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Eu3Si15-xAl1+xOxN23-x (x ≈ 5/3) as a commensurate composite crystal

Authors:

Michiue, Yuichi; Shioi, Kousuke; Hirosaki, Naoto; Takeda, Takashi; Xie, Rong-Jun; Sato, Akira; Onoda, Mitsuko; Matsushita, Yoshitaka

Journal:

Acta Crystallographica, Section B 65 575 (2009)

DOI:

https://doi.org/10.1107/S0108768109030419

B-IncStrDB ID: SMQYBZ1Bjzl Entry date: 2022-01-22 Last revision: 2024-01-02

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3d

Chemical data

Structural Formula Sum: Al2.667 Eu3 N21.333 O1.667 Si13.333 [ Help ]

Formula weight: 1227.8 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

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

Space group name (Hall): P 2yb [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -x,y+1/2,-z

a: 14.6970(9) Å [ Help ]

b: 9.036(2) Å [ Help ]

c: 7.4677(7) Å [ Help ]

α: 90 ° [ Help ]

β: 90.2240(10) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 991.7(2) Å3 [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

μ: 10.369 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: (SADABS; Sheldrick, 2004) [ Help ]

Minimum transmission factor: 0.0354 [ Help ]

Maximum transmission factor: 0.4324 [ Help ]

Refinement details

Total nb. of reflections: 10994 [ Help ]

Nb. of observed reflections: 10354 [ Help ]

Intense reflections threshold: I>2σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0573 [ Help ]

R(obs): 0.0534 [ Help ]

wR(obs): 0.1134 [ Help ]

wR(all): 0.1148 [ Help ]

S(all): 2.15 [ Help ]

Nb. of reflections: 10994 [ Help ]

Nb. of parameters: 266 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 161 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(I)+0.000004I2) [ Help ]

Δ/σ(max): 0.0204 [ Help ]

Δ/σ(mean): 0.0035 [ Help ]

Δρ(max): 5.13 e_Å-3 [ Help ]

