research papers
Analysis of Bragg diffraction is the normal route to the structure of crystalline materials. Here we demonstrate the use of total neutron diffraction in determining the local structure in the disordered lanthanum molybdate LaMo2O5. An average structure with space-group symmetry P63/mmc accounts for the Bragg scattering and shows that the compound contains the rare Mo6O18 cluster and a unique type of Mo-Mo bonded sheet. However, this gives an incomplete picture of the structure, since it does not reveal how the sites with fractional occupancy are occupied at a local level. Two models describing possible local structures are constructed by removing symmetry elements present in the average structure. Total correlation functions, T(r), calculated from these structures, with space-group symmetry P63mc and P3m1, are compared with the experimental T(r) to show the validity of these local structures. The close relationship between the T(r)'s of the component structures gives an insight into why disorder occurs in LaMo2O5. The calculated and experimental T(r)'s for a model compound, Zn2Mo3O8, are compared to show the agreement expected from an ordered crystalline material. Remaining discrepancies between our model and the experimental T(r) give an insight into the origin of additional disorder in LaMo2O5.
Keywords: Lanthanum dimolybdenum pentaoxide; Dizinc trimolybdenum octaoxide; Total neutron scattering.
Supporting information
Computing details top
Cell refinement: TF12LS (David et al., 1992) for lamo2o5; TF12LS (David et al. (1992) for zn2mo3o8. For both compounds, program(s) used to refine structure: TF12LS (David et al., 1992).
(lamo2o5) lanthanum molybdenum oxide top
Crystal data top
LaMo2O5 | Z = 12 |
Mr = 410.79 | Neutron radiation, λ = time-of-flight Å |
Hexagonal, P63/mmc | Cell parameters from 312 reflections |
Hall symbol: -P 6c 2c | T = 18 K |
a = 8.3680 (7) Å | Powder, black |
c = 19.13687 (4) Å | × × mm |
V = 1160.5 (1) Å3 |
Data collection top
Lad tof neutron diffractometer | h = 0→7 |
Radiation source: spallation source | k = 0→4 |
time of flight neutron diffraction scans | l = 0→20 |
312 measured reflections |
Refinement top
Refinement on Inet | 39 parameters |
Least-squares matrix: full | 1/[Yi] |
wR(F2) = 0.048 | (Δ/σ)max = 0.25 |
312 reflections |
Crystal data top
LaMo2O5 | V = 1160.5 (1) Å3 |
Mr = 410.79 | Z = 12 |
Hexagonal, P63/mmc | Neutron radiation, λ = time-of-flight Å |
a = 8.3680 (7) Å | T = 18 K |
c = 19.13687 (4) Å | × × mm |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | Occ. (<1) | |
La1 | 0.5112 (8) | 0.4888 (8) | 0.8438 (8) | 0.010 (2)* | 0.5 |
La2 | 0.00000 | 0.00000 | 0.260 (1) | 0.010 (2)* | 0.5 |
La3 | 0.33333 | 0.66667 | 0.984 (1) | 0.010 (2)* | 0.5 |
La4 | 0.33333 | 0.66667 | 0.012 (1) | 0.010 (2)* | 0.5 |
Mo1 | 0.1066 (6) | 0.8934 (6) | 0.9428 (3) | 0.008 (1)* | |
Mo2 | 0.769 (1) | 0.231 (1) | 0.6868 (8) | 0.008 (9)* | 0.5 |
Mo3 | 0.561 (1) | 0.439 (1) | 0.1784 (7) | 0.008 (9)* | 0.5 |
O1 | 0.330 (1) | 0.000 (1) | 0.242 (7) | 0.0044 (9)* | 0.5 |
O2 | 0.33333 | 0.66667 | 0.2617 (7) | 0.0044 (9)* | 0.5 |
O3 | 0.33333 | 0.66667 | 0.752 (1) | 0.0044 (9)* | 0.5 |
O4 | 0.1138 (6) | 0.2276 (7) | 0.1234 (3) | 0.0044 (9)* | |
O5 | 0.560 (2) | 0.120 (3) | 0.6157 (9) | 0.0044 (9)* | 0.5 |
O6 | 0.454 (1) | 0.2268 (7) | 0.1130 (5) | 0.0044 (9)* | |
O7 | 0.00000 | 0.334 (1) | 0.00000 | 0.0044 (9)* | |
O10 | 0.33333 | 0.66667 | 0.399 (1) | 0.0044 (9)* | 0.5 |
Bond lengths (Å) top
La1—O1 | 2.4 (1) | Mo1—O7 | 1.977 (8) |
La1—O2 | 2.75 (2) | Mo1—O6 | 2.05 (1) |
La1—O3 | 3.16 (1) | Mo1—O4 | 2.041 (8) |
La1—O7 | 3.30 (1) | Mo2—Mo2 | 2.56 (2) |
La1—O4 | 2.903 (9) | Mo2—Mo3 | 2.87 (1) |
La1—O10 | 2.48 (2) | Mo2—O1 | 1.99 (8) |
