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The modulated structure of intermediate plagioclase feldspar CaxNa1-xAl1+xSi3-xO8

Authors:

Yamamoto, A.; Nakazama, H.; Kitamura, M.; Morimoto, N.

Journal:

Acta Cryst. B 40 228-237 (1984)

DOI:

https://doi.org/10.1107/S0108768184002032

B-IncStrDB ID: 412EyBC6x Entry date: 2010-11-08 Last revision: 2021-12-30

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An52

Chemical data

Structural Formula Sum: Al0 Ca0.52 Na0.48 O8 Si4 [ Help ]

Formula weight: 272.2 Da [ Help ]

Mineral Name: Labradorite (An52) [ Help ]

Crystallographic data and experimental details

a: 8.178(1) Å [ Help ]

b: 12.865(1) Å [ Help ]

c: 14.218(1) Å [ Help ]

α: 93.53(1) ° [ Help ]

β: 116.21(1) ° [ Help ]

γ: 89.92(1) ° [ Help ]

Volume: 1339.0(2) Å3 [ Help ]

Z: 8 [ Help ]

Crystal system: triclinic [ Help ]

Superspace group name (WJJ): P:P -1:-1 [ Help ]

Superspace group name: X-1(αβγ)0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

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

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -x,-y,-z
3 1/2+x,1/2+y,1/2+z
4 1/2-x,1/2-y,1/2-z
5 1/2+x,1/2+y,z
6 1/2-x,1/2-y,-z
7 x,y,1/2+z
8 -x,-y,1/2-z

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.061 0.044 -0.222

Refinement details

Refinement remarks: For Al/Si sites the scattering factor is that of Si. [ Help ]

Modulation functions description: Displacive and occupational modulations:Fourier series. 1st-order harmonics. [ Help ]

Structure factors calc. details: Gaussian integration [ Help ]

Nb. of observed reflections: 4735 [ Help ]

R(obs): 0.074 [ Help ]

Structural Information

Average Structure: [ Help ]

Site description Atom site label Atom symbol Symmetry multiplicity Occupancy x y z Uiso/equiv ADP type
Ca on Na(1) site Ca/Na(1) Ca 8 0.32(18) 0.2678(9) -0.0144(24) 0.0801(22) ? Uani
Na on Na(1) site Na/Na(1) Na 8 0.22(18) 0.2678(9) -0.0144(24) 0.0801(22) ? Uani
Ca on Na(2) site Ca/Na(2) Ca 8 0.20(18) 0.2709(8) 0.0283(7) 0.0497(6) ? Uani
Na on Na(2) site Na/Na(2) Na 8 0.26(18) 0.2709(8) 0.0283(7) 0.0497(6) ? Uani
Si on Al/Si(1) site Al/Si(1) Si 8 1 0.0065(1) 0.1647(1) 0.1069(1) ? Uani
Si on Al/Si(2) site Al/Si(2) Si 8 1 0.0031(1) 0.8175(1) 0.1160(1) ? Uani
Si on Al/Si(3) site Al/Si(3) Si 8 1 0.6864(1) 0.1095(1) 0.1585(1) ? Uani
Si on Al/Si(4) site Al/Si(4) Si 8 1 0.6822(1) 0.8797(1) 0.1783(1) ? Uani
. O(1) O 8 1 0.0030(4) 0.1299(2) 0.4897(1) ? Uani
. O(2) O 8 1 0.5827(3) 0.9931(1) 0.1392(2) ? Uani
. O(3) O 8 1 0.8127(3) 0.1062(2) 0.0950(2) ? Uani
. O(4) O 8 1 0.8175(4) 0.8538(2) 0.1230(2) ? Uani
. O(5) O 8 1 0.0142(3) 0.2925(2) 0.1390(2) ? Uani
. O(6) O 8 1 0.0156(4) 0.6889(2) 0.1087(2) ? Uani
. O(7) O 8 1 0.1992(3) 0.1079(2) 0.1920(2) ? Uani
. O(8) O 8 1 0.1897(4) 0.8670(2) 0.2155(2) ? Uani

