Alloy systems element

Molybdenum, an unusually versatile alloying element, imparts numerous beneficial properties to irons and steels and to some alloy systems based on cobalt, nickel, or titanium. Comprehensive summaries of uses through 1948 (24) and 1980 (25) are available. 

Quantitative aluminum deterrninations in aluminum and aluminum base alloys is rarely done. The aluminum content is generally inferred as the balance after determining alloying additions and tramp elements. When aluminum is present as an alloying component in alternative alloy systems it is commonly deterrnined by some form of spectroscopy (qv) spark source emission, x-ray fluorescence, plasma emission (both inductively coupled and d-c plasmas), or atomic absorption using a nitrous oxide acetylene flame. 

It will be shown that a more elegant and more easily applicable solution of the problem is given by choosing another reference system. Both the dilute alloy and the unperturbed host can be described with respect to a common reference system, which consists of the unperturbed part of the alloy system and for obvious reasons is called void system. This void system allows for a single-site evaluation of the matrix element describing the wind force in electromigration and the t-matrix element required for the calculation of the residual resistivity due to a saddle-point defect. 

Trace elements which adversely affect intercrystalline attack are normally controlled at a safe level. Copper is particularly pertinent in this respect since relatively small additions can cause a marked increase in intercrystalline attack in some alloy systems (Sections 1.3 and 1.7). 

It should be remembered that the CALPHAD approach is based on the hypothesis that, for all the phases and structures existing across the complete alloy system, entire Gibbs energy vs. composition curves may be constructed even by extrapolation into regions where they are unstable or metastable. A particular case concerns the pure component elements for which the relative Gibbs energy for the different crystal structures (the so-called lattice stabilities) must also be established and defined as a function of temperature (and pressure). 

Teatum, E.T., Gschneidner Jr., K.A., and Waber, J.T. (1968) Compilation of Calculated Data Useful in Predicting Metallurgical Behavior of the Elements in Binary Alloy Systems, Report LA-4003, UC-25, Metals, Ceramics and Materials, TID-4500 (Los Alamos Scientific Laboratory, New Mexico, USA). 

Several phase diagrams of binary alloy systems have been shown (see for instance Fig. 2.18) in which the existence of intermediate phases may be noticed. In these systems we have seen the formation of AmB phases, which generally crystallize with structures other than those of the constituent elements, and which have negligible homogeneity ranges. Thermodynamically, the composition of any such phase is variable. In a number of cases, as those exemplified in Fig. 2.19, the possible variation in composition is very small (invariant composition phases or... 

According to Girgis (1983) the existence field of the electron phases may be especially related to the combinations of d elements with the elements of the Periodic Table columns from 11 to 14 (from the Cu to Si groups). It can also be observed that, for several alloy systems, the dependence of the structures (structure types) on the electron concentration (instead of on the composition) may be clearly illustrated by well-known diagrams such as those shown in Fig. 4.39. 

Analysis of the dependence of the behaviour of alloy systems on the properties of the component elements. In an examination of the binary structure types containing more than five representatives, Villars and Girgis (1982) observed that 85% exhibited the following regularities ... 

Notice that the structures presented in this paragraph are unary structures, that is one species only is present in all its atomic positions. In the prototypes listed (and in the chemically unary isostructural substances) this species is represented by a pure element. In a number of cases, however, more than one atomic species may be equally distributed in the various atomic positions. If each atomic site has the same probability of being occupied in a certain percentage by atoms X and Y and all the sites are compositionally equivalent, the unary prototype is still a valid structural reference. In this case, from a chemical point of view, the structure will correspond to a two-component phase. Notice that there can be many binary (or more complex) solid solution phases having for instance the Cu-type or the W-type structures. Such phases are formed in several metallic alloy systems either as terminal or intermediate phases. 

Solution databases now exist for a niunber of the major metallic alloy systems such as steels, Ni- based superalloys and other alloy systems, and highly accurate calculation have been made which even a few years ago would have been considered impossible. The number of substance databases are increasing and the numbers of substances they include is reaching well into the thousands. Substance and solution databases are increasingly being combined to predict complex reactions such as in gas evolution in cast-irons and for oxidation reactions, and it is already possible to consider calculations of extreme complexity such as the reactions which may occur in the burning of coal in a industrial power generator or the distribution of elements in meteorites. 

Determination of transformation enthalpies in binary systems. Just as consistent values of for elements can be obtained by back-extrapolation from binary systems, so it is possible to obtain values of by extrapolating the enthalpy of mixing vs composition in an alloy system where the phase has a reasonable range of existence. The archetypal use of this technique was the derivation of the lattice stability of f.c.c. Cr from the measured thermodynamic properties of the Ni-based f c.c. solid solution (7) in the Ni-Cr system (Kaufman 1972). If it is assumed that the f.c.c. phase is a regular solution, the following expression can be obtained ... 

The most famous example of the crystal structure correlating with the average number of valence electrons per atom or band filling, N, is the Hume-Rothery alloy system of noble metals with sp-valent elements, such as Zn, Al, Si, Ge, and Sn. Assuming that Cu and Ag have a valence of 1, then the fee -phase is found to extend to a value of N around 1.38, the bcc / -phase to be stabilized around 1.48, the -phase around 1.62, and the hep e-phase around 1.75, as illustrated for the specific case of Cu-Zn alloys in Fig. 6.15. In 1936 Mott and Jones pointed out that the fee and bcc electron per atom ratios correlate with the number of electrons required for a free-electron Fermi sphere first to make contact with the fee and bcc Brillouin zone faces. The corresponding values of the Fermi vector, fcF, are given by... 

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