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
CCDC references: 2120875; 2120876; 2120877; 2120878; 2120879
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)4 | Dx = 4.563 Mg m−3 |
Mr = 552.8 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R32 | Cell parameters from 18531 reflections |
Hall symbol: R 3 2" | θ = 4.2–74.1° |
a = 9.5814 (1) Å | µ = 13.12 mm−1 |
c = 7.5908 (1) Å | T = 90 K |
V = 603.50 (1) Å3 | Sphere, light green |
Z = 3 | 0.07 (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 tube | 2706 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.030 |
Detector resolution: 16.1745 pixels mm-1 | θmax = 74.4°, θmin = 3.6° |
ω scans | h = −25→25 |
Absorption correction: for a sphere (JANA2006; Petříček et al., 2014) | k = −24→25 |
Tmin = 0.252, Tmax = 0.333 | l = −19→17 |
20875 measured reflections | |
Refinement top
Refinement on F2 | Weighting 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) = 0.029 | Δρmax = 0.84 e Å−3 |
S = 1.02 | Δρmin = −1.47 e Å−3 |
2707 reflections | Extinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) |
36 parameters | Extinction coefficient: 1230 (30) |
0 restraints | Absolute structure: 1224 of Friedel pairs used in the refinement |
2 constraints | Absolute structure parameter: 0.478 (4) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Nd1 | 0 | 0 | 0 | 0.003628 (10) | 0.91 |
Bi1 | 0 | 0 | 0 | 0.003628 (10) | 0.09 |
Fe1 | 0.217477 (12) | 0.333333 | 0.333333 | 0.00302 (2) | |
O1 | 0.14420 (6) | 0.14420 (6) | 0.5 | 0.00430 (9) | |
O2 | 0.40981 (7) | 0.40981 (7) | 0.5 | 0.00574 (11) | |
O3 | 0.02648 (5) | 0.21492 (6) | 0.18474 (7) | 0.00499 (8) | |
B1 | 0 | 0 | 0.5 | 0.00390 (19) | |
B2 | 0.55382 (9) | 0.55382 (9) | 0.5 | 0.00434 (16) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Nd1 | 0.003673 (11) | 0.003673 (11) | 0.00354 (2) | 0.001837 (6) | 0 | 0 |
Bi1 | 0.003673 (11) | 0.003673 (11) | 0.00354 (2) | 0.001837 (6) | 0 | 0 |
Fe1 | 0.00293 (2) | 0.00297 (2) | 0.00316 (4) | 0.001487 (12) | −0.000028 (8) | −0.000056 (17) |
O1 | 0.00351 (9) | 0.00351 (9) | 0.00498 (19) | 0.00107 (10) | −0.00039 (6) | 0.00039 (6) |
O2 | 0.00411 (10) | 0.00411 (10) | 0.0071 (2) | 0.00065 (12) | −0.00146 (7) | 0.00146 (7) |
O3 | 0.00398 (9) | 0.00583 (10) | 0.00542 (14) | 0.00266 (8) | −0.00068 (8) | −0.00076 (9) |
B1 | 0.00378 (19) | 0.00378 (19) | 0.0041 (4) | 0.00189 (9) | 0 | 0 |
B2 | 0.00376 (15) | 0.00376 (15) | 0.0052 (2) | 0.0017 (2) | −0.00018 (11) | 0.00018 (11) |
Geometric parameters (Å, º) top
Nd1—Bi1 | 0 | Bi1—O3iv | 2.3977 (5) |
Nd1—O3 | 2.3977 (6) | Bi1—O3v | 2.3977 (7) |
Nd1—O3i | 2.3977 (5) | Fe1—O1 | 2.0261 (4) |
Nd1—O3ii | 2.3977 (7) | Fe1—O1vi | 2.0261 (4) |
Nd1—O3iii | 2.3977 (6) | Fe1—O2 | 2.0453 (5) |
Nd1—O3iv | 2.3977 (5) | Fe1—O2vi | 2.0453 (8) |
Nd1—O3v | 2.3977 (7) | Fe1—O3 | 1.9576 (5) |
Bi1—O3 | 2.3977 (6) | Fe1—O3vii | 1.9576 (7) |
Bi1—O3i | 2.3977 (5) | O1—B1 | 1.3816 (4) |
Bi1—O3ii | 2.3977 (7) | O2—B2 | 1.3798 (8) |
Bi1—O3iii | 2.3977 (6) | O3—B2viii | 1.3693 (12) |
| | | |
Bi1—Nd1—O3 | 0 | O3ii—Bi1—O3v | 142.237 (14) |
Bi1—Nd1—O3i | 0 | O3iii—Bi1—O3iv | 89.249 (19) |
Bi1—Nd1—O3ii | 0 | O3iii—Bi1—O3v | 89.249 (19) |
Bi1—Nd1—O3iii | 0 | O3iv—Bi1—O3v | 89.249 (19) |
Bi1—Nd1—O3iv | 0 | O1—Fe1—O1vi | 168.44 (3) |
Bi1—Nd1—O3v | 0 | O1—Fe1—O2 | 77.374 (18) |
O3—Nd1—O3i | 89.249 (19) | O1—Fe1—O2vi | 94.20 (2) |
O3—Nd1—O3ii | 89.249 (19) | O1—Fe1—O3 | 92.060 (18) |
O3—Nd1—O3iii | 122.325 (14) | O1—Fe1—O3vii | 95.39 (2) |
