Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270108015862/sq3145sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270108015862/sq3145Isup2.hkl |
To avoid losses of magnesium and zinc due to their vapour pressure at higher temperatures, the alloys were prepared in two steps. First, powders of the pure metals with a stoichiometry Ce:Mg:Zn = 1:1:4 were pressed into a pellet, enclosed in an evacuated silica ampoule (internal pressure 10-5 – 10 -6 Pa) and placed in a resistance furnace with a thermocouple controller. The heating process was carried out in a consecutive order, increasing the temperature from 673 to 1073 K over 6 d. The alloy was then annealed at this temperature for 4 h and slowly cooled down to room temperature. In the second step, the pellet was remelted in an arc furnace under an argon atmosphere at least three times in order to ensure homogeneity. The total weight loss after the melting procedures was less than 2 wt.%. The brittle sample was stable in air, showing a metallic lustre. Wavelength-dispersive spectrometry and electron probe microanalysis (CAMECA SX100 analyser) were used to control [determine?] the number of phases and their content in the sample. Various point analyses on this phase were in good agreement with the ideal composition determined by the single-crystal X-ray data (an average result is 17.6 at.% Ce, 14.7 at.% Mg and 67.7 at.% Zn). Irregularly shaped single crystals, exhibiting metallic lustre, were isolated by mechanical fragmentation from the alloys.
The systematic absences indicated five possible space groups, Fm3 (No. 202), F23 (No. 196), F43m (No. 216), Fm3m (No. 225) and F432 (No. 209). The statistical test of the distribution of the E values (Farrugia, 1999) suggested that the structure is non-centrosymmetric with a probability of 73.49%. The structure solution and refinement clearly indicated that Ce20Mg19Zn81 crystallizes in the non-centrosymmetric space group F43m. The occupancy parameters were refined in separate series of least-squares cycles. No significant deviations were found and in the final cycles the ideal values were assumed again. After that, the data were refined with anisotropic displacement parameters for all atoms. The atomic coordinates were standardized using the STRUCTURETIDY program (Gelato & Parthé, 1987). The final difference Fourier syntheses revealed no significant residual peaks: the highest maximum residual electron density was 1.62 e Å-3 from Zn3 and the deepest hole was -1.89 e Å-3 from Zn1.
Data collection: CrysAlis CCD (Oxford Diffraction, 2004); cell refinement: CrysAlis CCD (Oxford Diffraction, 2004); data reduction: CrysAlis RED (Oxford Diffraction, 2005); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).
Ce20Mg19Zn81 | Dx = 5.969 Mg m−3 |
Mr = 8559.26 | Mo Kα radiation, λ = 0.71073 Å |
Cubic, F43m | Cell parameters from 544 reflections |
Hall symbol: F -4 2 3 | θ = 3.8–26.3° |
a = 21.1979 (8) Å | µ = 29.39 mm−1 |
V = 9525.3 (6) Å3 | T = 295 K |
Z = 4 | Irregularly shaped, metallic dark grey |
F(000) = 15272 | 0.11 × 0.09 × 0.07 mm |
Oxford Diffraction Xcalibur diffractometer | 544 independent reflections |
Radiation source: fine-focus sealed tube | 388 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.034 |
Detector resolution: 0 pixels mm-1 | θmax = 26.3°, θmin = 3.8° |
ω scans | h = −15→15 |
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2005) | k = 0→18 |
Tmin = 0.056, Tmax = 0.122 | l = 3→26 |
1009 measured reflections |
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0544P)2] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.044 | (Δ/σ)max < 0.001 |
wR(F2) = 0.101 | Δρmax = 1.63 e Å−3 |
S = 1.01 | Δρmin = −1.89 e Å−3 |
544 reflections | Extinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
73 parameters | Extinction coefficient: 0.000081 (14) |
0 restraints | Absolute structure: Flack (1983), with how many Friedel pairs? |
Primary atom site location: structure-invariant direct methods | Absolute structure parameter: 0.3 (2) |
Ce20Mg19Zn81 | Z = 4 |
Mr = 8559.26 | Mo Kα radiation |
Cubic, F43m | µ = 29.39 mm−1 |
a = 21.1979 (8) Å | T = 295 K |
V = 9525.3 (6) Å3 | 0.11 × 0.09 × 0.07 mm |
Oxford Diffraction Xcalibur diffractometer | 544 independent reflections |
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2005) | 388 reflections with I > 2σ(I) |
Tmin = 0.056, Tmax = 0.122 | Rint = 0.034 |
1009 measured reflections |
R[F2 > 2σ(F2)] = 0.044 | 0 restraints |
wR(F2) = 0.101 | Δρmax = 1.63 e Å−3 |
S = 1.01 | Δρmin = −1.89 e Å−3 |
544 reflections | Absolute structure: Flack (1983), with how many Friedel pairs? |
73 parameters | Absolute structure parameter: 0.3 (2) |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger. |
x | y | z | Uiso*/Ueq | ||
Ce1 | 0.39743 (11) | 0.39743 (11) | 0.39743 (11) | 0.0322 (10) | |
Ce2 | 0.15367 (10) | 0.15367 (10) | 0.15367 (10) | 0.0333 (10) | |
Ce3 | 0.17469 (15) | 0.0000 | 0.0000 | 0.0363 (8) | |
Ce4 | −0.03469 (16) | 0.2500 | 0.2500 | 0.0341 (7) | |
Mg1 | 0.2500 | 0.2500 | 0.2500 | 0.036 (10) | |
Mg2 | 0.3314 (7) | 0.0000 | 0.0000 | 0.040 (4) | |
Mg3 | 0.1049 (5) | 0.1049 (5) | −0.2255 (7) | 0.050 (4) | |
Zn1 | 0.0000 | 0.0000 | 0.0000 | 0.045 (4) | |
Zn2 | 0.0776 (3) | 0.0776 (3) | −0.0776 (3) | 0.059 (3) | |
Zn3 | 0.2005 (3) | 0.2005 (3) | −0.2005 (3) | 0.074 (3) | |
Zn4 | 0.1718 (2) | 0.3282 (2) | −0.1718 (2) | 0.045 (2) | |
Zn5 | 0.0452 (2) | 0.4548 (2) | −0.0452 (2) | 0.0348 (19) | |
Zn6 | 0.0708 (2) | 0.0708 (2) | 0.0708 (2) | 0.0374 (19) | |
Zn7 | 0.20822 (16) | 0.20822 (16) | 0.3834 (2) | 0.0443 (13) | |
Zn8 | 0.14745 (15) | 0.14745 (15) | 0.0018 (3) | 0.0371 (11) | |
Zn9 | 0.14003 (19) | 0.35997 (19) | −0.0455 (3) | 0.0669 (17) | |
Zn10 | 0.03414 (15) | 0.11980 (15) | 0.26195 (15) | 0.0393 (9) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ce1 | 0.0322 (10) | 0.0322 (10) | 0.0322 (10) | 0.0015 (10) | 0.0015 (10) | 0.0015 (10) |
Ce2 | 0.0333 (10) | 0.0333 (10) | 0.0333 (10) | 0.0029 (10) | 0.0029 (10) | 0.0029 (10) |
Ce3 | 0.0403 (18) | 0.0344 (10) | 0.0344 (10) | 0.000 | 0.000 | −0.0036 (16) |
Ce4 | 0.0469 (19) | 0.0278 (9) | 0.0278 (9) | 0.000 | 0.000 | −0.0008 (14) |
