B-IncStrDB

Orthorhombic charge density wave on the tetragonal lattice of EuAl₄

Authors:

Sitaram Ramakrishnan; Surya Rohith Kotla; Toms Rekis; Jin-Ke Bao; Claudio Eisele; Leila Noohinejad; Martin Tolkiehn; Carsten Paulmann; Birender Singh; Rahul Verma; Biplab Bag; Ruta Kulkarni; Arumugam Thamizhavel; Bahadur Singh; Srinivasan Ramakrishnan; Sander van Smaalen

Journal:

IUCrJ 9 378-385 (2022)

DOI:

https://doi.org/10.1107/S2052252522003888

B-IncStrDB ID: KGB6B0qsuYG Entry date: 2022-04-24 Last revision: 2022-05-21

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I

Chemical data

Common Name: EuAl4 [ Help ]

Structural Formula Sum: Al4 Eu1 [ Help ]

Formula weight: 259.9 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): I 4/m m m [ Help ]

Space group name (Hall): -I 4;-2 [ Help ]

Space group nb.: 139 [ Help ]

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

Operation code	Operation in algebraic form
1	x,y,z
2	-x,-y,z
3	-y,x,z
4	y,-x,z
5	-x,y,-z
6	x,-y,-z
7	y,x,-z
8	-y,-x,-z
9	-x,-y,-z
10	x,y,-z
11	y,-x,-z
12	-y,x,-z
13	x,-y,z
14	-x,y,z
15	-y,-x,z
16	y,x,z
17	x+1/2,y+1/2,z+1/2
18	-x+1/2,-y+1/2,z+1/2
19	-y+1/2,x+1/2,z+1/2
20	y+1/2,-x+1/2,z+1/2
21	-x+1/2,y+1/2,-z+1/2
22	x+1/2,-y+1/2,-z+1/2
23	y+1/2,x+1/2,-z+1/2
24	-y+1/2,-x+1/2,-z+1/2
25	-x+1/2,-y+1/2,-z+1/2
26	x+1/2,y+1/2,-z+1/2
27	y+1/2,-x+1/2,-z+1/2
28	-y+1/2,x+1/2,-z+1/2
29	x+1/2,-y+1/2,z+1/2
30	-x+1/2,y+1/2,z+1/2
31	-y+1/2,-x+1/2,z+1/2
32	y+1/2,x+1/2,z+1/2

a: 4.39490(10) Å [ Help ]

b: 4.39490(10) Å [ Help ]

c: 11.1607(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 215.571(9) Å³ [ Help ]

Z: 2 [ Help ]

Cell determination reflection Nb.: 1000 [ Help ]

θ(min) for cell determination: 1.5 ° [ Help ]

θ(max) for cell determination: 20 ° [ Help ]

Cell measurement temperature: 250 K [ Help ]

μ: 5.873 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: SADABS, Program for Empirical Absorption Correction of Area Detector Data, G. M. Sheldrick, 1996 [ Help ]

Minimum transmission factor: 0.3211 [ Help ]

Maximum transmission factor: 0.3712 [ Help ]

Refinement details

Refinement remarks: ? [ Help ]

Total nb. of reflections: 109 [ Help ]

Nb. of observed reflections: 109 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0147 [ Help ]

wR(obs): 0.0214 [ Help ]

R(all): 0.0147 [ Help ]

wR(all): 0.0214 [ Help ]

S(all): 1.53 [ Help ]

S(obs): 1.53 [ Help ]

Nb. of reflections: 109 [ Help ]

Nb. of parameters: 9 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0001 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 1.15 e_Å^-3 [ Help ]

Δρ(min): -1.35 e_Å^-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 80(70) [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Eu1	Eu	0	0	Uani	0.0098(2)	2	1	d	.	.	.
Al1	Al	0.5	0.25	Uani	0.0107(5)	4	1	d	.	.	.
Al2	Al	0	0.3849(2)	Uani	0.0102(5)	4	1	d	.	.	.

