The α <-> β phase transitions of Zn2P2O7 revisited: existence of an additional intermediate phase with an incommensurately modulated structure
Authors:Stoger, Berthold; Weil, Matthias; Dusek, Michal
Journal:Acta Crystallographica, Section B 70 539-554 (2014)
DOI:https://doi.org/10.1107/s205252061401049x
B-IncStrDB ID: 9142Ec1aK6 Entry date: 2014-06-09 Last revision: 2021-12-12
alpha1_zn2p2o7
Chemical data
Structural Formula Sum: O7 P2 Zn2 [ Help ]
Formula weight: 304.7 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Space group name (H-M): I2/c [ Help ]
Space group name (Hall): -I 2yc [ 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+1/2 |
| 3 | -x,-y,-z |
| 4 | x,-y,z+1/2 |
| 5 | x+1/2,y+1/2,z+1/2 |
| 6 | -x+1/2,y+1/2,-z |
| 7 | -x+1/2,-y+1/2,-z+1/2 |
| 8 | x+1/2,-y+1/2,z |
a: 20.1131(13) Å [ Help ]
b: 8.2769(6) Å [ Help ]
c: 9.109(3) Å [ Help ]
α: 90 ° [ Help ]
β: 106.338(16) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 1455.2(5) Å3 [ Help ]
Z: 12 [ Help ]
Cell determination reflection Nb.: 9829 [ Help ]
θ(min) for cell determination: 3.4 ° [ Help ]
θ(max) for cell determination: 35.0 ° [ Help ]
Cell measurement temperature: 350 K [ Help ]
μ: 10.528 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: SADABS [ Help ]
Minimum transmission factor: 0.022 [ Help ]
Maximum transmission factor: 0.73 [ Help ]
Refinement details
Total nb. of reflections: 3215 [ Help ]
Nb. of observed reflections: 2822 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0159 [ Help ]
wR(obs): 0.0222 [ Help ]
R(all): 0.0198 [ Help ]
wR(all): 0.0229 [ Help ]
S(all): 1.47 [ Help ]
S(obs): 1.53 [ Help ]
Nb. of reflections: 3215 [ Help ]
Nb. of parameters: 151 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0024 [ Help ]
Δ/σ(mean): 0.0003 [ Help ]
Δρ(max): 0.82 e_Å-3 [ Help ]
Δρ(min): -0.87 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 4210(70) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn1 | Zn | 0.318103(6) | 0.189033(13) | 0.023504(13) | Uani | 0.00927(4) | 8 | 1 | d | ? | ? | ? |
| Zn2 | Zn | 0.512812(6) | -0.311694(13) | 0.477093(13) | Uani | 0.00847(4) | 8 | 1 | d | ? | ? | ? |
| Zn3 | Zn | 0.336359(5) | -0.183166(14) | -0.001330(12) | Uani | 0.00808(4) | 8 | 1 | d | ? | ? | ? |
| P1 | P | 0.433584(11) | 0.01883(3) | 0.29562(3) | Uani | 0.00537(6) | 8 | 1 | d | ? | ? | ? |
| P2 | P | 0.261362(11) | 0.48226(3) | -0.20166(3) | Uani | 0.00510(6) | 8 | 1 | d | ? | ? | ? |
| P3 | P | 0.398295(12) | 0.49306(3) | -0.28479(3) | Uani | 0.00592(6) | 8 | 1 | d | ? | ? | ? |
| O31 | O | 0.44822(4) | -0.13908(9) | 0.37880(9) | Uani | 0.0138(2) | 8 | 1 | d | ? | ? | ? |
| O32 | O | 0.41750(4) | 0.15581(9) | 0.39221(8) | Uani | 0.00823(18) | 8 | 1 | d | ? | ? | ? |
| O33 | O | 0.26469(4) | 0.64249(9) | -0.11770(8) | Uani | 0.00883(18) | 8 | 1 | d | ? | ? | ? |
| O34 | O | 0.24690(4) | 0.34051(8) | -0.10924(8) | Uani | 0.00868(18) | 8 | 1 | d | ? | ? | ? |
| O35 | O | 0.38337(4) | 0.64524(9) | -0.37560(9) | Uani | 0.0165(2) | 8 | 1 | d | ? | ? | ? |
| O36 | O | 0.40633(4) | 0.34861(9) | -0.38204(8) | Uani | 0.00815(18) | 8 | 1 | d | ? | ? | ? |
| O21 | O | 0.5 | 0.08403(13) | 0.25 | Uani | 0.0134(3) | 4 | 1 | d | ? | ? | ? |
| O22 | O | 0.33546(4) | 0.44334(10) | -0.21952(9) | Uani | 0.0158(2) | 8 | 1 | d | ? | ? | ? |
| O11 | O | 0.37651(4) | 0.00583(8) | 0.14465(8) | Uani | 0.00797(17) | 8 | 1 | d | ? | ? | ? |
| O12 | O | 0.21052(4) | 0.49030(8) | -0.36065(7) | Uani | 0.00839(17) | 8 | 1 | d | ? | ? | ? |
| O13 | O | 0.45958(4) | 0.50579(8) | -0.14125(7) | Uani | 0.00795(17) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Zn1 | Zn | 0.01028(6) | 0.00581(6) | 0.00959(6) | 0.00013(3) | -0.00070(4) | -0.00005(3) |
| Zn2 | Zn | 0.00869(6) | 0.00575(6) | 0.00966(6) | -0.00011(3) | 0.00044(4) | -0.00010(3) |
| Zn3 | Zn | 0.00808(6) | 0.00605(6) | 0.00953(6) | 0.00048(3) | 0.00154(5) | 0.00005(3) |
| P1 | P | 0.00512(9) | 0.00516(9) | 0.00538(9) | 0.00050(7) | 0.00075(8) | -0.00052(7) |
| P2 | P | 0.00533(9) | 0.00520(9) | 0.00475(9) | 0.00028(7) | 0.00140(7) | -0.00006(7) |
| P3 | P | 0.00591(9) | 0.00550(9) | 0.00550(9) | 0.00145(7) | 0.00022(7) | -0.00097(7) |
| O31 | O | 0.0176(3) | 0.0076(3) | 0.0130(3) | 0.0036(3) | -0.0010(3) | 0.0031(3) |
| O32 | O | 0.0097(3) | 0.0072(3) | 0.0084(3) | -0.0011(2) | 0.0035(2) | -0.0031(2) |
| O33 | O | 0.0102(3) | 0.0066(3) | 0.0100(3) | -0.0018(2) | 0.0034(2) | -0.0035(2) |
| O34 | O | 0.0107(3) | 0.0068(3) | 0.0087(3) | 0.0014(2) | 0.0031(2) | 0.0031(2) |
| O35 | O | 0.0221(4) | 0.0082(3) | 0.0140(3) | 0.0043(3) | -0.0033(3) | 0.0022(3) |
| O36 | O | 0.0086(3) | 0.0075(3) | 0.0088(3) | -0.0010(2) | 0.0032(2) | -0.0040(2) |
| O21 | O | 0.0073(4) | 0.0164(5) | 0.0184(5) | 0 | 0.0065(4) | 0 |
| O22 | O | 0.0089(3) | 0.0228(4) | 0.0179(3) | 0.0017(3) | 0.0071(3) | -0.0019(3) |
| O11 | O | 0.0085(3) | 0.0071(3) | 0.0063(3) | 0.0005(2) | -0.0014(2) | -0.0007(2) |
| O12 | O | 0.0109(3) | 0.0073(3) | 0.0052(3) | 0.0012(2) | -0.0007(2) | 0.0000(2) |
| O13 | O | 0.0080(3) | 0.0076(3) | 0.0065(3) | 0.0008(2) | -0.0010(2) | -0.0012(2) |
alpha2_zn2p2o7_400
Chemical data
Full Name: zinc(II) diphosphate(V) [ Help ]
Common Name: zinc pyrophosphate [ Help ]
Structural Formula Sum: O7 P2 Zn2 [ Help ]
Formula weight: 304.7 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/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,-x4+1/2 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,x4+1/2 |
| 5 | x1+1/2,x2+1/2,x3,x4 |
| 6 | -x1+1/2,x2+1/2,-x3,-x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3,x4+1/2 |
a: 6.6082(2) Å [ Help ]
b: 8.2821(3) Å [ Help ]
c: 4.5238(2) Å [ Help ]
α: 90 ° [ Help ]
β: 105.4390(17) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 238.652(16) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.332680 | 0.000000 | 0.407590 |
Z: 2 [ Help ]
Cell determination reflection Nb.: 6552 [ Help ]
θ(min) for cell determination: 3.5 ° [ Help ]
θ(max) for cell determination: 45.2 ° [ Help ]
Cell measurement temperature: 400 K [ Help ]
μ: 10.7 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: SADABS [ Help ]
Minimum transmission factor: 0.025 [ Help ]
Maximum transmission factor: 0.60 [ Help ]
Refinement details
Total nb. of reflections: 5020 [ Help ]
Nb. of observed reflections: 2280 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0255 [ Help ]
wR(obs): 0.0356 [ Help ]
R(all): 0.0609 [ Help ]
wR(all): 0.0397 [ Help ]
S(all): 1.24 [ Help ]
S(obs): 1.68 [ Help ]
Nb. of reflections: 5020 [ Help ]
Nb. of parameters: 146 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0169 [ Help ]
Δ/σ(mean): 0.0034 [ Help ]
Δρ(max): 0.90 e_Å-3 [ Help ]
Δρ(min): -0.83 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 1840(80) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.5 | 0.18921(3) | 1 | Uani | 0.01797(6) | 4 | 1 | d | ? | ? | ? |
| P | P | 0.78961(3) | 0 | 0.59052(4) | Uani | 0.00896(4) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0.62199(8) | 0 | 0.28617(12) | Uani | 0.01031(11) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 1 | -0.0528(10) | 0.5 | Uani | 0.0240(10) | 4 | 0.234(6) | d | ? | ? | ? |
| O2' | O | 1 | -0.011(3) | 0.5 | Uani | 0.068(6) | 4 | 0.266(6) | d | ? | ? | ? |
| O3 | O | 0.78239(9) | -0.15146(6) | 0.77458(11) | Uani | 0.01910(12) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.02176(12) | 0.00790(5) | 0.01688(11) | 0 | -0.00773(6) | 0 |
| P | P | 0.00772(6) | 0.01115(7) | 0.00709(7) | 0 | 0.00037(5) | 0 |
| O1 | O | 0.01022(17) | 0.01108(17) | 0.00771(17) | 0 | -0.00095(13) | 0 |
| O2 | O | 0.0090(10) | 0.035(2) | 0.0299(13) | 0 | 0.0086(9) | 0 |
| O2' | O | 0.0090(13) | 0.151(17) | 0.047(2) | 0 | 0.0122(14) | 0 |
| O3 | O | 0.0298(2) | 0.01099(15) | 0.01290(16) | 0.00574(14) | -0.00059(15) | 0.00268(12) |
Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Atom symbol | C111 | C112 | C113 | C122 | C123 | C133 | C222 | C223 | C233 | C333 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0 | -0.00002(4) | 0 | 0 | -0.00051(4) | 0 | -0.00009(3) | 0 | 0.00091(8) | 0 |
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 |
| 2 | 2 |
| 3 | 3 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| Zn | 0.75 | 1 |
| O2 | 0.25 | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Px1 | P | x | 1 |
| Py1 | P | y | 1 |
| Pz1 | P | z | 1 |
| Px2 | P | x | 2 |
| Py2 | P | y | 2 |
| Pz2 | P | 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 |
| 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: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Px1 | 0 | 0 |
| Py1 | -0.00443(3) | -0.00700(3) |
| Pz1 | 0 | 0 |
| Px2 | -0.00066(7) | -0.00087(6) |
| Py2 | 0 | 0 |
| Pz2 | 0.00104(9) | 0.00143(10) |
| O1x1 | 0 | 0 |
| O1y1 | -0.00248(6) | 0.00502(6) |
| O1z1 | 0 | 0 |
| O1x2 | 0.00069(16) | -0.00018(17) |
| O1y2 | 0 | 0 |
| O1z2 | 0.0000(2) | -0.0001(2) |
| O3x1 | 0.00726(9) | -0.01796(9) |
| O3y1 | -0.00021(5) | -0.00421(5) |
| O3z1 | 0.00349(11) | 0.00495(10) |
| O3x2 | 0.00134(13) | -0.00274(13) |
| O3y2 | 0.00009(10) | -0.00059(10) |
| O3z2 | 0.00002(16) | 0.00089(18) |
Displacive (translational) Legendre coefficients: (Show/hide table) [ Help ]
| Atom site label | Displacement axis | Polynomial order | Polynomial coeff. |
|---|---|---|---|
| Zn | x | 1 | 0.01665(11) |
| Zn | y | 1 | 0 |
| Zn | z | 1 | -0.01698(17) |
| Zn | x | 2 | 0 |
| Zn | y | 2 | -0.001381(19) |
| Zn | z | 2 | 0 |
| Zn | x | 3 | 0.00019(11) |
| Zn | y | 3 | 0 |
| Zn | z | 3 | 0.00132(18) |
| Zn | x | 4 | 0 |
| Zn | y | 4 | -0.00005(3) |
| Zn | z | 4 | 0 |
| Zn | x | 5 | 0.00612(13) |
| Zn | y | 5 | 0 |
| Zn | z | 5 | -0.0077(2) |
| Zn | x | 6 | 0 |
| Zn | y | 6 | 0 |
| Zn | z | 6 | 0 |
| O2 | x | 1 | -0.0038(10) |
| O2 | y | 1 | 0 |
| O2 | z | 1 | -0.0240(17) |
| O2 | x | 2 | 0 |
| O2 | y | 2 | 0.0137(14) |
| O2 | z | 2 | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| PU111 | P | U11 | 1 |
| PU221 | P | U22 | 1 |
| PU331 | P | U33 | 1 |
| PU121 | P | U12 | 1 |
| PU131 | P | U13 | 1 |
| PU231 | P | U23 | 1 |
| PU112 | P | U11 | 2 |
| PU222 | P | U22 | 2 |
| PU332 | P | U33 | 2 |
| PU122 | P | U12 | 2 |
| PU132 | P | U13 | 2 |
| PU232 | P | U23 | 2 |
| O1U111 | O1 | U11 | 1 |
| O1U221 | O1 | U22 | 1 |
| O1U331 | O1 | U33 | 1 |
| O1U121 | O1 | U12 | 1 |
| O1U131 | O1 | U13 | 1 |
| O1U231 | O1 | U23 | 1 |
| O2'U111 | O2' | U11 | 1 |
| O2'U221 | O2' | U22 | 1 |
| O2'U331 | O2' | U33 | 1 |
| O2'U121 | O2' | U12 | 1 |
| O2'U131 | O2' | U13 | 1 |
| O2'U231 | O2' | U23 | 1 |
| O3U111 | O3 | U11 | 1 |
| O3U221 | O3 | U22 | 1 |
| O3U331 | O3 | U33 | 1 |
| O3U121 | O3 | U12 | 1 |
| O3U131 | O3 | U13 | 1 |
| O3U231 | O3 | U23 | 1 |
| O3U112 | O3 | U11 | 2 |
| O3U222 | O3 | U22 | 2 |
| O3U332 | O3 | U33 | 2 |
| O3U122 | O3 | U12 | 2 |
| O3U132 | O3 | U13 | 2 |
| O3U232 | O3 | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| PU111 | 0 | 0 |
| PU221 | 0 | 0 |
| PU331 | 0 | 0 |
| PU121 | 0.00214(6) | -0.00169(6) |
| PU131 | 0 | 0 |
| PU231 | -0.00142(6) | 0.00071(5) |
| PU112 | 0.00018(17) | -0.00117(18) |
| PU222 | 0.0019(2) | -0.00122(19) |
| PU332 | 0.00007(18) | -0.00033(18) |
| PU122 | 0 | 0 |
| PU132 | -0.00025(16) | 0.00021(16) |
| PU232 | 0 | 0 |
| O1U111 | 0 | 0 |
| O1U221 | 0 | 0 |
| O1U331 | 0 | 0 |
| O1U121 | -0.00090(17) | -0.00077(16) |
| O1U131 | 0 | 0 |
| O1U231 | 0.00035(15) | 0.00032(15) |
| O2'U111 | 0 | -0.006(4) |
| O2'U221 | 0 | -0.11(2) |
| O2'U331 | 0 | -0.001(8) |
| O2'U121 | 0.006(3) | 0 |
| O2'U131 | 0 | 0.005(4) |
| O2'U231 | -0.038(4) | 0 |
| O3U111 | 0.0173(3) | -0.0043(3) |
| O3U221 | 0.00046(15) | -0.00051(15) |
| O3U331 | 0.00068(17) | -0.00075(18) |
| O3U121 | 0.00291(17) | -0.00174(17) |
| O3U131 | -0.00441(19) | 0.00213(18) |
| O3U231 | -0.00115(13) | 0.00010(13) |
| O3U112 | 0.0060(5) | -0.0014(5) |
| O3U222 | 0.0003(4) | 0.0010(4) |
| O3U332 | -0.0013(4) | 0.0002(3) |
| O3U122 | 0.0010(3) | 0.0000(3) |
| O3U132 | -0.0031(4) | 0.0011(4) |
| O3U232 | -0.0012(3) | -0.0006(3) |
Modulated anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Tensor element | Wave vector code | Cos coeff. | Sin coeff. |
|---|---|---|---|---|
| Zn | C111 | 1 | 0 | -0.0070(2) |
| Zn | C112 | 1 | 0.00058(7) | 0 |
| Zn | C113 | 1 | 0 | 0.00561(18) |
| Zn | C122 | 1 | 0 | -0.00037(4) |
| Zn | C123 | 1 | -0.00001(7) | 0 |
| Zn | C133 | 1 | 0 | -0.0054(3) |
| Zn | C222 | 1 | 0.00013(3) | 0 |
| Zn | C223 | 1 | 0 | 0.00032(5) |
| Zn | C233 | 1 | -0.00041(14) | 0 |
| Zn | C333 | 1 | 0 | 0.0096(5) |
alpha2_zn2p2o7_405
Chemical data
Full Name: zinc(II) diphosphate(V) [ Help ]
Common Name: zinc pyrophosphate [ Help ]
Structural Formula Sum: O7 P2 Zn2 [ Help ]
Formula weight: 304.7 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/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,-x4+1/2 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,x4+1/2 |
| 5 | x1+1/2,x2+1/2,x3,x4 |
| 6 | -x1+1/2,x2+1/2,-x3,-x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3,x4+1/2 |
a: 6.6053(2) Å [ Help ]
b: 8.2821(2) Å [ Help ]
c: 4.52430(10) Å [ Help ]
α: 90 ° [ Help ]
β: 105.4163(14) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 238.600(11) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.33153(12) | 0.000000 | 0.40487(8) |
Z: 2 [ Help ]
Cell determination reflection Nb.: 6325 [ Help ]
θ(min) for cell determination: 2.5 ° [ Help ]
θ(max) for cell determination: 45.2 ° [ Help ]
Cell measurement temperature: 405 K [ Help ]
μ: 10.702 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: SADABS [ Help ]
Minimum transmission factor: 0.025 [ Help ]
Maximum transmission factor: 0.60 [ Help ]
Refinement details
Total nb. of reflections: 5038 [ Help ]
Nb. of observed reflections: 2245 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0242 [ Help ]
wR(obs): 0.0327 [ Help ]
R(all): 0.0633 [ Help ]
wR(all): 0.0380 [ Help ]
S(all): 1.18 [ Help ]
S(obs): 1.55 [ Help ]
Nb. of reflections: 5038 [ Help ]
Nb. of parameters: 146 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0366 [ Help ]
Δ/σ(mean): 0.0051 [ Help ]
Δρ(max): 0.96 e_Å-3 [ Help ]
Δρ(min): -0.76 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 2180(80) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.5 | 0.18950(2) | 1 | Uani | 0.01805(6) | 4 | 1 | d | ? | ? | ? |
| P | P | 0.78950(3) | 0 | 0.59053(4) | Uani | 0.00889(4) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0.62167(8) | 0 | 0.28594(12) | Uani | 0.01034(10) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 1 | -0.0566(7) | 0.5 | Uani | 0.0181(9) | 4 | 0.208(3) | d | ? | ? | ? |
| O2' | O | 1 | -0.0202(8) | 0.5 | Uani | 0.0332(18) | 4 | 0.292(3) | d | ? | ? | ? |
| O3 | O | 0.78233(8) | -0.15128(5) | 0.77488(10) | Uani | 0.01919(11) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.02193(11) | 0.00802(5) | 0.01689(11) | 0 | -0.00762(5) | 0 |
| P | P | 0.00760(6) | 0.01115(7) | 0.00713(7) | 0 | 0.00055(5) | 0 |
| O1 | O | 0.01032(16) | 0.01113(17) | 0.00783(16) | 0 | -0.00064(13) | 0 |
| O2 | O | 0.0067(8) | 0.022(2) | 0.0268(12) | 0 | 0.0063(8) | 0 |
| O2' | O | 0.0110(7) | 0.043(5) | 0.0494(17) | 0 | 0.0150(9) | 0 |
| O3 | O | 0.0301(2) | 0.01076(14) | 0.01322(16) | 0.00600(14) | -0.00024(15) | 0.00261(12) |
Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Atom symbol | C111 | C112 | C113 | C122 | C123 | C133 | C222 | C223 | C233 | C333 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0 | 0.00010(4) | 0 | 0 | -0.00049(4) | 0 | 0.00009(3) | 0 | 0.00123(8) | 0 |
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 |
| 2 | 2 |
| 3 | 3 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| Zn | 0.75 | 1 |
| O2 | 0.25 | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Px1 | P | x | 1 |