Mg1 | 0.036 (10) | 0.036 (10) | 0.036 (10) | 0.000 | 0.000 | 0.000 |
Mg2 | 0.022 (9) | 0.049 (7) | 0.049 (7) | 0.000 | 0.000 | −0.031 (11) |
Mg3 | 0.044 (5) | 0.044 (5) | 0.061 (9) | −0.001 (7) | 0.018 (5) | 0.018 (5) |
Zn1 | 0.045 (4) | 0.045 (4) | 0.045 (4) | 0.000 | 0.000 | 0.000 |
Zn2 | 0.059 (3) | 0.059 (3) | 0.059 (3) | 0.031 (4) | −0.031 (4) | −0.031 (4) |
Zn3 | 0.074 (3) | 0.074 (3) | 0.074 (3) | 0.003 (4) | −0.003 (4) | −0.003 (4) |
Zn4 | 0.045 (2) | 0.045 (2) | 0.045 (2) | 0.003 (2) | 0.003 (2) | −0.003 (2) |
Zn5 | 0.0348 (19) | 0.0348 (19) | 0.0348 (19) | −0.001 (2) | −0.001 (2) | 0.001 (2) |
Zn6 | 0.0374 (19) | 0.0374 (19) | 0.0374 (19) | 0.003 (2) | 0.003 (2) | 0.003 (2) |
Zn7 | 0.0442 (18) | 0.0442 (18) | 0.044 (3) | 0.003 (2) | 0.0069 (17) | 0.0069 (17) |
Zn8 | 0.0389 (15) | 0.0389 (15) | 0.033 (2) | 0.0114 (19) | 0.0052 (16) | 0.0052 (16) |
Zn9 | 0.073 (3) | 0.073 (3) | 0.054 (4) | 0.027 (3) | −0.0068 (19) | 0.0068 (19) |
Zn10 | 0.0401 (18) | 0.0391 (17) | 0.039 (2) | 0.0089 (15) | −0.0053 (15) | 0.0001 (14) |
Ce1—Zn7i | 3.181 (6) | Zn1—Zn6xxxii | 2.598 (8) |
Ce1—Zn7ii | 3.181 (6) | Zn1—Zn6xxiv | 2.598 (8) |
Ce1—Zn7iii | 3.181 (6) | Zn1—Zn6xvii | 2.598 (8) |
Ce1—Zn10iv | 3.238 (4) | Zn1—Zn2xxxii | 2.850 (12) |
Ce1—Zn10iii | 3.238 (4) | Zn1—Zn2xxiv | 2.850 (12) |
Ce1—Zn10i | 3.238 (4) | Zn1—Zn2 | 2.850 (12) |
Ce1—Zn10v | 3.238 (4) | Zn1—Zn2xvii | 2.850 (12) |
Ce1—Zn10vi | 3.238 (4) | Zn2—Zn8 | 2.686 (6) |
Ce1—Zn10ii | 3.238 (4) | Zn2—Zn8xxvi | 2.686 (6) |
Ce1—Zn9vii | 3.334 (5) | Zn2—Zn8xviii | 2.686 (6) |
Ce1—Zn9viii | 3.334 (5) | Zn2—Ce3xxx | 3.106 (7) |
Ce1—Zn9ix | 3.334 (5) | Zn2—Ce3x | 3.106 (7) |
Ce2—Zn6 | 3.044 (9) | Zn2—Zn6xvii | 3.152 (7) |
Ce2—Zn8x | 3.225 (6) | Zn2—Zn6xxiv | 3.152 (7) |
Ce2—Zn8xi | 3.225 (6) | Zn2—Zn6 | 3.152 (7) |
Ce2—Zn8 | 3.225 (6) | Zn2—Mg3xviii | 3.241 (16) |
Ce2—Zn7ix | 3.244 (3) | Zn3—Zn4 | 2.842 (8) |
Ce2—Zn7xii | 3.244 (3) | Zn3—Zn4xxvii | 2.842 (8) |
Ce2—Zn7viii | 3.244 (3) | Zn3—Zn4ii | 2.842 (8) |
Ce2—Zn7xiii | 3.244 (3) | Zn3—Mg3xviii | 2.914 (16) |
Ce2—Zn7xiv | 3.244 (3) | Zn3—Mg3xxvi | 2.914 (16) |
Ce2—Zn7vii | 3.244 (3) | Zn3—Zn3ii | 2.968 (9) |
Ce2—Zn10xv | 3.493 (3) | Zn3—Zn3xxvii | 2.968 (9) |
Ce2—Zn10xvi | 3.493 (3) | Zn3—Zn3xxxiii | 2.968 (9) |
Ce3—Zn6xvii | 3.059 (3) | Zn4—Zn3ii | 2.842 (8) |
Ce3—Zn6 | 3.059 (3) | Zn4—Zn3xxvii | 2.842 (8) |
Ce3—Zn2xvii | 3.106 (7) | Zn4—Zn9xxxiv | 2.840 (9) |
Ce3—Zn2 | 3.106 (7) | Zn4—Zn9xxxv | 2.840 (9) |
Ce3—Zn8xi | 3.179 (3) | Zn4—Zn9 | 2.840 (9) |
Ce3—Zn8 | 3.179 (3) | Zn4—Mg3xviii | 2.959 (13) |
Ce3—Zn8xviii | 3.179 (3) | Zn4—Mg3xxxvi | 2.959 (13) |
Ce3—Zn8xvii | 3.179 (3) | Zn4—Mg3xxvii | 2.959 (13) |
Ce3—Zn10x | 3.224 (3) | Zn5—Zn5xxxvii | 2.713 (12) |
Ce3—Zn10xix | 3.224 (3) | Zn5—Zn5xxxviii | 2.713 (12) |
Ce3—Zn10xx | 3.224 (3) | Zn5—Zn5xxiv | 2.713 (12) |
Ce3—Zn10xxi | 3.224 (3) | Zn5—Zn9 | 2.842 (8) |
Ce4—Zn10xxii | 3.132 (3) | Zn5—Zn9xxxv | 2.841 (8) |
Ce4—Zn10xiv | 3.132 (3) | Zn5—Zn9xxxiv | 2.842 (8) |
Ce4—Zn10 | 3.132 (3) | Zn5—Mg2xxxix | 2.945 (14) |
Ce4—Zn10xvi | 3.132 (3) | Zn5—Mg2x | 2.945 (14) |
Ce4—Zn8iii | 3.170 (4) | Zn5—Mg2ii | 2.945 (14) |
Ce4—Zn8x | 3.170 (4) | Zn5—Ce1xl | 3.574 (4) |
Ce4—Zn9x | 3.305 (6) | Zn5—Ce1vii | 3.574 (4) |
Ce4—Zn9iii | 3.305 (6) | Zn5—Ce1xli | 3.574 (4) |
Ce4—Zn7xii | 3.443 (6) | Zn6—Zn8x | 2.724 (6) |
Ce4—Zn7ix | 3.443 (6) | Zn6—Zn8xi | 2.724 (6) |
Ce4—Mg3xxiii | 3.456 (11) | Zn6—Zn8 | 2.724 (6) |
Ce4—Mg3xxiv | 3.456 (11) | Zn6—Ce3xi | 3.058 (3) |
Mg1—Zn7ii | 3.092 (5) | Zn6—Ce3x | 3.058 (3) |
Mg1—Zn7xii | 3.092 (5) | Zn6—Zn2xxiv | 3.152 (7) |
Mg1—Zn7ix | 3.092 (5) | Zn6—Zn2xvii | 3.152 (7) |
Mg1—Zn7i | 3.092 (5) | Zn7—Zn7ii | 2.505 (10) |
Mg1—Zn7viii | 3.092 (5) | Zn7—Zn10viii | 2.640 (5) |
Mg1—Zn7iii | 3.092 (5) | Zn7—Zn10xlii | 2.640 (5) |
Mg1—Zn7 | 3.092 (5) | Zn7—Zn7xii | 2.746 (8) |
Mg1—Zn7xiii | 3.092 (5) | Zn7—Zn7viii | 2.746 (8) |
Mg1—Zn7xi | 3.092 (5) | Zn7—Ce1ii | 3.181 (6) |
Mg1—Zn7xiv | 3.092 (5) | Zn7—Ce2xiv | 3.244 (3) |
Mg1—Zn7vii | 3.092 (5) | Zn7—Ce2vii | 3.244 (3) |
Mg1—Zn7x | 3.092 (5) | Zn7—Ce4i | 3.443 (5) |
Mg2—Zn5xxv | 2.945 (14) | Zn8—Zn10xi | 2.589 (4) |
Mg2—Zn5ii | 2.945 (14) | Zn8—Zn10xix | 2.589 (4) |
Mg2—Zn10x | 3.024 (8) | Zn8—Mg3xviii | 2.944 (10) |
Mg2—Zn10xix | 3.024 (8) | Zn8—Mg3xxvi | 2.945 (10) |
Mg2—Zn10xx | 3.024 (8) | Zn8—Ce4xi | 3.170 (4) |
Mg2—Zn10xxi | 3.024 (8) | Zn8—Ce3x | 3.179 (3) |
Mg2—Zn9xxv | 3.179 (5) | Zn9—Zn10xliii | 2.712 (5) |
Mg2—Zn9ii | 3.179 (5) | Zn9—Zn10xi | 2.712 (5) |
Mg2—Zn9xi | 3.179 (5) | Zn9—Zn9xxxv | 2.833 (10) |
Mg2—Zn9xviii | 3.179 (5) | Zn9—Zn9xxxiv | 2.833 (10) |
Mg2—Ce1xiv | 3.378 (7) | Zn9—Mg2x | 3.179 (5) |
Mg3—Zn3 | 2.914 (16) | Zn9—Mg2ii | 3.179 (5) |
Mg3—Zn8xxvi | 2.944 (10) | Zn9—Mg3xviii | 3.203 (14) |
Mg3—Zn8xviii | 2.945 (10) | Zn9—Mg3xxxvi | 3.203 (14) |
Mg3—Zn4xxvii | 2.959 (13) | Zn9—Ce4xi | 3.305 (6) |
Mg3—Zn10xxiv | 3.063 (10) | Zn9—Ce1vii | 3.334 (5) |
Mg3—Zn10xxviii | 3.064 (10) | Zn10—Zn10xv | 2.568 (6) |
Mg3—Zn9xxix | 3.203 (14) | Zn10—Zn8x | 2.589 (4) |
Mg3—Zn9xxvi | 3.203 (14) | Zn10—Zn7xii | 2.640 (5) |
Mg3—Zn2 | 3.241 (16) | Zn10—Zn9x | 2.712 (5) |
Mg3—Ce3xxx | 3.325 (13) | Zn10—Mg2xi | 3.024 (8) |
Mg3—Ce4xxxi | 3.456 (11) | Zn10—Mg3xxiv | 3.063 (10) |
Mg3—Ce4xx | 3.456 (11) | Zn10—Ce3xi | 3.224 (3) |
Zn1—Zn6 | 2.598 (8) | Zn10—Ce1ii | 3.238 (4) |
Zn7i—Ce1—Zn7ii | 51.14 (16) | Zn6xvii—Zn1—Zn2xxiv | 180.00 (16) |
Zn7i—Ce1—Zn7iii | 51.14 (16) | Zn2xxxii—Zn1—Zn2xxiv | 109.5 |
Zn7ii—Ce1—Zn7iii | 51.14 (16) | Zn6—Zn1—Zn2 | 70.53 (16) |
Zn7i—Ce1—Zn10iv | 71.36 (8) | Zn6xxxii—Zn1—Zn2 | 180.00 (16) |
Zn7ii—Ce1—Zn10iv | 48.56 (9) | Zn6xxiv—Zn1—Zn2 | 70.53 (16) |
Zn7iii—Ce1—Zn10iv | 98.80 (14) | Zn6xvii—Zn1—Zn2 | 70.53 (16) |
Zn7i—Ce1—Zn10iii | 48.56 (9) | Zn2xxxii—Zn1—Zn2 | 109.5 |
Zn7ii—Ce1—Zn10iii | 71.36 (8) | Zn2xxiv—Zn1—Zn2 | 109.5 |
Zn7iii—Ce1—Zn10iii | 98.80 (14) | Zn6—Zn1—Zn2xvii | 70.53 (16) |
Zn10iv—Ce1—Zn10iii | 46.72 (11) | Zn6xxxii—Zn1—Zn2xvii | 70.53 (16) |
Zn7i—Ce1—Zn10i | 98.80 (14) | Zn6xxiv—Zn1—Zn2xvii | 180.00 (16) |
Zn7ii—Ce1—Zn10i | 48.56 (9) | Zn6xvii—Zn1—Zn2xvii | 70.53 (16) |
Zn7iii—Ce1—Zn10i | 71.36 (8) | Zn2xxxii—Zn1—Zn2xvii | 109.5 |
Zn10iv—Ce1—Zn10i | 66.38 (11) | Zn2xxiv—Zn1—Zn2xvii | 109.5 |
Zn10iii—Ce1—Zn10i | 110.35 (8) | Zn2—Zn1—Zn2xvii | 109.5 |
