E/a determination for 4d- and 5d-transition metal elements and their intermetallic compounds with Mg, Al, Zn, Cd and In

Abstract

The present work is devoted to the determination of the effective electrons per atom ratio e/a by means of first-principles full-potential linearized augmented plane wave-Fourier method for elements from Rb to Ag in Period 5 and from Cs to Au in Period 6 of the periodic table and is regarded as a continuation of the preceding work done for elements from K to Cu in Period 4. The value of e/a was determined by reading off the square of the Fermi diameter, from the dispersion relation for electrons outside the Muffin-Tin spheres. A straightforward reading of the ordinate at the Fermi level, i.e. local reading method was validated for Rb and Cs in Group 1, Sr in Group 2, Y in Group 3, Pd and Pt in Group 10 and Ag and Au in Group 11. Instead, the nearly free electron (NFE) method was found to be indispensable for TM elements from Zr to Rh in Period 5 and those from Ba to Ir in Period 6. The composition dependence of e/a values for intermetallic compounds in X–TM (X = Mg, Al, Zn, Cd and In) alloy systems was also studied. The new Hume–Rothery electron concentration rule was established by constructing e/uc, the number of electrons per unit cell, vs. square of critical reciprocal lattice vector, , diagram for structurally complex metallic alloys having a pseudogap at the Fermi level. A proper use of either the local reading- or the NFE-e/a for the elements as indicated above is found to be essential.