| Py1 | P | y | 1 |
| Pz1 | P | z | 1 |
| Px2 | P | x | 2 |
| Py2 | P | y | 2 |
| Pz2 | P | 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 |
| 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: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Px1 | 0 | 0 |
| Py1 | -0.00421(2) | -0.00665(2) |
| Pz1 | 0 | 0 |
| Px2 | -0.00077(7) | -0.00087(6) |
| Py2 | 0 | 0 |
| Pz2 | 0.00070(10) | 0.00150(10) |
| O1x1 | 0 | 0 |
| O1y1 | -0.00231(5) | 0.00475(5) |
| O1z1 | 0 | 0 |
| O1x2 | 0.00050(16) | 0.00040(17) |
| O1y2 | 0 | 0 |
| O1z2 | 0.0001(3) | 0.0003(3) |
| O3x1 | 0.00703(9) | -0.01691(8) |
| O3y1 | -0.00016(4) | -0.00397(4) |
| O3z1 | 0.00329(9) | 0.00482(9) |
| O3x2 | 0.00083(13) | -0.00229(14) |
| O3y2 | 0.00025(10) | -0.00090(11) |
| O3z2 | -0.00030(17) | 0.0008(2) |
Displacive (translational) Legendre coefficients: (Show/hide table) [ Help ]
| Atom site label | Displacement axis | Polynomial order | Polynomial coeff. |
|---|---|---|---|
| Zn | x | 1 | 0.01596(11) |
| Zn | y | 1 | 0 |
| Zn | z | 1 | -0.01662(17) |
| Zn | x | 2 | 0 |
| Zn | y | 2 | -0.001366(18) |
| Zn | z | 2 | 0 |
| Zn | x | 3 | 0.00013(11) |
| Zn | y | 3 | 0 |
| Zn | z | 3 | 0.00183(19) |
| Zn | x | 4 | 0 |
| Zn | y | 4 | -0.00018(3) |
| Zn | z | 4 | 0 |
| Zn | x | 5 | 0.00597(13) |
| Zn | y | 5 | 0 |
| Zn | z | 5 | -0.0080(2) |
| Zn | x | 6 | 0 |
| Zn | y | 6 | 0 |
| Zn | z | 6 | 0 |
| O2 | x | 1 | -0.0051(10) |
| O2 | y | 1 | 0 |
| O2 | z | 1 | -0.0323(19) |
| O2 | x | 2 | 0 |
| O2 | y | 2 | 0.0120(11) |
| O2 | z | 2 | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| PU111 | P | U11 | 1 |
| PU221 | P | U22 | 1 |
| PU331 | P | U33 | 1 |
| PU121 | P | U12 | 1 |
| PU131 | P | U13 | 1 |
| PU231 | P | U23 | 1 |
| PU112 | P | U11 | 2 |
| PU222 | P | U22 | 2 |
| PU332 | P | U33 | 2 |
| PU122 | P | U12 | 2 |
| PU132 | P | U13 | 2 |
| PU232 | P | U23 | 2 |
| O1U111 | O1 | U11 | 1 |
| O1U221 | O1 | U22 | 1 |
| O1U331 | O1 | U33 | 1 |
| O1U121 | O1 | U12 | 1 |
| O1U131 | O1 | U13 | 1 |
| O1U231 | O1 | U23 | 1 |
| O2'U111 | O2' | U11 | 1 |
| O2'U221 | O2' | U22 | 1 |
| O2'U331 | O2' | U33 | 1 |
| O2'U121 | O2' | U12 | 1 |
| O2'U131 | O2' | U13 | 1 |
| O2'U231 | O2' | U23 | 1 |
| O3U111 | O3 | U11 | 1 |
| O3U221 | O3 | U22 | 1 |
| O3U331 | O3 | U33 | 1 |
| O3U121 | O3 | U12 | 1 |
| O3U131 | O3 | U13 | 1 |
| O3U231 | O3 | U23 | 1 |
| O3U112 | O3 | U11 | 2 |
| O3U222 | O3 | U22 | 2 |
| O3U332 | O3 | U33 | 2 |
| O3U122 | O3 | U12 | 2 |
| O3U132 | O3 | U13 | 2 |
| O3U232 | O3 | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| PU111 | 0 | 0 |
| PU221 | 0 | 0 |
| PU331 | 0 | 0 |
| PU121 | 0.00188(6) | -0.00157(5) |
| PU131 | 0 | 0 |
| PU231 | -0.00128(5) | 0.00070(5) |
| PU112 | 0.00034(17) | -0.00110(17) |
| PU222 | 0.0019(2) | -0.00133(19) |
| PU332 | 0.00019(18) | 0.00069(18) |
| PU122 | 0 | 0 |
| PU132 | 0.00002(15) | 0.00119(15) |
| PU232 | 0 | 0 |
| O1U111 | 0 | 0 |
| O1U221 | 0 | 0 |
| O1U331 | 0 | 0 |
| O1U121 | -0.00068(15) | -0.00063(15) |
| O1U131 | 0 | 0 |
| O1U231 | 0.00025(14) | 0.00065(14) |
| O2'U111 | 0 | 0.002(2) |
| O2'U221 | 0 | -0.025(3) |
| O2'U331 | 0 | -0.002(4) |
| O2'U121 | 0.0048(18) | 0 |
| O2'U131 | 0 | 0.006(2) |
| O2'U231 | -0.013(2) | 0 |
| O3U111 | 0.0165(3) | -0.0038(2) |
| O3U221 | 0.00034(14) | -0.00042(14) |
| O3U331 | 0.00058(16) | -0.00084(16) |
| O3U121 | 0.00271(17) | -0.00145(16) |
| O3U131 | -0.00435(18) | 0.00227(16) |
| O3U231 | -0.00103(12) | 0.00022(12) |
| O3U112 | 0.0069(5) | -0.0020(4) |
| O3U222 | 0.0003(4) | 0.0010(4) |
| O3U332 | -0.0008(4) | 0.0005(4) |
| O3U122 | 0.0015(3) | 0.0005(3) |
| O3U132 | -0.0020(4) | 0.0015(4) |
| O3U232 | -0.0015(3) | -0.0005(3) |
Modulated anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Tensor element | Wave vector code | Cos coeff. | Sin coeff. |
|---|---|---|---|---|
| Zn | C111 | 1 | 0 | -0.0064(2) |
| Zn | C112 | 1 | 0.00054(7) | 0 |
| Zn | C113 | 1 | 0 | 0.00561(17) |
| Zn | C122 | 1 | 0 | -0.00032(3) |
| Zn | C123 | 1 | -0.00003(7) | 0 |
| Zn | C133 | 1 | 0 | -0.0049(3) |
| Zn | C222 | 1 | 0.00006(3) | 0 |
| Zn | C223 | 1 | 0 | 0.00024(4) |
| Zn | C233 | 1 | -0.00053(14) | 0 |
| Zn | C333 | 1 | 0 | 0.0075(5) |
alpha2_zn2p2o7_410
Chemical data
Full Name: zinc(II) diphosphate(V) [ Help ]
Common Name: zinc pyrophosphate [ Help ]
Structural Formula Sum: O7 P2 Zn2 [ Help ]
Formula weight: 304.7 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/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,-x4+1/2 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,x4+1/2 |
| 5 | x1+1/2,x2+1/2,x3,x4 |
| 6 | -x1+1/2,x2+1/2,-x3,-x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3,x4+1/2 |
a: 6.6041(2) Å [ Help ]
b: 8.2827(2) Å [ Help ]
c: 4.52490(10) Å [ Help ]
α: 90 ° [ Help ]
β: 105.4064(13) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 238.617(11) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.33062(11) | 0.000000 | 0.40287(8) |
Z: 2 [ Help ]
Cell determination reflection Nb.: 6378 [ Help ]
θ(min) for cell determination: 2.5 ° [ Help ]
θ(max) for cell determination: 45.2 ° [ Help ]
Cell measurement temperature: 410 K [ Help ]
μ: 10.701 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: SADABS [ Help ]
Minimum transmission factor: 0.025 [ Help ]
Maximum transmission factor: 0.60 [ Help ]
Refinement details
Total nb. of reflections: 5059 [ Help ]
Nb. of observed reflections: 2230 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0242 [ Help ]
wR(obs): 0.0329 [ Help ]
R(all): 0.0620 [ Help ]
wR(all): 0.0382 [ Help ]
S(all): 1.16 [ Help ]
S(obs): 1.54 [ Help ]
Nb. of reflections: 5059 [ Help ]
Nb. of parameters: 146 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0254 [ Help ]
Δ/σ(mean): 0.0039 [ Help ]
Δρ(max): 0.85 e_Å-3 [ Help ]
Δρ(min): -0.90 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 2370(80) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.5 | 0.18943(2) | 1 | Uani | 0.01840(6) | 4 | 1 | d | ? | ? | ? |
| P | P | 0.78941(3) | 0 | 0.59057(4) | Uani | 0.00902(4) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0.62166(8) | 0 | 0.28602(11) | Uani | 0.01067(10) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 1 | -0.0572(10) | 0.5 | Uani | 0.0193(10) | 4 | 0.192(4) | d | ? | ? | ? |
| O2' | O | 1 | -0.0215(9) | 0.5 | Uani | 0.035(2) | 4 | 0.308(4) | d | ? | ? | ? |
| O3 | O | 0.78202(8) | -0.15135(5) | 0.77490(10) | Uani | 0.01933(11) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.02252(11) | 0.00821(5) | 0.01706(11) | 0 | -0.00771(5) | 0 |
| P | P | 0.00772(6) | 0.01148(7) | 0.00710(6) | 0 | 0.00067(5) | 0 |
| O1 | O | 0.01089(16) | 0.01137(17) | 0.00798(15) | 0 | -0.00059(12) | 0 |
| O2 | O | 0.0073(9) | 0.024(3) | 0.0289(14) | 0 | 0.0082(9) | 0 |
| O2' | O | 0.0111(7) | 0.052(6) | 0.0476(15) | 0 | 0.0158(8) | 0 |
| O3 | O | 0.0300(2) | 0.01112(14) | 0.01342(15) | 0.00610(14) | -0.00017(14) | 0.00258(11) |
Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Atom symbol | C111 | C112 | C113 | C122 | C123 | C133 | C222 | C223 | C233 | C333 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0 | 0.00009(4) | 0 | 0 | -0.00055(4) | 0 | -0.00001(3) | 0 | 0.00123(8) | 0 |
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 |
| 2 | 2 |
| 3 | 3 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| Zn | 0.75 | 1 |
| O2 | 0.25 | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Px1 | P | x | 1 |
| Py1 | P | y | 1 |
| Pz1 | P | z | 1 |
| Px2 | P | x | 2 |
| Py2 | P | y | 2 |
| Pz2 | P | 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 |
| 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: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Px1 | 0 | 0 |
| Py1 | -0.00396(2) | -0.00615(2) |
| Pz1 | 0 | 0 |
| Px2 | -0.00051(7) | -0.00069(6) |
| Py2 | 0 | 0 |
| Pz2 | 0.00066(9) | 0.00141(10) |
| O1x1 | 0 | 0 |
| O1y1 | -0.00216(5) | 0.00440(5) |
