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Superspace description of wagnerite-group minerals (Mg,Fe,Mn)2(PO4)(F,OH)

Authors:

Lazic, Biljana; Armbruster, Thomas; Chopin, Christian; Grew, Edward S.; Baronnet, Alain; Palatinus, Lukas

Journal:

Acta Crystallographica, Section B 70 243-258 (2014)

DOI:

https://doi.org/10.1107/S2052520613031247

B-IncStrDB ID: 8712E0W5yP Entry date: 2014-06-12 Last revision: 2024-01-02

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I

Chemical data

Mineral Name: wagnerite [ Help ]

Formula analytical: F1 Mg1.98 Mn0.02 O4 P1 [ Help ]

Structural Formula Sum: F1 Mg2 O4 P1 [ Help ]

Formula weight: 162.6 Da [ Help ]

Compound Source: Webing, Austria [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Space group name (H-M): P 1 21/n 1 [ Help ]

Space group name (Hall): -P 2yabc [ Help ]

Space group nb.: 14 [ Help ]

Symmetry operations of the space group: [ Help ]

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

a: 12.7628(4) Å [ Help ]

b: 12.6564(4) Å [ Help ]

c: 9.6348(3) Å [ Help ]

α: 90 ° [ Help ]

β: 117.5995(10) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1379.22(8) Å3 [ Help ]

Z: 16 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 1.069 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS V2012/1 (Bruker AXS Inc.) [ Help ]

Minimum transmission factor: 0.693 [ Help ]

Maximum transmission factor: 0.746 [ Help ]

Refinement details

Total nb. of reflections: 4216 [ Help ]

Nb. of observed reflections: 3753 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0232 [ Help ]

wR(obs): 0.0384 [ Help ]

R(all): 0.0256 [ Help ]

wR(all): 0.0389 [ Help ]

S(all): 2.71 [ Help ]

S(obs): 2.85 [ Help ]

Nb. of reflections: 4216 [ Help ]

Nb. of parameters: 289 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0264 [ Help ]

Δ/σ(mean): 0.0059 [ Help ]

Δρ(max): 0.65 e_Å-3 [ Help ]

Δρ(min): -1.40 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated Coords restraints or constraints Disordered cluster Disordered group
P1 P 0.425703(19) 0.076466(18) 0.30969(3) Uani 0.00408(9) 4 1 d ? ? ?
P2 P 0.076043(19) 0.071794(18) -0.80361(3) Uani 0.00421(9) 4 1 d ? ? ?
P3 P 0.075387(19) 0.174968(18) -0.30744(3) Uani 0.00414(9) 4 1 d ? ? ?
P4 P 0.424129(19) 0.177235(18) -0.19676(3) Uani 0.00415(9) 4 1 d ? ? ?
Mg1 Mg 0.91195(3) 0.07041(2) 0.36132(4) Uani 0.00651(12) 4 1 d ? ? ?
Mg2 Mg 0.59995(3) 0.06944(3) 0.13479(4) Uani 0.00641(11) 4 1 d ? ? ?
Mg3 Mg 0.91857(3) 0.18215(2) 0.87221(4) Uani 0.00628(11) 4 1 d ? ? ?
Mg4 Mg 0.60682(3) 0.17777(3) -0.35736(4) Uani 0.00639(11) 4 1 d ? ? ?
Mg5 Mg 0.19088(3) 0.01888(3) -0.00045(4) Uani 0.00656(11) 4 1 d ? ? ?
Mg6 Mg 0.30731(3) 0.00470(3) -0.48274(4) Uani 0.00683(12) 4 1 d ? ? ?
Mg7 Mg 0.31278(3) 0.23253(3) 0.00688(4) Uani 0.00662(11) 4 1 d ? ? ?
Mg8 Mg 0.19398(3) 0.24447(3) -0.51291(4) Uani 0.00710(11) 4 1 d ? ? ?
O1 O 0.32657(6) 0.11098(5) 0.14876(8) Uani 0.0072(2) 4 1 d ? ? ?
O2 O 0.16464(6) 0.09502(5) -0.63367(8) Uani 0.0076(2) 4 1 d ? ? ?
O3 O 0.17118(6) 0.14367(5) -0.14321(8) Uani 0.0075(2) 4 1 d ? ? ?
O4 O 0.33025(6) 0.15108(5) -0.36360(8) Uani 0.0072(2) 4 1 d ? ? ?
O5 O 0.53641(6) 0.04663(5) 0.29504(8) Uani 0.0072(2) 4 1 d ? ? ?
O6 O 0.95297(6) 0.05275(6) 0.18442(8) Uani 0.0078(2) 4 1 d ? ? ?
O7 O 0.95939(6) 0.20171(6) 0.69681(8) Uani 0.0077(2) 4 1 d ? ? ?
O8 O 0.54107(6) 0.20199(6) -0.19814(8) Uani 0.0072(2) 4 1 d ? ? ?
O9 O 0.62083(6) 0.01785(5) -0.36505(8) Uani 0.0067(2) 4 1 d ? ? ?
O10 O 0.88352(6) 0.02615(5) 0.86120(8) Uani 0.0067(2) 4 1 d ? ? ?
O11 O 0.61859(6) 0.23022(5) 0.13444(8) Uani 0.0068(2) 4 1 d ? ? ?
O12 O 0.88140(6) 0.22592(5) 0.36135(8) Uani 0.0066(2) 4 1 d ? ? ?
O13 O 0.05128(6) 0.08289(5) -0.42166(8) Uani 0.0075(2) 4 1 d ? ? ?
O14 O 0.43958(6) 0.08749(5) -0.07988(8) Uani 0.0072(2) 4 1 d ? ? ?
O15 O 0.45500(6) 0.16598(5) 0.42979(8) Uani 0.0069(2) 4 1 d ? ? ?
O16 O 0.06839(6) 0.16267(5) -0.91490(8) Uani 0.0073(2) 4 1 d ? ? ?
F1 F 0.75481(5) 0.04941(4) 0.34108(6) Uani 0.00959(19) 4 1 d ? ? ?
F2 F 0.71697(5) 0.08346(4) 0.04855(7) Uani 0.0112(2) 4 1 d ? ? ?
F3 F 0.72166(5) 0.16259(4) 0.55240(7) Uani 0.0109(2) 4 1 d ? ? ?
F4 F 0.75948(4) 0.20213(4) -0.15155(6) Uani 0.00925(19) 4 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
P1 P 0.00424(12) 0.00396(12) 0.00353(12) -0.00010(6) 0.00137(9) 0.00003(7)
P2 P 0.00453(12) 0.00423(12) 0.00339(12) -0.00006(7) 0.00142(9) -0.00013(7)
P3 P 0.00447(12) 0.00390(12) 0.00352(12) -0.00007(6) 0.00139(9) 0.00009(7)
P4 P 0.00418(12) 0.00420(12) 0.00350(12) 0.00000(6) 0.00129(9) -0.00005(7)
Mg1 Mg 0.00768(15) 0.00561(15) 0.00721(16) 0.00026(10) 0.00426(12) -0.00021(10)
Mg2 Mg 0.00700(14) 0.00561(15) 0.00641(16) -0.00020(10) 0.00293(12) 0.00020(10)
Mg3 Mg 0.00681(15) 0.00532(14) 0.00752(16) -0.00028(10) 0.00400(12) 0.00008(10)
Mg4 Mg 0.00683(15) 0.00595(15) 0.00577(16) 0.00015(10) 0.00240(12) -0.00031(10)
Mg5 Mg 0.00614(15) 0.00734(15) 0.00607(15) -0.00147(10) 0.00270(12) -0.00057(11)
Mg6 Mg 0.00603(15) 0.00828(15) 0.00611(16) 0.00137(10) 0.00275(12) 0.00085(11)
Mg7 Mg 0.00651(15) 0.00711(15) 0.00629(15) -0.00142(10) 0.00300(12) -0.00031(11)
Mg8 Mg 0.00587(15) 0.00925(15) 0.00621(15) 0.00161(10) 0.00282(12) 0.00132(11)
O1 O 0.0063(3) 0.0074(3) 0.0051(3) -0.0006(2) 0.0003(2) 0.0016(2)
O2 O 0.0073(3) 0.0079(3) 0.0048(3) 0.0007(2) 0.0005(2) -0.0011(2)
O3 O 0.0072(3) 0.0075(3) 0.0053(3) -0.0006(2) 0.0006(2) 0.0017(2)
O4 O 0.0065(3) 0.0076(3) 0.0049(3) 0.0004(2) 0.0006(2) -0.0013(2)
O5 O 0.0054(3) 0.0101(3) 0.0071(3) 0.0010(2) 0.0037(2) 0.0006(2)
O6 O 0.0055(3) 0.0116(3) 0.0068(3) -0.0020(2) 0.0033(2) -0.0021(2)
O7 O 0.0058(3) 0.0111(3) 0.0071(3) 0.0017(2) 0.0038(2) 0.0016(2)
O8 O 0.0050(3) 0.0104(3) 0.0066(3) -0.0013(2) 0.0032(2) -0.0012(2)
O9 O 0.0077(3) 0.0049(3) 0.0080(3) -0.0007(2) 0.0042(2) 0.0010(2)
O10 O 0.0081(3) 0.0047(3) 0.0079(3) 0.0002(2) 0.0042(2) -0.0009(2)
O11 O 0.0080(3) 0.0051(3) 0.0078(3) 0.0007(2) 0.0041(2) -0.0009(2)
O12 O 0.0077(3) 0.0047(3) 0.0081(3) -0.0002(2) 0.0043(2) 0.0009(2)
O13 O 0.0093(3) 0.0051(3) 0.0066(3) 0.0007(2) 0.0023(2) -0.0008(2)
O14 O 0.0081(3) 0.0061(3) 0.0064(3) -0.0010(2) 0.0026(2) 0.0010(2)
O15 O 0.0080(3) 0.0053(3) 0.0060(3) 0.0003(2) 0.0021(2) -0.0008(2)
O16 O 0.0082(3) 0.0062(3) 0.0065(3) -0.0012(2) 0.0026(2) 0.0011(2)
F1 F 0.0065(2) 0.0116(2) 0.0106(3) 0.00025(18) 0.0039(2) 0.00256(19)
F2 F 0.0115(3) 0.0103(2) 0.0147(3) 0.00192(19) 0.0086(2) 0.0001(2)
F3 F 0.0115(3) 0.0094(2) 0.0144(3) -0.00207(18) 0.0083(2) -0.0001(2)
F4 F 0.0059(2) 0.0114(2) 0.0104(3) -0.00022(18) 0.0038(2) -0.00235(19)

3b

Chemical data

Mineral Name: wagnerite [ Help ]

Formula analytical: F0.8 Fe0.5 H0.2 Mg0.8 Mn0.7 O4.2 P1 [ Help ]

Structural Formula Sum: F1 Fe1.078 Mg0.922 O4 P1 [ Help ]

Formula weight: 196.6 Da [ Help ]

Compound Source: Panasqueira mine, Portugal [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/c(0β0)s0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 13.0183(2) Å [ Help ]

b: 6.41490(10) Å [ Help ]

c: 9.84110(10) Å [ Help ]

α: 90 ° [ Help ]

β: 118.5620(10) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 721.823(19) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.000000 0.345990 0.000000

Z: 8 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 4.994 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS V2012/1 (Bruker AXS Inc.) [ Help ]

Minimum transmission factor: 0.521 [ Help ]

Maximum transmission factor: 0.745 [ Help ]

Refinement details

Total nb. of reflections: 2484 [ Help ]

Nb. of observed reflections: 2086 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0217 [ Help ]

wR(obs): 0.0629 [ Help ]

R(all): 0.0252 [ Help ]

wR(all): 0.0640 [ Help ]

S(all): 1.75 [ Help ]

S(obs): 1.90 [ Help ]

Nb. of reflections: 2484 [ Help ]

Nb. of parameters: 167 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(I)+0.0004I2) [ Help ]

Refinement of hydrogen atoms: constr [ Help ]

Δ/σ(max): 0.0280 [ Help ]

Δ/σ(mean): 0.0040 [ Help ]

Δρ(max): 0.40 e_Å-3 [ Help ]

