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Neodymium iron bor­ate NdFe3(BO3)4 is an intensively studied multiferroic with high electric polarization values controlled by a magnetic field. It is char­ac­ter­ized by a large quadratic magnetoelectric effect, rigidity in the base plane and a rather strong piezoelectric effect. In this work, the atomic structure of (Nd0.91Bi0.09)Fe3(BO3)4 was studied by single-crystal X-ray diffraction in the tem­per­ature range 20–500 K (space group R32, Z = 3). The Bi atoms found in the com­position partially substitute the Nd atoms in the 3a position; they entered the structure due to the growth conditions in the presence of Bi2Mo3O12. It was shown that in the tem­per­ature range 20–500 K there is no structural phase transition R32→P3121, which occurs in rare-earth iron bor­ates (RE = Eu–Er, Y) with an effective rare-earth cation radius smaller than that of Nd. The tem­per­ature dependence of the unit-cell c parameter reveals a slight increase on cooling below 90 K, which is similar to the results obtained previously for iron bor­ates of Gd, Y and Ho. The atomic distances (Nd,Bi)—O, (Nd,Bi)—B, (Nd,Bi)—Fe, Fe—O, Fe—B and Fe—Fe in the iron chains and between chains decrease steadily with decreasing tem­per­ature from 500 to 90 K, whereas the B1(3b)—O distance does not change and the average B2(9e)—O distance increases slightly. There is a uniform decrease in the atomic displacement parameters with decreasing tem­per­ature, with a more pronounced decrease for the Nd(3a) and O2(9e) atoms. The O2(9e) atoms are characterized by the maximum atomic displacement parameters and the most elongated atomic displacement ellipsoids. The characteristic Debye and Einstein tem­per­atures, and the static com­ponent in the atomic displacements were determined for cations using multi-tem­per­ature diffraction data. It was shown that the Nd cations have the weakest bonds with the surrounding atoms and the B cations have the strongest.

Supporting information

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Crystallographic Information File (CIF) https://doi.org/10.1107/S205252062101180X/xk5089sup1.cif
Contains datablocks global, 90K, 200K, 293K, 400K, 500K

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Structure factor file (CIF format) https://doi.org/10.1107/S205252062101180X/xk508990Ksup2.hkl
Contains datablock I

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Structure factor file (CIF format) https://doi.org/10.1107/S205252062101180X/xk5089200Ksup3.hkl
Contains datablock I

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Structure factor file (CIF format) https://doi.org/10.1107/S205252062101180X/xk5089293Ksup4.hkl
Contains datablock I

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Structure factor file (CIF format) https://doi.org/10.1107/S205252062101180X/xk5089400Ksup5.hkl
Contains datablock I

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Structure factor file (CIF format) https://doi.org/10.1107/S205252062101180X/xk5089500Ksup6.hkl
Contains datablock I

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Portable Document Format (PDF) file https://doi.org/10.1107/S205252062101180X/xk5089sup7.pdf
Supplementary material

CCDC references: 2120875; 2120876; 2120877; 2120878; 2120879

Computing details top

For all structures, data collection: CrysAlis PRO (Rigaku OD, 2019); cell refinement: CrysAlis PRO (Rigaku OD, 2019); data reduction: CrysAlis PRO (Rigaku OD, 2019); software used to prepare material for publication: JANA2006 (Petříček et al., 2014).

Neodymium/bismuth triiron tetrakis(borate) (90K) top
Crystal data top
(Nd0.91Bi0.09)Fe3(BO3)4Dx = 4.563 Mg m3
Mr = 552.8Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32Cell parameters from 18531 reflections
Hall symbol: R 3 2"θ = 4.2–74.1°
a = 9.5814 (1) ŵ = 13.12 mm1
c = 7.5908 (1) ÅT = 90 K
V = 603.50 (1) Å3Sphere, light green
Z = 30.07 (1) mm (radius)
F(000) = 768
Data collection top