| O1z1 | 0 | 0 |
| O1x2 | 0.00033(16) | 0.00040(17) |
| O1y2 | 0 | 0 |
| O1z2 | 0.0000(3) | 0.0003(2) |
| O3x1 | 0.00637(8) | -0.01568(8) |
| O3y1 | -0.00012(4) | -0.00367(4) |
| O3z1 | 0.00324(9) | 0.00439(8) |
| O3x2 | 0.00077(13) | -0.00180(14) |
| O3y2 | 0.00008(10) | -0.00071(11) |
| O3z2 | -0.00004(17) | 0.0008(2) |
Displacive (translational) Legendre coefficients: (Show/hide table) [ Help ]
| Atom site label | Displacement axis | Polynomial order | Polynomial coeff. |
|---|---|---|---|
| Zn | x | 1 | 0.01477(11) |
| Zn | y | 1 | 0 |
| Zn | z | 1 | -0.01578(17) |
| Zn | x | 2 | 0 |
| Zn | y | 2 | -0.001234(17) |
| Zn | z | 2 | 0 |
| Zn | x | 3 | -0.00004(11) |
| Zn | y | 3 | 0 |
| Zn | z | 3 | 0.00237(19) |
| Zn | x | 4 | 0 |
| Zn | y | 4 | -0.00010(3) |
| Zn | z | 4 | 0 |
| Zn | x | 5 | 0.00589(14) |
| Zn | y | 5 | 0 |
| Zn | z | 5 | -0.0083(2) |
| Zn | x | 6 | 0 |
| Zn | y | 6 | 0 |
| Zn | z | 6 | 0 |
| O2 | x | 1 | -0.0035(12) |
| O2 | y | 1 | 0 |
| O2 | z | 1 | -0.025(2) |
| O2 | x | 2 | 0 |
| O2 | y | 2 | 0.0110(12) |
| O2 | z | 2 | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| PU111 | P | U11 | 1 |
| PU221 | P | U22 | 1 |
| PU331 | P | U33 | 1 |
| PU121 | P | U12 | 1 |
| PU131 | P | U13 | 1 |
| PU231 | P | U23 | 1 |
| PU112 | P | U11 | 2 |
| PU222 | P | U22 | 2 |
| PU332 | P | U33 | 2 |
| PU122 | P | U12 | 2 |
| PU132 | P | U13 | 2 |
| PU232 | P | U23 | 2 |
| O1U111 | O1 | U11 | 1 |
| O1U221 | O1 | U22 | 1 |
| O1U331 | O1 | U33 | 1 |
| O1U121 | O1 | U12 | 1 |
| O1U131 | O1 | U13 | 1 |
| O1U231 | O1 | U23 | 1 |
| O2'U111 | O2' | U11 | 1 |
| O2'U221 | O2' | U22 | 1 |
| O2'U331 | O2' | U33 | 1 |
| O2'U121 | O2' | U12 | 1 |
| O2'U131 | O2' | U13 | 1 |
| O2'U231 | O2' | U23 | 1 |
| O3U111 | O3 | U11 | 1 |
| O3U221 | O3 | U22 | 1 |
| O3U331 | O3 | U33 | 1 |
| O3U121 | O3 | U12 | 1 |
| O3U131 | O3 | U13 | 1 |
| O3U231 | O3 | U23 | 1 |
| O3U112 | O3 | U11 | 2 |
| O3U222 | O3 | U22 | 2 |
| O3U332 | O3 | U33 | 2 |
| O3U122 | O3 | U12 | 2 |
| O3U132 | O3 | U13 | 2 |
| O3U232 | O3 | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| PU111 | 0 | 0 |
| PU221 | 0 | 0 |
| PU331 | 0 | 0 |
| PU121 | 0.00181(5) | -0.00150(5) |
| PU131 | 0 | 0 |
| PU231 | -0.00122(5) | 0.00069(5) |
| PU112 | 0.00010(17) | -0.00140(17) |
| PU222 | 0.0027(2) | -0.00090(18) |
| PU332 | -0.00005(18) | 0.00044(17) |
| PU122 | 0 | 0 |
| PU132 | -0.00041(15) | 0.00100(15) |
| PU232 | 0 | 0 |
| O1U111 | 0 | 0 |
| O1U221 | 0 | 0 |
| O1U331 | 0 | 0 |
| O1U121 | -0.00072(15) | -0.00061(15) |
| O1U131 | 0 | 0 |
| O1U231 | 0.00021(14) | 0.00038(14) |
| O2'U111 | 0 | -0.0012(19) |
| O2'U221 | 0 | -0.027(3) |
| O2'U331 | 0 | -0.001(4) |
| O2'U121 | 0.0025(19) | 0 |
| O2'U131 | 0 | 0.002(2) |
| O2'U231 | -0.018(2) | 0 |
| O3U111 | 0.0153(3) | -0.0036(2) |
| O3U221 | 0.00061(14) | -0.00046(13) |
| O3U331 | 0.00058(15) | -0.00097(15) |
| O3U121 | 0.00283(16) | -0.00147(15) |
| O3U131 | -0.00411(17) | 0.00176(15) |
| O3U231 | -0.00105(11) | 0.00033(11) |
| O3U112 | 0.0066(5) | -0.0014(4) |
| O3U222 | 0.0004(4) | 0.0002(4) |
| O3U332 | -0.0005(4) | 0.0001(4) |
| O3U122 | 0.0015(3) | 0.0000(3) |
| O3U132 | -0.0018(4) | 0.0013(3) |
| O3U232 | -0.0013(3) | -0.0001(3) |
Modulated anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Tensor element | Wave vector code | Cos coeff. | Sin coeff. |
|---|---|---|---|---|
| Zn | C111 | 1 | 0 | -0.0067(2) |
| Zn | C112 | 1 | 0.00059(7) | 0 |
| Zn | C113 | 1 | 0 | 0.00564(16) |
| Zn | C122 | 1 | 0 | -0.00032(3) |
| Zn | C123 | 1 | 0.00003(6) | 0 |
| Zn | C133 | 1 | 0 | -0.0046(3) |
| Zn | C222 | 1 | 0.00013(3) | 0 |
| Zn | C223 | 1 | 0 | 0.00035(4) |
| Zn | C233 | 1 | -0.00059(13) | 0 |
| Zn | C333 | 1 | 0 | 0.0065(5) |
alpha2_zn2p2o7_415
Chemical data
Full Name: zinc(II) diphosphate(V) [ Help ]
Common Name: zinc pyrophosphate [ Help ]
Structural Formula Sum: O7 P2 Zn2 [ Help ]
Formula weight: 304.7 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/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,-x4+1/2 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,x4+1/2 |
| 5 | x1+1/2,x2+1/2,x3,x4 |
| 6 | -x1+1/2,x2+1/2,-x3,-x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3,x4+1/2 |
a: 6.6036(2) Å [ Help ]
b: 8.2830(2) Å [ Help ]
c: 4.52500(10) Å [ Help ]
α: 90 ° [ Help ]
β: 105.4028(13) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 238.617(11) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.33004(12) | 0.000000 | 0.40167(8) |
Z: 2 [ Help ]
Cell determination reflection Nb.: 6135 [ Help ]
θ(min) for cell determination: 2.4 ° [ Help ]
θ(max) for cell determination: 45.3 ° [ Help ]
Cell measurement temperature: 415 K [ Help ]
μ: 10.701 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: SADABS [ Help ]
Minimum transmission factor: 0.025 [ Help ]
Maximum transmission factor: 0.60 [ Help ]
Refinement details
Total nb. of reflections: 5064 [ Help ]
Nb. of observed reflections: 2147 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0243 [ Help ]
wR(obs): 0.0342 [ Help ]
R(all): 0.0639 [ Help ]
wR(all): 0.0391 [ Help ]
S(all): 1.16 [ Help ]
S(obs): 1.59 [ Help ]
Nb. of reflections: 5064 [ Help ]
Nb. of parameters: 146 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0282 [ Help ]
Δ/σ(mean): 0.0040 [ Help ]
Δρ(max): 0.87 e_Å-3 [ Help ]
Δρ(min): -0.82 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 2400(80) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.5 | 0.18966(2) | 1 | Uani | 0.01864(6) | 4 | 1 | d | ? | ? | ? |
| P | P | 0.78938(3) | 0 | 0.59065(4) | Uani | 0.00910(4) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0.62157(8) | 0 | 0.28621(11) | Uani | 0.01072(10) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 1 | -0.0561(12) | 0.5 | Uani | 0.0183(11) | 4 | 0.178(4) | d | ? | ? | ? |
| O2' | O | 1 | -0.0210(10) | 0.5 | Uani | 0.035(2) | 4 | 0.322(4) | d | ? | ? | ? |
| O3 | O | 0.78182(8) | -0.15135(5) | 0.77494(10) | Uani | 0.01944(11) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.02279(12) | 0.00831(5) | 0.01731(12) | 0 | -0.00782(6) | 0 |
| P | P | 0.00774(6) | 0.01165(7) | 0.00720(6) | 0 | 0.00072(5) | 0 |
| O1 | O | 0.01077(15) | 0.01164(17) | 0.00801(15) | 0 | -0.00056(12) | 0 |
| O2 | O | 0.0060(9) | 0.024(3) | 0.0266(14) | 0 | 0.0070(9) | 0 |
| O2' | O | 0.0123(7) | 0.048(6) | 0.0495(17) | 0 | 0.0160(9) | 0 |
| O3 | O | 0.0302(2) | 0.01116(15) | 0.01367(15) | 0.00617(14) | 0.00000(14) | 0.00265(12) |
Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Atom symbol | C111 | C112 | C113 | C122 | C123 | C133 | C222 | C223 | C233 | C333 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0 | 0.00008(4) | 0 | 0 | -0.00049(4) | 0 | 0.00013(3) | 0 | 0.00156(8) | 0 |
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 |
| 2 | 2 |
| 3 | 3 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| Zn | 0.75 | 1 |
| O2 | 0.25 | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Px1 | P | x | 1 |
| Py1 | P | y | 1 |
| Pz1 | P | z | 1 |
| Px2 | P | x | 2 |
| Py2 | P | y | 2 |
| Pz2 | P | 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 |
| 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: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Px1 | 0 | 0 |
| Py1 | -0.00364(2) | -0.00569(2) |
| Pz1 | 0 | 0 |
| Px2 | -0.00037(7) | -0.00053(7) |
| Py2 | 0 | 0 |
| Pz2 | 0.00072(11) | 0.00140(11) |
| O1x1 | 0 | 0 |
| O1y1 | -0.00204(5) | 0.00414(5) |
| O1z1 | 0 | 0 |
| O1x2 | 0.00044(18) | 0.00053(20) |
| O1y2 | 0 | 0 |
| O1z2 | 0.0000(3) | 0.0005(3) |
| O3x1 | 0.00582(8) | -0.01447(8) |
| O3y1 | -0.00017(4) | -0.00347(4) |
| O3z1 | 0.00293(9) | 0.00408(8) |
| O3x2 | 0.00066(16) | -0.00154(16) |
| O3y2 | 0.00017(12) | -0.00077(12) |
| O3z2 | -0.0002(2) | 0.0006(2) |
Displacive (translational) Legendre coefficients: (Show/hide table) [ Help ]
| Atom site label | Displacement axis | Polynomial order | Polynomial coeff. |
