B-IncStrDB

Compositely modulated structures of phosphor materials Sr_xLi_2+xAl_2-xO₄:Eu²⁺

Authors:

Ooishi, Atsushi; Michiue, Yuichi; Funahashi, Shiro; Takeda, Takashi; Hirosaki, Naoto

Journal:

Acta Crystallographica Section B 76 76-84 (2020)

DOI:

https://doi.org/10.1107/S2052520619016391

B-IncStrDB ID: 16142EOMIY2 Entry date: 2019-12-16 Last revision: 2021-12-30

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I_3d

Chemical data

Structural Formula Sum: Sr0.8333 Al1.1667 Li2.8333 O4 [ Help ]

Formula weight: 188.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): P 4/n [ Help ]

Space group name (Hall): -P 4a [ Help ]

Space group nb.: 85 [ 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
3	-y+1/2,x+1/2,z
4	y+1/2,-x+1/2,z
5	-x+1/2,-y+1/2,-z
6	x+1/2,y+1/2,-z
7	y,-x,-z
8	-y,x,-z

a: 7.8733(4) Å [ Help ]

b: 7.8733(4) Å [ Help ]

c: 19.0635(19) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1181.72(15) Å³ [ Help ]

Z: 12 [ Help ]

Cell determination reflection Nb.: 28522 [ Help ]

θ(min) for cell determination: 1.07 ° [ Help ]

θ(max) for cell determination: 35.72 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 11.58 mm^-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS [ Help ]

Minimum transmission factor: 0.8139 [ Help ]

Maximum transmission factor: 0.8625 [ Help ]

Refinement details

Total nb. of reflections: 2758 [ Help ]

Nb. of observed reflections: 898 [ Help ]

Intense reflections threshold: I>2σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(obs): 0.0382 [ Help ]

wR(obs): 0.0420 [ Help ]

R(all): 0.1346 [ Help ]

wR(all): 0.0484 [ Help ]

S(all): 1.84 [ Help ]

S(obs): 2.96 [ Help ]

Nb. of reflections: 2758 [ Help ]

Nb. of parameters: 138 [ Help ]

Number of constraints: 62 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.000004I²) [ Help ]

Δ/σ(max): 0.0080 [ Help ]

Δ/σ(mean): 0.0020 [ Help ]

Δρ(max): 2.97 e_Å^-3 [ Help ]

Δρ(min): -3.08 e_Å^-3 [ Help ]

Extinction method: none [ 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
Sr1	Sr	0	0.5	-0.02698(12)	Uani	0.0259(5)	2	1	d	?	?	?
Sr2b	Sr	0	0.5	0.15286(19)	Uani	0.0275(8)	2	0.653(7)	d	?	?	?
Sr2a	Sr	0	0.5	0.2567(2)	Uani	0.0193(10)	2	0.299(9)	d	?	?	?
Sr3b	Sr	0	0.5	0.3059(13)	Uani	0.076(9)	2	0.176(12)	d	?	?	?
Sr3a	Sr	0	0.5	0.43643(14)	Uani	0.0261(6)	2	0.872(4)	d	?	?	?
Sr4	Sr	0	0.5	0.61806(11)	Uani	0.0176(4)	2	1	d	?	?	?
Sr5	Sr	0	0.5	0.79350(12)	Uani	0.0136(2)	2	1	d	?	?	?
Al1	Al	0.1916(3)	1.1506(4)	0.2921(3)	Uani	0.0142(8)	8	0.523(6)	d	?	?	?
Al2	Al	0.3068(5)	1.3504(5)	-0.1236(2)	Uani	0.0036(11)	8	0.387(8)	d	?	?	?
Al3	Al	0.6918(6)	0.6450(6)	0.5394(3)	Uani	0.0084(13)	8	0.328(7)	d	?	?	?
Al4	Al	0.3222(8)	1.3622(8)	0.0443(3)	Uani	0.0287(19)	8	0.276(7)	d	?	?	?
Al5	Al	-0.1398(10)	1.1828(8)	0.3738(4)	Uani	0.0150(18)	8	0.144(8)	d	?	?	?
Al6	Al	-0.1340(9)	1.1615(10)	0.2076(8)	Uani	0.042(2)	8	0.092(16)	d	?	?	?
Li1	Li	0.1916(3)	1.1506(4)	0.2921(3)	Uani	0.0142(8)	8	0.477(6)	d	?	?	?
Li2	Li	0.3068(5)	1.3504(5)	-0.1236(2)	Uani	0.0036(11)	8	0.613(8)	d	?	?	?
Li3	Li	0.6918(6)	0.6450(6)	0.5394(3)	Uani	0.0084(13)	8	0.672(7)	d	?	?	?
Li4	Li	0.3222(8)	1.3622(8)	0.0443(3)	Uani	0.0287(19)	8	0.724(7)	d	?	?	?
Li5	Li	-0.1398(10)	1.1828(8)	0.3738(4)	Uani	0.0150(18)	8	0.856(8)	d	?	?	?
Li6	Li	-0.1340(9)	1.1615(10)	0.2076(8)	Uani	0.042(2)	8	0.908(16)	d	?	?	?
O1	O	0.0992(5)	1.2237(5)	0.2086(5)	Uani	0.0167(11)	8	1	d	?	?	?
O2	O	0.0975(7)	1.2306(8)	0.3744(4)	Uani	0.0218(19)	8	1	d	?	?	?
O3	O	0.4062(7)	1.2606(8)	-0.0443(4)	Uani	0.026(2)	8	1	d	?	?	?
O4	O	0.4144(7)	1.2526(8)	0.1221(4)	Uani	0.0193(18)	8	1	d	?	?	?
O5	O	0.4172(5)	1.2504(5)	0.2928(5)	Uani	0.0198(12)	8	1	d	?	?	?
O6	O	0.5897(7)	0.7426(8)	0.4617(4)	Uani	0.0223(18)	8	1	d	?	?	?