Rigaku OD Xcalibur
diffractometer with an EosS2 (high theta cut) detector
2707 independent reflections
Radiation source: X-ray tube2706 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.030
Detector resolution: 16.1745 pixels mm-1θmax = 74.4°, θmin = 3.6°
ω scansh = 2525
Absorption correction: for a sphere
(JANA2006; Petříček et al., 2014)
k = 2425
Tmin = 0.252, Tmax = 0.333l = 1917
20875 measured reflections
Refinement top
Refinement on F2Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.000256I2)
R[F2 > 2σ(F2)] = 0.012(Δ/σ)max = 0.047
wR(F2) = 0.029Δρmax = 0.84 e Å3
S = 1.02Δρmin = 1.47 e Å3
2707 reflectionsExtinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974)
36 parametersExtinction coefficient: 1230 (30)
0 restraintsAbsolute structure: 1224 of Friedel pairs used in the refinement
2 constraintsAbsolute structure parameter: 0.478 (4)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Nd10000.003628 (10)0.91
Bi10000.003628 (10)0.09
Fe10.217477 (12)0.3333330.3333330.00302 (2)
O10.14420 (6)0.14420 (6)0.50.00430 (9)
O20.40981 (7)0.40981 (7)0.50.00574 (11)
O30.02648 (5)0.21492 (6)0.18474 (7)0.00499 (8)
B1000.50.00390 (19)
B20.55382 (9)0.55382 (9)0.50.00434 (16)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Nd10.003673 (11)0.003673 (11)0.00354 (2)0.001837 (6)00
Bi10.003673 (11)0.003673 (11)0.00354 (2)0.001837 (6)00
Fe10.00293 (2)0.00297 (2)0.00316 (4)0.001487 (12)0.000028 (8)0.000056 (17)
O10.00351 (9)0.00351 (9)0.00498 (19)0.00107 (10)0.00039 (6)0.00039 (6)
O20.00411 (10)0.00411 (10)0.0071 (2)0.00065 (12)0.00146 (7)0.00146 (7)
O30.00398 (9)0.00583 (10)0.00542 (14)0.00266 (8)0.00068 (8)0.00076 (9)
B10.00378 (19)0.00378 (19)0.0041 (4)0.00189 (9)00
B20.00376 (15)0.00376 (15)0.0052 (2)0.0017 (2)0.00018 (11)0.00018 (11)
Geometric parameters (Å, º) top
Nd1—Bi10Bi1—O3iv2.3977 (5)
Nd1—O32.3977 (6)Bi1—O3v2.3977 (7)
Nd1—O3i2.3977 (5)Fe1—O12.0261 (4)
Nd1—O3ii2.3977 (7)Fe1—O1vi2.0261 (4)
Nd1—O3iii2.3977 (6)Fe1—O22.0453 (5)
Nd1—O3iv2.3977 (5)Fe1—O2vi2.0453 (8)
Nd1—O3v2.3977 (7)Fe1—O31.9576 (5)
Bi1—O32.3977 (6)Fe1—O3vii1.9576 (7)
Bi1—O3i2.3977 (5)O1—B11.3816 (4)
Bi1—O3ii2.3977 (7)O2—B21.3798 (8)
Bi1—O3iii2.3977 (6)O3—B2viii1.3693 (12)
Bi1—Nd1—O30O3ii—Bi1—O3v142.237 (14)
Bi1—Nd1—O3i0O3iii—Bi1—O3iv89.249 (19)
Bi1—Nd1—O3ii0O3iii—Bi1—O3v89.249 (19)
Bi1—Nd1—O3iii0O3iv—Bi1—O3v89.249 (19)
Bi1—Nd1—O3iv0O1—Fe1—O1vi168.44 (3)
Bi1—Nd1—O3v0O1—Fe1—O277.374 (18)
O3—Nd1—O3i89.249 (19)O1—Fe1—O2vi94.20 (2)
O3—Nd1—O3ii89.249 (19)O1—Fe1—O392.060 (18)
O3—Nd1—O3iii122.325 (14)O1—Fe1—O3vii95.39 (2)
O3—Nd1—O3iv142.24 (2)O1vi—Fe1—O294.20 (2)
O3—Nd1—O3v72.60 (2)O1vi—Fe1—O2vi77.37 (3)
O3i—Nd1—O3ii89.249 (19)O1vi—Fe1—O395.39 (2)
O3i—Nd1—O3iii142.24 (2)O1vi—Fe1—O3vii92.06 (2)
O3i—Nd1—O3iv72.598 (18)O2—Fe1—O2vi87.58 (3)
O3i—Nd1—O3v122.33 (2)O2—Fe1—O3167.90 (3)
O3ii—Nd1—O3iii72.60 (2)O2—Fe1—O3vii87.33 (3)
O3ii—Nd1—O3iv122.33 (2)O2vi—Fe1—O387.33 (3)
O3ii—Nd1—O3v142.237 (14)O2vi—Fe1—O3vii167.90 (2)
O3iii—Nd1—O3iv89.249 (19)O3—Fe1—O3vii99.66 (3)
O3iii—Nd1—O3v89.249 (19)Fe1—O1—Fe1ix103.300 (19)
O3iv—Nd1—O3v89.249 (19)Fe1—O1—B1128.35 (3)
Nd1—Bi1—O30Fe1ix—O1—B1128.35 (3)
Nd1—Bi1—O3i0Fe1—O2—Fe1ix101.95 (2)
Nd1—Bi1—O3ii0Fe1—O2—B2129.02 (4)
Nd1—Bi1—O3iii0Fe1ix—O2—B2129.02 (4)
Nd1—Bi1—O3iv0Nd1—O3—Bi10.0 (5)
Nd1—Bi1—O3v0Nd1—O3—Fe1120.10 (3)
O3—Bi1—O3i89.249 (19)Nd1—O3—B2viii106.76 (3)
O3—Bi1—O3ii89.249 (19)Bi1—O3—Fe1120.10 (3)
O3—Bi1—O3iii122.325 (14)Bi1—O3—B2viii106.76 (3)
O3—Bi1—O3iv142.24 (2)Fe1—O3—B2viii133.02 (4)
O3—Bi1—O3v72.60 (2)O1—B1—O1i120.00 (4)
O3i—Bi1—O3ii89.249 (19)O1—B1—O1ii120.00 (4)
O3i—Bi1—O3iii142.24 (2)O1i—B1—O1ii120.00 (4)
O3i—Bi1—O3iv72.598 (18)O2—B2—O3x117.90 (8)
O3i—Bi1—O3v122.33 (2)O2—B2—O3xi117.90 (8)
O3ii—Bi1—O3iii72.60 (2)O3x—B2—O3xi124.20 (5)
O3ii—Bi1—O3iv122.33 (2)
Symmetry codes: (i) y, xy, z; (ii) x+y, x, z; (iii) y, x, z; (iv) xy, y, z; (v) x, x+y, z; (vi) x+y+1/3, x+2/3, z1/3; (vii) xy+1/3, y+2/3, z+2/3; (viii) x2/3, y1/3, z1/3; (ix) y+2/3, xy+1/3, z+1/3; (x) x+2/3, y+1/3, z+1/3; (xi) y+1/3, x+2/3, z+2/3.