Δρ(min): -0.45 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated Coords restraints or constraints Disordered cluster Disordered group
Fe1 Fe 0.058512(19) 0.27144(4) 0.00197(3) Uani 0.00876(11) 8 0.691(2) d ? ? ?
Mg1 Mg 0.058512(19) 0.27144(4) 0.00197(3) Uani 0.00876(11) 8 0.309(2) d ? ? ?
Fe2 Fe -0.15729(3) 0.10648(5) 0.14075(3) Uani 0.00817(13) 8 0.3874(16) d ? ? ?
Mg2 Mg -0.15729(3) 0.10648(5) 0.14075(3) Uani 0.00817(13) 8 0.6126(16) d ? ? ?
P1 P 0.17535(3) 0.59597(5) 0.30569(4) Uani 0.00575(14) 8 1 d ? ? ?
F1 F -0.01035(14) 0.1317(3) 0.13959(16) Uani 0.0248(5) 8 0.531(3) d ? ? ?
F2 F -0.0283(2) 0.0835(3) 0.0704(4) Uani 0.0217(7) 8 0.469(3) d ? ? ?
O1 O 0.08125(7) 0.53788(14) 0.14224(10) Uani 0.0114(3) 8 1 d ? ? ?
O2 O 0.19389(8) 0.41819(14) 0.42004(11) Uani 0.0101(4) 8 1 d ? ? ?
O3 O 0.13343(9) 0.21184(13) -0.14023(11) Uani 0.0099(4) 8 1 d ? ? ?
O4 O 0.29025(8) 0.64362(15) 0.30467(11) Uani 0.0105(4) 8 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Fe1 Fe 0.00776(15) 0.01085(14) 0.00696(15) 0.00271(8) 0.00296(11) 0.00080(8)
Mg1 Mg 0.00776(15) 0.01085(14) 0.00696(15) 0.00271(8) 0.00296(11) 0.00080(8)
Fe2 Fe 0.01027(17) 0.00634(17) 0.00807(18) 0.00035(10) 0.00453(13) -0.00048(10)
Mg2 Mg 0.01027(17) 0.00634(17) 0.00807(18) 0.00035(10) 0.00453(13) -0.00048(10)
P1 P 0.00524(18) 0.00566(18) 0.00505(18) -0.00003(11) 0.00140(14) -0.00011(11)
F1 F 0.0120(6) 0.0255(6) 0.0372(8) 0.0038(5) 0.0121(6) 0.0173(6)
F2 F 0.0183(7) 0.0155(6) 0.0378(11) 0.0004(5) 0.0187(8) 0.0071(6)
O1 O 0.0097(5) 0.0125(5) 0.0078(4) 0.0009(3) 0.0009(4) -0.0015(4)
O2 O 0.0133(5) 0.0077(4) 0.0088(5) -0.0002(3) 0.0049(4) 0.0018(3)
O3 O 0.0104(5) 0.0080(4) 0.0109(5) -0.0020(3) 0.0047(4) 0.0016(4)
O4 O 0.0078(5) 0.0134(4) 0.0107(5) -0.0020(3) 0.0048(4) -0.0009(4)

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

Wave vector code q_1
1 1

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Fe1o1 Fe1 1
Mg1o1 Mg1 1
Fe2o1 Fe2 1
Mg2o1 Mg2 1

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1o1 0.0153(8) -0.0082(9)
Mg1o1 -0.0153(8) 0.0082(9)
Fe2o1 0.0113(8) 0.0983(9)
Mg2o1 -0.0113(8) -0.0983(9)

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
F1 0.2975(6) 0.531(3)
F2 0.7808(7) 0.469(3)

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

Modulation code Atom site label Displacement axis Wave vector code
Fe1x1 Fe1 x 1
Fe1y1 Fe1 y 1
Fe1z1 Fe1 z 1
Mg1x1 Mg1 x 1
Mg1y1 Mg1 y 1
Mg1z1 Mg1 z 1
Fe2x1 Fe2 x 1
Fe2y1 Fe2 y 1
Fe2z1 Fe2 z 1
Mg2x1 Mg2 x 1
Mg2y1 Mg2 y 1
Mg2z1 Mg2 z 1
P1x1 P1 x 1
P1y1 P1 y 1
P1z1 P1 z 1
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1x1 0.000954(17) -0.002922(18)
Fe1y1 0.00460(3) -0.00891(3)
Fe1z1 -0.00372(2) 0.00041(2)
Mg1x1 0.000954(17) -0.002922(18)
Mg1y1 0.00460(3) -0.00891(3)
Mg1z1 -0.00372(2) 0.00041(2)
Fe2x1 -0.00005(2) -0.00911(3)
Fe2y1 0.00209(4) 0.00183(4)
Fe2z1 -0.00201(3) -0.00410(3)
Mg2x1 -0.00005(2) -0.00911(3)
Mg2y1 0.00209(4) 0.00183(4)
Mg2z1 -0.00201(3) -0.00410(3)
P1x1 0.00040(3) -0.00129(3)
P1y1 -0.00088(4) -0.00146(4)
P1z1 0.00140(3) -0.00076(3)
O1x1 -0.00153(7) 0.00100(6)
O1y1 -0.00833(11) 0.00029(11)
O1z1 0.00360(8) -0.00230(8)
O2x1 0.00505(7) -0.00559(7)
O2y1 -0.00173(11) -0.00289(11)
O2z1 0.00208(8) -0.00432(8)
O3x1 0.00135(6) -0.00131(6)
O3y1 -0.00271(11) 0.00237(11)
O3z1 -0.00068(8) -0.00103(8)
O4x1 -0.00256(6) 0.00052(6)
O4y1 0.00622(11) -0.00301(11)
O4z1 -0.00489(8) 0.00304(8)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
F1 x 1 0.00173(16)
F1 y 1 0.0005(3)
F1 z 1 0.0026(3)
F1 x 2 0.0033(7)
F1 y 2 0.0061(16)
F1 z 2 0.0093
F2 x 1 -0.0026(2)
F2 y 1 0.0039(3)
F2 z 1 -0.0018(4)
F2 x 2 -0.0080(12)
F2 y 2 -0.005(2)
F2 z 2 -0.0106(19)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Fe1U111 Fe1 U11 1
Fe1U221 Fe1 U22 1
Fe1U331 Fe1 U33 1
Fe1U121 Fe1 U12 1
Fe1U131 Fe1 U13 1
Fe1U231 Fe1 U23 1
Mg1U111 Mg1 U11 1
Mg1U221 Mg1 U22 1
Mg1U331 Mg1 U33 1
Mg1U121 Mg1 U12 1
Mg1U131 Mg1 U13 1
Mg1U231 Mg1 U23 1
Fe2U111 Fe2 U11 1
Fe2U221 Fe2 U22 1
Fe2U331 Fe2 U33 1
Fe2U121 Fe2 U12 1
Fe2U131 Fe2 U13 1
Fe2U231 Fe2 U23 1
Mg2U111 Mg2 U11 1
Mg2U221 Mg2 U22 1
Mg2U331 Mg2 U33 1
Mg2U121 Mg2 U12 1
Mg2U131 Mg2 U13 1
Mg2U231 Mg2 U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1U111 -0.00029(12) -0.00016(12)
Fe1U221 -0.00043(12) -0.00011(12)
Fe1U331 -0.00001(12) 0.00017(12)
Fe1U121 0.00005(9) -0.00018(9)
Fe1U131 0.00023(10) -0.00023(10)
Fe1U231 0.00016(9) -0.00060(9)
Mg1U111 -0.00029(12) -0.00016(12)
Mg1U221 -0.00043(12) -0.00011(12)
Mg1U331 -0.00001(12) 0.00017(12)
Mg1U121 0.00005(9) -0.00018(9)
Mg1U131 0.00023(10) -0.00023(10)
Mg1U231 0.00016(9) -0.00060(9)
Fe2U111 -0.00089(17) -0.00009(17)
Fe2U221 -0.00019(14) -0.00054(14)
Fe2U331 -0.00048(16) 0.00122(15)
Fe2U121 0.00046(11) 0.00015(11)
Fe2U131 -0.00045(13) 0.00151(13)
Fe2U231 0.00038(11) -0.00007(11)
Mg2U111 -0.00089(17) -0.00009(17)
Mg2U221 -0.00019(14) -0.00054(14)
Mg2U331 -0.00048(16) 0.00122(15)
Mg2U121 0.00046(11) 0.00015(11)
Mg2U131 -0.00045(13) 0.00151(13)
Mg2U231 0.00038(11) -0.00007(11)

5b

Chemical data

Mineral Name: wagnerite [ Help ]

Formula analytical: F0.7 H0.3 Fe0.5 Mg1.3 Mn0.2 O4.3 P1 [ Help ]

Structural Formula Sum: F1 Fe0.649 Mg1.351 O4 P1 [ Help ]

Formula weight: 183 Da [ Help ]

Compound Source: H°alsj\öberg [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/c(0β0)s0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 12.8840(2) Å [ Help ]

b: 6.38890(10) Å [ Help ]

c: 9.73840(10) Å [ Help ]

α: 90 ° [ Help ]

β: 117.7990(10) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 709.098(18) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.000000 0.410660 0.000000

Z: 8 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 3.474 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS V2012/1 (Bruker AXS Inc.) [ Help ]

Minimum transmission factor: 0.6479 [ Help ]

Maximum transmission factor: 0.7456 [ Help ]

Refinement details

Total nb. of reflections: 2439 [ Help ]

Nb. of observed reflections: 2216 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0228 [ Help ]

wR(obs): 0.0643 [ Help ]

R(all): 0.0243 [ Help ]

wR(all): 0.0647 [ Help ]

S(all): 2.06 [ Help ]

S(obs): 2.15 [ Help ]

Nb. of reflections: 2439 [ Help ]

Nb. of parameters: 228 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(I)+0.0004I2) [ Help ]

Δ/σ(max): 0.0191 [ Help ]

Δ/σ(mean): 0.0024 [ Help ]

Δρ(max): 0.48 e_Å-3 [ Help ]

Δρ(min): -0.57 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated Coords restraints or constraints Disordered cluster Disordered group
Fe1 Fe 0.05876(2) 0.27212(4) 0.00649(3) Uani 0.00826(12) 8 0.429(2) d ? ? ?
Mg1 Mg 0.05876(2) 0.27212(4) 0.00649(3) Uani 0.00826(12) 8 0.571(2) d ? ? ?
Fe2 Fe -0.15593(3) 0.10788(5) 0.13668(4) Uani 0.00846(14) 8 0.2019(17) d ? ? ?
Mg2 Mg -0.15593(3) 0.10788(5) 0.13668(4) Uani 0.00846(14) 8 0.7981(17) d ? ? ?
P1 P 0.17494(3) 0.59944(4) 0.30565(3) Uani 0.00481(12) 8 1 d ? ? ?
F1 F -0.00797(14) 0.1513(3) 0.15536(19) Uani 0.0198(4) 8 0.5042(19) d ? ? ?
F2 F -0.03358(14) 0.0799(2) 0.0500(2) Uani 0.0204(4) 8 0.4958(19) d ? ? ?
O1 O 0.08041(7) 0.54146(13) 0.14224(10) Uani 0.0101(3) 8 1 d ? ? ?
O2 O 0.19424(8) 0.42072(13) 0.42064(10) Uani 0.0092(3) 8 1 d ? ? ?
O3 O 0.13283(8) 0.20889(13) -0.13783(10) Uani 0.0085(3) 8 1 d ? ? ?
O4 O 0.29017(7) 0.64788(13) 0.30248(10) Uani 0.0092(3) 8 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Fe1 Fe 0.00733(16) 0.01029(14) 0.00707(16) 0.00228(9) 0.00327(12) 0.00041(8)
Mg1 Mg 0.00733(16) 0.01029(14) 0.00707(16) 0.00228(9) 0.00327(12) 0.00041(8)
Fe2 Fe 0.01196(18) 0.00600(17) 0.00815(18) 0.00030(11) 0.00530(14) -0.00044(10)
Mg2 Mg 0.01196(18) 0.00600(17) 0.00815(18) 0.00030(11) 0.00530(14) -0.00044(10)
P1 P 0.00453(17) 0.00506(16) 0.00447(17) 0.00009(10) 0.00179(13) -0.00010(9)
F1 F 0.0126(5) 0.0244(5) 0.0221(5) 0.0002(4) 0.0079(4) 0.0071(4)
F2 F 0.0206(5) 0.0170(5) 0.0294(6) -0.0026(4) 0.0166(5) 0.0008(4)
O1 O 0.0087(4) 0.0115(4) 0.0067(4) 0.0010(3) 0.0007(3) -0.0021(3)
O2 O 0.0122(4) 0.0072(3) 0.0078(4) -0.0007(3) 0.0043(3) 0.0015(3)
O3 O 0.0096(4) 0.0063(4) 0.0104(4) -0.0013(3) 0.0052(4) 0.0014(3)
O4 O 0.0069(4) 0.0123(4) 0.0100(4) -0.0016(3) 0.0051(3) -0.0013(3)

