Electrons specific heat

Table III presents integral excess entropies of formation for some solid and liquid solutions obtained by means of equilibrium techniques. Except for the alloys marked by a letter b, the excess entropy can be taken as a measure of the effect of the change of the vibrational spectrum in the formation of the solution. The entropy change associated with the electrons, although a real effect as shown by Rayne s54 measurements of the electronic specific heat of a-brasses, is too small to be of importance in these numbers. Attention is directed to the very appreciable magnitude of the vibrational entropy contribution in many of these alloys, and to the fact that whether the alloy is solid or liquid is not of primary importance. It is difficult to relate even the sign of the excess entropy to the properties of the individual constituents.

Electronic specific heat of a brasses, 131 Electrostatic interaction, 391 Energy, of binding, 34 matrix, 271... 

It is a matter of speculation as to whether or not the activity would pass through a significant maximum at a surface composition between 0 and 30% Rh. It is interesting to note in this connection that the magnetic susceptibility (156, 157) and the electronic specific heat coefficient (156) increase from low values at 60% Ag-Pd through pure palladium and reach a maximum at - 5% Rh-Pd, thereafter decreasing smoothly to pure rhodium. Activity maxima have also been reported for reduced mixed oxides and supported alloys of group VIII metal pairs. For example, in the... 

We can conclude that the new behaviour of the superconducting material is due to a new state for the electrons in fact, at the critical temperature, there is a jump of the electronic specific heat. In no external magnetic field, it is a second-order transition, which does not involve latent heat. 

Below rc, the electronic specific heat ces decreases with the temperature as (see Fig. 3.4 (c)) ... 

The orbitals of the d states in clusters of the 3d, 4d, and 5d transition elements (or in the bulk metals) are fairly localized on the atoms as compared with the sp valence states of comparable energy. Consequently, the d states are not much perturbed by the cluster potential, and the d orbitals of one atom do not strongly overlap with the d orbitals of other atoms. Intraatomic d-d correlations tend to give a fixed integral number of d electrons in each atomic d-shell. However, the small interatomic d-d overlap terms and s-d hybridization induce intraatomic charge fluctuations in each d shell. In fact, a d orbital contribution to the conductivity of the metals and to the low temperature electronic specific heat is obtained only by starting with an extended description of the d electrons.7... 

It may of course be unnecessary to consider all these terms and the equation is much simplified in the absence of magnetism and multiple electronic states. In the case of Ti, it is possible to deduce values of the Debye temperature and the electronic specific heat for each structure the pressure term is also available and lambda transitions do not seem to be present. Kaufman and Bernstein (1970) therefore used Eq. (6.2), which yields the results shown in Fig. 6.1(c). 

The right-hand side can be separated into five parts. The first part is the enthalpy at 0 K, the second represents the zero point energy, the third is the Debye energy term, the fourth is an approximation for the Cp — C correction while the last part arises from the difference in electronic specific heats. 

Other phases are then characterised relative to this ground state, using the best approximation to Eq. (6.1) that is appropriate to the available data. For instance, if die electronic specific heats are reasonably similar, there are no lambda transitions and T 6o, then the entropy difference between two phases can be expressed just as a function of the difference in their Debye temperatures (Domb 1958) ... 

The excess term should allow the total Gibbs energy to be fitted to match that of Eq. (6.3) while at the same time incorporating a return to the inclusion of f 6) and f i) in the lattice stabilities. With the increased potential for calculating metastable Debye temperatures and electronic specific heats from first principles (Haglund et al. 1993), a further step forward would be to also replace Eq. (6.5) by some function of Eq. (6.8). 

However, most of the examples quoted in these earlier papers do not include the higher melting-point elements such as W, where a detailed treatment shows that the total entropy (at least of the solid phases) must include many other components such as the electronic specific heat, anharmonicity terms and the temperature dependence of 9d (Grimwall et al. 1987, Moroni et al. 1996). An estimate for the Debye temperature of the high-temperature 0 phase was included in the seminal... 

We have described in some detail these two properties. Measurements of the magnetic susceptibility and of the electronic specific heat give very clear information, from N(pf), on the presence of an f narrow band. They will be discussed in more detail in Chap. D. 

Its constant paramagnetism is well explained by a Van Vleck susceptibility, the ground state being the non-magnetic J = 0 due to the 5f configuration this interpretation is well confirmed by the very low electronic specific heat. Accordingly, band calcula-... 

At the beginning of this section we said that a localized picture is very often the best starting point for U, Np and Pu compounds. Is there any clear-cut criterion to direct us in the way of itinerant magnetism Good experimental evidence seems to be - a reduced ordered moment (in particular when it is incompatible with the effective moment in the crystal field scheme ) and - a large electronic specific heat (> 10 mJ/mol K ) and - a reduced magnetic entropy at the transition ( RLn2)... 

Fig. 1. Cg/T versus T for NpSn3 where Ce is the electronic specific heat. The solid curve is the mean-field theoretical prediction. The electronic specific heat coefficients of the paramagnetic and ordered states are designated by Vpa, = 242 andVoni = 88 mJ/(mol K ), respectively. (Trainor et al. )...

Many light actinide alloys which are not magnetic have a T dependence of the resistivity at low temperature as well as a large electronic specific heat coefficient y (Table 4). However, the archetype of a spin fluctuation system is UAI2. The electrical resistivity is proportional to T with a very large coefficient a = 0.15 qQcm/K up to 5... 

More recent measurements have shown (61)(62) that the problem with the experiment was that the thermal effect at Tc is actually very small. In fact, after the true heat had been determined, research was (and still is) directed toward finding out why the Tc is so high (63). The Sommerfeld parameter or electronic specific heat parameter appears to be identical (1.5mJ/mol K2) in BaPbj B Og... 

The large phase shifts t 2 give a large enhancement of the resistivity when transitional metals are dissolved in other metals. A survey for solid metals is given by Friedel (1956), and for solutions of Fe and Co in liquid germanium and tin by Dreirach et al (1972). The resonance will also enhance the electronic specific heat and the Pauli paramagnetism, but these quantities cannot be treated quantitatively without including correlation as shown in Chapter 3. 

In addition, there are certain metals involving 4f- or 5f-states, formerly called Kondo metals and now described as heavy-fermion materials, which have a very large electronic specific heat and may be described as crystals in which every rare-earth metal is envisaged, coherently, in a Kondo-type spin flip. 

---