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Metallic radii rm are correlated with the ionic radii ri by linear relationships. For groups 1 up to 7 as well as for Al, Ga, In, Tl, Sn, and Pb the ionic radii refer to the maximum valences (oxidation states) as known from compounds according to rm ~ 1.16 x (ri + 0.64) [A° ]. For groups 8 up to 12, rm ~ 0.48 x (ri + 2.26) [°A] with valences W = 14 - G (G = group number). These valences are considered regular (Wr). For groups 1 up to 12, they obey the equation Wr = 7 - |G - 7|. According to this equation all outer s electrons and the unpaired d electrons should be involved in chemical bonding, i.e. in the cohesion of the element in the solid state. From the melting temperatures and the atomic volumes it is concluded, however, that only 19 out of the 30 d-block elements have regular valences, namely the elements of groups 3, 5, 6, 10, 11 as well as Os, Ir, Zn, Cd, and possibly Ru. All of the non-regular valences are lower than the regular ones. Four of them are integers: Mn 3; Fe, Co 4; Re 6.
In the body-centered cubic structure and in closest sphere-packings the atoms are arranged to give structures with equal densities. A measure of the packing density of atoms is derived. Several crystal structures of elements, including the bcc structure and the closest sphere packings, represent a state of maximum density in which the atomic volume is characteristic of each element. From any crystal structure of an element its atomic volume in this state can be calculated to a good approximation.
Relationships between bond lengths and bond numbers and also between atomic volumes and valencies are derived and parameters for their calculation are given for the s-block, p-block, and d-block metals. From the atomic volumes under pressure, the valencies of three solid lanthanoids have been confirmed or redetermined: La 3; Ce 2. 3. and 4; Yb 2 and 3.