Energy gap formation mechanism through the interference phenomena of electrons in face-centered cubic elements and compounds with the emphasis on half-Heusler and Heusler compounds

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Many face-centred cubic elements and compounds with the number of atoms per unit cell N equal to 8, 12 and 16 are known to be stabilised by forming either a band gap or a pseudogap at the Fermi level. They are conveniently expressed as cF8, cF12 and cF16, respectively, in the Pearson symbol. From the cF8 family, we worked on three tetravalent elements C (diamond), Si and Ge, SZn-type AsGa compound and NaCl-type compounds like BiLu, AsSc, etc. From the cF12 family, more than 80 compounds were selected, with a particular emphasis on ABC- and half-Heusler-type ternary equiatomic compounds. Among cF16 compounds, both the Heusler compounds ABC2 and Zintl compounds were studied. We revealed that, regardless of whether or not the transition metal (TM) and/or rare-earth (RE) elements are involved as constituent elements, the energy gap formation mechanism for cF8, cF12 and cF16 compounds can be universally discussed in terms of interference phenomenon of itinerant electrons with set of reciprocal lattice planes with = 8, 11 and 12, where refers to square of the critical reciprocal of lattice vector of an fcc lattice. The number of itinerant electrons per unit cell, e/uc, for all these band gap/pseudogap-bearing compounds is found to fall on a universal line called “3/2-power law” when plotted against on a logarithmic scale. This proves the validity of the fulfilment of the interference condition in conformity with other pseudogap compounds with different crystal symmetries and different sizes of the unit cell reported in literature.