B-IncStrDB

Incommensurately modulated structures of the M_1/8Pr_5/8MoO₄ (M = Li, Na, K) scheelites

Authors:

Morozov, Vladimir A.; Deyneko, Dina V.; Filatova, Darya G.; Belik, Alexei A.; Basovich, Olga M.; Khaikina, Elena G.; Lazoryak, Bogdan I.

Journal:

Acta Crystallographica Section B 82 120-130 (2026)

DOI:

https://doi.org/10.1107/S2052520626000375

B-IncStrDB ID: L8zZeSPwZg1 Entry date: 2026-02-04 Last revision: 2026-05-19

Download CIF

Open in JSmol

NaPr5Mo8O32

Chemical data

Common Name: Na0.125 Pr0.625 Mo1 O4 [ Help ]

Formula moiety: Na0.125 Pr0.625 Mo O4 [ Help ]

Structural Formula: Na0.125 Pr0.625 Mo1 O4 [ Help ]

Formula analytical: Na0.125 Pr0.625 Mo1 O4 [ Help ]

Formula (IUPAC): Na0.125 Pr0.625 Mo1 O4 [ Help ]

Structural Formula Sum: Na0.125 Pr0.625 Mo O4 [ Help ]

Formula weight: 250.9 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: I2/b(αβ0)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+1/2,x3,-x4
3	-x1,-x2,-x3,-x4
4	x1,x2+1/2,-x3,x4
5	x1+1/2,x2+1/2,x3+1/2,x4
6	-x1+1/2,-x2,x3+1/2,-x4
7	-x1+1/2,-x2+1/2,-x3+1/2,-x4
8	x1+1/2,x2,-x3+1/2,x4

a: 5.30752(3) Å [ Help ]

b: 5.30900(3) Å [ Help ]

c: 11.75478(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90.0084(9) ° [ Help ]

Volume: 331.222(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	0.578340	0.837694	0.000000

Z: 4 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 12.573 mm^-1 [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

R(obs): 0.0340 [ Help ]

wR(obs): 0.0248 [ Help ]

R(all): 0.0619 [ Help ]

wR(all): 0.0276 [ Help ]

S(all): 0.98 [ Help ]

Nb. of parameters: 60 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.01875 [ Help ]

Δ/σ(mean): 0.1446 [ Help ]

Δρ(max): 2.35 e_Å^-3 [ Help ]

Δρ(min): -4.99 e_Å^-3 [ 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
Pr	Pr	0.5	0.25	0.8734(5)	Uiso	0.0053(3)	4	0.625	d	.	.	.
Na	Na	0.5	0.25	0.8734(5)	Uiso	0.0053(3)	4	0.125	d	.	.	.
Mo	Mo	0.5	0.25	0.3758(4)	Uiso	0.0114(3)	4	1	d	.	.	.
O1	O	0.754(3)	0.396(3)	0.4568(12)	Uiso	0.020(4)	8	1	d	.	.	.
O2	O	0.858(3)	0.486(2)	0.2087(12)	Uiso	0.010(3)	8	1	d	.	.	.

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

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

Atom site label	Occupancy
Pr	0.625
Na	0.125

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

Modulation code	Atom site label	Wave vector code
Pro1	Pr	1
Nao1	Na	1

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

Modulation code	Cosine coefficient	Sine coefficient
Pro1	0.345(2)	0
Nao1	-0.0689(4)	0

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Prx1	Pr	x	1
Pry1	Pr	y	1
Prz1	Pr	z	1
Nax1	Na	x	1
Nay1	Na	y	1
Naz1	Na	z	1
Mox1	Mo	x	1
Moy1	Mo	y	1
Moz1	Mo	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

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

Modulation code	Cosine coefficient	Sine coefficient
Prx1	0	0.0130(4)
Pry1	0	0.0081(4)
Prz1	0.0017(5)	0
Nax1	0	0.0130(4)
Nay1	0	0.0081(4)
Naz1	0.0017(5)	0
Mox1	0	-0.0070(4)
Moy1	0	-0.0105(4)
Moz1	0.0016(4)	0
O1x1	0	-0.013(2)
O1y1	0	0
O1z1	0.0077(8)	0.0070(9)
O2x1	0	-0.0129(18)
O2y1	0.018(2)	-0.0176(19)
O2z1	-0.0088(8)	0

KPr5MoO32

Chemical data

Common Name: K0.145 Pr0.618 Mo1 O4 [ Help ]

Formula moiety: K0.145 Mo1 O4 Pr0.618 [ Help ]

Structural Formula: K0.145 Pr0.618 Mo1 O4 [ Help ]

Formula analytical: K0.145 Pr0.618 Mo1 O4 [ Help ]

Formula (IUPAC): K0.145 Pr0.618 Mo1 O4 [ Help ]