O3—Nd1—O3iv | 142.24 (2) | O1vi—Fe1—O2 | 94.20 (2) |
O3—Nd1—O3v | 72.60 (2) | O1vi—Fe1—O2vi | 77.37 (3) |
O3i—Nd1—O3ii | 89.249 (19) | O1vi—Fe1—O3 | 95.39 (2) |
O3i—Nd1—O3iii | 142.24 (2) | O1vi—Fe1—O3vii | 92.06 (2) |
O3i—Nd1—O3iv | 72.598 (18) | O2—Fe1—O2vi | 87.58 (3) |
O3i—Nd1—O3v | 122.33 (2) | O2—Fe1—O3 | 167.90 (3) |
O3ii—Nd1—O3iii | 72.60 (2) | O2—Fe1—O3vii | 87.33 (3) |
O3ii—Nd1—O3iv | 122.33 (2) | O2vi—Fe1—O3 | 87.33 (3) |
O3ii—Nd1—O3v | 142.237 (14) | O2vi—Fe1—O3vii | 167.90 (2) |
O3iii—Nd1—O3iv | 89.249 (19) | O3—Fe1—O3vii | 99.66 (3) |
O3iii—Nd1—O3v | 89.249 (19) | Fe1—O1—Fe1ix | 103.300 (19) |
O3iv—Nd1—O3v | 89.249 (19) | Fe1—O1—B1 | 128.35 (3) |
Nd1—Bi1—O3 | 0 | Fe1ix—O1—B1 | 128.35 (3) |
Nd1—Bi1—O3i | 0 | Fe1—O2—Fe1ix | 101.95 (2) |
Nd1—Bi1—O3ii | 0 | Fe1—O2—B2 | 129.02 (4) |
Nd1—Bi1—O3iii | 0 | Fe1ix—O2—B2 | 129.02 (4) |
Nd1—Bi1—O3iv | 0 | Nd1—O3—Bi1 | 0.0 (5) |
Nd1—Bi1—O3v | 0 | Nd1—O3—Fe1 | 120.10 (3) |
O3—Bi1—O3i | 89.249 (19) | Nd1—O3—B2viii | 106.76 (3) |
O3—Bi1—O3ii | 89.249 (19) | Bi1—O3—Fe1 | 120.10 (3) |
O3—Bi1—O3iii | 122.325 (14) | Bi1—O3—B2viii | 106.76 (3) |
O3—Bi1—O3iv | 142.24 (2) | Fe1—O3—B2viii | 133.02 (4) |
O3—Bi1—O3v | 72.60 (2) | O1—B1—O1i | 120.00 (4) |
O3i—Bi1—O3ii | 89.249 (19) | O1—B1—O1ii | 120.00 (4) |
O3i—Bi1—O3iii | 142.24 (2) | O1i—B1—O1ii | 120.00 (4) |
O3i—Bi1—O3iv | 72.598 (18) | O2—B2—O3x | 117.90 (8) |
O3i—Bi1—O3v | 122.33 (2) | O2—B2—O3xi | 117.90 (8) |
O3ii—Bi1—O3iii | 72.60 (2) | O3x—B2—O3xi | 124.20 (5) |
O3ii—Bi1—O3iv | 122.33 (2) | | |
Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z; (iv) x−y, −y, −z; (v) −x, −x+y, −z; (vi) −x+y+1/3, −x+2/3, z−1/3; (vii) x−y+1/3, −y+2/3, −z+2/3; (viii) x−2/3, y−1/3, z−1/3; (ix) −y+2/3, x−y+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)4 | Dx = 4.561 Mg m−3 |
Mr = 552.8 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R32 | Cell parameters from 17088 reflections |
Hall symbol: R 3 2" | θ = 4.2–73.9° |
a = 9.5805 (1) Å | µ = 13.11 mm−1 |
c = 7.5970 (1) Å | T = 200 K |
V = 603.88 (1) Å3 | Sphere, light green |
Z = 3 | 0.07 (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 tube | 2712 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.031 |
Detector resolution: 16.1745 pixels mm-1 | θmax = 74.4°, θmin = 3.6° |
ω scans | h = −25→25 |
Absorption correction: for a sphere (JANA2006; Petříček et al., 2014) | k = −24→25 |
Tmin = 0.256, Tmax = 0.336 | l = −19→17 |
20885 measured reflections | |
Refinement top
Refinement on F2 | Weighting 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) = 0.034 | Δρmax = 0.78 e Å−3 |
S = 1.02 | Δρmin = −1.33 e Å−3 |
2714 reflections | Extinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) |
36 parameters | Extinction coefficient: 1320 (40) |
0 restraints | Absolute structure: 1227 of Friedel pairs used in the refinement |
2 constraints | Absolute structure parameter: 0.479 (5) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Nd1 | 0 | 0 | 0 | 0.005895 (12) | 0.91 |
Bi1 | 0 | 0 | 0 | 0.005895 (12) | 0.09 |
Fe1 | 0.217486 (13) | 0.333333 | 0.333333 | 0.00416 (2) | |
O1 | 0.14417 (6) | 0.14417 (6) | 0.5 | 0.00553 (10) | |
O2 | 0.41001 (8) | 0.41001 (8) | 0.5 | 0.00826 (12) | |
O3 | 0.02652 (6) | 0.21503 (6) | 0.18481 (8) | 0.00669 (9) | |
B1 | 0 | 0 | 0.5 | 0.00471 (19) | |
B2 | 0.55384 (9) | 0.55384 (9) | 0.5 | 0.00523 (16) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Nd1 | 0.005985 (13) | 0.005985 (13) | 0.00571 (3) | 0.002992 (7) | 0 | 0 |
