B-IncStrDB

Vacancy-ordering effects in AlB₂-type ErGe_2-x (0.4 < x ≤ 0.5)

Authors:

Christensen, Jeppe; Lidin, Sven; Malaman, Bernard; Venturini, Gerard

Journal:

Acta Crystallographica, Section B 64 272-280 (2008)

DOI:

https://doi.org/10.1107/S0108768108005119

B-IncStrDB ID: GOAMfvpRv7i Entry date: 2022-01-24 Last revision: 2022-01-24

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I

Chemical data

Structural Formula Sum: Er2 Ge3.188 [ Help ]

Formula weight: 565.9 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,1/2-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2+x4
5	1/2+x1,1/2+x2,x3,1/2+x4
6	1/2-x1,1/2+x2,-x3,-x4
7	1/2-x1,1/2-x2,-x3,1/2-x4
8	1/2+x1,1/2-x2,x3,x4

a: 3.9208(2) Å [ Help ]

b: 6.7547(4) Å [ Help ]

c: 4.0945(2) Å [ Help ]

α: 90 ° [ Help ]

β: 89.811(4) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 108.439(13) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.40577(17)	0.00000	0.2205(3)

μ: 91.766 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

Refinement remarks: Impurities present are ErGe1.83 and Er2O3 Parameters for these were not refined. [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0588 [ Help ]

R(obs): 0.0566 [ Help ]

wR(obs): 0.0304 [ Help ]

wR(all): 0.0304 [ Help ]

S(all): 3.99 [ Help ]

Nb. of parameters: 51 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0495 [ Help ]

Δ/σ(mean): 0.0040 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Ge	Ge	0.5	0.180(3)	0.5	0.0149(19)	Uiso	d	.	1	.	.
Er	Er	0	0	0	0.0069(11)	Uiso	d	.	1	.	.

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

Wave vector code	q_x	q_z
1	0.40576	0.22052
2	0.81153	0.44104

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Gex1	Ge	x	1
Gey1	Ge	y	1
Gez1	Ge	z	1
Gex2	Ge	x	2
Gey2	Ge	y	2
Gez2	Ge	z	2
Erx1	Er	x	1
Ery1	Er	y	1
Erz1	Er	z	1
Erx2	Er	x	2
Ery2	Er	y	2
Erz2	Er	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Gex1	-0.082(2)	0
Gey1	0	-0.051(5)
Gez1	-0.005(3)	0
Gex2	0	0.054(4)
Gey2	0.011(5)	0
Gez2	0	-0.014(5)
Erx1	0	0
Ery1	0	0.0199(10)
Erz1	0	0
Erx2	0	-0.011(3)
Ery2	0	0
Erz2	0	0.017(3)

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Ge	0.25	0.7971

II

Chemical data

Structural Formula Sum: Er2 Ge3.188 [ Help ]

Formula weight: 565.94 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,1/2-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2+x4
5	1/2+x1,1/2+x2,x3,1/2+x4
6	1/2-x1,1/2+x2,-x3,-x4
7	1/2-x1,1/2-x2,-x3,1/2-x4
8	1/2+x1,1/2-x2,x3,x4

a: 3.9206(2) Å [ Help ]

b: 6.7543(4) Å [ Help ]

c: 4.09383(19) Å [ Help ]

α: 90 ° [ Help ]

β: 89.813(4) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 108.409(13) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.40612(16)	0.00000	0.2206(2)

μ: 91.791 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

Refinement remarks: Impurities present are ErGe1.83 and Er2O3 Parameters for these were not refined. [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0540 [ Help ]

R(obs): 0.0531 [ Help ]

wR(obs): 0.0304 [ Help ]

wR(all): 0.0304 [ Help ]

S(all): 3.85 [ Help ]

Nb. of parameters: 51 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0498 [ Help ]

Δ/σ(mean): 0.0046 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Ge	Ge	0.5	0.181(2)	0.5	0.0122(18)	Uiso	d	.	1	.	.
Er	Er	0	0	0	0.0066(10)	Uiso	d	.	1	.	.