|---|---|---|---|
| Zn | x | 1 | 0.01385(12) |
| Zn | y | 1 | 0 |
| Zn | z | 1 | -0.01483(19) |
| Zn | x | 2 | 0 |
| Zn | y | 2 | -0.001174(18) |
| Zn | z | 2 | 0 |
| Zn | x | 3 | -0.00039(13) |
| Zn | y | 3 | 0 |
| Zn | z | 3 | 0.0027(2) |
| Zn | x | 4 | 0 |
| Zn | y | 4 | -0.00004(4) |
| Zn | z | 4 | 0 |
| Zn | x | 5 | 0.00586(16) |
| Zn | y | 5 | 0 |
| Zn | z | 5 | -0.0083(2) |
| Zn | x | 6 | 0 |
| Zn | y | 6 | 0 |
| Zn | z | 6 | 0 |
| O2 | x | 1 | -0.0045(14) |
| O2 | y | 1 | 0 |
| O2 | z | 1 | -0.025(2) |
| O2 | x | 2 | 0 |
| O2 | y | 2 | 0.0109(15) |
| O2 | z | 2 | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| PU111 | P | U11 | 1 |
| PU221 | P | U22 | 1 |
| PU331 | P | U33 | 1 |
| PU121 | P | U12 | 1 |
| PU131 | P | U13 | 1 |
| PU231 | P | U23 | 1 |
| PU112 | P | U11 | 2 |
| PU222 | P | U22 | 2 |
| PU332 | P | U33 | 2 |
| PU122 | P | U12 | 2 |
| PU132 | P | U13 | 2 |
| PU232 | P | U23 | 2 |
| O1U111 | O1 | U11 | 1 |
| O1U221 | O1 | U22 | 1 |
| O1U331 | O1 | U33 | 1 |
| O1U121 | O1 | U12 | 1 |
| O1U131 | O1 | U13 | 1 |
| O1U231 | O1 | U23 | 1 |
| O2'U111 | O2' | U11 | 1 |
| O2'U221 | O2' | U22 | 1 |
| O2'U331 | O2' | U33 | 1 |
| O2'U121 | O2' | U12 | 1 |
| O2'U131 | O2' | U13 | 1 |
| O2'U231 | O2' | U23 | 1 |
| O3U111 | O3 | U11 | 1 |
| O3U221 | O3 | U22 | 1 |
| O3U331 | O3 | U33 | 1 |
| O3U121 | O3 | U12 | 1 |
| O3U131 | O3 | U13 | 1 |
| O3U231 | O3 | U23 | 1 |
| O3U112 | O3 | U11 | 2 |
| O3U222 | O3 | U22 | 2 |
| O3U332 | O3 | U33 | 2 |
| O3U122 | O3 | U12 | 2 |
| O3U132 | O3 | U13 | 2 |
| O3U232 | O3 | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| PU111 | 0 | 0 |
| PU221 | 0 | 0 |
| PU331 | 0 | 0 |
| PU121 | 0.00174(6) | -0.00141(5) |
| PU131 | 0 | 0 |
| PU231 | -0.00118(5) | 0.00067(5) |
| PU112 | -0.00021(19) | -0.00123(19) |
| PU222 | 0.0022(2) | -0.0012(2) |
| PU332 | 0.00019(20) | 0.00061(18) |
| PU122 | 0 | 0 |
| PU132 | -0.00037(17) | 0.00118(16) |
| PU232 | 0 | 0 |
| O1U111 | 0 | 0 |
| O1U221 | 0 | 0 |
| O1U331 | 0 | 0 |
| O1U121 | -0.00078(16) | -0.00041(16) |
| O1U131 | 0 | 0 |
| O1U231 | 0.00018(14) | 0.00034(14) |
| O2'U111 | 0 | -0.0007(19) |
| O2'U221 | 0 | -0.020(3) |
| O2'U331 | 0 | 0.002(4) |
| O2'U121 | 0.004(2) | 0 |
| O2'U131 | 0 | 0.004(2) |
| O2'U231 | -0.015(2) | 0 |
| O3U111 | 0.0144(3) | -0.0037(2) |
| O3U221 | 0.00053(14) | -0.00036(14) |
| O3U331 | 0.00047(15) | -0.00078(15) |
| O3U121 | 0.00255(16) | -0.00144(15) |
| O3U131 | -0.00391(17) | 0.00198(16) |
| O3U231 | -0.00087(12) | 0.00032(12) |
| O3U112 | 0.0051(5) | -0.0010(5) |
| O3U222 | 0.0009(4) | 0.0015(5) |
| O3U332 | -0.0004(4) | 0.0005(4) |
| O3U122 | 0.0011(3) | -0.0004(4) |
| O3U132 | -0.0017(4) | 0.0020(4) |
| O3U232 | -0.0007(3) | -0.0009(3) |
Modulated anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Tensor element | Wave vector code | Cos coeff. | Sin coeff. |
|---|---|---|---|---|
| Zn | C111 | 1 | 0 | -0.0064(2) |
| Zn | C112 | 1 | 0.00091(7) | 0 |
| Zn | C113 | 1 | 0 | 0.00533(18) |
| Zn | C122 | 1 | 0 | -0.00040(3) |
| Zn | C123 | 1 | -0.00018(7) | 0 |
| Zn | C133 | 1 | 0 | -0.0044(3) |
| Zn | C222 | 1 | 0.00010(3) | 0 |
| Zn | C223 | 1 | 0 | 0.00031(4) |
| Zn | C233 | 1 | -0.00080(14) | 0 |
| Zn | C333 | 1 | 0 | 0.0068(5) |
alpha2_zn2p2o7_420
Chemical data
Full Name: zinc(II) diphosphate(V) [ Help ]
Common Name: zinc pyrophosphate [ Help ]
Structural Formula Sum: O7 P2 Zn2 [ Help ]
Formula weight: 304.7 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/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,-x4+1/2 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,x4+1/2 |
| 5 | x1+1/2,x2+1/2,x3,x4 |
| 6 | -x1+1/2,x2+1/2,-x3,-x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3,x4+1/2 |
a: 6.6025(2) Å [ Help ]
b: 8.2826(2) Å [ Help ]
c: 4.52510(10) Å [ Help ]
α: 90 ° [ Help ]
β: 105.3996(14) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 238.575(11) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.32940(14) | 0.000000 | 0.40083(9) |
Z: 2 [ Help ]
Cell determination reflection Nb.: 5902 [ Help ]
θ(min) for cell determination: 3.4 ° [ Help ]
θ(max) for cell determination: 45.3 ° [ Help ]
Cell measurement temperature: 420 K [ Help ]
μ: 10.703 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: SADABS [ Help ]
Minimum transmission factor: 0.025 [ Help ]
Maximum transmission factor: 0.60 [ Help ]
Refinement details
Total nb. of reflections: 5064 [ Help ]
Nb. of observed reflections: 2089 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0246 [ Help ]
wR(obs): 0.0360 [ Help ]
R(all): 0.0694 [ Help ]
wR(all): 0.0414 [ Help ]
S(all): 1.19 [ Help ]
S(obs): 1.64 [ Help ]
Nb. of reflections: 5064 [ Help ]
Nb. of parameters: 146 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0391 [ Help ]
Δ/σ(mean): 0.0082 [ Help ]
Δρ(max): 0.94 e_Å-3 [ Help ]
Δρ(min): -0.83 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 2380(80) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.5 | 0.18963(2) | 1 | Uani | 0.01887(7) | 4 | 1 | d | ? | ? | ? |
| P | P | 0.78928(3) | 0 | 0.59062(4) | Uani | 0.00919(4) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0.62148(8) | 0 | 0.28611(12) | Uani | 0.01086(10) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 1 | -0.0563(14) | 0.5 | Uani | 0.0183(13) | 4 | 0.153(5) | d | ? | ? | ? |
| O2' | O | 1 | -0.0219(13) | 0.5 | Uani | 0.041(3) | 4 | 0.347(5) | d | ? | ? | ? |
| O3 | O | 0.78161(8) | -0.15143(5) | 0.77487(10) | Uani | 0.01948(11) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.02312(13) | 0.00841(5) | 0.01745(13) | 0 | -0.00798(7) | 0 |
| P | P | 0.00769(6) | 0.01192(8) | 0.00725(7) | 0 | 0.00074(5) | 0 |
| O1 | O | 0.01088(16) | 0.01193(18) | 0.00802(16) | 0 | -0.00057(13) | 0 |
| O2 | O | 0.0053(13) | 0.025(3) | 0.0263(18) | 0 | 0.0071(12) | 0 |
| O2' | O | 0.0116(7) | 0.066(7) | 0.0486(16) | 0 | 0.0155(9) | 0 |
| O3 | O | 0.0303(2) | 0.01123(15) | 0.01359(16) | 0.00608(14) | 0.00000(15) | 0.00262(12) |
Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Atom symbol | C111 | C112 | C113 | C122 | C123 | C133 | C222 | C223 | C233 | C333 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0 | 0.00016(4) | 0 | 0 | -0.00061(4) | 0 | 0.00009(3) | 0 | 0.00162(9) | 0 |
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 |
| 2 | 2 |
| 3 | 3 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| Zn | 0.75 | 1 |
| O2 | 0.25 | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Px1 | P | x | 1 |
| Py1 | P | y | 1 |
| Pz1 | P | z | 1 |
| Px2 | P | x | 2 |
| Py2 | P | y | 2 |
| Pz2 | P | 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 |
| 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: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Px1 | 0 | 0 |
| Py1 | -0.00328(2) | -0.00518(2) |
| Pz1 | 0 | 0 |
| Px2 | -0.00046(8) | -0.00079(8) |
| Py2 | 0 | 0 |
| Pz2 | 0.00065(12) | 0.00139(12) |
| O1x1 | 0 | 0 |
| O1y1 | -0.00188(6) | 0.00373(6) |
| O1z1 | 0 | 0 |
| O1x2 | 0.0004(2) | 0.0001(2) |
| O1y2 | 0 | 0 |
| O1z2 | 0.0006(3) | -0.0003(3) |
| O3x1 | 0.00543(8) | -0.01337(8) |
| O3y1 | -0.00008(5) | -0.00313(4) |
| O3z1 | 0.00286(9) | 0.00378(9) |
| O3x2 | 0.00058(17) | -0.00063(17) |
| O3y2 | 0.00036(13) | -0.00072(13) |
| O3z2 | -0.0001(2) | 0.0013(3) |
Displacive (translational) Legendre coefficients: (Show/hide table) [ Help ]
| Atom site label | Displacement axis | Polynomial order | Polynomial coeff. |
|---|---|---|---|
| Zn | x | 1 | 0.01264(14) |
| Zn | y | 1 | 0 |
| Zn | z | 1 | -0.0140(2) |
| Zn | x | 2 | 0 |
| Zn | y | 2 | -0.001097(18) |
| Zn | z | 2 | 0 |
| Zn | x | 3 | -0.00057(15) |
| Zn | y | 3 | 0 |
| Zn | z | 3 | 0.0032(2) |
| Zn | x | 4 | 0 |
| Zn | y | 4 | -0.00005(4) |
| Zn | z | 4 | 0 |
| Zn | x | 5 | 0.00573(18) |
| Zn | y | 5 | 0 |
| Zn | z | 5 | -0.0086(3) |
| Zn | x | 6 | 0 |
| Zn | y | 6 | 0 |
| Zn | z | 6 | 0 |