Bi1 | 0.005985 (13) | 0.005985 (13) | 0.00571 (3) | 0.002992 (7) | 0 | 0 |
Fe1 | 0.00396 (2) | 0.00409 (2) | 0.00447 (4) | 0.002047 (12) | −0.000053 (8) | −0.000107 (17) |
O1 | 0.00426 (9) | 0.00426 (9) | 0.0068 (2) | 0.00118 (10) | −0.00076 (6) | 0.00076 (6) |
O2 | 0.00543 (10) | 0.00543 (10) | 0.0109 (3) | 0.00044 (13) | −0.00262 (9) | 0.00262 (9) |
O3 | 0.00512 (10) | 0.00808 (12) | 0.00731 (15) | 0.00362 (9) | −0.00119 (8) | −0.00145 (10) |
B1 | 0.00436 (19) | 0.00436 (19) | 0.0054 (4) | 0.00218 (10) | 0 | 0 |
B2 | 0.00470 (15) | 0.00470 (15) | 0.0061 (2) | 0.0022 (2) | −0.00021 (11) | 0.00021 (11) |
Geometric parameters (Å, º) top
Nd1—Bi1 | 0 | Bi1—O3iv | 2.3992 (5) |
Nd1—O3 | 2.3992 (6) | Bi1—O3v | 2.3992 (8) |
Nd1—O3i | 2.3992 (5) | Fe1—O1 | 2.0268 (4) |
Nd1—O3ii | 2.3992 (8) | Fe1—O1vi | 2.0268 (4) |
Nd1—O3iii | 2.3992 (6) | Fe1—O2 | 2.0469 (5) |
Nd1—O3iv | 2.3992 (5) | Fe1—O2vi | 2.0469 (9) |
Nd1—O3v | 2.3992 (8) | Fe1—O3 | 1.9574 (5) |
Bi1—O3 | 2.3992 (6) | Fe1—O3vii | 1.9574 (8) |
Bi1—O3i | 2.3992 (5) | O1—B1 | 1.3812 (4) |
Bi1—O3ii | 2.3992 (8) | O2—B2 | 1.3780 (8) |
Bi1—O3iii | 2.3992 (6) | O3—B2viii | 1.3690 (12) |
| | | |
Bi1—Nd1—O3 | 0 | O3ii—Bi1—O3v | 142.260 (15) |
Bi1—Nd1—O3i | 0 | O3iii—Bi1—O3iv | 89.22 (2) |
Bi1—Nd1—O3ii | 0 | O3iii—Bi1—O3v | 89.22 (2) |
Bi1—Nd1—O3iii | 0 | O3iv—Bi1—O3v | 89.22 (2) |
Bi1—Nd1—O3iv | 0 | O1—Fe1—O1vi | 168.46 (3) |
Bi1—Nd1—O3v | 0 | O1—Fe1—O2 | 77.391 (19) |
O3—Nd1—O3i | 89.22 (2) | O1—Fe1—O2vi | 94.20 (2) |
O3—Nd1—O3ii | 89.22 (2) | O1—Fe1—O3 | 92.10 (2) |
O3—Nd1—O3iii | 122.332 (15) | O1—Fe1—O3vii | 95.34 (2) |
O3—Nd1—O3iv | 142.26 (2) | O1vi—Fe1—O2 | 94.20 (2) |
O3—Nd1—O3v | 72.64 (2) | O1vi—Fe1—O2vi | 77.39 (3) |
O3i—Nd1—O3ii | 89.22 (2) | O1vi—Fe1—O3 | 95.34 (2) |
O3i—Nd1—O3iii | 142.26 (2) | O1vi—Fe1—O3vii | 92.10 (3) |
O3i—Nd1—O3iv | 72.64 (2) | O2—Fe1—O2vi | 87.62 (3) |
O3i—Nd1—O3v | 122.33 (2) | O2—Fe1—O3 | 167.96 (3) |
O3ii—Nd1—O3iii | 72.64 (2) | O2—Fe1—O3vii | 87.32 (3) |
O3ii—Nd1—O3iv | 122.33 (2) | O2vi—Fe1—O3 | 87.32 (3) |
O3ii—Nd1—O3v | 142.260 (15) | O2vi—Fe1—O3vii | 167.96 (2) |
O3iii—Nd1—O3iv | 89.22 (2) | O3—Fe1—O3vii | 99.64 (3) |
O3iii—Nd1—O3v | 89.22 (2) | Fe1—O1—Fe1ix | 103.316 (19) |
O3iv—Nd1—O3v | 89.22 (2) | Fe1—O1—B1 | 128.34 (3) |
Nd1—Bi1—O3 | 0 | Fe1ix—O1—B1 | 128.34 (3) |
Nd1—Bi1—O3i | 0 | Fe1—O2—Fe1ix | 101.90 (2) |
Nd1—Bi1—O3ii | 0 | Fe1—O2—B2 | 129.05 (4) |
Nd1—Bi1—O3iii | 0 | Fe1ix—O2—B2 | 129.05 (4) |
Nd1—Bi1—O3iv | 0 | Nd1—O3—Bi1 | 0.0 (5) |
Nd1—Bi1—O3v | 0 | Nd1—O3—Fe1 | 120.10 (3) |
O3—Bi1—O3i | 89.22 (2) | Nd1—O3—B2viii | 106.70 (4) |
O3—Bi1—O3ii | 89.22 (2) | Bi1—O3—Fe1 | 120.10 (3) |
O3—Bi1—O3iii | 122.332 (15) | Bi1—O3—B2viii | 106.70 (4) |
O3—Bi1—O3iv | 142.26 (2) | Fe1—O3—B2viii | 133.07 (5) |
O3—Bi1—O3v | 72.64 (2) | O1—B1—O1i | 120.00 (4) |
O3i—Bi1—O3ii | 89.22 (2) | O1—B1—O1ii | 120.00 (4) |
O3i—Bi1—O3iii | 142.26 (2) | O1i—B1—O1ii | 120.00 (4) |
O3i—Bi1—O3iv | 72.64 (2) | O2—B2—O3x | 117.93 (8) |
O3i—Bi1—O3v | 122.33 (2) | O2—B2—O3xi | 117.93 (8) |
O3ii—Bi1—O3iii | 72.64 (2) | O3x—B2—O3xi | 124.13 (6) |
O3ii—Bi1—O3iv | 122.33 (2) | | |
Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z; (iv) x−y, −y, −z; (v) −x, −x+y, −z; (vi) −x+y+1/3, −x+2/3, z−1/3; (vii) x−y+1/3, −y+2/3, −z+2/3; (viii) x−2/3, y−1/3, z−1/3; (ix) −y+2/3, x−y+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)4 | Dx = 4.556 Mg m−3 |