Δρ(min): -3.47 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom symbol Atom site label x y z Uiso/equiv ADP type Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occupancy Disordered cluster Disordered group
Eu Eu1 0.08342(5) 0.5 0.25328(7) 0.03310(16) Uani d . 1 . .
Eu Eu2 0.41856(4) 0.46605(5) 0.26321(6) 0.03438(17) Uani d . 1 . .
Eu Eu3 0.74871(5) 0.48118(11) 0.24819(6) 0.02618(8) Uani d . 1 . .
Si Si1 0.08997(18) 0.1734(2) 0.5566(3) 0.0121(5) Uani d . 0.8333 . .
Si Si2 0.40923(17) 0.1485(2) 0.4895(3) 0.0093(4) Uani d . 0.8333 . .
Si Si3a 0.7768(3) 0.1504(4) 0.4897(5) 0.0059(8) Uiso d . 0.439(6) . .
Si Si3b 0.7205(3) 0.1675(5) 0.5596(7) 0.0114(10) Uiso d . 0.395(6) . .
Si Si4 0.59182(19) 0.2950(2) 0.4426(3) 0.0124(5) Uani d . 0.8333 . .
Si Si5 0.90848(19) 0.3230(2) 0.5149(3) 0.0116(4) Uani d . 0.8333 . .
Si Si6a 0.2776(3) 0.3220(5) 0.5133(6) 0.0099(9) Uiso d . 0.439(6) . .
Si Si6b 0.2222(3) 0.3010(5) 0.4433(6) 0.0071(9) Uiso d . 0.394(6) . .
Si Si7 0.10085(17) 0.6257(2) 0.8478(3) 0.0104(4) Uani d . 0.8333 . .
Si Si8 0.30079(19) 0.6243(3) 0.8636(3) 0.0119(5) Uani d . 0.8333 . .
Si Si9 0.50042(16) 0.6194(2) 0.8653(3) 0.0086(5) Uani d . 0.8333 . .
Si Si10 0.69905(16) 0.6218(3) 0.8549(3) 0.0087(4) Uani d . 0.8333 . .
Si Si11 0.89925(18) 0.6298(2) 0.8569(3) 0.0098(4) Uani d . 0.8333 . .
Si Si12 -0.00006(17) 0.8313(3) 0.1244(3) 0.0088(5) Uani d . 0.8333 . .
Si Si13 0.19813(18) 0.8277(3) 0.1308(3) 0.0096(5) Uani d . 0.8333 . .
Si Si14 0.39969(18) 0.8210(2) 0.1319(3) 0.0108(4) Uani d . 0.8333 . .
Si Si15 0.60138(18) 0.8225(3) 0.1386(3) 0.0118(5) Uani d . 0.8333 . .
Si Si16 0.80161(15) 0.8270(3) 0.1270(3) 0.0081(4) Uani d . 0.8333 . .
Al Al1 0.08997(18) 0.1734(2) 0.5566(3) 0.0121(5) Uani d . 0.1667 . .
Al Al2 0.40923(17) 0.1485(2) 0.4895(3) 0.0093(4) Uani d . 0.1667 . .
Al Al3a 0.7768(3) 0.1504(4) 0.4897(5) 0.0059(8) Uiso d . 0.0877(12) . .
Al Al3b 0.7205(3) 0.1675(5) 0.5596(7) 0.0114(10) Uiso d . 0.0789(12) . .
Al Al4 0.59182(19) 0.2950(2) 0.4426(3) 0.0124(5) Uani d . 0.1667 . .
Al Al5 0.90848(19) 0.3230(2) 0.5149(3) 0.0116(4) Uani d . 0.1667 . .
Al Al6a 0.2776(3) 0.3220(5) 0.5133(6) 0.0099(9) Uiso d . 0.0878(12) . .
Al Al6b 0.2222(3) 0.3010(5) 0.4433(6) 0.0071(9) Uiso d . 0.0788(12) . .
Al Al7 0.10085(17) 0.6257(2) 0.8478(3) 0.0104(4) Uani d . 0.1667 . .
Al Al8 0.30079(19) 0.6243(3) 0.8636(3) 0.0119(5) Uani d . 0.1667 . .
Al Al9 0.50042(16) 0.6194(2) 0.8653(3) 0.0086(5) Uani d . 0.1667 . .
Al Al10 0.69905(16) 0.6218(3) 0.8549(3) 0.0087(4) Uani d . 0.1667 . .
Al Al11 0.89925(18) 0.6298(2) 0.8569(3) 0.0098(4) Uani d . 0.1667 . .
Al Al12 -0.00006(17) 0.8313(3) 0.1244(3) 0.0088(5) Uani d . 0.1667 . .
Al Al13 0.19813(18) 0.8277(3) 0.1308(3) 0.0096(5) Uani d . 0.1667 . .
Al Al14 0.39969(18) 0.8210(2) 0.1319(3) 0.0108(4) Uani d . 0.1667 . .
Al Al15 0.60138(18) 0.8225(3) 0.1386(3) 0.0118(5) Uani d . 0.1667 . .
Al Al16 0.80161(15) 0.8270(3) 0.1270(3) 0.0081(4) Uani d . 0.1667 . .
N N1 0.0903(4) 0.9889(5) 0.5900(6) 0.0148(8) Uiso d . 0.4444 . .
N N2 0.4236(4) 0.9811(7) 0.5901(7) 0.0202(12) Uiso d . 0.4444 . .
N N3 0.7596(4) 0.9858(8) 0.5918(7) 0.0201(10) Uiso d . 0.4444 . .
N N4 0.1118(4) 0.2301(6) 0.3426(8) 0.0113(9) Uiso d . 1 . .
N N5 0.3120(4) 0.1915(6) 0.3591(7) 0.0046(7) Uiso d . 1 . .
N N6 0.4980(5) 0.2099(7) 0.3455(10) 0.0158(12) Uiso d . 1 . .
N N7 0.6890(5) 0.2132(8) 0.3490(11) 0.0173(13) Uiso d . 1 . .
N N8 0.8970(6) 0.1873(8) 0.3637(10) 0.0262(15) Uiso d . 1 . .
N N9 -0.0012(4) 0.2710(6) 0.6516(7) 0.0065(8) Uiso d . 1 . .
N N10 0.1905(4) 0.2468(6) 0.6571(8) 0.0083(9) Uiso d . 1 . .
N N11 0.3836(4) 0.2900(6) 0.6392(8) 0.0111(10) Uiso d . 1 . .
N N12 0.6011(5) 0.2411(7) 0.6597(8) 0.0172(11) Uiso d . 1 . .
N N13 0.8086(6) 0.2821(10) 0.6446(13) 0.0259(18) Uiso d . 1 . .
N N14 0.0996(5) 0.2734(5) 0.9850(7) 0.0143(8) Uiso d . 1 . .
N N15 0.2980(4) 0.2530(6) 0.9697(8) 0.0165(10) Uiso d . 1 . .
N N16 0.4982(5) 0.2528(6) 0.9712(8) 0.0152(9) Uiso d . 1 . .
N N17 0.7043(4) 0.2646(6) 0.9777(8) 0.0148(9) Uiso d . 1 . .
N N18 0.8986(4) 0.2602(5) 0.9798(6) 0.0122(8) Uiso d . 1 . .
N N19 0.0003(4) 0.0225(6) 0.1155(8) 0.0151(9) Uiso d . 1 . .
N N20 0.2008(4) 0.0221(5) 0.1078(7) 0.0113(8) Uiso d . 1 . .
N N21 0.4011(5) 0.0151(5) 0.1204(6) 0.0143(8) Uiso d . 1 . .
N N22 0.6014(4) 0.0159(5) 0.0967(6) 0.0129(8) Uiso d . 1 . .
N N23 0.7980(4) 0.0189(5) 0.1222(7) 0.0111(8) Uiso d . 1 . .
O O1 0.0903(4) 0.9889(5) 0.5900(6) 0.0148(8) Uiso d . 0.5556 . .
O O2 0.4236(4) 0.9811(7) 0.5901(7) 0.0202(12) Uiso d . 0.5556 . .
O O3 0.7596(4) 0.9858(8) 0.5918(7) 0.0201(10) Uiso d . 0.5556 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
Eu1 0.0618(4) 0.0177(2) 0.01984(18) 0.0007(2) 0.0084(4) -0.00048(16) Eu
Eu2 0.0549(3) 0.01547(18) 0.0326(3) 0.0079(2) -0.0228(3) -0.00263(19) Eu
Eu3 0.03942(19) 0.02678(12) 0.01233(11) -0.01618(13) -0.0003(3) -0.0052(2) Eu
Si1 0.0157(10) 0.0104(7) 0.0100(7) 0.0115(8) -0.0038(9) -0.0012(5) Si
Si2 0.0102(8) 0.0092(6) 0.0085(6) 0.0016(8) 0.0024(9) 0.0003(5) Si
Si4 0.0164(10) 0.0115(7) 0.0094(7) 0.0039(8) -0.0059(10) -0.0007(5) Si
Si5 0.0189(10) 0.0091(6) 0.0069(6) 0.0027(9) 0.0016(10) 0.0004(5) Si
Si7 0.0102(9) 0.0112(7) 0.0098(7) -0.0011(7) 0.0026(8) 0.0010(5) Si
Si8 0.0174(10) 0.0114(8) 0.0069(9) -0.0015(8) -0.0007(8) 0.0023(6) Si
Si9 0.0069(8) 0.0092(7) 0.0096(9) -0.0005(7) 0.0013(8) 0.0013(6) Si
Si10 0.0071(8) 0.0128(8) 0.0062(8) -0.0013(7) 0.0005(7) 0.0001(6) Si
Si11 0.0101(8) 0.0108(7) 0.0087(7) -0.0043(7) 0.0040(8) -0.0008(5) Si
Si12 0.0099(8) 0.0101(7) 0.0063(8) 0.0006(7) 0.0025(8) 0.0004(6) Si
Si13 0.0128(9) 0.0081(7) 0.0079(8) 0.0018(7) 0.0048(8) 0.0009(6) Si
Si14 0.0146(9) 0.0096(6) 0.0082(7) -0.0027(8) 0.0040(9) 0.0008(5) Si
Si15 0.0117(9) 0.0129(7) 0.0109(7) 0.0037(8) 0.0012(8) 0.0017(5) Si
Si16 0.0017(7) 0.0139(8) 0.0088(9) 0.0024(7) 0.0005(7) -0.0017(6) Si
Al1 0.0157(10) 0.0104(7) 0.0100(7) 0.0115(8) -0.0038(9) -0.0012(5) Al
Al2 0.0102(8) 0.0092(6) 0.0085(6) 0.0016(8) 0.0024(9) 0.0003(5) Al
Al4 0.0164(10) 0.0115(7) 0.0094(7) 0.0039(8) -0.0059(10) -0.0007(5) Al
Al5 0.0189(10) 0.0091(6) 0.0069(6) 0.0027(9) 0.0016(10) 0.0004(5) Al
Al7 0.0102(9) 0.0112(7) 0.0098(7) -0.0011(7) 0.0026(8) 0.0010(5) Al
Al8 0.0174(10) 0.0114(8) 0.0069(9) -0.0015(8) -0.0007(8) 0.0023(6) Al
Al9 0.0069(8) 0.0092(7) 0.0096(9) -0.0005(7) 0.0013(8) 0.0013(6) Al
Al10 0.0071(8) 0.0128(8) 0.0062(8) -0.0013(7) 0.0005(7) 0.0001(6) Al
Al11 0.0101(8) 0.0108(7) 0.0087(7) -0.0043(7) 0.0040(8) -0.0008(5) Al
Al12 0.0099(8) 0.0101(7) 0.0063(8) 0.0006(7) 0.0025(8) 0.0004(6) Al
Al13 0.0128(9) 0.0081(7) 0.0079(8) 0.0018(7) 0.0048(8) 0.0009(6) Al
Al14 0.0146(9) 0.0096(6) 0.0082(7) -0.0027(8) 0.0040(9) 0.0008(5) Al
Al15 0.0117(9) 0.0129(7) 0.0109(7) 0.0037(8) 0.0012(8) 0.0017(5) Al
Al16 0.0017(7) 0.0139(8) 0.0088(9) 0.0024(7) 0.0005(7) -0.0017(6) Al