Zn7i—Ce1—Zn10v | 98.80 (14) | Zn8—Zn2—Zn8xxvi | 112.8 (2) |
Zn7ii—Ce1—Zn10v | 71.36 (8) | Zn8—Zn2—Zn8xviii | 112.8 (2) |
Zn7iii—Ce1—Zn10v | 48.56 (9) | Zn8xxvi—Zn2—Zn8xviii | 112.8 (2) |
Zn10iv—Ce1—Zn10v | 110.35 (8) | Zn8—Zn2—Zn1 | 105.9 (3) |
Zn10iii—Ce1—Zn10v | 141.44 (17) | Zn8xxvi—Zn2—Zn1 | 105.9 (3) |
Zn10i—Ce1—Zn10v | 46.72 (11) | Zn8xviii—Zn2—Zn1 | 105.9 (3) |
Zn7i—Ce1—Zn10vi | 48.56 (9) | Zn8—Zn2—Ce3xxx | 177.3 (5) |
Zn7ii—Ce1—Zn10vi | 98.80 (14) | Zn8xxvi—Zn2—Ce3xxx | 66.10 (16) |
Zn7iii—Ce1—Zn10vi | 71.36 (8) | Zn8xviii—Zn2—Ce3xxx | 66.10 (16) |
Zn10iv—Ce1—Zn10vi | 110.35 (8) | Zn1—Zn2—Ce3xxx | 76.8 (2) |
Zn10iii—Ce1—Zn10vi | 66.38 (11) | Zn8—Zn2—Ce3x | 66.10 (16) |
Zn10i—Ce1—Zn10vi | 141.44 (17) | Zn8xxvi—Zn2—Ce3x | 66.10 (16) |
Zn10v—Ce1—Zn10vi | 110.35 (8) | Zn8xviii—Zn2—Ce3x | 177.3 (5) |
Zn7i—Ce1—Zn10ii | 71.36 (8) | Zn1—Zn2—Ce3x | 76.8 (2) |
Zn7ii—Ce1—Zn10ii | 98.80 (14) | Ce3xxx—Zn2—Ce3x | 114.91 (17) |
Zn7iii—Ce1—Zn10ii | 48.56 (9) | Zn8—Zn2—Ce3 | 66.10 (16) |
Zn10iv—Ce1—Zn10ii | 141.44 (17) | Zn8xxvi—Zn2—Ce3 | 177.3 (5) |
Zn10iii—Ce1—Zn10ii | 110.35 (8) | Zn8xviii—Zn2—Ce3 | 66.10 (16) |
Zn10i—Ce1—Zn10ii | 110.35 (8) | Zn1—Zn2—Ce3 | 76.8 (2) |
Zn10v—Ce1—Zn10ii | 66.38 (11) | Ce3xxx—Zn2—Ce3 | 114.91 (17) |
Zn10vi—Ce1—Zn10ii | 46.72 (11) | Ce3x—Zn2—Ce3 | 114.91 (17) |
Zn7i—Ce1—Zn9vii | 118.23 (11) | Zn8—Zn2—Zn6xvii | 123.12 (18) |
Zn7ii—Ce1—Zn9vii | 75.69 (13) | Zn8xxvi—Zn2—Zn6xvii | 123.12 (18) |
Zn7iii—Ce1—Zn9vii | 118.23 (11) | Zn8xviii—Zn2—Zn6xvii | 54.93 (17) |
Zn10iv—Ce1—Zn9vii | 48.71 (8) | Zn1—Zn2—Zn6xvii | 51.0 (2) |
Zn10iii—Ce1—Zn9vii | 90.10 (6) | Ce3xxx—Zn2—Zn6xvii | 58.50 (11) |
Zn10i—Ce1—Zn9vii | 48.71 (8) | Ce3x—Zn2—Zn6xvii | 127.8 (5) |
Zn10v—Ce1—Zn9vii | 90.10 (6) | Ce3—Zn2—Zn6xvii | 58.51 (11) |
Zn10vi—Ce1—Zn9vii | 156.19 (6) | Zn8—Zn2—Zn6xxiv | 123.12 (18) |
Zn10ii—Ce1—Zn9vii | 156.19 (6) | Zn8xxvi—Zn2—Zn6xxiv | 54.93 (17) |
Zn7i—Ce1—Zn9viii | 75.69 (13) | Zn8xviii—Zn2—Zn6xxiv | 123.12 (18) |
Zn7ii—Ce1—Zn9viii | 118.23 (11) | Zn1—Zn2—Zn6xxiv | 51.0 (2) |
Zn7iii—Ce1—Zn9viii | 118.23 (11) | Ce3xxx—Zn2—Zn6xxiv | 58.50 (11) |
Zn10iv—Ce1—Zn9viii | 90.10 (6) | Ce3x—Zn2—Zn6xxiv | 58.50 (11) |
Zn10iii—Ce1—Zn9viii | 48.71 (8) | Ce3—Zn2—Zn6xxiv | 127.8 (5) |
Zn10i—Ce1—Zn9viii | 156.19 (6) | Zn6xvii—Zn2—Zn6xxiv | 84.6 (4) |
Zn10v—Ce1—Zn9viii | 156.19 (6) | Zn8—Zn2—Zn6 | 54.93 (17) |
Zn10vi—Ce1—Zn9viii | 48.71 (8) | Zn8xxvi—Zn2—Zn6 | 123.12 (18) |
Zn10ii—Ce1—Zn9viii | 90.10 (6) | Zn8xviii—Zn2—Zn6 | 123.12 (18) |
Zn9vii—Ce1—Zn9viii | 113.06 (9) | Zn1—Zn2—Zn6 | 51.0 (2) |
Zn7i—Ce1—Zn9ix | 118.23 (11) | Ce3xxx—Zn2—Zn6 | 127.8 (5) |
Zn7ii—Ce1—Zn9ix | 118.23 (11) | Ce3x—Zn2—Zn6 | 58.50 (11) |
Zn7iii—Ce1—Zn9ix | 75.69 (13) | Ce3—Zn2—Zn6 | 58.51 (11) |
Zn10iv—Ce1—Zn9ix | 156.19 (6) | Zn6xvii—Zn2—Zn6 | 84.6 (4) |
Zn10iii—Ce1—Zn9ix | 156.19 (6) | Zn6xxiv—Zn2—Zn6 | 84.6 (4) |
Zn10i—Ce1—Zn9ix | 90.10 (6) | Zn8—Zn2—Mg3 | 114.2 (5) |
Zn10v—Ce1—Zn9ix | 48.71 (8) | Zn8xxvi—Zn2—Mg3 | 58.69 (19) |
Zn10vi—Ce1—Zn9ix | 90.10 (6) | Zn8xviii—Zn2—Mg3 | 58.69 (19) |
Zn10ii—Ce1—Zn9ix | 48.71 (8) | Zn1—Zn2—Mg3 | 139.9 (3) |
Zn9vii—Ce1—Zn9ix | 113.06 (9) | Ce3xxx—Zn2—Mg3 | 63.1 (3) |
Zn9viii—Ce1—Zn9ix | 113.06 (9) | Ce3x—Zn2—Mg3 | 119.3 (2) |
Zn6—Ce2—Zn8x | 51.42 (10) | Ce3—Zn2—Mg3 | 119.3 (2) |
Zn6—Ce2—Zn8xi | 51.42 (10) | Zn6xvii—Zn2—Mg3 | 103.4 (2) |
Zn8x—Ce2—Zn8xi | 85.22 (14) | Zn6xxiv—Zn2—Mg3 | 103.4 (2) |
Zn6—Ce2—Zn8 | 51.42 (10) | Zn6—Zn2—Mg3 | 169.1 (5) |
Zn8x—Ce2—Zn8 | 85.22 (14) | Zn8—Zn2—Mg3xviii | 58.69 (19) |
Zn8xi—Ce2—Zn8 | 85.22 (14) | Zn8xxvi—Zn2—Mg3xviii | 58.69 (19) |
Zn6—Ce2—Zn7ix | 125.95 (10) | Zn8xviii—Zn2—Mg3xviii | 114.2 (5) |
Zn8x—Ce2—Zn7ix | 79.03 (11) | Zn1—Zn2—Mg3xviii | 139.9 (3) |
Zn8xi—Ce2—Zn7ix | 154.90 (9) | Ce3xxx—Zn2—Mg3xviii | 119.3 (2) |
Zn8—Ce2—Zn7ix | 112.51 (8) | Ce3x—Zn2—Mg3xviii | 63.1 (3) |
Zn6—Ce2—Zn7xii | 125.95 (10) | Ce3—Zn2—Mg3xviii | 119.3 (2) |
Zn8x—Ce2—Zn7xii | 79.03 (11) | Zn6xvii—Zn2—Mg3xviii | 169.1 (5) |
Zn8xi—Ce2—Zn7xii | 112.51 (8) | Zn6xxiv—Zn2—Mg3xviii | 103.4 (2) |
Zn8—Ce2—Zn7xii | 154.90 (9) | Zn6—Zn2—Mg3xviii | 103.4 (2) |
Zn7ix—Ce2—Zn7xii | 45.42 (16) | Mg3—Zn2—Mg3xviii | 67.8 (5) |
Zn6—Ce2—Zn7viii | 125.95 (10) | Zn4—Zn3—Zn4xxvii | 111.3 (2) |
Zn8x—Ce2—Zn7viii | 112.51 (8) | Zn4—Zn3—Zn4ii | 111.3 (2) |
Zn8xi—Ce2—Zn7viii | 79.03 (11) | Zn4xxvii—Zn3—Zn4ii | 111.3 (2) |
Zn8—Ce2—Zn7viii | 154.90 (9) | Zn4—Zn3—Mg3xviii | 61.9 (3) |
Zn7ix—Ce2—Zn7viii | 89.03 (14) | Zn4xxvii—Zn3—Mg3xviii | 123.55 (18) |
Zn7xii—Ce2—Zn7viii | 50.08 (18) | Zn4ii—Zn3—Mg3xviii | 123.54 (18) |
Zn6—Ce2—Zn7xiii | 125.95 (10) | Zn4—Zn3—Mg3 | 123.54 (18) |
Zn8x—Ce2—Zn7xiii | 154.90 (9) | Zn4xxvii—Zn3—Mg3 | 61.9 (3) |
Zn8xi—Ce2—Zn7xiii | 79.03 (11) | Zn4ii—Zn3—Mg3 | 123.55 (18) |
Zn8—Ce2—Zn7xiii | 112.51 (8) | Mg3xviii—Zn3—Mg3 | 76.7 (5) |
Zn7ix—Ce2—Zn7xiii | 108.05 (19) | Zn4—Zn3—Mg3xxvi | 123.55 (18) |
Zn7xii—Ce2—Zn7xiii | 89.03 (14) | Zn4xxvii—Zn3—Mg3xxvi | 123.54 (18) |
Zn7viii—Ce2—Zn7xiii | 45.42 (16) | Zn4ii—Zn3—Mg3xxvi | 61.9 (3) |
Zn6—Ce2—Zn7xiv | 125.95 (10) | Mg3xviii—Zn3—Mg3xxvi | 76.7 (5) |
Zn8x—Ce2—Zn7xiv | 112.51 (8) | Mg3—Zn3—Mg3xxvi | 76.7 (5) |
Zn8xi—Ce2—Zn7xiv | 154.90 (9) | Zn4—Zn3—Zn3ii | 58.51 (19) |
Zn8—Ce2—Zn7xiv | 79.03 (11) | Zn4xxvii—Zn3—Zn3ii | 107.6 (2) |
Zn7ix—Ce2—Zn7xiv | 50.08 (18) | Zn4ii—Zn3—Zn3ii | 58.52 (19) |
Zn7xii—Ce2—Zn7xiv | 89.03 (14) | Mg3xviii—Zn3—Zn3ii | 111.3 (3) |
Zn7viii—Ce2—Zn7xiv | 108.05 (19) | Mg3—Zn3—Zn3ii | 169.5 (3) |
Zn7xiii—Ce2—Zn7xiv | 89.03 (14) | Mg3xxvi—Zn3—Zn3ii | 111.3 (3) |
Zn6—Ce2—Zn7vii | 125.95 (10) | Zn4—Zn3—Zn3xxvii | 58.51 (19) |
Zn8x—Ce2—Zn7vii | 154.90 (9) | Zn4xxvii—Zn3—Zn3xxvii | 58.51 (19) |
Zn8xi—Ce2—Zn7vii | 112.51 (8) | Zn4ii—Zn3—Zn3xxvii | 107.6 (2) |
Zn8—Ce2—Zn7vii | 79.03 (11) | Mg3xviii—Zn3—Zn3xxvii | 111.3 (3) |
Zn7ix—Ce2—Zn7vii | 89.03 (14) | Mg3—Zn3—Zn3xxvii | 111.3 (3) |
Zn7xii—Ce2—Zn7vii | 108.05 (19) | Mg3xxvi—Zn3—Zn3xxvii | 169.5 (3) |
Zn7viii—Ce2—Zn7vii | 89.03 (14) | Zn3ii—Zn3—Zn3xxvii | 60.0 |
Zn7xiii—Ce2—Zn7vii | 50.08 (18) | Zn4—Zn3—Zn3xxxiii | 107.6 (2) |
Zn7xiv—Ce2—Zn7vii | 45.42 (16) | Zn4xxvii—Zn3—Zn3xxxiii | 58.51 (19) |
Zn6—Ce2—Zn10xv | 80.91 (8) | Zn4ii—Zn3—Zn3xxxiii | 58.52 (19) |
Zn8x—Ce2—Zn10xv | 78.00 (7) | Mg3xviii—Zn3—Zn3xxxiii | 169.5 (3) |