Mr = 552.8 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R32 | Cell parameters from 15414 reflections |
Hall symbol: R 3 2" | θ = 4.2–74.1° |
a = 9.5815 (1) Å | µ = 13.10 mm−1 |
c = 7.6028 (1) Å | T = 293 K |
V = 604.47 (1) Å3 | Sphere, light green |
Z = 3 | 0.07 (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 tube | 2699 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.033 |
Detector resolution: 16.1745 pixels mm-1 | θmax = 74.3°, θmin = 3.6° |
ω scans | h = −25→25 |
Absorption correction: for a sphere (JANA2006; Petříček et al., 2014) | k = −24→25 |
Tmin = 0.255, Tmax = 0.335 | l = −19→17 |
20900 measured reflections | |
Refinement top
Refinement on F2 | Weighting 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) = 0.027 | Δρmax = 0.71 e Å−3 |
S = 1.09 | Δρmin = −1.47 e Å−3 |
2716 reflections | Extinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) |
36 parameters | Extinction coefficient: 1290 (20) |
0 restraints | Absolute structure: 1229 of Friedel pairs used in the refinement |
2 constraints | Absolute structure parameter: 0.474 (5) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Nd1 | 0 | 0 | 0 | 0.007899 (16) | 0.91 |
Bi1 | 0 | 0 | 0 | 0.007899 (16) | 0.09 |
Fe1 | 0.217434 (13) | 0.333333 | 0.333333 | 0.00530 (2) | |
O1 | 0.14411 (6) | 0.14411 (6) | 0.5 | 0.00679 (11) | |
O2 | 0.41011 (8) | 0.41011 (8) | 0.5 | 0.01057 (15) | |
O3 | 0.02649 (6) | 0.21516 (7) | 0.18501 (8) | 0.00836 (11) | |
B1 | 0 | 0 | 0.5 | 0.0055 (2) | |
B2 | 0.55389 (9) | 0.55389 (9) | 0.5 | 0.00638 (19) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Nd1 | 0.008038 (17) | 0.008038 (17) | 0.00762 (3) | 0.004019 (8) | 0 | 0 |
Bi1 | 0.008038 (17) | 0.008038 (17) | 0.00762 (3) | 0.004019 (8) | 0 | 0 |
Fe1 | 0.00497 (2) | 0.00519 (3) | 0.00581 (5) | 0.002593 (15) | −0.000087 (12) | −0.00017 (2) |
O1 | 0.00521 (10) | 0.00521 (10) | 0.0083 (2) | 0.00138 (12) | −0.00083 (7) | 0.00083 (7) |
O2 | 0.00661 (12) | 0.00661 (12) | 0.0140 (3) | −0.00007 (15) | −0.00362 (11) | 0.00362 (11) |
O3 | 0.00618 (12) | 0.01021 (14) | 0.00912 (19) | 0.00443 (11) | −0.00166 (11) | −0.00219 (12) |
B1 | 0.0051 (2) | 0.0051 (2) | 0.0064 (5) | 0.00253 (10) | 0 | 0 |
B2 | 0.00543 (18) | 0.00543 (18) | 0.0077 (3) | 0.0023 (3) | −0.00027 (15) | 0.00027 (15) |
Geometric parameters (Å, º) top
Nd1—Bi1 | 0 | Bi1—O3iv | 2.4020 (6) |
Nd1—O3 | 2.4020 (7) | Bi1—O3v | 2.4020 (8) |
Nd1—O3i | 2.4020 (6) | Fe1—O1 | 2.0279 (4) |
Nd1—O3ii | 2.4020 (8) | Fe1—O1vi | 2.0279 (4) |
Nd1—O3iii | 2.4020 (7) | Fe1—O2 | 2.0486 (5) |
Nd1—O3iv | 2.4020 (6) | Fe1—O2vi | 2.0486 (9) |
Nd1—O3v | 2.4020 (8) | Fe1—O3 | 1.9569 (5) |
Bi1—O3 | 2.4020 (7) | Fe1—O3vii | 1.9569 (8) |
Bi1—O3i | 2.4020 (6) | O1—B1 | 1.3808 (4) |
Bi1—O3ii | 2.4020 (8) | O2—B2 | 1.3776 (8) |
Bi1—O3iii | 2.4020 (7) | O3—B2viii | 1.3681 (12) |
| | | |
Bi1—Nd1—O3 | 0 | O3ii—Bi1—O3v | 142.255 (16) |
Bi1—Nd1—O3i | 0 | O3iii—Bi1—O3iv | 89.18 (2) |
Bi1—Nd1—O3ii | 0 | O3iii—Bi1—O3v | 89.18 (2) |
Bi1—Nd1—O3iii | 0 | O3iv—Bi1—O3v | 89.18 (2) |
Bi1—Nd1—O3iv | 0 | O1—Fe1—O1vi | 168.45 (3) |
Bi1—Nd1—O3v | 0 | O1—Fe1—O2 | 77.392 (19) |
O3—Nd1—O3i | 89.18 (2) | O1—Fe1—O2vi | 94.19 (2) |
O3—Nd1—O3ii | 89.18 (2) | O1—Fe1—O3 | 92.12 (2) |
O3—Nd1—O3iii | 122.373 (16) | O1—Fe1—O3vii | 95.33 (2) |
O3—Nd1—O3iv | 142.26 (3) | O1vi—Fe1—O2 | 94.19 (2) |
O3—Nd1—O3v | 72.70 (2) | O1vi—Fe1—O2vi | 77.39 (3) |
O3i—Nd1—O3ii | 89.18 (2) | O1vi—Fe1—O3 | 95.33 (2) |
O3i—Nd1—O3iii | 142.26 (3) | O1vi—Fe1—O3vii | 92.12 (3) |