| O2 | x | 1 | -0.0092(18) |
| O2 | y | 1 | 0 |
| O2 | z | 1 | -0.028(3) |
| O2 | x | 2 | 0 |
| O2 | y | 2 | 0.0117(19) |
| O2 | z | 2 | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| PU111 | P | U11 | 1 |
| PU221 | P | U22 | 1 |
| PU331 | P | U33 | 1 |
| PU121 | P | U12 | 1 |
| PU131 | P | U13 | 1 |
| PU231 | P | U23 | 1 |
| PU112 | P | U11 | 2 |
| PU222 | P | U22 | 2 |
| PU332 | P | U33 | 2 |
| PU122 | P | U12 | 2 |
| PU132 | P | U13 | 2 |
| PU232 | P | U23 | 2 |
| O1U111 | O1 | U11 | 1 |
| O1U221 | O1 | U22 | 1 |
| O1U331 | O1 | U33 | 1 |
| O1U121 | O1 | U12 | 1 |
| O1U131 | O1 | U13 | 1 |
| O1U231 | O1 | U23 | 1 |
| O2'U111 | O2' | U11 | 1 |
| O2'U221 | O2' | U22 | 1 |
| O2'U331 | O2' | U33 | 1 |
| O2'U121 | O2' | U12 | 1 |
| O2'U131 | O2' | U13 | 1 |
| O2'U231 | O2' | U23 | 1 |
| O3U111 | O3 | U11 | 1 |
| O3U221 | O3 | U22 | 1 |
| O3U331 | O3 | U33 | 1 |
| O3U121 | O3 | U12 | 1 |
| O3U131 | O3 | U13 | 1 |
| O3U231 | O3 | U23 | 1 |
| O3U112 | O3 | U11 | 2 |
| O3U222 | O3 | U22 | 2 |
| O3U332 | O3 | U33 | 2 |
| O3U122 | O3 | U12 | 2 |
| O3U132 | O3 | U13 | 2 |
| O3U232 | O3 | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| PU111 | 0 | 0 |
| PU221 | 0 | 0 |
| PU331 | 0 | 0 |
| PU121 | 0.00156(6) | -0.00130(6) |
| PU131 | 0 | 0 |
| PU231 | -0.00109(6) | 0.00068(5) |
| PU112 | 0.0000(2) | -0.0010(2) |
| PU222 | 0.0030(2) | -0.0029(2) |
| PU332 | 0.0002(2) | 0.0006(2) |
| PU122 | 0 | 0 |
| PU132 | -0.00035(18) | 0.00131(18) |
| PU232 | 0 | 0 |
| O1U111 | 0 | 0 |
| O1U221 | 0 | 0 |
| O1U331 | 0 | 0 |
| O1U121 | -0.00044(17) | -0.00050(17) |
| O1U131 | 0 | 0 |
| O1U231 | 0.00029(15) | 0.00028(15) |
| O2'U111 | 0 | 0.000(2) |
| O2'U221 | 0 | -0.028(4) |
| O2'U331 | 0 | -0.003(4) |
| O2'U121 | 0.009(2) | 0 |
| O2'U131 | 0 | 0.002(2) |
| O2'U231 | -0.014(3) | 0 |
| O3U111 | 0.0137(3) | -0.0040(3) |
| O3U221 | 0.00044(15) | -0.00052(15) |
| O3U331 | 0.00032(15) | -0.00068(16) |
| O3U121 | 0.00254(17) | -0.00149(17) |
| O3U131 | -0.00360(18) | 0.00180(17) |
| O3U231 | -0.00086(12) | 0.00028(13) |
| O3U112 | 0.0056(6) | -0.0020(5) |
| O3U222 | 0.0004(5) | 0.0003(5) |
| O3U332 | -0.0019(5) | 0.0000(5) |
| O3U122 | 0.0016(4) | 0.0002(4) |
| O3U132 | -0.0020(4) | 0.0009(4) |
| O3U232 | -0.0011(4) | -0.0004(4) |
Modulated anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Tensor element | Wave vector code | Cos coeff. | Sin coeff. |
|---|---|---|---|---|
| Zn | C111 | 1 | 0 | -0.0066(2) |
| Zn | C112 | 1 | 0.00072(7) | 0 |
| Zn | C113 | 1 | 0 | 0.00495(19) |
| Zn | C122 | 1 | 0 | -0.00043(4) |
| Zn | C123 | 1 | 0.00005(7) | 0 |
| Zn | C133 | 1 | 0 | -0.0042(3) |
| Zn | C222 | 1 | 0.00006(4) | 0 |
| Zn | C223 | 1 | 0 | 0.00032(5) |
| Zn | C233 | 1 | -0.00094(15) | 0 |
| Zn | C333 | 1 | 0 | 0.0067(5) |
alpha2_zn2p2o7_430
Chemical data
Full Name: zinc(II) diphosphate(V) [ Help ]
Common Name: zinc pyrophosphate [ Help ]
Structural Formula Sum: O7 P2 Zn2 [ Help ]
Formula weight: 304.7 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/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,-x4+1/2 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,x4+1/2 |
| 5 | x1+1/2,x2+1/2,x3,x4 |
| 6 | -x1+1/2,x2+1/2,-x3,-x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3,x4+1/2 |
a: 6.6018(2) Å [ Help ]
b: 8.2835(2) Å [ Help ]
c: 4.52600(10) Å [ Help ]
α: 90 ° [ Help ]
β: 105.3906(15) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 238.633(11) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.32790(8) | 0 | 0.40041(5) |
Z: 2 [ Help ]
Cell determination reflection Nb.: 5548 [ Help ]
θ(min) for cell determination: 3.4 ° [ Help ]
θ(max) for cell determination: 45.3 ° [ Help ]
Cell measurement temperature: 430 K [ Help ]
μ: 10.701 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: SADABS [ Help ]
Minimum transmission factor: 0.025 [ Help ]
Maximum transmission factor: 0.60 [ Help ]
Refinement details
Total nb. of reflections: 5061 [ Help ]
Nb. of observed reflections: 1949 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0266 [ Help ]
wR(obs): 0.0393 [ Help ]
R(all): 0.0803 [ Help ]
wR(all): 0.0439 [ Help ]
S(all): 1.22 [ Help ]
S(obs): 1.80 [ Help ]
Nb. of reflections: 5061 [ Help ]
Nb. of parameters: 146 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0431 [ Help ]
Δ/σ(mean): 0.0036 [ Help ]
Δρ(max): 0.79 e_Å-3 [ Help ]
Δρ(min): -0.78 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 2260(90) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.5 | 0.18972(2) | 1 | Uani | 0.01846(8) | 4 | 1 | d | ? | ? | ? |
| P | P | 0.78924(3) | 0 | 0.59062(4) | Uani | 0.00869(4) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0.62139(8) | 0 | 0.28648(12) | Uani | 0.01024(11) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 1 | -0.0579(18) | 0.5 | Uani | 0.0140(16) | 4 | 0.105(4) | d | ? | ? | ? |
| O2' | O | 1 | -0.0244(9) | 0.5 | Uani | 0.038(2) | 4 | 0.395(4) | d | ? | ? | ? |
| O3 | O | 0.78147(9) | -0.15150(6) | 0.77500(11) | Uani | 0.01886(12) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.02256(16) | 0.00800(5) | 0.01712(16) | 0 | -0.00821(8) | 0 |
| P | P | 0.00694(7) | 0.01182(8) | 0.00663(7) | 0 | 0.00062(5) | 0 |
| O1 | O | 0.00970(17) | 0.01160(18) | 0.00768(16) | 0 | -0.00075(13) | 0 |
| O2 | O | 0.0037(17) | 0.018(4) | 0.022(2) | 0 | 0.0051(16) | 0 |
| O2' | O | 0.0104(6) | 0.060(6) | 0.0482(14) | 0 | 0.0147(8) | 0 |
| O3 | O | 0.0290(2) | 0.01106(16) | 0.01344(16) | 0.00644(15) | 0.00022(15) | 0.00268(12) |
Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Atom symbol | C111 | C112 | C113 | C122 | C123 | C133 | C222 | C223 | C233 | C333 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0 | 0.00051(5) | 0 | 0 | -0.00073(4) | 0 | 0.00009(3) | 0 | 0.00144(9) | 0 |
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 |
| 2 | 2 |
| 3 | 3 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| Zn | 0.75 | 1 |
| O2 | 0.25 | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Px1 | P | x | 1 |
| Py1 | P | y | 1 |
| Pz1 | P | z | 1 |
| Px2 | P | x | 2 |
| Py2 | P | y | 2 |
| Pz2 | P | 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 |
| 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: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Px1 | 0 | 0 |
| Py1 | -0.00259(3) | -0.00404(2) |
| Pz1 | 0 | 0 |
| Px2 | -0.00026(9) | -0.00068(9) |
| Py2 | 0 | 0 |
| Pz2 | 0.00002(14) | 0.00125(14) |
| O1x1 | 0 | 0 |
| O1y1 | -0.00151(6) | 0.00298(6) |
| O1z1 | 0 | 0 |
| O1x2 | -0.0021(2) | 0.0007(2) |
| O1y2 | 0 | 0 |
| O1z2 | -0.0006(4) | 0.0001(4) |
| O3x1 | 0.00413(9) | -0.01031(9) |
| O3y1 | -0.00017(5) | -0.00244(5) |
| O3z1 | 0.00210(9) | 0.00316(9) |
| O3x2 | 0.0011(2) | -0.0008(2) |
| O3y2 | 0.00016(16) | -0.00042(16) |
| O3z2 | -0.0007(3) | 0.0017(3) |
Displacive (translational) Legendre coefficients: (Show/hide table) [ Help ]
| Atom site label | Displacement axis | Polynomial order | Polynomial coeff. |
|---|---|---|---|
| Zn | x | 1 | 0.01050(17) |
| Zn | y | 1 | 0 |
| Zn | z | 1 | -0.0122(3) |
| Zn | x | 2 | 0 |
| Zn | y | 2 | -0.000862(19) |
| Zn | z | 2 | 0 |
| Zn | x | 3 | -0.00152(19) |
| Zn | y | 3 | 0 |
| Zn | z | 3 | 0.0044(3) |
| Zn | x | 4 | 0 |
| Zn | y | 4 | -0.00002(4) |
| Zn | z | 4 | 0 |
| Zn | x | 5 | 0.0062(2) |
| Zn | y | 5 | 0 |
| Zn | z | 5 | -0.0090(3) |
| Zn | x | 6 | 0 |
| Zn | y | 6 | 0 |
| Zn | z | 6 | 0 |
| O2 | x | 1 | -0.005(3) |
| O2 | y | 1 | 0 |
| O2 | z | 1 | -0.028(5) |
| O2 | x | 2 | 0 |
| O2 | y | 2 | 0.014(3) |
| O2 | z | 2 | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| PU111 | P | U11 | 1 |
| PU221 | P | U22 | 1 |
| PU331 | P | U33 | 1 |
| PU121 | P | U12 | 1 |
| PU131 | P | U13 | 1 |
| PU231 | P | U23 | 1 |
| PU112 | P | U11 | 2 |
| PU222 | P | U22 | 2 |
| PU332 | P | U33 | 2 |
| PU122 | P | U12 | 2 |
| PU132 | P | U13 | 2 |
| PU232 | P | U23 | 2 |
| O1U111 | O1 | U11 | 1 |
