Alloy analogy

Another striking example of the decisive role of the mode of preparation may be found in the behavior of Cu-Pd alloys [Rienacker et al. (65)] (see Fig. 18). When copper is alloyed with palladium the activation energy remains practically constant up to 65% Pd on further addition of Pd, E falls rapidly down to the low value of Pd. This is only true, however, for normally prepared, disordered alloys. If, by tempering, the so-called ordered alloys are prepared, in which the Pd-atoms have definite crystallographic positions, the result is essentially different (see Fig. 18) now the activation energy of the alloys is nearly additively composed of the contributions of the components in the alloy. Analogous results were obtained for the system Cu-Pt [Rienacker (69)]. 

Up to now, we have concentrated on the physics at zero kelvin. In this section, we extend the studies to finite temperatures and discuss finite temperature phase diagrams. The physics at finite temperatures is dominated by thermal fluctuations between low lying excited states of the system. These fluctuations can include spin fluctuations, fluctuations between different valence states, or fluctuations between different orbitally ordered states, if present. Such fluctuations can be addressed througih a so-called alloy analogy. If there is a timescale that is slow compared to the motion of the valence electrons, and on which the configurations persist between the system fluctuations, one can replace the temporal average over all fluctuations by an ensemble average over all possible (spatially... 

This static alloy analogy picture should be a good description as long as there is a separation of timescales. If this breaks down, dynamical fluctuations—or quantum fluctuations— which are beyond this static picture, become important. These quantum fluctuations are the main emphasis of DMFT (Georges et al., 1996), which maps the system onto an effective Anderson impurity model, describing a dynamically fluctuating impurity in a self-consistently determined effective host. So far, DMFT has been formulated for model Hamiltonians, such as the Hubbard model, and material-specific results have been achieved by constructing these model Hamiltonians from realistic band structure calculations. In... 

DYNAMICAL FLUCTUATIONS THE ALLOY ANALOGY AND THE LANDAU THEORY OF PHASE TRANSITIONS... 

A particular general shortcoming of the alloy analogy approximation is that it cannot describe quantum fluctuations such as the zero point fluctuations of spin waves. Evidently, these can be important at and near T = 0. Moreover, an ensemble average of static fluctuations depicted by the alloy configurations will, within the CPA, inevitably lead to quasi-particles with finite lifetime even at T = 0. Namely, the ground state is genetically not that of a Fermi liquid as it mostly should be. In what follows we shall summarize briefly the current state of conceptual framework that needs to be invoked to deal with these issues. 

In spite of the fact that the fits in figs. 25 and 26 are very good, it leaves one rather unsatisfied because the degree of valence mixing for SmBs (0.3 and 0.7) is not what the more recent numbers yield (0.4 and 0.6). However, the model used for the computation of the susceptibility corresponds in a simple way to the alloy analog of the Anderson lattice model, which has been shown to give good results, e.g. by... 

Our discussion shows that the Ising model, lattice gas and binary alloy are related and present one and the same statistical mechanical problem. The solution to one provides, by means of the transcription tables, the solution to the others. Flistorically, however, they were developed independently before the analogy between the models was recognized. 

Trichloroethanol may be used analogously. The 2,2,2-trichloroethyl (Tee) group is best removed by reduction with copper-zinc alloy in DMF at 30 °C (F. Eckstein, nucleic acid synthesis see section 4.1.1. 

Chromium—Cobalt—Iron Alloys. In 1971, a family of ductile Cr—Co—Fe permanent-magnet alloys was developed (79). The Cr—Co—Fe alloys are analogous to the Alnicos in metallurgical stmcture and in permanent magnetic properties, but are cold formable at room temperature. Equivalent magnetic properties also can be attained with substantially less Co, thereby offering savings in materials cost. 

These reactions are thermodynamically unfavorable at temperatures below ca 1500°C. However, at temperatures in the range from 1000 to 1200°C a small but finite equiUbrium pressure of barium vapor is formed at the reaction site. By means of a vacuum pump, the barium vapor can be transported to a cooled region of the reactor where condensation takes place. This destroys the equiUbrium at the reaction site and allows more barium vapor to be formed. The process is completely analogous to that used in the thermal reduction of CaO with aluminum to produce metallic calcium (see Calcium AND CALCIUM alloys). 

H 72.8, O 141.0 and I 295.2 kJ mol . Consistent with this the compound CsAu has many salt-like rather than alloy-like properties and, when fused, behaves much like other molten salts. Similarly when Au is dissolved in solutions of Cs, Rb or K in liquid ammonia, the spectroscopic and other properties are best interpreted in terms of the solvated Au ion (d °s ) analogous to a halide ion (s p ). 

Using the so-called "block copolymers (a block of Na A-monomers at one end is covalently bonded to a block of Nb B-monomers) one can also realize the analogy of order-disorder phenomena in metallic alloys with polymers one observes transitions from the disordered melt to mesophases with various types of long range order (lamellar, hexagonal, cubic, etc ). We shall not consider these phenomena here further, however... 

Sulfidation is analogous, but catastrophic sulfidation is common because of the generally lower melting points of sulfides than corresponding oxide. This is especially true in the case of nickel alloys, when a nickel/nickel sulfide eutectic is formed. 

---