O3i—Nd1—O3iv | 72.70 (2) | O2—Fe1—O2vi | 87.63 (3) |
O3i—Nd1—O3v | 122.37 (2) | O2—Fe1—O3 | 168.00 (3) |
O3ii—Nd1—O3iii | 72.70 (2) | O2—Fe1—O3vii | 87.34 (3) |
O3ii—Nd1—O3iv | 122.37 (2) | O2vi—Fe1—O3 | 87.34 (3) |
O3ii—Nd1—O3v | 142.255 (16) | O2vi—Fe1—O3vii | 168.00 (2) |
O3iii—Nd1—O3iv | 89.18 (2) | O3—Fe1—O3vii | 99.57 (3) |
O3iii—Nd1—O3v | 89.18 (2) | Fe1—O1—Fe1ix | 103.33 (2) |
O3iv—Nd1—O3v | 89.18 (2) | Fe1—O1—B1 | 128.33 (3) |
Nd1—Bi1—O3 | 0 | Fe1ix—O1—B1 | 128.33 (3) |
Nd1—Bi1—O3i | 0 | Fe1—O2—Fe1ix | 101.88 (2) |
Nd1—Bi1—O3ii | 0 | Fe1—O2—B2 | 129.06 (4) |
Nd1—Bi1—O3iii | 0 | Fe1ix—O2—B2 | 129.06 (4) |
Nd1—Bi1—O3iv | 0 | Nd1—O3—Bi1 | 0.0 (5) |
Nd1—Bi1—O3v | 0 | Nd1—O3—Fe1 | 120.07 (3) |
O3—Bi1—O3i | 89.18 (2) | Nd1—O3—B2viii | 106.63 (4) |
O3—Bi1—O3ii | 89.18 (2) | Bi1—O3—Fe1 | 120.07 (3) |
O3—Bi1—O3iii | 122.373 (16) | Bi1—O3—B2viii | 106.63 (4) |
O3—Bi1—O3iv | 142.26 (3) | Fe1—O3—B2viii | 133.18 (5) |
O3—Bi1—O3v | 72.70 (2) | O1—B1—O1i | 120.00 (4) |
O3i—Bi1—O3ii | 89.18 (2) | O1—B1—O1ii | 120.00 (4) |
O3i—Bi1—O3iii | 142.26 (3) | O1i—B1—O1ii | 120.00 (4) |
O3i—Bi1—O3iv | 72.70 (2) | O2—B2—O3x | 117.96 (8) |
O3i—Bi1—O3v | 122.37 (2) | O2—B2—O3xi | 117.96 (8) |
O3ii—Bi1—O3iii | 72.70 (2) | O3x—B2—O3xi | 124.09 (6) |
O3ii—Bi1—O3iv | 122.37 (2) | | |
Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z; (iv) x−y, −y, −z; (v) −x, −x+y, −z; (vi) −x+y+1/3, −x+2/3, z−1/3; (vii) x−y+1/3, −y+2/3, −z+2/3; (viii) x−2/3, y−1/3, z−1/3; (ix) −y+2/3, x−y+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)4 | Dx = 4.550 Mg m−3 |
Mr = 552.8 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R32 | Cell parameters from 12909 reflections |
Hall symbol: R 3 2" | θ = 4.2–73.6° |
a = 9.5822 (1) Å | µ = 13.08 mm−1 |
c = 7.6128 (1) Å | T = 400 K |
V = 605.35 (1) Å3 | Sphere, light green |
Z = 3 | 0.07 (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 tube | 2645 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.035 |
Detector resolution: 16.1745 pixels mm-1 | θmax = 74.2°, θmin = 3.6° |
ω scans | h = −25→25 |
Absorption correction: for a sphere (JANA2006; Petříček et al., 2014) | k = −24→25 |
Tmin = 0.253, Tmax = 0.334 | l = −19→17 |
20978 measured reflections | |
Refinement top
Refinement on F2 | Weighting 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) = 0.028 | Δρmax = 0.53 e Å−3 |
S = 1.02 | Δρmin = −1.39 e Å−3 |
2727 reflections | Extinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) |
36 parameters | Extinction coefficient: 1300 (20) |
0 restraints | Absolute structure: 1234 of Friedel pairs used in the refinement |
2 constraints | Absolute structure parameter: 0.479 (5) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Nd1 | 0 | 0 | 0 | 0.010271 (19) | 0.91 |
Bi1 | 0 | 0 | 0 | 0.010271 (19) | 0.09 |
Fe1 | 0.217381 (14) | 0.333333 | 0.333333 | 0.00673 (3) | |
O1 | 0.14417 (7) | 0.14417 (7) | 0.5 | 0.00854 (13) | |
O2 | 0.41019 (8) | 0.41019 (8) | 0.5 | 0.01326 (17) | |
O3 | 0.02642 (6) | 0.21516 (7) | 0.18520 (9) | 0.01051 (13) | |
B1 | 0 | 0 | 0.5 | 0.0065 (2) | |
B2 | 0.55393 (10) | 0.55393 (10) | 0.5 | 0.0076 (2) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Nd1 | 0.01047 (2) | 0.01047 (2) | 0.00986 (4) | 0.005237 (10) | 0 | 0 |
Bi1 | 0.01047 (2) | 0.01047 (2) | 0.00986 (4) | 0.005237 (10) | 0 | 0 |
Fe1 | 0.00632 (2) | 0.00662 (3) | 0.00735 (5) | 0.003310 (16) | −0.000104 (13) | −0.00021 (3) |
O1 | 0.00641 (11) | 0.00641 (11) | 0.0106 (3) | 0.00157 (13) | −0.00123 (8) | 0.00123 (8) |
