Actinide specific heats

For solids in which IN([Xf) is very near to 1, often, although no magnetic order occurs, long-range fluctuations of coupled spins may take place, giving particular form to properties such as the (Stoner enhanced) magnetic susceptibility x, the electrical resistivity, and the specific heat of the solid. Spin fluctuations have been observed in actinides, and will be discussed in more detail in Chap. D. 

The Stoner product (30), calculated across the actinide series for homologous compounds, may interpret (or predict) the magnetic behaviour of these solids, and hence suggest a localized or itinerant picture (see Chap. D), provided that we know I for the different actinides across the series, since N(pf) is measurable (e.g. through specific heat measurements) and roughly reciprocal to the bandwidth W (N(pf) W ). I is not directly measurable and must be calculated. (Of course, the discussion above shows that the two quantities are not really independent, since the interactions determining I also play a role in determining the bandwidth, and hence N([Xf).)... 

Table 3. Density of states at the Fenni level for actinide metals from band calculations (model) from the electronic contribution y to the specific heat from magnetic susceptibility measurements. The increasing values indicate a decreasing 5 f bandwidth pinned at Ep for americium metal (not shown) there is a sudden decrease in N(np)...

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... 

For non-magnetic actinide metals, specific heat data have been employed very usefully to corroborate 5 f localization starting with Am, as indicated by the sudden drop in y values (ypu 12 mJ/mol K, yAm 2 mJ/mol K ). It allowed also the discovery of superconductivity in Pa and Am metals ... 

We now give a simple application of the present method to Plutonium which is a good test case. Pu lies between light actinides with itinerant 5/ electrons and heavy actinides with localized 5/ electrons. The competition between these two electronic regimes in Pu is responsible for a lot of unusual properties as large values of the linear term in the specific heat coefficient and of the electrical resistivity or a very complex phase diagram. 

Mortimer (32) has reviewed data on specific heats of actinide metals. 

For the actinides the crystal entropies follow approximately the decreasing average radius produced by f-electron participation in metallic bonding. They are also clearly shown to be non-magne-tic, as the f s are itinerant. However, the entropy correlation itself cannot predict these values, since there is no model in terms of a like metal that can be used to compare these totally unique early actinides. There are also of course perturbations due to the high electronic specific heats, caused by high densities of states at the Fermi level. 

It, therefore, seems appropriate to use the same classification scheme as outlined above for actinide systems. According to the specific-heat data above the Neel temperature short-range correlations, as indicative of local-moment behaviour, seem to be present in UCdu, see fig. 57 (Fisk et al. 1984). Similar to CeAl2 (cf. fig. 43), one observes a shoulder in C T)IT on the low-T side of the phase-transition anomaly that supports an interpretation in terms of a more... 

Only one specific-heat measurement is reported for a late actinide. Data presented by Getting et al. (1984) for PuH show a sharp magnetic inflection at 36.4 K. The result is in reasonable agreement with the transition seen at 44 K for the 1.93 composition in a magnetic study by Ward (1983), considering the observed sharp dependence of transition temperature on composition. 

For the itinerant systems (light actinides and a-like cerium compounds) there is less guidance Ifom theory. As discussed above, the relationship between susceptibility x(0) and specific heat coefiBcient y is believed to be the same as for nearly localized heavy fermions, i.e., x(0)oc l/Tsf. Hence, differences between the two cases may not be... 

In this section we describe how the specific heat, magnetic susceptibility and electrical resistivity of anomalous lanthanide and actinide intermetallics respond to applied pressure. Generally each subsection is organized by material type first Ce-based compounds, then those based on Yb and finally U-based systems. Only in the last subsection on semiconductors are these systematics broken. Although on occasions we digress into a brief discussion of the experimental observations, ihe bulk of critical discussion related to data presented here and in sect. 3 is reserved for sect. 4. 

Electrical resistivity has been a popular means of studying the pressure response of anomalous lanthanide and actinide compounds, both because of the relative simplicity of the measurement and because techniques are readily available for extending the measurements to pressures substantially higher than achievable with specific heat or susceptibility. Consequently, there is a rather large body of p T,P) data that can be chosen... 

We have focused on two issues (1) the degree to which the pressure response of the electrical resistivity, magnetic susceptibility and specific heat is similar in a given material or class of materials and how this pressure dependence is related to the Griineisen parameter obtained from ambient pressure measurements and (2) the extent to which this comparison holds in both anomalous lanthanide and actinide compounds. 

The electronic specific heat coefficient, y, is proportional to the DOSs at the Fermi level. In general, in pure metals, it is of the order of a few mj/ mol K. Simply thinking, the electronic DOSs at the Fermi level is proportional to the effective mass of conduction electrons. The most conspicuous and noticeable systems with respect to their electronic specific heat coefficients are heavy electron systems that include some actinide and cerium compounds to be mentioned later. For example, in the case of a typical heavy electron system CeCug, the electronic specific heat coefficient reaches 1.5 J/mol K, which is more than 1000 times larger than that of a normal metal (Satoh et al., 1989). 

Fig. 40. The specific heat per lanthanide or actinide atom as a function of temperature, as predicted by the electronic polaron model (Liu 1987, 1988).

The calculated state densities at the Fermi energy have been collected and compared to experimentally observed specific heat coefficients in fig. 19. One should bear in mind that most of the calculations assume an fee structure, and therefore one cannot expect too detailed an agreement between theory and experiment. In the beginning of the series, i.e. for Fr-Th, the 5f contribution is small, and N Ep) for Th is typical for a transition metal. In Pa the 5f contribution starts to dominate the state density, which by Am has increased by an order of magnitude. The measured electronic specific heat coefficients show a similar trend up to, and including, Pu. However, in Am it is down by one order of magnitude with respect to the value for Pu, and is in fact close to the spd contribution to the state density. Hence, in this respect Am behaves like a rare earth metal. The interpretation of the above-mentioned observations is that the 5f electrons in Pa Pu are metallic, hence the high electronic specific heat, in the same sense that the 3d, 4d and 5d electrons in the ordinary transition series are metallic, and that this metallic 5f state turns into a localized one at Am, hence the relatively low electronic specific heat. Am and the later actinides form a second rare earth series. 

The electronic specific heat coefficient, y, the magnetic susceptiMSty, y, at 300 K and the coefficient A in the term of the resistivity for non-magnetic rare earth and actinide metals as well as for Pd. 

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