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Incommmensurately modulated crystal structure of flamite-natural analogue of α'H-Ca2Si_O4

Authors:

Rashchenko, Sergey V.; Seryotkin, Yurii V.; Sokol, Ella V.; Kokh, Svenlana N.

Journal:

Acta Crystallographica, Section B 75 1137-1143 (2019)

DOI:

https://doi.org/10.1107/S2052520619013623

B-IncStrDB ID: 15142EGPJV9 Entry date: 2019-10-25 Last revision: 2022-01-13

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I

Chemical data

Structural Formula Sum: Ca1.75 Na0.12 K0.12 Si0.74 P0.26 O4 [ Help ]

Formula weight: 170.4 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Pnma(0β0)00s [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 6.8588(2) Å [ Help ]

b: 5.4301(2) Å [ Help ]

c: 9.4052(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 350.29(2) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.000000 0.2728(2) 0.000000

Z: 4 [ Help ]

Cell determination reflection Nb.: 10460 [ Help ]

θ(min) for cell determination: 3.13 ° [ Help ]

θ(max) for cell determination: 25 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 3.27 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: CrysAlisPro 1.171.39.46 (Rigaku Oxford Diffraction, 2018) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.834 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details

Total nb. of reflections: 4505 [ Help ]

Nb. of observed reflections: 3283 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0874 [ Help ]

wR(obs): 0.1643 [ Help ]

R(all): 0.1126 [ Help ]

wR(all): 0.1671 [ Help ]

S(all): 3.70 [ Help ]

S(obs): 4.29 [ Help ]

Nb. of reflections: 4505 [ Help ]

Nb. of parameters: 144 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0001 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 2.76 e_Å-3 [ Help ]

Δρ(min): -2.39 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
Ca1 Ca 0.67002(15) 0.25 0.07550(10) Uani 0.0260(4) 4 0.880(5) d ? ? ?
Ca2 Ca 0.00538(12) 0.75 0.21004(9) Uani 0.0209(3) 4 0.980(6) d ? ? ?
Si1 Si 0.27271(16) 0.75 0.57986(12) Uani 0.0184(4) 4 1 d ? ? ?
O1 O 0.1943(5) 0.75 0.4261(3) Uani 0.0317(10) 4 1 d ? ? ?
O2 O 0.1948(3) 0.5155(4) 0.6545(2) Uani 0.0378(8) 8 1 d ? ? ?
O3 O 0.4895(5) 0.75 0.5788(4) Uani 0.0423(13) 4 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Ca1 Ca 0.0334(7) 0.0188(6) 0.0258(7) 0 0.0053(5) 0
Ca2 Ca 0.0239(5) 0.0175(5) 0.0215(5) 0 -0.0003(4) 0
Si1 Si 0.0311(7) 0.0081(5) 0.0161(7) 0 -0.0033(5) 0
O1 O 0.0419(19) 0.0282(17) 0.0250(18) 0 -0.0071(14) 0
O2 O 0.0642(18) 0.0207(12) 0.0286(13) -0.0031(10) 0.0078(12) 0.0073(9)
O3 O 0.051(2) 0.043(2) 0.033(2) 0 -0.014(2) 0

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

Table: [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label _jana_atom_site_occ_Fourier_absolute
Ca1 1
Ca2 1

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Ca1o1 Ca1 1
Ca1o2 Ca1 2
Ca2o1 Ca2 1
Ca2o2 Ca2 2

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ca1o1 0 -0.128(4)
Ca1o2 0.073(4) 0
Ca2o1 0 -0.014(3)
Ca2o2 0.004(4) 0

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
O1 0.25 1

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

Modulation code Atom site label Displacement axis Wave vector code
Ca1x1 Ca1 x 1
Ca1y1 Ca1 y 1
Ca1z1 Ca1 z 1
Ca1x2 Ca1 x 2
Ca1y2 Ca1 y 2
Ca1z2 Ca1 z 2
Ca2x1 Ca2 x 1
Ca2y1 Ca2 y 1
Ca2z1 Ca2 z 1
Ca2x2 Ca2 x 2
Ca2y2 Ca2 y 2
Ca2z2 Ca2 z 2
Si1x1 Si1 x 1
Si1y1 Si1 y 1
Si1z1 Si1 z 1
Si1x2 Si1 x 2
Si1y2 Si1 y 2
Si1z2 Si1 z 2
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 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: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ca1x1 0 0.0134(2)
Ca1y1 -0.0295(2) 0
Ca1z1 0 0.03908(18)
Ca1x2 0.0058(2) 0
Ca1y2 0 0.0165(3)
Ca1z2 -0.00245(18) 0
Ca2x1 0 -0.00599(17)
Ca2y1 0.0423(2) 0
Ca2z1 0 0.03491(12)
Ca2x2 -0.0109(2) 0
Ca2y2 0 0.0058(2)
Ca2z2 0.00261(14) 0
Si1x1 0 -0.0259(2)
Si1y1 0.0117(2) 0
Si1z1 0 0.03672(19)
Si1x2 -0.0015(3) 0
Si1y2 0 -0.0037(3)
Si1z2 -0.0028(2) 0
O2x1 -0.0590(5) -0.0242(4)
O2y1 -0.0025(5) -0.0029(5)
O2z1 -0.0235(3) 0.0303(3)
O2x2 0.0174(5) 0.0100(6)
O2y2 0.0004(6) -0.0127(5)
O2z2 0.0042(3) -0.0050(3)
O3x1 0 -0.0299(7)
O3y1 -0.0646(9) 0
O3z1 0 0.0941(5)
O3x2 0.0025(8) 0
O3y2 0 0.0232(10)
O3z2 -0.0280(6) 0