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

Wave vector code	q_x	q_z
1	0.40612	0.22059
2	0.81223	0.44117

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Gex1	Ge	x	1
Gey1	Ge	y	1
Gez1	Ge	z	1
Gex2	Ge	x	2
Gey2	Ge	y	2
Gez2	Ge	z	2
Erx1	Er	x	1
Ery1	Er	y	1
Erz1	Er	z	1
Erx2	Er	x	2
Ery2	Er	y	2
Erz2	Er	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Gex1	-0.084(2)	0
Gey1	0	-0.051(5)
Gez1	-0.008(3)	0
Gex2	0	0.058(4)
Gey2	0.010(4)	0
Gez2	0	-0.017(5)
Erx1	0	0
Ery1	0	0.0206(9)
Erz1	0	0
Erx2	0	-0.010(3)
Ery2	0	0
Erz2	0	0.016(3)

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Ge	0.25	0.7969

III

Chemical data

Structural Formula Sum: Er2 Ge3.186 [ Help ]

Formula weight: 565.79 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,1/2-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2+x4
5	1/2+x1,1/2+x2,x3,1/2+x4
6	1/2-x1,1/2+x2,-x3,-x4
7	1/2-x1,1/2-x2,-x3,1/2-x4
8	1/2+x1,1/2-x2,x3,x4

a: 3.92030(18) Å [ Help ]

b: 6.7532(3) Å [ Help ]

c: 4.09406(16) Å [ Help ]

α: 90 ° [ Help ]

β: 89.813(3) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 108.389(11) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.40712(13)	0.00000	0.22091(19)

μ: 91.793 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

Refinement remarks: Impurities present are ErGe1.83 and Er2O3 Parameters for these were not refined. [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0481 [ Help ]

R(obs): 0.0477 [ Help ]

wR(obs): 0.0269 [ Help ]

wR(all): 0.0269 [ Help ]

S(all): 3.88 [ Help ]

Nb. of parameters: 51 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0465 [ Help ]

Δ/σ(mean): 0.0073 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Ge	Ge	0.5	0.181(2)	0.5	0.0151(17)	Uiso	d	.	1	.	.
Er	Er	0	0	0	0.0080(10)	Uiso	d	.	1	.	.

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

Wave vector code	q_x	q_z
1	0.40712	0.22091
2	0.81425	0.44182

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Gex1	Ge	x	1
Gey1	Ge	y	1
Gez1	Ge	z	1
Gex2	Ge	x	2
Gey2	Ge	y	2
Gez2	Ge	z	2
Erx1	Er	x	1
Ery1	Er	y	1
Erz1	Er	z	1
Erx2	Er	x	2
Ery2	Er	y	2
Erz2	Er	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Gex1	-0.0844(19)	0
Gey1	0	-0.052(4)
Gez1	-0.008(3)	0
Gex2	0	0.053(4)
Gey2	0.010(4)	0
Gez2	0	-0.011(5)
Erx1	0	0
Ery1	0	0.0208(8)
Erz1	0	0
Erx2	0	-0.011(2)
Ery2	0	0
Erz2	0	0.018(3)

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Ge	0.25	0.7964

IV

Chemical data

Structural Formula Sum: Er2 Ge3.182 [ Help ]

Formula weight: 565.50 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,1/2-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2+x4
5	1/2+x1,1/2+x2,x3,1/2+x4
6	1/2-x1,1/2+x2,-x3,-x4
7	1/2-x1,1/2-x2,-x3,1/2-x4
8	1/2+x1,1/2-x2,x3,x4

a: 3.9198(2) Å [ Help ]

b: 6.7518(4) Å [ Help ]

c: 4.0941(2) Å [ Help ]

α: 90 ° [ Help ]

β: 89.813(4) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 108.354(13) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.40890(17)	0.00000	0.2214(2)

μ: 91.792 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

Refinement remarks: Impurities present are ErGe1.83 and Er2O3 Parameters for these were not refined. [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0625 [ Help ]

R(obs): 0.0612 [ Help ]

wR(obs): 0.0362 [ Help ]

wR(all): 0.0362 [ Help ]

S(all): 4.01 [ Help ]

Nb. of parameters: 51 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.4157 [ Help ]

Δ/σ(mean): 0.0320 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Ge	Ge	0.5	0.182(3)	0.5	0.015(2)	Uiso	d	.	1	.	.
Er	Er	0	0	0	0.0094(13)	Uiso	d	.	1	.	.