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33
Eu1	Eu	0.0083(3)	0.0083(3)	0.0126(4)
Al1	Al	0.0112(8)	0.0112(8)	0.0098(10)
Al2	Al	0.0103(8)	0.0103(8)	0.0099(10)

II

Chemical data

Common Name: EuAl4 [ Help ]

Structural Formula Sum: Al4 Eu1 [ Help ]

Formula weight: 259.9 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Fmmm(00γ)s00 [ 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,x4+1/2
3	-x1,x2,-x3,-x4
4	x1,-x2,-x3,-x4+1/2
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4+1/2
7	x1,-x2,x3,x4
8	-x1,x2,x3,x4+1/2
9	x1,x2+1/2,x3+1/2,x4
10	-x1,-x2+1/2,x3+1/2,x4+1/2
11	-x1,x2+1/2,-x3+1/2,-x4
12	x1,-x2+1/2,-x3+1/2,-x4+1/2
13	-x1,-x2+1/2,-x3+1/2,-x4
14	x1,x2+1/2,-x3+1/2,-x4+1/2
15	x1,-x2+1/2,x3+1/2,x4
16	-x1,x2+1/2,x3+1/2,x4+1/2
17	x1+1/2,x2,x3+1/2,x4
18	-x1+1/2,-x2,x3+1/2,x4+1/2
19	-x1+1/2,x2,-x3+1/2,-x4
20	x1+1/2,-x2,-x3+1/2,-x4+1/2
21	-x1+1/2,-x2,-x3+1/2,-x4
22	x1+1/2,x2,-x3+1/2,-x4+1/2
23	x1+1/2,-x2,x3+1/2,x4
24	-x1+1/2,x2,x3+1/2,x4+1/2
25	x1+1/2,x2+1/2,x3,x4
26	-x1+1/2,-x2+1/2,x3,x4+1/2
27	-x1+1/2,x2+1/2,-x3,-x4
28	x1+1/2,-x2+1/2,-x3,-x4+1/2
29	-x1+1/2,-x2+1/2,-x3,-x4
30	x1+1/2,x2+1/2,-x3,-x4+1/2
31	x1+1/2,-x2+1/2,x3,x4
32	-x1+1/2,x2+1/2,x3,x4+1/2

a: 6.1991(3) Å [ Help ]

b: 6.1987(4) Å [ Help ]

c: 11.1488(4) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 428.41(4) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.174100

Z: 4 [ Help ]

Cell determination reflection Nb.: 1000 [ Help ]

θ(min) for cell determination: 1.5 ° [ Help ]

θ(max) for cell determination: 22 ° [ Help ]

Cell measurement temperature: 20 K [ Help ]

μ: 5.91 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: SADABS, Program for Empirical Absorption Correction of Area Detector Data, G. M. Sheldrick, 1996 [ Help ]

Minimum transmission factor: 0.3192 [ Help ]

Maximum transmission factor: 0.3676 [ Help ]

Refinement details

Refinement remarks: ? [ Help ]

Total nb. of reflections: 498 [ Help ]

Nb. of observed reflections: 439 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0242 [ Help ]

wR(obs): 0.0248 [ Help ]

R(all): 0.0255 [ Help ]

wR(all): 0.0250 [ Help ]

S(all): 0.88 [ Help ]

S(obs): 0.93 [ Help ]

Nb. of reflections: 498 [ Help ]

Nb. of parameters: 18 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0000 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 1.58 e_Å^-3 [ Help ]

Δρ(min): -1.49 e_Å^-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 130(30) [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Eu1	Eu	0	0	0	Uani	0.0061(2)	4	1	d	.	.	.
Al1	Al	0.25	0.25	0.25	Uani	0.0074(10)	8	1	d	.	.	.
Al2	Al	0	0	0.38495(13)	Uani	0.0061(8)	8	1	d	.	.	.

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33
Eu1	Eu	0.0000(4)	0.0124(5)	0.00587(17)
Al1	Al	0.0038(17)	0.011(2)	0.0074(6)
Al2	Al	0.0016(15)	0.011(2)	0.0058(6)

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

Wave vector code	q_1
1	1

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Eu1x1	Eu1	x	1
Eu1y1	Eu1	y	1
Eu1z1	Eu1	z	1
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al2x1	Al2	x	1
Al2y1	Al2	y	1
Al2z1	Al2	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Eu1x1	0	-0.02349(10)
Eu1y1	0	0
Eu1z1	0	0
Al1x1	0	-0.0225(4)
Al1y1	-0.0118(5)	0
Al1z1	0	0
Al2x1	-0.0108(4)	-0.0242(4)
Al2y1	0	0
Al2z1	0	0

III

Chemical data

Common Name: EuAl4 [ Help ]

Structural Formula Sum: Al4 Eu1 [ Help ]

