B-IncStrDB

Incommensurate modulation and thermal expansion of Sr₃B_2+xSi_1-xO_8-x/2 solid solutions

Authors:

Volkov, Sergey; Bubnova, Rimma; Bolotina, Nadezhda; Krzhizhanovskaya, Maria; Belousova, Olga; Filatov, Stanislav

Journal:

Acta Crystallographica, Section B 71 489-497 (2015)

DOI:

https://doi.org/10.1107/S2052520615011713

B-IncStrDB ID: 11322EzrAh2 Entry date: 2015-10-02 Last revision: 2022-01-02

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I

Chemical data

Structural Formula Sum: B3.041 O10.479 Si0.959 Sr4 [ Help ]

Formula weight: 577.9 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Space group name (H-M): P n m a [ Help ]

Space group name (Hall): -P -2xabc;-2yb;-2zac [ Help ]

Symmetry operations of the space group: (Show/hide table) [ Help ]

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

a: 12.2774 Å [ Help ]

b: 3.9006 Å [ Help ]

c: 5.4091 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 259.038 Å³ [ Help ]

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 20.637 mm^-1 [ Help ]

Refinement details

Total nb. of reflections: 1031 [ Help ]

Nb. of observed reflections: 428 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.2015 [ Help ]

R(obs): 0.0765 [ Help ]

wR(obs): 0.0772 [ Help ]

wR(all): 0.0907 [ Help ]

S(all): 2.34 [ Help ]

Nb. of reflections: 1031 [ Help ]

Nb. of parameters: 29 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0012 [ Help ]

Δ/σ(mean): 0.0003 [ Help ]

Δρ(max): 3.58 e_Å^-3 [ Help ]

Δρ(min): -5.05 e_Å^-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom symbol	Atom site label	x	y	z	Uiso/equiv	ADP type	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Occupancy	Disordered cluster	Disordered group
Sr	Sr	0.14594(9)	0.75	0.90476(13)	0.0386(3)	Uani	d	?	1	?	?
B	B	0.4073(18)	0.82(4)	0.914(4)	0.0208(18)	Uiso	d	?	0.3802	?	?
Si	Si	0.4199(10)	0.75	0.944(2)	0.0208(18)	Uiso	d	?	0.2395	?	?
O	O1	0.4236(12)	0.75	0.681(2)	0.024(2)	Uiso	d	?	0.5	?	?
O	O2	0.51(3)	0.527(7)	0.919(3)	0.078(7)	Uiso	d	?	0.3097	?	?
O	O3	0.334(9)	0.75	0.1031(11)	0.056(3)	Uani	d	?	1	?	?
O	O4	0.3665(12)	0.75	0.675(2)	0.025(2)	Uiso	d	?	0.5	?	?

ADP components: (Show/hide table) [ Help ]

Atom site label	U11	U22	U33	U12	U13	U23	Atom site symbol
Sr	0.0765(8)	0.0153(3)	0.0241(4)	0	-0.0166(4)	0	Sr
O3	0.102(8)	0.026(3)	0.04(4)	0	0.024(4)	0	O

II

Chemical data

Structural Formula Sum: B3.376 O10.312 Si0.624 Sr4 [ Help ]

Formula weight: 569.5 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Space group name (H-M): P n m a [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4,x5
2	-x1+1/2,-x2,x3+1/2,x5,x4
3	-x1,x2+1/2,-x3,-x5,-x4
4	x1+1/2,-x2+1/2,-x3+1/2,-x4,-x5
5	-x1,-x2,-x3,-x4,-x5
6	x1+1/2,x2,-x3+1/2,-x5,-x4
7	x1,-x2+1/2,x3,x5,x4
8	-x1+1/2,x2+1/2,x3+1/2,x4,x5

a: 12.178(2) Å [ Help ]

b: 3.8801(8) Å [ Help ]

c: 5.387(11) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 254.55(9) Å³ [ Help ]

