BaGe6 and BaGe6-x: Incommensurately Ordered Vacancies as Electron Traps

Authors:

Akselrud, Lev; Wosylus, Aron; Castillo, Rodrigo; Aydemir, Unut; Prots, Yurii; Schnelle, Walter; Grin, Yuri; Schwarz, Ulrich

Journal:

Inorganic Chemistry 53 12699-12705 (2014)

DOI:

https://dx.doi.org/10.1021/ic5021065

B-IncStrDB ID: xhPRd0zaxOu Entry date: 2021-12-22 Last revision: 2022-02-15

BaGe5_x

Chemical data


Structural Formula Sum: Ba2 Ge11.01 [ Help ]

Formula weight: 1073.896 Da [ Help ]

Crystallographic data and experimental details


Symmetry operations of the superspace group: [ Help ]

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

Crystal system: orthorhombic [ Help ]

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

a: 4.2251(2) Å [ Help ]

b: 11.2208(5) Å [ Help ]

c: 12.7992(5) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 606.79(8) Å3 [ Help ]

Z: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.5700(1) 0.0 0.0

Minimum transmission factor: 0.461 [ Help ]

Maximum transmission factor: 1.000 [ Help ]

Absorption correction remarks: Blessing, R. H. (1995) Acta Cryst. A51, 33-38 [ Help ]

Absorption correction type: multi-scan [ Help ]

μ: 33.143 mm-1 [ Help ]

Cell measurement temperature: 295.0 K [ Help ]

Cell determination reflection Nb.: 4322 [ Help ]

θ(min) for cell determination: 1.9 ° [ Help ]

θ(max) for cell determination: 33.5 ° [ Help ]

Refinement details


Total nb. of reflections: 586 [ Help ]

Nb. of observed reflections: 586 [ Help ]

Intense reflections threshold: [ Help ]

Refinement based on: Inet [ Help ]

Matrix type used for the least-squares: fullcycle [ Help ]

Weighting scheme: calc [ Help ]

Weighting scheme remarks: 0.9998Log(Fo)4 [ Help ]

Extinction method: none [ Help ]

Nb. of reflections: 991 [ Help ]

Nb. of parameters: 79 [ Help ]

R(obs): 0.0342 [ Help ]

wR(all): 0.0000 [ Help ]

S(all): 1.01 [ Help ]

Refinement remarks: WARNING: The published thermal displacement parameters have been converted to U,s. [ Help ]

Structural Information


Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy
Ba Ba 0 0.28989(5) 0.25 Uani 1.03(2) 4 0.013
Ge1 Ge 0 0.2476(5) 0.5362(3) Uani 0.80(4) 8 0.00782(5)
Ge2 Ge 0 0.57333(6) 0.35025(5) Uani 0.81(2) 8 0.013
Ge3 Ge 0 0.03511(6) 0.59242(5) Uani 0.71(4) 8 0.013
Ge4 Ge 0.186(2) 0.2556(7) 0.5131(5) Uani 1.0(3) 16 0.00085(3)

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23
Ba 0.0117(3) 0.0144(3) 0.0130(4) 0 0 0
Ge1 0.010(1) 0.0123(6) 0.0324(5) 0 0 -0.0001(3)
Ge2 0.0100(4) 0.0109(6) 0.0100(3) 0 0 0.0003(3)
Ge3 0.006(1) 0.0118(9) 0.0090(6) 0 0 0.0016(3)
Ge4 0.014(9) 0.013(4) 0.010(5) -0.001(3) -0.001(3) -0.003(3)

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 0.57000 0.00000 0.00000
2 1.14000 0.00000 0.00000
3 1.71000 0.00000 0.00000