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

Atom site label	Atom site symbol	U11	U22	U33	U12	U13	U23
Sr1	Sr	0.0183(5)	0.0183(5)	0.0412(12)	0	0	0
Sr2b	Sr	0.0193(11)	0.0193(11)	0.044(2)	0	0	0
Sr2a	Sr	0.0207(15)	0.0207(15)	0.017(2)	0	0	0
Sr3b	Sr	0.031(2)	0.031(2)	0.17(3)	0	0	0
Sr3a	Sr	0.0178(7)	0.0178(7)	0.0427(14)	0	0	0
Sr4	Sr	0.0151(5)	0.0151(5)	0.0228(9)	0	0	0
Sr5	Sr	0.0145(3)	0.0145(3)	0.0117(4)	0	0	0
Al1	Al	0.0166(14)	0.0168(14)	0.0093(12)	0.0056(10)	0.001(2)	0.000(2)
Al2	Al	0.0032(19)	0.0048(19)	0.003(2)	-0.0026(15)	0.0001(17)	-0.0020(17)
Al3	Al	0.007(2)	0.009(2)	0.009(2)	-0.0002(17)	-0.0036(19)	-0.001(2)
Al4	Al	0.053(4)	0.021(3)	0.012(3)	0.018(3)	0.002(2)	0.000(2)
Al5	Al	0.014(3)	0.010(2)	0.021(4)	0.0011(19)	0.001(3)	-0.008(2)
Al6	Al	0.021(3)	0.088(5)	0.018(3)	-0.022(3)	-0.008(6)	0.006(7)
Li1	Li	0.0166(14)	0.0168(14)	0.0093(12)	0.0056(10)	0.001(2)	0.000(2)
Li2	Li	0.0032(19)	0.0048(19)	0.003(2)	-0.0026(15)	0.0001(17)	-0.0020(17)
Li3	Li	0.007(2)	0.009(2)	0.009(2)	-0.0002(17)	-0.0036(19)	-0.001(2)
Li4	Li	0.053(4)	0.021(3)	0.012(3)	0.018(3)	0.002(2)	0.000(2)
Li5	Li	0.014(3)	0.010(2)	0.021(4)	0.0011(19)	0.001(3)	-0.008(2)
Li6	Li	0.021(3)	0.088(5)	0.018(3)	-0.022(3)	-0.008(6)	0.006(7)
O1	O	0.0101(18)	0.0192(19)	0.0209(19)	0.0020(14)	-0.002(3)	0.001(3)
O2	O	0.012(3)	0.032(4)	0.022(3)	0.001(3)	0.002(3)	-0.008(3)
O3	O	0.015(3)	0.039(4)	0.024(3)	0.002(3)	-0.004(3)	0.012(4)
O4	O	0.018(3)	0.032(4)	0.008(3)	0.011(3)	0.000(3)	-0.002(3)
O5	O	0.021(2)	0.026(2)	0.0122(18)	0.0075(17)	0.000(4)	0.002(4)
O6	O	0.016(3)	0.036(4)	0.015(3)	0.007(3)	-0.003(3)	0.008(3)