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0	0.033	0.418
2	0	-0.033	0.418

μ: 20.959 mm^-1 [ Help ]

Refinement details

Total nb. of reflections: 1403 [ Help ]

Nb. of observed reflections: 441 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.1756 [ Help ]

R(obs): 0.0605 [ Help ]

wR(obs): 0.0607 [ Help ]

wR(all): 0.0677 [ Help ]

S(all): 2.35 [ Help ]

Nb. of reflections: 1403 [ Help ]

Nb. of parameters: 35 [ Help ]

Number of constraints: 4 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0053 [ Help ]

Δ/σ(mean): 0.0011 [ Help ]

Δρ(max): 0.94 e_Å^-3 [ Help ]

Δρ(min): -1.19 e_Å^-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom symbol	Atom site label	x	y	z	Uiso/equiv	ADP type	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Occupancy	Disordered cluster	Disordered group
Sr	Sr	0.14481(6)	0.75	0.90534(10)	0.02953(19)	Uani	d	?	1	?	?
B	B	0.4089(10)	0.815(2)	0.916(2)	0.0202(15)	Uiso	d	?	0.422	?	?
Si	Si	0.4202(11)	0.75	0.949(2)	0.0202(15)	Uiso	d	?	0.156	?	?
O	O1	0.4301(7)	0.75	0.6826(15)	0.0221(11)	Uiso	d	?	0.5	?	?
O	O2	0.5088(11)	0.519(4)	0.917(2)	0.049(3)	Uiso	d	?	0.289	?	?
O	O3	0.3323(4)	0.75	0.1005(9)	0.0354(13)	Uiso	d	?	1	?	?
O	O4	0.3681(7)	0.75	0.6769(15)	0.0221(11)	Uiso	d	?	0.5	?	?

ADP components: (Show/hide table) [ Help ]

Atom site label	U11	U22	U33	U12	U13	U23	Atom site symbol
Sr	0.0546(4)	0.0136(2)	0.0204(3)	0	-0.0167(3)	0	Sr

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	q_2
1	1	0
2	0	1

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Srx1	Sr	x	1
Sry1	Sr	y	1
Srz1	Sr	z	1
Srx2	Sr	x	2
Sry2	Sr	y	2
Srz2	Sr	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
Srx1	0.00399(15)	0.00361(15)
Sry1	0	0
Srz1	0(4)	0.0044(5)
Srx2	0.00399(15)	0.00361(15)
Sry2	0	0
Srz2	0(4)	0.0044(5)
O3x1	0.0048(10)	0.0076(10)
O3y1	0	0
O3z1	0	0
O3x2	0.0048(10)	0.0076(10)
O3y2	0	0
O3z2	0	0

Definition of the occupation Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Wave vector code
O1o1	O1	1
O1o2	O1	2
O2o1	O2	1
O2o2	O2	2
O4o1	O4	1
O4o2	O4	2

Occupation Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
O1o1	-0.048(19)	0.04(2)
O1o2	-0.048(19)	0.04(2)
O2o1	0	0.18(4)
O2o2	0	0.18(4)
O4o1	0.048(19)	-0.04(2)
O4o2	0.048(19)	-0.04(2)

III

Chemical data

Structural Formula Sum: B3.704 O10.148 Si0.296 Sr4 [ Help ]

Formula weight: 561.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Space group name (H-M): P n m a [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4,x5
2	-x1+1/2,-x2,x3+1/2,x5,x4
3	-x1,x2+1/2,-x3,-x5,-x4
4	x1+1/2,-x2+1/2,-x3+1/2,-x4,-x5
5	-x1,-x2,-x3,-x4,-x5
6	x1+1/2,x2,-x3+1/2,-x5,-x4
7	x1,-x2+1/2,x3,x5,x4
8	-x1+1/2,x2+1/2,x3+1/2,x4,x5

a: 12.089 Å [ Help ]

b: 3.8635 Å [ Help ]

c: 5.378 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 251.184 Å³ [ Help ]