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

Modulation code Atom site label Displacement axis Wave vector code
Baz1 Ba z 1
Bax2 Ba x 2
Bay2 Ba y 2
Baz3 Ba z 3
Ge1x1 Ge1 x 1
Ge1y1 Ge1 y 1
Ge1z1 Ge1 z 1
Ge1x2 Ge1 x 2
Ge1y2 Ge1 y 2
Ge1z2 Ge1 z 2
Ge1x3 Ge1 x 3
Ge1y3 Ge1 y 3
Ge2x1 Ge2 x 1
Ge2y1 Ge2 y 1
Ge2z1 Ge2 z 1
Ge2x2 Ge2 x 2
Ge2y2 Ge2 y 2
Ge2z2 Ge2 z 2
Ge2x3 Ge2 x 3
Ge2y3 Ge2 y 3
Ge2z3 Ge2 z 3
Ge3x1 Ge3 x 1
Ge3y1 Ge3 y 1
Ge3z1 Ge3 z 1
Ge3x2 Ge3 x 2
Ge3y2 Ge3 y 2
Ge3z2 Ge3 z 2
Ge3x3 Ge3 x 3
Ge3y3 Ge3 y 3
Ge3z3 Ge3 z 3
Ge4x1 Ge4 x 1
Ge4y1 Ge4 y 1
Ge4z1 Ge4 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Baz1 0 0.00925(9)
Bax2 0 -0.0010(5)
Bay2 -0.0012(3) 0
Baz3 0 0.0036(7)
Ge1x1 0.0903(9) 0
Ge1y1 0 0.0047(9)
Ge1z1 0 -0.0099(6)
Ge1x2 0 -0.000(2)
Ge1y2 0.0037(7) 0
Ge1z2 -0.0115(4) 0
Ge1x3 0.039(2) 0
Ge1y3 0 0.001(1)
Ge2x1 0.0022(4) 0
Ge2y1 0 0.0060(2)
Ge2z1 0 0.0032(1)
Ge2x2 0 -0.0046(6)
Ge2y2 -0.0021(3) 0
Ge2z2 -0.0002(4) 0
Ge2x3 0.005(4) 0
Ge2y3 0 -0.0054(9)
Ge2z3 0 0.000(2)
Ge3x1 0.0030(4) 0
Ge3y1 0 -0.0058(2)
Ge3z1 0 -0.0015(1)
Ge3x2 0 -0.0019(6)
Ge3y2 -0.0018(4) 0
Ge3z2 -0.0005(3) 0
Ge3x3 0.022(3) 0
Ge3y3 0 -0.0077(9)
Ge3z3 0 0.0050(8)
Ge4x1 0.007(6) 0.007(7)
Ge4y1 -0.006(3) -0.007(2)
Ge4z1 0.003(3) -0.003(2)

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Ge1o1 Ge1 1
Ge1o2 Ge1 2
Ge1o3 Ge1 3
Ge4o1 Ge4 1
Ge4o2 Ge4 2
Ge4o3 Ge4 3

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ge1o1 0 0.070(5)
Ge1o2 0.335(7) 0
Ge1o3 0 -0.01(2)
Ge4o1 0.099(2) -0.038(3)
Ge4o2 0.030(3) -0.026(2)
Ge4o3 0.000(2) 0

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Ge1 0.490 0.360

BaGe55com

Chemical data


Structural Formula Sum: Ba14 Ge78 [ Help ]

Formula weight: 7584.64 Da [ Help ]

Crystallographic data and experimental details


Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -x,y,z
3 x,-y,1/2+z
4 -x,-y,1/2+z
5 1/2+x,1/2+y,z
6 1/2-x,1/2+y,z
7 1/2+x,1/2-y,1/2+z
8 1/2-x,1/2-y,1/2+z

Crystal system: orthorhombic [ Help ]

Space group name (H-M): C m c 21 [ Help ]

a: 29.5729(8) Å [ Help ]

b: 11.2228(3) Å [ Help ]

c: 12.7992(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 4247.9(4) Å3 [ Help ]

Z: 2 [ Help ]

