Transition elements atomic size

The atoms of transition elements do not display the same general trend as the main group elements. A key reason for this is that electrons are added to inner energy levels — the d orbitals — rather than to the outer energy levels. As a result, Zgff changes relatively little, so atomic size remains fairly constant. In later chemistry courses, you will learn a more complete explanation for the atomic radii of transition-element atoms. 

The size of atoms of transition elements within the same period changes only slightly because electrons are filling d orbitals rather than the ontermost energy level. Because the increase in nuclear charge is canceled by an increase in d electrons, the attraction of the valence electrons by the nuclens remains abont the same. Becanse there is little change in the nuclear attraction for the valence electrons, the atomic size remains relatively constant for the transition elements. 

Borides, in contrast to carbides and nitrides, are characterized by an unusual structural complexity for both metal-rich and B-rich compositions. This complexity has its origin in the tendency of B atoms to form one- two-, or three-dimensional covalent arrangements and to show uncommon coordination numbers because of their large size (rg = 0.88 10 pm) and their electronic structure (deficiency in valence electrons). The structures of the transition-element borides are well established " . 

Other single-crystal x-ray diffraction studies of transition element dopants in jS-rh boron are based on the results of a refinement of the /3-rh boron structure that establishes the occurrence of four new low-occupancy (3.7, 6.6, 6.8 and 8.5%) B positions in addition to the earlier known ones. The dopant elements studied, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zr, Nb, Hf and Ta, do not enter B positions in the framework, but they enter the Al, A2, D and E positions. In some cases the doping elements have been studied at several concentrations for each element and for different cooling rates. The percentage occupancies of certain positions are eorrelated with the atomie sizes of the dopants. The bond distances between the polyhedra are shorter than those within the polyhedra. The mechanism of doping for some cases is denoted displacive, rather than interstitial or substitutional, because of competing interactions between the six different partially occupied B positions and dopant atoms. 

Line compounds. These are phases where sublattice occupation is restricted by particular combinations of atomic size, electronegativity, etc., and there is a well-defined stoichiometry with respect to the components. Many examples occur in transition metal borides and silicides, III-V compounds and a number of carbides. Although such phases are considered to be stoichiometric in the relevant binary systems, they can have partial or complete solubility of other components with preferential substitution for one of the binary elements. This can be demonstrated for the case of a compound such as the orthorhombic Cr2B-type boride which exists in a number or refractory metal-boride phase diagrams. Mixing then occurs by substitution on the metal sublattice. 

The atomic radii of the second- and third-series transition elements from group 4B on are nearly identical, though we would expect an increase in size on adding an entire principal quantum shell of electrons. The small sizes of the third-series atoms are associated with what is called the lanthanide contraction, the general decrease in atomic radii of the /-block lanthanide elements between the second and third transition series (Figure 20.4). 

It has already been emphasized that within a family of non transition elements, metallic character increases with increase in atomic number, atomic weight, and atomic size. There is no better illustration of this trend than Periodic Group Vb the lightest members of the group, nitrogen (Z = 7), and phosphorus (Z — 15), are typical nonmetals, whereas the heaviest member, bismuth (Z = 83) is a typical metal. The remaining members, arsenic (Z = 33) and antimony (Z 51) are intermediate in character and are often appropriately called metalloids. 

From the discussion of Chapter I, it follows that metallic conduction is to be associated with partially filled bands of collective-electron states. Since the s-p bands of an ionic compound are either full or empty, metallic conduction implies partially filled d bands, and collective d electrons imply Rtt < Rc(n,d). From the requirement Rtt < Rc(n4) it is apparent that the metallic conduction in ionic compounds must be restricted either to transition element compounds in which the anions are relatively small or to compounds with a cation/anion ratio > 1. Also Rc(n,d) decreases, for a given n, with increasing atomic number, that is with increasing nuclear charge, and the presence of eQ electrons increases the effective size of an octahedral cation (627) (see Fig. 66) and similarly UQ electrons the size of a tetrahedral cation. It follows that If the cation/anion ratio < 1, MO d electrons are more probable in ionic compounds with octahedral-site cations if the cations contain three or less d electrons MO d electrons are more probable in ionic compounds with tetrahedral-site cations if the cations contain two or less d electrons. 

Next we study the effects of the cluster size on DOS. When the cluster size is increased, the interactions between neighboring atoms with long distances are taken into account, then the electronic state approaches that of btilk. Figure 12 compares DOS of the clusters Nig, Nij3, Nijj and Ni j, as well as bulk crystaP by a band structure calculation. Usually the band structure of the bulk crystal can be rather well reproduced if we take several ten atoms in the model cluster for transition elements, though the small cluster model provides somewhat narrower d band. In the case of the element with a d band which is almost completely occupied, for example the case of silver, the size effect is not very large, but a small cluster already well represents the band structure of bulk as shown in Fig. 13. 

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