Zn8xi—Ce2—Zn10xv | 45.12 (7) | Mg3—Zn3—Zn3xxxiii | 111.3 (3) |
Zn8—Ce2—Zn10xv | 128.16 (14) | Mg3xxvi—Zn3—Zn3xxxiii | 111.3 (3) |
Zn7ix—Ce2—Zn10xv | 111.75 (10) | Zn3ii—Zn3—Zn3xxxiii | 60.0 |
Zn7xii—Ce2—Zn10xv | 67.41 (10) | Zn3xxvii—Zn3—Zn3xxxiii | 60.0 |
Zn7viii—Ce2—Zn10xv | 45.95 (9) | Zn3—Zn4—Zn3ii | 63.0 (4) |
Zn7xiii—Ce2—Zn10xv | 77.04 (10) | Zn3—Zn4—Zn3xxvii | 63.0 (4) |
Zn7xiv—Ce2—Zn10xv | 152.48 (15) | Zn3ii—Zn4—Zn3xxvii | 63.0 (4) |
Zn7vii—Ce2—Zn10xv | 127.09 (12) | Zn3—Zn4—Zn9xxxiv | 178.1 (3) |
Zn6—Ce2—Zn10xvi | 80.91 (8) | Zn3ii—Zn4—Zn9xxxiv | 118.58 (19) |
Zn8x—Ce2—Zn10xvi | 45.12 (7) | Zn3xxvii—Zn4—Zn9xxxiv | 118.58 (19) |
Zn8xi—Ce2—Zn10xvi | 128.16 (14) | Zn3—Zn4—Zn9xxxv | 118.58 (19) |
Zn8—Ce2—Zn10xvi | 78.00 (7) | Zn3ii—Zn4—Zn9xxxv | 178.1 (3) |
Zn7ix—Ce2—Zn10xvi | 45.95 (9) | Zn3xxvii—Zn4—Zn9xxxv | 118.58 (19) |
Zn7xii—Ce2—Zn10xvi | 77.04 (10) | Zn9xxxiv—Zn4—Zn9xxxv | 59.8 (2) |
Zn7viii—Ce2—Zn10xvi | 127.09 (12) | Zn3—Zn4—Zn9 | 118.58 (19) |
Zn7xiii—Ce2—Zn10xvi | 152.48 (15) | Zn3ii—Zn4—Zn9 | 118.58 (19) |
Zn7xiv—Ce2—Zn10xvi | 67.41 (10) | Zn3xxvii—Zn4—Zn9 | 178.1 (3) |
Zn7vii—Ce2—Zn10xvi | 111.75 (10) | Zn9xxxiv—Zn4—Zn9 | 59.8 (2) |
Zn10xv—Ce2—Zn10xvi | 117.55 (4) | Zn9xxxv—Zn4—Zn9 | 59.8 (2) |
Zn6xvii—Ce3—Zn6 | 87.8 (3) | Zn3—Zn4—Mg3xviii | 60.3 (4) |
Zn6xvii—Ce3—Zn2xvii | 61.50 (14) | Zn3ii—Zn4—Mg3xviii | 113.7 (3) |
Zn6—Ce3—Zn2xvii | 61.50 (14) | Zn3xxvii—Zn4—Mg3xviii | 113.7 (3) |
Zn6xvii—Ce3—Zn2 | 61.50 (14) | Zn9xxxiv—Zn4—Mg3xviii | 117.8 (4) |
Zn6—Ce3—Zn2 | 61.50 (14) | Zn9xxxv—Zn4—Mg3xviii | 67.0 (3) |
Zn2xvii—Ce3—Zn2 | 97.0 (5) | Zn9—Zn4—Mg3xviii | 67.0 (3) |
Zn6xvii—Ce3—Zn8xi | 110.94 (15) | Zn3—Zn4—Mg3xxxvi | 113.7 (3) |
Zn6—Ce3—Zn8xi | 51.75 (11) | Zn3ii—Zn4—Mg3xxxvi | 60.3 (4) |
Zn2xvii—Ce3—Zn8xi | 50.59 (13) | Zn3xxvii—Zn4—Mg3xxxvi | 113.7 (3) |
Zn2—Ce3—Zn8xi | 113.21 (18) | Zn9xxxiv—Zn4—Mg3xxxvi | 67.0 (3) |
Zn6xvii—Ce3—Zn8 | 110.94 (15) | Zn9xxxv—Zn4—Mg3xxxvi | 117.8 (4) |
Zn6—Ce3—Zn8 | 51.75 (11) | Zn9—Zn4—Mg3xxxvi | 67.0 (3) |
Zn2xvii—Ce3—Zn8 | 113.21 (18) | Mg3xviii—Zn4—Mg3xxxvi | 118.39 (15) |
Zn2—Ce3—Zn8 | 50.59 (13) | Zn3—Zn4—Mg3xxvii | 113.7 (3) |
Zn8xi—Ce3—Zn8 | 86.8 (2) | Zn3ii—Zn4—Mg3xxvii | 113.7 (3) |
Zn6xvii—Ce3—Zn8xviii | 51.75 (11) | Zn3xxvii—Zn4—Mg3xxvii | 60.3 (4) |
Zn6—Ce3—Zn8xviii | 110.94 (15) | Zn9xxxiv—Zn4—Mg3xxvii | 67.0 (3) |
Zn2xvii—Ce3—Zn8xviii | 113.21 (18) | Zn9xxxv—Zn4—Mg3xxvii | 67.0 (3) |
Zn2—Ce3—Zn8xviii | 50.59 (13) | Zn9—Zn4—Mg3xxvii | 117.8 (4) |
Zn8xi—Ce3—Zn8xviii | 159.07 (17) | Mg3xviii—Zn4—Mg3xxvii | 118.38 (15) |
Zn8—Ce3—Zn8xviii | 89.5 (2) | Mg3xxxvi—Zn4—Mg3xxvii | 118.39 (15) |
Zn6xvii—Ce3—Zn8xvii | 51.75 (11) | Zn5xxxvii—Zn5—Zn5xxxviii | 60.0 |
Zn6—Ce3—Zn8xvii | 110.94 (15) | Zn5xxxvii—Zn5—Zn5xxiv | 60.0 |
Zn2xvii—Ce3—Zn8xvii | 50.59 (13) | Zn5xxxviii—Zn5—Zn5xxiv | 60.0 |
Zn2—Ce3—Zn8xvii | 113.21 (18) | Zn5xxxvii—Zn5—Zn9 | 120.10 (11) |
Zn8xi—Ce3—Zn8xvii | 89.5 (2) | Zn5xxxviii—Zn5—Zn9 | 179.88 (13) |
Zn8—Ce3—Zn8xvii | 159.07 (17) | Zn5xxiv—Zn5—Zn9 | 120.10 (11) |
Zn8xviii—Ce3—Zn8xvii | 86.8 (2) | Zn5xxxvii—Zn5—Zn9xxxv | 179.88 (12) |
Zn6xvii—Ce3—Zn10x | 155.47 (8) | Zn5xxxviii—Zn5—Zn9xxxv | 120.10 (11) |
Zn6—Ce3—Zn10x | 85.22 (15) | Zn5xxiv—Zn5—Zn9xxxv | 120.10 (11) |
Zn2xvii—Ce3—Zn10x | 94.69 (16) | Zn9—Zn5—Zn9xxxv | 59.8 (2) |
Zn2—Ce3—Zn10x | 132.72 (8) | Zn5xxxvii—Zn5—Zn9xxxiv | 120.10 (11) |
Zn8xi—Ce3—Zn10x | 47.70 (9) | Zn5xxxviii—Zn5—Zn9xxxiv | 120.10 (11) |
Zn8—Ce3—Zn10x | 82.76 (11) | Zn5xxiv—Zn5—Zn9xxxiv | 179.88 (13) |
Zn8xviii—Ce3—Zn10x | 151.82 (13) | Zn9—Zn5—Zn9xxxiv | 59.8 (2) |
Zn8xvii—Ce3—Zn10x | 109.54 (10) | Zn9xxxv—Zn5—Zn9xxxiv | 59.8 (2) |
Zn6xvii—Ce3—Zn10xix | 155.47 (8) | Zn5xxxvii—Zn5—Mg2xxxix | 113.41 (16) |
Zn6—Ce3—Zn10xix | 85.22 (15) | Zn5xxxviii—Zn5—Mg2xxxix | 62.6 (2) |
Zn2xvii—Ce3—Zn10xix | 132.72 (8) | Zn5xxiv—Zn5—Mg2xxxix | 113.41 (16) |
Zn2—Ce3—Zn10xix | 94.69 (16) | Zn9—Zn5—Mg2xxxix | 117.3 (3) |
Zn8xi—Ce3—Zn10xix | 82.76 (11) | Zn9xxxv—Zn5—Mg2xxxix | 66.63 (16) |
Zn8—Ce3—Zn10xix | 47.70 (9) | Zn9xxxiv—Zn5—Mg2xxxix | 66.63 (16) |
Zn8xviii—Ce3—Zn10xix | 109.54 (10) | Zn5xxxvii—Zn5—Mg2x | 113.41 (16) |
Zn8xvii—Ce3—Zn10xix | 151.82 (13) | Zn5xxxviii—Zn5—Mg2x | 113.41 (16) |
Zn10x—Ce3—Zn10xix | 46.94 (11) | Zn5xxiv—Zn5—Mg2x | 62.6 (2) |
Zn6xvii—Ce3—Zn10xx | 85.22 (15) | Zn9—Zn5—Mg2x | 66.63 (16) |
Zn6—Ce3—Zn10xx | 155.47 (8) | Zn9xxxv—Zn5—Mg2x | 66.63 (16) |
Zn2xvii—Ce3—Zn10xx | 132.72 (8) | Zn9xxxiv—Zn5—Mg2x | 117.3 (3) |
Zn2—Ce3—Zn10xx | 94.69 (16) | Mg2xxxix—Zn5—Mg2x | 118.17 (9) |
Zn8xi—Ce3—Zn10xx | 151.82 (13) | Zn5xxxvii—Zn5—Mg2ii | 62.6 (2) |
Zn8—Ce3—Zn10xx | 109.54 (10) | Zn5xxxviii—Zn5—Mg2ii | 113.41 (16) |
Zn8xviii—Ce3—Zn10xx | 47.70 (9) | Zn5xxiv—Zn5—Mg2ii | 113.41 (16) |
Zn8xvii—Ce3—Zn10xx | 82.76 (11) | Zn9—Zn5—Mg2ii | 66.63 (16) |
Zn10x—Ce3—Zn10xx | 109.98 (14) | Zn9xxxv—Zn5—Mg2ii | 117.3 (3) |
Zn10xix—Ce3—Zn10xx | 91.41 (13) | Zn9xxxiv—Zn5—Mg2ii | 66.63 (16) |
Zn6xvii—Ce3—Zn10xxi | 85.22 (15) | Mg2xxxix—Zn5—Mg2ii | 118.17 (9) |
Zn6—Ce3—Zn10xxi | 155.47 (8) | Mg2x—Zn5—Mg2ii | 118.17 (9) |
Zn2xvii—Ce3—Zn10xxi | 94.69 (16) | Zn5xxxvii—Zn5—Ce1xl | 118.75 (12) |
Zn2—Ce3—Zn10xxi | 132.72 (8) | Zn5xxxviii—Zn5—Ce1xl | 67.70 (10) |
Zn8xi—Ce3—Zn10xxi | 109.54 (10) | Zn5xxiv—Zn5—Ce1xl | 67.70 (10) |
Zn8—Ce3—Zn10xxi | 151.82 (13) | Zn9—Zn5—Ce1xl | 112.26 (13) |
Zn8xviii—Ce3—Zn10xxi | 82.76 (11) | Zn9xxxv—Zn5—Ce1xl | 61.37 (12) |
Zn8xvii—Ce3—Zn10xxi | 47.70 (9) | Zn9xxxiv—Zn5—Ce1xl | 112.26 (13) |
Zn10x—Ce3—Zn10xxi | 91.41 (13) | Mg2xxxix—Zn5—Ce1xl | 61.53 (3) |
Zn10xix—Ce3—Zn10xxi | 109.98 (14) | Mg2x—Zn5—Ce1xl | 61.53 (3) |
Zn10xx—Ce3—Zn10xxi | 46.94 (11) | Mg2ii—Zn5—Ce1xl | 178.7 (3) |
Zn10xxii—Ce4—Zn10xiv | 85.73 (13) | Zn5xxxvii—Zn5—Ce1vii | 67.70 (10) |
Zn10xxii—Ce4—Zn10 | 68.93 (12) | Zn5xxxviii—Zn5—Ce1vii | 118.75 (12) |
Zn10xiv—Ce4—Zn10 | 124.47 (16) | Zn5xxiv—Zn5—Ce1vii | 67.70 (10) |
Zn10xxii—Ce4—Zn10xvi | 124.47 (16) | Zn9—Zn5—Ce1vii | 61.37 (12) |
Zn10xiv—Ce4—Zn10xvi | 68.93 (12) | Zn9xxxv—Zn5—Ce1vii | 112.26 (13) |
Zn10—Ce4—Zn10xvi | 85.73 (13) | Zn9xxxiv—Zn5—Ce1vii | 112.26 (13) |
Zn10xxii—Ce4—Zn8iii | 48.51 (8) | Mg2xxxix—Zn5—Ce1vii | 178.7 (3) |
Zn10xiv—Ce4—Zn8iii | 48.51 (8) | Mg2x—Zn5—Ce1vii | 61.53 (3) |
Zn10—Ce4—Zn8iii | 115.79 (11) | Mg2ii—Zn5—Ce1vii | 61.53 (3) |
