Incommensurately modulated lanthanide coinage-metal diarsenides. I. CeAu1-δAs2 [δ = 0.015(2)] - a new distortion variant of the HfCuSi2 type with irregularly stacked cis-trans chains of arsenic atoms
Authors:Rutzinger, Dieter; Doert, Thomas; Ruck, Michael
Journal:Acta Crystallographica, Section B 65 519-526 (2009)
DOI:https://doi.org/10.1107/S0108768109026986
B-IncStrDB ID: tTvwKhyf9aX Entry date: 2022-01-22 Last revision: 2022-01-24
I
Chemical data
Common Name: Cerium gold diarsenide [ Help ]
Formula moiety: As2 Au1 Ce1 [ Help ]
Structural Formula Sum: As2 Au1 Ce1 [ Help ]
Structural Formula: As2 Au1 Ce1 [ Help ]
Formula analytical: As2 Au1 Ce1 [ Help ]
Formula (IUPAC): As2 Au1 Ce1 [ Help ]
Formula weight: 486.93 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: P21/m(α0γ)00 [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | -x1,1/2+x2,-x3,-x4 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,1/2-x2,x3,x4 |
a: 5.804(1) Å [ Help ]
b: 5.814(1) Å [ Help ]
c: 10.179(1) Å [ Help ]
α: 90 ° [ Help ]
β: 90.09(8) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 343.48(9) Å3 [ Help ]
Z: 4 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.08(1) | 0.00000 | -0.39(1) |
μ: 74.55 mm-1 [ Help ]
Absorption correction type: numerical [ Help ]
Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]
Minimum transmission factor: 0.015 [ Help ]
Maximum transmission factor: 0.306 [ Help ]
Refinement details
Total nb. of reflections: 4210 [ Help ]
Nb. of observed reflections: 1422 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(all): 0.0984 [ Help ]
R(obs): 0.0342 [ Help ]
wR(obs): 0.0364 [ Help ]
wR(all): 0.0395 [ Help ]
S(all): 1.25 [ Help ]
Nb. of reflections: 4210 [ Help ]
Nb. of parameters: 134 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0414 [ Help ]
Δ/σ(mean): 0.0116 [ Help ]
Δρ(max): 2.49 e_Å-3 [ Help ]
Δρ(min): -2.29 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 0.53(2) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ce | Ce1 | 0.0005(4) | 0.25 | 0.23003(4) | 0.01262(12) | Uani | d | . | 1 | . | . |
| Ce | Ce2 | 0.5001(4) | 0.75 | 0.24019(4) | 0.01220(13) | Uani | d | . | 1 | . | . |
| Au | Au1 | 0.24822(4) | -0.0005(2) | 0.49929(10) | 0.01869(7) | Uani | d | . | 0.9858(17) | . | . |
| As | As1 | 0.9978(6) | 0.25 | 0.68044(9) | 0.0142(2) | Uani | d | . | 1 | . | . |
| As | As2 | 0.4991(6) | 0.75 | 0.67811(8) | 0.0141(2) | Uani | d | . | 1 | . | . |
| As | As3 | 0.27901(14) | -0.0038(6) | 0.0001(3) | 0.02084(18) | Uani | d | . | 1 | . | . |
ADP components: (Show/hide table) [ Help ]
| Atom site label | U11 | U22 | U33 | U12 | U13 | U23 | Atom site symbol |
|---|---|---|---|---|---|---|---|
| Ce1 | 0.0136(2) | 0.0104(2) | 0.0139(2) | 0 | 0.0004(8) | 0 | Ce |
| Ce2 | 0.0142(2) | 0.0101(2) | 0.0122(2) | 0 | -0.0019(9) | 0 | Ce |
| Au1 | 0.02132(13) | 0.01698(10) | 0.01778(11) | -0.0024(3) | -0.0011(7) | -0.00082(10) | Au |
| As1 | 0.0140(4) | 0.0106(3) | 0.0179(4) | 0 | -0.0090(12) | 0 | As |
| As2 | 0.0142(4) | 0.0111(3) | 0.0169(4) | 0 | -0.0079(12) | 0 | As |
| As3 | 0.0148(3) | 0.0352(4) | 0.0124(2) | 0.0049(9) | -0.0025(11) | -0.0019(3) | As |
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 | 0.08000 | -0.38890 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Ce1x1 | Ce1 | x | 1 |
| Ce1y1 | Ce1 | y | 1 |
| Ce1z1 | Ce1 | z | 1 |
| Ce2x1 | Ce2 | x | 1 |
| Ce2y1 | Ce2 | y | 1 |
| Ce2z1 | Ce2 | z | 1 |
| Au1x1 | Au1 | x | 1 |
