Table 1. Bond-length statistics for the five common alkali-metal ions.
Ion | Coordination number | Number of bonds | Number of coordination polyhedra | Mean bond length (Å) | Standard deviation (Å) | Range (Å) | Maximum bond length (Å) | Minimum bond length (Å) | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|---|---|---|
Li+ | 3 | 12 | 4 | 1.913 | 0.040 | 0.113 | 1.984 | 1.871 | – | – |
4 | 1676 | 419 | 1.972 | 0.075 | 0.754 | 2.444 | 1.690 | 1.563 | 6.273 | |
5 | 455 | 91 | 2.108 | 0.161 | 0.858 | 2.673 | 1.815 | 1.265 | 1.362 | |
6 | 1038 | 173 | 2.178 | 0.137 | 0.866 | 2.692 | 1.826 | 1.293 | 1.996 | |
7 | 14 | 2 | 2.331 | 0.244 | 0.728 | 2.658 | 1.930 | – | – | |
8 | 8 | 1 | 2.513 | 0.000 | 0.000 | 2.513 | 2.513 | – | – | |
Total | 3203 | 690 | ||||||||
Na+ | 3 | 21 | 7 | 2.307 | 0.045 | 0.153 | 2.367 | 2.214 | – | – |
4 | 524 | 131 | 2.359 | 0.076 | 0.586 | 2.775 | 2.189 | 0.878 | 2.032 | |
5 | 710 | 142 | 2.413 | 0.108 | 0.808 | 2.968 | 2.160 | 1.455 | 3.522 | |
6 | 5520 | 920 | 2.441 | 0.112 | 0.926 | 3.055 | 2.129 | 1.317 | 3.246 | |
7 | 1351 | 193 | 2.541 | 0.180 | 1.002 | 3.180 | 2.178 | 0.723 | −0.020 | |
8 | 1608 | 201 | 2.599 | 0.192 | 1.069 | 3.211 | 2.142 | 0.461 | −0.197 | |
9 | 450 | 50 | 2.686 | 0.224 | 1.044 | 3.204 | 2.160 | 0.121 | −0.879 | |
10 | 170 | 17 | 2.741 | 0.240 | 0.899 | 3.156 | 2.257 | −0.063 | −1.075 | |
12 | 252 | 21 | 2.795 | 0.182 | 0.950 | 3.272 | 2.322 | 0.053 | −0.295 | |
Total | 10606 | 1682 | ||||||||
K+ | 4 | 96 | 24 | 2.708 | 0.078 | 0.365 | 2.892 | 2.527 | – | – |
5 | 295 | 59 | 2.796 | 0.162 | 1.032 | 3.537 | 2.505 | 1.404 | 3.349 | |
6 | 714 | 119 | 2.828 | 0.177 | 1.140 | 3.587 | 2.447 | 1.299 | 2.268 | |
7 | 469 | 67 | 2.861 | 0.179 | 1.030 | 3.554 | 2.524 | 1.269 | 1.474 | |
8 | 2272 | 284 | 2.894 | 0.172 | 1.107 | 3.644 | 2.537 | 1.195 | 1.642 | |
9 | 2772 | 308 | 2.955 | 0.214 | 1.306 | 3.797 | 2.491 | 1.079 | 0.917 | |
10 | 2430 | 243 | 3.013 | 0.246 | 1.248 | 3.773 | 2.525 | 0.839 | 0.084 | |
11 | 957 | 87 | 3.089 | 0.290 | 1.181 | 3.793 | 2.612 | 0.550 | −0.763 | |
12 | 2328 | 194 | 3.095 | 0.264 | 1.204 | 3.790 | 2.586 | 0.578 | −0.535 | |
13 | 455 | 35 | 3.149 | 0.298 | 1.290 | 3.808 | 2.518 | 0.364 | −0.834 | |