O2 | 0.00827 (14) | 0.00827 (14) | 0.0174 (4) | −0.00025 (17) | −0.00464 (13) | 0.00464 (13) |
O3 | 0.00747 (13) | 0.01285 (17) | 0.0118 (2) | 0.00550 (13) | −0.00236 (12) | −0.00293 (14) |
B1 | 0.0059 (2) | 0.0059 (2) | 0.0076 (5) | 0.00295 (11) | 0 | 0 |
B2 | 0.00653 (19) | 0.00653 (19) | 0.0089 (3) | 0.0026 (3) | −0.00038 (17) | 0.00038 (17) |
Geometric parameters (Å, º) top
Nd1—Bi1 | 0 | Bi1—O3iv | 2.4042 (6) |
Nd1—O3 | 2.4042 (7) | Bi1—O3v | 2.4042 (9) |
Nd1—O3i | 2.4042 (6) | Fe1—O1 | 2.0288 (5) |
Nd1—O3ii | 2.4042 (9) | Fe1—O1vi | 2.0288 (4) |
Nd1—O3iii | 2.4042 (7) | Fe1—O2 | 2.0506 (6) |
Nd1—O3iv | 2.4042 (6) | Fe1—O2vi | 2.0506 (9) |
Nd1—O3v | 2.4042 (9) | Fe1—O3 | 1.9571 (6) |
Bi1—O3 | 2.4042 (7) | Fe1—O3vii | 1.9571 (9) |
Bi1—O3i | 2.4042 (6) | O1—B1 | 1.3815 (5) |
Bi1—O3ii | 2.4042 (9) | O2—B2 | 1.3773 (9) |
Bi1—O3iii | 2.4042 (7) | O3—B2viii | 1.3676 (13) |
| | | |
Bi1—Nd1—O3 | 0 | O3ii—Bi1—O3v | 142.256 (17) |
Bi1—Nd1—O3i | 0 | O3iii—Bi1—O3iv | 89.09 (2) |
Bi1—Nd1—O3ii | 0 | O3iii—Bi1—O3v | 89.09 (2) |
Bi1—Nd1—O3iii | 0 | O3iv—Bi1—O3v | 89.09 (2) |
Bi1—Nd1—O3iv | 0 | O1—Fe1—O1vi | 168.41 (4) |
Bi1—Nd1—O3v | 0 | O1—Fe1—O2 | 77.34 (2) |
O3—Nd1—O3i | 89.09 (2) | O1—Fe1—O2vi | 94.22 (3) |
O3—Nd1—O3ii | 89.09 (2) | O1—Fe1—O3 | 92.17 (2) |
O3—Nd1—O3iii | 122.445 (17) | O1—Fe1—O3vii | 95.31 (3) |
O3—Nd1—O3iv | 142.26 (3) | O1vi—Fe1—O2 | 94.22 (2) |
O3—Nd1—O3v | 72.81 (3) | O1vi—Fe1—O2vi | 77.34 (3) |
O3i—Nd1—O3ii | 89.09 (2) | O1vi—Fe1—O3 | 95.31 (2) |
O3i—Nd1—O3iii | 142.26 (3) | O1vi—Fe1—O3vii | 92.17 (3) |
O3i—Nd1—O3iv | 72.81 (2) | O2—Fe1—O2vi | 87.66 (3) |
O3i—Nd1—O3v | 122.45 (3) | O2—Fe1—O3 | 168.00 (3) |
O3ii—Nd1—O3iii | 72.81 (3) | O2—Fe1—O3vii | 87.33 (3) |
O3ii—Nd1—O3iv | 122.45 (3) | O2vi—Fe1—O3 | 87.33 (3) |
O3ii—Nd1—O3v | 142.256 (17) | O2vi—Fe1—O3vii | 168.00 (2) |
O3iii—Nd1—O3iv | 89.09 (2) | O3—Fe1—O3vii | 99.57 (3) |
O3iii—Nd1—O3v | 89.09 (2) | Fe1—O1—Fe1ix | 103.42 (2) |
O3iv—Nd1—O3v | 89.09 (2) | Fe1—O1—B1 | 128.29 (3) |
Nd1—Bi1—O3 | 0 | Fe1ix—O1—B1 | 128.29 (3) |
Nd1—Bi1—O3i | 0 | Fe1—O2—Fe1ix | 101.89 (2) |
Nd1—Bi1—O3ii | 0 | Fe1—O2—B2 | 129.05 (5) |
Nd1—Bi1—O3iii | 0 | Fe1ix—O2—B2 | 129.05 (5) |
Nd1—Bi1—O3iv | 0 | Nd1—O3—Bi1 | 0.0 (5) |
Nd1—Bi1—O3v | 0 | Nd1—O3—Fe1 | 120.08 (4) |
O3—Bi1—O3i | 89.09 (2) | Nd1—O3—B2viii | 106.59 (4) |
O3—Bi1—O3ii | 89.09 (2) | Bi1—O3—Fe1 | 120.08 (4) |
O3—Bi1—O3iii | 122.445 (17) | Bi1—O3—B2viii | 106.59 (4) |
O3—Bi1—O3iv | 142.26 (3) | Fe1—O3—B2viii | 133.22 (5) |
O3—Bi1—O3v | 72.81 (3) | O1—B1—O1i | 120.00 (5) |
O3i—Bi1—O3ii | 89.09 (2) | O1—B1—O1ii | 120.00 (5) |
O3i—Bi1—O3iii | 142.26 (3) | O1i—B1—O1ii | 120.00 (5) |
O3i—Bi1—O3iv | 72.81 (2) | O2—B2—O3x | 117.94 (9) |
O3i—Bi1—O3v | 122.45 (3) | O2—B2—O3xi | 117.94 (9) |
O3ii—Bi1—O3iii | 72.81 (3) | O3x—B2—O3xi | 124.13 (6) |
O3ii—Bi1—O3iv | 122.45 (3) | | |
Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z; (iv) x−y, −y, −z; (v) −x, −x+y, −z; (vi) −x+y+1/3, −x+2/3, z−1/3; (vii) x−y+1/3, −y+2/3, −z+2/3; (viii) x−2/3, y−1/3, z−1/3; (ix) −y+2/3, x−y+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)4 | Dx = 4.544 Mg m−3 |
Mr = 552.8 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R32 | Cell parameters from 8164 reflections |
Hall symbol: R 3 2" | θ = 4.2–74.0° |
a = 9.5841 (2) Å | µ = 13.06 mm−1 |
c = 7.6194 (1) Å | T = 500 K |
V = 606.11 (2) Å3 | Sphere, light green |