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

Wave vector code q_1
1 1

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Fe1o1 Fe1 1
Mg1o1 Mg1 1
Fe2o1 Fe2 1
Mg2o1 Mg2 1

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1o1 -0.0075(9) 0.0423(10)
Mg1o1 0.0075(9) -0.0423(10)
Fe2o1 0.0158(9) 0.0674(10)
Mg2o1 -0.0158(9) -0.0674(10)

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
F1 0.3126(3) 0.5042(19)
F2 0.7833(4) 0.4958(19)

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

Modulation code Atom site label Displacement axis Wave vector code
Fe1x1 Fe1 x 1
Fe1y1 Fe1 y 1
Fe1z1 Fe1 z 1
Mg1x1 Mg1 x 1
Mg1y1 Mg1 y 1
Mg1z1 Mg1 z 1
Fe2x1 Fe2 x 1
Fe2y1 Fe2 y 1
Fe2z1 Fe2 z 1
Mg2x1 Mg2 x 1
Mg2y1 Mg2 y 1
Mg2z1 Mg2 z 1
P1x1 P1 x 1
P1y1 P1 y 1
P1z1 P1 z 1
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1x1 0.00205(2) -0.00418(2)
Fe1y1 0.00992(4) -0.01321(4)
Fe1z1 -0.00603(3) 0.00099(3)
Mg1x1 0.00205(2) -0.00418(2)
Mg1y1 0.00992(4) -0.01321(4)
Mg1z1 -0.00603(3) 0.00099(3)
Fe2x1 0.00003(3) -0.01454(3)
Fe2y1 0.00332(4) 0.00276(4)
Fe2z1 -0.00359(3) -0.00648(3)
Mg2x1 0.00003(3) -0.01454(3)
Mg2y1 0.00332(4) 0.00276(4)
Mg2z1 -0.00359(3) -0.00648(3)
P1x1 0.00076(2) -0.00074(2)
P1y1 -0.00268(4) -0.00139(4)
P1z1 0.00239(3) -0.00031(3)
O1x1 -0.00277(6) 0.00218(6)
O1y1 -0.01413(11) 0.00168(11)
O1z1 0.00624(8) -0.00261(8)
O2x1 0.00866(7) -0.00764(7)
O2y1 -0.00369(11) -0.00315(10)
O2z1 0.00339(8) -0.00606(8)
O3x1 0.00217(6) -0.00109(6)
O3y1 -0.00480(10) 0.00430(10)
O3z1 -0.00082(8) 0.00006(8)
O4x1 -0.00441(6) 0.00155(6)
O4y1 0.00850(10) -0.00306(11)
O4z1 -0.00847(8) 0.00456(8)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
F1 x 1 0.00222(14)
F1 y 1 -0.0003(2)
F1 z 1 0.00507(20)
F1 x 2 0.0000(7)
F1 y 2 -0.0096(14)
F1 z 2 -0.0081(10)
F2 x 1 -0.00463(15)
F2 y 1 0.0067(3)
F2 z 1 -0.0045(2)
F2 x 2 0.0005(8)
F2 y 2 0.0031(13)
F2 z 2 0.0067(11)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Fe1U111 Fe1 U11 1
Fe1U221 Fe1 U22 1
Fe1U331 Fe1 U33 1
Fe1U121 Fe1 U12 1
Fe1U131 Fe1 U13 1
Fe1U231 Fe1 U23 1
Mg1U111 Mg1 U11 1
Mg1U221 Mg1 U22 1
Mg1U331 Mg1 U33 1
Mg1U121 Mg1 U12 1
Mg1U131 Mg1 U13 1
Mg1U231 Mg1 U23 1
Fe2U111 Fe2 U11 1
Fe2U221 Fe2 U22 1
Fe2U331 Fe2 U33 1
Fe2U121 Fe2 U12 1
Fe2U131 Fe2 U13 1
Fe2U231 Fe2 U23 1
Mg2U111 Mg2 U11 1
Mg2U221 Mg2 U22 1
Mg2U331 Mg2 U33 1
Mg2U121 Mg2 U12 1
Mg2U131 Mg2 U13 1
Mg2U231 Mg2 U23 1
P1U111 P1 U11 1
P1U221 P1 U22 1
P1U331 P1 U33 1
P1U121 P1 U12 1
P1U131 P1 U13 1
P1U231 P1 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
O2U111 O2 U11 1
O2U221 O2 U22 1
O2U331 O2 U33 1
O2U121 O2 U12 1
O2U131 O2 U13 1
O2U231 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
O4U111 O4 U11 1
O4U221 O4 U22 1
O4U331 O4 U33 1
O4U121 O4 U12 1
O4U131 O4 U13 1
O4U231 O4 U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1U111 -0.00021(12) -0.00043(13)
Fe1U221 0.00001(12) 0.00093(13)
Fe1U331 0.00053(12) 0.00025(12)
Fe1U121 -0.00021(9) -0.00031(10)
Fe1U131 0.00024(10) 0.00006(10)
Fe1U231 -0.00044(9) -0.00016(9)
Mg1U111 -0.00021(12) -0.00043(13)
Mg1U221 0.00001(12) 0.00093(13)
Mg1U331 0.00053(12) 0.00025(12)
Mg1U121 -0.00021(9) -0.00031(10)
Mg1U131 0.00024(10) 0.00006(10)
Mg1U231 -0.00044(9) -0.00016(9)
Fe2U111 -0.00478(18) -0.0022(2)
Fe2U221 -0.00017(14) 0.00009(15)
Fe2U331 -0.00037(15) 0.00163(16)
Fe2U121 0.00049(12) 0.00093(13)
Fe2U131 -0.00113(13) 0.00092(14)
Fe2U231 0.00032(10) 0.00015(11)
Mg2U111 -0.00478(18) -0.0022(2)
Mg2U221 -0.00017(14) 0.00009(15)
Mg2U331 -0.00037(15) 0.00163(16)
Mg2U121 0.00049(12) 0.00093(13)
Mg2U131 -0.00113(13) 0.00092(14)
Mg2U231 0.00032(10) 0.00015(11)
P1U111 -0.00025(13) 0.00028(13)
P1U221 -0.00030(11) -0.00031(12)
P1U331 0.00017(12) -0.00025(12)
P1U121 0.00008(10) 0.00015(10)
P1U131 -0.00008(11) -0.00002(11)
P1U231 -0.00019(9) 0.00013(9)
O1U111 -0.0012(4) 0.0016(4)
O1U221 -0.0001(4) -0.0008(4)
O1U331 0.0014(4) -0.0004(4)
O1U121 0.0002(3) 0.0006(3)
O1U131 -0.0001(3) 0.0001(3)
O1U231 -0.0015(3) 0.0006(3)
O2U111 0.0023(4) 0.0017(4)
O2U221 -0.0008(3) 0.0002(4)
O2U331 0.0009(4) -0.0004(4)
O2U121 0.0004(3) 0.0005(3)
O2U131 0.0005(3) 0.0000(3)
O2U231 0.0002(3) 0.0003(3)
O3U111 0.0004(4) 0.0001(4)
O3U221 -0.0001(3) 0.0000(3)
O3U331 -0.0001(4) 0.0001(4)
O3U121 -0.0001(3) -0.0003(3)
O3U131 0.0001(3) -0.0002(3)
O3U231 -0.0005(3) 0.0000(3)
O4U111 0.0002(4) 0.0010(4)
O4U221 -0.0007(4) 0.0017(4)
O4U331 -0.0011(4) 0.0007(4)
O4U121 0.0008(3) -0.0009(3)
O4U131 -0.0003(3) 0.0009(3)
O4U231 0.0016(3) -0.0018(3)

7b

Chemical data

Mineral Name: wagnerite [ Help ]

Formula analytical: F1 Fe0.25 Mg1.7 Mn0.05 O4 P1 [ Help ]

Structural Formula Sum: F1 Fe0.185 Mg1.815 O4 P1 [ Help ]

Formula weight: 168.43 Da [ Help ]

Compound Source: Khyakhta, Russia [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/c(0β0)s0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 12.7978(2) Å [ Help ]

b: 6.35230(10) Å [ Help ]

c: 9.66420(10) Å [ Help ]

α: 90 ° [ Help ]

β: 117.5670(10) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 696.460(18) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.000000 0.427560 0.000000

Z: 8 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 1.8 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS V2012/1 (Bruker AXS Inc.) [ Help ]

Minimum transmission factor: 0.664 [ Help ]

Maximum transmission factor: 0.746 [ Help ]

Refinement details

Total nb. of reflections: 7370 [ Help ]

Nb. of observed reflections: 3766 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0306 [ Help ]

wR(obs): 0.0788 [ Help ]

R(all): 0.0611 [ Help ]

wR(all): 0.0909 [ Help ]

S(all): 1.63 [ Help ]

S(obs): 2.05 [ Help ]

Nb. of reflections: 7370 [ Help ]

Nb. of parameters: 504 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(I)+0.0004I2) [ Help ]

Refinement of hydrogen atoms: constr [ Help ]

Δ/σ(max): 0.0080 [ Help ]

Δ/σ(mean): 0.0011 [ Help ]

Δρ(max): 0.68 e_Å-3 [ Help ]

Δρ(min): -0.95 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated Coords restraints or constraints Disordered cluster Disordered group
Fe1 Fe 0.05889(2) 0.27302(4) 0.00846(3) Uani 0.00757(10) 8 0.1456(14) d ? ? ?
Mg1 Mg 0.05889(2) 0.27302(4) 0.00846(3) Uani 0.00757(10) 8 0.8544(14) d ? ? ?
Fe2 Fe -0.15599(3) 0.10911(4) 0.13584(3) Uani 0.00669(11) 8 0.0399(13) d ? ? ?
Mg2 Mg -0.15599(3) 0.10911(4) 0.13584(3) Uani 0.00669(11) 8 0.9601(13) d ? ? ?
P1 P 0.174704(18) 0.60129(3) 0.30584(2) Uani 0.00448(8) 8 1 d ? ? ?
F1 F -0.00762(6) 0.15371(11) 0.15615(8) Uani 0.0145(3) 8 0.5040(9) d ? ? ?
F2 F -0.03186(6) 0.07923(11) 0.04913(8) Uani 0.0147(3) 8 0.4960(9) d ? ? ?
O1 O 0.08029(5) 0.54360(10) 0.14142(7) Uani 0.0084(2) 8 1 d ? ? ?
O2 O 0.19394(6) 0.42101(9) 0.42128(7) Uani 0.0080(2) 8 1 d ? ? ?
O3 O 0.13194(6) 0.20713(9) -0.13696(7) Uani 0.0074(2) 8 1 d ? ? ?
O4 O 0.29091(5) 0.65083(10) 0.30309(7) Uani 0.0080(2) 8 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Fe1 Fe 0.00720(14) 0.00883(13) 0.00658(13) 0.00174(8) 0.00309(10) 0.00026(8)
Mg1 Mg 0.00720(14) 0.00883(13) 0.00658(13) 0.00174(8) 0.00309(10) 0.00026(8)
Fe2 Fe 0.00922(16) 0.00469(14) 0.00670(15) 0.00024(9) 0.00414(12) -0.00027(9)
Mg2 Mg 0.00922(16) 0.00469(14) 0.00670(15) 0.00024(9) 0.00414(12) -0.00027(9)
P1 P 0.00484(11) 0.00405(11) 0.00430(10) 0.00011(6) 0.00191(8) 0.00005(6)
F1 F 0.0095(4) 0.0162(4) 0.0182(4) 0.0000(3) 0.0068(3) 0.0056(3)
F2 F 0.0150(4) 0.0119(4) 0.0220(4) -0.0020(3) 0.0126(3) 0.0002(3)
O1 O 0.0081(3) 0.0087(3) 0.0060(2) 0.0007(2) 0.0011(2) -0.0016(2)
O2 O 0.0106(3) 0.0056(2) 0.0068(3) -0.0007(2) 0.0033(2) 0.0009(2)
O3 O 0.0085(3) 0.0055(2) 0.0089(3) -0.0010(2) 0.0045(2) 0.0011(2)
O4 O 0.0064(3) 0.0106(3) 0.0081(3) -0.0018(2) 0.0042(2) -0.0010(2)

