Table 3. Mean bond-length statistics for the transition metal ions bonded to O2− .
Ion | Coordination number | Number of coordination polyhedra | Grand mean bond length (Å) | Standard deviation (Å) | Mean bond-length range (Å) | Maximum mean bond length (Å) | Minimum mean bond length (Å) | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|---|---|
Sc3+ | 6 | 75 | 2.098 | 0.017 | 0.071 | 2.133 | 2.063 | 0.074 | −0.586 |
7 | 5 | 2.163 | 0.017 | 0.043 | 2.188 | 2.146 | 0.846 | −0.505 | |
8 | 8 | 2.234 | 0.026 | 0.066 | 2.273 | 2.207 | 0.622 | −1.817 | |
Ti3+ | 6 | 21 | 2.037 | 0.019 | 0.081 | 2.072 | 1.991 | −0.666 | 1.075 |
7 | 2 | 2.108 | 0.008 | 0.012 | 2.114 | 2.102 | – | – | |
8 | 1 | 2.195 | – | 0.000 | 2.195 | 2.195 | – | – | |
Ti4+ | 4 | 4 | 1.821 | 0.011 | 0.026 | 1.836 | 1.811 | 1.416 | 2.442 |
5 | 17 | 1.917 | 0.014 | 0.048 | 1.940 | 1.892 | 0.241 | −0.518 | |
6 | 293 | 1.971 | 0.017 | 0.094 | 2.020 | 1.926 | −0.209 | 0.118 | |
7 | 1 | 2.064 | – | 0.000 | 2.064 | 2.064 | – | – | |
V3+ | 6 | 67 | 2.007 | 0.017 | 0.079 | 2.048 | 1.968 | 0.084 | −0.235 |
V4+ | 5 | 95 | 1.893 | 0.010 | 0.066 | 1.929 | 1.863 | 0.411 | 1.187 |
6 | 128 | 1.980 | 0.019 | 0.103 | 2.023 | 1.921 | −0.323 | 0.130 | |
V5+ | 4 | 345 | 1.717 | 0.010 | 0.075 | 1.758 | 1.682 | 0.075 | 1.991 |
5 | 65 | 1.827 | 0.013 | 0.073 | 1.869 | 1.796 | 0.569 | 1.397 | |
6 | 293 | 1.924 | 0.013 | 0.079 | 1.976 | 1.896 | 1.045 | 1.486 | |
Cr2+ | 4 | 6 | 2.004 | 0.010 | 0.027 | 2.024 | 1.997 | 2.082 | 4.523 |
5 | 2 | 2.113 | 0.004 | 0.006 | 2.116 | 2.110 | – | – | |
6 | 9 | 2.188 | 0.020 | 0.067 | 2.233 | 2.165 | 1.644 | 3.308 | |
Cr3+ | 6 | 104 | 1.976 | 0.014 | 0.064 | 2.013 | 1.949 | 0.409 | −0.583 |
Cr4+ | 4 | 1 | 1.784 | – | 0.000 | 1.784 | 1.784 | – | – |
6 | 6 | 1.950 | 0.019 | 0.052 | 1.988 | 1.937 | 2.130 | 4.777 | |
Cr5+ | 4 | 1 | 1.693 | – | 0.000 | 1.693 | 1.693 | – | – |
Cr6+ | 4 | 169 | 1.652 | 0.011 | 0.072 | 1.696 | 1.624 | 0.295 | 1.051 |
Mn2+ | 4 | 10 | 2.046 | 0.025 | 0.085 | 2.085 | 2.001 | −0.040 | −0.021 |
