10) 16 0.4013(14) d . . .
Cd5b Cd 0.2587(3) 0.0540(5) -0.0251(7) Uani 0.0292(6) 16 0.5 d . . .
Cd6a Cd 0.20899(4) -0.07506(7) -0.25 Uani 0.0162(3) 8 1 d . . .
Cd6b Cd 0.43161(4) 0.35502(7) -0.25 Uani 0.0193(4) 8 1 d . . .
Cd6c Cd 0.39263(4) 0.47136(6) 0.25 Uani 0.0180(3) 8 1 d . . .
Cd7a Cd 0.03052(3) -0.40872(5) -0.14002(6) Uani 0.0172(2) 16 1 d . . .
Cd7b Cd 0.68816(4) 0.25 -0.14441(8) Uani 0.0154(3) 8 1 d . . .
Cd8a Cd -0.04765(3) 0.35230(5) -0.05012(6) Uani 0.0214(3) 16 1 d . . .
Cd8b Cd 0.35230(5) -0.25 -0.05273(8) Uani 0.0182(4) 8 1 d . . .
Cd9a Cd -0.13135(3) 0.10111(5) -0.15821(5) Uani 0.0144(2) 16 1 d . . .
Cd9b Cd 0.51721(4) -0.25 -0.15800(7) Uani 0.0141(3) 8 1 d . . .
Cd10a Cd 0.11416(4) -0.15268(6) -0.25 Uani 0.0152(3) 8 1 d . . .
Cd10b Cd 0.48241(6) 0.75 0.25 Uani 0.0156(5) 4 1 d . . .
Cd11 Cd 0.24931(7) 0.25 -0.25 Uani 0.0334(9) 4 1 d . . .
Cd12a Cd 0.5 0 0 Uani 0.0390(9) 8 0.585(6) d . . .
Cd12b Cd 0.25 0.75 0 Uani 0.0414(10) 4 1 d . . .
Cd13 Cd 0.24985(10) 0.25 -0.09140(19) Uani 0.0268(9) 8 0.4013(14) d . . .
Cd14 Cd 0.86762(11) 0.75 0.0811(2) Uani 0.0676(16) 8 0.4013(14) d . . .

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Ce1a Ce 0.0113(4) 0.0116(4) 0.0182(5) -0.0023(3) 0 0
Ce1b Ce 0.0066(7) 0.0135(5) 0.0171(8) 0 0 0
Ce2a Ce 0.0106(3) 0.0130(3) 0.0120(3) -0.0017(2) -0.0001(3) -0.0001(2)
Ce2b Ce 0.0096(4) 0.0127(4) 0.0125(5) 0 0.0003(4) 0
Ce3a Ce 0.0115(5) 0.0118(4) 0.0385(16) -0.0010(4) -0.0026(6) -0.0033(5)
Ce3b Ce 0.0090(8) 0.0136(6) 0.0311(13) 0 -0.0064(8) 0
Ce4 Ce 0.0117(12) 0.0107(8) 0.0202(12) 0 -0.0008(11) 0
Cd1a Cd 0.0242(8) 0.0170(7) 0.0202(7) -0.0070(6) -0.0061(7) 0.0044(6)
Cd1b Cd 0.0140(7) 0.0833(14) 0.0197(9) 0.0089(7) -0.0038(6) -0.0148(7)
Cd1b2 Cd 0.0092(7) 0.0271(12) 0.0213(10) 0.0002(6) -0.0005(7) -0.0075(7)
Cd1c Cd 0.0326(16) 0.0197(10) 0.0307(14) -0.0128(10) 0.0181(13) -0.0096(9)
Cd1c2 Cd 0.0271(10) 0.0183(7) 0.0184(8) -0.0087(7) 0.0060(8) -0.0022(6)
Cd2 Cd 0.0111(8) 0.0109(6) 0.0322(11) 0 0 0
Cd3 Cd 0.0137(6) 0.0145(5) 0.0157(6) 0 -0.0003(5) 0
Cd4a Cd 0.0286(7) 0.0230(5) 0.0245(6) -0.0023(5) 0.0026(6) 0.0052(4)
Cd4b Cd 0.0169(9) 0.0275(6) 0.0215(8) 0 -0.0053(7) 0