Zn10xvi—Ce4—Zn8iii | 115.79 (11) | Ce1xl—Zn5—Ce1vii | 118.73 (5) |
Zn10xxii—Ce4—Zn8x | 115.79 (11) | Zn5xxxvii—Zn5—Ce1xli | 67.70 (10) |
Zn10xiv—Ce4—Zn8x | 115.79 (11) | Zn5xxxviii—Zn5—Ce1xli | 67.70 (10) |
Zn10—Ce4—Zn8x | 48.51 (8) | Zn5xxiv—Zn5—Ce1xli | 118.75 (12) |
Zn10xvi—Ce4—Zn8x | 48.51 (8) | Zn9—Zn5—Ce1xli | 112.26 (13) |
Zn8iii—Ce4—Zn8x | 151.8 (2) | Zn9xxxv—Zn5—Ce1xli | 112.26 (13) |
Zn10xxii—Ce4—Zn9x | 49.74 (9) | Zn9xxxiv—Zn5—Ce1xli | 61.37 (12) |
Zn10xiv—Ce4—Zn9x | 135.31 (10) | Mg2xxxix—Zn5—Ce1xli | 61.53 (3) |
Zn10—Ce4—Zn9x | 49.74 (9) | Mg2x—Zn5—Ce1xli | 178.7 (3) |
Zn10xvi—Ce4—Zn9x | 135.31 (10) | Mg2ii—Zn5—Ce1xli | 61.53 (3) |
Zn8iii—Ce4—Zn9x | 90.97 (3) | Ce1xl—Zn5—Ce1xli | 118.73 (5) |
Zn8x—Ce4—Zn9x | 90.97 (3) | Ce1vii—Zn5—Ce1xli | 118.73 (5) |
Zn10xxii—Ce4—Zn9iii | 135.31 (10) | Zn1—Zn6—Zn8x | 112.28 (19) |
Zn10xiv—Ce4—Zn9iii | 49.74 (9) | Zn1—Zn6—Zn8xi | 112.28 (19) |
Zn10—Ce4—Zn9iii | 135.31 (10) | Zn8x—Zn6—Zn8xi | 106.5 (2) |
Zn10xvi—Ce4—Zn9iii | 49.74 (9) | Zn1—Zn6—Zn8 | 112.28 (19) |
Zn8iii—Ce4—Zn9iii | 90.97 (3) | Zn8x—Zn6—Zn8 | 106.5 (2) |
Zn8x—Ce4—Zn9iii | 90.97 (3) | Zn8xi—Zn6—Zn8 | 106.5 (2) |
Zn9x—Ce4—Zn9iii | 172.0 (2) | Zn1—Zn6—Ce2 | 180.00 (16) |
Zn10xxii—Ce4—Zn7xii | 47.05 (9) | Zn8x—Zn6—Ce2 | 67.72 (19) |
Zn10xiv—Ce4—Zn7xii | 79.25 (11) | Zn8xi—Zn6—Ce2 | 67.72 (19) |
Zn10—Ce4—Zn7xii | 47.05 (9) | Zn8—Zn6—Ce2 | 67.72 (19) |
Zn10xvi—Ce4—Zn7xii | 79.25 (11) | Zn1—Zn6—Ce3xi | 81.34 (16) |
Zn8iii—Ce4—Zn7xii | 76.86 (11) | Zn8x—Zn6—Ce3xi | 66.40 (12) |
Zn8x—Ce4—Zn7xii | 76.86 (11) | Zn8xi—Zn6—Ce3xi | 66.40 (12) |
Zn9x—Ce4—Zn7xii | 72.65 (13) | Zn8—Zn6—Ce3xi | 166.4 (3) |
Zn9iii—Ce4—Zn7xii | 115.31 (15) | Ce2—Zn6—Ce3xi | 98.66 (16) |
Zn10xxii—Ce4—Zn7ix | 79.25 (11) | Zn1—Zn6—Ce3x | 81.34 (16) |
Zn10xiv—Ce4—Zn7ix | 47.05 (9) | Zn8x—Zn6—Ce3x | 66.40 (12) |
Zn10—Ce4—Zn7ix | 79.25 (11) | Zn8xi—Zn6—Ce3x | 166.4 (3) |
Zn10xvi—Ce4—Zn7ix | 47.05 (9) | Zn8—Zn6—Ce3x | 66.40 (12) |
Zn8iii—Ce4—Zn7ix | 76.86 (11) | Ce2—Zn6—Ce3x | 98.66 (16) |
Zn8x—Ce4—Zn7ix | 76.86 (11) | Ce3xi—Zn6—Ce3x | 117.78 (8) |
Zn9x—Ce4—Zn7ix | 115.31 (15) | Zn1—Zn6—Ce3 | 81.34 (16) |
Zn9iii—Ce4—Zn7ix | 72.65 (13) | Zn8x—Zn6—Ce3 | 166.4 (3) |
Zn7xii—Ce4—Zn7ix | 42.66 (16) | Zn8xi—Zn6—Ce3 | 66.40 (12) |
Zn10xxii—Ce4—Mg3xxiii | 55.2 (2) | Zn8—Zn6—Ce3 | 66.40 (12) |
Zn10xiv—Ce4—Mg3xxiii | 98.1 (2) | Ce2—Zn6—Ce3 | 98.66 (16) |
Zn10—Ce4—Mg3xxiii | 105.1 (3) | Ce3xi—Zn6—Ce3 | 117.77 (8) |
Zn10xvi—Ce4—Mg3xxiii | 166.6 (2) | Ce3x—Zn6—Ce3 | 117.77 (8) |
Zn8iii—Ce4—Mg3xxiii | 52.6 (2) | Zn1—Zn6—Zn2xxiv | 58.5 (2) |
Zn8x—Ce4—Mg3xxiii | 144.9 (2) | Zn8x—Zn6—Zn2xxiv | 53.8 (2) |
Zn9x—Ce4—Mg3xxiii | 56.5 (3) | Zn8xi—Zn6—Zn2xxiv | 126.34 (7) |
Zn9iii—Ce4—Mg3xxiii | 119.5 (3) | Zn8—Zn6—Zn2xxiv | 126.34 (7) |
Zn7xii—Ce4—Mg3xxiii | 102.2 (2) | Ce2—Zn6—Zn2xxiv | 121.5 (2) |
Zn7ix—Ce4—Mg3xxiii | 126.3 (2) | Ce3xi—Zn6—Zn2xxiv | 59.99 (14) |
Zn10xxii—Ce4—Mg3xxiv | 105.1 (3) | Ce3x—Zn6—Zn2xxiv | 59.99 (14) |
Zn10xiv—Ce4—Mg3xxiv | 166.6 (2) | Ce3—Zn6—Zn2xxiv | 139.8 (4) |
Zn10—Ce4—Mg3xxiv | 55.2 (2) | Zn1—Zn6—Zn2 | 58.5 (2) |
Zn10xvi—Ce4—Mg3xxiv | 98.1 (2) | Zn8x—Zn6—Zn2 | 126.34 (7) |
Zn8iii—Ce4—Mg3xxiv | 144.9 (2) | Zn8xi—Zn6—Zn2 | 126.34 (7) |
Zn8x—Ce4—Mg3xxiv | 52.6 (2) | Zn8—Zn6—Zn2 | 53.8 (2) |
Zn9x—Ce4—Mg3xxiv | 56.5 (3) | Ce2—Zn6—Zn2 | 121.5 (2) |
Zn9iii—Ce4—Mg3xxiv | 119.5 (3) | Ce3xi—Zn6—Zn2 | 139.8 (4) |
Zn7xii—Ce4—Mg3xxiv | 102.2 (2) | Ce3x—Zn6—Zn2 | 59.99 (14) |
Zn7ix—Ce4—Mg3xxiv | 126.3 (2) | Ce3—Zn6—Zn2 | 59.99 (14) |
Mg3xxiii—Ce4—Mg3xxiv | 94.7 (4) | Zn2xxiv—Zn6—Zn2 | 95.1 (3) |
Zn7ii—Mg1—Zn7xii | 94.70 (3) | Zn1—Zn6—Zn2xvii | 58.5 (2) |
Zn7ii—Mg1—Zn7ix | 116.21 (6) | Zn8x—Zn6—Zn2xvii | 126.35 (7) |
Zn7xii—Mg1—Zn7ix | 47.78 (18) | Zn8xi—Zn6—Zn2xvii | 53.8 (2) |
Zn7ii—Mg1—Zn7i | 52.72 (15) | Zn8—Zn6—Zn2xvii | 126.34 (7) |
Zn7xii—Mg1—Zn7i | 116.21 (6) | Ce2—Zn6—Zn2xvii | 121.5 (2) |
Zn7ix—Mg1—Zn7i | 94.70 (3) | Ce3xi—Zn6—Zn2xvii | 59.99 (14) |
Zn7ii—Mg1—Zn7viii | 94.70 (3) | Ce3x—Zn6—Zn2xvii | 139.8 (4) |
Zn7xii—Mg1—Zn7viii | 52.72 (15) | Ce3—Zn6—Zn2xvii | 59.99 (14) |
Zn7ix—Mg1—Zn7viii | 94.70 (3) | Zn2xxiv—Zn6—Zn2xvii | 95.1 (3) |
Zn7i—Mg1—Zn7viii | 146.72 (12) | Zn2—Zn6—Zn2xvii | 95.1 (3) |
Zn7ii—Mg1—Zn7iii | 52.72 (15) | Zn7ii—Zn7—Zn10viii | 109.43 (12) |
Zn7xii—Mg1—Zn7iii | 146.72 (12) | Zn7ii—Zn7—Zn10xlii | 109.43 (12) |
Zn7ix—Mg1—Zn7iii | 146.72 (12) | Zn10viii—Zn7—Zn10xlii | 84.35 (19) |
Zn7i—Mg1—Zn7iii | 52.72 (15) | Zn7ii—Zn7—Zn7xii | 120.0 |
Zn7viii—Mg1—Zn7iii | 116.21 (6) | Zn10viii—Zn7—Zn7xii | 88.06 (12) |
Zn7ii—Mg1—Zn7 | 47.78 (18) | Zn10xlii—Zn7—Zn7xii | 129.61 (12) |
Zn7xii—Mg1—Zn7 | 52.72 (15) | Zn7ii—Zn7—Zn7viii | 120.000 (1) |
Zn7ix—Mg1—Zn7 | 94.70 (3) | Zn10viii—Zn7—Zn7viii | 129.61 (12) |
Zn7i—Mg1—Zn7 | 94.70 (3) | Zn10xlii—Zn7—Zn7viii | 88.06 (12) |
Zn7viii—Mg1—Zn7 | 52.72 (15) | Zn7xii—Zn7—Zn7viii | 60.0 |
Zn7iii—Mg1—Zn7 | 94.70 (3) | Zn7ii—Zn7—Mg1 | 66.11 (9) |
Zn7ii—Mg1—Zn7xiii | 116.21 (6) | Zn10viii—Zn7—Mg1 | 137.75 (9) |
Zn7xii—Mg1—Zn7xiii | 94.70 (3) | Zn10xlii—Zn7—Mg1 | 137.75 (9) |
Zn7ix—Mg1—Zn7xiii | 116.21 (6) | Zn7xii—Zn7—Mg1 | 63.64 (8) |
Zn7i—Mg1—Zn7xiii | 146.72 (12) | Zn7viii—Zn7—Mg1 | 63.64 (8) |
Zn7viii—Mg1—Zn7xiii | 47.78 (18) | Zn7ii—Zn7—Ce1ii | 174.63 (9) |
Zn7iii—Mg1—Zn7xiii | 94.70 (3) | Zn10viii—Zn7—Ce1ii | 66.85 (12) |
Zn7—Mg1—Zn7xiii | 94.70 (3) | Zn10xlii—Zn7—Ce1ii | 66.85 (12) |
Zn7ii—Mg1—Zn7xi | 94.70 (3) | Zn7xii—Zn7—Ce1ii | 64.43 (8) |
Zn7xii—Mg1—Zn7xi | 94.70 (3) | Zn7viii—Zn7—Ce1ii | 64.43 (8) |
Zn7ix—Mg1—Zn7xi | 52.72 (15) | Mg1—Zn7—Ce1ii | 119.26 (16) |
Zn7i—Mg1—Zn7xi | 47.78 (18) | Zn7ii—Zn7—Ce2xiv | 67.29 (8) |
Zn7viii—Mg1—Zn7xi | 146.72 (12) | Zn10viii—Zn7—Ce2xiv | 72.01 (9) |
Zn7iii—Mg1—Zn7xi | 94.70 (3) | Zn10xlii—Zn7—Ce2xiv | 152.42 (18) |
Zn7—Mg1—Zn7xi | 116.21 (6) | Zn7xii—Zn7—Ce2xiv | 64.96 (9) |
Zn7xiii—Mg1—Zn7xi | 146.72 (12) | Zn7viii—Zn7—Ce2xiv | 117.83 (10) |
Zn7ii—Mg1—Zn7xiv | 146.72 (12) | Mg1—Zn7—Ce2xiv | 67.81 (10) |
Zn7xii—Mg1—Zn7xiv | 94.70 (3) | Ce1ii—Zn7—Ce2xiv | 114.02 (9) |
Zn7ix—Mg1—Zn7xiv | 52.72 (15) | Zn7ii—Zn7—Ce2vii | 67.29 (8) |
Zn7i—Mg1—Zn7xiv | 94.70 (3) | Zn10viii—Zn7—Ce2vii | 152.42 (18) |
Zn7viii—Mg1—Zn7xiv | 116.21 (6) | Zn10xlii—Zn7—Ce2vii | 72.01 (9) |
Zn7iii—Mg1—Zn7xiv | 116.21 (6) | Zn7xii—Zn7—Ce2vii | 117.83 (10) |