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

Wave vector code q_1
1 1
2 2
3 3

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Fe1o1 Fe1 1
Mg1o1 Mg1 1
Fe2o1 Fe2 1
Mg2o1 Mg2 1

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1o1 -0.0087(9) 0.0286(10)
Mg1o1 0.0087(9) -0.0286(10)
Fe2o1 0.0064(10) 0.0143(10)
Mg2o1 -0.0064(10) -0.0143(10)

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
F1 0.3157(2) 0.5040(9)
F2 0.7838(2) 0.4960(9)

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

Modulation code Atom site label Displacement axis Wave vector code
Fe1x1 Fe1 x 1
Fe1y1 Fe1 y 1
Fe1z1 Fe1 z 1
Fe1x2 Fe1 x 2
Fe1y2 Fe1 y 2
Fe1z2 Fe1 z 2
Fe1x3 Fe1 x 3
Fe1y3 Fe1 y 3
Fe1z3 Fe1 z 3
Mg1x1 Mg1 x 1
Mg1y1 Mg1 y 1
Mg1z1 Mg1 z 1
Mg1x2 Mg1 x 2
Mg1y2 Mg1 y 2
Mg1z2 Mg1 z 2
Mg1x3 Mg1 x 3
Mg1y3 Mg1 y 3
Mg1z3 Mg1 z 3
Fe2x1 Fe2 x 1
Fe2y1 Fe2 y 1
Fe2z1 Fe2 z 1
Fe2x2 Fe2 x 2
Fe2y2 Fe2 y 2
Fe2z2 Fe2 z 2
Fe2x3 Fe2 x 3
Fe2y3 Fe2 y 3
Fe2z3 Fe2 z 3
Mg2x1 Mg2 x 1
Mg2y1 Mg2 y 1
Mg2z1 Mg2 z 1
Mg2x2 Mg2 x 2
Mg2y2 Mg2 y 2
Mg2z2 Mg2 z 2
Mg2x3 Mg2 x 3
Mg2y3 Mg2 y 3
Mg2z3 Mg2 z 3
P1x1 P1 x 1
P1y1 P1 y 1
P1z1 P1 z 1
P1x2 P1 x 2
P1y2 P1 y 2
P1z2 P1 z 2
P1x3 P1 x 3
P1y3 P1 y 3
P1z3 P1 z 3
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O1x3 O1 x 3
O1y3 O1 y 3
O1z3 O1 z 3
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 z 2
O2x3 O2 x 3
O2y3 O2 y 3
O2z3 O2 z 3
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O3x3 O3 x 3
O3y3 O3 y 3
O3z3 O3 z 3
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1
O4x2 O4 x 2
O4y2 O4 y 2
O4z2 O4 z 2
O4x3 O4 x 3
O4y3 O4 y 3
O4z3 O4 z 3

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1x1 0.00188(2) -0.00397(2)
Fe1y1 0.01135(5) -0.01361(4)
Fe1z1 -0.00700(3) 0.00148(3)
Fe1x2 -0.00076(4) 0.00003(4)
Fe1y2 0.00063(8) 0.00038(8)
Fe1z2 -0.00055(4) -0.00014(4)
Fe1x3 -0.00019(3) 0.00051(3)
Fe1y3 0.00525(6) 0.00237(5)
Fe1z3 -0.00169(3) -0.00084(4)
Mg1x1 0.00188(2) -0.00397(2)
Mg1y1 0.01135(5) -0.01361(4)
Mg1z1 -0.00700(3) 0.00148(3)
Mg1x2 -0.00076(4) 0.00003(4)
Mg1y2 0.00063(8) 0.00038(8)
Mg1z2 -0.00055(4) -0.00014(4)
Mg1x3 -0.00019(3) 0.00051(3)
Mg1y3 0.00525(6) 0.00237(5)
Mg1z3 -0.00169(3) -0.00084(4)
Fe2x1 0.00002(3) -0.01455(3)
Fe2y1 0.00327(4) 0.00295(4)
Fe2z1 -0.00392(3) -0.00609(3)
Fe2x2 0.00030(5) 0.00062(4)
Fe2y2 0.00041(9) -0.00033(9)
Fe2z2 0.00127(5) -0.00021(5)
Fe2x3 0.00246(3) -0.00090(4)
Fe2y3 -0.00067(6) 0.00007(6)
Fe2z3 0.00138(4) 0.00071(4)
Mg2x1 0.00002(3) -0.01455(3)
Mg2y1 0.00327(4) 0.00295(4)
Mg2z1 -0.00392(3) -0.00609(3)
Mg2x2 0.00030(5) 0.00062(4)
Mg2y2 0.00041(9) -0.00033(9)
Mg2z2 0.00127(5) -0.00021(5)
Mg2x3 0.00246(3) -0.00090(4)
Mg2y3 -0.00067(6) 0.00007(6)
Mg2z3 0.00138(4) 0.00071(4)
P1x1 0.00080(2) -0.00070(2)
P1y1 -0.00360(3) -0.00111(3)
P1z1 0.00276(2) -0.00013(2)
P1x2 0.00031(3) -0.00032(4)
P1y2 0.00000(7) 0.00046(7)
P1z2 0.00058(4) -0.00063(4)
P1x3 -0.00051(3) 0.00009(3)
P1y3 -0.00020(5) 0.00197(5)
P1z3 -0.00063(3) -0.00055(3)
O1x1 -0.00329(6) 0.00213(6)
O1y1 -0.01511(10) 0.00166(10)
O1z1 0.00669(7) -0.00219(7)
O1x2 0.00036(9) -0.00093(9)
O1y2 -0.00100(19) 0.00051(18)
O1z2 0.00036(10) -0.00090(10)
O1x3 0.00039(7) 0.00099(6)
O1y3 0.00252(12) 0.00424(12)
O1z3 -0.00148(8) -0.00093(7)
O2x1 0.00936(6) -0.00772(6)
O2y1 -0.00491(9) -0.00168(9)
O2z1 0.00333(7) -0.00570(7)
O2x2 0.00086(9) 0.00000(9)
O2y2 0.00012(18) -0.00059(18)
O2z2 -0.00019(10) -0.00098(10)
O2x3 -0.00176(7) 0.00115(7)
O2y3 0.00136(12) -0.00012(12)
O2z3 -0.00179(8) 0.00028(8)
O3x1 0.00227(6) -0.00102(5)
O3y1 -0.00651(9) 0.00498(9)
O3z1 -0.00155(7) 0.00070(7)
O3x2 0.00011(9) 0.00029(9)
O3y2 0.00033(19) -0.00020(19)
O3z2 -0.00003(10) 0.00008(10)
O3x3 0.00026(6) -0.00064(7)
O3y3 -0.00178(12) 0.00005(12)
O3z3 0.00001(8) -0.00084(8)
O4x1 -0.00480(6) 0.00140(5)
O4y1 0.00832(10) -0.00262(10)
O4z1 -0.00904(7) 0.00411(7)
O4x2 0.00044(9) -0.00062(9)
O4y2 -0.00075(19) 0.00198(19)
O4z2 0.00129(10) -0.00124(10)
O4x3 -0.00093(6) 0.00094(7)
O4y3 -0.00042(12) 0.00097(12)
O4z3 -0.00117(8) 0.00162(8)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
F1 x 1 0.00372(10)
F1 y 1 -0.00019(19)
F1 z 1 0.00658(14)
F1 x 2 0.00094(18)
F1 y 2 -0.0086(3)
F1 z 2 -0.0058(2)
F2 x 1 -0.00498(11)
F2 y 1 0.0069(2)
F2 z 1 -0.00455(15)
F2 x 2 0.00178(18)
F2 y 2 0.0043(3)
F2 z 2 0.0080(2)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Fe1U111 Fe1 U11 1
Fe1U221 Fe1 U22 1
Fe1U331 Fe1 U33 1
Fe1U121 Fe1 U12 1
Fe1U131 Fe1 U13 1
Fe1U231 Fe1 U23 1
Fe1U112 Fe1 U11 2
Fe1U222 Fe1 U22 2
Fe1U332 Fe1 U33 2
Fe1U122 Fe1 U12 2
Fe1U132 Fe1 U13 2
Fe1U232 Fe1 U23 2
Fe1U113 Fe1 U11 3
Fe1U223 Fe1 U22 3
Fe1U333 Fe1 U33 3
Fe1U123 Fe1 U12 3
Fe1U133 Fe1 U13 3
Fe1U233 Fe1 U23 3
Mg1U111 Mg1 U11 1
Mg1U221 Mg1 U22 1
Mg1U331 Mg1 U33 1
Mg1U121 Mg1 U12 1
Mg1U131 Mg1 U13 1
Mg1U231 Mg1 U23 1
Mg1U112 Mg1 U11 2
Mg1U222 Mg1 U22 2
Mg1U332 Mg1 U33 2
Mg1U122 Mg1 U12 2
Mg1U132 Mg1 U13 2
Mg1U232 Mg1 U23 2
Mg1U113 Mg1 U11 3
Mg1U223 Mg1 U22 3
Mg1U333 Mg1 U33 3
Mg1U123 Mg1 U12 3
Mg1U133 Mg1 U13 3
Mg1U233 Mg1 U23 3
Fe2U111 Fe2 U11 1
Fe2U221 Fe2 U22 1
Fe2U331 Fe2 U33 1
Fe2U121 Fe2 U12 1
Fe2U131 Fe2 U13 1
Fe2U231 Fe2 U23 1
Fe2U112 Fe2 U11 2
Fe2U222 Fe2 U22 2
Fe2U332 Fe2 U33 2
Fe2U122 Fe2 U12 2
Fe2U132 Fe2 U13 2
Fe2U232 Fe2 U23 2
Fe2U113 Fe2 U11 3
Fe2U223 Fe2 U22 3
Fe2U333 Fe2 U33 3
Fe2U123 Fe2 U12 3
Fe2U133 Fe2 U13 3
Fe2U233 Fe2 U23 3
Mg2U111 Mg2 U11 1
Mg2U221 Mg2 U22 1
Mg2U331 Mg2 U33 1
Mg2U121 Mg2 U12 1
Mg2U131 Mg2 U13 1
Mg2U231 Mg2 U23 1
Mg2U112 Mg2 U11 2
Mg2U222 Mg2 U22 2
Mg2U332 Mg2 U33 2
Mg2U122 Mg2 U12 2
Mg2U132 Mg2 U13 2
Mg2U232 Mg2 U23 2
Mg2U113 Mg2 U11 3
Mg2U223 Mg2 U22 3
Mg2U333 Mg2 U33 3
Mg2U123 Mg2 U12 3
Mg2U133 Mg2 U13 3
Mg2U233 Mg2 U23 3
P1U111 P1 U11 1
P1U221 P1 U22 1
P1U331 P1 U33 1
P1U121 P1 U12 1
P1U131 P1 U13 1
P1U231 P1 U23 1
P1U112 P1 U11 2
P1U222 P1 U22 2
P1U332 P1 U33 2
P1U122 P1 U12 2
P1U132 P1 U13 2
P1U232 P1 U23 2
P1U113 P1 U11 3
P1U223 P1 U22 3
P1U333 P1 U33 3
P1U123 P1 U12 3
P1U133 P1 U13 3
P1U233 P1 U23 3
O1U111 O1 U11 1
O1U221 O1 U22 1
O1U331 O1 U33 1
O1U121 O1 U12 1
O1U131 O1 U13 1
O1U231 O1 U23 1
O1U112 O1 U11 2
O1U222 O1 U22 2
O1U332 O1 U33 2
O1U122 O1 U12 2
O1U132 O1 U13 2
O1U232 O1 U23 2
O1U113 O1 U11 3
O1U223 O1 U22 3
O1U333 O1 U33 3
O1U123 O1 U12 3
O1U133 O1 U13 3
O1U233 O1 U23 3
O2U111 O2 U11 1
O2U221 O2 U22 1
O2U331 O2 U33 1
O2U121 O2 U12 1
O2U131 O2 U13 1
O2U231 O2 U23 1
O2U112 O2 U11 2
O2U222 O2 U22 2
O2U332 O2 U33 2
O2U122 O2 U12 2
O2U132 O2 U13 2
O2U232 O2 U23 2
O2U113 O2 U11 3
O2U223 O2 U22 3
O2U333 O2 U33 3
O2U123 O2 U12 3
O2U133 O2 U13 3
O2U233 O2 U23 3
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
O3U113 O3 U11 3
O3U223 O3 U22 3
O3U333 O3 U33 3
O3U123 O3 U12 3
O3U133 O3 U13 3
O3U233 O3 U23 3
O4U111 O4 U11 1
O4U221 O4 U22 1
O4U331 O4 U33 1
O4U121 O4 U12 1
O4U131 O4 U13 1
O4U231 O4 U23 1
O4U112 O4 U11 2
O4U222 O4 U22 2
O4U332 O4 U33 2
O4U122 O4 U12 2
O4U132 O4 U13 2
O4U232 O4 U23 2
O4U113 O4 U11 3
O4U223 O4 U22 3
O4U333 O4 U33 3
O4U123 O4 U12 3
O4U133 O4 U13 3
O4U233 O4 U23 3