| O1U221 | O1 | U22 | 1 |
| O1U331 | O1 | U33 | 1 |
| O1U121 | O1 | U12 | 1 |
| O1U131 | O1 | U13 | 1 |
| O1U231 | O1 | U23 | 1 |
| O2'U111 | O2' | U11 | 1 |
| O2'U221 | O2' | U22 | 1 |
| O2'U331 | O2' | U33 | 1 |
| O2'U121 | O2' | U12 | 1 |
| O2'U131 | O2' | U13 | 1 |
| O2'U231 | O2' | U23 | 1 |
| O3U111 | O3 | U11 | 1 |
| O3U221 | O3 | U22 | 1 |
| O3U331 | O3 | U33 | 1 |
| O3U121 | O3 | U12 | 1 |
| O3U131 | O3 | U13 | 1 |
| O3U231 | O3 | U23 | 1 |
| O3U112 | O3 | U11 | 2 |
| O3U222 | O3 | U22 | 2 |
| O3U332 | O3 | U33 | 2 |
| O3U122 | O3 | U12 | 2 |
| O3U132 | O3 | U13 | 2 |
| O3U232 | O3 | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| PU111 | 0 | 0 |
| PU221 | 0 | 0 |
| PU331 | 0 | 0 |
| PU121 | 0.00125(7) | -0.00111(7) |
| PU131 | 0 | 0 |
| PU231 | -0.00091(6) | 0.00052(6) |
| PU112 | 0.0023(2) | -0.0016(2) |
| PU222 | 0.0038(3) | -0.0038(3) |
| PU332 | 0.0001(2) | 0.0002(2) |
| PU122 | 0 | 0 |
| PU132 | 0.0014(2) | 0.00200(19) |
| PU232 | 0 | 0 |
| O1U111 | 0 | 0 |
| O1U221 | 0 | 0 |
| O1U331 | 0 | 0 |
| O1U121 | -0.00038(20) | -0.00043(19) |
| O1U131 | 0 | 0 |
| O1U231 | 0.00016(17) | 0.00018(17) |
| O2'U111 | 0 | -0.0036(18) |
| O2'U221 | 0 | -0.023(3) |
| O2'U331 | 0 | -0.004(3) |
| O2'U121 | 0.004(2) | 0 |
| O2'U131 | 0 | 0.0025(19) |
| O2'U231 | -0.010(3) | 0 |
| O3U111 | 0.0107(3) | -0.0032(3) |
| O3U221 | 0.00040(17) | -0.00023(17) |
| O3U331 | 0.00021(17) | -0.00073(17) |
| O3U121 | 0.00207(19) | -0.00135(18) |
| O3U131 | -0.0027(2) | 0.00165(18) |
| O3U231 | -0.00070(13) | 0.00038(13) |
| O3U112 | 0.0063(7) | -0.0002(7) |
| O3U222 | -0.0008(6) | 0.0005(6) |
| O3U332 | -0.0021(5) | 0.0008(5) |
| O3U122 | 0.0020(4) | 0.0016(4) |
| O3U132 | -0.0014(5) | 0.0014(5) |
| O3U232 | 0.0005(5) | 0.0004(5) |
Modulated anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Tensor element | Wave vector code | Cos coeff. | Sin coeff. |
|---|---|---|---|---|
| Zn | C111 | 1 | 0 | -0.0063(3) |
| Zn | C112 | 1 | 0.00013(8) | 0 |
| Zn | C113 | 1 | 0 | 0.0038(2) |
| Zn | C122 | 1 | 0 | -0.00059(4) |
| Zn | C123 | 1 | 0.00011(8) | 0 |
| Zn | C133 | 1 | 0 | -0.0032(3) |
| Zn | C222 | 1 | 0.00014(4) | 0 |
| Zn | C223 | 1 | 0 | 0.00051(5) |
| Zn | C233 | 1 | -0.00028(17) | 0 |
| Zn | C333 | 1 | 0 | 0.0062(6) |
alpha2_zn2p2o7_450
Chemical data
Full Name: zinc(II) diphosphate(V) [ Help ]
Common Name: zinc pyrophosphate [ Help ]
Structural Formula Sum: O7 P2 Zn2 [ Help ]
Formula weight: 304.7 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/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,-x4+1/2 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,x4+1/2 |
| 5 | x1+1/2,x2+1/2,x3,x4 |
| 6 | -x1+1/2,x2+1/2,-x3,-x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3,x4+1/2 |
a: 6.6011(2) Å [ Help ]
b: 8.2839(3) Å [ Help ]
c: 4.5266(2) Å [ Help ]
α: 90 ° [ Help ]
β: 105.3869(17) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 238.655(16) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.3268(3) | 0.000000 | 0.3989(2) |
Z: 2 [ Help ]
Cell determination reflection Nb.: 4377 [ Help ]
θ(min) for cell determination: 4.0 ° [ Help ]
θ(max) for cell determination: 45.3 ° [ Help ]
Cell measurement temperature: 450 K [ Help ]
μ: 10.7 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: SADABS [ Help ]
Minimum transmission factor: 0.025 [ Help ]
Maximum transmission factor: 0.60 [ Help ]
Refinement details
Total nb. of reflections: 5061 [ Help ]
Nb. of observed reflections: 1643 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0287 [ Help ]
wR(obs): 0.0424 [ Help ]
R(all): 0.1015 [ Help ]
wR(all): 0.0475 [ Help ]
S(all): 1.22 [ Help ]
S(obs): 1.97 [ Help ]
Nb. of reflections: 5061 [ Help ]
Nb. of parameters: 143 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0408 [ Help ]
Δ/σ(mean): 0.0061 [ Help ]
Δρ(max): 0.81 e_Å-3 [ Help ]
Δρ(min): -0.82 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 2610(90) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.5 | 0.18982(3) | 1 | Uani | 0.02042(11) | 4 | 1 | d | ? | ? | ? |
| P | P | 0.78911(3) | 0 | 0.59073(4) | Uani | 0.00965(5) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0.62120(8) | 0 | 0.28642(13) | Uani | 0.01136(11) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 1 | -0.068(3) | 0.5 | Uani | 0.009(2) | 4 | 0.050(3) | d | ? | ? | ? |
| O2' | O | 1 | -0.0281(6) | 0.5 | Uani | 0.0337(17) | 4 | 0.450(3) | d | ? | ? | ? |
| O3 | O | 0.78150(10) | -0.15154(6) | 0.77508(12) | Uani | 0.02031(14) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.02518(18) | 0.00904(5) | 0.0185(3) | 0 | -0.00906(10) | 0 |
| P | P | 0.00785(7) | 0.01289(8) | 0.00750(7) | 0 | 0.00081(5) | 0 |
| O1 | O | 0.01101(17) | 0.01278(19) | 0.00846(17) | 0 | -0.00059(13) | 0 |
| O2 | O | 0.001(2) | 0.004(5) | 0.023(4) | 0 | 0.004(2) | 0 |
| O2' | O | 0.0116(5) | 0.046(5) | 0.0470(12) | 0 | 0.0141(6) | 0 |
| O3 | O | 0.0309(3) | 0.01222(17) | 0.01455(18) | 0.00677(16) | 0.00043(18) | 0.00303(13) |
Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Atom symbol | C111 | C112 | C113 | C122 | C123 | C133 | C222 | C223 | C233 | C333 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0 | 0.00055(5) | 0 | 0 | -0.00083(5) | 0 | 0.00009(3) | 0 | 0.00177(11) | 0 |
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 |
| 2 | 2 |
| 3 | 3 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| Zn | 0.75 | 1 |
| O2 | 0.25 | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Px1 | P | x | 1 |
| Py1 | P | y | 1 |
| Pz1 | P | z | 1 |
| Px2 | P | x | 2 |
| Py2 | P | y | 2 |
| Pz2 | P | 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 |
| 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: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Px1 | 0 | 0 |
| Py1 | -0.00173(3) | -0.00268(3) |
| Pz1 | 0 | 0 |
| Px2 | -0.00020(12) | -0.00056(12) |
| Py2 | 0 | 0 |
| Pz2 | 0.0002(2) | 0.0008(2) |
| O1x1 | 0 | 0 |
| O1y1 | -0.00077(8) | 0.00181(8) |
| O1z1 | 0 | 0 |
| O1x2 | 0.0001(3) | 0.0002(3) |
| O1y2 | 0 | 0 |
| O1z2 | -0.0007(5) | -0.0007(6) |
| O3x1 | 0.00241(11) | -0.00617(10) |
| O3y1 | -0.00018(6) | -0.00169(6) |
| O3z1 | 0.00131(13) | 0.00182(13) |
| O3x2 | 0.0027(3) | 0.0032(3) |
| O3y2 | -0.0001(2) | -0.0005(2) |
| O3z2 | -0.0012(4) | -0.0012(5) |
Displacive (translational) Legendre coefficients: (Show/hide table) [ Help ]
| Atom site label | Displacement axis | Polynomial order | Polynomial coeff. |
|---|---|---|---|
| Zn | x | 1 | 0.0059(2) |
| Zn | y | 1 | 0 |
| Zn | z | 1 | -0.0087(4) |
| Zn | x | 2 | 0 |
| Zn | y | 2 | -0.00046(3) |
| Zn | z | 2 | 0 |
| Zn | x | 3 | -0.0012(3) |
| Zn | y | 3 | 0 |
| Zn | z | 3 | 0.0055(5) |
| Zn | x | 4 | 0 |
| Zn | y | 4 | -0.00018(6) |
| Zn | z | 4 | 0 |
| Zn | x | 5 | 0.0043(3) |
| Zn | y | 5 | 0 |
| Zn | z | 5 | -0.0087(5) |
| Zn | x | 6 | 0 |
| Zn | y | 6 | 0 |
| Zn | z | 6 | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| PU111 | P | U11 | 1 |
| PU221 | P | U22 | 1 |
| PU331 | P | U33 | 1 |
| PU121 | P | U12 | 1 |
| PU131 | P | U13 | 1 |
| PU231 | P | U23 | 1 |
| PU112 | P | U11 | 2 |
| PU222 | P | U22 | 2 |
| PU332 | P | U33 | 2 |
| PU122 | P | U12 | 2 |
| PU132 | P | U13 | 2 |
| PU232 | P | U23 | 2 |
| O1U111 | O1 | U11 | 1 |
| O1U221 | O1 | U22 | 1 |
| O1U331 | O1 | U33 | 1 |
| O1U121 | O1 | U12 | 1 |
| O1U131 | O1 | U13 | 1 |
| O1U231 | O1 | U23 | 1 |
| O2'U111 | O2' | U11 | 1 |
| O2'U221 | O2' | U22 | 1 |
| O2'U331 | O2' | U33 | 1 |
| O2'U121 | O2' | U12 | 1 |
| O2'U131 | O2' | U13 | 1 |
| O2'U231 | O2' | U23 | 1 |
| O3U111 | O3 | U11 | 1 |
| O3U221 | O3 | U22 | 1 |
| O3U331 | O3 | U33 | 1 |
| O3U121 | O3 | U12 | 1 |
| O3U131 | O3 | U13 | 1 |
| O3U231 | O3 | U23 | 1 |
| O3U112 | O3 | U11 | 2 |
| O3U222 | O3 | U22 | 2 |
| O3U332 | O3 | U33 | 2 |
| O3U122 | O3 | U12 | 2 |
| O3U132 | O3 | U13 | 2 |
| O3U232 | O3 | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| PU111 | 0 | 0 |
