Specific heat simple metals

Determining the Approximate Value of the Atomic Mass of Lead from Its Specific Heat Capacity. To determine the specific heat capacity of a metal, use a calorimeter and a device for heating the metal. A very simple calorimeter can be made from several beakers inserted one into another (Fig. 38). The inner beaker should have a volume of 100 ml, the middle one—300-400 ml, and the outer one—500 ml. Water is poured into the small beaker, while the others are needed to produce an air thermal-insulating layer. 

The theory of the electronic properties of the simple metals that has been built from simple free-electron theory is extraordinary. It extends to thermal properties such as the specific heat, magnetic properties such as the magnetic susceptibility, and transport properties such as thermal, electrical, thermoelectric, and galvano-magnetic effects. This theory is discussed in standard solid state physios texts (see, for example, Harrison, 1970) and will not be discussed here. As a universal theory for all metals, it is not sensitive to the electronic structure it depends only upon the composition of the metals through simple parameters such as those of Table... 

Once we have obtained the dispersion curves for the metal, wc may proceed to other properties just as we did with the covalent solids. In particular, we may quantize the vibrations as was done for the covalent solids and obtain the appropriate contribution to the specific heat. We shall not repeat that analysis now for the simple metals but shall wish to use the customary terminology by referring to the vibrations as phonons. 

We indicated in our discussion of simple metals that the electronic specific heat at low temperatures is linear in temperature and proportional to the density of states at the Fermi energy. The density of states so obtained from the specific heat is shown in Fig. 20-9, and the correlation is apparent. Notice in particular the low value at four electrons per atom for Ti, Zr, and Hf, all of which occur in the hexagonal closc-packcd structure this corresponds to the dip we noted in the density of states in Fig. 20-8,a. Similarly the minimum at six electrons per atom corresponds to the minimum in the body-centered cubic density of states of Fig. 20-7, at the Fermi energy for chromium. 

Pure and Mixed Oxides. The specific heat and magnetic susceptibility of ReOj have been measured and the results shown to agree closely with the corresponding parameters calculated from the free electron model with ReOa behaving as a simple metal. ... 

In this section we will show that some specific-heat measurements support and others contradict the existence of an MDOS at EF. After the subtraction of the lattice contribution, a term yexp T is left at low temperatures. The experimentally derived y-value consists of simple metallic glasses of several contributions [5.20,74] ... 

Deformation potential coupling constants are of the order of fip, (Ziman 1960). To observe deformation potential effects in the temperature dependence of elastic constants several conditions have to be met as discussed above dpA(,(0) must be large and - Eq has to be of the order of k T. This excludes normal metals and only d-band metals with rather narrow bands can exhibit this behavior. Typical examples have been given above. In intermetallic rare-earth compounds simple density of states arguments show why elastic constant effects can be observed only for CsCl-type and Th3P4-type materials. In table 4 electronic specific heat values are listed for various rare earth compounds. This is an updated list of a previous work, see Liithi et al. (1982). This table indicates that monopnictides and monochalcogenides have smaller values of y than CsCl- and Th3P4-structure materials, i.e., the 5d band of the former structure is more hybridized than in the latter. 

We shall see in section 6.2 that this extremely simple model provides a qualitatively correct picture of high-energy spectra of light lanthanide solids. Similar approaches to excitation spectra of lanthanides have been introduced for clusters (Fujimori 1983, Fujimori and Weaver 1985) and have been considered for solids (Kotani et al. 1985). It must be emphazised, however, that the use of a few molecular orbitals in these simplified models of the Anderson impurity Hamiltonian leads to spectra where the excitations appear necessarily as discrete lines. This approach to a solid is missing irremediably the continuum aspects of the band states interacting with the f state. For example, one unrealistic consequence of a cluster model is the fact that the lowest excitation energies are typically of the order of the hybridization energy for both, metals and insulators. This implies zero specific heat and too small susceptibilities for metallic systems (Fujimori et al. 1984). Nevertheless, such models... 

---