Cd5a Cd 0.0133(7) 0.0213(6) 0.0385(10) 0.0013(6) 0.0057(7) 0.0120(6)
Cd5a2 Cd 0.0455(15) 0.0478(15) 0.058(2) 0.0123(12) 0.0179(15) 0.0316(15)
Cd5b Cd 0.0253(10) 0.0215(7) 0.0409(14) 0.0019(7) -0.0181(9) 0.0020(7)
Cd6a Cd 0.0117(6) 0.0206(5) 0.0162(7) -0.0009(5) 0 0
Cd6b Cd 0.0181(6) 0.0195(5) 0.0203(7) 0.0004(5) 0 0
Cd6c Cd 0.0169(6) 0.0180(5) 0.0192(7) 0.0017(5) 0 0
Cd7a Cd 0.0139(4) 0.0152(4) 0.0226(5) -0.0020(3) 0.0000(4) -0.0030(3)
Cd7b Cd 0.0109(6) 0.0175(5) 0.0179(6) 0 0.0002(5) 0
Cd8a Cd 0.0181(5) 0.0286(4) 0.0174(5) 0.0092(4) 0.0022(4) 0.0045(4)
Cd8b Cd 0.0233(9) 0.0129(5) 0.0184(7) 0 -0.0043(7) 0
Cd9a Cd 0.0133(4) 0.0169(4) 0.0131(5) 0.0006(3) 0.0005(4) 0.0002(3)
Cd9b Cd 0.0146(7) 0.0141(5) 0.0135(6) 0 -0.0010(5) 0
Cd10a Cd 0.0148(6) 0.0153(5) 0.0154(6) -0.0023(5) 0 0
Cd10b Cd 0.0118(8) 0.0193(7) 0.0158(9) 0 0 0
Cd11 Cd 0.0124(9) 0.0143(8) 0.074(2) 0 0 0
Cd12a Cd 0.0459(17) 0.0313(14) 0.0396(18) -0.0115(11) 0.0083(13) 0.0115(11)
Cd12b Cd 0.0213(15) 0.0743(16) 0.029(2) 0 -0.0019(14) 0
Cd13 Cd 0.0297(16) 0.0310(14) 0.0197(17) 0 -0.0009(14) 0
Cd14 Cd 0.0180(16) 0.149(4) 0.036(2) 0 0.0075(16) 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 0.66670 0.00000 0.00000
2 1.33340 0.00000 0.00000

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Ce3ao1 Ce3a 1
Ce3bo1 Ce3b 1
Ce4o1 Ce4 1
Ce4o2 Ce4 2
Cd1ao1 Cd1a 1
Cd1bo1 Cd1b 1
Cd1b2o1 Cd1b2 1
Cd1co1 Cd1c 1
Cd1c2o1 Cd1c2 1
Cd5ao1 Cd5a 1
Cd5a2o1 Cd5a2 1
Cd5bo1 Cd5b 1
Cd5bo2 Cd5b 2
Cd12ao1 Cd12a 1
Cd13o1 Cd13 1
Cd13o2 Cd13 2
Cd14o1 Cd14 1

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ce3ao1 0.152(5) -0.557(7)
Ce3bo1 -0.320(5) -0.509(5)
Ce4o1 -0.434(4) 0
Ce4o2 -0.021(11) 0
Cd1ao1 0.031(4) 0.098(4)
Cd1bo1 -0.017(5) 0.790(14)
Cd1b2o1 0.016(5) -0.790(14)
Cd1co1 -0.565(10) -0.220(10)
Cd1c2o1 0.549(10) 0.258(10)
Cd5ao1 0.335(3) 0.456(3)
Cd5a2o1 -0.315(3) -0.470(3)
Cd5bo1 0.015(4) -0.609(6)
Cd5bo2 0.043(12) 0.035(14)
Cd12ao1 0.557(6) 0
Cd13o1 0.434(4) 0
Cd13o2 -0.021(11) 0
Cd14o1 -0.425(7) 0.336(7)

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

Modulation code Atom site label Displacement axis Wave vector code