I_4d

Chemical data

Structural Formula Sum: Sr0.833 Al1.167 Li2.833 O4 [ Help ]

Formula weight: 188.1 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Superspace group name: I4/m(00γ)00 [ 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
3	-x2,x1,x3,x4
4	x2,-x1,x3,x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4
7	x2,-x1,-x3,-x4
8	-x2,x1,-x3,-x4
9	x1+1/2,x2+1/2,x3+1/2,x4
10	-x1+1/2,-x2+1/2,x3+1/2,x4
11	-x2+1/2,x1+1/2,x3+1/2,x4
12	x2+1/2,-x1+1/2,x3+1/2,x4
13	-x1+1/2,-x2+1/2,-x3+1/2,-x4
14	x1+1/2,x2+1/2,-x3+1/2,-x4
15	x2+1/2,-x1+1/2,-x3+1/2,-x4
16	-x2+1/2,x1+1/2,-x3+1/2,-x4

a: 7.8957(3) Å [ Help ]

b: 7.8957(3) Å [ Help ]

c: 3.1830(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 198.43(2) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.833333

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2nd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	0.0	1.0
0.0	0.0	1.0	0.0

Z: 2 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 11.489 mm^-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS [ Help ]

Minimum transmission factor: 0.7929 [ Help ]

Maximum transmission factor: 0.8625 [ Help ]

Refinement details

Total nb. of reflections: 1641 [ Help ]

Nb. of observed reflections: 866 [ Help ]

Intense reflections threshold: I>2σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(obs): 0.0314 [ Help ]

wR(obs): 0.0386 [ Help ]

R(all): 0.0746 [ Help ]

wR(all): 0.0408 [ Help ]

S(all): 1.98 [ Help ]

S(obs): 2.63 [ Help ]

Nb. of reflections: 1641 [ Help ]

Nb. of parameters: 69 [ Help ]

Number of constraints: 28 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.000004I²) [ Help ]

Δ/σ(max): 0.0048 [ Help ]

Δ/σ(mean): 0.0008 [ Help ]

Δρ(max): 1.47 e_Å^-3 [ Help ]

Δρ(min): -1.22 e_Å^-3 [ Help ]

Extinction method: none [ 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	Subsystem
Al1	Al	0.14298(9)	0.31593(12)	0.5	Uani	0.0185(2)	8	0.2917	d	?	?	?	1
Li1	Li	0.14298(9)	0.31593(12)	0.5	Uani	0.0185(2)	8	0.7083	d	?	?	?	1
O1	O	0.26113(8)	0.09144(7)	0.5	Uani	0.02143(18)	8	1	d	?	?	?	1
Sr1	Sr	0	0	0	Uani	0.0629(18)	2	0.6	d	?	?	?	2
Sr2	Sr	0	0	0.433(6)	Uani	0.085(3)	4	0.2	d	?	?	?	2

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

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0151(4)	0.0285(5)	0.0120(4)	-0.0061(3)
Li1	Li	0.0151(4)	0.0285(5)	0.0120(4)	-0.0061(3)
O1	O	0.0310(3)	0.0154(3)	0.0178(3)	-0.0050(2)
Sr1	Sr	0.044(3)	0.044(3)	0.101(2)	0
Sr2	Sr	0.036(4)	0.036(4)	0.182(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

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Al1	1
Li1	1

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

Modulation code	Atom site label	Wave vector code
Al1o1	Al1	1
Li1o1	Li1	1
Sr2o1	Sr2	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1o1	-0.678(7)	0
Li1o1	0.279(3)	0
Sr2o1	-0.107(3)	0.924(7)