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

Wave vector code	q_x	q_z
1	0.40890	0.22142
2	0.81780	0.44285

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Gex1	Ge	x	1
Gey1	Ge	y	1
Gez1	Ge	z	1
Gex2	Ge	x	2
Gey2	Ge	y	2
Gez2	Ge	z	2
Erx1	Er	x	1
Ery1	Er	y	1
Erz1	Er	z	1
Erx2	Er	x	2
Ery2	Er	y	2
Erz2	Er	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Gex1	-0.085(3)	0
Gey1	0	-0.053(6)
Gez1	-0.010(4)	0
Gex2	0	0.053(5)
Gey2	0.010(5)	0
Gez2	0	-0.011(6)
Erx1	0	0
Ery1	0	0.0217(11)
Erz1	0	0
Erx2	0	-0.012(3)
Ery2	0	0
Erz2	0	0.016(3)

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Ge	0.25	0.7955

V

Chemical data

Structural Formula Sum: Er2 Ge3.171 [ Help ]

Formula weight: 564.70 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,1/2-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2+x4
5	1/2+x1,1/2+x2,x3,1/2+x4
6	1/2-x1,1/2+x2,-x3,-x4
7	1/2-x1,1/2-x2,-x3,1/2-x4
8	1/2+x1,1/2-x2,x3,x4

a: 3.9183(2) Å [ Help ]

b: 6.7475(4) Å [ Help ]

c: 4.0932(2) Å [ Help ]

α: 90 ° [ Help ]

β: 89.813(4) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 108.217(13) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.41484(17)	0.00000	0.2236(2)

μ: 91.825 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

Refinement remarks: Impurity present is Er2O3 Parameters for this were not refined. [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0621 [ Help ]

R(obs): 0.0594 [ Help ]

wR(obs): 0.0366 [ Help ]

wR(all): 0.0367 [ Help ]

S(all): 4.14 [ Help ]

Nb. of parameters: 41 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0921 [ Help ]

Δ/σ(mean): 0.0150 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Ge	Ge	0.5	0.178(3)	0.5	0.016(2)	Uiso	d	.	1	.	.
Er	Er	0	0	0	0.0098(13)	Uiso	d	.	1	.	.

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

Wave vector code	q_x	q_z
1	0.41484	0.22361
2	0.82967	0.44721

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Gex1	Ge	x	1
Gey1	Ge	y	1
Gez1	Ge	z	1
Gex2	Ge	x	2
Gey2	Ge	y	2
Gez2	Ge	z	2
Erx1	Er	x	1
Ery1	Er	y	1
Erz1	Er	z	1
Erx2	Er	x	2
Ery2	Er	y	2
Erz2	Er	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Gex1	-0.082(3)	0
Gey1	0	-0.048(6)
Gez1	-0.009(4)	0
Gex2	0	0.043(6)
Gey2	0.015(6)	0
Gez2	0	-0.007(6)
Erx1	0	0
Ery1	0	0.0221(12)
Erz1	0	0
Erx2	0	-0.013(3)
Ery2	0	0
Erz2	0	0.019(3)

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Ge	0.25	0.7926

VI

Chemical data

Structural Formula Sum: Er2 Ge3.14 [ Help ]

Formula weight: 562.45 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,1/2-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2+x4
5	1/2+x1,1/2+x2,x3,1/2+x4
6	1/2-x1,1/2+x2,-x3,-x4
7	1/2-x1,1/2-x2,-x3,1/2-x4
8	1/2+x1,1/2-x2,x3,x4

a: 3.9142(2) Å [ Help ]

b: 6.7363(4) Å [ Help ]

c: 4.0917(2) Å [ Help ]

α: 90 ° [ Help ]

β: 89.810(4) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 107.885(14) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.42980(16)	0.00000	0.2278(2)

μ: 91.872 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

Refinement remarks: Impurity present is Er2O3. Parameters for this were not refined. [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0615 [ Help ]

R(obs): 0.0544 [ Help ]

wR(obs): 0.0362 [ Help ]

wR(all): 0.0362 [ Help ]

S(all): 4.15 [ Help ]

Nb. of parameters: 42 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0499 [ Help ]

Δ/σ(mean): 0.0099 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Ge	Ge	0.5	0.176(4)	0.5	0.015(2)	Uiso	d	.	1	.	.
Er	Er	0	0	0	0.0079(14)	Uiso	d	.	1	.	.