5 | 24 | 2.141 | 0.023 | 0.096 | 2.175 | 2.079 | −0.830 | 1.283 | |
6 | 318 | 2.199 | 0.027 | 0.172 | 2.305 | 2.134 | 0.434 | 0.597 | |
7 | 2 | 2.352 | 0.061 | 0.087 | 2.395 | 2.309 | – | – | |
8 | 18 | 2.321 | 0.025 | 0.081 | 2.356 | 2.275 | −0.415 | −0.636 | |
Mn3+ | 4 | 2 | 1.901 | 0.003 | 0.005 | 1.903 | 1.898 | – | – |
5 | 10 | 1.959 | 0.017 | 0.047 | 1.980 | 1.933 | −0.240 | −1.269 | |
6 | 82 | 2.031 | 0.019 | 0.094 | 2.086 | 1.992 | 0.106 | −0.320 | |
Mn4+ | 4 | 1 | 1.750 | – | 0.000 | 1.750 | 1.750 | – | – |
6 | 20 | 1.903 | 0.012 | 0.043 | 1.928 | 1.885 | 0.202 | −0.364 | |
Mn5+ | 4 | 8 | 1.698 | 0.007 | 0.023 | 1.706 | 1.683 | −1.095 | 1.556 |
Mn6+ | 4 | 2 | 1.662 | 0.008 | 0.015 | 1.670 | 1.655 | – | – |
Mn7+ | 4 | 7 | 1.610 | 0.007 | 0.020 | 1.622 | 1.603 | 0.913 | 0.421 |
Fe2+ | 3 | 8 | 1.844 | 0.018 | 0.049 | 1.860 | 1.811 | −1.274 | 0.568 |
4 | 6 | 1.985 | 0.021 | 0.066 | 2.008 | 1.942 | −1.667 | 3.509 | |
5 | 19 | 2.097 | 0.027 | 0.117 | 2.142 | 2.024 | −1.036 | 1.866 | |
6 | 146 | 2.147 | 0.028 | 0.156 | 2.246 | 2.090 | 0.543 | 0.419 | |
8 | 5 | 2.333 | 0.041 | 0.087 | 2.383 | 2.296 | 0.519 | −2.945 | |
Fe3+ | 4 | 65 | 1.875 | 0.016 | 0.070 | 1.910 | 1.840 | 0.086 | −0.642 |
5 | 21 | 1.966 | 0.015 | 0.049 | 1.984 | 1.935 | −0.717 | −0.491 | |
6 | 378 | 2.015 | 0.019 | 0.114 | 2.091 | 1.977 | 1.123 | 2.171 | |
8 | 2 | 2.125 | 0.008 | 0.011 | 2.130 | 2.119 | – | – | |
Co2+ | 3 | 14 | 1.854 | 0.017 | 0.055 | 1.869 | 1.814 | −1.659 | 1.756 |
4 | 27 | 1.967 | 0.017 | 0.069 | 1.995 | 1.926 | −0.648 | 0.341 | |
5 | 16 | 2.066 | 0.026 | 0.101 | 2.129 | 2.027 | 0.557 | 0.775 | |
6 | 243 | 2.108 | 0.021 | 0.121 | 2.182 | 2.061 | 0.678 | 0.947 | |
8 | 1 | 2.272 | – | 0.000 | 2.272 | 2.272 | – | – | |
Co3+ | 6 | 15 | 1.908 | 0.013 | 0.049 | 1.942 | 1.893 | 1.575 | 2.638 |
Co4+ | 6 | 1 | 1.874 | – | 0.000 | 1.874 | 1.874 | – | – |
Ni2+ | 2 | 2 | 1.686 | 0.001 | 0.002 | 1.687 | 1.685 | – | – |
4 | 3 | 1.950 | 0.047 | 0.082 | 1.977 | 1.895 | −1.732 | – | |
5 | 8 | 2.028 | 0.012 | 0.031 | 2.044 | 2.013 | 0.089 | −1.701 | |