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1U111 -0.00019(15) -0.00012(15)
Fe1U221 -0.00044(15) 0.00098(15)
Fe1U331 0.00004(13) 0.00028(13)
Fe1U121 0.00007(11) 0.00004(11)
Fe1U131 -0.00018(11) 0.00014(11)
Fe1U231 -0.00028(10) 0.00032(10)
Fe1U112 0.0006(2) 0.0001(2)
Fe1U222 0.0008(2) 0.0016(3)
Fe1U332 0.00042(17) 0.00018(18)
Fe1U122 0.00031(17) 0.00039(19)
Fe1U132 0.00030(16) -0.00011(17)
Fe1U232 0.00005(16) -0.00070(18)
Fe1U113 0.0005(2) 0.0002(2)
Fe1U223 0.0003(2) 0.0001(2)
Fe1U333 0.00042(16) 0.00042(17)
Fe1U123 0.00012(16) -0.00022(16)
Fe1U133 0.00014(14) -0.00017(15)
Fe1U233 0.00044(15) -0.00049(15)
Mg1U111 -0.00019(15) -0.00012(15)
Mg1U221 -0.00044(15) 0.00098(15)
Mg1U331 0.00004(13) 0.00028(13)
Mg1U121 0.00007(11) 0.00004(11)
Mg1U131 -0.00018(11) 0.00014(11)
Mg1U231 -0.00028(10) 0.00032(10)
Mg1U112 0.0006(2) 0.0001(2)
Mg1U222 0.0008(2) 0.0016(3)
Mg1U332 0.00042(17) 0.00018(18)
Mg1U122 0.00031(17) 0.00039(19)
Mg1U132 0.00030(16) -0.00011(17)
Mg1U232 0.00005(16) -0.00070(18)
Mg1U113 0.0005(2) 0.0002(2)
Mg1U223 0.0003(2) 0.0001(2)
Mg1U333 0.00042(16) 0.00042(17)
Mg1U123 0.00012(16) -0.00022(16)
Mg1U133 0.00014(14) -0.00017(15)
Mg1U233 0.00044(15) -0.00049(15)
Fe2U111 -0.0008(2) -0.00132(19)
Fe2U221 0.00010(14) -0.00011(14)
Fe2U331 0.00021(15) 0.00068(15)
Fe2U121 0.00004(12) 0.00020(12)
Fe2U131 -0.00011(14) 0.00030(13)
Fe2U231 0.00013(11) 0.00000(11)
Fe2U112 0.0033(2) 0.0008(2)
Fe2U222 0.0004(3) -0.0007(3)
Fe2U332 0.0011(2) -0.00078(19)
Fe2U122 -0.0004(2) -0.0001(2)
Fe2U132 0.00163(18) -0.00039(18)
Fe2U232 -0.00019(19) -0.00022(19)
Fe2U113 0.0002(2) -0.0006(3)
Fe2U223 0.0003(2) 0.0000(2)
Fe2U333 -0.00006(19) 0.00066(19)
Fe2U123 0.00021(18) 0.00022(18)
Fe2U133 -0.00006(17) 0.00055(18)
Fe2U233 0.00004(17) 0.00003(16)
Mg2U111 -0.0008(2) -0.00132(19)
Mg2U221 0.00010(14) -0.00011(14)
Mg2U331 0.00021(15) 0.00068(15)
Mg2U121 0.00004(12) 0.00020(12)
Mg2U131 -0.00011(14) 0.00030(13)
Mg2U231 0.00013(11) 0.00000(11)
Mg2U112 0.0033(2) 0.0008(2)
Mg2U222 0.0004(3) -0.0007(3)
Mg2U332 0.0011(2) -0.00078(19)
Mg2U122 -0.0004(2) -0.0001(2)
Mg2U132 0.00163(18) -0.00039(18)
Mg2U232 -0.00019(19) -0.00022(19)
Mg2U113 0.0002(2) -0.0006(3)
Mg2U223 0.0003(2) 0.0000(2)
Mg2U333 -0.00006(19) 0.00066(19)
Mg2U123 0.00021(18) 0.00022(18)
Mg2U133 -0.00006(17) 0.00055(18)
Mg2U233 0.00004(17) 0.00003(16)
P1U111 -0.00006(11) 0.00010(11)
P1U221 -0.00018(9) -0.00008(9)
P1U331 0.00008(9) -0.00021(9)
P1U121 0.00017(8) 0.00013(8)
P1U131 0.00002(9) -0.00009(8)
P1U231 -0.00001(8) 0.00005(8)
P1U112 0.00012(20) -0.00018(19)
P1U222 0.0000(3) 0.0004(3)
P1U332 -0.00017(16) 0.00002(15)
P1U122 0.00005(17) -0.00015(17)
P1U132 0.00007(16) 0.00002(14)
P1U232 0.00015(16) -0.00011(16)
P1U113 0.00019(17) 0.00021(18)
P1U223 -0.00012(16) 0.00012(17)
P1U333 0.00010(14) -0.00008(14)
P1U123 0.00020(14) -0.00010(13)
P1U133 0.00007(13) -0.00002(13)
P1U233 0.00009(13) -0.00009(12)
O1U111 -0.0006(3) 0.0005(3)
O1U221 -0.0003(3) -0.0003(3)
O1U331 0.0004(3) -0.0003(3)
O1U121 0.0002(3) 0.0001(3)
O1U131 -0.0002(3) -0.0001(3)
O1U231 -0.0007(2) 0.0004(3)
O1U112 0.0001(5) -0.0001(5)
O1U222 -0.0002(7) -0.0006(6)
O1U332 0.0000(4) 0.0007(4)
O1U122 0.0000(5) 0.0004(4)
O1U132 0.0003(4) -0.0002(4)
O1U232 0.0000(4) 0.0002(4)
O1U113 -0.0001(5) 0.0005(4)
O1U223 -0.0006(5) 0.0000(5)
O1U333 0.0000(4) 0.0007(4)
O1U123 -0.0004(4) 0.0000(4)
O1U133 0.0000(4) 0.0005(3)
O1U233 0.0001(3) -0.0001(4)
O2U111 0.0003(4) 0.0007(4)
O2U221 -0.0006(3) 0.0003(3)
O2U331 0.0001(3) 0.0001(3)
O2U121 0.0003(3) -0.0001(3)
O2U131 -0.0004(3) 0.0004(3)
O2U231 -0.0001(2) 0.0000(2)
O2U112 -0.0006(6) 0.0013(5)
O2U222 -0.0010(7) 0.0004(7)
O2U332 0.0008(5) 0.0004(4)
O2U122 0.0004(5) 0.0007(5)
O2U132 0.0001(4) 0.0007(4)
O2U232 0.0009(4) 0.0004(4)
O2U113 -0.0008(5) 0.0000(5)
O2U223 0.0004(5) -0.0001(5)
O2U333 -0.0001(4) 0.0003(4)
O2U123 -0.0007(4) 0.0004(4)
O2U133 -0.0005(4) 0.0000(4)
O2U233 0.0001(3) 0.0000(3)
O3U111 0.0001(3) 0.0001(3)
O3U221 0.0002(3) 0.0001(3)
O3U331 0.0000(3) 0.0003(3)
O3U121 -0.0001(2) 0.0001(2)
O3U131 0.0000(3) 0.0000(3)
O3U231 -0.0004(2) 0.0003(2)
O3U112 0.0003(6) 0.0002(6)
O3U222 0.0007(7) -0.0004(7)
O3U332 -0.0004(5) -0.0003(4)
O3U122 0.0000(5) -0.0006(5)
O3U132 0.0000(4) -0.0002(4)
O3U232 -0.0001(4) -0.0007(4)
O3U113 0.0004(5) 0.0003(5)
O3U223 0.0003(5) 0.0004(5)
O3U333 -0.0005(4) 0.0003(4)
O3U123 -0.0005(4) -0.0003(4)
O3U133 0.0000(3) 0.0002(4)
O3U233 -0.0005(3) -0.0002(3)
O4U111 0.0004(3) 0.0001(3)
O4U221 -0.0006(3) 0.0004(3)
O4U331 0.0002(3) -0.0003(3)
O4U121 0.0002(3) -0.0001(2)
O4U131 0.0002(3) -0.0002(3)
O4U231 0.0004(3) -0.0006(2)
O4U112 -0.0001(5) -0.0005(5)
O4U222 0.0010(7) -0.0007(7)
O4U332 0.0002(4) 0.0007(4)
O4U122 -0.0002(5) -0.0001(5)
O4U132 0.0001(4) 0.0001(4)
O4U232 -0.0002(4) -0.0001(4)
O4U113 -0.0005(5) -0.0006(5)
O4U223 0.0003(5) 0.0001(5)
O4U333 0.0000(4) -0.0003(4)
O4U123 0.0001(4) 0.0003(4)
O4U133 -0.0003(4) -0.0003(4)
O4U233 0.0005(4) 0.0005(4)

ADP Legendre coefficients: [ Help ]

Atom site label Tensor element Polynomial order Polynomial coeff.
F1 U11 1 -0.0002(7)
F1 U22 1 -0.0019(7)
F1 U33 1 -0.0012(7)
F1 U12 1 -0.0003(5)
F1 U13 1 -0.0001(6)
F1 U23 1 -0.0018(6)
F1 U11 2 0.0030(12)
F1 U22 2 0.0000(14)
F1 U33 2 0.0150(11)
F1 U12 2 0.0007(10)
F1 U13 2 0.0046(9)
F1 U23 2 0.0052(10)
F2 U11 1 0.0020(7)
F2 U22 1 -0.0005(7)
F2 U33 1 0.0015(7)
F2 U12 1 -0.0006(5)
F2 U13 1 0.0019(6)
F2 U23 1 -0.0020(6)
F2 U11 2 0.0025(13)
F2 U22 2 0.0041(13)
F2 U33 2 0.0110(12)
F2 U12 2 0.0026(10)
F2 U13 2 0.0038(10)
F2 U23 2 0.0040(10)

9b

Chemical data

Mineral Name: wagnerite [ Help ]

Formula analytical: F0.98 H0.02 Mg1.94 Mn0.06 O4.02 P1 [ Help ]

Structural Formula Sum: F1 Fe0.029 Mg1.971 O4 P1 [ Help ]

Formula weight: 163.5 Da [ Help ]

Compound Source: Reynolds Range, Australia [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/c(0β0)s0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 12.7707(2) Å [ Help ]

b: 6.33940(10) Å [ Help ]

c: 9.64620(10) Å [ Help ]

α: 90 ° [ Help ]

β: 117.5240(5) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 692.553(17) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.000000 0.446520 0.000000

Z: 8 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 1.176 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS V2012/1 (Bruker AXS Inc.) [ Help ]

Minimum transmission factor: 0.688 [ Help ]

Maximum transmission factor: 0.746 [ Help ]

Refinement details

Total nb. of reflections: 7409 [ Help ]

Nb. of observed reflections: 4855 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0328 [ Help ]

wR(obs): 0.0993 [ Help ]