Minimum transmission factor: 0.461 [ Help ]

Maximum transmission factor: 1.000 [ Help ]

Absorption correction remarks: Blessing, R. H. (1995) Acta Cryst. A51, 33-38 [ Help ]

Absorption correction type: multi-scan [ Help ]

μ: 33.463 mm-1 [ Help ]

Cell measurement temperature: 295.0 K [ Help ]

Cell determination reflection Nb.: 4322 [ Help ]

θ(min) for cell determination: 1.9 ° [ Help ]

θ(max) for cell determination: 33.5 ° [ Help ]

Refinement details


Total nb. of reflections: 4416 [ Help ]

Nb. of observed reflections: 4416 [ Help ]

Intense reflections threshold: 5.9σ [ Help ]

Refinement based on: Inet [ Help ]

Matrix type used for the least-squares: fullcycle [ Help ]

Weighting scheme: calc [ Help ]

Weighting scheme remarks: 0.0593Log(Fo)4 [ Help ]

Extinction method: none [ Help ]

Nb. of reflections: 4416 [ Help ]

Nb. of parameters: 217 [ Help ]

R(obs): 0.0386 [ Help ]

wR(all): 0.0410 [ Help ]

S(all): 1.01 [ Help ]

Refinement remarks: WARNING: The published thermal displacement parameters have been converted to U,s. [ Help ]

Structural Information


Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type _atom_site_B_iso_or_equiv Symmetry multiplicity Occupancy
Ba1 Ba 0 0.2858(4) 0.25000 Uani 1.05(13) 4 0.013
Ba2 Ba 0.4295(1) 0.2852(2) 0.2589(5) Uani 1.11(8) 8 0.013
Ba3 Ba 0.1416(1) 0.2915(3) 0.2689(4) Uani 0.84(7) 8 0.013
Ba4 Ba 0.28665(8) 0.2943(3) 0.2550(6) Uani 0.85(9) 8 0.013
Ge1 Ge 0 0.5638(7) 0.3565(7) Uani 0.5(2) 4 0.013
Ge2 Ge 0 0.0348(9) 0.9145(8) Uani 1.1(3) 4 0.013
Ge3 Ge 0 0.5815(8) 0.1536(8) Uani 0.7(3) 4 0.013
Ge4 Ge 0 0.2452(8) 0.9739(7) Uani 0.8(2) 4 0.013
Ge5 Ge 0 0.0490(8) 0.6033(8) Uani 1.2(3) 4 0.013
Ge6 Ge 0.0723(2) 0.0672(5) 0.3590(6) Uani 0.9(2) 8 0.013
Ge7 Ge 0.3551(2) 0.0820(5) 0.3618(6) Uani 0.83(14) 8 0.013
Ge8 Ge 0.3548(1) 0.2508(4) 0.0415(5) Uani 0.86(11) 8 0.013
Ge9 Ge 0.4283(3) 0.0324(8) 0.9135(7) Uani 1.6(2) 8 0.013
Ge10 Ge 0.2135(3) 0.0768(5) 0.3553(6) Uani 1.4(2) 8 0.013
Ge11 Ge 0.0714(3) 0.0743(6) 0.1556(6) Uani 0.8(2) 8 0.013
Ge12 Ge 0.1434(3) 0.0273(5) 0.6001(6) Uani 1.00(13) 8 0.013
Ge13 Ge 0.4275(2) 0.0396(5) 0.6005(6) Uani 0.78(15) 8 0.013
Ge14 Ge 0.1428(4) 0.0434(6) 0.9160(6) Uani 1.03(14) 8 0.013
Ge15 Ge 0.2859(2) 0.0296(6) 0.9207(6) Uani 0.5(2) 8 0.013
Ge16 Ge 0.3568(3) 0.0681(5) 0.1622(5) Uani 0.54(13) 8 0.013
Ge17 Ge 0.2147(2) 0.0732(7) 0.1581(7) Uani 1.1(2) 8 0.013
Ge18 Ge 0.2859(2) 0.0331(5) 0.6024(6) Uani 0.57(15) 8 0.013
Ge19 Ge 0.2772(2) 0.2576(5) 0.9776(6) Uani 1.4(2) 8 0.013
Ge20 Ge 0.0865(2) 0.2569(4) 0.0384(6) Uani 1.38(13) 8 0.013
Ge21 Ge 0.1902(1) 0.2454(4) 0.0264(5) Uani 1.30(11) 8 0.013
Ge22 Ge 0.4435(2) 0.2516(6) 0.9809(6) Uani 1.24(14) 8 0.013