Neodymium/bismuth triiron tetrakis(borate) (200K) top
Crystal data top
(Nd0.91Bi0.09)Fe3(BO3)4Dx = 4.561 Mg m3
Mr = 552.8Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32Cell parameters from 17088 reflections
Hall symbol: R 3 2"θ = 4.2–73.9°
a = 9.5805 (1) ŵ = 13.11 mm1
c = 7.5970 (1) ÅT = 200 K
V = 603.88 (1) Å3Sphere, light green
Z = 30.07 (1) mm (radius)
F(000) = 768
Data collection top
Rigaku OD Xcalibur
diffractometer with an EosS2 (high theta cut) detector
2714 independent reflections
Radiation source: X-ray tube2712 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.031
Detector resolution: 16.1745 pixels mm-1θmax = 74.4°, θmin = 3.6°
ω scansh = 2525
Absorption correction: for a sphere
(JANA2006; Petříček et al., 2014)
k = 2425
Tmin = 0.256, Tmax = 0.336l = 1917
20885 measured reflections
Refinement top
Refinement on F2Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0004I2)
R[F2 > 2σ(F2)] = 0.013(Δ/σ)max = 0.049
wR(F2) = 0.034Δρmax = 0.78 e Å3
S = 1.02Δρmin = 1.33 e Å3
2714 reflectionsExtinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974)
36 parametersExtinction coefficient: 1320 (40)
0 restraintsAbsolute structure: 1227 of Friedel pairs used in the refinement
2 constraintsAbsolute structure parameter: 0.479 (5)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Nd10000.005895 (12)0.91
Bi10000.005895 (12)0.09
Fe10.217486 (13)0.3333330.3333330.00416 (2)
O10.14417 (6)0.14417 (6)0.50.00553 (10)
O20.41001 (8)0.41001 (8)0.50.00826 (12)
O30.02652 (6)0.21503 (6)0.18481 (8)0.00669 (9)
B1000.50.00471 (19)
B20.55384 (9)0.55384 (9)0.50.00523 (16)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Nd10.005985 (13)0.005985 (13)0.00571 (3)0.002992 (7)00
Bi10.005985 (13)0.005985 (13)0.00571 (3)0.002992 (7)00
Fe10.00396 (2)0.00409 (2)0.00447 (4)0.002047 (12)0.000053 (8)0.000107 (17)
O10.00426 (9)0.00426 (9)0.0068 (2)0.00118 (10)0.00076 (6)0.00076 (6)
O20.00543 (10)0.00543 (10)0.0109 (3)0.00044 (13)0.00262 (9)0.00262 (9)
O30.00512 (10)0.00808 (12)0.00731 (15)0.00362 (9)0.00119 (8)0.00145 (10)
B10.00436 (19)0.00436 (19)0.0054 (4)0.00218 (10)00
B20.00470 (15)0.00470 (15)0.0061 (2)0.0022 (2)0.00021 (11)0.00021 (11)
Geometric parameters (Å, º) top
Nd1—Bi10Bi1—O3iv2.3992 (5)
Nd1—O32.3992 (6)Bi1—O3v2.3992 (8)
Nd1—O3i2.3992 (5)Fe1—O12.0268 (4)
Nd1—O3ii2.3992 (8)Fe1—O1vi2.0268 (4)
Nd1—O3iii2.3992 (6)Fe1—O22.0469 (5)
Nd1—O3iv2.3992 (5)Fe1—O2vi2.0469 (9)
Nd1—O3v2.3992 (8)Fe1—O31.9574 (5)
Bi1—O32.3992 (6)Fe1—O3vii1.9574 (8)
Bi1—O3i2.3992 (5)O1—B11.3812 (4)
Bi1—O3ii2.3992 (8)O2—B21.3780 (8)
Bi1—O3iii2.3992 (6)O3—B2viii1.3690 (12)
Bi1—Nd1—O30O3ii—Bi1—O3v142.260 (15)
Bi1—Nd1—O3i0O3iii—Bi1—O3iv89.22 (2)
Bi1—Nd1—O3ii0O3iii—Bi1—O3v89.22 (2)
Bi1—Nd1—O3iii0O3iv—Bi1—O3v89.22 (2)
Bi1—Nd1—O3iv0O1—Fe1—O1vi168.46 (3)
Bi1—Nd1—O3v0O1—Fe1—O277.391 (19)
O3—Nd1—O3i89.22 (2)O1—Fe1—O2vi94.20 (2)
O3—Nd1—O3ii89.22 (2)O1—Fe1—O392.10 (2)
O3—Nd1—O3iii122.332 (15)O1—Fe1—O3vii95.34 (2)
O3—Nd1—O3iv142.26 (2)O1vi—Fe1—O294.20 (2)
O3—Nd1—O3v72.64 (2)O1vi—Fe1—O2vi77.39 (3)
O3i—Nd1—O3ii89.22 (2)O1vi—Fe1—O395.34 (2)
O3i—Nd1—O3iii142.26 (2)O1vi—Fe1—O3vii92.10 (3)
O3i—Nd1—O3iv72.64 (2)O2—Fe1—O2vi87.62 (3)
O3i—Nd1—O3v122.33 (2)O2—Fe1—O3167.96 (3)
O3ii—Nd1—O3iii72.64 (2)O2—Fe1—O3vii87.32 (3)
O3ii—Nd1—O3iv122.33 (2)O2vi—Fe1—O387.32 (3)
O3ii—Nd1—O3v142.260 (15)O2vi—Fe1—O3vii167.96 (2)
O3iii—Nd1—O3iv89.22 (2)O3—Fe1—O3vii99.64 (3)
O3iii—Nd1—O3v89.22 (2)Fe1—O1—Fe1ix103.316 (19)
O3iv—Nd1—O3v89.22 (2)Fe1—O1—B1128.34 (3)
Nd1—Bi1—O30Fe1ix—O1—B1128.34 (3)
Nd1—Bi1—O3i0Fe1—O2—Fe1ix101.90 (2)
Nd1—Bi1—O3ii0Fe1—O2—B2129.05 (4)
Nd1—Bi1—O3iii0Fe1ix—O2—B2129.05 (4)
Nd1—Bi1—O3iv0Nd1—O3—Bi10.0 (5)
Nd1—Bi1—O3v0Nd1—O3—Fe1120.10 (3)
O3—Bi1—O3i89.22 (2)Nd1—O3—B2viii106.70 (4)
O3—Bi1—O3ii89.22 (2)Bi1—O3—Fe1120.10 (3)
O3—Bi1—O3iii122.332 (15)Bi1—O3—B2viii106.70 (4)
O3—Bi1—O3iv142.26 (2)Fe1—O3—B2viii133.07 (5)
O3—Bi1—O3v72.64 (2)O1—B1—O1i120.00 (4)
O3i—Bi1—O3ii89.22 (2)O1—B1—O1ii120.00 (4)
O3i—Bi1—O3iii142.26 (2)O1i—B1—O1ii120.00 (4)
O3i—Bi1—O3iv72.64 (2)O2—B2—O3x117.93 (8)
O3i—Bi1—O3v122.33 (2)O2—B2—O3xi117.93 (8)
O3ii—Bi1—O3iii72.64 (2)O3x—B2—O3xi124.13 (6)
O3ii—Bi1—O3iv122.33 (2)
Symmetry codes: (i) y, xy, z; (ii) x+y, x, z; (iii) y, x, z; (iv) xy, y, z; (v) x, x+y, z; (vi) x+y+1/3, x+2/3, z1/3; (vii) xy+1/3, y+2/3, z+2/3; (viii) x2/3, y1/3, z1/3; (ix) y+2/3, xy+1/3, z+1/3; (x) x+2/3, y+1/3, z+1/3; (xi) y+1/3, x+2/3, z+2/3.