R(all): 0.0479 [ Help ]

wR(all): 0.1036 [ Help ]

S(all): 2.38 [ Help ]

S(obs): 2.87 [ Help ]

Nb. of reflections: 7409 [ Help ]

Nb. of parameters: 503 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(I)+0.0004I2) [ Help ]

Δ/σ(max): 0.0272 [ Help ]

Δ/σ(mean): 0.0029 [ Help ]

Δρ(max): 0.71 e_Å-3 [ Help ]

Δρ(min): -0.35 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated Coords restraints or constraints Disordered cluster Disordered group
Fe1 Fe 0.05882(2) 0.27289(4) 0.00922(3) Uani 0.00693(11) 8 0.0292(16) d ? ? ?
Mg1 Mg 0.05882(2) 0.27289(4) 0.00922(3) Uani 0.00693(11) 8 0.9707(16) d ? ? ?
Fe2 Fe -0.15619(2) 0.10962(4) 0.13559(3) Uani 0.00585(10) 8 0 d ? ? ?
Mg2 Mg -0.15619(2) 0.10962(4) 0.13559(3) Uani 0.00585(10) 8 1 d ? ? ?
P1 P 0.174600(16) 0.60201(3) 0.30588(2) Uani 0.00369(8) 8 1 d ? ? ?
F1 F -0.00761(5) 0.15484(10) 0.15630(7) Uani 0.0126(2) 8 0.5016(7) d ? ? ?
F2 F -0.03140(6) 0.07905(9) 0.04856(7) Uani 0.0134(2) 8 0.4984(7) d ? ? ?
O1 O 0.08031(5) 0.54440(9) 0.14104(7) Uani 0.00726(18) 8 1 d ? ? ?
O2 O 0.19384(5) 0.42137(9) 0.42132(7) Uani 0.00723(18) 8 1 d ? ? ?
O3 O 0.13158(5) 0.20648(9) -0.13671(7) Uani 0.00655(19) 8 1 d ? ? ?
O4 O 0.29115(5) 0.65210(10) 0.30350(6) Uani 0.00720(19) 8 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Fe1 Fe 0.00632(16) 0.00825(15) 0.00614(14) 0.00162(9) 0.00280(11) 0.00055(8)
Mg1 Mg 0.00632(16) 0.00825(15) 0.00614(14) 0.00162(9) 0.00280(11) 0.00055(8)
Fe2 Fe 0.00745(13) 0.00435(13) 0.00604(13) 0.00020(8) 0.00336(10) -0.00029(8)
Mg2 Mg 0.00745(13) 0.00435(13) 0.00604(13) 0.00020(8) 0.00336(10) -0.00029(8)
P1 P 0.00396(11) 0.00329(11) 0.00342(10) -0.00006(5) 0.00136(8) -0.00008(5)
F1 F 0.0073(3) 0.0146(3) 0.0154(3) 0.0001(2) 0.0048(2) 0.0048(2)
F2 F 0.0132(3) 0.0103(3) 0.0205(3) -0.0017(2) 0.0111(3) 0.0011(2)
O1 O 0.0070(3) 0.0072(3) 0.0052(2) 0.00087(18) 0.00078(19) -0.00156(18)
O2 O 0.0093(2) 0.0052(2) 0.0060(2) -0.00108(18) 0.0025(2) 0.00080(18)
O3 O 0.0072(3) 0.0043(2) 0.0084(2) -0.00074(18) 0.0038(2) 0.00104(17)
O4 O 0.0053(3) 0.0098(3) 0.0070(2) -0.00186(19) 0.0032(2) -0.00122(19)

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

Wave vector code q_1
1 1
2 2
3 3

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Fe1o1 Fe1 1
Mg1o1 Mg1 1
Fe2o1 Fe2 1
Mg2o1 Mg2 1

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1o1 -0.0041(8) 0.0066(9)
Mg1o1 0.0041(8) -0.0066(9)
Fe2o1 0.0017(9) 0.0008(9)
Mg2o1 -0.0017(9) -0.0008(9)

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
F1 0.31979(19) 0.5016(7)
F2 0.7860(2) 0.4984(7)

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

Modulation code Atom site label Displacement axis Wave vector code
Fe1x1 Fe1 x 1
Fe1y1 Fe1 y 1
Fe1z1 Fe1 z 1
Fe1x2 Fe1 x 2
Fe1y2 Fe1 y 2
Fe1z2 Fe1 z 2
Fe1x3 Fe1 x 3
Fe1y3 Fe1 y 3
Fe1z3 Fe1 z 3
Mg1x1 Mg1 x 1
Mg1y1 Mg1 y 1
Mg1z1 Mg1 z 1
Mg1x2 Mg1 x 2
Mg1y2 Mg1 y 2
Mg1z2 Mg1 z 2
Mg1x3 Mg1 x 3
Mg1y3 Mg1 y 3
Mg1z3 Mg1 z 3
Fe2x1 Fe2 x 1
Fe2y1 Fe2 y 1
Fe2z1 Fe2 z 1
Fe2x2 Fe2 x 2
Fe2y2 Fe2 y 2
Fe2z2 Fe2 z 2
Fe2x3 Fe2 x 3
Fe2y3 Fe2 y 3
Fe2z3 Fe2 z 3
Mg2x1 Mg2 x 1
Mg2y1 Mg2 y 1
Mg2z1 Mg2 z 1
Mg2x2 Mg2 x 2
Mg2y2 Mg2 y 2
Mg2z2 Mg2 z 2
Mg2x3 Mg2 x 3
Mg2y3 Mg2 y 3
Mg2z3 Mg2 z 3
P1x1 P1 x 1
P1y1 P1 y 1
P1z1 P1 z 1
P1x2 P1 x 2
P1y2 P1 y 2
P1z2 P1 z 2
P1x3 P1 x 3
P1y3 P1 y 3
P1z3 P1 z 3
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O1x3 O1 x 3
O1y3 O1 y 3
O1z3 O1 z 3
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 z 2
O2x3 O2 x 3
O2y3 O2 y 3
O2z3 O2 z 3
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O3x3 O3 x 3
O3y3 O3 y 3
O3z3 O3 z 3
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1
O4x2 O4 x 2
O4y2 O4 y 2
O4z2 O4 z 2
O4x3 O4 x 3
O4y3 O4 y 3
O4z3 O4 z 3

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1x1 0.00162(2) -0.00352(2)
Fe1y1 0.01258(4) -0.01278(4)
Fe1z1 -0.00742(3) 0.00190(3)
Fe1x2 -0.00082(3) 0.00002(3)
Fe1y2 0.00070(6) 0.00030(6)
Fe1z2 -0.00064(4) -0.00021(4)
Fe1x3 -0.00016(3) 0.00065(3)
Fe1y3 0.00486(5) 0.00301(5)
Fe1z3 -0.00194(3) -0.00105(3)
Mg1x1 0.00162(2) -0.00352(2)
Mg1y1 0.01258(4) -0.01278(4)
Mg1z1 -0.00742(3) 0.00190(3)
Mg1x2 -0.00082(3) 0.00002(3)
Mg1y2 0.00070(6) 0.00030(6)
Mg1z2 -0.00064(4) -0.00021(4)
Mg1x3 -0.00016(3) 0.00065(3)
Mg1y3 0.00486(5) 0.00301(5)
Mg1z3 -0.00194(3) -0.00105(3)
Fe2x1 0.00009(3) -0.01398(3)
Fe2y1 0.00302(4) 0.00310(4)
Fe2z1 -0.00422(3) -0.00575(3)
Fe2x2 0.00012(3) 0.00029(3)
Fe2y2 0.00009(6) -0.00043(6)
Fe2z2 0.00102(4) -0.00041(4)
Fe2x3 0.00292(3) -0.00071(3)
Fe2y3 -0.00085(5) -0.00012(5)
Fe2z3 0.00162(3) 0.00100(3)
Mg2x1 0.00009(3) -0.01398(3)
Mg2y1 0.00302(4) 0.00310(4)
Mg2z1 -0.00422(3) -0.00575(3)
Mg2x2 0.00012(3) 0.00029(3)
Mg2y2 0.00009(6) -0.00043(6)
Mg2z2 0.00102(4) -0.00041(4)
Mg2x3 0.00292(3) -0.00071(3)
Mg2y3 -0.00085(5) -0.00012(5)
Mg2z3 0.00162(3) 0.00100(3)
P1x1 0.000811(16) -0.000422(16)
P1y1 -0.00410(3) -0.00071(3)
P1z1 0.00298(2) 0.00016(2)
P1x2 0.00032(2) -0.00032(2)
P1y2 -0.00003(5) 0.00037(5)
P1z2 0.00058(3) -0.00068(3)
P1x3 -0.000419(19) -0.00002(2)
P1y3 -0.00003(4) 0.00185(3)
P1z3 -0.00060(2) -0.00076(2)
O1x1 -0.00349(5) 0.00207(5)
O1y1 -0.01552(9) 0.00205(9)
O1z1 0.00705(6) -0.00193(6)
O1x2 0.00029(7) -0.00098(6)
O1y2 -0.00075(12) 0.00071(12)
O1z2 0.00030(7) -0.00093(7)
O1x3 0.00033(5) 0.00101(5)
O1y3 0.00279(9) 0.00418(9)
O1z3 -0.00180(6) -0.00112(6)
O2x1 0.00945(5) -0.00752(5)
O2y1 -0.00541(8) -0.00071(8)
O2z1 0.00349(6) -0.00551(6)
O2x2 0.00063(7) 0.00007(6)
O2y2 -0.00004(12) -0.00049(12)
O2z2 -0.00030(8) -0.00097(7)
O2x3 -0.00239(5) 0.00133(5)
O2y3 0.00129(9) -0.00049(9)
O2z3 -0.00204(6) 0.00038(6)
O3x1 0.00212(5) -0.00065(5)
O3y1 -0.00697(8) 0.00511(8)
O3z1 -0.00175(6) 0.00136(6)
O3x2 0.00001(6) 0.00021(6)
O3y2 0.00011(12) -0.00006(12)
O3z2 -0.00019(7) 0.00007(8)
O3x3 0.00025(5) -0.00059(5)
O3y3 -0.00232(9) -0.00015(9)
O3z3 -0.00040(6) -0.00079(6)
O4x1 -0.00483(5) 0.00140(5)
O4y1 0.00722(9) -0.00247(9)
O4z1 -0.00913(6) 0.00397(6)
O4x2 0.00045(6) -0.00051(7)
O4y2 -0.00105(13) 0.00184(12)
O4z2 0.00137(7) -0.00111(7)
O4x3 -0.00097(5) 0.00109(5)
O4y3 0.00017(9) 0.00023(9)
O4z3 -0.00140(6) 0.00186(6)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
F1 x 1 0.00401(9)
F1 y 1 -0.00124(17)
F1 z 1 0.00678(12)
F1 x 2 0.00070(14)
F1 y 2 -0.0067(2)
F1 z 2 -0.00488(17)
F2 x 1 -0.00480(9)
F2 y 1 0.00695(17)
F2 z 1 -0.00429(12)
F2 x 2 0.00130(14)
F2 y 2 0.0040(3)
F2 z 2 0.00657(17)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Fe1U111 Fe1 U11 1
Fe1U221 Fe1 U22 1
Fe1U331 Fe1 U33 1
Fe1U121 Fe1 U12 1
Fe1U131 Fe1 U13 1
Fe1U231 Fe1 U23 1
Fe1U112 Fe1 U11 2
Fe1U222 Fe1 U22 2
Fe1U332 Fe1 U33 2
Fe1U122 Fe1 U12 2
Fe1U132 Fe1 U13 2
Fe1U232 Fe1 U23 2
Fe1U113 Fe1 U11 3
Fe1U223 Fe1 U22 3
Fe1U333 Fe1 U33 3
Fe1U123 Fe1 U12 3
Fe1U133 Fe1 U13 3
Fe1U233 Fe1 U23 3
Mg1U111 Mg1 U11 1
Mg1U221 Mg1 U22 1
Mg1U331 Mg1 U33 1
Mg1U121 Mg1 U12 1
Mg1U131 Mg1 U13 1
Mg1U231 Mg1 U23 1
Mg1U112 Mg1 U11 2
Mg1U222 Mg1 U22 2
Mg1U332 Mg1 U33 2
Mg1U122 Mg1 U12 2
Mg1U132 Mg1 U13 2
Mg1U232 Mg1 U23 2
Mg1U113 Mg1 U11 3
Mg1U223 Mg1 U22 3
Mg1U333 Mg1 U33 3
Mg1U123 Mg1 U12 3
Mg1U133 Mg1 U13 3
Mg1U233 Mg1 U23 3
Fe2U111 Fe2 U11 1
Fe2U221 Fe2 U22 1
Fe2U331 Fe2 U33 1
Fe2U121 Fe2 U12 1
Fe2U131 Fe2 U13 1
Fe2U231 Fe2 U23 1
Fe2U112 Fe2 U11 2
Fe2U222 Fe2 U22 2
Fe2U332 Fe2 U33 2
Fe2U122 Fe2 U12 2
Fe2U132 Fe2 U13 2
Fe2U232 Fe2 U23 2
Fe2U113 Fe2 U11 3
Fe2U223 Fe2 U22 3
Fe2U333 Fe2 U33 3
Fe2U123 Fe2 U12 3
Fe2U133 Fe2 U13 3
Fe2U233 Fe2 U23 3
Mg2U111 Mg2 U11 1
Mg2U221 Mg2 U22 1
Mg2U331 Mg2 U33 1
Mg2U121 Mg2 U12 1
Mg2U131 Mg2 U13 1
Mg2U231 Mg2 U23 1
Mg2U112 Mg2 U11 2
Mg2U222 Mg2 U22 2
Mg2U332 Mg2 U33 2
Mg2U122 Mg2 U12 2
Mg2U132 Mg2 U13 2
Mg2U232 Mg2 U23 2
Mg2U113 Mg2 U11 3
Mg2U223 Mg2 U22 3
Mg2U333 Mg2 U33 3
Mg2U123 Mg2 U12 3
Mg2U133 Mg2 U13 3
Mg2U233 Mg2 U23 3
P1U111 P1 U11 1
P1U221 P1 U22 1
P1U331 P1 U33 1
P1U121 P1 U12 1
P1U131 P1 U13 1
P1U231 P1 U23 1
P1U112 P1 U11 2
P1U222 P1 U22 2
P1U332 P1 U33 2
P1U122 P1 U12 2
P1U132 P1 U13 2
P1U232 P1 U23 2
P1U113 P1 U11 3
P1U223 P1 U22 3
P1U333 P1 U33 3
P1U123 P1 U12 3
P1U133 P1 U13 3
P1U233 P1 U23 3
O1U111 O1 U11 1
O1U221 O1 U22 1
O1U331 O1 U33 1
O1U121 O1 U12 1
O1U131 O1 U13 1
O1U231 O1 U23 1
O1U112 O1 U11 2
O1U222 O1 U22 2
O1U332 O1 U33 2
O1U122 O1 U12 2
O1U132 O1 U13 2
O1U232 O1 U23 2
O1U113 O1 U11 3
O1U223 O1 U22 3
O1U333 O1 U33 3
O1U123 O1 U12 3
O1U133 O1 U13 3
O1U233 O1 U23 3
O2U111 O2 U11 1
O2U221 O2 U22 1
O2U331 O2 U33 1
O2U121 O2 U12 1
O2U131 O2 U13 1
O2U231 O2 U23 1
O2U112 O2 U11 2
O2U222 O2 U22 2
O2U332 O2 U33 2
O2U122 O2 U12 2
O2U132 O2 U13 2
O2U232 O2 U23 2
O2U113 O2 U11 3
O2U223 O2 U22 3
O2U333 O2 U33 3
O2U123 O2 U12 3
O2U133 O2 U13 3
O2U233 O2 U23 3
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
O3U113 O3 U11 3
O3U223 O3 U22 3
O3U333 O3 U33 3
O3U123 O3 U12 3
O3U133 O3 U13 3
O3U233 O3 U23 3
O4U111 O4 U11 1
O4U221 O4 U22 1
O4U331 O4 U33 1
O4U121 O4 U12 1
O4U131 O4 U13 1
O4U231 O4 U23 1
O4U112 O4 U11 2
O4U222 O4 U22 2
O4U332 O4 U33 2
O4U122 O4 U12 2
O4U132 O4 U13 2
O4U232 O4 U23 2
O4U113 O4 U11 3
O4U223 O4 U22 3
O4U333 O4 U33 3
O4U123 O4 U12 3
O4U133 O4 U13 3
O4U233 O4 U23 3