Structural Formula Sum: K0.145 Mo1 O4 Pr0.618 [ Help ]

Formula weight: 252.7 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: I2/b(αβ0)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+1/2,x3,-x4
3	-x1,-x2,-x3,-x4
4	x1,x2+1/2,-x3,x4
5	x1+1/2,x2+1/2,x3+1/2,x4
6	-x1+1/2,-x2,x3+1/2,-x4
7	-x1+1/2,-x2+1/2,-x3+1/2,-x4
8	x1+1/2,x2,-x3+1/2,x4

a: 5.318570(10) Å [ Help ]

b: 5.339590(10) Å [ Help ]

c: 11.87729(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90.0509(2) ° [ Help ]

Volume: 337.3028(12) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.566419	0.836554	0.000000

Z: 4 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 12.367 mm^-1 [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

R(obs): 0.0400 [ Help ]

wR(obs): 0.0237 [ Help ]

R(all): 0.0476 [ Help ]

wR(all): 0.0241 [ Help ]

S(all): 1.41 [ Help ]

Nb. of parameters: 69 [ Help ]

Number of restraints: 4 [ Help ]

Number of constraints: 4 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.01823 [ Help ]

Δ/σ(mean): 0.0167 [ Help ]

Δρ(max): 2.62 e_Å^-3 [ Help ]

Δρ(min): -3.01 e_Å^-3 [ 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
Pr1	Pr	0.5	0.25	0.8708(3)	Uiso	0.0060(2)	4	0.3541(3)	d	.	.	.
K	K	0.5	0.25	0.8708(3)	Uiso	0.0060(2)	8	0.0724(5)	d	.	.	.
Mo	Mo	0.5	0.25	0.37519(17)	Uiso	0.0159(3)	4	1	d	.	.	.
O1	O	0.7459(7)	0.3911(7)	0.4560(4)	Uiso	0.0159(14)	8	1	d	.	.	.
O2	O	0.3593(7)	0.4901(7)	0.2929(4)	Uiso	0.0109(12)	8	1	d	.	.	.
Pr2	Pr	0.5	0.25	0.8708(3)	Uiso	0.0060(2)	8	0.1321	d	.	.	.

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

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

Atom site label	Center (x0)	Width
Pr1	0.5	0.3541(3)
K	0.28675(8)	0.0724(5)
Pr2	0.1845(3)	0.1322

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Pr1x1	Pr1	x	1
Pr1y1	Pr1	y	1
Pr1z1	Pr1	z	1
Pr1x2	Pr1	x	2
Pr1y2	Pr1	y	2
Pr1z2	Pr1	z	2
Kx1	K	x	1
Ky1	K	y	1
Kz1	K	z	1
Kx2	K	x	2
Ky2	K	y	2
Kz2	K	z	2
Mox1	Mo	x	1
Moy1	Mo	y	1
Moz1	Mo	z	1
Mox2	Mo	x	2
Moy2	Mo	y	2
Moz2	Mo	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
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O2x2	O2	x	2
O2y2	O2	y	2
O2z2	O2	z	2
Pr2x1	Pr2	x	1
Pr2y1	Pr2	y	1
Pr2z1	Pr2	z	1
Pr2x2	Pr2	x	2
Pr2y2	Pr2	y	2
Pr2z2	Pr2	z	2

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

Modulation code	Cosine coefficient	Sine coefficient
Pr1x1	0	-0.0134(2)
Pr1y1	0	-0.0069(2)
Pr1z1	-0.0101(4)	0
Pr1x2	0	-0.0005(5)
Pr1y2	0	0.0034(5)
Pr1z2	-0.0098(4)	0
Kx1	0	-0.0134(2)
Ky1	0	-0.0069(2)
Kz1	-0.0101(4)	0
Kx2	0	-0.0005(5)
Ky2	0	0.0034(5)
Kz2	-0.0098(4)	0
Mox1	0	0.0085(3)
Moy1	0	0.0164(2)
Moz1	-0.00415(16)	0
Mox2	0	-0.0011(6)
Moy2	0	-0.0032(6)
Moz2	-0.0014(3)	0
O1x1	-0.0059(12)	0
O1y1	0.0104(11)	0
O1z1	-0.0126(5)	-0.0088
O1x2	0.009(2)	-0.009(2)
O1y2	-0.007(3)	0.012(2)
O1z2	-0.0023(10)	0.0036(9)
O2x1	0.0084(12)	0.0129(12)
O2y1	-0.0289(12)	0.0264(12)
O2z1	-0.0128(5)	-0.0018(5)
O2x2	-0.009(2)	0.006(2)
O2y2	0.003(2)	0.012(2)
O2z2	0.0025(9)	0.0044(9)
Pr2x1	0	-0.0134(2)
Pr2y1	0	-0.0069(2)
Pr2z1	-0.0101(4)	0
Pr2x2	0	-0.0005(5)
Pr2y2	0	0.0034(5)
Pr2z2	-0.0098(4)	0