Ce1ax1 Ce1a x 1
Ce1ay1 Ce1a y 1
Ce1az1 Ce1a z 1
Ce1bx1 Ce1b x 1
Ce1by1 Ce1b y 1
Ce1bz1 Ce1b z 1
Ce1bx2 Ce1b x 2
Ce1by2 Ce1b y 2
Ce1bz2 Ce1b z 2
Ce2ax1 Ce2a x 1
Ce2ay1 Ce2a y 1
Ce2az1 Ce2a z 1
Ce2bx1 Ce2b x 1
Ce2by1 Ce2b y 1
Ce2bz1 Ce2b z 1
Ce3bx1 Ce3b x 1
Ce3by1 Ce3b y 1
Ce3bz1 Ce3b z 1
Ce4x1 Ce4 x 1
Ce4y1 Ce4 y 1
Ce4z1 Ce4 z 1
Cd1ax1 Cd1a x 1
Cd1ay1 Cd1a y 1
Cd1az1 Cd1a z 1
Cd1ax2 Cd1a x 2
Cd1ay2 Cd1a y 2
Cd1az2 Cd1a z 2
Cd1cx1 Cd1c x 1
Cd1cy1 Cd1c y 1
Cd1cz1 Cd1c z 1
Cd1c2x1 Cd1c2 x 1
Cd1c2y1 Cd1c2 y 1
Cd1c2z1 Cd1c2 z 1
Cd2x1 Cd2 x 1
Cd2y1 Cd2 y 1
Cd2z1 Cd2 z 1
Cd3x1 Cd3 x 1
Cd3y1 Cd3 y 1
Cd3z1 Cd3 z 1
Cd4ax1 Cd4a x 1
Cd4ay1 Cd4a y 1
Cd4az1 Cd4a z 1
Cd4bx1 Cd4b x 1
Cd4by1 Cd4b y 1
Cd4bz1 Cd4b z 1
Cd4bx2 Cd4b x 2
Cd4by2 Cd4b y 2
Cd4bz2 Cd4b z 2
Cd5ax1 Cd5a x 1
Cd5ay1 Cd5a y 1
Cd5az1 Cd5a z 1
Cd5a2x1 Cd5a2 x 1
Cd5a2y1 Cd5a2 y 1
Cd5a2z1 Cd5a2 z 1
Cd5bx1 Cd5b x 1
Cd5by1 Cd5b y 1
Cd5bz1 Cd5b z 1
Cd6ax1 Cd6a x 1
Cd6ay1 Cd6a y 1
Cd6az1 Cd6a z 1
Cd6bx1 Cd6b x 1
Cd6by1 Cd6b y 1
Cd6bz1 Cd6b z 1
Cd6cx1 Cd6c x 1
Cd6cy1 Cd6c y 1
Cd6cz1 Cd6c z 1
Cd7ax1 Cd7a x 1
Cd7ay1 Cd7a y 1
Cd7az1 Cd7a z 1
Cd7bx1 Cd7b x 1
Cd7by1 Cd7b y 1
Cd7bz1 Cd7b z 1
Cd8ax1 Cd8a x 1
Cd8ay1 Cd8a y 1
Cd8az1 Cd8a z 1
Cd8bx1 Cd8b x 1
Cd8by1 Cd8b y 1
Cd8bz1 Cd8b z 1
Cd8bx2 Cd8b x 2
Cd8by2 Cd8b y 2
Cd8bz2 Cd8b z 2
Cd9ax1 Cd9a x 1
Cd9ay1 Cd9a y 1
Cd9az1 Cd9a z 1
Cd9bx1 Cd9b x 1
Cd9by1 Cd9b y 1
Cd9bz1 Cd9b z 1
Cd9bx2 Cd9b x 2
Cd9by2 Cd9b y 2
Cd9bz2 Cd9b z 2
Cd10ax1 Cd10a x 1
Cd10ay1 Cd10a y 1
Cd10az1 Cd10a z 1
Cd10bx1 Cd10b x 1
Cd10by1 Cd10b y 1
Cd10bz1 Cd10b z 1
Cd11x1 Cd11 x 1
Cd11y1 Cd11 y 1
Cd11z1 Cd11 z 1
Cd12ax1 Cd12a x 1
Cd12ay1 Cd12a y 1
Cd12az1 Cd12a z 1
Cd12bx1 Cd12b x 1
Cd12by1 Cd12b y 1
Cd12bz1 Cd12b z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ce1ax1 0 0
Ce1ay1 0 0
Ce1az1 0.00679(12) -0.00255(12)
Ce1bx1 0 0
Ce1by1 0 0
Ce1bz1 -0.00147(18) 0.01020(17)
Ce1bx2 0.0013(2) -0.0015(2)
Ce1by2 0 0
Ce1bz2 0 0
Ce2ax1 -0.00060(4) -0.00072(4)
Ce2ay1 0.00356(6) 0.00199(7)
Ce2az1 0.00043(8) -0.00038(8)
Ce2bx1 0.00005(6) -0.00015(6)
Ce2by1 0 0
Ce2bz1 0.00298(12) -0.00125(12)
Ce3bx1 -0.0015(2) 0.0008(3)
Ce3by1 0 0