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23
Ba1 0.010(3) 0.014(3) 0.015(3) 0 0 -0.001(3)
Ba2 0.011(3) 0.013(1) 0.017(1) 0.002(2) -0.002(2) -0.002(2)
Ba3 0.010(1) 0.011(2) 0.011(1) 0.001(3) 0.003(2) -0.000(1)
Ba4 0.010(3) 0.012(2) 0.010(2) -0.001(1) 0.001(2) 0.001(1)
Ge1 0.006(5) 0.005(5) 0.008(4) 0 0 0.000(4)
Ge2 0.010(5) 0.015(5) 0.019(5) 0 0 -0.000(4)
Ge3 0.016(6) 0.004(4) 0.006(4) 0 0 0.001(4)
Ge4 0.003(4) 0.016(5) 0.010(4) 0 0 0.003(4)
Ge5 0.019(5) 0.011(5) 0.015(5) 0 0 0.004(4)
Ge6 0.014(4) 0.009(4) 0.010(4) 0.004(4) -0.000(4) -0.000(4)
Ge7 0.005(4) 0.014(3) 0.011(3) 0.006(3) 0.001(3) 0.001(3)
Ge8 0.016(3) 0.006(3) 0.009(3) 0.000(3) 0.001(1) -0.000(3)
Ge9 0.016(4) 0.028(4) 0.016(4) -0.003(4) 0.003(3) 0.001(3)
Ge10 0.018(4) 0.019(4) 0.015(4) 0.003(4) 0.001(3) -0.000(3)
Ge11 0.010(4) 0.008(4) 0.011(3) -0.004(3) -0.004(3) -0.003(3)
Ge12 0.009(3) 0.016(3) 0.013(3) -0.000(4) -0.000(4) -0.001(2)
Ge13 0.011(4) 0.016(4) 0.011(3) -0.003(4) -0.003(4) 0.001(3)
Ge15 0.010(4) 0.003(4) 0.005(3) -0.001(3) 0.000(3) -0.001(3)
Ge16 0.008(3) 0.008(3) 0.006(3) 0.003(3) 0.005(3) 0.002(2)
Ge17 0.005(5) 0.024(5) 0.014(4) -0.005(3) -0.004(3) 0.000(4)
Ge18 0.006(4) 0.008(4) 0.008(3) 0.001(3) -0.001(3) 0.000(3)
Ge19 0.024(4) 0.015(4) 0.014(3) 0.001(4) -0.006(3) 0.001(3)
Ge20 0.023(3) 0.014(3) 0.016(3) -0.001(3) -0.006(3) 0.000(3)
Ge21 0.030(3) 0.010(3) 0.009(2) 0.001(3) 0.009(2) 0.001(2)
Ge22 0.020(3) 0.011(4) 0.015(3) 0.001(3) -0.001(3) -0.001(3)

BaGe6

Chemical data


Structural Formula Sum: Ba1 Ge6 [ Help ]

Formula weight: 572.9 Da [ Help ]

Crystallographic data and experimental details


Crystal system: orthorhombic [ Help ]

Space group name (H-M): C m c m [ Help ]

