Hume-Rothery

Hume-Rothery s rule The statement that the phase of many alloys is determined by the ratio.s of total valency electrons to the number of atoms in the empirical formula. See electron compounds. 

W. Hume-Rothery, ]. W. Christian and W. B. Pearson, Metallurgical Equilibrium Diagrams, Institute of Physics, 1952. 

Understanding alloys in terms of electron theory. The band theory of solids had no impact on the thinking of metallurgists until the early 1930s, and the link which was eventually made was entirely due to two remarkable men - William Hume-Rothery in Oxford and Harry Jones in Bristol, the first a chemist by education and the second a mathematical physicist. 

Figure 3.28. William Hume-Rothery as a young man (courtesy Mrs. Jennifer Moss).

Hume-Rothery s position as one of the key creators of modern physical metallurgy remains unchallenged. 

Hume-Rothery s ideas and their theoretical development by Mott and Jones stimulated much consequential research around the world. The most impressive early eonvert was a Freneh physicist, Jacques Friedel, who should have been mentioned in connection with dislocations, in the theory of whieh he played an early part (see the Corrigenda). After a very disturbed war, which ranged from study at the... 

Meanwhile, electron theory was revived effectively in Hume-Rothery s own base of Oxford, and is now led by a distinguished mathematical physicist, David Pettifor. 

The nature of the exchange energy, and just how unbalanced spin systems become stabilised, was studied more deeply after Hume-Rothery had written, and a very clear non-mathematical exposition of the present position can be found in (Cottrell 1988, p. 101). 

Hume-Rothery (1936) The Structure of Metals and Alloys (The Institute of Metals, London). 

Pettifor, D.G. (2000) William Hume-Rothery his life and science, in The Science of Alloys for the list Century A Hume-Rothery Symposium Celebration, eds. Turchi, P. et a . (TMS, Warrendale). 

Most treatments, even when intended for materials scientists, of these competing forms of quantum-mechanical simplification are written in terms accessible only to mathematical physicists. Fortunately, a few translators , following in the tradition of William Hume-Rothery, have explained the essentials of the various approaches in simple terms, notably David Pettifor and Alan Cottrell (e.g., Cottrell 1998), from whom the formulation at the end of the preceding paragraph has been borrowed. 

Just as the saturated solubility of sugar in water is limited, so the solid solubility of element B in metal A may also be limited, or may even be so low as to be negligible, as for example with lead in iron or carbon in aluminium. There is extensive interstitial solid solubility only when the solvent metal is a transition element and when the diameter of the solute atoms is < 0 6 of the diameter of the solvent atom. The Hume-Rothery rules state that there is extensive substitutional solid solubility of B in >1 only if ... 

Hume-Rothery and Bradley have mentioned that the a manganese structure can be explained only by assuming that the atoms are of different sixes (/. Inst, Metals, 11,252,257 (1944)). 

The indication from interatomic distances that less than 4 bonding electrons per atom are operating in white tin has been recognized by W. Hume-Rothery, The Structure of Metals and Alloys/ The Institute of Metals Monograph and Report Series No. 1, p. 26... 

It should not be thought that the structure of every intermetallic compound can be treated so simply the discussion of such struetural features as the transfer of electrons between atoms, the occurrence of strained bonds, the significance of relative atomic sizes, and the electron-atom ratio (Hume-Rothery ratio) must, however, be postponed to later papers. 

The Hume-Rothery valences described above have the values zero for manganese, iron, cobalt,... 

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