Li-scheelite

Chemical data

Common Name: Li0.125 Pr0.625 Mo1 O4 [ Help ]

Formula moiety: Li0.125 Mo1 O4 Pr0.625 [ Help ]

Structural Formula: Li0.125 Pr0.625 Mo1 O4 [ Help ]

Formula analytical: Li0.125 Pr0.625 Mo1 O4 [ Help ]

Formula (IUPAC): Li0.125 Pr0.625 Mo1 O4 [ Help ]

Structural Formula Sum: Li0.125 Pr0.625 Mo1 O4 [ Help ]

Formula weight: 246.5 Da [ Help ]

Absolute configuration: . [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: I2/b(αβ0)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+1/2,x3,-x4
3	-x1,-x2,-x3,-x4
4	x1,x2+1/2,-x3,x4
5	x1+1/2,x2+1/2,x3+1/2,x4
6	-x1+1/2,-x2,x3+1/2,-x4
7	-x1+1/2,-x2+1/2,-x3+1/2,-x4
8	x1+1/2,x2,-x3+1/2,x4

a: 5.302630(10) Å [ Help ]

b: 5.297920(10) Å [ Help ]

c: 11.75179(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90.0184(4) ° [ Help ]

Volume: 330.1420(10) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.568641	0.835383	0.000000

Z: 4 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 12.497 mm^-1 [ Help ]

Absorption correction remarks: (Jana2000; Petricek, Dusek & Palatinus, 2000) [ Help ]

Refinement details

R(obs): 0.0391 [ Help ]

wR(obs): 0.0232 [ Help ]

R(all): 0.0589 [ Help ]

wR(all): 0.0241 [ Help ]

S(all): 1.35 [ Help ]

Nb. of parameters: 52 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0232 [ Help ]

Δ/σ(mean): 0.1435 [ Help ]

Δρ(max): 2.77 e_Å^-3 [ Help ]

Δρ(min): -4.70 e_Å^-3 [ 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
Pr	Pr	0.5	0.25	0.8737(3)	Uiso	0.0069(2)	4	0.625	d	.	.	.
Li	Li	0.5	0.25	0.8737(3)	Uiso	0.0069(2)	4	0.125	d	.	.	.
Mo	Mo	0.5	0.25	0.3745(3)	Uiso	0.0145(2)	4	1	d	.	.	.
O1	O	0.7473(12)	0.3894(10)	0.4587(6)	Uiso	0.0188(15)	8	1	d	.	.	.
O2	O	0.8498(9)	0.4892(11)	0.2068(6)	Uiso	0.0158(15)	8	1	d	.	.	.

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

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

Atom site label	Occupancy
Pr	0.625
Li	0.125

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

Modulation code	Atom site label	Wave vector code
Pro1	Pr	1
Lio1	Li	1

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

Modulation code	Cosine coefficient	Sine coefficient
Pro1	-0.3523(12)	0
Lio1	0.0705(2)	0

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Prx1	Pr	x	1
Pry1	Pr	y	1
Prz1	Pr	z	1
Lix1	Li	x	1
Liy1	Li	y	1
Liz1	Li	z	1
Mox1	Mo	x	1
Moy1	Mo	y	1
Moz1	Mo	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

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

Modulation code	Cosine coefficient	Sine coefficient
Prx1	0	-0.0133(3)
Pry1	0	-0.0094(3)
Prz1	-0.0028(3)	0
Lix1	0	-0.0133(3)
Liy1	0	-0.0094(3)
Liz1	-0.0028(3)	0
Mox1	0	0.0086(3)
Moy1	0	0.0110(2)
Moz1	-0.00224(19)	0
O1x1	-0.0049(15)	0.0056(14)
O1y1	0.0037(12)	0.0040(13)
O1z1	-0.0085(5)	-0.0070(5)
O2x1	0	0.0110(12)
O2y1	-0.0211(14)	0.0151(13)
O2z1	0.0081(5)	0.0028(6)

Incommensurately modulated structures of the M1/8Pr5/8MoO4 (M = Li, Na, K) scheelites

Morozov, Vladimir A.; Deyneko, Dina V.; Filatova, Darya G.; Belik, Alexei A.; Basovich, Olga M.; Khaikina, Elena G.; Lazoryak, Bogdan I.

Acta Crystallographica Section B 82 120-130 (2026)

https://doi.org/10.1107/S2052520626000375

Download CIF

Open in JSmol

NaPr5Mo8O32

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

KPr5MoO32

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Li-scheelite

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Incommensurately modulated structures of the M_1/8Pr_5/8MoO₄ (M = Li, Na, K) scheelites