Structure modulations in nonlinear optical (NLO) materials Cs2TB4O9 (T=Ge,Si)

Authors:

Zhou, Zhengyang; Xu, Xiang; Fei, Rao; Mao, Jianggao; Sun, Junliang

Journal:

Acta Crystallographica, Section B 72 194-200 (2016)

DOI:

https://doi.org/10.1107/S2052520615019733

B-IncStrDB ID: 11442EEvkyY Entry date: 2016-04-04 Last revision: 2022-01-19

Cs2GeB4O9

Chemical data


Structural Formula Sum: B4 Cs2 Ge1 O9 [ Help ]

Formula weight: 525.6 Da [ Help ]

Crystallographic data and experimental details


Crystal system: monoclinic [ Help ]

Superspace group name: I2(αβ0)0 [ 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 x1+1/2,x2+1/2,x3+1/2,x4
4 -x1+1/2,-x2+1/2,x3+1/2,-x4

a: 6.7863(10) Å [ Help ]

b: 6.7914(10) Å [ Help ]

c: 9.9686(15) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90.135(12) ° [ Help ]

Volume: 459.44(12) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 -0.482300 0.119200 0.000000

Z: 2 [ Help ]

Cell determination reflection Nb.: 3052 [ Help ]

θ(min) for cell determination: 3.62 ° [ Help ]

θ(max) for cell determination: 29.16 ° [ Help ]

Cell measurement temperature: 100.00(10) K [ Help ]

μ: 11.17 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: CrysAlisPro, Agilent Technologies, Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET) (compiled Aug 13 2014,18:06:01) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.779 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details


Total nb. of reflections: 4440 [ Help ]

Nb. of observed reflections: 3004 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0503 [ Help ]

wR(obs): 0.0582 [ Help ]

R(all): 0.0768 [ Help ]

wR(all): 0.0649 [ Help ]

S(all): 1.69 [ Help ]

S(obs): 1.85 [ Help ]

Nb. of reflections: 4440 [ Help ]

Nb. of parameters: 177 [ Help ]

Number of restraints: 13 [ Help ]

Number of constraints: 6 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0079 [ Help ]

Δ/σ(mean): 0.0018 [ Help ]

Δρ(max): 3.39 e_Å-3 [ Help ]

Δρ(min): -5.58 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Absolute structure remarks: 1517 of Friedel pairs used in the refinement [ 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
Cs1 Cs 0 0 0.00120(10) Uani 0.00767(17) 2 1 d ? ? ?
Cs2 Cs -0.5 0 0.24904(7) Uani 0.0083(2) 2 1 d ? ? ?
Ge1 Ge 0 -0.5 0.25095(17) Uani 0.0041(4) 2 1 d ? ? ?
O5b O 0 0 0.6619(13) Uiso 0.0029(14) 2 0.5 d ? ? ?
O5a O 0 0 0.3372(12) Uiso 0.0029(14) 2 0.5 d ? ? ?
O1 O -0.8417(8) -0.6483(7) 0.1559(5) Uiso 0.0068(11) 4 1 d ? ? ?
O4 O -0.7269(6) -0.3979(5) 0.0047(8) Uiso 0.0058(9) 4 1 d ? ? ?
O2 O -0.3523(8) -0.8399(7) 0.8419(5) Uiso 0.0070(11) 4 1 d ? ? ?
O3 O -0.6055(6) -0.7311(5) 0.9930(8) Uiso 0.0062(9) 4 1 d ? ? ?
B2a B -0.1661(17) -0.0615(16) 0.5797(12) Uiso 0.003(2) 4 0.5 d ? ? ?
B1a B 0.0579(18) -0.1663(16) 0.4192(13) Uiso 0.004(2) 4 0.5 d ? ? ?
B2b B -0.227(2) -0.0876(17) 0.5555(14) Uiso 0.006(3) 4 0.5 d ? ? ?
B1b B 0.0886(19) -0.2241(19) 0.4423(14) Uiso 0.007(3) 4 0.5 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Cs1 Cs 0.0053(3) 0.0056(3) 0.0121(3) 0.00035(19) 0 0
Cs2 Cs 0.0106(4) 0.0092(4) 0.0050(3) 0.0006(3) 0 0
Ge1 Ge 0.0062(7) 0.0042(6) 0.0020(6) 0.0002(5) 0 0