4d

Chemical data

Structural Formula Sum: Al1.778 Eu2 N14.222 O1.111 Si8.889 [ Help ]

Formula weight: 818.5 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Pm21n(α00)000 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 4.8990(3) Å [ Help ]

b: 9.036(2) Å [ Help ]

c: 7.4677(7) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 330.58(8) Å3 [ Help ]

Z: 1 [ Help ]

Modulation dimension: 1 [ Help ]

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ Help ]

W matrix:

1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0 1.0 0.0
0.0 0.0 0.0 1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2-nd subsystem [ Help ]

W matrix:

0.0 0.0 0.0 1.0
0.0 1.0 0.0 0.0
0.0 0.0 1.0 0.0
1.0 0.0 0.0 0.0

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 1.66667 0.00000 0.00000

μ: 10.369 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: (SADABS; Sheldrick, 2004) [ Help ]

Minimum transmission factor: 0.0354 [ Help ]

Maximum transmission factor: 0.4324 [ Help ]

Refinement details

Total nb. of reflections: 10994 [ Help ]

Nb. of observed reflections: 10354 [ Help ]

Intense reflections threshold: I>2σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0587 [ Help ]

R(obs): 0.0549 [ Help ]

wR(obs): 0.1176 [ Help ]

wR(all): 0.1190 [ Help ]

S(all): 2.23 [ Help ]

Nb. of reflections: 10994 [ Help ]

Nb. of parameters: 248 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(I)+0.000004I2) [ Help ]

Δ/σ(max): 0.0418 [ Help ]

Δ/σ(mean): 0.0052 [ Help ]

Δρ(max): 4.59 e_Å-3 [ Help ]