Z = 3 | 0.07 (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 tube | 2092 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.040 |
Detector resolution: 16.1745 pixels mm-1 | θmax = 74.1°, θmin = 3.6° |
ω scans | h = −25→24 |
Absorption correction: for a sphere (JANA2006; Petříček et al., 2014) | k = −25→25 |
Tmin = 0.291, Tmax = 0.365 | l = −17→19 |
14607 measured reflections | |
Refinement top
Refinement on F2 | Weighting 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) = 0.033 | Δρmax = 1.29 e Å−3 |
S = 1.08 | Δρmin = −1.46 e Å−3 |
2557 reflections | Extinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) |
36 parameters | Extinction coefficient: 1440 (30) |
0 restraints | Absolute structure: 1101 of Friedel pairs used in the refinement |
2 constraints | Absolute structure parameter: 0.477 (7) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Nd1 | 0 | 0 | 0 | 0.01219 (3) | 0.91 |
Bi1 | 0 | 0 | 0 | 0.01219 (3) | 0.09 |
Fe1 | 0.21730 (2) | 0.333333 | 0.333333 | 0.00786 (4) | |
O1 | 0.14399 (9) | 0.14399 (9) | 0.5 | 0.0098 (2) | |
O2 | 0.41041 (11) | 0.41041 (11) | 0.5 | 0.0153 (3) | |
O3 | 0.02643 (9) | 0.21507 (10) | 0.18507 (12) | 0.0123 (2) | |
B1 | 0 | 0 | 0.5 | 0.0077 (4) | |
B2 | 0.55400 (13) | 0.55400 (13) | 0.5 | 0.0088 (3) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Nd1 | 0.01240 (3) | 0.01240 (3) | 0.01176 (6) | 0.006201 (16) | 0 | 0 |
Bi1 | 0.01240 (3) | 0.01240 (3) | 0.01176 (6) | 0.006201 (16) | 0 | 0 |
Fe1 | 0.00735 (4) | 0.00773 (5) | 0.00863 (9) | 0.00387 (3) | −0.00012 (2) | −0.00023 (5) |
O1 | 0.00730 (18) | 0.00730 (18) | 0.0122 (4) | 0.0017 (2) | −0.00149 (14) | 0.00149 (14) |
O2 | 0.0098 (2) | 0.0098 (2) | 0.0197 (6) | 0.0001 (3) | −0.0052 (2) | 0.0052 (2) |
O3 | 0.0083 (2) | 0.0151 (3) | 0.0141 (3) | 0.0063 (2) | −0.0028 (2) | −0.0036 (2) |
B1 | 0.0067 (3) | 0.0067 (3) | 0.0098 (8) | 0.00333 (17) | 0 | 0 |
B2 | 0.0077 (3) | 0.0077 (3) | 0.0106 (5) | 0.0035 (5) | −0.0008 (3) | 0.0008 (3) |
Geometric parameters (Å, º) top
Nd1—Bi1 | 0 | Bi1—O3iv | 2.4040 (8) |
Nd1—O3 | 2.4040 (10) | Bi1—O3v | 2.4040 (12) |
Nd1—O3i | 2.4040 (8) | Fe1—O1 | 2.0309 (7) |
Nd1—O3ii | 2.4040 (12) | Fe1—O1vi | 2.0309 (6) |
Nd1—O3iii | 2.4040 (10) | Fe1—O2 | 2.0534 (8) |
Nd1—O3iv | 2.4040 (8) | Fe1—O2vi | 2.0534 (13) |
Nd1—O3v | 2.4040 (12) | Fe1—O3 | 1.9580 (8) |
Bi1—O3 | 2.4040 (10) | Fe1—O3vii | 1.9580 (12) |
Bi1—O3i | 2.4040 (8) | O1—B1 | 1.3800 (6) |
Bi1—O3ii | 2.4040 (12) | O2—B2 | 1.3762 (12) |
Bi1—O3iii | 2.4040 (10) | O3—B2viii | 1.3680 (17) |
| | | |
Bi1—Nd1—O3 | 0 | O3ii—Bi1—O3v | 142.27 (2) |
Bi1—Nd1—O3i | 0 | O3iii—Bi1—O3iv | 89.08 (3) |
Bi1—Nd1—O3ii | 0 | O3iii—Bi1—O3v | 89.08 (3) |
Bi1—Nd1—O3iii | 0 | O3iv—Bi1—O3v | 89.08 (3) |
Bi1—Nd1—O3iv | 0 | O1—Fe1—O1vi | 168.43 (5) |
Bi1—Nd1—O3v | 0 | O1—Fe1—O2 | 77.39 (3) |
O3—Nd1—O3i | 89.08 (3) | O1—Fe1—O2vi | 94.18 (4) |
O3—Nd1—O3ii | 89.08 (3) | O1—Fe1—O3 | 92.17 (3) |
O3—Nd1—O3iii | 122.45 (2) | O1—Fe1—O3vii | 95.29 (4) |
O3—Nd1—O3iv | 142.27 (4) | O1vi—Fe1—O2 | 94.18 (3) |
O3—Nd1—O3v | 72.83 (3) | O1vi—Fe1—O2vi | 77.39 (4) |
O3i—Nd1—O3ii | 89.08 (3) | O1vi—Fe1—O3 | 95.29 (3) |
O3i—Nd1—O3iii | 142.27 (4) | O1vi—Fe1—O3vii | 92.17 (4) |
O3i—Nd1—O3iv | 72.83 (3) | O2—Fe1—O2vi | 87.65 (4) |
O3i—Nd1—O3v | 122.45 (4) | O2—Fe1—O3 | 168.01 (4) |
O3ii—Nd1—O3iii | 72.83 (3) | O2—Fe1—O3vii | 87.26 (4) |
O3ii—Nd1—O3iv | 122.45 (4) | O2vi—Fe1—O3 | 87.26 (4) |
O3ii—Nd1—O3v | 142.27 (2) | O2vi—Fe1—O3vii | 168.01 (3) |
O3iii—Nd1—O3iv | 89.08 (3) | O3—Fe1—O3vii | 99.70 (4) |