Displacive (translational) Legendre coefficients: [ Help ]

Atom site label Displacement axis Polynomial order Polynomial coeff.
O1 x 1 0
O1 y 1 -0.1002(8)
O1 z 1 0
O1 x 2 0.0197(6)
O1 y 2 0
O1 z 2 0.0229(4)
O1 x 3 0
O1 y 3 -0.0452(8)
O1 z 3 0
O1 x 4 0.0139(7)
O1 y 4 0
O1 z 4 -0.0018(5)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Ca1U111 Ca1 U11 1
Ca1U221 Ca1 U22 1
Ca1U331 Ca1 U33 1
Ca1U121 Ca1 U12 1
Ca1U131 Ca1 U13 1
Ca1U231 Ca1 U23 1
Ca1U112 Ca1 U11 2
Ca1U222 Ca1 U22 2
Ca1U332 Ca1 U33 2
Ca1U122 Ca1 U12 2
Ca1U132 Ca1 U13 2
Ca1U232 Ca1 U23 2
Ca2U111 Ca2 U11 1
Ca2U221 Ca2 U22 1
Ca2U331 Ca2 U33 1
Ca2U121 Ca2 U12 1
Ca2U131 Ca2 U13 1
Ca2U231 Ca2 U23 1
Ca2U112 Ca2 U11 2
Ca2U222 Ca2 U22 2
Ca2U332 Ca2 U33 2
Ca2U122 Ca2 U12 2
Ca2U132 Ca2 U13 2
Ca2U232 Ca2 U23 2
Si1U111 Si1 U11 1
Si1U221 Si1 U22 1
Si1U331 Si1 U33 1
Si1U121 Si1 U12 1
Si1U131 Si1 U13 1
Si1U231 Si1 U23 1
Si1U112 Si1 U11 2
Si1U222 Si1 U22 2
Si1U332 Si1 U33 2
Si1U122 Si1 U12 2
Si1U132 Si1 U13 2
Si1U232 Si1 U23 2
O2U111 O2 U11 1
O2U221 O2 U22 1
O2U331 O2 U33 1
O2U121 O2 U12 1
O2U131 O2 U13 1
O2U231 O2 U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ca1U111 0 0.0017(10)
Ca1U221 0 0.0046(8)
Ca1U331 0 0.0036(11)
Ca1U121 -0.0034(5) 0
Ca1U131 0 0.0002(7)
Ca1U231 0.0009(6) 0
Ca1U112 -0.0084(11) 0
Ca1U222 0.0008(9) 0
Ca1U332 -0.0104(11) 0
Ca1U122 0 0.0046(8)
Ca1U132 -0.0126(9) 0
Ca1U232 0 0.0053(7)
Ca2U111 0 -0.0012(7)
Ca2U221 0 -0.0014(6)
Ca2U331 0 -0.0049(8)
Ca2U121 -0.0019(5) 0
Ca2U131 0 0.0019(6)
Ca2U231 0.0020(5) 0
Ca2U112 0.0030(10) 0
Ca2U222 -0.0006(8) 0
Ca2U332 -0.0002(9) 0
Ca2U122 0 0.0011(6)
Ca2U132 0.0036(7) 0
Ca2U232 0 -0.0037(6)
Si1U111 0 0.0075(10)
Si1U221 0 -0.0010(6)
Si1U331 0 0.0062(11)
Si1U121 -0.0003(6) 0
Si1U131 0 -0.0041(7)
Si1U231 0.0001(6) 0
Si1U112 -0.0129(12) 0
Si1U222 -0.0003(8) 0
Si1U332 -0.0065(12) 0
Si1U122 0 0.0006(8)
Si1U132 0.0092(9) 0
Si1U232 0 0.0053(7)
O2U111 0.019(3) 0.037(3)
O2U221 -0.0006(15) 0.0012(15)
O2U331 0.0010(19) -0.004(2)
O2U121 -0.0117(15) 0.0020(15)
O2U131 0.0019(17) 0.0014(19)
O2U231 -0.0039(14) -0.0034(13)