Δρ(min): -4.18 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom symbol Atom site label Subsystem x y z Uiso/equiv ADP type Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occupancy Disordered cluster Disordered group
Eu Eu11 1 0.25 0.5 0.25486(3) 0.03111(7) Uani d . 1 . .
Si Si11a 1 0.25 0.1662(3) 0.4901(3) 0.0113(5) Uani d . 0.8333 . .
Si Si11b 1 0.25 0.1911(3) 0.5558(3) 0.0138(5) Uani d . 0.8333 . .
Si Si11c 1 0.1678(8) 0.1674(4) 0.4895(5) 0.0009(7) Uiso d . 0.441(6) . .
Si Si11d 1 0.3348(11) 0.1845(5) 0.5596(7) 0.0053(10) Uiso d . 0.392(6) . .
Si Si12a 1 0.75 0.3404(2) 0.5149(3) 0.0110(4) Uani d . 0.8333 . .
Si Si12b 1 0.75 0.3126(2) 0.4419(3) 0.0115(5) Uani d . 0.8333 . .
Si Si12c 1 0.8293(9) 0.3387(5) 0.5134(6) 0.0105(9) Uiso d . 0.442(6) . .
Si Si12d 1 0.6644(10) 0.3182(5) 0.4443(6) 0.0070(9) Uiso d . 0.391(6) . .
Al Al11a 1 0.25 0.166167 0.490075 0.0113(5) Uani d . 0.1667 . .
Al Al11b 1 0.25 0.19115 0.555797 0.0138(5) Uani d . 0.1667 . .
Al Al11c 1 0.167833 0.167406 0.489479 0.0009(7) Uiso d . 0.0882(13) . .
Al Al11d 1 0.3348 0.184457 0.559631 0.0053(10) Uiso d . 0.0785(13) . .
Al Al12a 1 0.75 0.340416 0.514937 0.0110(4) Uani d . 0.1667 . .
Al Al12b 1 0.75 0.312581 0.441946 0.0115(5) Uani d . 0.1667 . .
Al Al12c 1 0.829298 0.338669 0.513421 0.0105(9) Uiso d . 0.0884(12) . .
Al Al12d 1 0.664376 0.318156 0.444298 0.0070(9) Uiso d . 0.0783(12) . .
N N11 1 0.25 0.0019(5) 0.5905(3) 0.0189(5) Uiso d . 0.4444 . .
O O11 1 0.25 0.001894 0.590478 0.0189(5) Uiso d . 0.5556 . .
Si Si21 2 0.5 0.64182(10) 0.85767(9) 0.00978(16) Uani d . 0.8333 . .
Si Si22 2 0 0.84351(10) 0.13046(9) 0.00973(16) Uani d . 0.8333 . .
Al Al21 2 0.5 0.641818 0.857673 0.00978(16) Uani d . 0.1667 . .
Al Al22 2 0 0.843511 0.130462 0.00973(16) Uani d . 0.1667 . .
N N21 2 0.5 0.2237(3) 0.3520(3) 0.0152(5) Uiso d . 1 . .
N N22 2 0 0.2837(3) 0.6502(3) 0.0122(4) Uiso d . 1 . .
N N23 2 0.5 0.2781(2) 0.9769(3) 0.0144(3) Uiso d . 1 . .
N N24 2 0 0.0365(2) 0.1125(3) 0.0128(3) Uiso d . 1 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
Eu11 0.05212(17) 0.01990(7) 0.02132(11) 0 0 -0.00303(9) Eu
Si11a 0.0078(9) 0.0138(8) 0.0124(8) 0 0 0.0007(6) Si
Si11b 0.0161(11) 0.0132(8) 0.0121(8) 0 0 -0.0003(6) Si
Si12a 0.0181(10) 0.0081(6) 0.0070(6) 0 0 0.0000(5) Si
Si12b 0.0141(10) 0.0112(7) 0.0092(7) 0 0 -0.0008(5) Si
Al11a 0.0078(9) 0.0138(8) 0.0124(8) 0 0 0.0007(6) Al
Al11b 0.0161(11) 0.0132(8) 0.0121(8) 0 0 -0.0003(6) Al
Al12a 0.0181(10) 0.0081(6) 0.0070(6) 0 0 0.0000(5) Al
Al12b 0.0141(10) 0.0112(7) 0.0092(7) 0 0 -0.0008(5) Al
Si21 0.0104(3) 0.0109(2) 0.0080(3) 0 0 0.00067(19) Si
Si22 0.0097(3) 0.0113(2) 0.0082(3) 0 0 0.00031(19) Si
Al21 0.0104(3) 0.0109(2) 0.0080(3) 0 0 0.00067(19) Al
Al22 0.0097(3) 0.0113(2) 0.0082(3) 0 0 0.00031(19) Al

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): [ Help ]

Wave vector code q_x q_z
1 1.66667 0.00000
2 3.33333 0.00000
3 5.00000 0.00000
4 6.66667 0.00000
5 8.33333 0.00000

