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

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.