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

Wave vector code	q_x	q_z
1	0.42980	0.22783
2	0.85961	0.45567

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Gex1	Ge	x	1
Gey1	Ge	y	1
Gez1	Ge	z	1
Gex2	Ge	x	2
Gey2	Ge	y	2
Gez2	Ge	z	2
Erx1	Er	x	1
Ery1	Er	y	1
Erz1	Er	z	1
Erx2	Er	x	2
Ery2	Er	y	2
Erz2	Er	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Gex1	-0.079(3)	0
Gey1	0	-0.044(7)
Gez1	-0.010(4)	0
Gex2	0	0.044(6)
Gey2	0.020(6)	0
Gez2	0	-0.006(6)
Erx1	0	0
Ery1	0	0.0216(12)
Erz1	0	0
Erx2	0	-0.016(3)
Ery2	0	0
Erz2	0	0.023(3)

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Ge	0.25	0.7851

VII

Chemical data

Structural Formula Sum: Er2 Ge3.125 [ Help ]

Formula weight: 561.36 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,1/2-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2+x4
5	1/2+x1,1/2+x2,x3,1/2+x4
6	1/2-x1,1/2+x2,-x3,-x4
7	1/2-x1,1/2-x2,-x3,1/2-x4
8	1/2+x1,1/2-x2,x3,x4

a: 3.9117(2) Å [ Help ]

b: 6.7296(3) Å [ Help ]

c: 4.09129(19) Å [ Help ]

α: 90 ° [ Help ]

β: 89.805(4) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 107.699(12) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.43766(14)	0.00000	0.23005(19)

μ: 91.917 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

Refinement remarks: Impurity present is Er2O3. Parameters for this were not refined. [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0623 [ Help ]

R(obs): 0.0579 [ Help ]

wR(obs): 0.0307 [ Help ]

wR(all): 0.0308 [ Help ]

S(all): 3.97 [ Help ]

Nb. of parameters: 37 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0457 [ Help ]

Δ/σ(mean): 0.0059 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Ge	Ge	0.5	0.170(3)	0.5	0.0172(19)	Uiso	d	.	1	.	.
Er	Er	0	0	0	0.0109(12)	Uiso	d	.	1	.	.

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

Wave vector code	q_x	q_z
1	0.43766	0.23005
2	0.87531	0.46010

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Gex1	Ge	x	1
Gey1	Ge	y	1
Gez1	Ge	z	1
Gex2	Ge	x	2
Gey2	Ge	y	2
Gez2	Ge	z	2
Erx1	Er	x	1
Ery1	Er	y	1
Erz1	Er	z	1
Erx2	Er	x	2
Ery2	Er	y	2
Erz2	Er	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Gex1	-0.077(2)	0
Gey1	0	-0.035(6)
Gez1	-0.006(3)	0
Gex2	0	0.043(5)
Gey2	0.027(5)	0
Gez2	0	-0.003(5)
Erx1	0	0
Ery1	0	0.0204(11)
Erz1	0	0
Erx2	0	-0.016(3)
Ery2	0	0
Erz2	0	0.025(3)

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Ge	0.25	0.7812

VIII

Chemical data

Structural Formula Sum: Er2 Ge3.122 [ Help ]

Formula weight: 561.15 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,1/2-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2+x4
5	1/2+x1,1/2+x2,x3,1/2+x4
6	1/2-x1,1/2+x2,-x3,-x4
7	1/2-x1,1/2-x2,-x3,1/2-x4
8	1/2+x1,1/2-x2,x3,x4

a: 3.9113(3) Å [ Help ]

b: 6.7290(5) Å [ Help ]

c: 4.0912(2) Å [ Help ]

α: 90 ° [ Help ]

β: 89.805(5) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 107.674(16) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.43886(17)	0.00000	0.2302(2)

μ: 91.915 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

Refinement remarks: Second phase present is Er2Ge3. Parameters for this were refined. Impurity present is Er2O3 Parameters for this were not refined. [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0611 [ Help ]

R(obs): 0.0558 [ Help ]

wR(obs): 0.0317 [ Help ]

wR(all): 0.0318 [ Help ]

S(all): 3.79 [ Help ]

Nb. of parameters: 36 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 8 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0486 [ Help ]

Δ/σ(mean): 0.0070 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Ge	Ge	0.5	0.167(3)	0.5	0.0139(16)	Uiso	d	.	1	.	.
Er	Er	0	0	0	0.0094(9)	Uiso	d	.	1	.	.