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

Modulation code Atom site label Displacement axis Wave vector code
Eu11x1 Eu11 x 1
Eu11y1 Eu11 y 1
Eu11z1 Eu11 z 1
Eu11x2 Eu11 x 2
Eu11y2 Eu11 y 2
Eu11z2 Eu11 z 2
Eu11x3 Eu11 x 3
Eu11y3 Eu11 y 3
Eu11z3 Eu11 z 3
Si11ax1 Si11a x 1
Si11ay1 Si11a y 1
Si11az1 Si11a z 1
Si11bx1 Si11b x 1
Si11by1 Si11b y 1
Si11bz1 Si11b z 1
Si12ax1 Si12a x 1
Si12ay1 Si12a y 1
Si12az1 Si12a z 1
Si12bx1 Si12b x 1
Si12by1 Si12b y 1
Si12bz1 Si12b z 1
Al11ax1 Al11a x 1
Al11ay1 Al11a y 1
Al11az1 Al11a z 1
Al11bx1 Al11b x 1
Al11by1 Al11b y 1
Al11bz1 Al11b z 1
Al12ax1 Al12a x 1
Al12ay1 Al12a y 1
Al12az1 Al12a z 1
Al12bx1 Al12b x 1
Al12by1 Al12b y 1
Al12bz1 Al12b z 1
N11x1 N11 x 1
N11y1 N11 y 1
N11z1 N11 z 1
N11x2 N11 x 2
N11y2 N11 y 2
N11z2 N11 z 2
N11x3 N11 x 3
N11y3 N11 y 3
N11z3 N11 z 3
O11x1 O11 x 1
O11y1 O11 y 1
O11z1 O11 z 1
O11x2 O11 x 2
O11y2 O11 y 2
O11z2 O11 z 2
O11x3 O11 x 3
O11y3 O11 y 3
O11z3 O11 z 3
Si21x1 Si21 x 1
Si21y1 Si21 y 1
Si21z1 Si21 z 1
Si21x2 Si21 x 2
Si21y2 Si21 y 2
Si21z2 Si21 z 2
Si21x3 Si21 x 3
Si21y3 Si21 y 3
Si21z3 Si21 z 3
Si21x4 Si21 x 4
Si21y4 Si21 y 4
Si21z4 Si21 z 4
Si21x5 Si21 x 5
Si21y5 Si21 y 5
Si21z5 Si21 z 5
Si22x1 Si22 x 1
Si22y1 Si22 y 1
Si22z1 Si22 z 1
Si22x2 Si22 x 2
Si22y2 Si22 y 2
Si22z2 Si22 z 2
Si22x3 Si22 x 3
Si22y3 Si22 y 3
Si22z3 Si22 z 3
Si22x4 Si22 x 4
Si22y4 Si22 y 4
Si22z4 Si22 z 4
Si22x5 Si22 x 5
Si22y5 Si22 y 5
Si22z5 Si22 z 5
Al21x1 Al21 x 1
Al21y1 Al21 y 1
Al21z1 Al21 z 1
Al21x2 Al21 x 2
Al21y2 Al21 y 2
Al21z2 Al21 z 2
Al21x3 Al21 x 3
Al21y3 Al21 y 3
Al21z3 Al21 z 3
Al21x4 Al21 x 4
Al21y4 Al21 y 4
Al21z4 Al21 z 4
Al21x5 Al21 x 5
Al21y5 Al21 y 5
Al21z5 Al21 z 5
Al22x1 Al22 x 1
Al22y1 Al22 y 1
Al22z1 Al22 z 1
Al22x2 Al22 x 2
Al22y2 Al22 y 2
Al22z2 Al22 z 2
Al22x3 Al22 x 3
Al22y3 Al22 y 3
Al22z3 Al22 z 3
Al22x4 Al22 x 4
Al22y4 Al22 y 4
Al22z4 Al22 z 4
Al22x5 Al22 x 5
Al22y5 Al22 y 5
Al22z5 Al22 z 5
N21x1 N21 x 1
N21y1 N21 y 1
N21z1 N21 z 1
N21x2 N21 x 2
N21y2 N21 y 2
N21z2 N21 z 2
N21x3 N21 x 3
N21y3 N21 y 3
N21z3 N21 z 3
N21x4 N21 x 4
N21y4 N21 y 4
N21z4 N21 z 4
N21x5 N21 x 5
N21y5 N21 y 5
N21z5 N21 z 5
N22x1 N22 x 1
N22y1 N22 y 1
N22z1 N22 z 1
N22x2 N22 x 2
N22y2 N22 y 2
N22z2 N22 z 2
N22x3 N22 x 3
N22y3 N22 y 3
N22z3 N22 z 3
N22x4 N22 x 4
N22y4 N22 y 4
N22z4 N22 z 4
N22x5 N22 x 5
N22y5 N22 y 5
N22z5 N22 z 5
N23x1 N23 x 1
N23y1 N23 y 1
N23z1 N23 z 1
N23x2 N23 x 2
N23y2 N23 y 2
N23z2 N23 z 2
N23x3 N23 x 3
N23y3 N23 y 3
N23z3 N23 z 3
N23x4 N23 x 4
N23y4 N23 y 4
N23z4 N23 z 4
N23x5 N23 x 5
N23y5 N23 y 5
N23z5 N23 z 5
N24x1 N24 x 1
N24y1 N24 y 1
N24z1 N24 z 1
N24x2 N24 x 2
N24y2 N24 y 2
N24z2 N24 z 2
N24x3 N24 x 3
N24y3 N24 y 3
N24z3 N24 z 3
N24x4 N24 x 4
N24y4 N24 y 4
N24z4 N24 z 4
N24x5 N24 x 5
N24y5 N24 y 5
N24z5 N24 z 5

