Electron-to-atom ratio

Alternatively, the effects of valency may be felt through the decrease in stacking fault energy (SFE) of fee alloys having increasing electron to atom ratio (14). 

The alloy /J NiAl is a solid with a CsCl-type structure in which one atom is located at the corners, and the second atom at the center of the unit cell. The valence-electron to atom ratio is often quoted as 1.5, using a counting scheme in which the transition metal has zero valence and the A1 is considered as trivalent. 

Figure 1 Tritium-protium separation factors for alloys of varying electron-to-atom ratio...

Levy and Boudart speculated that the catalytic properties of WC resulted from its electronic structure. They suggested that carbon ip-electrons increased the apparent electron to atom ratio, producing a more Pt-like electronic structure. This observation was wrongly interpreted in... 

The Cu-Zn system (brass) is complex as shown in Figure 9.1. The a phase is a ccp solid solution of Zn in Cu. The (3-brass is body-centered cubic, the composition corresponding to CuZn. Each phase exists over a range of Cu/Zn ratios corresponding to a solid solution with Zn or Cu added to the compound. The y-brass, CupZns, has a complex cubic structure and e-brass, CuZn3, has an hep structure. Hume-Rothery found that many intermetallic compounds have structures similar to (3-, y-, and e-brass at the same electron-to-atom ratio as the corresponding brass compounds. Some examples of these so-called electron... 

Fig. 8. (a) Experimentally obtained [57] plot of Tc vs. electron concentration in forms of (e/a) electron to atom ratio, (b) Theoretical model of plot of plasmon wave intensity vs. N(e) electron concentration. 

An interesting area still under debate in the field of metallurgy is the consequences of Fermi surface topology on the phase equilibria in alloy systems. Elucidation of the connection between these two, seemingly unrelated, features started with the work of William Hume-Rothery, who reported that the critical-valence electron to atom ratios. 

The interplay of the two defects, and LIai, has an interesting effect on the number of valence electrons in the crystals LixAli, . In the present work the valence electron concentration Cve is defined by the number of valence electrons per lattice site. For the stoichiometric phase AB with the ideal lattice Cve is equal to the electron-to-atom ratio e/a (1.5 for AB " and 2.0 for AB " ). In the last column of Table 4 Cve is given as a function of x for the LixAlj-, phases ... 

Table 7. Fermi energies (in eV) and densities of states per eV and lattice site at the Fermi level for B32-type compounds AB deduced from the RAPW procedure " . (The values in brackets are gained from the ASA method - >.) The bottom of the valence states is the zero of the energy scale. For the AB compounds the Fermi energies Ep arc listed for both the ideal stoichiometric compounds (cvE is equal to the electron to atom ratio e/a = 2) and the compounds with defect structure, for which it is assumed that the fifths valence bands are non-occupied and Ep lies in the minimum of the density states curve, see Figs. 5-7. (cve = 1-98)...

Apart from the amorphous rare earth base materials mentioned above, numerous other amorphous metals and alloys have been studied. Collver and Hammond (1973) made a systematic study of amorphous transition metal films obtained by vapour deposition on cryogenic substrates. The superconducting properties of these amorphous alloys show clear differences with those of crystalline alloys. The 7J, values of the latter vary continuously with valency and give rise to two sharp peaks for electron-to-atom ratios equal to 4.5 and 6.5, respectively (Matthias, 1957). In contrast, the Tq values of the amorphous alloys show a more moderate variation with... 

Fig. 80. Superconducting transition tent perature of transition metals and alloys of the 4d series in the amorphous and crystalline states, as a function of electron-to-atom ratio. The result obtained on amorphous La0j0AUo2o ( ) has been included for comparison (after Johnson, 1978).

The alloying of Cu with group IIB to IVB metals results in a series of alloy systems with a characteristic sequence of intermetallic phases characterised by their outer electron to atom ratio (e/a), as first recognised by and named after Hume-Rothery. This behavior is attributed to the fact that the electronic structure rather than ionic radius, directed bonds, or other factors of influence for alloy formation is dominating the and crystal... 

The study of QC surfaces has led to interest in the surfaces of related CMAs. QCs typically exist in a narrow composition region of the phase diagram due to the Hume-Rothery constraint of specific valence electron to atom ratio, which is related to electronic stabilization of QCs [196-198]. In the neighborhood of this composition region, phases with giant unit cells and local atomic order related to that of the QC can usually be found. The surfaces of these approximant phases offer the possibility of exploring surface structure and properties as a function of increasing complexity, which can be most simply defined in terms of atoms f>er unit cell. 

The substitution of Ge for some of the Al in Nb3Al results in an increase of 7, (i57-i60) Specifically, Nb3(Alo jGeo 2s) er proper annealing, exhibits 7 = 20.5°K, the highest reported to date. Although the electron to atom ratio e/a is increased from 4.50 to 4.56, the exact reason for the increase is not known. 

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