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

Atom site label	Center (x0)	Width
Sr1	0	0.6
Sr2	0.020(7)	0.4

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al1x2	Al1	x	2
Al1y2	Al1	y	2
Al1z2	Al1	z	2
Li1x1	Li1	x	1
Li1y1	Li1	y	1
Li1z1	Li1	z	1
Li1x2	Li1	x	2
Li1y2	Li1	y	2
Li1z2	Li1	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
Sr1x1	Sr1	x	1
Sr1y1	Sr1	y	1
Sr1z1	Sr1	z	1
Sr1x2	Sr1	x	2
Sr1y2	Sr1	y	2
Sr1z2	Sr1	z	2
Sr2x1	Sr2	x	1
Sr2y1	Sr2	y	1
Sr2z1	Sr2	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1x1	-0.00838(19)	0
Al1y1	0.0120(2)	0
Al1z1	0	0.0135(4)
Al1x2	0.0006(2)	0
Al1y2	0.0039(3)	0
Al1z2	0	0.0000(5)
Li1x1	-0.00838(19)	0
Li1y1	0.0120(2)	0
Li1z1	0	0.0135(4)
Li1x2	0.0006(2)	0
Li1y2	0.0039(3)	0
Li1z2	0	0.0000(5)
O1x1	0.01268(13)	0
O1y1	0.00857(13)	0
O1z1	0	0.0166(4)
O1x2	0.0027(2)	0
O1y2	-0.0005(2)	0
O1z2	0	-0.0072(4)
Sr1x1	0	0
Sr1y1	0	0
Sr1z1	0	-0.1070(9)
Sr1x2	0	0
Sr1y2	0	0
Sr1z2	0	-0.0105(11)
Sr2x1	0	0
Sr2y1	0	0
Sr2z1	-0.162(6)	-0.163(3)

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

Modulation code	Atom site label	Tensor element	Wave vector code
Al1U111	Al1	U11	1
Al1U221	Al1	U22	1
Al1U331	Al1	U33	1
Al1U121	Al1	U12	1
Al1U131	Al1	U13	1
Al1U231	Al1	U23	1
Al1U112	Al1	U11	2
Al1U222	Al1	U22	2
Al1U332	Al1	U33	2
Al1U122	Al1	U12	2
Al1U132	Al1	U13	2
Al1U232	Al1	U23	2
Li1U111	Li1	U11	1
Li1U221	Li1	U22	1
Li1U331	Li1	U33	1
Li1U121	Li1	U12	1
Li1U131	Li1	U13	1
Li1U231	Li1	U23	1
Li1U112	Li1	U11	2
Li1U222	Li1	U22	2
Li1U332	Li1	U33	2
Li1U122	Li1	U12	2
Li1U132	Li1	U13	2
Li1U232	Li1	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
O1U112	O1	U11	2
O1U222	O1	U22	2
O1U332	O1	U33	2
O1U122	O1	U12	2
O1U132	O1	U13	2
O1U232	O1	U23	2
Sr1U111	Sr1	U11	1
Sr1U221	Sr1	U22	1
Sr1U331	Sr1	U33	1
Sr1U121	Sr1	U12	1
Sr1U131	Sr1	U13	1
Sr1U231	Sr1	U23	1
Sr1U112	Sr1	U11	2
Sr1U222	Sr1	U22	2
Sr1U332	Sr1	U33	2
Sr1U122	Sr1	U12	2
Sr1U132	Sr1	U13	2
Sr1U232	Sr1	U23	2
Sr2U111	Sr2	U11	1
Sr2U221	Sr2	U22	1
Sr2U331	Sr2	U33	1
Sr2U121	Sr2	U12	1
Sr2U131	Sr2	U13	1
Sr2U231	Sr2	U23	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1U111	0.0058(7)	0
Al1U221	0.0275(10)	0
Al1U331	0.0061(7)	0
Al1U121	-0.0073(6)	0
Al1U131	0	0.0007(4)
Al1U231	0	-0.0034(5)
Al1U112	0.0026(9)	0
Al1U222	0.0116(10)	0
Al1U332	0.0011(7)	0
Al1U122	-0.0033(8)	0
Al1U132	0	-0.0004(6)
Al1U232	0	-0.0015(6)
Li1U111	0.0058(7)	0
Li1U221	0.0275(10)	0
Li1U331	0.0061(7)	0
Li1U121	-0.0073(6)	0
Li1U131	0	0.0007(4)
Li1U231	0	-0.0034(5)
Li1U112	0.0026(9)	0
Li1U222	0.0116(10)	0
Li1U332	0.0011(7)	0
Li1U122	-0.0033(8)	0
Li1U132	0	-0.0004(6)
Li1U232	0	-0.0015(6)
O1U111	-0.0029(5)	0
O1U221	-0.0047(4)	0
O1U331	0.0075(5)	0
O1U121	0.0049(4)	0
O1U131	0	-0.0072(5)
O1U231	0	-0.0026(4)
O1U112	-0.0089(10)	0
O1U222	0.0004(9)	0
O1U332	-0.0019(6)	0
O1U122	-0.0003(7)	0
O1U132	0	-0.0043(6)
O1U232	0	-0.0017(6)
Sr1U111	-0.046(5)	0
Sr1U221	-0.046(5)	0
Sr1U331	-0.135(4)	0
Sr1U121	0	0
Sr1U131	0	0
Sr1U231	0	0
Sr1U112	0.020(3)	0
Sr1U222	0.020(3)	0
Sr1U332	0.062(2)	0
Sr1U122	0	0
Sr1U132	0	0
Sr1U232	0	0
Sr2U111	-0.014(4)	-0.014(2)
Sr2U221	-0.014(4)	-0.014(2)
Sr2U331	-0.143(8)	-0.079(6)
Sr2U121	0	0
Sr2U131	0	0
Sr2U231	0	0