Neodymium/bismuth triiron tetrakis(borate) (293K) top
Crystal data top
(Nd0.91Bi0.09)Fe3(BO3)4Dx = 4.556 Mg m3
Mr = 552.8Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32Cell parameters from 15414 reflections
Hall symbol: R 3 2"θ = 4.2–74.1°
a = 9.5815 (1) ŵ = 13.10 mm1
c = 7.6028 (1) ÅT = 293 K
V = 604.47 (1) Å3Sphere, light green
Z = 30.07 (1) mm (radius)
F(000) = 768
Data collection top
Rigaku OD Xcalibur
diffractometer with an EosS2 (high theta cut) detector
2716 independent reflections
Radiation source: X-ray tube2699 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.033
Detector resolution: 16.1745 pixels mm-1θmax = 74.3°, θmin = 3.6°
ω scansh = 2525
Absorption correction: for a sphere
(JANA2006; Petříček et al., 2014)
k = 2425
Tmin = 0.255, Tmax = 0.335l = 1917
20900 measured reflections
Refinement top
Refinement on F2Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.000036I2)
R[F2 > 2σ(F2)] = 0.014(Δ/σ)max = 0.046
wR(F2) = 0.027Δρmax = 0.71 e Å3
S = 1.09Δρmin = 1.47 e Å3
2716 reflectionsExtinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974)
36 parametersExtinction coefficient: 1290 (20)
0 restraintsAbsolute structure: 1229 of Friedel pairs used in the refinement
2 constraintsAbsolute structure parameter: 0.474 (5)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Nd10000.007899 (16)0.91
Bi10000.007899 (16)0.09
Fe10.217434 (13)0.3333330.3333330.00530 (2)
O10.14411 (6)0.14411 (6)0.50.00679 (11)
O20.41011 (8)0.41011 (8)0.50.01057 (15)
O30.02649 (6)0.21516 (7)0.18501 (8)0.00836 (11)
B1000.50.0055 (2)
B20.55389 (9)0.55389 (9)0.50.00638 (19)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Nd10.008038 (17)0.008038 (17)0.00762 (3)0.004019 (8)00
Bi10.008038 (17)0.008038 (17)0.00762 (3)0.004019 (8)00
Fe10.00497 (2)0.00519 (3)0.00581 (5)0.002593 (15)0.000087 (12)0.00017 (2)
O10.00521 (10)0.00521 (10)0.0083 (2)0.00138 (12)0.00083 (7)0.00083 (7)
O20.00661 (12)0.00661 (12)0.0140 (3)0.00007 (15)0.00362 (11)0.00362 (11)
O30.00618 (12)0.01021 (14)0.00912 (19)0.00443 (11)0.00166 (11)0.00219 (12)
B10.0051 (2)0.0051 (2)0.0064 (5)0.00253 (10)00
B20.00543 (18)0.00543 (18)0.0077 (3)0.0023 (3)0.00027 (15)0.00027 (15)
Geometric parameters (Å, º) top
Nd1—Bi10Bi1—O3iv2.4020 (6)
Nd1—O32.4020 (7)Bi1—O3v2.4020 (8)
Nd1—O3i2.4020 (6)Fe1—O12.0279 (4)
Nd1—O3ii2.4020 (8)Fe1—O1vi2.0279 (4)
Nd1—O3iii2.4020 (7)Fe1—O22.0486 (5)
Nd1—O3iv2.4020 (6)Fe1—O2vi2.0486 (9)
Nd1—O3v2.4020 (8)Fe1—O31.9569 (5)
Bi1—O32.4020 (7)Fe1—O3vii1.9569 (8)
Bi1—O3i2.4020 (6)O1—B11.3808 (4)
Bi1—O3ii2.4020 (8)O2—B21.3776 (8)
Bi1—O3iii2.4020 (7)O3—B2viii1.3681 (12)
Bi1—Nd1—O30O3ii—Bi1—O3v142.255 (16)
Bi1—Nd1—O3i0O3iii—Bi1—O3iv89.18 (2)
Bi1—Nd1—O3ii0O3iii—Bi1—O3v89.18 (2)
Bi1—Nd1—O3iii0O3iv—Bi1—O3v89.18 (2)
Bi1—Nd1—O3iv0O1—Fe1—O1vi168.45 (3)
Bi1—Nd1—O3v0O1—Fe1—O277.392 (19)
O3—Nd1—O3i89.18 (2)O1—Fe1—O2vi94.19 (2)
O3—Nd1—O3ii89.18 (2)O1—Fe1—O392.12 (2)
