Abstract:
The lecture will address one of the key aspects of the behavior of electrons in metallic systems, which explains why certain specific atomic architectures form in so-called intermetallics. This mechanism is known after the name of its discoverer, William Hume-Rothery (1899-1968), a most famous British metallurgist.
The Hume-Rothery electron concentration rule was empirically established by Hume-Rothery (1926) almost a century ago [1] and has significantly affected subsequent tremendous developments in the field of metal physics. Academic aspirations have been revived in the late 1980s to early 1990s, when stable quasicrystals were synthesized by using the empirical Hume-Rothery rule as a guide [2]. We have soon realized that a pseudogap at the Fermi level plays a key role in stabilizing these complex compounds. Mizutani and Sato developed a unique electron theory of metals, which allows us to link the Hume-Rothery rule with the formation of a pseudogap [3-5]. It fully relies on the interference phenomena of itinerant electrons with the set of lattice planes, regardless of the degree of orbital hybridization effects involved, and the theoretical Hume-Rothery rule thus established have been extended to alloys and compounds with bonding types of metallic, ionic, or covalent, or a changing mixture of these, unless the number of itinerant electrons in the valence band is too low.
The original Hume-Rothery rule was claimed to hold in randomly substituted alloys. More recently, we have confirmed that the theoretical Hume-Rothery rule is extendable to randomly substituted alloys beyond first-principles electronic structure calculations. It has therefore direct relevance to a huge variety of compounds that show electronic conductivity. Examples are quasicrystals Al86Mn14 [6], Al65Cu20Fe15 [2], Samson compound Al3Mg2 containing 1178 atoms per unit cell [7], amorphous alloys VxSi100-x (x>20) [8], marginal conductor FeS2 [9] and so on.
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