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

Wave vector code q_x q_y q_z
1 0.061 0.044 -0.222

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

Modulation code Atom site label Displacement axis Wave vector code
Ca/Na(1)x1 Ca/Na(1) x 1
Ca/Na(1)y1 Ca/Na(1) y 1
Ca/Na(1)z1 Ca/Na(1) z 1
Ca/Na(2)x1 Ca/Na(2) x 1
Ca/Na(2)y1 Ca/Na(2) y 1
Ca/Na(2)z1 Ca/Na(2) z 1
Al/Si(1)x1 Al/Si(1) x 1
Al/Si(1)y1 Al/Si(1) y 1
Al/Si(1)z1 Al/Si(1) z 1
Al/Si(2)x1 Al/Si(2) x 1
Al/Si(2)y1 Al/Si(2) y 1
Al/Si(2)z1 Al/Si(2) z 1
Al/Si(3)x1 Al/Si(3) x 1
Al/Si(3)y1 Al/Si(3) y 1
Al/Si(3)z1 Al/Si(3) z 1
Al/Si(4)x1 Al/Si(4) x 1
Al/Si(4)y1 Al/Si(4) y 1
Al/Si(4)z1 Al/Si(4) z 1
O(1)x1 O(1) x 1
O(1)y1 O(1) y 1
O(1)z1 O(1) z 1
O(2)x1 O(2) x 1
O(2)y1 O(2) y 1
O(2)z1 O(2) z 1
O(3)x1 O(3) x 1
O(3)y1 O(3) y 1
O(3)z1 O(3) z 1
O(4)x1 O(4) x 1
O(4)y1 O(4) y 1
O(4)z1 O(4) z 1
O(5)x1 O(5) x 1
O(5)y1 O(5) y 1
O(5)z1 O(5) z 1
O(6)x1 O(6) x 1
O(6)y1 O(6) y 1
O(6)z1 O(6) z 1
O(7)x1 O(7) x 1
O(7)y1 O(7) y 1
O(7)z1 O(7) z 1
O(8)x1 O(8) x 1
O(8)y1 O(8) y 1
O(8)z1 O(8) z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ca/Na(1)x1 -0.0031(9) 0.0021(14)
Ca/Na(1)y1 0.0126(23) -0.0250(35)
Ca/Na(1)z1 -0.0085(19) 0.0103(32)
Ca/Na(2)x1 -0.0040(9) -0.0008(12)
Ca/Na(2)y1 -0.0004(9) -0.0048(7)
Ca/Na(2)z1 -0.0021(6) -0.0008(6)
Al/Si(1)x1 -0.0025(2) 0.0046(1)
Al/Si(1)y1 0.0023(1) -0.0080(1)
Al/Si(1)z1 0.0031(1) -0.0013(1)
Al/Si(2)x1 0.0024(2) -0.0058(1)
Al/Si(2)y1 0.0005(1) -0.0073(1)
Al/Si(2)z1 -0.0028(1) 0.0003(1)
Al/Si(3)x1 -0.0048(2) 0.0017(1)
Al/Si(3)y1 -0.0026(1) 0.0047(1)
Al/Si(3)z1 0.0007(1) -0.0013(1)
Al/Si(4)x1 0.0019(2) -0.0037(1)
Al/Si(4)y1 -0.0020(1) 0.0058(1)
Al/Si(4)z1 -0.0025(1) 0.0000(1)
O(1)x1 0.0073(6) -0.0022(6)
O(1)y1 -0.0010(3) 0.0122(3)
O(1)z1 0.0009(3) 0.0018(2)
O(2)x1 -0.0030(5) -0.0032(4)
O(2)y1 0.0013(3) 0.0068(2)
O(2)z1 0.0001(3) 0.0003(2)
O(3)x1 -0.0078(6) 0.0028(5)
O(3)y1 -0.0012(3) -0.0050(2)
O(3)z1 0.0031(3) -0.0003(3)
O(4)x1 0.0011(7) -0.0087(5)
O(4)y1 0.0011(3) 0.0005(3)
O(4)z1 -0.0092(4) -0.0039(3)
O(5)x1 0.0026(6) 0.0087(5)
O(5)y1 0.0070(3) -0.0079(2)
O(5)z1 0.0046(3) -0.0016(2)
O(6)x1 0.0002(6) -0.0111(5)
O(6)y1 0.0044(3) -0.0096(2)
O(6)z1 -0.0027(3) 0.0037(2)
O(7)x1 0.0083(6) 0.0032(5)
O(7)y1 -0.0009(3) -0.0080(2)
O(7)z1 0.0018(3) -0.0005(2)
O(8)x1 -0.0077(6) -0.0016(5)
O(8)y1 -0.0018(3) -0.0072(2)
O(8)z1 -0.0025(3) 0.0009(2)

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Ca/Na(1)o1 Ca/Na(1) 1
Na/Na(1)o1 Na/Na(1) 1
Ca/Na(2)o1 Ca/Na(2) 1
Na/Na(2)o1 Na/Na(2) 1

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ca/Na(1)o1 0.00(24) 0.08(22)
Na/Na(1)o1 -0.02(24) -0.02(22)
Ca/Na(2)o1 0.10(24) -0.14(22)
Na/Na(2)o1 -0.08(24) 0.08(22)