Determination of electrons per atom ratio for transition metal compounds studied by FLAPW-Fourier calculations

Abstract

Among 54 elements in the periodic table, whose electrons per atom ratio e/a has been consistently determined within the framework of the Full-potential Linearised Augmented Plane Wave-Fourier theory, the present authors have claimed the need of properly differentiating two distinct e/a values for Ca in the Group 2 and for Sc and Y in Group 3 in the periodic table, depending on whether they are dissolved in transition metal (TM) (TM from Group 4–10) matrix or in non-TM (Al, Zn, etc.) matrix. It is also emphasised that this unique alloying environment effects are essentially absent in other elements Sr and Ba in Group 2 and La in Group 3. We could also show that the linear interpolation rule stating that e/a of any binary compounds is estimated by taking a composition average of those of constituent elements, holds within the accuracy of ±20%, even when elements in Groups 2 and 3 are involved. The Hume-Rothery electron concentration rule for Laves compounds with Pearson symbol cF24 has been successfully elucidated by classifying them into subgroups with respect to square of critical reciprocal lattice vector serving as a key parameter in the interference condition.

Keywords:

• Band calculations
• bonding
• electron theory
• electronic structure
• transitionmetal compounds

Acknowledgements

We thank Dr. Manabu Inukai, Nagoya Institute of Technology, for his assistance with programming and computational skills involved in running WIEN2k and FLAPW-Fourier analysis and Prof. Yoichi Nishino, Nagoya Institute of Technology, for exchanging valuable information through discussions.

Notes

1. It covers elements Li, Be, B and C in the Period 2, Na, Mg, Al, Si and P in the Period 3, K, Ca, Sc to Ni, Cu, Zn, Ga, Ge, As in the Period 4, Rb, Sr, Y to Pd, Ag, Cd, In, Sn, Sb in the period 5 and Cs, Ba, La to Pt, Au, Hg, Tl, Pb and Bi in the Period 6 of the periodic table [3].

2. A composition dependence of e/a in an A-B alloy system can be often fitted to a line given by , where and indicate e/a values of the constituent elements A and B, respectively, for an A_xB_1-x compound [3–8]. Since this relation has been confirmed to hold well in many cases, we hereafter call it the linear interpolation rule.