Engel-Brewer correlation theory

The CD-embryo model and the Engel-Brewer correlation theory... 

The correlation between the valence electron counts and the stabilities of intermetallic phases and stmctures were also espoused by others, like the physical chemists Neds N. Engel (b. 1904) and Leo Brewer (1919-2005), although Hume-Rothery found their result somewhat controversial. The Engel-Brewer theory asserts that the crystal stmctures of transition metals and their intermetallic compounds are determined solely by the number of valence s and p electrons. For example, Engel suggested in 1949 that the BCC stmcture correlated with (where n is the total number of valence... 

In the course of the past decade several explanations have been put forward to account for the anomalous diffusion in bcc metals. The different models based on the presence of extrinsic vacancies (Kidson, 1963), on the temperature dependence of elastic constants (Aaronson and Shewmon, 1967), on dislocation enhanced diffusion (Peart and Askill, 1967) or on vacancy anharmonicity (Gilder and Lazarus, 1975) have been thoroughly discussed in the original and in the various review papers. Two additional models, the activated interstitial and, more recently, the w-embryo model, have been proposed as alternative explanations for anomalous bcc diffusion. These two models and their possible common interpretation on the basis of the Engel-Brewer electron correlation theory will be discussed in the next sub-section. 

Brewer 1967) were qualitative and based upon the Engel (1949) correlation, involving the number of sp electrons. The first physical theories were due to Ducastelle and Cyrot-Lackman (1971) and Dalton and Deegan (1969), here relationships between crystal structure and band structure were sought. A more complete treatment for the transition metals, due to Pettifor (1970, 1972), related the hcp bcc hcp fcc sequence to the change in d occupation number across the transition metal series. 

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