II

Chemical data

Structural Formula Sum: Sr0.824 Al1.176 Li2.824 O4 [ Help ]

Formula weight: 187.5 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Superspace group name: I4/m(00γ)00 [ 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
3	-x2,x1,x3,x4
4	x2,-x1,x3,x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4
7	x2,-x1,-x3,-x4
8	-x2,x1,-x3,-x4
9	x1+1/2,x2+1/2,x3+1/2,x4
10	-x1+1/2,-x2+1/2,x3+1/2,x4
11	-x2+1/2,x1+1/2,x3+1/2,x4
12	x2+1/2,-x1+1/2,x3+1/2,x4
13	-x1+1/2,-x2+1/2,-x3+1/2,-x4
14	x1+1/2,x2+1/2,-x3+1/2,-x4
15	x2+1/2,-x1+1/2,-x3+1/2,-x4
16	-x2+1/2,x1+1/2,-x3+1/2,-x4

a: 7.8785(2) Å [ Help ]

b: 7.8785(2) Å [ Help ]

c: 3.1736(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 196.988(14) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.824370

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2nd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	0.0	1.0
0.0	0.0	1.0	0.0

Z: 2 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 11.455 mm^-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS [ Help ]

Minimum transmission factor: 0.7992 [ Help ]

Maximum transmission factor: 0.8625 [ Help ]

Refinement details

Total nb. of reflections: 1489 [ Help ]

Nb. of observed reflections: 852 [ Help ]

Intense reflections threshold: I>2σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(obs): 0.0405 [ Help ]

wR(obs): 0.0487 [ Help ]

R(all): 0.0852 [ Help ]

wR(all): 0.0504 [ Help ]

S(all): 2.37 [ Help ]

S(obs): 3.09 [ Help ]

Nb. of reflections: 1489 [ Help ]

Nb. of parameters: 63 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.000004I²) [ Help ]

Δ/σ(max): 0.0491 [ Help ]

Δ/σ(mean): 0.0019 [ Help ]

Δρ(max): 3.01 e_Å^-3 [ Help ]

Δρ(min): -2.69 e_Å^-3 [ Help ]

Extinction method: none [ 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	Subsystem
Al1	Al	0.14277(14)	0.31657(18)	0.5	Uani	0.0201(4)	8	0.2939	d	?	?	?	1
Li1	Li	0.14277(14)	0.31657(18)	0.5	Uani	0.0201(4)	8	0.7061	d	?	?	?	1
O1	O	0.26153(11)	0.09127(9)	0.5	Uani	0.0199(2)	8	1	d	?	?	?	1
Sr1	Sr	0	0	0	Uani	0.0221(10)	2	0.668(7)	d	?	?	?	2
Sr2	Sr	0	0	0.4838(11)	Uani	0.0206(4)	4	0.166(3)	d	?	?	?	2

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

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0160(6)	0.0313(9)	0.0130(6)	-0.0070(6)
Li1	Li	0.0160(6)	0.0313(9)	0.0130(6)	-0.0070(6)
O1	O	0.0295(5)	0.0140(4)	0.0162(4)	-0.0044(3)
Sr1	Sr	0.0167(5)	0.0167(5)	0.033(3)	0
Sr2	Sr	0.0202(5)	0.0202(5)	0.0216(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

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Al1	1
Li1	1

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

Modulation code	Atom site label	Wave vector code
Al1o1	Al1	1
Li1o1	Li1	1
Sr2o1	Sr2	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1o1	-0.693(12)	0
Li1o1	0.288(5)	0
Sr2o1	-0.475(2)	0.761(3)

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

Atom site label	Center (x0)	Width
Sr1	0	0.668(7)
Sr2	0.0869(13)	0.332(7)