| Au1y1 | Au1 | y | 1 |
| Au1z1 | Au1 | z | 1 |
| As1x1 | As1 | x | 1 |
| As1y1 | As1 | y | 1 |
| As1z1 | As1 | z | 1 |
| As2x1 | As2 | x | 1 |
| As2y1 | As2 | y | 1 |
| As2z1 | As2 | z | 1 |
| As3x1 | As3 | x | 1 |
| As3y1 | As3 | y | 1 |
| As3z1 | As3 | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Ce1x1 | 0.0039(3) | 0.0044(3) |
| Ce1y1 | 0 | 0 |
| Ce1z1 | 0.0005(2) | -0.0012(2) |
| Ce2x1 | 0.0043(3) | 0.0067(3) |
| Ce2y1 | 0 | 0 |
| Ce2z1 | -0.0011(2) | 0.0000(2) |
| Au1x1 | 0.0001(3) | 0.00738(11) |
| Au1y1 | 0.00014(6) | -0.00106(15) |
| Au1z1 | 0.00042(13) | 0.00017(10) |
| As1x1 | -0.0030(4) | 0.0062(4) |
| As1y1 | 0 | 0 |
| As1z1 | 0.0011(4) | -0.0022(4) |
| As2x1 | -0.0028(4) | 0.0056(4) |
| As2y1 | 0 | 0 |
| As2z1 | 0.0006(4) | -0.0015(4) |
| As3x1 | -0.0037(7) | 0.0052(3) |
| As3y1 | -0.01407(19) | -0.0005(5) |
| As3z1 | 0.0010(3) | 0.0006(2) |
Definition of the occupation Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Wave vector code |
|---|---|---|
| Au1o1 | Au1 | 1 |
Occupation Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Au1o1 | -0.057(4) | -0.008(7) |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| Ce1U111 | Ce1 | U11 | 1 |
| Ce1U221 | Ce1 | U22 | 1 |
| Ce1U331 | Ce1 | U33 | 1 |
| Ce1U121 | Ce1 | U12 | 1 |
| Ce1U131 | Ce1 | U13 | 1 |
| Ce1U231 | Ce1 | U23 | 1 |
| Ce2U111 | Ce2 | U11 | 1 |
| Ce2U221 | Ce2 | U22 | 1 |
| Ce2U331 | Ce2 | U33 | 1 |
| Ce2U121 | Ce2 | U12 | 1 |
| Ce2U131 | Ce2 | U13 | 1 |
| Ce2U231 | Ce2 | U23 | 1 |
| Au1U111 | Au1 | U11 | 1 |
| Au1U221 | Au1 | U22 | 1 |
| Au1U331 | Au1 | U33 | 1 |
| Au1U121 | Au1 | U12 | 1 |
| Au1U131 | Au1 | U13 | 1 |
| Au1U231 | Au1 | U23 | 1 |
| As1U111 | As1 | U11 | 1 |
| As1U221 | As1 | U22 | 1 |
| As1U331 | As1 | U33 | 1 |
| As1U121 | As1 | U12 | 1 |
| As1U131 | As1 | U13 | 1 |
| As1U231 | As1 | U23 | 1 |
| As2U111 | As2 | U11 | 1 |
| As2U221 | As2 | U22 | 1 |
| As2U331 | As2 | U33 | 1 |
| As2U121 | As2 | U12 | 1 |
| As2U131 | As2 | U13 | 1 |
| As2U231 | As2 | U23 | 1 |
| As3U111 | As3 | U11 | 1 |
| As3U221 | As3 | U22 | 1 |
| As3U331 | As3 | U33 | 1 |
| As3U121 | As3 | U12 | 1 |
| As3U131 | As3 | U13 | 1 |
| As3U231 | As3 | U23 | 1 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Ce1U111 | -0.0024(11) | -0.0022(10) |
| Ce1U221 | 0.0001(6) | 0.0017(6) |
| Ce1U331 | 0.0013(8) | 0.0006(8) |
| Ce1U121 | 0 | 0 |
| Ce1U131 | -0.0005(5) | -0.0021(5) |
| Ce1U231 | 0 | 0 |
| Ce2U111 | 0.0022(12) | -0.0079(9) |
| Ce2U221 | 0.0049(6) | 0.0057(6) |
| Ce2U331 | 0.0014(8) | -0.0003(8) |
| Ce2U121 | 0 | 0 |
| Ce2U131 | 0.0003(5) | 0.0015(5) |
| Ce2U231 | 0 | 0 |
| Au1U111 | 0.0012(7) | -0.0001(6) |
| Au1U221 | -0.0031(4) | -0.0013(6) |
| Au1U331 | -0.0027(4) | -0.0011(5) |
| Au1U121 | -0.0006(3) | 0.0000(4) |
| Au1U131 | -0.00023(18) | -0.0004(6) |
| Au1U231 | -0.0004(3) | -0.00013(15) |
| As1U111 | 0.0030(17) | 0.0011(16) |
| As1U221 | -0.0036(10) | 0.0027(10) |
| As1U331 | 0.0007(16) | -0.0069(16) |
| As1U121 | 0 | 0 |
| As1U131 | 0.0009(10) | 0.0001(10) |
| As1U231 | 0 | 0 |
| As2U111 | 0.0020(17) | 0.0034(16) |
| As2U221 | 0.0001(11) | 0.0001(10) |
| As2U331 | 0.0003(16) | -0.0042(16) |
| As2U121 | 0 | 0 |
| As2U131 | -0.0013(10) | -0.0006(10) |
| As2U231 | 0 | 0 |
| As3U111 | -0.0090(16) | -0.0030(7) |
| As3U221 | -0.0067(15) | 0.0051(11) |
| As3U331 | -0.0032(9) | 0.0039(9) |
| As3U121 | -0.0009(6) | -0.0060(11) |
| As3U131 | 0.0003(7) | 0.0024(14) |
| As3U231 | -0.0068(10) | -0.0017(5) |