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Fe1U111 -0.00004(13) -0.00039(13)
Fe1U221 -0.00057(15) 0.00118(15)
Fe1U331 -0.00018(12) 0.00012(12)
Fe1U121 0.00007(10) 0.00002(10)
Fe1U131 -0.00016(10) 0.00003(10)
Fe1U231 -0.00028(9) 0.00036(9)
Fe1U112 0.00026(17) -0.00024(17)
Fe1U222 -0.00011(19) 0.0029(2)
Fe1U332 -0.00041(14) 0.00048(15)
Fe1U122 0.00007(13) 0.00031(13)
Fe1U132 0.00006(13) -0.00035(14)
Fe1U232 0.00003(12) -0.00032(13)
Fe1U113 0.00014(16) -0.00004(16)
Fe1U223 0.00012(17) -0.00008(18)
Fe1U333 -0.00021(13) 0.00027(14)
Fe1U123 0.00026(12) -0.00023(12)
Fe1U133 -0.00018(12) -0.00006(13)
Fe1U233 0.00041(12) -0.00033(12)
Mg1U111 -0.00004(13) -0.00039(13)
Mg1U221 -0.00057(15) 0.00118(15)
Mg1U331 -0.00018(12) 0.00012(12)
Mg1U121 0.00007(10) 0.00002(10)
Mg1U131 -0.00016(10) 0.00003(10)
Mg1U231 -0.00028(9) 0.00036(9)
Mg1U112 0.00026(17) -0.00024(17)
Mg1U222 -0.00011(19) 0.0029(2)
Mg1U332 -0.00041(14) 0.00048(15)
Mg1U122 0.00007(13) 0.00031(13)
Mg1U132 0.00006(13) -0.00035(14)
Mg1U232 0.00003(12) -0.00032(13)
Mg1U113 0.00014(16) -0.00004(16)
Mg1U223 0.00012(17) -0.00008(18)
Mg1U333 -0.00021(13) 0.00027(14)
Mg1U123 0.00026(12) -0.00023(12)
Mg1U133 -0.00018(12) -0.00006(13)
Mg1U233 0.00041(12) -0.00033(12)
Fe2U111 -0.00025(16) -0.00005(16)
Fe2U221 0.00007(14) -0.00002(14)
Fe2U331 0.00024(13) 0.00050(13)
Fe2U121 -0.00002(10) 0.00022(10)
Fe2U131 0.00005(11) 0.00073(11)
Fe2U231 0.00004(9) 0.00005(9)
Fe2U112 0.00222(17) 0.00040(17)
Fe2U222 -0.0006(2) 0.0001(2)
Fe2U332 0.00053(15) -0.00039(14)
Fe2U122 -0.00029(13) 0.00015(13)
Fe2U132 0.00110(13) -0.00030(13)
Fe2U232 0.00016(13) 0.00010(13)
Fe2U113 -0.00003(18) 0.00000(19)
Fe2U223 0.00025(17) -0.00003(18)
Fe2U333 -0.00029(14) 0.00030(14)
Fe2U123 0.00003(13) -0.00002(12)
Fe2U133 -0.00025(13) 0.00046(14)
Fe2U233 0.00001(12) -0.00007(11)
Mg2U111 -0.00025(16) -0.00005(16)
Mg2U221 0.00007(14) -0.00002(14)
Mg2U331 0.00024(13) 0.00050(13)
Mg2U121 -0.00002(10) 0.00022(10)
Mg2U131 0.00005(11) 0.00073(11)
Mg2U231 0.00004(9) 0.00005(9)
Mg2U112 0.00222(17) 0.00040(17)
Mg2U222 -0.0006(2) 0.0001(2)
Mg2U332 0.00053(15) -0.00039(14)
Mg2U122 -0.00029(13) 0.00015(13)
Mg2U132 0.00110(13) -0.00030(13)
Mg2U232 0.00016(13) 0.00010(13)
Mg2U113 -0.00003(18) 0.00000(19)
Mg2U223 0.00025(17) -0.00003(18)
Mg2U333 -0.00029(14) 0.00030(14)
Mg2U123 0.00003(13) -0.00002(12)
Mg2U133 -0.00025(13) 0.00046(14)
Mg2U233 0.00001(12) -0.00007(11)
P1U111 -0.00010(8) 0.00017(8)
P1U221 -0.00021(8) -0.00006(8)
P1U331 0.00010(7) -0.00018(7)
P1U121 0.00015(6) 0.00002(6)
P1U131 -0.00007(7) -0.00002(7)
P1U231 -0.00001(6) -0.00002(6)
P1U112 -0.00003(13) -0.00007(13)
P1U222 -0.00006(15) -0.00011(16)
P1U332 -0.00033(11) 0.00012(10)
P1U122 -0.00002(10) 0.00005(10)
P1U132 -0.00023(10) -0.00014(10)
P1U232 0.00005(9) -0.00001(10)
P1U113 0.00002(12) 0.00005(12)
P1U223 0.00005(12) -0.00001(13)
P1U333 -0.00002(10) 0.00006(10)
P1U123 0.00015(9) -0.00006(8)
P1U133 -0.00008(9) 0.00008(9)
P1U233 0.00010(8) -0.00006(8)
O1U111 -0.0006(3) 0.0004(3)
O1U221 -0.0008(3) 0.0001(3)
O1U331 0.0003(2) -0.0003(2)
O1U121 0.0002(2) 0.0001(2)
O1U131 -0.0001(2) -0.0001(2)
O1U231 -0.0004(2) 0.00006(19)
O1U112 -0.0003(4) 0.0000(3)
O1U222 0.0001(4) -0.0002(4)
O1U332 -0.0006(3) 0.0009(3)
O1U122 -0.0003(3) 0.0007(3)
O1U132 -0.0004(3) -0.0002(3)
O1U232 0.0000(3) 0.0001(3)
O1U113 0.0009(3) -0.0001(3)
O1U223 -0.0003(4) 0.0002(4)
O1U333 0.0002(3) 0.0001(3)
O1U123 -0.0004(2) -0.0001(3)
O1U133 0.0006(3) 0.0001(3)
O1U233 0.0001(2) -0.0004(2)
O2U111 0.0006(3) 0.0005(3)
O2U221 -0.0007(3) 0.0003(3)
O2U331 0.0002(2) -0.0001(2)
O2U121 0.0002(2) -0.0001(2)
O2U131 -0.0003(2) 0.0000(2)
O2U231 -0.00006(19) 0.00025(19)
O2U112 -0.0007(4) 0.0012(4)
O2U222 -0.0002(4) -0.0006(4)
O2U332 0.0005(3) 0.0006(3)
O2U122 -0.0002(3) 0.0001(3)
O2U132 -0.0002(3) 0.0004(3)
O2U232 -0.0001(3) -0.0001(3)
O2U113 -0.0007(4) -0.0001(4)
O2U223 0.0002(4) -0.0001(3)
O2U333 0.0002(3) 0.0006(3)
O2U123 0.0000(3) 0.0000(3)
O2U133 0.0000(3) 0.0002(3)
O2U233 0.0003(2) -0.0003(2)
O3U111 0.0003(3) 0.0002(3)
O3U221 0.0000(3) 0.0001(2)
O3U331 -0.0001(2) 0.0002(2)
O3U121 0.00014(19) -0.00027(19)
O3U131 0.0002(2) -0.0001(2)
O3U231 -0.00018(19) 0.00010(18)
O3U112 -0.0003(4) 0.0003(4)
O3U222 0.0007(4) -0.0002(4)
O3U332 -0.0003(3) 0.0002(3)
O3U122 0.0000(3) -0.0004(3)
O3U132 -0.0001(3) -0.0003(3)
O3U232 0.0000(3) -0.0005(3)
O3U113 -0.0001(3) 0.0002(3)
O3U223 0.0003(4) 0.0004(3)
O3U333 0.0000(3) -0.0007(3)
O3U123 0.0002(2) -0.0001(2)
O3U133 -0.0002(3) -0.0003(3)
O3U233 0.0001(2) -0.0001(2)
O4U111 0.0002(3) 0.0002(3)
O4U221 -0.0002(3) 0.0005(3)
O4U331 0.0002(2) 0.0001(2)
O4U121 0.0004(2) -0.00024(20)
O4U131 0.0004(2) 0.0000(2)
O4U231 0.0007(2) -0.00053(19)
O4U112 0.0005(3) 0.0003(4)
O4U222 0.0002(4) -0.0003(4)
O4U332 -0.0006(3) -0.0002(3)
O4U122 0.0003(3) 0.0001(3)
O4U132 0.0001(3) 0.0000(3)
O4U232 0.0000(3) -0.0005(3)
O4U113 -0.0005(3) -0.0008(4)
O4U223 0.0003(4) -0.0001(4)
O4U333 -0.0002(3) -0.0012(3)
O4U123 0.0000(2) 0.0004(2)
O4U133 -0.0006(3) -0.0009(3)
O4U233 0.0002(2) 0.0002(2)