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al1x2	Al1	x	2
Al1y2	Al1	y	2
Al1z2	Al1	z	2
Li1x1	Li1	x	1
Li1y1	Li1	y	1
Li1z1	Li1	z	1
Li1x2	Li1	x	2
Li1y2	Li1	y	2
Li1z2	Li1	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
Sr1x1	Sr1	x	1
Sr1y1	Sr1	y	1
Sr1z1	Sr1	z	1
Sr1x2	Sr1	x	2
Sr1y2	Sr1	y	2
Sr1z2	Sr1	z	2
Sr2x1	Sr2	x	1
Sr2y1	Sr2	y	1
Sr2z1	Sr2	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1x1	-0.0085(3)	0
Al1y1	0.0135(4)	0
Al1z1	0	0.0149(7)
Al1x2	0.0007(4)	0
Al1y2	0.0043(4)	0
Al1z2	0	0.0004(10)
Li1x1	-0.0085(3)	0
Li1y1	0.0135(4)	0
Li1z1	0	0.0149(7)
Li1x2	0.0007(4)	0
Li1y2	0.0043(4)	0
Li1z2	0	0.0004(10)
O1x1	0.01314(19)	0
O1y1	0.00862(19)	0
O1z1	0	0.0173(5)
O1x2	0.0027(3)	0
O1y2	-0.0004(3)	0
O1z2	0	-0.0075(8)
Sr1x1	0	0
Sr1y1	0	0
Sr1z1	0	-0.124(3)
Sr1x2	0	0
Sr1y2	0	0
Sr1z2	0	0.010(4)
Sr2x1	0	0
Sr2y1	0	0
Sr2z1	-0.143	-0.2409(12)

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

Modulation code	Atom site label	Tensor element	Wave vector code
Al1U111	Al1	U11	1
Al1U221	Al1	U22	1
Al1U331	Al1	U33	1
Al1U121	Al1	U12	1
Al1U131	Al1	U13	1
Al1U231	Al1	U23	1
Al1U112	Al1	U11	2
Al1U222	Al1	U22	2
Al1U332	Al1	U33	2
Al1U122	Al1	U12	2
Al1U132	Al1	U13	2
Al1U232	Al1	U23	2
Li1U111	Li1	U11	1
Li1U221	Li1	U22	1
Li1U331	Li1	U33	1
Li1U121	Li1	U12	1
Li1U131	Li1	U13	1
Li1U231	Li1	U23	1
Li1U112	Li1	U11	2
Li1U222	Li1	U22	2
Li1U332	Li1	U33	2
Li1U122	Li1	U12	2
Li1U132	Li1	U13	2
Li1U232	Li1	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
O1U112	O1	U11	2
O1U222	O1	U22	2
O1U332	O1	U33	2
O1U122	O1	U12	2
O1U132	O1	U13	2
O1U232	O1	U23	2
Sr1U111	Sr1	U11	1
Sr1U221	Sr1	U22	1
Sr1U331	Sr1	U33	1
Sr1U121	Sr1	U12	1
Sr1U131	Sr1	U13	1
Sr1U231	Sr1	U23	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1U111	0.0087(12)	0
Al1U221	0.0326(17)	0
Al1U331	0.0062(13)	0
Al1U121	-0.0092(10)	0
Al1U131	0	0.0021(7)
Al1U231	0	-0.0032(8)
Al1U112	0.0053(15)	0
Al1U222	0.0153(17)	0
Al1U332	0.0015(14)	0
Al1U122	-0.0050(13)	0
Al1U132	0	-0.0002(10)
Al1U232	0	-0.0021(10)
Li1U111	0.0087(12)	0
Li1U221	0.0326(17)	0
Li1U331	0.0062(13)	0
Li1U121	-0.0092(10)	0
Li1U131	0	0.0021(7)
Li1U231	0	-0.0032(8)
Li1U112	0.0053(15)	0
Li1U222	0.0153(17)	0
Li1U332	0.0015(14)	0
Li1U122	-0.0050(13)	0
Li1U132	0	-0.0002(10)
Li1U232	0	-0.0021(10)
O1U111	-0.0032(8)	0
O1U221	-0.0043(7)	0
O1U331	0.0069(7)	0
O1U121	0.0038(6)	0
O1U131	0	-0.0075(7)
O1U231	0	-0.0028(6)
O1U112	-0.0087(15)	0
O1U222	0.0000(13)	0
O1U332	-0.0018(11)	0
O1U122	-0.0013(12)	0
O1U132	0	-0.0038(10)
O1U232	0	-0.0022(9)
Sr1U111	-0.0017(8)	0
Sr1U221	-0.0017(8)	0
Sr1U331	-0.020(4)	0
Sr1U121	0	0
Sr1U131	0	0
Sr1U231	0	0

III

Chemical data

Structural Formula Sum: Sr0.827 Al1.173 Li2.827 O4 [ Help ]