| PU221 | 0 | 0 |
| PU331 | 0 | 0 |
| PU121 | 0.00119(9) | -0.00092(8) |
| PU131 | 0 | 0 |
| PU231 | -0.00067(9) | 0.00043(8) |
| PU112 | 0.0023(3) | -0.0005(3) |
| PU222 | 0.0035(3) | -0.0030(3) |
| PU332 | -0.0004(3) | -0.0005(3) |
| PU122 | 0 | 0 |
| PU132 | -0.0005(3) | 0.0016(2) |
| PU232 | 0 | 0 |
| O1U111 | 0 | 0 |
| O1U221 | 0 | 0 |
| O1U331 | 0 | 0 |
| O1U121 | -0.0003(2) | 0.0001(2) |
| O1U131 | 0 | 0 |
| O1U231 | 0.0005(2) | 0.0004(2) |
| O2'U111 | 0 | -0.0045(14) |
| O2'U221 | 0 | -0.0123(17) |
| O2'U331 | 0 | -0.007(3) |
| O2'U121 | -0.0004(9) | 0 |
| O2'U131 | 0 | 0.0016(15) |
| O2'U231 | -0.0139(11) | 0 |
| O3U111 | 0.0083(4) | -0.0024(3) |
| O3U221 | 0.0001(2) | -0.0004(2) |
| O3U331 | 0.0003(2) | -0.0006(2) |
| O3U121 | 0.0014(2) | -0.0014(2) |
| O3U131 | -0.0026(3) | 0.0013(2) |
| O3U231 | -0.00061(18) | 0.00041(19) |
| O3U112 | 0.0104(9) | 0.0067(9) |
| O3U222 | -0.0008(7) | -0.0020(7) |
| O3U332 | -0.0013(8) | -0.0018(8) |
| O3U122 | 0.0020(6) | 0.0034(6) |
| O3U132 | -0.0042(7) | -0.0012(7) |
| O3U232 | 0.0015(7) | 0.0003(7) |
Modulated anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Tensor element | Wave vector code | Cos coeff. | Sin coeff. |
|---|---|---|---|---|
| Zn | C111 | 1 | 0 | -0.0092(3) |
| Zn | C112 | 1 | 0.00038(9) | 0 |
| Zn | C113 | 1 | 0 | 0.0046(3) |
| Zn | C122 | 1 | 0 | -0.00111(5) |
| Zn | C123 | 1 | 0.00010(10) | 0 |
| Zn | C133 | 1 | 0 | -0.0034(4) |
| Zn | C222 | 1 | 0.00031(6) | 0 |
| Zn | C223 | 1 | 0 | 0.00104(8) |
| Zn | C233 | 1 | -0.0004(2) | 0 |
| Zn | C333 | 1 | 0 | 0.0113(8) |
alpha2_zn2p2o7_500
Chemical data
Full Name: zinc(II) diphosphate(V) [ Help ]
Common Name: zinc pyrophosphate [ Help ]
Structural Formula Sum: O7 P2 Zn2 [ Help ]
Formula weight: 304.7 Da [ Help ]
Crystallographic data and experimental details
Crystal system: monoclinic [ Help ]
Superspace group name: C2/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,-x4+1/2 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,x4+1/2 |
| 5 | x1+1/2,x2+1/2,x3,x4 |
| 6 | -x1+1/2,x2+1/2,-x3,-x4+1/2 |
| 7 | -x1+1/2,-x2+1/2,-x3,-x4 |
| 8 | x1+1/2,-x2+1/2,x3,x4+1/2 |
a: 6.5998(4) Å [ Help ]
b: 8.2845(5) Å [ Help ]
c: 4.5300(3) Å [ Help ]
α: 90 ° [ Help ]
β: 105.335(3) ° [ Help ]
γ: 90 ° [ Help ]
Volume: 238.86(3) Å3 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.3239(14) | 0.000000 | 0.3966(9) |
Z: 2 [ Help ]
Cell determination reflection Nb.: 3836 [ Help ]
θ(min) for cell determination: 4.0 ° [ Help ]
θ(max) for cell determination: 45.3 ° [ Help ]
Cell measurement temperature: 500 K [ Help ]
μ: 10.69 mm-1 [ Help ]
Absorption correction type: multi-scan [ Help ]
Absorption correction remarks: SADABS [ Help ]
Minimum transmission factor: 0.025 [ Help ]
Maximum transmission factor: 0.60 [ Help ]
Refinement details
Total nb. of reflections: 2969 [ Help ]
Nb. of observed reflections: 1331 [ Help ]
Intense reflections threshold: I>3σ(I) [ Help ]
Refinement based on: F [ Help ]
R(obs): 0.0295 [ Help ]
wR(obs): 0.0445 [ Help ]
R(all): 0.0653 [ Help ]
wR(all): 0.0467 [ Help ]
S(all): 1.50 [ Help ]
S(obs): 2.18 [ Help ]
Nb. of reflections: 2969 [ Help ]
Nb. of parameters: 98 [ Help ]
Number of constraints: 1 [ Help ]
Weighting scheme: sigma [ Help ]
Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]
Δ/σ(max): 0.0199 [ Help ]
Δ/σ(mean): 0.0034 [ Help ]
Δρ(max): 1.04 e_Å-3 [ Help ]
Δρ(min): -1.13 e_Å-3 [ Help ]
Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]
Extinction coefficient: 2750(110) [ 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.5 | 0.18988(3) | 1 | Uani | 0.02339(5) | 4 | 1 | d | ? | ? | ? |
| P | P | 0.78921(3) | 0 | 0.59064(5) | Uani | 0.01022(6) | 4 | 1 | d | ? | ? | ? |
| O1 | O | 0.62136(11) | 0 | 0.28655(16) | Uani | 0.01244(14) | 4 | 1 | d | ? | ? | ? |
| O2 | O | 1 | -0.072(5) | 0.5 | Uani | 0.013(6) | 4 | 0.027(4) | d | ? | ? | ? |
| O2' | O | 1 | -0.0304(7) | 0.5 | Uani | 0.037(2) | 4 | 0.473(4) | d | ? | ? | ? |
| O3 | O | 0.78098(12) | -0.15170(8) | 0.77509(15) | Uani | 0.02105(15) | 8 | 1 | d | ? | ? | ? |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Zn | Zn | 0.02790(9) | 0.00998(6) | 0.02228(9) | 0 | -0.01094(6) | 0 |
| P | P | 0.00840(8) | 0.01341(10) | 0.00826(9) | 0 | 0.00114(6) | 0 |
| O1 | O | 0.0124(2) | 0.0138(2) | 0.0092(2) | 0 | -0.00059(17) | 0 |
| O2 | O | 0.007(7) | 0.002(8) | 0.024(11) | 0 | -0.008(7) | 0 |
| O2' | O | 0.0111(6) | 0.056(6) | 0.0486(14) | 0 | 0.0155(8) | 0 |
| O3 | O | 0.0313(3) | 0.0131(2) | 0.0157(2) | 0.00649(19) | 0.0007(2) | 0.00333(17) |
Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Atom symbol | C111 | C112 | C113 | C122 | C123 | C133 | C222 | C223 | C233 | C333 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Zn | Zn | 0 | 0.00054(5) | 0 | 0 | -0.00086(5) | 0 | 0.00013(4) | 0 | 0.00169(10) | 0 |
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 |
Occupation crenel coefficients: (Show/hide table) [ Help ]
| Atom site label | Center (x0) | Width |
|---|---|---|
| Zn | 0.75 | 1 |
| O2 | 0.25 | 0.5 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Px1 | P | x | 1 |
| Py1 | P | y | 1 |
| Pz1 | P | z | 1 |
| O1x1 | O1 | x | 1 |
| O1y1 | O1 | y | 1 |
| O1z1 | O1 | z | 1 |
| O3x1 | O3 | x | 1 |
| O3y1 | O3 | y | 1 |
| O3z1 | O3 | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Px1 | 0 | 0 |
| Py1 | -0.00097(6) | -0.00153(6) |
| Pz1 | 0 | 0 |
| O1x1 | 0 | 0 |
| O1y1 | -0.00030(15) | 0.00117(15) |
| O1z1 | 0 | 0 |
| O3x1 | 0.00171(16) | -0.00358(16) |
| O3y1 | -0.00011(12) | -0.00080(10) |
| O3z1 | 0.0004(2) | 0.0004(2) |
Displacive (translational) Legendre coefficients: (Show/hide table) [ Help ]
| Atom site label | Displacement axis | Polynomial order | Polynomial coeff. |
|---|---|---|---|
| Zn | x | 1 | 0.00197(8) |
| Zn | y | 1 | 0 |
| Zn | z | 1 | -0.00104(13) |
| Zn | x | 2 | 0 |
| Zn | y | 2 | -0.00008(5) |
| Zn | z | 2 | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| PU111 | P | U11 | 1 |
| PU221 | P | U22 | 1 |
| PU331 | P | U33 | 1 |
| PU121 | P | U12 | 1 |
| PU131 | P | U13 | 1 |
| PU231 | P | U23 | 1 |
| O1U111 | O1 | U11 | 1 |
| O1U221 | O1 | U22 | 1 |
| O1U331 | O1 | U33 | 1 |
| O1U121 | O1 | U12 | 1 |
| O1U131 | O1 | U13 | 1 |
| O1U231 | O1 | U23 | 1 |
| O2'U111 | O2' | U11 | 1 |
| O2'U221 | O2' | U22 | 1 |
| O2'U331 | O2' | U33 | 1 |
| O2'U121 | O2' | U12 | 1 |
| O2'U131 | O2' | U13 | 1 |
| O2'U231 | O2' | U23 | 1 |
| O3U111 | O3 | U11 | 1 |
| O3U221 | O3 | U22 | 1 |
| O3U331 | O3 | U33 | 1 |
| O3U121 | O3 | U12 | 1 |
| O3U131 | O3 | U13 | 1 |
| O3U231 | O3 | U23 | 1 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| PU111 | 0 | 0 |
| PU221 | 0 | 0 |
| PU331 | 0 | 0 |
| PU121 | 0.00088(14) | -0.00095(14) |
| PU131 | 0 | 0 |
| PU231 | -0.00051(15) | 0.00028(15) |
| O1U111 | 0 | 0 |
| O1U221 | 0 | 0 |
| O1U331 | 0 | 0 |
| O1U121 | -0.0007(4) | -0.0003(4) |
| O1U131 | 0 | 0 |
| O1U231 | 0.0006(4) | 0.0005(4) |
| O2'U111 | 0 | -0.004(2) |
| O2'U221 | 0 | -0.011(3) |
| O2'U331 | 0 | -0.002(4) |
| O2'U121 | -0.0022(16) | 0 |
| O2'U131 | 0 | 0.002(3) |
| O2'U231 | -0.009(2) | 0 |
| O3U111 | 0.0067(5) | -0.0014(5) |
| O3U221 | -0.0003(4) | -0.0003(4) |
| O3U331 | -0.0001(5) | -0.0006(5) |
| O3U121 | 0.0014(4) | -0.0004(4) |
| O3U131 | -0.0020(4) | 0.0001(4) |
| O3U231 | -0.0002(3) | 0.0002(4) |
Modulated anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]
| Atom site label | Tensor element | Wave vector code | Cos coeff. | Sin coeff. |
|---|---|---|---|---|
| Zn | C111 | 1 | 0 | -0.0109(4) |
| Zn | C112 | 1 | 0.00046(14) | 0 |
| Zn | C113 | 1 | 0 | 0.0058(4) |
| Zn | C122 | 1 | 0 | -0.00133(10) |
| Zn | C123 | 1 | 0.00008(16) | 0 |
| Zn | C133 | 1 | 0 | -0.0039(6) |
| Zn | C222 | 1 | 0.00059(12) | 0 |
| Zn | C223 | 1 | 0 | 0.00158(16) |
| Zn | C233 | 1 | 0.0006(3) | 0 |
| Zn | C333 | 1 | 0 | 0.0179(12) |