O3—Nd1—O3iii122.373 (16)O1—Fe1—O3vii95.33 (2)
O3—Nd1—O3iv142.26 (3)O1vi—Fe1—O294.19 (2)
O3—Nd1—O3v72.70 (2)O1vi—Fe1—O2vi77.39 (3)
O3i—Nd1—O3ii89.18 (2)O1vi—Fe1—O395.33 (2)
O3i—Nd1—O3iii142.26 (3)O1vi—Fe1—O3vii92.12 (3)
O3i—Nd1—O3iv72.70 (2)O2—Fe1—O2vi87.63 (3)
O3i—Nd1—O3v122.37 (2)O2—Fe1—O3168.00 (3)
O3ii—Nd1—O3iii72.70 (2)O2—Fe1—O3vii87.34 (3)
O3ii—Nd1—O3iv122.37 (2)O2vi—Fe1—O387.34 (3)
O3ii—Nd1—O3v142.255 (16)O2vi—Fe1—O3vii168.00 (2)
O3iii—Nd1—O3iv89.18 (2)O3—Fe1—O3vii99.57 (3)
O3iii—Nd1—O3v89.18 (2)Fe1—O1—Fe1ix103.33 (2)
O3iv—Nd1—O3v89.18 (2)Fe1—O1—B1128.33 (3)
Nd1—Bi1—O30Fe1ix—O1—B1128.33 (3)
Nd1—Bi1—O3i0Fe1—O2—Fe1ix101.88 (2)
Nd1—Bi1—O3ii0Fe1—O2—B2129.06 (4)
Nd1—Bi1—O3iii0Fe1ix—O2—B2129.06 (4)
Nd1—Bi1—O3iv0Nd1—O3—Bi10.0 (5)
Nd1—Bi1—O3v0Nd1—O3—Fe1120.07 (3)
O3—Bi1—O3i89.18 (2)Nd1—O3—B2viii106.63 (4)
O3—Bi1—O3ii89.18 (2)Bi1—O3—Fe1120.07 (3)
O3—Bi1—O3iii122.373 (16)Bi1—O3—B2viii106.63 (4)
O3—Bi1—O3iv142.26 (3)Fe1—O3—B2viii133.18 (5)
O3—Bi1—O3v72.70 (2)O1—B1—O1i120.00 (4)
O3i—Bi1—O3ii89.18 (2)O1—B1—O1ii120.00 (4)
O3i—Bi1—O3iii142.26 (3)O1i—B1—O1ii120.00 (4)
O3i—Bi1—O3iv72.70 (2)O2—B2—O3x117.96 (8)
O3i—Bi1—O3v122.37 (2)O2—B2—O3xi117.96 (8)
O3ii—Bi1—O3iii72.70 (2)O3x—B2—O3xi124.09 (6)
O3ii—Bi1—O3iv122.37 (2)
Symmetry codes: (i) y, xy, z; (ii) x+y, x, z; (iii) y, x, z; (iv) xy, y, z; (v) x, x+y, z; (vi) x+y+1/3, x+2/3, z1/3; (vii) xy+1/3, y+2/3, z+2/3; (viii) x2/3, y1/3, z1/3; (ix) y+2/3, xy+1/3, z+1/3; (x) x+2/3, y+1/3, z+1/3; (xi) y+1/3, x+2/3, z+2/3.
Neodymium/bismuth triiron tetrakis(borate) (400K) top
Crystal data top
(Nd0.91Bi0.09)Fe3(BO3)4Dx = 4.550 Mg m3
Mr = 552.8Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32Cell parameters from 12909 reflections
Hall symbol: R 3 2"θ = 4.2–73.6°
a = 9.5822 (1) ŵ = 13.08 mm1
c = 7.6128 (1) ÅT = 400 K
V = 605.35 (1) Å3Sphere, light green
Z = 30.07 (1) mm (radius)
F(000) = 768
Data collection top
Rigaku OD Xcalibur
diffractometer with an EosS2 (high theta cut) detector
2727 independent reflections
Radiation source: X-ray tube2645 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.035
Detector resolution: 16.1745 pixels mm-1θmax = 74.2°, θmin = 3.6°
ω scansh = 2525
Absorption correction: for a sphere
(JANA2006; Petříček et al., 2014)
k = 2425
Tmin = 0.253, Tmax = 0.334l = 1917
20978 measured reflections
Refinement top
Refinement on F2Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.000036I2)
R[F2 > 2σ(F2)] = 0.015(Δ/σ)max = 0.049
wR(F2) = 0.028Δρmax = 0.53 e Å3
S = 1.02Δρmin = 1.39 e Å3
2727 reflectionsExtinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974)
36 parametersExtinction coefficient: 1300 (20)
0 restraintsAbsolute structure: 1234 of Friedel pairs used in the refinement
2 constraintsAbsolute structure parameter: 0.479 (5)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Nd10000.010271 (19)0.91
Bi10000.010271 (19)0.09
Fe10.217381 (14)0.3333330.3333330.00673 (3)
O10.14417 (7)0.14417 (7)0.50.00854 (13)