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0	0.041	0.378
2	0	-0.041	0.378

μ: 21.198 mm^-1 [ Help ]

Refinement details

Total nb. of reflections: 1431 [ Help ]

Nb. of observed reflections: 431 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.2089 [ Help ]

R(obs): 0.0806 [ Help ]

wR(obs): 0.0758 [ Help ]

wR(all): 0.083 [ Help ]

S(all): 2.64 [ Help ]

Nb. of reflections: 1431 [ Help ]

Nb. of parameters: 35 [ Help ]

Number of constraints: 4 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0055 [ Help ]

Δ/σ(mean): 0.0007 [ Help ]

Δρ(max): 1.09 e_Å^-3 [ Help ]

Δρ(min): -4.63 e_Å^-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom symbol	Atom site label	x	y	z	Uiso/equiv	ADP type	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Occupancy	Disordered cluster	Disordered group
Sr	Sr	0.14443(7)	0.75	0.90653(14)	0.0238(3)	Uani	d	?	1	?	?
B	B	0.4082(12)	0.816(2)	0.924(3)	0.019(3)	Uiso	d	?	0.463	?	?
Si	Si	0.422(3)	0.75	0.952(8)	0.019(3)	Uiso	d	?	0.074	?	?
O	O1	0.4304(10)	0.75	0.692(2)	0.0244(15)	Uiso	d	?	0.5	?	?
O	O2	0.5067(15)	0.493(5)	0.908(3)	0.046(4)	Uiso	d	?	0.2685	?	?
O	O3	0.3336(6)	0.75	0.0995(13)	0.0335(17)	Uiso	d	?	1	?	?
O	O4	0.3669(10)	0.75	0.683(2)	0.0244(15)	Uiso	d	?	0.5	?	?

ADP components: (Show/hide table) [ Help ]

Atom site label	U11	U22	U33	U12	U13	U23	Atom site symbol
Sr	0.0433(7)	0.0125(3)	0.0157(5)	0	-0.0109(5)	0	Sr

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	q_2
1	1	0
2	0	1

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Srx1	Sr	x	1
Sry1	Sr	y	1
Srz1	Sr	z	1
Srx2	Sr	x	2
Sry2	Sr	y	2
Srz2	Sr	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
Srx1	0.0052(2)	0.0058(2)
Sry1	0	0
Srz1	-0.0078(6)	-0.0048(6)
Srx2	0.0052(2)	0.0058(2)
Sry2	0	0
Srz2	-0.0078(6)	-0.0048(6)
O3x1	0.0042(17)	0.0086(14)
O3y1	0	0
O3z1	0	0
O3x2	0.0042(17)	0.0086(14)
O3y2	0	0
O3z2	0	0

Definition of the occupation Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Wave vector code
O1o1	O1	1
O1o2	O1	2
O2o1	O2	1
O2o2	O2	2
O4o1	O4	1
O4o2	O4	2

Occupation Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
O1o1	-0.14(3)	-0.31(4)
O1o2	-0.14(3)	-0.31(4)
O2o1	0	0.33(7)
O2o2	0	0.32(7)
O4o1	0.14(3)	0.31(4)
O4o2	0.14(3)	0.31(4)

Incommensurate modulation and thermal expansion of Sr3B2+xSi1-xO8-x/2 solid solutions

Volkov, Sergey; Bubnova, Rimma; Bolotina, Nadezhda; Krzhizhanovskaya, Maria; Belousova, Olga; Filatov, Stanislav

Acta Crystallographica, Section B 71 489-497 (2015)

https://doi.org/10.1107/S2052520615011713

Download CIF

Open in JSmol

I

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

II

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

III

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Incommensurate modulation and thermal expansion of Sr₃B_2+xSi_1-xO_8-x/2 solid solutions