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

Wave vector code q_1
1 1
2 2

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
O5b 0.5 0.5
O5a 0 0.5
B2a 0.5728(9) 0.5
B1a -0.0478(9) 0.5
B2b 0.0989(10) 0.5
B1b 0.4305(10) 0.5

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

Modulation code Atom site label Displacement axis Wave vector code
Cs1x1 Cs1 x 1
Cs1y1 Cs1 y 1
Cs1z1 Cs1 z 1
Cs1x2 Cs1 x 2
Cs1y2 Cs1 y 2
Cs1z2 Cs1 z 2
Cs2x1 Cs2 x 1
Cs2y1 Cs2 y 1
Cs2z1 Cs2 z 1
Cs2x2 Cs2 x 2
Cs2y2 Cs2 y 2
Cs2z2 Cs2 z 2
Ge1x1 Ge1 x 1
Ge1y1 Ge1 y 1
Ge1z1 Ge1 z 1
Ge1x2 Ge1 x 2
Ge1y2 Ge1 y 2
Ge1z2 Ge1 z 2
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1
O4x2 O4 x 2
O4y2 O4 y 2
O4z2 O4 z 2
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 z 2
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Cs1x1 0 0.00636(14)
Cs1y1 0 -0.03334(12)
Cs1z1 0.02157(10) 0
Cs1x2 0 0.00066(16)
Cs1y2 0 0.00123(12)
Cs1z2 0.00108(10) 0
Cs2x1 0 0.01377(13)
Cs2y1 0 -0.00300(15)
Cs2z1 -0.00416(11) 0
Cs2x2 0 0.00036(15)
Cs2y2 0 0.00230(12)
Cs2z2 0.00031(10) 0
Ge1x1 0 -0.0187(2)
Ge1y1 0 -0.0084(2)
Ge1z1 0.00445(17) 0
Ge1x2 0 0.0013(2)
Ge1y2 0 -0.00156(19)
Ge1z2 0.00055(16) 0
O1x1 -0.0038(9) -0.0182(9)
O1y1 0.0054(8) -0.0125(8)
O1z1 0.0003(6) -0.0018(6)
O1x2 0.0033(11) 0.0017(11)
O1y2 -0.0005(9) -0.0002(9)
O1z2 0.0012(7) -0.0004(7)
O4x1 0.0099(9) 0.0017(9)
O4y1 0.0075(7) -0.0091(7)
O4z1 0.0104(6) 0.0113(6)
O4x2 0.0002(11) 0.0001(11)
O4y2 -0.0007(8) 0.0003(8)
O4z2 0.0010(6) -0.0006(6)
O2x1 -0.0082(9) -0.0022(9)
O2y1 0.0042(8) -0.0187(8)
O2z1 -0.0002(6) -0.0016(6)
O2x2 -0.0012(11) 0.0007(11)
O2y2 0.0008(8) -0.0005(8)
O2z2 0.0012(7) 0.0014(7)
O3x1 -0.0048(8) -0.0059(8)
O3y1 -0.0031(7) -0.0116(7)
O3z1 0.0100(6) 0.0014(6)
O3x2 -0.0011(11) -0.0018(10)
O3y2 -0.0009(8) 0.0005(8)
O3z2 0.0003(6) 0.0000(6)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
O5b x 1 0.004(3)
O5b y 1 0.019(3)
O5b z 1 0
O5b x 2 0
O5b y 2 0
O5b z 2 0.002(4)
O5b x 3 -0.002(9)
O5b y 3 -0.003(9)
O5b z 3 0
O5b x 4 0
O5b y 4 0
O5b z 4 0.011(12)
O5a x 1 -0.010(4)
O5a y 1 -0.015(3)
O5a z 1 0
O5a x 2 0
O5a y 2 0
O5a z 2 0.006(4)
O5a x 3 -0.006(11)
O5a y 3 -0.008(8)
O5a z 3 0
O5a x 4 0
O5a y 4 0
O5a z 4 0.005(15)
B2a x 1 0.004(3)
B2a y 1 0.015(2)
B2a z 1 0.0000(18)
B2a x 2 -0.006(4)
B2a y 2 -0.003(3)
B2a z 2 0.005(3)
B2a x 3 0.001(6)
B2a y 3 -0.004(5)
B2a z 3 0.001(4)
B2a x 4 0.007(8)
B2a y 4 0.000(6)
B2a z 4 0.003(5)
B1a x 1 -0.008(3)
B1a y 1 -0.013(2)
B1a z 1 0.000(2)
B1a x 2 0.008(4)
B1a y 2 -0.003(4)
B1a z 2 -0.002(3)
B1a x 3 0.004(6)
B1a y 3 -0.001(5)
B1a z 3 0.000(5)
B1a x 4 -0.001(9)
B1a y 4 -0.002(7)
B1a z 4 0.006(7)
B2b x 1 -0.010(4)
B2b y 1 -0.015(3)
B2b z 1 -0.001(3)
B2b x 2 0.004(8)
B2b y 2 0.004(5)
B2b z 2 -0.004(5)
B2b x 3 0.007(11)
B2b y 3 0.002(6)
B2b z 3 0.004(8)
B2b x 4 0.01(3)
B2b y 4 0.007(10)
B2b z 4 0.004(19)
B1b x 1 0.004(3)
B1b y 1 0.014(3)
B1b z 1 0.002(2)
B1b x 2 0.000(5)
B1b y 2 0.003(9)
B1b z 2 0.005(6)
B1b x 3 0.000(7)
B1b y 3 0.002(10)
B1b z 3 -0.004(7)
B1b x 4 -0.004(15)
B1b y 4 0.01(4)
B1b z 4 0.00(2)