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Eu11x1 0 0.00492(12)
Eu11y1 -0.01960(3) 0
Eu11z1 0.00569(6) 0
Eu11x2 0 0.00282(9)
Eu11y2 0.00154(7) 0
Eu11z2 0.00675(6) 0
Eu11x3 0 0.00082(10)
Eu11y3 0 0
Eu11z3 0 0
Si11ax1 0 -0.0345(10)
Si11ay1 0 0
Si11az1 0 0
Si11bx1 0 0.0330(12)
Si11by1 0 0
Si11bz1 0 0
Si12ax1 0 0.0521(11)
Si12ay1 0 0
Si12az1 0 0
Si12bx1 0 -0.0516(12)
Si12by1 0 0
Si12bz1 0 0
Al11ax1 0 -0.0345(10)
Al11ay1 0 0
Al11az1 0 0
Al11bx1 0 0.0330(12)
Al11by1 0 0
Al11bz1 0 0
Al12ax1 0 0.0521(11)
Al12ay1 0 0
Al12az1 0 0
Al12bx1 0 -0.0516(12)
Al12by1 0 0
Al12bz1 0 0
N11x1 0 -0.0067(11)
N11y1 -0.0050(3) 0
N11z1 -0.0004(6) 0
N11x2 0 -0.0016(9)
N11y2 -0.0016(6) 0
N11z2 -0.0013(6) 0
N11x3 0 0.0223(9)
N11y3 0 0
N11z3 0 0
O11x1 0 -0.0067(11)
O11y1 -0.0050(3) 0
O11z1 -0.0004(6) 0
O11x2 0 -0.0016(9)
O11y2 -0.0016(6) 0
O11z2 -0.0013(6) 0
O11x3 0 0.0223(9)
O11y3 0 0
O11z3 0 0
Si21x1 -0.0018(5) 0
Si21y1 0 -0.00221(15)
Si21z1 0 -0.00549(14)
Si21x2 0 -0.0065(5)
Si21y2 -0.00428(14) 0
Si21z2 0.00710(17) 0
Si21x3 0.0015(5) 0
Si21y3 0 -0.00008(17)
Si21z3 0 -0.0012(2)
Si21x4 0 0.0029(6)
Si21y4 0.00055(19) 0
Si21z4 -0.0002(3) 0
Si21x5 0.0004(5) 0
Si21y5 0 0
Si21z5 0 0
Si22x1 0.0007(5) 0
Si22y1 0 -0.00084(15)
Si22z1 0 -0.00336(15)
Si22x2 0 -0.0072(5)
Si22y2 0.00506(16) 0
Si22z2 -0.00589(18) 0
Si22x3 -0.0006(6) 0
Si22y3 0 0.00019(18)
Si22z3 0 -0.0001(2)
Si22x4 0 -0.0031(5)
Si22y4 0.00090(19) 0
Si22z4 -0.0013(3) 0
Si22x5 0.0005(5) 0
Si22y5 0 0
Si22z5 0 0
Al21x1 -0.0018(5) 0
Al21y1 0 -0.00221(15)
Al21z1 0 -0.00549(14)
Al21x2 0 -0.0065(5)
Al21y2 -0.00428(14) 0
Al21z2 0.00710(17) 0
Al21x3 0.0015(5) 0
Al21y3 0 -0.00008(17)
Al21z3 0 -0.0012(2)
Al21x4 0 0.0029(6)
Al21y4 0.00055(19) 0
Al21z4 -0.0002(3) 0
Al21x5 0.0004(5) 0
Al21y5 0 0
Al21z5 0 0
Al22x1 0.0007(5) 0
Al22y1 0 -0.00084(15)
Al22z1 0 -0.00336(15)
Al22x2 0 -0.0072(5)
Al22y2 0.00506(16) 0
Al22z2 -0.00589(18) 0
Al22x3 -0.0006(6) 0
Al22y3 0 0.00019(18)
Al22z3 0 -0.0001(2)
Al22x4 0 -0.0031(5)
Al22y4 0.00090(19) 0
Al22z4 -0.0013(3) 0
Al22x5 0.0005(5) 0
Al22y5 0 0
Al22z5 0 0
N21x1 0.0067(13) 0
N21y1 0 0.0211(4)
N21z1 0 -0.0110(5)
N21x2 0 -0.0597(15)
N21y2 -0.0024(4) 0
N21z2 -0.0027(5) 0
N21x3 -0.0051(17) 0
N21y3 0 -0.0012(5)
N21z3 0 0.0010(7)
N21x4 0 -0.0037(15)
N21y4 0.0028(6) 0
N21z4 -0.0029(9) 0
N21x5 0.0013(13) 0
N21y5 0 0
N21z5 0 0
N22x1 -0.0066(13) 0
N22y1 0 0.0275(4)
N22z1 0 -0.0099(5)
N22x2 0 -0.0657(13)
N22y2 0.0000(4) 0
N22z2 0.0021(5) 0
N22x3 0.0050(15) 0
N22y3 0 -0.0022(4)
N22z3 0 -0.0005(7)
N22x4 0 0.0227(14)
N22y4 0.0031(5) 0
N22z4 -0.0007(8) 0
N22x5 -0.0079(13) 0
N22y5 0 0
N22z5 0 0
N23x1 0.0066(13) 0
N23y1 0 0.0074(3)
N23z1 0 0.0040(4)
N23x2 0 0.0107(11)
N23y2 -0.0072(3) 0
N23z2 -0.0064(4) 0
N23x3 0.0002(13) 0
N23y3 0 0.0000(4)
N23z3 0 0.0014(5)
N23x4 0 0.0061(14)
N23y4 -0.0010(4) 0
N23z4 0.0006(6) 0
N23x5 0.0006(13) 0
N23y5 0 0
N23z5 0 0
N24x1 0.0033(10) 0
N24y1 0 -0.0009(3)
N24z1 0 0.0123(4)
N24x2 0 0.0043(11)
N24y2 0.0041(3) 0
N24z2 0.0043(4) 0
N24x3 -0.0067(12) 0
N24y3 0 -0.0009(4)
N24z3 0 0.0003(5)
N24x4 0 0.0057(14)
N24y4 -0.0009(5) 0
N24z4 -0.0009(6) 0
N24x5 0.0006(13) 0
N24y5 0 0
N24z5 0 0

