Atomic dimensions, interatomic distances in the intermetallic phases

We underline these results and the implied concepts quoting from a comprehensive review on this subject (Simon 1983). We remember indeed that, ever since it was experimentally possible to determine atomic distances in molecules and crystals, efforts have been made to draw conclusions about the nature of the chemical bonding, and to compare interatomic distances (dimensions) in the compounds with those in the chemical elements. Distances between atoms in an element can be measured with high precision. As such, however, they cannot be simply used in predicting interatomic distances in the compounds. In a rational procedure, reference values (atomic radii) have to be extracted from the individual (interatomic distances) measured values. Various functions have been suggested for this purpose. In the specific case of the metals it has been pointed out that interatomic distances depend primarily on the number of ligands and on the number of valence electrons of the atoms (Pearson 1972). 

Pauling has found empirically that there was a simple logarithmic relationship between the bond length R and the bond order 0, namely  

The radii in the two structures, calculated at the same temperature by means of the known expansion coefficients, were compared and used to construct the reported equation. For the other metals, that is for the more general problem of the radius conversion from any coordination to CN 12, a percentage correction was applied by using a curve which ranges from about +3% for the conversion from CN 8 to CN 12 to about +20% for the conversion from CN 3 to CN 12, as suggested by Laves (1956) in a detailed paper dealing with several aspects of crystal structure and atomic sizes (see Fig. 4.13). 

For an indication of the values of the atomic radii of the different elements and of their trend along the Periodic Table, see Figs 4.5 and 4.14. Notice the variations along each period (each horizontal sequence in Fig. 4.14) and the smaller values (and their small changes) for the metals in the middle of the transition block. Notice also in the lanthanide sequence the greater dimensions of the divalent Eu andYb. 

In the cP2-W type (CN 8) structure Vsph is 0.68 Vat (only a portion of the available space is occupied by the atomic sphere ). In the cF4-Cu type and in the ideal hP2-Mg type (CN 12) structures, Vsph is 0.74 Vat. Considering now the previously reported relationship between RCs n and i CN8, we may compute for a given element very little volume (Vat) change in the allotropic transformation from a form with CN 12 to the form with CN 8, because the radius variation is nearly 

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