O20.41019 (8)0.41019 (8)0.50.01326 (17)
O30.02642 (6)0.21516 (7)0.18520 (9)0.01051 (13)
B1000.50.0065 (2)
B20.55393 (10)0.55393 (10)0.50.0076 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Nd10.01047 (2)0.01047 (2)0.00986 (4)0.005237 (10)00
Bi10.01047 (2)0.01047 (2)0.00986 (4)0.005237 (10)00
Fe10.00632 (2)0.00662 (3)0.00735 (5)0.003310 (16)0.000104 (13)0.00021 (3)
O10.00641 (11)0.00641 (11)0.0106 (3)0.00157 (13)0.00123 (8)0.00123 (8)
O20.00827 (14)0.00827 (14)0.0174 (4)0.00025 (17)0.00464 (13)0.00464 (13)
O30.00747 (13)0.01285 (17)0.0118 (2)0.00550 (13)0.00236 (12)0.00293 (14)
B10.0059 (2)0.0059 (2)0.0076 (5)0.00295 (11)00
B20.00653 (19)0.00653 (19)0.0089 (3)0.0026 (3)0.00038 (17)0.00038 (17)
Geometric parameters (Å, º) top
Nd1—Bi10Bi1—O3iv2.4042 (6)
Nd1—O32.4042 (7)Bi1—O3v2.4042 (9)
Nd1—O3i2.4042 (6)Fe1—O12.0288 (5)
Nd1—O3ii2.4042 (9)Fe1—O1vi2.0288 (4)
Nd1—O3iii2.4042 (7)Fe1—O22.0506 (6)
Nd1—O3iv2.4042 (6)Fe1—O2vi2.0506 (9)
Nd1—O3v2.4042 (9)Fe1—O31.9571 (6)
Bi1—O32.4042 (7)Fe1—O3vii1.9571 (9)
Bi1—O3i2.4042 (6)O1—B11.3815 (5)
Bi1—O3ii2.4042 (9)O2—B21.3773 (9)
Bi1—O3iii2.4042 (7)O3—B2viii1.3676 (13)
Bi1—Nd1—O30O3ii—Bi1—O3v142.256 (17)
Bi1—Nd1—O3i0O3iii—Bi1—O3iv89.09 (2)
Bi1—Nd1—O3ii0O3iii—Bi1—O3v89.09 (2)
Bi1—Nd1—O3iii0O3iv—Bi1—O3v89.09 (2)
Bi1—Nd1—O3iv0O1—Fe1—O1vi168.41 (4)
Bi1—Nd1—O3v0O1—Fe1—O277.34 (2)
O3—Nd1—O3i89.09 (2)O1—Fe1—O2vi94.22 (3)
O3—Nd1—O3ii89.09 (2)O1—Fe1—O392.17 (2)
O3—Nd1—O3iii122.445 (17)O1—Fe1—O3vii95.31 (3)
O3—Nd1—O3iv142.26 (3)O1vi—Fe1—O294.22 (2)
O3—Nd1—O3v72.81 (3)O1vi—Fe1—O2vi77.34 (3)
O3i—Nd1—O3ii89.09 (2)O1vi—Fe1—O395.31 (2)
O3i—Nd1—O3iii142.26 (3)O1vi—Fe1—O3vii92.17 (3)
O3i—Nd1—O3iv72.81 (2)O2—Fe1—O2vi87.66 (3)
O3i—Nd1—O3v122.45 (3)O2—Fe1—O3168.00 (3)
O3ii—Nd1—O3iii72.81 (3)O2—Fe1—O3vii87.33 (3)
O3ii—Nd1—O3iv122.45 (3)O2vi—Fe1—O387.33 (3)
O3ii—Nd1—O3v142.256 (17)O2vi—Fe1—O3vii168.00 (2)
O3iii—Nd1—O3iv89.09 (2)O3—Fe1—O3vii99.57 (3)
O3iii—Nd1—O3v89.09 (2)Fe1—O1—Fe1ix103.42 (2)
O3iv—Nd1—O3v89.09 (2)Fe1—O1—B1128.29 (3)
Nd1—Bi1—O30Fe1ix—O1—B1128.29 (3)
Nd1—Bi1—O3i0Fe1—O2—Fe1ix101.89 (2)
Nd1—Bi1—O3ii0Fe1—O2—B2129.05 (5)
Nd1—Bi1—O3iii0Fe1ix—O2—B2129.05 (5)
Nd1—Bi1—O3iv0Nd1—O3—Bi10.0 (5)
Nd1—Bi1—O3v0Nd1—O3—Fe1120.08 (4)
O3—Bi1—O3i89.09 (2)Nd1—O3—B2viii106.59 (4)
O3—Bi1—O3ii89.09 (2)Bi1—O3—Fe1120.08 (4)
O3—Bi1—O3iii122.445 (17)Bi1—O3—B2viii106.59 (4)
O3—Bi1—O3iv142.26 (3)Fe1—O3—B2viii133.22 (5)
O3—Bi1—O3v72.81 (3)O1—B1—O1i120.00 (5)
O3i—Bi1—O3ii89.09 (2)O1—B1—O1ii120.00 (5)
O3i—Bi1—O3iii142.26 (3)O1i—B1—O1ii120.00 (5)
O3i—Bi1—O3iv72.81 (2)O2—B2—O3x117.94 (9)
O3i—Bi1—O3v122.45 (3)O2—B2—O3xi117.94 (9)
O3ii—Bi1—O3iii72.81 (3)O3x—B2—O3xi124.13 (6)
O3ii—Bi1—O3iv122.45 (3)
Symmetry codes: (i) y, xy, z; (ii) x+y, x, z; (iii) y, x, z; (iv) xy, y, z; (v) x, x+y, z; (vi) x+y+1/3, x+2/3, z1/3; (vii) xy+1/3, y+2/3, z+2/3; (viii) x2/3, y1/3, z1/3; (ix) y+2/3, xy+1/3, z+1/3; (x) x+2/3, y+1/3, z+1/3; (xi) y+1/3, x+2/3, z+2/3.