ADP Legendre coefficients: [ Help ]

Atom site label Tensor element Polynomial order Polynomial coeff.
F1 U11 1 -0.0003(5)
F1 U22 1 -0.0023(6)
F1 U33 1 0.0001(5)
F1 U12 1 -0.0003(4)
F1 U13 1 0.0002(4)
F1 U23 1 -0.0015(4)
F1 U11 2 -0.0001(8)
F1 U22 2 0.0047(10)
F1 U33 2 0.0113(8)
F1 U12 2 0.0014(6)
F1 U13 2 0.0008(7)
F1 U23 2 0.0064(7)
F2 U11 1 0.0012(6)
F2 U22 1 0.0002(6)
F2 U33 1 0.0009(6)
F2 U12 1 0.0001(4)
F2 U13 1 0.0013(5)
F2 U23 1 -0.0007(4)
F2 U11 2 0.0024(9)
F2 U22 2 0.0069(10)
F2 U33 2 0.0147(9)
F2 U12 2 0.0018(6)
F2 U13 2 0.0043(7)
F2 U23 2 0.0063(7)

2b

Chemical data

Mineral Name: wagnerite [ Help ]

Formula analytical: F1 Mg1.98 Mn0.02 O4 P1 [ Help ]

Structural Formula Sum: F1 Fe0 Mg2 O4 P1 [ Help ]

Formula weight: 162.6 Da [ Help ]

Compound Source: Webing, Austria [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/c(0β0)s0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 12.7633(4) Å [ Help ]

b: 6.3282(2) Å [ Help ]

c: 9.6350(3) Å [ Help ]

α: 90 ° [ Help ]

β: 117.5985(11) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 689.66(4) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.000000 0.500000 0.000000

Z: 8 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 1.069 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS V2012/1 (Bruker AXS Inc.) [ Help ]

Minimum transmission factor: 0.693 [ Help ]

Maximum transmission factor: 0.746 [ Help ]

Refinement details

Total nb. of reflections: 3160 [ Help ]

Nb. of observed reflections: 2999 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0158 [ Help ]

wR(obs): 0.0544 [ Help ]

R(all): 0.0167 [ Help ]

wR(all): 0.0549 [ Help ]

S(all): 2.01 [ Help ]

S(obs): 2.04 [ Help ]

Nb. of reflections: 3160 [ Help ]

Nb. of parameters: 227 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(I)+0.0004I2) [ Help ]

Δ/σ(max): 0.0031 [ Help ]

Δ/σ(mean): 0.0006 [ Help ]

Δρ(max): 0.43 e_Å-3 [ Help ]

Δρ(min): -0.31 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated Coords restraints or constraints Disordered cluster Disordered group
Mg1 Mg 0.058804(17) 0.27328(3) 0.00936(2) Uani 0.00724(7) 8 1 d ? ? ?
Mg2 Mg -0.155930(16) 0.10997(3) 0.13591(2) Uani 0.00677(7) 8 1 d ? ? ?
P1 P 0.174579(11) 0.60199(2) 0.305995(17) Uani 0.00451(6) 8 1 d ? ? ?
F1 F -0.00712(3) 0.15274(6) 0.15522(5) Uani 0.01013(14) 8 0.5 d ? ? ?
F2 F -0.03064(4) 0.07910(6) 0.05042(5) Uani 0.01167(15) 8 0.5 d ? ? ?
O1 O 0.08028(3) 0.54446(6) 0.14062(5) Uani 0.00783(13) 8 1 d ? ? ?
O2 O 0.19369(4) 0.42109(6) 0.42158(5) Uani 0.00767(13) 8 1 d ? ? ?
O3 O 0.13137(4) 0.20622(7) -0.13675(5) Uani 0.00706(14) 8 1 d ? ? ?
O4 O 0.29141(4) 0.65201(7) 0.30402(5) Uani 0.00794(14) 8 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Mg1 Mg 0.00668(10) 0.00846(9) 0.00656(10) 0.00133(6) 0.00304(8) 0.00062(6)
Mg2 Mg 0.00736(9) 0.00591(10) 0.00729(11) 0.00018(6) 0.00360(7) -0.00025(6)
P1 P 0.00461(8) 0.00443(8) 0.00404(9) -0.00003(4) 0.00162(6) -0.00010(4)
F1 F 0.00704(17) 0.01214(18) 0.0113(2) 0.00020(13) 0.00434(15) 0.00264(14)
F2 F 0.01217(18) 0.01044(18) 0.0153(2) -0.00177(13) 0.00886(16) 0.00015(15)
O1 O 0.00750(17) 0.00798(17) 0.00552(18) 0.00067(12) 0.00092(14) -0.00125(13)
O2 O 0.00915(16) 0.00607(16) 0.00643(19) -0.00069(12) 0.00245(14) 0.00106(13)
O3 O 0.00806(18) 0.00545(17) 0.00824(19) -0.00049(13) 0.00427(15) 0.00094(13)
O4 O 0.00579(17) 0.01112(18) 0.00753(19) -0.00164(13) 0.00361(15) -0.00143(14)

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

Wave vector code q_1
1 1

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
F1 0.3262 0.5
F2 0.78942(4) 0.5

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

Modulation code Atom site label Displacement axis Wave vector code
Mg1x1 Mg1 x 1
Mg1y1 Mg1 y 1
Mg1z1 Mg1 z 1
Mg2x1 Mg2 x 1
Mg2y1 Mg2 y 1
Mg2z1 Mg2 z 1
P1x1 P1 x 1
P1y1 P1 y 1
P1z1 P1 z 1
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Mg1x1 0.001156(16) -0.003276(16)
Mg1y1 0.01497(3) -0.01077(3)
Mg1z1 -0.00856(3) 0.00239(2)
Mg2x1 -0.000030(17) -0.01391(2)
Mg2y1 0.00272(3) 0.00353(3)
Mg2z1 -0.00490(2) -0.00584(3)
P1x1 0.000890(10) -0.000184(11)
P1y1 -0.005166(19) 0.000079(19)
P1z1 0.003646(15) 0.000506(16)
O1x1 -0.00393(3) 0.00206(3)
O1y1 -0.01714(7) 0.00366(6)
O1z1 0.00805(5) -0.00181(5)
O2x1 0.00993(3) -0.00775(4)
O2y1 -0.00558(6) 0.00045(6)
O2z1 0.00446(5) -0.00601(5)
O3x1 0.00214(3) -0.00029(3)
O3y1 -0.00763(6) 0.00544(6)
O3z1 -0.00163(5) 0.00233(5)
O4x1 -0.00510(3) 0.00137(3)
O4y1 0.00568(6) -0.00208(6)
O4z1 -0.00950(5) 0.00370(5)

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
F1 x 1 0.00468(7)
F1 y 1 -0.00309(14)
F1 z 1 0.00744(11)
F1 x 2 0
F1 y 2 0
F1 z 2 0
F2 x 1 -0.00461(8)
F2 y 1 0.00796(15)
F2 z 1 -0.00378(12)
F2 x 2 0
F2 y 2 0
F2 z 2 0

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Mg1U111 Mg1 U11 1
Mg1U221 Mg1 U22 1
Mg1U331 Mg1 U33 1
Mg1U121 Mg1 U12 1
Mg1U131 Mg1 U13 1
Mg1U231 Mg1 U23 1
Mg2U111 Mg2 U11 1
Mg2U221 Mg2 U22 1
Mg2U331 Mg2 U33 1
Mg2U121 Mg2 U12 1
Mg2U131 Mg2 U13 1
Mg2U231 Mg2 U23 1
P1U111 P1 U11 1
P1U221 P1 U22 1
P1U331 P1 U33 1
P1U121 P1 U12 1
P1U131 P1 U13 1
P1U231 P1 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
O2U111 O2 U11 1
O2U221 O2 U22 1
O2U331 O2 U33 1
O2U121 O2 U12 1
O2U131 O2 U13 1
O2U231 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
O4U111 O4 U11 1
O4U221 O4 U22 1
O4U331 O4 U33 1
O4U121 O4 U12 1
O4U131 O4 U13 1
O4U231 O4 U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Mg1U111 -0.00005(8) -0.00088(7)
Mg1U221 -0.00019(9) 0.00137(8)
Mg1U331 0.00068(9) 0.00030(9)
Mg1U121 -0.00058(6) -0.00037(6)
Mg1U131 0.00043(7) -0.00006(7)
Mg1U231 -0.00076(7) 0.00002(7)
Mg2U111 -0.00049(8) 0.00004(10)
Mg2U221 -0.00012(7) -0.00032(7)
Mg2U331 0.00024(9) 0.00187(9)
Mg2U121 0.00013(6) 0.00013(7)
Mg2U131 0.00067(7) 0.00166(8)
Mg2U231 0.00001(6) -0.00010(7)
P1U111 -0.00004(5) 0.00016(5)
P1U221 -0.00010(5) -0.00016(5)
P1U331 0.00022(6) -0.00031(6)
P1U121 0.00004(4) 0.00009(4)
P1U131 0.00006(4) -0.00005(4)
P1U231 -0.00010(4) 0.00013(4)
O1U111 -0.00084(16) 0.00119(16)
O1U221 0.00009(18) -0.00040(17)
O1U331 0.00064(18) -0.00075(19)
O1U121 -0.00035(13) 0.00086(13)
O1U131 -0.00005(14) -0.00023(14)
O1U231 -0.00073(14) 0.00075(14)
O2U111 0.00018(18) 0.0018(2)
O2U221 -0.00043(15) 0.00034(15)
O2U331 0.00045(18) -0.00054(19)
O2U121 0.00024(13) -0.00079(14)
O2U131 -0.00014(15) -0.00051(16)
O2U231 0.00001(13) 0.00019(13)
O3U111 0.00021(16) 0.00001(15)
O3U221 0.00003(15) 0.00016(14)
O3U331 -0.00007(18) -0.00007(17)
O3U121 0.00017(12) -0.00022(12)
O3U131 0.00000(14) -0.00016(14)
O3U231 -0.00005(13) 0.00004(13)
O4U111 -0.00038(16) 0.00066(15)
O4U221 -0.00136(16) 0.00074(16)
O4U331 -0.00188(20) 0.00067(18)
O4U121 0.00110(13) -0.00059(12)
O4U131 -0.00085(15) 0.00063(14)
O4U231 0.00188(14) -0.00071(13)

ADP Legendre coefficients: [ Help ]

Atom site label Tensor element Polynomial order Polynomial coeff.
F1 U11 1 0.0003(4)
F1 U22 1 0.0002(4)
F1 U33 1 0.0001(5)
F1 U12 1 0.0000(3)
F1 U13 1 0.0000(3)
F1 U23 1 0.0002(3)
F1 U11 2 0.0001
F1 U22 2 0.0001
F1 U33 2 0.0001
F1 U12 2 0.0001
F1 U13 2 0.0001
F1 U23 2 0.0001
F2 U11 1 0.0002(4)
F2 U22 1 0.0010(4)
F2 U33 1 0.0007(5)
F2 U12 1 0.0001(3)
F2 U13 1 0.0006(4)
F2 U23 1 0.0000(3)
F2 U11 2 0.0001
F2 U22 2 0.0001
F2 U33 2 0.0001
F2 U12 2 0.0001
F2 U13 2 0.0001
F2 U23 2 0.0001