Bloch-Griineisen

These compounds are metallic conductors, and similar to YNiPb, the Bloch-Griineisen relation is also valid for Y2Ni2Pb. The magnetic ordering manifests in the temperature dependence of the resistivities through abrupt changes in the slopes (decrease of spin-disorder scattering). 

The Debye temperatures do and mean square deviations obtained by a fit procedure of the Bloch-Griineisen law (eq. (2)) to the experimental data. 

A detailed study of the electrical resistivity behavior of the La272ln and Ce272ln (T = Ni, Cu, Rh, Pd, Pt, Au) indides was performed by Kaczorowski et al. (1996a, 1996b). They evaluated the electrical resistivity data according to the modified Bloch-Griineisen relation and derived the Debye temperatures (table 17). 

Within the Debye approximation the spectral functions oc F are proportional to (o in the energy range co kgGo (0 denotes the Debye temperature). This leads to a temperature dependence of the matrix elements Qoo from which the well known Bloch-Griineisen relation for pp follows (see Blatt 1968). For the low- and high-temperature regions the Bloch-Griineisen law reveals ... 

Here we are mainly interested in temperatures T < 0d. For more than half a century, the Bloch-Griineisen (BG) formula has been used frequently to describe Peii>h(T) at intermediate and low temperatures. It is often given in the form... 

The Bloch-Griineisen formula is a special case of a more general expression. Within a variational solution of the Boltzmann equation we can, to a good approximation, write the resistivity Pei-ph that is limited by the scattering of conduction electrons by phonons as... 

Table 1 A Debye Temperature 0r Obtained by Fitting a Generalized Bloch-Griineisen Expression to the Measured Resistivity at Low and Intermediate Temperatures and an Entropy Debye Temperature 0s That Reproduces the Experimental High-Temperature Vibrational Entropy ...

Measurements of p T) for TiB2 by Williams et al. (9) from 4.2 to 300 K showed a resistivity minimum in the range 34-47 K. A normal resistivity term Pei.ph(r) could be extracted. It was well described by a Bloch-Griineisen expression varying as at low T and with Or = 720 K. The latter value seems reasonable, when compared with 0s see Table 1. The Kondo effect is caused by a spin-flip interaction between conduction electrons and localized magnetic moments of impurity atoms. Ni impurities are essential, but there are still several unsolved problems in the interpretation of the Kondo minimum in TiB2. 

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