Brewer-Engel theory

W. Hume-Rothery, The Engel-Brewer Theories of Metals and Alloys , Prog. Mat. Sci. 13 (5), 229-265 (1967). 

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... 

However, more details on the exact crystallographic stmeture determination are given by the analysis of their electronic properties. Engel-Brewer theory assumes that for metals the changes in structure depend on the number of valence sp electrons... 

Pti-x ZXjc supported on carbon or alumina, Kt/Kb is proportional to x, suggesting electron transfer from platinum to zirconium, as predicted by the Engel-Brewer theory, and (2) chemisorption of sulfur on platinum has been shown to decrease electron density of the surface, while carbon has the opposite effect. The ratio Kt/Kb was very large for ruthenium, about 10 for rhodium and about unity for palladium, which may help to explain their different activities in these and other reactions. An extensive kinetic study of the hydrogenation of mixtures of benzene and toluene on NiA zeolite has however revealed a situation of some complexity, and it is not certain that the original simple concept is totally valid. 

Jaksic has tried to propose a predictive basis for the hydrogen reaction beyond the volcano curve. The idea is based on Brewer-Engel s theory [82] for bonding in metals and intermetallic phases. According to this theory, a maximum in bond strength and stability of the intermetallic phases is expected as a metal lying at the beginning of a transition period in the Periodic Table (e.g., Ti or Zr) is combined with... 

If zl//f(ABn) were equal to zero, a mere linear dependence between activity and composition should be obtained. A corollary of this is that the higher zJ/ff(ABn), the more marked the synergetic effect, a rule which has been enunciated also by Jaksic [73] with reference to the Brewer-Engel stability theory of intermetallics. Therefore, some predictive basis for designing new materials can indeed be recognized in the specific field of intermetallics. 

The crystal structures adopted by the binary carbides and nitrides are similar to those found in noble metals. The resemblance is not coincidental, and has been explained using Engel-Brewer valence bond theory [5]. Briefly, the main group elements C and N increase the metal s effective s-p electron count, so that structures and chemical properties of the early transition metals resemble those of the Group 8 metals. This idea was first introduced by Levy and Boudart [6] who noted that tungsten carbide had platinum-like properties. 

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. 

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

Breit-Winger-Fano representation of edge structure, 34 261 Brewer-Engel theory, 38 62-63 Bridged hydroxyl groups, 34 159-174 acidity versus... 

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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