Cs2SiB4O9

Chemical data


Structural Formula Sum: B4 Cs2 O9 Si1 [ Help ]

Formula weight: 481.1 Da [ Help ]

Crystallographic data and experimental details


Crystal system: monoclinic [ Help ]

Superspace group name: I2(αβ0)0 [ 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 x1+1/2,x2+1/2,x3+1/2,x4
4 -x1+1/2,-x2+1/2,x3+1/2,-x4

a: 6.7489(10) Å [ Help ]

b: 6.7479(13) Å [ Help ]

c: 9.8894(13) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90.029(14) ° [ Help ]

Volume: 450.37(12) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 -0.478500 0.175300 0.000000

Z: 2 [ Help ]

Cell determination reflection Nb.: 2986 [ Help ]

θ(min) for cell determination: 3.53 ° [ Help ]

θ(max) for cell determination: 28.81 ° [ Help ]

Cell measurement temperature: 180.01(10) K [ Help ]

μ: 8.255 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: CrysAlisPro, Agilent Technologies, Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET) (compiled Aug 13 2014,18:06:01) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.93 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details


Total nb. of reflections: 4933 [ Help ]

Nb. of observed reflections: 3155 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0362 [ Help ]

wR(obs): 0.0385 [ Help ]

R(all): 0.0651 [ Help ]

wR(all): 0.0474 [ Help ]

S(all): 1.25 [ Help ]

S(obs): 1.28 [ Help ]

Nb. of reflections: 4933 [ Help ]

Nb. of parameters: 178 [ Help ]

Number of restraints: 14 [ Help ]

Number of constraints: 6 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0368 [ Help ]

Δ/σ(mean): 0.0052 [ Help ]