6 | 242 | 2.070 | 0.020 | 0.118 | 2.148 | 2.030 | 0.900 | 1.669 | |
Ni4+ | 6 | 5 | 1.870 | 0.004 | 0.011 | 1.875 | 1.865 | 0.408 | 1.817 |
Cu+ | 2 | 42 | 1.839 | 0.022 | 0.087 | 1.882 | 1.794 | −0.286 | −0.503 |
3 | 2 | 1.969 | 0.002 | 0.003 | 1.971 | 1.968 | – | – | |
4 | 13 | 2.084 | 0.042 | 0.137 | 2.171 | 2.034 | 0.619 | −0.190 | |
Cu2+ | 4 | 129 | 1.943 | 0.017 | 0.085 | 1.986 | 1.901 | 0.285 | 0.160 |
5 | 218 | 2.037 | 0.022 | 0.122 | 2.106 | 1.984 | 0.534 | 0.244 | |
6 | 365 | 2.130 | 0.030 | 0.174 | 2.225 | 2.051 | 0.678 | 0.322 | |
8 | 4 | 2.302 | 0.033 | 0.069 | 2.349 | 2.280 | 1.689 | 2.751 | |
Cu3+ | 4 | 11 | 1.846 | 0.018 | 0.055 | 1.872 | 1.817 | 0.070 | −1.052 |
Zn2+ | 4 | 227 | 1.952 | 0.016 | 0.115 | 2.020 | 1.905 | 0.166 | 1.334 |
5 | 36 | 2.051 | 0.015 | 0.073 | 2.085 | 2.012 | −0.304 | 0.138 | |
6 | 193 | 2.110 | 0.023 | 0.144 | 2.200 | 2.056 | 1.050 | 1.676 | |
Y3+ | 6 | 25 | 2.264 | 0.019 | 0.069 | 2.291 | 2.222 | −0.208 | −0.894 |
7 | 35 | 2.332 | 0.018 | 0.065 | 2.366 | 2.302 | 0.002 | −0.708 | |
8 | 99 | 2.390 | 0.019 | 0.096 | 2.438 | 2.342 | −0.690 | 0.473 | |
9 | 15 | 2.422 | 0.019 | 0.071 | 2.468 | 2.397 | 1.140 | 1.142 | |
10 | 1 | 2.496 | – | 0.000 | 2.496 | 2.496 | – | – | |
12 | 1 | 2.541 | – | 0.000 | 2.541 | 2.541 | – | – | |
Zr4+ | 6 | 73 | 2.078 | 0.013 | 0.082 | 2.129 | 2.048 | 1.057 | 3.431 |
7 | 13 | 2.146 | 0.012 | 0.032 | 2.162 | 2.129 | 0.187 | −1.758 | |
8 | 21 | 2.199 | 0.006 | 0.022 | 2.211 | 2.189 | −0.219 | −0.686 | |
9 | 3 | 2.263 | 0.019 | 0.036 | 2.278 | 2.242 | −1.132 | – | |
10 | 7 | 2.283 | 0.005 | 0.011 | 2.288 | 2.277 | −0.147 | −2.054 | |
Nb4+ | 6 | 3 | 2.054 | 0.006 | 0.011 | 2.061 | 2.049 | 1.449 | – |
Nb5+ | 4 | 2 | 1.831 | 0.005 | 0.007 | 1.834 | 1.827 | – | – |
5 | 4 | 1.926 | 0.011 | 0.025 | 1.933 | 1.907 | −1.982 | 3.938 | |
6 | 240 | 1.993 | 0.018 | 0.102 | 2.046 | 1.944 | 0.137 | 0.150 | |
7 | 3 | 2.069 | 0.013 | 0.026 | 2.082 | 2.056 | −0.217 | – | |
8 | 1 | 2.080 | – | 0.000 | 2.080 | 2.080 | – | – | |
Mo3+ | 6 | 5 | 2.095 | 0.009 | 0.023 | 2.109 | 2.086 | 1.468 | 2.769 |