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Eu11U111 Eu11 U11 1
Eu11U221 Eu11 U22 1
Eu11U331 Eu11 U33 1
Eu11U121 Eu11 U12 1
Eu11U131 Eu11 U13 1
Eu11U231 Eu11 U23 1
Eu11U112 Eu11 U11 2
Eu11U222 Eu11 U22 2
Eu11U332 Eu11 U33 2
Eu11U122 Eu11 U12 2
Eu11U132 Eu11 U13 2
Eu11U232 Eu11 U23 2
Eu11U113 Eu11 U11 3
Eu11U223 Eu11 U22 3
Eu11U333 Eu11 U33 3
Eu11U123 Eu11 U12 3
Eu11U133 Eu11 U13 3
Eu11U233 Eu11 U23 3
Si11aU111 Si11a U11 1
Si11aU221 Si11a U22 1
Si11aU331 Si11a U33 1
Si11aU121 Si11a U12 1
Si11aU131 Si11a U13 1
Si11aU231 Si11a U23 1
Si11bU111 Si11b U11 1
Si11bU221 Si11b U22 1
Si11bU331 Si11b U33 1
Si11bU121 Si11b U12 1
Si11bU131 Si11b U13 1
Si11bU231 Si11b U23 1
Si12aU111 Si12a U11 1
Si12aU221 Si12a U22 1
Si12aU331 Si12a U33 1
Si12aU121 Si12a U12 1
Si12aU131 Si12a U13 1
Si12aU231 Si12a U23 1
Si12bU111 Si12b U11 1
Si12bU221 Si12b U22 1
Si12bU331 Si12b U33 1
Si12bU121 Si12b U12 1
Si12bU131 Si12b U13 1
Si12bU231 Si12b U23 1
Si12U111 Si21 U11 1
Si12U221 Si21 U22 1
Si12U331 Si21 U33 1
Si12U121 Si21 U12 1
Si12U131 Si21 U13 1
Si12U231 Si21 U23 1
Si12U112 Si21 U11 2
Si12U222 Si21 U22 2
Si12U332 Si21 U33 2
Si12U122 Si21 U12 2
Si12U132 Si21 U13 2
Si12U232 Si21 U23 2
Si12U113 Si21 U11 3
Si12U223 Si21 U22 3
Si12U333 Si21 U33 3
Si12U123 Si21 U12 3
Si12U133 Si21 U13 3
Si12U233 Si21 U23 3
Si12U114 Si21 U11 4
Si12U224 Si21 U22 4
Si12U334 Si21 U33 4
Si12U124 Si21 U12 4
Si12U134 Si21 U13 4
Si12U234 Si21 U23 4
Si12U115 Si21 U11 5
Si12U225 Si21 U22 5
Si12U335 Si21 U33 5
Si12U125 Si21 U12 5
Si12U135 Si21 U13 5
Si12U235 Si21 U23 5
Si22U111 Si22 U11 1
Si22U221 Si22 U22 1
Si22U331 Si22 U33 1
Si22U121 Si22 U12 1
Si22U131 Si22 U13 1
Si22U231 Si22 U23 1
Si22U112 Si22 U11 2
Si22U222 Si22 U22 2
Si22U332 Si22 U33 2
Si22U122 Si22 U12 2
Si22U132 Si22 U13 2
Si22U232 Si22 U23 2
Si22U113 Si22 U11 3
Si22U223 Si22 U22 3
Si22U333 Si22 U33 3
Si22U123 Si22 U12 3
Si22U133 Si22 U13 3
Si22U233 Si22 U23 3
Si22U114 Si22 U11 4
Si22U224 Si22 U22 4
Si22U334 Si22 U33 4
Si22U124 Si22 U12 4
Si22U134 Si22 U13 4
Si22U234 Si22 U23 4
Si22U115 Si22 U11 5
Si22U225 Si22 U22 5
Si22U335 Si22 U33 5
Si22U125 Si22 U12 5
Si22U135 Si22 U13 5
Si22U235 Si22 U23 5
Al21U111 Al21 U11 1
Al21U221 Al21 U22 1
Al21U331 Al21 U33 1
Al21U121 Al21 U12 1
Al21U131 Al21 U13 1
Al21U231 Al21 U23 1
Al21U112 Al21 U11 2
Al21U222 Al21 U22 2
Al21U332 Al21 U33 2
Al21U122 Al21 U12 2
Al21U132 Al21 U13 2
Al21U232 Al21 U23 2
Al21U113 Al21 U11 3
Al21U223 Al21 U22 3
Al21U333 Al21 U33 3
Al21U123 Al21 U12 3
Al21U133 Al21 U13 3
Al21U233 Al21 U23 3
Al21U114 Al21 U11 4
Al21U224 Al21 U22 4
Al21U334 Al21 U33 4
Al21U124 Al21 U12 4
Al21U134 Al21 U13 4
Al21U234 Al21 U23 4
Al21U115 Al21 U11 5
Al21U225 Al21 U22 5
Al21U335 Al21 U33 5
Al21U125 Al21 U12 5
Al21U135 Al21 U13 5
Al21U235 Al21 U23 5
Al22U111 Al22 U11 1
Al22U221 Al22 U22 1
Al22U331 Al22 U33 1
Al22U121 Al22 U12 1
Al22U131 Al22 U13 1
Al22U231 Al22 U23 1
Al22U112 Al22 U11 2
Al22U222 Al22 U22 2
Al22U332 Al22 U33 2
Al22U122 Al22 U12 2
Al22U132 Al22 U13 2
Al22U232 Al22 U23 2
Al22U113 Al22 U11 3
Al22U223 Al22 U22 3
Al22U333 Al22 U33 3
Al22U123 Al22 U12 3
Al22U133 Al22 U13 3
Al22U233 Al22 U23 3
Al22U114 Al22 U11 4
Al22U224 Al22 U22 4
Al22U334 Al22 U33 4
Al22U124 Al22 U12 4
Al22U134 Al22 U13 4
Al22U234 Al22 U23 4
Al22U115 Al22 U11 5
Al22U225 Al22 U22 5
Al22U335 Al22 U33 5
Al22U125 Al22 U12 5
Al22U135 Al22 U13 5
Al22U235 Al22 U23 5