Δρ(max): 2.57 e_Å-3 [ Help ]

Δρ(min): -2.47 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Absolute structure remarks: 2223 of Friedel pairs used in the refinement [ 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
Cs1 Cs 0 0 0.00139(7) Uani 0.01290(14) 2 1 d ? ? ?
Cs2 Cs -0.5 0 0.24894(8) Uani 0.0196(3) 2 1 d ? ? ?
Si1 Si 0 -0.5 0.2467(5) Uani 0.0043(8) 2 1 d ? ? ?
O5b O 0 0 0.6640(10) Uiso 0.0065(8) 2 0.5 d ? ? ?
O5a O 0 0 0.3347(10) Uiso 0.0065(8) 2 0.5 d ? ? ?
O1 O -0.8470(8) -0.6289(8) 0.1598(6) Uiso 0.0091(12) 4 1 d ? ? ?
O4 O -0.7229(7) -0.3871(7) 0.0051(6) Uiso 0.0099(10) 4 1 d ? ? ?
O2 O -0.3705(8) -0.8463(7) 0.8405(6) Uiso 0.0063(11) 4 1 d ? ? ?
O3 O -0.6143(8) -0.7262(7) 0.9957(6) Uiso 0.0106(10) 4 1 d ? ? ?
B2a B -0.1696(15) -0.0558(14) 0.5840(10) Uiso 0.009(2) 4 0.5 d ? ? ?
B1a B 0.0527(14) -0.1691(14) 0.4188(10) Uiso 0.0075(19) 4 0.5 d ? ? ?
B2b B -0.2264(14) -0.0773(13) 0.5584(9) Uiso 0.0066(18) 4 0.5 d ? ? ?
B1b B 0.0789(15) -0.2286(16) 0.4439(10) Uiso 0.010(2) 4 0.5 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Cs1 Cs 0.0093(3) 0.0109(2) 0.0185(2) -0.0001(2) 0 0
Cs2 Cs 0.0237(6) 0.0227(5) 0.01224(17) 0.0017(5) 0 0
Si1 Si 0.0031(15) 0.0081(16) 0.0018(6) -0.0049(15) 0 0

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

Wave vector code q_1
1 1
2 2

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
O5b 0.5 0.5
O5a 0 0.5
B2a 0.5714(8) 0.5
B1a -0.0549(7) 0.5
B2b 0.0948(7) 0.5
B1b 0.4222(8) 0.5