Mo4+ | 6 | 9 | 2.003 | 0.007 | 0.023 | 2.016 | 1.992 | 0.559 | 0.323 |
Mo5+ | 5 | 2 | 1.916 | 0.004 | 0.009 | 1.920 | 1.911 | – | – |
6 | 74 | 1.992 | 0.015 | 0.070 | 2.026 | 1.955 | −0.034 | −0.410 | |
Mo6+ | 4 | 434 | 1.764 | 0.009 | 0.057 | 1.790 | 1.732 | −0.255 | 0.861 |
5 | 15 | 1.872 | 0.016 | 0.053 | 1.898 | 1.845 | 0.069 | −0.882 | |
6 | 506 | 1.972 | 0.015 | 0.091 | 2.024 | 1.933 | 0.096 | −0.282 | |
Tc7+ | 4 | 6 | 1.705 | 0.004 | 0.009 | 1.711 | 1.702 | 0.672 | −1.320 |
Ru3+ | 6 | 3 | 2.025 | 0.002 | 0.003 | 2.027 | 2.024 | – | – |
Ru4+ | 6 | 8 | 1.982 | 0.011 | 0.034 | 1.995 | 1.961 | −0.713 | −0.066 |
Ru5+ | 6 | 23 | 1.964 | 0.013 | 0.044 | 1.987 | 1.943 | 0.241 | −1.333 |
Rh3+ | 6 | 11 | 2.025 | 0.021 | 0.065 | 2.071 | 2.006 | 1.324 | 0.754 |
Rh4+ | 6 | 3 | 2.007 | 0.011 | 0.020 | 2.020 | 2.000 | 1.705 | – |
Pd2+ | 4 | 29 | 2.011 | 0.020 | 0.078 | 2.060 | 1.982 | 0.578 | −0.419 |
Pd4+ | 6 | 2 | 1.999 | 0.004 | 0.005 | 2.001 | 1.996 | – | – |
Ag+ | 2 | 5 | 2.136 | 0.009 | 0.043 | 2.164 | 2.121 | 0.862 | −1.700 |
3 | 15 | 2.278 | 0.025 | 0.083 | 2.319 | 2.236 | 0.003 | −0.865 | |
4 | 37 | 2.402 | 0.030 | 0.125 | 2.466 | 2.341 | −0.180 | −0.607 | |
5 | 45 | 2.489 | 0.036 | 0.147 | 2.555 | 2.408 | −0.190 | −0.438 | |
6 | 63 | 2.537 | 0.031 | 0.136 | 2.594 | 2.458 | −0.292 | −0.539 | |
7 | 9 | 2.589 | 0.028 | 0.084 | 2.618 | 2.534 | −1.001 | 0.480 | |
8 | 13 | 2.656 | 0.030 | 0.113 | 2.730 | 2.617 | 1.199 | 1.882 | |
9 | 3 | 2.704 | 0.024 | 0.041 | 2.731 | 2.690 | 1.732 | – | |
Cd2+ | 5 | 4 | 2.257 | 0.014 | 0.034 | 2.278 | 2.244 | 1.291 | 2.291 |
6 | 135 | 2.302 | 0.021 | 0.108 | 2.368 | 2.260 | 0.618 | 0.035 | |
7 | 6 | 2.377 | 0.047 | 0.132 | 2.466 | 2.334 | 1.758 | 3.604 | |
8 | 18 | 2.432 | 0.027 | 0.086 | 2.469 | 2.383 | −0.105 | −1.040 | |
9 | 1 | 2.530 | – | 0.000 | 2.530 | 2.530 | – | – | |
Hf4+ | 6 | 11 | 2.082 | 0.013 | 0.035 | 2.099 | 2.064 | 0.085 | −1.193 |
7 | 4 | 2.128 | 0.003 | 0.006 | 2.131 | 2.125 | −0.017 | −5.552 | |