Neodymium/bismuth triiron tetrakis(borate) (500K) top
Crystal data top
(Nd0.91Bi0.09)Fe3(BO3)4Dx = 4.544 Mg m3
Mr = 552.8Mo Kα radiation, λ = 0.71073 Å
Trigonal, R32Cell parameters from 8164 reflections
Hall symbol: R 3 2"θ = 4.2–74.0°
a = 9.5841 (2) ŵ = 13.06 mm1
c = 7.6194 (1) ÅT = 500 K
V = 606.11 (2) Å3Sphere, light green
Z = 30.07 (1) mm (radius)
F(000) = 768
Data collection top
Rigaku OD Xcalibur
diffractometer with an EosS2 (high theta cut) detector
2557 independent reflections
Radiation source: X-ray tube2092 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.040
Detector resolution: 16.1745 pixels mm-1θmax = 74.1°, θmin = 3.6°
ω scansh = 2524
Absorption correction: for a sphere
(JANA2006; Petříček et al., 2014)
k = 2525
Tmin = 0.291, Tmax = 0.365l = 1719
14607 measured reflections
Refinement top
Refinement on F2Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.000036I2)
R[F2 > 2σ(F2)] = 0.021(Δ/σ)max = 0.048
wR(F2) = 0.033Δρmax = 1.29 e Å3
S = 1.08Δρmin = 1.46 e Å3
2557 reflectionsExtinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974)
36 parametersExtinction coefficient: 1440 (30)
0 restraintsAbsolute structure: 1101 of Friedel pairs used in the refinement
2 constraintsAbsolute structure parameter: 0.477 (7)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Nd10000.01219 (3)0.91
Bi10000.01219 (3)0.09
Fe10.21730 (2)0.3333330.3333330.00786 (4)
O10.14399 (9)0.14399 (9)0.50.0098 (2)
O20.41041 (11)0.41041 (11)0.50.0153 (3)
O30.02643 (9)0.21507 (10)0.18507 (12)0.0123 (2)
B1000.50.0077 (4)
B20.55400 (13)0.55400 (13)0.50.0088 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Nd10.01240 (3)0.01240 (3)0.01176 (6)0.006201 (16)00
Bi10.01240 (3)0.01240 (3)0.01176 (6)0.006201 (16)00
Fe10.00735 (4)0.00773 (5)0.00863 (9)0.00387 (3)0.00012 (2)0.00023 (5)
O10.00730 (18)0.00730 (18)0.0122 (4)0.0017 (2)0.00149 (14)0.00149 (14)
O20.0098 (2)0.0098 (2)0.0197 (6)0.0001 (3)0.0052 (2)0.0052 (2)
O30.0083 (2)0.0151 (3)0.0141 (3)0.0063 (2)0.0028 (2)0.0036 (2)
B10.0067 (3)0.0067 (3)0.0098 (8)0.00333 (17)00
B20.0077 (3)0.0077 (3)0.0106 (5)0.0035 (5)0.0008 (3)0.0008 (3)
Geometric parameters (Å, º) top
Nd1—Bi10Bi1—O3iv2.4040 (8)
Nd1—O32.4040 (10)Bi1—O3v2.4040 (12)
Nd1—O3i2.4040 (8)Fe1—O12.0309 (7)
Nd1—O3ii2.4040 (12)Fe1—O1vi2.0309 (6)
Nd1—O3iii2.4040 (10)Fe1—O22.0534 (8)
Nd1—O3iv2.4040 (8)Fe1—O2vi2.0534 (13)
Nd1—O3v2.4040 (12)Fe1—O31.9580 (8)
Bi1—O32.4040 (10)Fe1—O3vii1.9580 (12)
Bi1—O3i2.4040 (8)O1—B11.3800 (6)
Bi1—O3ii2.4040 (12)O2—B21.3762 (12)
Bi1—O3iii2.4040 (10)O3—B2viii1.3680 (17)
Bi1—Nd1—O30O3ii—Bi1—O3v142.27 (2)
Bi1—Nd1—O3i0O3iii—Bi1—O3iv89.08 (3)
Bi1—Nd1—O3ii0O3iii—Bi1—O3v89.08 (3)
Bi1—Nd1—O3iii0O3iv—Bi1—O3v89.08 (3)
Bi1—Nd1—O3iv0O1—Fe1—O1vi168.43 (5)
Bi1—Nd1—O3v0O1—Fe1—O277.39 (3)
O3—Nd1—O3i89.08 (3)O1—Fe1—O2vi94.18 (4)
O3—Nd1—O3ii89.08 (3)O1—Fe1—O392.17 (3)
O3—Nd1—O3iii122.45 (2)O1—Fe1—O3vii95.29 (4)
O3—Nd1—O3iv142.27 (4)O1vi—Fe1—O294.18 (3)
O3—Nd1—O3v72.83 (3)O1vi—Fe1—O2vi77.39 (4)
O3i—Nd1—O3ii89.08 (3)O1vi—Fe1—O395.29 (3)
O3i—Nd1—O3iii142.27 (4)O1vi—Fe1—O3vii92.17 (4)
O3i—Nd1—O3iv72.83 (3)O2—Fe1—O2vi87.65 (4)
O3i—Nd1—O3v122.45 (4)O2—Fe1—O3168.01 (4)
O3ii—Nd1—O3iii72.83 (3)O2—Fe1—O3vii87.26 (4)
O3ii—Nd1—O3iv122.45 (4)O2vi—Fe1—O387.26 (4)