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

Wave vector code	q_x	q_z
1	0.43886	0.23024
2	0.87771	0.46048

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Gex1	Ge	x	1
Gey1	Ge	y	1
Gez1	Ge	z	1
Gex2	Ge	x	2
Gey2	Ge	y	2
Gez2	Ge	z	2
Erx1	Er	x	1
Ery1	Er	y	1
Erz1	Er	z	1
Erx2	Er	x	2
Ery2	Er	y	2
Erz2	Er	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Gex1	-0.079(2)	0
Gey1	0	-0.032(6)
Gez1	-0.008(3)	0
Gex2	0	0.044(5)
Gey2	0.033(5)	0
Gez2	0	-0.006(5)
Erx1	0	0
Ery1	0	0.0221(10)
Erz1	0	0
Erx2	0	-0.018(3)
Ery2	0	0
Erz2	0	0.030(2)

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Ge	0.25	0.7806

IX

Chemical data

Structural Formula Sum: Er2 Ge3 [ Help ]

Formula weight: 552.29 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: X2/m(α0γ)0s [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,1/2-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,1/2+x4
5	1/2+x1,1/2+x2,x3,1/2+x4
6	1/2-x1,1/2+x2,-x3,-x4
7	1/2-x1,1/2-x2,-x3,1/2-x4
8	1/2+x1,1/2-x2,x3,x4

a: 3.8901(10) Å [ Help ]

b: 6.6544(11) Å [ Help ]

c: 4.0980(8) Å [ Help ]

α: 90 ° [ Help ]

β: 89.74(2) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 106.081(15) Å³ [ Help ]

Z: 2 [ Help ]

Cell measurement temperature: 295 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.50000	0.00000	0.25000

μ: 92.354 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

Refinement remarks: Presented phase is a minority phase. The main phase is Er2Ge3.122 Impurity present is Er2O3 Parameters for this were not refined. [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0611 [ Help ]

R(obs): 0.0558 [ Help ]

wR(obs): 0.0317 [ Help ]

wR(all): 0.0318 [ Help ]

S(all): 3.79 [ Help ]

Nb. of parameters: 36 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 8 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0486 [ Help ]

Δ/σ(mean): 0.0070 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Ge	Ge	0.5	0.166775	0.5	0.0139(16)	Uiso	d	.	1	.	.
Er	Er	0	0	0	0.0094(9)	Uiso	d	.	1	.	.

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

Wave vector code	q_x	q_z
1	0.49998	0.25000
2	0.99996	0.50000

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Gex1	Ge	x	1
Gey1	Ge	y	1
Gez1	Ge	z	1
Gex2	Ge	x	2
Gey2	Ge	y	2
Gez2	Ge	z	2
Erx1	Er	x	1
Ery1	Er	y	1
Erz1	Er	z	1
Erx2	Er	x	2
Ery2	Er	y	2
Erz2	Er	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Gex1	-0.079(2)	0
Gey1	0	-0.032(6)
Gez1	-0.008(3)	0
Gex2	0	0.044(5)
Gey2	0.033(5)	0
Gez2	0	-0.006(5)
Erx1	0	0
Ery1	0	0.0221(10)
Erz1	0	0
Erx2	0	-0.018(3)
Ery2	0	0
Erz2	0	0.030(2)

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Ge	0.25	0.75

Vacancy-ordering effects in AlB2-type ErGe2-x (0.4 < x ≤ 0.5)

Christensen, Jeppe; Lidin, Sven; Malaman, Bernard; Venturini, Gerard

Acta Crystallographica, Section B 64 272-280 (2008)

https://doi.org/10.1107/S0108768108005119

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I

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Crystallographic data and experimental details

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II

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III

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IV

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V

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VI

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VII

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VIII

Chemical data

Crystallographic data and experimental details

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IX

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Vacancy-ordering effects in AlB₂-type ErGe_2-x (0.4 < x ≤ 0.5)