Formula weight: 259.9 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Fmmm(00γ)s00 [ 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,x4+1/2
3	-x1,x2,-x3,-x4
4	x1,-x2,-x3,-x4+1/2
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4+1/2
7	x1,-x2,x3,x4
8	-x1,x2,x3,x4+1/2
9	x1,x2+1/2,x3+1/2,x4
10	-x1,-x2+1/2,x3+1/2,x4+1/2
11	-x1,x2+1/2,-x3+1/2,-x4
12	x1,-x2+1/2,-x3+1/2,-x4+1/2
13	-x1,-x2+1/2,-x3+1/2,-x4
14	x1,x2+1/2,-x3+1/2,-x4+1/2
15	x1,-x2+1/2,x3+1/2,x4
16	-x1,x2+1/2,x3+1/2,x4+1/2
17	x1+1/2,x2,x3+1/2,x4
18	-x1+1/2,-x2,x3+1/2,x4+1/2
19	-x1+1/2,x2,-x3+1/2,-x4
20	x1+1/2,-x2,-x3+1/2,-x4+1/2
21	-x1+1/2,-x2,-x3+1/2,-x4
22	x1+1/2,x2,-x3+1/2,-x4+1/2
23	x1+1/2,-x2,x3+1/2,x4
24	-x1+1/2,x2,x3+1/2,x4+1/2
25	x1+1/2,x2+1/2,x3,x4
26	-x1+1/2,-x2+1/2,x3,x4+1/2
27	-x1+1/2,x2+1/2,-x3,-x4
28	x1+1/2,-x2+1/2,-x3,-x4+1/2
29	-x1+1/2,-x2+1/2,-x3,-x4
30	x1+1/2,x2+1/2,-x3,-x4+1/2
31	x1+1/2,-x2+1/2,x3,x4
32	-x1+1/2,x2+1/2,x3,x4+1/2

a: 6.1992(4) Å [ Help ]

b: 6.2001(4) Å [ Help ]

c: 11.1477(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 428.47(4) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.178100

Z: 4 [ Help ]

Cell determination reflection Nb.: 1000 [ Help ]

θ(min) for cell determination: 1.5 ° [ Help ]

θ(max) for cell determination: 22 ° [ Help ]

Cell measurement temperature: 70 K [ Help ]

μ: 5.909 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Absorption correction remarks: SADABS, Program for Empirical Absorption Correction of Area Detector Data, G. M. Sheldrick, 1996 [ Help ]

Minimum transmission factor: 0.3209 [ Help ]

Maximum transmission factor: 0.3732 [ Help ]

Refinement details

Total nb. of reflections: 490 [ Help ]

Nb. of observed reflections: 453 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0220 [ Help ]

wR(obs): 0.0242 [ Help ]

R(all): 0.0232 [ Help ]

wR(all): 0.0245 [ Help ]

S(all): 1.09 [ Help ]

S(obs): 1.13 [ Help ]

Nb. of reflections: 490 [ Help ]

Nb. of parameters: 18 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0001 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 3.58 e_Å^-3 [ Help ]

Δρ(min): -2.40 e_Å^-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 55(10) [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Eu1	Eu	0	0	0	Uani	0.0083(2)	4	2	d	.	.	.
Al1	Al	0.25	0.25	0.25	Uani	0.0080(9)	8	2	d	.	.	.
Al2	Al	0	0	0.38491(12)	Uani	0.0077(8)	8	2	d	.	.	.

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33
Eu1	Eu	0.0011(3)	0.0157(5)	0.00813(16)
Al1	Al	0.0080(16)	0.008(2)	0.0079(5)
Al2	Al	0.0034(14)	0.0127(19)	0.0069(6)

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

Wave vector code	q_1
1	1

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Eu1x1	Eu1	x	1
Eu1y1	Eu1	y	1
Eu1z1	Eu1	z	1
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al2x1	Al2	x	1
Al2y1	Al2	y	1
Al2z1	Al2	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Eu1x1	0	-0.01977(8)
Eu1y1	0	0
Eu1z1	0	0
Al1x1	0	-0.0199(4)
Al1y1	-0.0100(4)	0
Al1z1	0	0
Al2x1	-0.0093(3)	-0.0206(3)
Al2y1	0	0
Al2z1	0	0

Orthorhombic charge density wave on the tetragonal lattice of EuAl4

Sitaram Ramakrishnan; Surya Rohith Kotla; Toms Rekis; Jin-Ke Bao; Claudio Eisele; Leila Noohinejad; Martin Tolkiehn; Carsten Paulmann; Birender Singh; Rahul Verma; Biplab Bag; Ruta Kulkarni; Arumugam Thamizhavel; Bahadur Singh; Srinivasan Ramakrishnan; Sander van Smaalen

IUCrJ 9 378-385 (2022)

https://doi.org/10.1107/S2052252522003888

Download CIF

Open in JSmol

I

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

II

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

III

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Orthorhombic charge density wave on the tetragonal lattice of EuAl₄