O3ii—Nd1—O3v142.27 (2)O2vi—Fe1—O3vii168.01 (3)
O3iii—Nd1—O3iv89.08 (3)O3—Fe1—O3vii99.70 (4)
O3iii—Nd1—O3v89.08 (3)Fe1—O1—Fe1ix103.40 (3)
O3iv—Nd1—O3v89.08 (3)Fe1—O1—B1128.30 (4)
Nd1—Bi1—O30Fe1ix—O1—B1128.30 (4)
Nd1—Bi1—O3i0Fe1—O2—Fe1ix101.82 (3)
Nd1—Bi1—O3ii0Fe1—O2—B2129.09 (6)
Nd1—Bi1—O3iii0Fe1ix—O2—B2129.09 (6)
Nd1—Bi1—O3iv0Nd1—O3—Bi10.0 (5)
Nd1—Bi1—O3v0Nd1—O3—Fe1120.15 (5)
O3—Bi1—O3i89.08 (3)Nd1—O3—B2viii106.65 (5)
O3—Bi1—O3ii89.08 (3)Bi1—O3—Fe1120.15 (5)
O3—Bi1—O3iii122.45 (2)Bi1—O3—B2viii106.65 (5)
O3—Bi1—O3iv142.27 (4)Fe1—O3—B2viii133.09 (7)
O3—Bi1—O3v72.83 (3)O1—B1—O1i120.00 (6)
O3i—Bi1—O3ii89.08 (3)O1—B1—O1ii120.00 (6)
O3i—Bi1—O3iii142.27 (4)O1i—B1—O1ii120.00 (6)
O3i—Bi1—O3iv72.83 (3)O2—B2—O3x117.88 (12)
O3i—Bi1—O3v122.45 (4)O2—B2—O3xi117.88 (12)
O3ii—Bi1—O3iii72.83 (3)O3x—B2—O3xi124.24 (8)
O3ii—Bi1—O3iv122.45 (4)
Symmetry codes: (i) y, xy, z; (ii) x+y, x, z; (iii) y, x, z; (iv) xy, y, z; (v) x, x+y, z; (vi) x+y+1/3, x+2/3, z1/3; (vii) xy+1/3, y+2/3, z+2/3; (viii) x2/3, y1/3, z1/3; (ix) y+2/3, xy+1/3, z+1/3; (x) x+2/3, y+1/3, z+1/3; (xi) y+1/3, x+2/3, z+2/3.
Main interatomic distances (Å) and Fe—O—Fe angles (°) in Nd0.91Bi0.09Fe3(BO3)4 structure top
T (K)90200293400500
Nd1(3a) coordination
Nd1—O3 ×62.3977 (6)2.3992 (6)2.4020 (7)2.4042 (7)2.4040 (10)
Nd1—B1 ×23.7954 (1)3.7985 (1)3.8014 (1)3.8064 (1)3.8097 (1)
Nd1—B2 ×63.0849 (6)3.0851 (10)3.0859 (6)3.0868 (11)3.0879 (7)
Nd1—Fe1 ×63.7801 (1)3.7813 (1)3.7828 (1)3.7851 (1)3.7869 (1)
Fe1(9d) coordination,
Fe1—O1 ×22.0261 (4)2.0268 (4)2.0279 (4)2.0288 (4)2.0309 (7)
Fe1—O2 ×22.0453 (5)2.0469 (9)2.0486 (9)2.0506 (9)2.0534 (8)
Fe1—O3 ×21.9576 (7)1.9574 (8)1.9569 (8)1.9571 (6)1.9580 (12)
(Fe—O)ave2.0102.0102.0112.0122.014
Δ(min - max)0.0880.0900.0920.0940.095
Fe1—B1 ×23.0802 (1)3.0804 (1)3.0810 (10)3.0818 (1)3.0826 (1)
Fe1—B2 ×23.9256 (3)3.9286 (3)3.9314 (3)3.9363 (3)3.9395 (4)
B1(9b) coordination
B1—O1 ×31.3816 (4)1.3812 (4)1.3808 (4)1.3815 (5)1.3800 (6)
B2(9e) coordination
B2—O21.3798 (8)1.3780 (8)1.3776 (8)1.3773 (9)1.3762 (12)
B2–O3 ×21.3692 (12)1.3690 (12)1.3681 (12)1.3676 (13)1.3680 (17)
(B2—O3)ave1.3731.3721.3711.3711.371
Δ(min - max)0.0110.0090.0100.0100.008
Fe chains
Fe1—Fe1intra3.1779 (1)3.1793 (1)3.1815 (1)3.1848 (1)3.1876 (1)
Fe1—Fe1inter4.4077 (1)4.4088 (1)4.4095 (1)4.4109 (1)4.4116 (2)
Fe1—O1—Fe1103.300 (19)103.316 (19)103.33 (2)103.42 (2)103.40 (3)
Fe1—O2—Fe1101.95 (2)101.90 (2)101.88 (2)101.89 (2)101.82 (3)
Characteristic temperatures and static atomic displacements for (Nd0.91Bi0.09)Fe3(BO3)4 top
Debye TD and Einstein TE characteristic temperatures, values of zero-point oscillations <u2>zero and <u2>static (ushift = u0 + ustatic) for cations in the Nd0.91Bi0.09Fe3(BO3)4 structure, and Rfactors of model refinement. The top line <u2>zero и <u2>static is the Einstein approximation, and the bottom line is the Debye approximation.
TE (K)TD (K)<u2>zero2)<u2>static2)R (%)
(Nd.Bi)123 (1)213 (2)0.00136590.00126 (11)0.92
0.00118260.00126 (11)0.90
Fe1253 (2)439 (3)0.00171760.00106 (7)0.85
0.00148270.00110 (7)0.69
B1569 (13)1014 (16)0.00394380.0001 (2)2.12
0.00331770.00045 (14)1.52
B2528 (11)938 (12)0.00424750.0002 (2)2.02
0.00358880.00058 (13)1.08
 

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