Zn7—Mg1—Zn7xiv | 146.72 (12) | Zn7viii—Zn7—Ce2vii | 64.96 (9) |
Zn7xiii—Mg1—Zn7xiv | 94.70 (3) | Mg1—Zn7—Ce2vii | 67.81 (10) |
Zn7xi—Mg1—Zn7xiv | 52.72 (15) | Ce1ii—Zn7—Ce2vii | 114.02 (9) |
Zn7ii—Mg1—Zn7vii | 146.72 (12) | Ce2xiv—Zn7—Ce2vii | 125.78 (17) |
Zn7xii—Mg1—Zn7vii | 116.21 (6) | Zn7ii—Zn7—Ce4i | 68.67 (8) |
Zn7ix—Mg1—Zn7vii | 94.70 (3) | Zn10viii—Zn7—Ce4i | 60.27 (11) |
Zn7i—Mg1—Zn7vii | 116.21 (6) | Zn10xlii—Zn7—Ce4i | 60.27 (11) |
Zn7viii—Mg1—Zn7vii | 94.70 (3) | Zn7xii—Zn7—Ce4i | 147.20 (3) |
Zn7iii—Mg1—Zn7vii | 94.70 (3) | Zn7viii—Zn7—Ce4i | 147.20 (3) |
Zn7—Mg1—Zn7vii | 146.72 (12) | Mg1—Zn7—Ce4i | 134.78 (16) |
Zn7xiii—Mg1—Zn7vii | 52.72 (15) | Ce1ii—Zn7—Ce4i | 105.96 (14) |
Zn7xi—Mg1—Zn7vii | 94.70 (3) | Ce2xiv—Zn7—Ce4i | 94.88 (11) |
Zn7xiv—Mg1—Zn7vii | 47.78 (18) | Ce2vii—Zn7—Ce4i | 94.88 (11) |
Zn7ii—Mg1—Zn7x | 94.70 (3) | Zn10xi—Zn8—Zn10xix | 110.7 (2) |
Zn7xii—Mg1—Zn7x | 146.72 (12) | Zn10xi—Zn8—Zn2 | 123.90 (13) |
Zn7ix—Mg1—Zn7x | 146.72 (12) | Zn10xix—Zn8—Zn2 | 123.90 (13) |
Zn7i—Mg1—Zn7x | 94.70 (3) | Zn10xi—Zn8—Zn6 | 106.38 (16) |
Zn7viii—Mg1—Zn7x | 94.70 (3) | Zn10xix—Zn8—Zn6 | 106.39 (16) |
Zn7iii—Mg1—Zn7x | 47.78 (18) | Zn2—Zn8—Zn6 | 71.3 (3) |
Zn7—Mg1—Zn7x | 116.21 (6) | Zn10xi—Zn8—Mg3xviii | 66.9 (3) |
Zn7xiii—Mg1—Zn7x | 52.72 (15) | Zn10xix—Zn8—Mg3xviii | 128.1 (3) |
Zn7xi—Mg1—Zn7x | 116.21 (6) | Zn2—Zn8—Mg3xviii | 70.1 (3) |
Zn7xiv—Mg1—Zn7x | 94.70 (3) | Zn6—Zn8—Mg3xviii | 124.4 (3) |
Zn7vii—Mg1—Zn7x | 52.72 (15) | Zn10xi—Zn8—Mg3xxvi | 128.1 (3) |
Zn5xxv—Mg2—Zn5ii | 54.8 (4) | Zn10xix—Zn8—Mg3xxvi | 66.9 (3) |
Zn5xxv—Mg2—Zn10x | 103.70 (19) | Zn2—Zn8—Mg3xxvi | 70.1 (3) |
Zn5ii—Mg2—Zn10x | 128.9 (3) | Zn6—Zn8—Mg3xxvi | 124.4 (3) |
Zn5xxv—Mg2—Zn10xix | 128.9 (3) | Mg3xviii—Zn8—Mg3xxvi | 75.8 (6) |
Zn5ii—Mg2—Zn10xix | 103.70 (19) | Zn10xi—Zn8—Ce4xi | 64.98 (11) |
Zn10x—Mg2—Zn10xix | 50.25 (18) | Zn10xix—Zn8—Ce4xi | 64.98 (11) |
Zn5xxv—Mg2—Zn10xx | 128.9 (3) | Zn2—Zn8—Ce4xi | 127.1 (3) |
Zn5ii—Mg2—Zn10xx | 103.70 (19) | Zn6—Zn8—Ce4xi | 161.7 (3) |
Zn10x—Mg2—Zn10xx | 121.7 (5) | Mg3xviii—Zn8—Ce4xi | 68.7 (2) |
Zn10xix—Mg2—Zn10xx | 99.5 (4) | Mg3xxvi—Zn8—Ce4xi | 68.7 (2) |
Zn5xxv—Mg2—Zn10xxi | 103.70 (19) | Zn10xi—Zn8—Ce3x | 67.06 (9) |
Zn5ii—Mg2—Zn10xxi | 128.9 (3) | Zn10xix—Zn8—Ce3x | 165.0 (2) |
Zn10x—Mg2—Zn10xxi | 99.5 (4) | Zn2—Zn8—Ce3x | 63.31 (13) |
Zn10xix—Mg2—Zn10xxi | 121.7 (5) | Zn6—Zn8—Ce3x | 61.85 (10) |
Zn10xx—Mg2—Zn10xxi | 50.25 (18) | Mg3xviii—Zn8—Ce3x | 65.6 (2) |
Zn5xxv—Mg2—Zn9xxv | 55.1 (2) | Mg3xxvi—Zn8—Ce3x | 126.8 (3) |
Zn5ii—Mg2—Zn9xxv | 103.5 (4) | Ce4xi—Zn8—Ce3x | 123.14 (9) |
Zn10x—Mg2—Zn9xxv | 93.51 (14) | Zn10xi—Zn8—Ce3 | 165.0 (2) |
Zn10xix—Mg2—Zn9xxv | 143.5 (3) | Zn10xix—Zn8—Ce3 | 67.06 (9) |
Zn10xx—Mg2—Zn9xxv | 97.13 (14) | Zn2—Zn8—Ce3 | 63.30 (13) |
Zn10xxi—Mg2—Zn9xxv | 51.77 (11) | Zn6—Zn8—Ce3 | 61.85 (10) |
Zn5xxv—Mg2—Zn9ii | 103.5 (4) | Mg3xviii—Zn8—Ce3 | 126.8 (3) |
Zn5ii—Mg2—Zn9ii | 55.1 (2) | Mg3xxvi—Zn8—Ce3 | 65.6 (2) |
Zn10x—Mg2—Zn9ii | 97.13 (14) | Ce4xi—Zn8—Ce3 | 123.15 (9) |
Zn10xix—Mg2—Zn9ii | 51.77 (11) | Ce3x—Zn8—Ce3 | 110.92 (17) |
Zn10xx—Mg2—Zn9ii | 93.51 (14) | Zn10xi—Zn8—Ce2 | 72.94 (15) |
Zn10xxi—Mg2—Zn9ii | 143.5 (3) | Zn10xix—Zn8—Ce2 | 72.94 (15) |
Zn9xxv—Mg2—Zn9ii | 158.1 (6) | Zn2—Zn8—Ce2 | 132.1 (3) |
Zn5xxv—Mg2—Zn9xi | 55.1 (2) | Zn6—Zn8—Ce2 | 60.85 (19) |
Zn5ii—Mg2—Zn9xi | 103.5 (4) | Mg3xviii—Zn8—Ce2 | 139.2 (3) |
Zn10x—Mg2—Zn9xi | 51.77 (11) | Mg3xxvi—Zn8—Ce2 | 139.2 (3) |
Zn10xix—Mg2—Zn9xi | 97.13 (14) | Ce4xi—Zn8—Ce2 | 100.81 (16) |
Zn10xx—Mg2—Zn9xi | 143.5 (3) | Ce3x—Zn8—Ce2 | 92.56 (11) |
Zn10xxi—Mg2—Zn9xi | 93.51 (14) | Ce3—Zn8—Ce2 | 92.56 (11) |
Zn9xxv—Mg2—Zn9xi | 52.92 (19) | Zn10xliii—Zn9—Zn10xi | 81.6 (2) |
Zn9ii—Mg2—Zn9xi | 122.0 (3) | Zn10xliii—Zn9—Zn9xxxv | 169.17 (10) |
Zn5xxv—Mg2—Zn9xviii | 103.5 (4) | Zn10xi—Zn9—Zn9xxxv | 109.18 (10) |
Zn5ii—Mg2—Zn9xviii | 55.1 (2) | Zn10xliii—Zn9—Zn9xxxiv | 109.18 (10) |
Zn10x—Mg2—Zn9xviii | 143.5 (3) | Zn10xi—Zn9—Zn9xxxiv | 169.17 (10) |
Zn10xix—Mg2—Zn9xviii | 93.51 (14) | Zn9xxxv—Zn9—Zn9xxxiv | 60.0 |
Zn10xx—Mg2—Zn9xviii | 51.77 (11) | Zn10xliii—Zn9—Zn4 | 116.28 (18) |
Zn10xxi—Mg2—Zn9xviii | 97.13 (14) | Zn10xi—Zn9—Zn4 | 116.28 (19) |
Zn9xxv—Mg2—Zn9xviii | 122.0 (3) | Zn9xxxv—Zn9—Zn4 | 60.08 (12) |
Zn9ii—Mg2—Zn9xviii | 52.92 (19) | Zn9xxxiv—Zn9—Zn4 | 60.08 (12) |
Zn9xi—Mg2—Zn9xviii | 158.1 (6) | Zn10xliii—Zn9—Zn5 | 115.39 (17) |
Zn5xxv—Mg2—Ce3 | 152.6 (2) | Zn10xi—Zn9—Zn5 | 115.39 (17) |
Zn5ii—Mg2—Ce3 | 152.6 (2) | Zn9xxxv—Zn9—Zn5 | 60.10 (11) |
Zn10x—Mg2—Ce3 | 60.8 (3) | Zn9xxxiv—Zn9—Zn5 | 60.10 (11) |
Zn10xix—Mg2—Ce3 | 60.8 (3) | Zn4—Zn9—Zn5 | 109.7 (2) |
Zn10xx—Mg2—Ce3 | 60.8 (3) | Zn10xliii—Zn9—Mg2x | 123.8 (2) |
Zn10xxi—Mg2—Ce3 | 60.8 (3) | Zn10xi—Zn9—Mg2x | 61.2 (2) |
Zn9xxv—Mg2—Ce3 | 101.0 (3) | Zn9xxxv—Zn9—Mg2x | 63.54 (10) |
Zn9ii—Mg2—Ce3 | 101.0 (3) | Zn9xxxiv—Zn9—Mg2x | 110.4 (2) |
Zn9xi—Mg2—Ce3 | 101.0 (3) | Zn4—Zn9—Mg2x | 117.52 (17) |
Zn9xviii—Mg2—Ce3 | 101.0 (3) | Zn5—Zn9—Mg2x | 58.2 (3) |
Zn5xxv—Mg2—Ce1xiv | 68.4 (2) | Zn10xliii—Zn9—Mg2ii | 61.2 (2) |
Zn5ii—Mg2—Ce1xiv | 68.4 (2) | Zn10xi—Zn9—Mg2ii | 123.8 (2) |
Zn10x—Mg2—Ce1xiv | 60.47 (9) | Zn9xxxv—Zn9—Mg2ii | 110.4 (2) |
Zn10xix—Mg2—Ce1xiv | 60.47 (9) | Zn9xxxiv—Zn9—Mg2ii | 63.54 (10) |
Zn10xx—Mg2—Ce1xiv | 153.68 (10) | Zn4—Zn9—Mg2ii | 117.52 (17) |
Zn10xxi—Mg2—Ce1xiv | 153.68 (10) | Zn5—Zn9—Mg2ii | 58.2 (3) |
Zn9xxv—Mg2—Ce1xiv | 109.1 (2) | Mg2x—Zn9—Mg2ii | 105.3 (5) |
Zn9ii—Mg2—Ce1xiv | 61.03 (14) | Zn10xliii—Zn9—Mg3xviii | 124.3 (2) |
Zn9xi—Mg2—Ce1xiv | 61.03 (14) | Zn10xi—Zn9—Mg3xviii | 61.73 (19) |
Zn9xviii—Mg2—Ce1xiv | 109.1 (2) | Zn9xxxv—Zn9—Mg3xviii | 63.75 (17) |
Ce3—Mg2—Ce1xiv | 114.5 (2) | Zn9xxxiv—Zn9—Mg3xviii | 110.56 (19) |
Zn3—Mg3—Zn8xxvi | 102.6 (4) | Zn4—Zn9—Mg3xviii | 58.3 (2) |
Zn3—Mg3—Zn8xviii | 102.6 (4) | Zn5—Zn9—Mg3xviii | 117.8 (2) |
Zn8xxvi—Mg3—Zn8xviii | 98.9 (4) | Mg2x—Zn9—Mg3xviii | 74.5 (3) |
Zn3—Mg3—Zn4xxvii | 57.9 (3) | Mg2ii—Zn9—Mg3xviii | 173.8 (3) |
Zn8xxvi—Mg3—Zn4xxvii | 129.4 (2) | Zn10xliii—Zn9—Mg3xxxvi | 61.7 (2) |
Zn8xviii—Mg3—Zn4xxvii | 129.4 (2) | Zn10xi—Zn9—Mg3xxxvi | 124.3 (2) |
Zn3—Mg3—Zn10xxiv | 130.0 (2) | Zn9xxxv—Zn9—Mg3xxxvi | 110.56 (19) |
Zn8xxvi—Mg3—Zn10xxiv | 51.01 (16) | Zn9xxxiv—Zn9—Mg3xxxvi | 63.75 (17) |