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

Modulation code Atom site label Displacement axis Wave vector code
Cs1x1 Cs1 x 1
Cs1y1 Cs1 y 1
Cs1z1 Cs1 z 1
Cs1x2 Cs1 x 2
Cs1y2 Cs1 y 2
Cs1z2 Cs1 z 2
Cs2x1 Cs2 x 1
Cs2y1 Cs2 y 1
Cs2z1 Cs2 z 1
Cs2x2 Cs2 x 2
Cs2y2 Cs2 y 2
Cs2z2 Cs2 z 2
Si1x1 Si1 x 1
Si1y1 Si1 y 1
Si1z1 Si1 z 1
Si1x2 Si1 x 2
Si1y2 Si1 y 2
Si1z2 Si1 z 2
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1
O4x2 O4 x 2
O4y2 O4 y 2
O4z2 O4 z 2
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 z 2
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Cs1x1 0 0.00585(12)
Cs1y1 0 -0.02809(15)
Cs1z1 0.02111(9) 0
Cs1x2 0 -0.00191(12)
Cs1y2 0 -0.00068(10)
Cs1z2 0.00164(7) 0
Cs2x1 0 0.00754(10)
Cs2y1 0 0.00272(12)
Cs2z1 -0.00697(8) 0
Cs2x2 0 0.00225(14)
Cs2y2 0 0.00075(11)
Cs2z2 0.00006(7) 0
Si1x1 0 -0.0166(4)
Si1y1 0 -0.0077(5)
Si1z1 0.0032(3) 0
Si1x2 0 0.0008(5)
Si1y2 0 -0.0032(4)
Si1z2 0.0014(3) 0
O1x1 -0.0048(6) -0.0170(6)
O1y1 0.0030(6) -0.0105(6)
O1z1 -0.0008(4) -0.0025(4)
O1x2 0.0022(8) -0.0002(8)
O1y2 -0.0001(7) -0.0005(7)
O1z2 0.0014(5) -0.0002(5)
O4x1 0.0089(6) 0.0003(6)
O4y1 0.0040(5) -0.0050(5)
O4z1 0.0081(3) 0.0112(4)
O4x2 0.0008(9) 0.0028(9)
O4y2 -0.0001(6) -0.0004(6)
O4z2 0.0015(5) 0.0000(5)
O2x1 -0.0081(6) -0.0013(6)
O2y1 0.0040(5) -0.0122(6)
O2z1 -0.0008(3) -0.0022(3)
O2x2 -0.0025(9) 0.0005(9)
O2y2 0.0000(7) -0.0008(7)
O2z2 0.0001(5) 0.0006(5)
O3x1 -0.0039(6) -0.0065(6)
O3y1 -0.0020(5) -0.0062(5)
O3z1 0.0097(4) -0.0002(3)
O3x2 0.0009(8) -0.0020(8)
O3y2 -0.0012(7) -0.0016(7)
O3z2 -0.0003(5) -0.0001(5)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
O5b x 1 0.004(2)
O5b y 1 0.013(3)
O5b z 1 0
O5b x 2 0
O5b y 2 0
O5b z 2 0.000(3)
O5b x 3 0.000(7)
O5b y 3 0.003(7)
O5b z 3 0
O5b x 4 0
O5b y 4 0
O5b z 4 -0.002(15)
O5a x 1 -0.008(2)
O5a y 1 -0.008(3)
O5a z 1 0
O5a x 2 0
O5a y 2 0
O5a z 2 0.000(4)
O5a x 3 0.010(10)
O5a y 3 0.000(8)
O5a z 3 0
O5a x 4 0
O5a y 4 0
O5a z 4 0.000(17)
B2a x 1 0.002(2)
B2a y 1 0.009(2)
B2a z 1 0.0008(14)
B2a x 2 -0.005(3)
B2a y 2 0.002(3)
B2a z 2 0.005(2)
B2a x 3 0.002(5)
B2a y 3 -0.001(4)
B2a z 3 0.000(3)
B2a x 4 0.000(9)
B2a y 4 -0.004(6)
B2a z 4 0.000(5)
B1a x 1 -0.010(2)
B1a y 1 -0.0088(19)
B1a z 1 -0.0021(15)
B1a x 2 0.007(4)
B1a y 2 -0.001(3)
B1a z 2 0.001(3)
B1a x 3 0.004(5)
B1a y 3 0.000(5)
B1a z 3 0.000(4)
B1a x 4 -0.002(9)
B1a y 4 0.003(7)
B1a z 4 0.003(7)
B2b x 1 -0.009(2)
B2b y 1 -0.0089(12)
B2b z 1 -0.0014(14)
B2b x 2 0.006(5)
B2b y 2 0.006(2)
B2b z 2 -0.001(3)
B2b x 3 -0.007(7)
B2b y 3 -0.001(3)
B2b z 3 -0.005(5)
B2b x 4 0.001(19)
B2b y 4 0.001(5)
B2b z 4 0.002(12)
B1b x 1 0.006(2)
B1b y 1 0.007(2)
B1b z 1 0.0018(16)
B1b x 2 -0.003(3)
B1b y 2 -0.006(7)
B1b z 2 0.007(4)
B1b x 3 -0.001(5)
B1b y 3 -0.002(8)
B1b z 3 0.003(5)
B1b x 4 -0.002(10)
B1b y 4 0.01(3)
B1b z 4 -0.005(16)