Formula weight: 187.7 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Superspace group name: I4/m(00γ)00 [ 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
3	-x2,x1,x3,x4
4	x2,-x1,x3,x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4
7	x2,-x1,-x3,-x4
8	-x2,x1,-x3,-x4
9	x1+1/2,x2+1/2,x3+1/2,x4
10	-x1+1/2,-x2+1/2,x3+1/2,x4
11	-x2+1/2,x1+1/2,x3+1/2,x4
12	x2+1/2,-x1+1/2,x3+1/2,x4
13	-x1+1/2,-x2+1/2,-x3+1/2,-x4
14	x1+1/2,x2+1/2,-x3+1/2,-x4
15	x2+1/2,-x1+1/2,-x3+1/2,-x4
16	-x2+1/2,x1+1/2,-x3+1/2,-x4

a: 7.8908(6) Å [ Help ]

b: 7.8908(6) Å [ Help ]

c: 3.1767(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 197.80(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	0.000000	0.000000	0.827300

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2nd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	0.0	1.0
0.0	0.0	1.0	0.0

Z: 2 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 11.448 mm^-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: SADABS [ Help ]

Minimum transmission factor: 0.7699 [ Help ]

Maximum transmission factor: 0.8625 [ Help ]

Refinement details

Total nb. of reflections: 1410 [ Help ]

Nb. of observed reflections: 836 [ Help ]

Intense reflections threshold: I>2σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(obs): 0.0375 [ Help ]

wR(obs): 0.0406 [ Help ]

R(all): 0.0825 [ Help ]

wR(all): 0.0424 [ Help ]

S(all): 2.18 [ Help ]

S(obs): 2.76 [ Help ]

Nb. of reflections: 1410 [ Help ]

Nb. of parameters: 63 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.000004I²) [ Help ]

Δ/σ(max): 0.0496 [ Help ]

Δ/σ(mean): 0.0014 [ Help ]

Δρ(max): 2.51 e_Å^-3 [ Help ]

Δρ(min): -2.24 e_Å^-3 [ Help ]

Extinction method: none [ 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	Subsystem
Al1	Al	0.14221(13)	0.31750(16)	0.5	Uani	0.0239(4)	8	0.2932	d	?	?	?	1
Li1	Li	0.14221(13)	0.31750(16)	0.5	Uani	0.0239(4)	8	0.7068	d	?	?	?	1
O1	O	0.26203(10)	0.09135(8)	0.5	Uani	0.0232(2)	8	1	d	?	?	?	1
Sr1	Sr	0	0	0	Uani	0.0237(11)	2	0.617(9)	d	?	?	?	2
Sr2	Sr	0	0	0.4476(6)	Uani	0.0235(3)	4	0.192(4)	d	?	?	?	2

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

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0197(5)	0.0374(8)	0.0144(6)	-0.0080(5)
Li1	Li	0.0197(5)	0.0374(8)	0.0144(6)	-0.0080(5)
O1	O	0.0339(4)	0.0176(3)	0.0180(4)	-0.0056(3)
Sr1	Sr	0.0182(5)	0.0182(5)	0.035(3)	0
Sr2	Sr	0.0234(4)	0.0234(4)	0.0235(7)	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

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Al1	1
Li1	1

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

Modulation code	Atom site label	Wave vector code
Al1o1	Al1	1
Li1o1	Li1	1
Sr2o1	Sr2	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1o1	-0.718(11)	0
Li1o1	0.298(4)	0
Sr2o1	-0.2309(18)	1.083(4)

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

Atom site label	Center (x0)	Width
Sr1	0	0.617(9)
Sr2	0.0410(7)	0.383(9)