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Eu11U111 -0.0039(3) 0
Eu11U221 -0.0015(2) 0
Eu11U331 0.0069(3) 0
Eu11U121 0 0.01371(11)
Eu11U131 0 -0.0048(2)
Eu11U231 -0.00130(10) 0
Eu11U112 0.01313(18) 0
Eu11U222 -0.00680(9) 0
Eu11U332 0.00904(14) 0
Eu11U122 0 0.0051(2)
Eu11U132 0 -0.0178(2)
Eu11U232 0.0023(2) 0
Eu11U113 0 0
Eu11U223 0 0
Eu11U333 0 0
Eu11U123 0 -0.00259(9)
Eu11U133 0 -0.0050(3)
Eu11U233 0 0
Si11aU111 0 0
Si11aU221 0 0
Si11aU331 0 0
Si11aU121 0 0.0098(19)
Si11aU131 0 0.007(2)
Si11aU231 0 0
Si11bU111 0 0
Si11bU221 0 0
Si11bU331 0 0
Si11bU121 0 0.0310(19)
Si11bU131 0 -0.005(2)
Si11bU231 0 0
Si12aU111 0 0
Si12aU221 0 0
Si12aU331 0 0
Si12aU121 0 -0.010(2)
Si12aU131 0 -0.002(2)
Si12aU231 0 0
Si12bU111 0 0
Si12bU221 0 0
Si12bU331 0 0
Si12bU121 0 -0.0056(19)
Si12bU131 0 0.010(2)
Si12bU231 0 0
Si12U111 0 -0.0023(6)
Si12U221 0 0.0010(4)
Si12U331 0 0.0003(4)
Si12U121 0.0004(4) 0
Si12U131 -0.0021(4) 0
Si12U231 0 0.0001(3)
Si12U112 0.0002(6) 0
Si12U222 -0.0014(4) 0
Si12U332 -0.0001(4) 0
Si12U122 0 -0.0002(4)
Si12U132 0 0.0001(4)
Si12U232 0.0005(3) 0
Si12U113 0 -0.0023(6)
Si12U223 0 0.0003(5)
Si12U333 0 0.0001(5)
Si12U123 -0.0024(5) 0
Si12U133 0.0012(5) 0
Si12U233 0 -0.0017(4)
Si12U114 -0.0008(6) 0
Si12U224 -0.0010(6) 0
Si12U334 0.0005(7) 0
Si12U124 0 0.0023(4)
Si12U134 0 -0.0012(5)
Si12U234 -0.0002(5) 0
Si12U115 0 0
Si12U225 0 0
Si12U335 0 0
Si12U125 0.0014(4) 0
Si12U135 -0.0016(5) 0
Si12U235 0 0
Si22U111 0 -0.0019(6)
Si22U221 0 0.0004(4)
Si22U331 0 -0.0008(4)
Si22U121 -0.0011(4) 0
Si22U131 0.0000(4) 0
Si22U231 0 -0.0008(3)
Si22U112 -0.0040(6) 0
Si22U222 0.0002(4) 0
Si22U332 -0.0014(4) 0
Si22U122 0 -0.0016(4)
Si22U132 0 0.0022(4)
Si22U232 -0.0004(3) 0
Si22U113 0 -0.0033(6)
Si22U223 0 0.0038(5)
Si22U333 0 0.0009(6)
Si22U123 0.0015(5) 0
Si22U133 0.0005(5) 0
Si22U233 0 -0.0012(4)
Si22U114 0.0022(6) 0
Si22U224 0.0011(6) 0
Si22U334 -0.0005(7) 0
Si22U124 0 0.0025(5)
Si22U134 0 -0.0012(5)
Si22U234 0.0009(5) 0
Si22U115 0 0
Si22U225 0 0
Si22U335 0 0
Si22U125 0.0016(4) 0
Si22U135 0.0026(5) 0
Si22U235 0 0
Al21U111 0 -0.0023(6)
Al21U221 0 0.0010(4)
Al21U331 0 0.0003(4)
Al21U121 0.0004(4) 0
Al21U131 -0.0021(4) 0
Al21U231 0 0.0001(3)
Al21U112 0.0002(6) 0
Al21U222 -0.0014(4) 0
Al21U332 -0.0001(4) 0
Al21U122 0 -0.0002(4)
Al21U132 0 0.0001(4)
Al21U232 0.0005(3) 0
Al21U113 0 -0.0023(6)
Al21U223 0 0.0003(5)
Al21U333 0 0.0001(5)
Al21U123 -0.0024(5) 0
Al21U133 0.0012(5) 0
Al21U233 0 -0.0017(4)
Al21U114 -0.0008(6) 0
Al21U224 -0.0010(6) 0
Al21U334 0.0005(7) 0
Al21U124 0 0.0023(4)
Al21U134 0 -0.0012(5)
Al21U234 -0.0002(5) 0
Al21U115 0 0
Al21U225 0 0
Al21U335 0 0
Al21U125 0.0014(4) 0
Al21U135 -0.0016(5) 0
Al21U235 0 0
Al22U111 0 -0.0019(6)
Al22U221 0 0.0004(4)
Al22U331 0 -0.0008(4)
Al22U121 -0.0011(4) 0
Al22U131 0.0000(4) 0
Al22U231 0 -0.0008(3)
Al22U112 -0.0040(6) 0
Al22U222 0.0002(4) 0
Al22U332 -0.0014(4) 0
Al22U122 0 -0.0016(4)
Al22U132 0 0.0022(4)
Al22U232 -0.0004(3) 0
Al22U113 0 -0.0033(6)
Al22U223 0 0.0038(5)
Al22U333 0 0.0009(6)
Al22U123 0.0015(5) 0
Al22U133 0.0005(5) 0
Al22U233 0 -0.0012(4)
Al22U114 0.0022(6) 0
Al22U224 0.0011(6) 0
Al22U334 -0.0005(7) 0
Al22U124 0 0.0025(5)
Al22U134 0 -0.0012(5)
Al22U234 0.0009(5) 0
Al22U115 0 0
Al22U225 0 0
Al22U335 0 0
Al22U125 0.0016(4) 0
Al22U135 0.0026(5) 0
Al22U235 0 0

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Si11a 0 0.3333
Si11b 0.5 0.3333
Si11c 0.1131(13) 0.1667
Si11d 0.3913(18) 0.1667
Si12a 0.5 0.3333
Si12b 0 0.3333
Si12c 0.3822(15) 0.1667
Si12d 0.1073(16) 0.1667
Al11a 0 0.3333
Al11b 0.5 0.3333
Al11c 0.8854 0.1667
Al11d 0.6133 0.1667
Al12a 0.5 0.3333
Al12b 0 0.3333
Al12c 0.388 0.1667
Al12d 0.1079 0.1667