14 | 336 | 24 | 3.239 | 0.296 | 1.292 | 3.771 | 2.479 | 0.057 | −0.929 | |
15 | 525 | 35 | 3.182 | 0.265 | 1.148 | 3.748 | 2.600 | 0.257 | −1.164 | |
Total | 13649 | 1479 | ||||||||
Rb+ | 4 | 48 | 12 | 2.951 | 0.160 | 0.706 | 3.360 | 2.654 | – | – |
5 | 15 | 3 | 2.864 | 0.078 | 0.236 | 2.976 | 2.740 | – | – | |
6 | 84 | 14 | 2.989 | 0.148 | 0.734 | 3.488 | 2.754 | – | – | |
7 | 140 | 20 | 3.002 | 0.186 | 0.937 | 3.628 | 2.691 | 1.283 | 1.554 | |
8 | 480 | 60 | 3.033 | 0.190 | 1.055 | 3.711 | 2.656 | 1.030 | 1.236 | |
9 | 675 | 75 | 3.079 | 0.204 | 1.172 | 3.839 | 2.667 | 0.980 | 1.192 | |
10 | 1080 | 108 | 3.146 | 0.244 | 1.171 | 3.890 | 2.719 | 0.858 | 0.081 | |
11 | 484 | 44 | 3.188 | 0.248 | 1.211 | 3.884 | 2.673 | 0.725 | −0.242 | |
12 | 840 | 70 | 3.228 | 0.288 | 1.181 | 3.896 | 2.715 | 0.545 | −0.663 | |
13 | 247 | 19 | 3.293 | 0.314 | 1.148 | 3.932 | 2.784 | 0.376 | −1.163 | |
14 | 280 | 20 | 3.301 | 0.291 | 1.151 | 3.895 | 2.744 | 0.332 | −0.938 | |
15 | 195 | 13 | 3.338 | 0.278 | 1.065 | 3.945 | 2.880 | 0.485 | −0.934 | |
17 | 17 | 1 | 3.456 | 0.336 | 1.009 | 3.939 | 2.930 | – | – | |
18 | 90 | 5 | 3.478 | 0.239 | 0.695 | 3.771 | 3.076 | – | – | |
Total | 4675 | 464 | ||||||||
Cs+ | 6 | 102 | 17 | 3.124 | 0.139 | 0.702 | 3.568 | 2.866 | 0.922 | 1.040 |
7 | 70 | 10 | 3.193 | 0.166 | 0.858 | 3.806 | 2.948 | – | – | |
8 | 200 | 25 | 3.244 | 0.189 | 1.017 | 3.911 | 2.894 | 0.863 | 0.708 | |
9 | 432 | 48 | 3.251 | 0.181 | 1.052 | 3.882 | 2.830 | 0.656 | 0.186 | |
10 | 930 | 93 | 3.304 | 0.208 | 1.257 | 3.986 | 2.729 | 0.696 | 0.174 | |
11 | 748 | 68 | 3.333 | 0.226 | 1.136 | 4.023 | 2.887 | 0.630 | −0.106 | |
12 | 1080 | 90 | 3.377 | 0.250 | 1.162 | 4.072 | 2.910 | 0.670 | −0.437 | |
13 | 520 | 40 | 3.426 | 0.276 | 1.256 | 4.130 | 2.874 | 0.480 | −0.571 | |
14 | 714 | 51 | 3.444 | 0.297 | 1.242 | 4.169 | 2.927 | 0.528 | −0.764 | |
15 | 705 | 47 | 3.503 | 0.301 | 1.253 | 4.157 | 2.904 | 0.241 | −0.953 | |
16 | 224 | 14 | 3.550 | 0.321 | 1.276 | 4.199 | 2.923 | 0.341 | −0.870 | |
17 | 68 | 4 | 3.530 | 0.326 | 1.069 | 4.060 | 2.991 | – | – | |
18 | 648 | 36 | 3.570 | 0.277 | 1.243 | 4.195 | 2.952 | −0.010 | −0.807 | |
20 | 20 | 1 | 3.723 | 0.419 | 0.855 | 4.065 | 3.210 | – | – | |
Total | 6461 | 544 |