Zn8xviii—Mg3—Zn10xxiv | 121.0 (4) | Zn4—Zn9—Mg3xxxvi | 58.3 (2) |
Zn4xxvii—Mg3—Zn10xxiv | 103.1 (4) | Zn5—Zn9—Mg3xxxvi | 117.7 (2) |
Zn3—Mg3—Zn10xxviii | 130.0 (2) | Mg2x—Zn9—Mg3xxxvi | 173.8 (3) |
Zn8xxvi—Mg3—Zn10xxviii | 121.0 (4) | Mg2ii—Zn9—Mg3xxxvi | 74.5 (3) |
Zn8xviii—Mg3—Zn10xxviii | 51.01 (16) | Mg3xviii—Zn9—Mg3xxxvi | 105.0 (5) |
Zn4xxvii—Mg3—Zn10xxviii | 103.1 (4) | Zn10xliii—Zn9—Ce4xi | 61.82 (14) |
Zn10xxiv—Mg3—Zn10xxviii | 97.7 (5) | Zn10xi—Zn9—Ce4xi | 61.82 (14) |
Zn3—Mg3—Zn9xxix | 105.9 (4) | Zn9xxxv—Zn9—Ce4xi | 123.22 (9) |
Zn8xxvi—Mg3—Zn9xxix | 143.0 (5) | Zn9xxxiv—Zn9—Ce4xi | 123.22 (9) |
Zn8xviii—Mg3—Zn9xxix | 97.3 (2) | Zn4—Zn9—Ce4xi | 74.41 (17) |
Zn4xxvii—Mg3—Zn9xxix | 54.7 (3) | Zn5—Zn9—Ce4xi | 175.9 (2) |
Zn10xxiv—Mg3—Zn9xxix | 92.3 (4) | Mg2x—Zn9—Ce4xi | 120.2 (3) |
Zn10xxviii—Mg3—Zn9xxix | 51.2 (2) | Mg2ii—Zn9—Ce4xi | 120.2 (3) |
Zn3—Mg3—Zn9xxvi | 105.9 (4) | Mg3xviii—Zn9—Ce4xi | 64.13 (19) |
Zn8xxvi—Mg3—Zn9xxvi | 97.3 (2) | Mg3xxxvi—Zn9—Ce4xi | 64.13 (19) |
Zn8xviii—Mg3—Zn9xxvi | 143.0 (5) | Zn10xliii—Zn9—Ce1vii | 63.80 (13) |
Zn4xxvii—Mg3—Zn9xxvi | 54.7 (3) | Zn10xi—Zn9—Ce1vii | 63.80 (13) |
Zn10xxiv—Mg3—Zn9xxvi | 51.2 (2) | Zn9xxxv—Zn9—Ce1vii | 119.83 (9) |
Zn10xxviii—Mg3—Zn9xxvi | 92.3 (4) | Zn9xxxiv—Zn9—Ce1vii | 119.83 (9) |
Zn9xxix—Mg3—Zn9xxvi | 52.5 (3) | Zn4—Zn9—Ce1vii | 179.9 (3) |
Zn3—Mg3—Zn2 | 94.1 (5) | Zn5—Zn9—Ce1vii | 70.20 (16) |
Zn8xxvi—Mg3—Zn2 | 51.2 (2) | Mg2x—Zn9—Ce1vii | 62.43 (15) |
Zn8xviii—Mg3—Zn2 | 51.2 (2) | Mg2ii—Zn9—Ce1vii | 62.43 (15) |
Zn4xxvii—Mg3—Zn2 | 152.0 (6) | Mg3xviii—Zn9—Ce1vii | 121.8 (2) |
Zn10xxiv—Mg3—Zn2 | 95.2 (3) | Mg3xxxvi—Zn9—Ce1vii | 121.8 (2) |
Zn10xxviii—Mg3—Zn2 | 95.2 (3) | Ce4xi—Zn9—Ce1vii | 105.70 (17) |
Zn9xxix—Mg3—Zn2 | 146.3 (3) | Zn10xv—Zn10—Zn8x | 110.32 (12) |
Zn9xxvi—Mg3—Zn2 | 146.3 (3) | Zn10xv—Zn10—Zn7xii | 91.94 (12) |
Zn3—Mg3—Ce3xxx | 150.6 (6) | Zn8x—Zn10—Zn7xii | 103.84 (18) |
Zn8xxvi—Mg3—Ce3xxx | 60.6 (2) | Zn10xv—Zn10—Zn9x | 123.52 (14) |
Zn8xviii—Mg3—Ce3xxx | 60.6 (2) | Zn8x—Zn10—Zn9x | 121.2 (2) |
Zn4xxvii—Mg3—Ce3xxx | 151.5 (6) | Zn7xii—Zn10—Zn9x | 96.70 (14) |
Zn10xxiv—Mg3—Ce3xxx | 60.5 (2) | Zn10xv—Zn10—Mg2xi | 64.87 (9) |
Zn10xxviii—Mg3—Ce3xxx | 60.5 (2) | Zn8x—Zn10—Mg2xi | 125.7 (3) |
Zn9xxix—Mg3—Ce3xxx | 100.4 (4) | Zn7xii—Zn10—Mg2xi | 129.7 (3) |
Zn9xxvi—Mg3—Ce3xxx | 100.4 (4) | Zn9x—Zn10—Mg2xi | 67.1 (2) |
Zn2—Mg3—Ce3xxx | 56.5 (2) | Zn10xv—Zn10—Mg3xxiv | 127.4 (2) |
Zn3—Mg3—Ce4xxxi | 73.0 (2) | Zn8x—Zn10—Mg3xxiv | 62.1 (3) |
Zn8xxvi—Mg3—Ce4xxxi | 58.73 (10) | Zn7xii—Zn10—Mg3xxiv | 140.4 (3) |
Zn8xviii—Mg3—Ce4xxxi | 154.2 (5) | Zn9x—Zn10—Mg3xxiv | 67.1 (3) |
Zn4xxvii—Mg3—Ce4xxxi | 70.7 (2) | Mg2xi—Zn10—Mg3xxiv | 78.8 (3) |
Zn10xxiv—Mg3—Ce4xxxi | 57.05 (9) | Zn10xv—Zn10—Ce4 | 162.27 (8) |
Zn10xxviii—Mg3—Ce4xxxi | 149.6 (5) | Zn8x—Zn10—Ce4 | 66.51 (11) |
Zn9xxix—Mg3—Ce4xxxi | 108.4 (4) | Zn7xii—Zn10—Ce4 | 72.68 (14) |
Zn9xxvi—Mg3—Ce4xxxi | 59.36 (17) | Zn9x—Zn10—Ce4 | 68.44 (14) |
Zn2—Mg3—Ce4xxxi | 103.1 (3) | Mg2xi—Zn10—Ce4 | 131.91 (15) |
Ce3xxx—Mg3—Ce4xxxi | 110.8 (2) | Mg3xxiv—Zn10—Ce4 | 67.8 (2) |
Zn3—Mg3—Ce4xx | 73.0 (2) | Zn10xv—Zn10—Ce3xi | 66.53 (6) |
Zn8xxvi—Mg3—Ce4xx | 154.1 (5) | Zn8x—Zn10—Ce3xi | 65.23 (12) |
Zn8xviii—Mg3—Ce4xx | 58.73 (10) | Zn7xii—Zn10—Ce3xi | 147.71 (14) |
Zn4xxvii—Mg3—Ce4xx | 70.7 (2) | Zn9x—Zn10—Ce3xi | 115.11 (14) |
Zn10xxiv—Mg3—Ce4xx | 149.6 (5) | Mg2xi—Zn10—Ce3xi | 64.2 (3) |
Zn10xxviii—Mg3—Ce4xx | 57.05 (9) | Mg3xxiv—Zn10—Ce3xi | 63.8 (2) |
Zn9xxix—Mg3—Ce4xx | 59.36 (17) | Ce4—Zn10—Ce3xi | 122.89 (11) |
Zn9xxvi—Mg3—Ce4xx | 108.4 (4) | Zn10xv—Zn10—Ce1ii | 66.64 (6) |
Zn2—Mg3—Ce4xx | 103.1 (3) | Zn8x—Zn10—Ce1ii | 167.29 (19) |
Ce3xxx—Mg3—Ce4xx | 110.8 (2) | Zn7xii—Zn10—Ce1ii | 64.59 (13) |
Ce4xxxi—Mg3—Ce4xx | 138.1 (4) | Zn9x—Zn10—Ce1ii | 67.49 (14) |
Zn6—Zn1—Zn6xxxii | 109.5 | Mg2xi—Zn10—Ce1ii | 65.2 (2) |
Zn6—Zn1—Zn6xxiv | 109.5 | Mg3xxiv—Zn10—Ce1ii | 130.0 (3) |
Zn6xxxii—Zn1—Zn6xxiv | 109.5 | Ce4—Zn10—Ce1ii | 112.32 (10) |
Zn6—Zn1—Zn6xvii | 109.5 | Ce3xi—Zn10—Ce1ii | 121.37 (11) |
Zn6xxxii—Zn1—Zn6xvii | 109.5 | Zn10xv—Zn10—Ce2 | 68.44 (5) |
Zn6xxiv—Zn1—Zn6xvii | 109.5 | Zn8x—Zn10—Ce2 | 61.94 (14) |
Zn6—Zn1—Zn2xxxii | 180.00 (16) | Zn7xii—Zn10—Ce2 | 62.04 (11) |
Zn6xxxii—Zn1—Zn2xxxii | 70.53 (16) | Zn9x—Zn10—Ce2 | 157.32 (15) |
Zn6xxiv—Zn1—Zn2xxxii | 70.53 (16) | Mg2xi—Zn10—Ce2 | 131.78 (17) |
Zn6xvii—Zn1—Zn2xxxii | 70.53 (16) | Mg3xxiv—Zn10—Ce2 | 123.6 (3) |
Zn6—Zn1—Zn2xxiv | 70.53 (16) | Ce4—Zn10—Ce2 | 95.95 (9) |
Zn6xxxii—Zn1—Zn2xxiv | 70.53 (16) | Ce3xi—Zn10—Ce2 | 87.00 (10) |
Zn6xxiv—Zn1—Zn2xxiv | 70.53 (16) | Ce1ii—Zn10—Ce2 | 106.32 (11) |
Symmetry codes: (i) −y+1/2, z, −x+1/2; (ii) −x+1/2, −y+1/2, z; (iii) z, −x+1/2, −y+1/2; (iv) z, −y+1/2, −x+1/2; (v) −x+1/2, z, −y+1/2; (vi) −y+1/2, −x+1/2, z; (vii) −x+1/2, y, −z+1/2; (viii) y, −z+1/2, −x+1/2; (ix) −z+1/2, −x+1/2, y; (x) z, x, y; (xi) y, z, x; (xii) −z+1/2, x, −y+1/2; (xiii) −y+1/2, −z+1/2, x; (xiv) x, −y+1/2, −z+1/2; (xv) y, x, z; (xvi) x, z, y; (xvii) x, −y, −z; (xviii) y, −z, −x; (xix) z, y, x; (xx) z, −x, −y; (xxi) z, −y, −x; (xxii) x, −z+1/2, −y+1/2; (xxiii) −y, z+1/2, −x+1/2; (xxiv) −x, y, −z; (xxv) −x+1/2, y−1/2, −z; (xxvi) −z, x, −y; (xxvii) x, −y+1/2, −z−1/2; (xxviii) y, −x, −z; (xxix) −y+1/2, −z, x−1/2; (xxx) −y, z, −x; (xxxi) −x, −y+1/2, z−1/2; (xxxii) −x, −y, z; (xxxiii) −x+1/2, y, −z−1/2; (xxxiv) −y+1/2, z+1/2, −x; (xxxv) −z, −x+1/2, y−1/2; (xxxvi) z+1/2, −x+1/2, −y; (xxxvii) x, −y+1, −z; (xxxviii) −x, −y+1, z; (xxxix) y, z+1/2, x−1/2; (xl) x−1/2, y, z−1/2; (xli) −x+1/2, −y+1, z−1/2; (xlii) −z+1/2, y, −x+1/2; (xliii) −z+1/2, −y+1/2, x. |
Experimental details
Crystal data | |
Chemical formula | Ce20Mg19Zn81 |
Mr | 8559.26 |
Crystal system, space group | Cubic, F43m |
Temperature (K) | 295 |
a (Å) | 21.1979 (8) |
V (Å3) | 9525.3 (6) |
Z | 4 |
Radiation type | Mo Kα |
µ (mm−1) | 29.39 |
Crystal size (mm) | 0.11 × 0.09 × 0.07 |
Data collection | |
Diffractometer | Oxford Diffraction Xcalibur diffractometer |
Absorption correction | Analytical (CrysAlis RED; Oxford Diffraction, 2005) |
Tmin, Tmax | 0.056, 0.122 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 1009, 544, 388 |
Rint | 0.034 |
(sin θ/λ)max (Å−1) | 0.624 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.044, 0.101, 1.01 |