Space group nb.: 63 [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -x,y,z
3 x,-y,1/2+z
4 -x,-y,1/2+z
5 -x,-y,-z
6 x,-y,-z
7 -x,y,1/2-z
8 x,y,1/2-z
9 1/2+x,1/2+y,z
10 1/2-x,1/2+y,z
11 1/2+x,1/2-y,1/2+z
12 1/2-x,1/2-y,1/2+z
13 1/2-x,1/2-y,-z
14 1/2+x,1/2-y,-z
15 1/2-x,1/2+y,1/2-z
16 1/2+x,1/2+y,1/2-z

a: 4.7690(7) Å [ Help ]

b: 10.777(2) Å [ Help ]

c: 12.385(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 636.6(2) Å3 [ Help ]

Z: 4 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 78.845 mm-1 [ Help ]

Refinement details


R(obs): 0.0286 [ Help ]

wR(obs): 0.0477 [ Help ]

R(all): 0.0289 [ Help ]

wR(all): 0.0477 [ Help ]

S(all): 3.45 [ Help ]

Nb. of parameters: 24 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0428 [ Help ]

Δ/σ(mean): 0.0097 [ Help ]

Δρ(max): 1.13 e_Å-3 [ Help ]

Δρ(min): -1.12 e_Å-3 [ 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
Ba1 Ba 0 0.2696(18) 0.25 Uiso 0.014(5) 4 1 d . . .
Ge1 Ge 0 0.249(3) 0.5357(13) Uiso 0.017(3) 8 1 d . . .
Ge2 Ge 0 0.446(2) 0.6440(16) Uiso 0.017(3) 8 1 d . . .
Ge3 Ge 0 0.0234(18) 0.598(2) Uiso 0.017(3) 8 1 d . . .

BaGe5

Chemical data


Formula moiety: Ge5, Ba [ Help ]

Structural Formula Sum: Ba Ge5 [ Help ]

Formula weight: 500.38 Da [ Help ]

Crystallographic data and experimental details


Crystal system: orthorhombic [ Help ]

Space group name (H-M): I m m a [ Help ]

Space group name (Hall): -I 2b 2 [ Help ]

Space group nb.: 74 [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -x,-y+1/2,z
3 -x,y+1/2,-z
4 x,-y,-z
5 -x,-y,-z
6 x,y+1/2,-z
7 x,-y+1/2,z
8 -x,y,z
9 x+1/2,y+1/2,z+1/2
10 -x+1/2,-y,z+1/2
11 -x+1/2,y,-z+1/2
12 x+1/2,-y+1/2,-z+1/2
13 -x+1/2,-y+1/2,-z+1/2
14 x+1/2,y,-z+1/2
15 x+1/2,-y,z+1/2
16 -x+1/2,y+1/2,z+1/2

a: 8.3421(8) Å [ Help ]

b: 4.8728(5) Å [ Help ]

c: 13.7202(9) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 557.72(9) Å3 [ Help ]

Z: 4 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 8.419 mm-1 [ Help ]

Refinement details


R(obs): 0.0126 [ Help ]

wR(obs): 0.0186 [ Help ]

R(all): 0.0126 [ Help ]

wR(all): 0.0186 [ Help ]

S(all): 0.76 [ Help ]

Nb. of parameters: 12 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0065 [ Help ]

Δ/σ(mean): 0.0009 [ Help ]

Δρ(max): 0.53 e_Å-3 [ Help ]

Δρ(min): -0.44 e_Å-3 [ 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
Ba1 Ba 0 0.25 0.7826(3) Uiso 0.0104(10) 4 1 d . . .
Ge1 Ge 0 0.25 0.0397(6) Uiso 0.010(2) 4 1 d . . .
Ge2 Ge 0.1534(5) 0.25 0.5576(3) Uiso 0.0097(14) 8 1 d . . .
Ge3 Ge 0.2754(6) 0.25 0.1274(3) Uiso 0.0086(14) 8 1 d . . .