Ce3bz1 0.0043(6) 0.0051(9)
Ce4x1 0 0.00732(14)
Ce4y1 0 0
Ce4z1 0 -0.0002(3)
Cd1ax1 0.00311(6) -0.00371(7)
Cd1ay1 -0.00630(9) 0.00301(10)
Cd1az1 -0.00497(13) 0.00070(13)
Cd1ax2 -0.00413(15) -0.00410(15)
Cd1ay2 0.0070(3) 0.0057(3)
Cd1az2 0.0021(4) 0.0036(4)
Cd1cx1 0.0043(6) 0.0019(3)
Cd1cy1 0.0030(9) 0.0014(5)
Cd1cz1 0.0030(15) -0.0013(7)
Cd1c2x1 -0.0024(3) -0.0049(2)
Cd1c2y1 0.0016(5) 0.0048(3)
Cd1c2z1 -0.0009(6) -0.0048(3)
Cd2x1 0 0
Cd2y1 0 0
Cd2z1 0.0020(2) 0.0016(2)
Cd3x1 0.00127(7) 0.00085(7)
Cd3y1 0 0
Cd3z1 -0.00072(15) -0.00060(16)
Cd4ax1 0.00216(7) 0.01059(6)
Cd4ay1 -0.00396(10) -0.00721(9)
Cd4az1 -0.00420(12) 0.00538(12)
Cd4bx1 0.00192(8) 0.00143(8)
Cd4by1 0 0
Cd4bz1 -0.00067(17) -0.01025(16)
Cd4bx2 0.0039(2) 0.0010(2)
Cd4by2 0 0
Cd4bz2 -0.0008(5) 0.0007(5)
Cd5ax1 0.00227(14) -0.00592(17)
Cd5ay1 -0.0019(3) 0.0023(3)
Cd5az1 0.0001(3) -0.0078(4)
Cd5a2x1 0.0046(4) 0.0026(6)
Cd5a2y1 -0.0038(8) -0.0015(11)
Cd5a2z1 0.0075(11) 0.0060(15)
Cd5bx1 -0.00142(12) 0.0023(5)
Cd5by1 0.00481(17) 0.0016(7)
Cd5bz1 0.0014(2) -0.0004(11)
Cd6ax1 0 0
Cd6ay1 0 0
Cd6az1 -0.00133(15) -0.00273(15)
Cd6bx1 0 0
Cd6by1 0 0
Cd6bz1 -0.00547(16) -0.00193(16)
Cd6cx1 0 0
Cd6cy1 0 0
Cd6cz1 0.00367(15) 0.00076(15)
Cd7ax1 0.00008(6) 0.00003(5)
Cd7ay1 0.00426(9) -0.00006(8)
Cd7az1 -0.00399(11) -0.00032(12)
Cd7bx1 -0.00093(7) -0.00125(8)
Cd7by1 0 0
Cd7bz1 0.00039(15) -0.00175(15)
Cd8ax1 -0.00386(6) 0.00103(6)
Cd8ay1 -0.00511(9) 0.00384(10)
Cd8az1 0.00071(11) -0.00005(12)
Cd8bx1 -0.00448(9) 0.00836(9)
Cd8by1 0 0
Cd8bz1 0.00344(16) -0.00511(16)
Cd8bx2 -0.00005(16) -0.00270(17)
Cd8by2 0 0
Cd8bz2 0.0001(5) 0.0014(4)
Cd9ax1 -0.00074(5) -0.00026(5)
Cd9ay1 0.00383(9) -0.00491(8)
Cd9az1 0.00000(11) -0.00100(11)
Cd9bx1 -0.00423(8) -0.00240(8)
Cd9by1 0 0
Cd9bz1 -0.00007(14) 0.00095(15)
Cd9bx2 0.00068(19) 0.00054(19)
Cd9by2 0 0
Cd9bz2 -0.0001(6) -0.0011(6)
Cd10ax1 0 0
Cd10ay1 0 0
Cd10az1 -0.00080(15) -0.00137(15)
Cd10bx1 0 0
Cd10by1 0 0
Cd10bz1 0.0009(2) 0.0004(2)
Cd11x1 0 0
Cd11y1 0 0
Cd11z1 -0.0268(3) -0.0024(3)
Cd12ax1 0 -0.00698(16)
Cd12ay1 0 0.0111(2)
Cd12az1 0 0.0044(3)
Cd12bx1 0 0.01209(13)
Cd12by1 0 0
Cd12bz1 0 -0.0245(3)