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al1x2	Al1	x	2
Al1y2	Al1	y	2
Al1z2	Al1	z	2
Li1x1	Li1	x	1
Li1y1	Li1	y	1
Li1z1	Li1	z	1
Li1x2	Li1	x	2
Li1y2	Li1	y	2
Li1z2	Li1	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
Sr1x1	Sr1	x	1
Sr1y1	Sr1	y	1
Sr1z1	Sr1	z	1
Sr1x2	Sr1	x	2
Sr1y2	Sr1	y	2
Sr1z2	Sr1	z	2
Sr2x1	Sr2	x	1
Sr2y1	Sr2	y	1
Sr2z1	Sr2	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1x1	-0.0096(3)	0
Al1y1	0.0150(3)	0
Al1z1	0	0.0147(5)
Al1x2	0.0002(3)	0
Al1y2	0.0049(3)	0
Al1z2	0	-0.0007(7)
Li1x1	-0.0096(3)	0
Li1y1	0.0150(3)	0
Li1z1	0	0.0147(5)
Li1x2	0.0002(3)	0
Li1y2	0.0049(3)	0
Li1z2	0	-0.0007(7)
O1x1	0.01426(16)	0
O1y1	0.00925(16)	0
O1z1	0	0.0176(4)
O1x2	0.0032(2)	0
O1y2	-0.0002(3)	0
O1z2	0	-0.0097(6)
Sr1x1	0	0
Sr1y1	0	0
Sr1z1	0	-0.117(4)
Sr1x2	0	0
Sr1y2	0	0
Sr1z2	0	0.005(5)
Sr2x1	0	0
Sr2y1	0	0
Sr2z1	-0.1601	-0.2093(9)

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

Modulation code	Atom site label	Tensor element	Wave vector code
Al1U111	Al1	U11	1
Al1U221	Al1	U22	1
Al1U331	Al1	U33	1
Al1U121	Al1	U12	1
Al1U131	Al1	U13	1
Al1U231	Al1	U23	1
Al1U112	Al1	U11	2
Al1U222	Al1	U22	2
Al1U332	Al1	U33	2
Al1U122	Al1	U12	2
Al1U132	Al1	U13	2
Al1U232	Al1	U23	2
Li1U111	Li1	U11	1
Li1U221	Li1	U22	1
Li1U331	Li1	U33	1
Li1U121	Li1	U12	1
Li1U131	Li1	U13	1
Li1U231	Li1	U23	1
Li1U112	Li1	U11	2
Li1U222	Li1	U22	2
Li1U332	Li1	U33	2
Li1U122	Li1	U12	2
Li1U132	Li1	U13	2
Li1U232	Li1	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
O1U112	O1	U11	2
O1U222	O1	U22	2
O1U332	O1	U33	2
O1U122	O1	U12	2
O1U132	O1	U13	2
O1U232	O1	U23	2
Sr1U111	Sr1	U11	1
Sr1U221	Sr1	U22	1
Sr1U331	Sr1	U33	1
Sr1U121	Sr1	U12	1
Sr1U131	Sr1	U13	1
Sr1U231	Sr1	U23	1

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

Modulation code	Cosine coefficient	Sine coefficient
Al1U111	0.0096(11)	0
Al1U221	0.0387(15)	0
Al1U331	0.0080(11)	0
Al1U121	-0.0108(9)	0
Al1U131	0	0.0021(6)
Al1U231	0	-0.0043(7)
Al1U112	0.0052(13)	0
Al1U222	0.0185(14)	0
Al1U332	0.0015(10)	0
Al1U122	-0.0046(10)	0
Al1U132	0	0.0000(8)
Al1U232	0	-0.0021(9)
Li1U111	0.0096(11)	0
Li1U221	0.0387(15)	0
Li1U331	0.0080(11)	0
Li1U121	-0.0108(9)	0
Li1U131	0	0.0021(6)
Li1U231	0	-0.0043(7)
Li1U112	0.0052(13)	0
Li1U222	0.0185(14)	0
Li1U332	0.0015(10)	0
Li1U122	-0.0046(10)	0
Li1U132	0	0.0000(8)
Li1U232	0	-0.0021(9)
O1U111	-0.0024(6)	0
O1U221	-0.0050(6)	0
O1U331	0.0088(6)	0
O1U121	0.0046(5)	0
O1U131	0	-0.0089(6)
O1U231	0	-0.0022(6)
O1U112	-0.0104(12)	0
O1U222	-0.0003(11)	0
O1U332	-0.0010(9)	0
O1U122	-0.0015(9)	0
O1U132	0	-0.0043(8)
O1U232	0	-0.0013(8)
Sr1U111	-0.0032(8)	0
Sr1U221	-0.0032(8)	0
Sr1U331	-0.027(4)	0
Sr1U121	0	0
Sr1U131	0	0
Sr1U231	0	0

Compositely modulated structures of phosphor materials SrxLi2+xAl2-xO4:Eu2+

Ooishi, Atsushi; Michiue, Yuichi; Funahashi, Shiro; Takeda, Takashi; Hirosaki, Naoto

Acta Crystallographica Section B 76 76-84 (2020)

https://doi.org/10.1107/S2052520619016391

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I_3d

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I_4d

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II

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III

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Compositely modulated structures of phosphor materials Sr_xLi_2+xAl_2-xO₄:Eu²⁺