No. of reflections | 544 |
No. of parameters | 73 |
Δρmax, Δρmin (e Å−3) | 1.63, −1.89 |
Absolute structure | Flack (1983), with how many Friedel pairs? |
Absolute structure parameter | 0.3 (2) |
Computer programs: CrysAlis CCD (Oxford Diffraction, 2004), CrysAlis RED (Oxford Diffraction, 2005), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Brandenburg, 1999).
Ce2—Zn6 | 3.044 (9) | Mg3—Ce3ii | 3.325 (13) |
Mg2—Zn10i | 3.024 (8) | Zn1—Zn6 | 2.598 (8) |
Symmetry codes: (i) z, x, y; (ii) −y, z, −x. |
Ternary compounds containing a rare earth (RE), a transition metal (M) and magnesium represent a growing class of materials which attract attention due to their physical properties and applications as modern light-weight alloys and hydrogen storage materials. The crystal structures, physical properties and hydrogenation behaviour of these materials have been reviewed (Rodewald et al., 2007). The appearance of numerous quasicrystals has also been observed in these systems (Steurer & Deloudi, 2008). The Ce–Mg–Zn ternary system was first reported by Melnyk et al. (1978). The isothermal section of the phase diagram was partially constructed up to 60 at.% of Zn and 50 at.% of Ce at 573 K. Four new ternary compounds with preliminary compositions ~ CeMg7Zn12, \sim Ce(Mg0.5-0.85Zn0.5-0.15)9, ~CeMg3Zn5, and Ce2Mg3Zn3 were reported in this region. The last compound was found to crystallize with a cubic unit cell (a = 7.064 Å), whereas the crystal structures of the first three compounds remain unknown. We decided to explore the rest of the phase diagram starting from the Zn-rich corner.
The most transition metal-rich phases known in the literature so far are REMg2M9 and REMgM4. The first series adopts either a rhombohedral PuNi3 type (space group R3m; Kadir et al., 1997) or a hexagonal TbCu9Mg2 type (space group P63/mmc) structure (Solokha et al., 2006). The second series crystallizes with the cubic MgCu4Sn structure type (space group F3m), an ordered version of the Laves phase relative [related?] structure AuBe5 (Kadir et al., 2002; Sarrao et al., 1999). Many of these REMgM4 alloys have been studied intensively for hydrogen storage purposes (Wang, Zhou, Cheng et al., 2004 or Wang, Zhou, Gu et al., 2004 ?; Xu et al., 2005). They show excellent discharge capacities of the order of 400 mAh g-1 and can keep their discharge stability over 50 cycles. The influence of different factors (e.g. mechanical alloying, or rare earth or transition metal substitution) on the discharge characteristics of these alloys has also been investigated (Wang , Zhou, Cheng et al., 2004 or Wang, Zhou, Gu et al., 2004 ?; Zhang et al., 2005; Li et al., 2005). Here, we present the results of a crystallographic study of a new transition metal-rich compound, Ce20Mg19Zn81.
The crystal structure of this compound is fairly complicated, with a cubic unit cell containing 480 atoms. The projection of the unit cell of Ce20Mg19Zn81 and the coordination polyhedra of the atoms are shown in Fig. 1. The number of neighbour atoms correlates well with the sizes of the central atoms. The largest Ce atoms are enclosed in 16-, 17- and 18-vertex polyhedra. Mg atoms are characterized by Frank–Kasper or pseudo-Frank–Kasper polyhedra, having coordination number (CN) 15 or 16. Atom Zn1 is surrounded by 14 neighbours in the form of a distorted rhombododecahedron (CN 14). The remaining Zn atoms (Zn2–Zn10) have icosahedral symmetry with CN 10–13. The shortest interatomic distances (Table 1) are in the ranges typical for intermetallic compounds of these elements and indicate metallic-type bonding. The structure can be assigned to the class No. 5 (CN 12 for the smallest atom, icosahedron as a coordination polyhedron), according to the classification scheme of Krypyakevich (1977).
Chabot et al. (1981) proposed the geometric concept of nested polyhedral units for the description of complicated cubic structures. According to this concept, seven different polyhedral units were proposed as basic units, with the outermost polyhedron always being a cubo-octahedron. With respect to the spatial arrangement of nested polyhedral units, cubic structures were divided into two groups with isolated and linked units, respectively. The crystal structure of Ce20Mg19Zn81 can also be described by means of isolated polyhedral units, although the construction units here are different from those proposed earlier. We can distinguish four different units, A, B, C and D (Fig. 2a). Unit A (27 atoms) consists of a central atom (C) surrounded by a small inner tetrahedron (IT) and a larger outer tetrahedron (OT). Further away from the centre are a cubo-octahedron (CO) and an octahedron (OH). The B unit (45 atoms) includes the following elements: (C)–(TT)–(IT)–(TCO)–(OT).As the construction elements of the B nested unit, a truncated tetrahedron (TT) and a truncated cubo-octahedron (TCO) also occur. The C unit (22 atoms) includes (T)–(CO)–(OH), and the D unit (26 atoms) is characterized by an (IT)–(OT)–(CO)–(OH) sequence.
If we compare the A and D units we can see that they are almost the same and only differ by one atom, which centres the A unit. Both these units correspond to the γ-brass basic unit with or without a central atom. Unit C is related to the Ti2Ni structure type with a slightly different sequence of geometric forms. The B unit cannot be fully described by the Chabot concept. Instead, we can apply here the ideas of Bodak et al. (2006), who proposed the description of complicated cubic structures starting from four `arystotypes', namely diamond, Cu, CsCl and W, from the example of cubic rare earth-containing compounds. On this basis, we can assume that the B unit is a `hybrid' of α-Mn and face-centred cubic (fcc) Cu units in which the internal part (C–TT–IT) is the same as in α-Mn and the external part (TCO) is identical to that in fcc Cu (Fig. 2b). The number of atoms in the unit cell is equal to the sum of the atoms in each unit: (4 × 27) + (4 × 22) + (4 × 26) + (4 × 45) = 480 (Pearson code cF480). Taking the nested polyhedral units as `pseudo-atoms', we can also consider Ce20Mg19Zn81 to belong to the LiMgPdSn structure type (F43m, cF16).