La2—O1 | 2.76 (1) | Mo2—O2 | 2.06 (2) |
La2—O4 | 2.78 (2) | Mo2—O4 | 2.09 (2) |
La2—O4 | 3.09 (2) | Mo2—O5 | 2.03 (2) |
La3—O5 | 2.95 (3) | Mo3—Mo3 | 2.65 (2) |
La3—O7 | 2.804 (5) | Mo3—O1 | 2.07 (8) |
La3—O6 | 2.42 (2) | Mo3—O3 | 2.03 (1) |
La4—O6 | 2.52 (4) | Mo3—O5 | 2.13 (3) |
La4—O7 | 2.797 (5) | Mo3—O6 | 1.98 (1) |
La4—O10 | 2.16 (3) | Mo1—Mo1 | 2.678 (7) |
Mo1—Mo1 | 2.675 (7) | Mo1—O6 | 2.05 (1) |
Mo1—Mo1 | 2.678 (7) | Mo3—O6 | 1.977 (8) |
(zn2mo3o8) zinc molybdate top
Crystal data top
Zn2Mo3O8 | Z = 12 |
Mr = 546.6 | Neutron radiation, λ = time-of-flight Å |
Hexagonal, P63mc | Cell parameters from 309 reflections |
Hall symbol: P 6c -2c | T = 18 K |
a = 5.77322 (1) Å | Powder, black/green |
c = 9.91231 (4) Å | × × mm |
V = 286.12 (1) Å3 |
Data collection top
Lad tof neutron diffractometer | h = 0→6 |
Radiation source: spallation source | k = 0→3 |
time of flight neutron diffraction scans | l = −13→13 |
309 measured reflections |
Refinement top
Refinement on Inet | 29 parameters |
Least-squares matrix: full | 1/[Yi] |
wR(F2) = 0.047 | (Δ/σ)max = 0.001 |
309 reflections |
Crystal data top
Zn2Mo3O8 | V = 286.12 (1) Å3 |
Mr = 546.6 | Z = 12 |
Hexagonal, P63mc | Neutron radiation, λ = time-of-flight Å |
a = 5.77322 (1) Å | T = 18 K |
c = 9.91231 (4) Å | × × mm |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | ||
Zn1 | 0.33333 | 0.66667 | 0.5155 (4) | 0.0039 (5)* | |
Zn2 | 0.33333 | 0.66667 | 0.9491 (6) | 0.0039 (5)* | |
Mo1 | 0.1475 (2) | 0.8525 (2) | 0.25 | 0.0032 (5)* | |
O1 | 0.00000 | 0.00000 | 0.8921 (5) | 0.0044 (3)* | |
O2 | 0.33333 | 0.66667 | 0.1450 (5) | 0.0044 (3)* | |
O3 | 0.4881 (3) | 0.5119 (3) | 0.3658 (3) | 0.0044 (3)* | |
O4 | 0.1662 (3) | 0.8338 (3) | 0.6334 (4) | 0.0044 (3)* |
Bond lengths (Å) top
Mo1—Mo1 | 2.554 (2) | Zn1—O3 | 2.144 (4) |
Mo1—O1 | 2.039 (4) | Zn1—O4 | 2.039 (3) |
Mo1—O2 | 2.194 (3) | Zn2—O2 | 1.942 (8) |
Mo1—O3 | 2.071 (3) | Zn2—O4 | 1.968 (3) |
Mo1—O4 | 1.955 (4) |
Experimental details
(lamo2o5) | (zn2mo3o8) | |
Crystal data | ||
Chemical formula | LaMo2O5 | Zn2Mo3O8 |
Mr | 410.79 | 546.6 |
Crystal system, space group | Hexagonal, P63/mmc | Hexagonal, P63mc |
Temperature (K) | 18 | 18 |
a, c (Å) | 8.3680 (7), 19.13687 (4) | 5.77322 (1), 9.91231 (4) |
V (Å3) | 1160.5 (1) | 286.12 (1) |
Z | 12 | 12 |
Radiation type | Neutron, λ = time-of-flight Å | Neutron, λ = time-of-flight Å |
µ (mm−1) | ? | ? |
Crystal size (mm) | × × | × × |
Data collection | ||
Diffractometer | Lad tof neutron diffractometer | Lad tof neutron diffractometer |
Absorption correction | – | – |
No. of measured, independent and observed (?) reflections | 312, ?, ? | 309, ?, ? |
Rint | ? | ? |
Refinement | ||
R[F2 > 2σ(F2)], wR(F2), S | ?, 0.048, ? | ?, 0.047, ? |
No. of reflections | 312 | 309 |
No. of parameters | 39 | 29 |
No. of restraints | ? | ? |
(Δ/σ)max | 0.25 | 0.001 |
Δρmax, Δρmin (e Å−3) | ?, ? | ?, ? |
Computer programs: TF12LS (David et al., 1992), TF12LS (David et al. (1992).
Selected bond lengths (Å) for (lamo2o5) top
La1—O1 | 2.4 (1) | Mo1—O7 | 1.977 (8) |
La1—O2 | 2.75 (2) | Mo1—O6 | 2.05 (1) |
La1—O3 | 3.16 (1) | Mo1—O4 | 2.041 (8) |
La1—O7 | 3.30 (1) | Mo2—Mo2 | 2.56 (2) |
La1—O4 | 2.903 (9) | Mo2—Mo3 | 2.87 (1) |
La1—O10 | 2.48 (2) | Mo2—O1 | 1.99 (8) |
La2—O1 | 2.76 (1) | Mo2—O2 | 2.06 (2) |
La2—O4 | 2.78 (2) | Mo2—O4 | 2.09 (2) |
La2—O4 | 3.09 (2) | Mo2—O5 | 2.03 (2) |
La3—O5 | 2.95 (3) | Mo3—Mo3 | 2.65 (2) |
La3—O7 | 2.804 (5) | Mo3—O1 | 2.07 (8) |
La3—O6 | 2.42 (2) | Mo3—O3 | 2.03 (1) |
La4—O6 | 2.52 (4) | Mo3—O5 | 2.13 (3) |
La4—O7 | 2.797 (5) | Mo3—O6 | 1.98 (1) |
La4—O10 | 2.16 (3) | Mo1—Mo1 | 2.678 (7) |
Mo1—Mo1 | 2.675 (7) | Mo1—O6 | 2.05 (1) |
Mo1—Mo1 | 2.678 (7) | Mo3—O6 | 1.977 (8) |