8 | 7 | 2.190 | 0.004 | 0.013 | 2.199 | 2.186 | 1.365 | 2.285 | |
Ta5+ | 6 | 138 | 1.988 | 0.018 | 0.100 | 2.052 | 1.951 | 0.477 | 0.131 |
7 | 14 | 2.057 | 0.007 | 0.023 | 2.069 | 2.046 | 0.459 | −0.831 | |
W5+ | 6 | 4 | 1.956 | 0.019 | 0.043 | 1.976 | 1.933 | −0.225 | −2.734 |
W6+ | 4 | 35 | 1.773 | 0.012 | 0.050 | 1.797 | 1.747 | −0.172 | 0.581 |
5 | 12 | 1.859 | 0.013 | 0.040 | 1.879 | 1.839 | 0.133 | −1.593 | |
6 | 363 | 1.951 | 0.017 | 0.100 | 1.995 | 1.894 | −0.455 | 0.408 | |
Re5+ | 6 | 3 | 1.940 | 0.005 | 0.009 | 1.945 | 1.936 | 1.597 | – |
Re7+ | 4 | 41 | 1.716 | 0.011 | 0.053 | 1.740 | 1.686 | −0.443 | 0.444 |
5 | 8 | 1.810 | 0.010 | 0.035 | 1.827 | 1.792 | −0.155 | 1.651 | |
6 | 10 | 1.882 | 0.012 | 0.037 | 1.906 | 1.869 | 0.909 | 0.092 | |
Os5+ | 6 | 4 | 1.960 | 0.004 | 0.008 | 1.963 | 1.954 | −1.846 | 3.508 |
Os6+ | 6 | 1 | 1.926 | – | 0.000 | 1.926 | 1.926 | – | – |
Os7+ | 5 | 1 | 1.825 | – | 0.000 | 1.825 | 1.825 | – | – |
6 | 3 | 1.887 | 0.014 | 0.034 | 1.904 | 1.870 | – | – | |
Os8+ | 4 | 1 | 1.698 | – | 0.000 | 1.698 | 1.698 | – | – |
5 | 3 | 1.793 | 0.020 | 0.039 | 1.811 | 1.772 | −0.726 | – | |
6 | 4 | 1.885 | 0.018 | 0.040 | 1.902 | 1.862 | −0.798 | −0.968 | |
Ir3+ | 6 | 1 | 2.042 | – | 0.000 | 2.042 | 2.042 | – | – |
Ir4+ | 4 | 5 | 1.909 | 0.007 | 0.017 | 1.919 | 1.902 | 0.448 | −0.638 |
6 | 12 | 2.015 | 0.010 | 0.034 | 2.031 | 1.997 | −0.353 | −0.043 | |
Ir5+ | 6 | 6 | 1.990 | 0.013 | 0.030 | 2.001 | 1.971 | −0.928 | −1.725 |
Pt2+ | 4 | 2 | 2.007 | 0.011 | 0.022 | 2.017 | 1.995 | −1.008 | – |
Pt4+ | 6 | 33 | 2.021 | 0.014 | 0.057 | 2.055 | 1.998 | 0.345 | −0.452 |
Au3+ | 4 | 24 | 1.999 | 0.013 | 0.040 | 2.020 | 1.980 | 0.161 | −1.363 |
Hg2+ | 2 | 1 | 1.955 | – | 0.000 | 1.955 | 1.955 | – | – |
4 | 6 | 2.316 | 0.081 | 0.227 | 2.403 | 2.176 | −1.116 | 1.176 | |
5 | 3 | 2.380 | 0.090 | 0.168 | 2.445 | 2.277 | −1.565 | – | |
6 | 25 | 2.429 | 0.072 | 0.242 | 2.584 | 2.342 | 0.532 | −0.474 | |
7 | 9 | 2.505 | 0.045 | 0.140 | 2.593 | 2.453 | 0.723 | 0.440 | |
8 | 8 | 2.502 | 0.021 | 0.050 | 2.530 | 2.479 | 0.435 | −2.040 |