O3iii—Nd1—O3v | 89.08 (3) | Fe1—O1—Fe1ix | 103.40 (3) |
O3iv—Nd1—O3v | 89.08 (3) | Fe1—O1—B1 | 128.30 (4) |
Nd1—Bi1—O3 | 0 | Fe1ix—O1—B1 | 128.30 (4) |
Nd1—Bi1—O3i | 0 | Fe1—O2—Fe1ix | 101.82 (3) |
Nd1—Bi1—O3ii | 0 | Fe1—O2—B2 | 129.09 (6) |
Nd1—Bi1—O3iii | 0 | Fe1ix—O2—B2 | 129.09 (6) |
Nd1—Bi1—O3iv | 0 | Nd1—O3—Bi1 | 0.0 (5) |
Nd1—Bi1—O3v | 0 | Nd1—O3—Fe1 | 120.15 (5) |
O3—Bi1—O3i | 89.08 (3) | Nd1—O3—B2viii | 106.65 (5) |
O3—Bi1—O3ii | 89.08 (3) | Bi1—O3—Fe1 | 120.15 (5) |
O3—Bi1—O3iii | 122.45 (2) | Bi1—O3—B2viii | 106.65 (5) |
O3—Bi1—O3iv | 142.27 (4) | Fe1—O3—B2viii | 133.09 (7) |
O3—Bi1—O3v | 72.83 (3) | O1—B1—O1i | 120.00 (6) |
O3i—Bi1—O3ii | 89.08 (3) | O1—B1—O1ii | 120.00 (6) |
O3i—Bi1—O3iii | 142.27 (4) | O1i—B1—O1ii | 120.00 (6) |
O3i—Bi1—O3iv | 72.83 (3) | O2—B2—O3x | 117.88 (12) |
O3i—Bi1—O3v | 122.45 (4) | O2—B2—O3xi | 117.88 (12) |
O3ii—Bi1—O3iii | 72.83 (3) | O3x—B2—O3xi | 124.24 (8) |
O3ii—Bi1—O3iv | 122.45 (4) | | |
Symmetry codes: (i) −y, x−y, z; (ii) −x+y, −x, z; (iii) y, x, −z; (iv) x−y, −y, −z; (v) −x, −x+y, −z; (vi) −x+y+1/3, −x+2/3, z−1/3; (vii) x−y+1/3, −y+2/3, −z+2/3; (viii) x−2/3, y−1/3, z−1/3; (ix) −y+2/3, x−y+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 topT (K) | 90 | 200 | 293 | 400 | 500 |
Nd1(3a) coordination | | | | | |
Nd1—O3 ×6 | 2.3977 (6) | 2.3992 (6) | 2.4020 (7) | 2.4042 (7) | 2.4040 (10) |
Nd1—B1 ×2 | 3.7954 (1) | 3.7985 (1) | 3.8014 (1) | 3.8064 (1) | 3.8097 (1) |
Nd1—B2 ×6 | 3.0849 (6) | 3.0851 (10) | 3.0859 (6) | 3.0868 (11) | 3.0879 (7) |
Nd1—Fe1 ×6 | 3.7801 (1) | 3.7813 (1) | 3.7828 (1) | 3.7851 (1) | 3.7869 (1) |
| | | | | |
Fe1(9d) coordination | | | | | , |
Fe1—O1 ×2 | 2.0261 (4) | 2.0268 (4) | 2.0279 (4) | 2.0288 (4) | 2.0309 (7) |
Fe1—O2 ×2 | 2.0453 (5) | 2.0469 (9) | 2.0486 (9) | 2.0506 (9) | 2.0534 (8) |
Fe1—O3 ×2 | 1.9576 (7) | 1.9574 (8) | 1.9569 (8) | 1.9571 (6) | 1.9580 (12) |
(Fe—O)ave | 2.010 | 2.010 | 2.011 | 2.012 | 2.014 |
Δ(min - max) | 0.088 | 0.090 | 0.092 | 0.094 | 0.095 |
Fe1—B1 ×2 | 3.0802 (1) | 3.0804 (1) | 3.0810 (10) | 3.0818 (1) | 3.0826 (1) |
Fe1—B2 ×2 | 3.9256 (3) | 3.9286 (3) | 3.9314 (3) | 3.9363 (3) | 3.9395 (4) |
| | | | | |
B1(9b) coordination | | | | | |
B1—O1 ×3 | 1.3816 (4) | 1.3812 (4) | 1.3808 (4) | 1.3815 (5) | 1.3800 (6) |
| | | | | |
B2(9e) coordination | | | | | |
B2—O2 | 1.3798 (8) | 1.3780 (8) | 1.3776 (8) | 1.3773 (9) | 1.3762 (12) |
B2–O3 ×2 | 1.3692 (12) | 1.3690 (12) | 1.3681 (12) | 1.3676 (13) | 1.3680 (17) |
(B2—O3)ave | 1.373 | 1.372 | 1.371 | 1.371 | 1.371 |
Δ(min - max) | 0.011 | 0.009 | 0.010 | 0.010 | 0.008 |
| | | | | |
Fe chains | | | | | |
Fe1—Fe1intra | 3.1779 (1) | 3.1793 (1) | 3.1815 (1) | 3.1848 (1) | 3.1876 (1) |
Fe1—Fe1inter | 4.4077 (1) | 4.4088 (1) | 4.4095 (1) | 4.4109 (1) | 4.4116 (2) |
Fe1—O1—Fe1 | 103.300 (19) | 103.316 (19) | 103.33 (2) | 103.42 (2) | 103.40 (3) |
Fe1—O2—Fe1 | 101.95 (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 topDebye 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>zero (Å2) | <u2>static (Å2) | R (%) |
(Nd.Bi) | 123 (1) | 213 (2) | 0.0013659 | 0.00126 (11) | 0.92 |
| | | 0.0011826 | 0.00126 (11) | 0.90 |
Fe1 | 253 (2) | 439 (3) | 0.0017176 | 0.00106 (7) | 0.85 |
| | | 0.0014827 | 0.00110 (7) | 0.69 |
B1 | 569 (13) | 1014 (16) | 0.0039438 | 0.0001 (2) | 2.12 |
| | | 0.0033177 | 0.00045 (14) | 1.52 |
B2 | 528 (11) | 938 (12) | 0.0042475 | 0.0002 (2) | 2.02 |
| | | 0.0035888 | 0.00058 (13) | 1.08 |