Schottky curve anomaly

The electronic contribution is generally only a relatively small part of the total heat capacity in solids. In a few compounds like PrfOHE with excited electronic states just a few wavenumbers above the ground state, the Schottky anomaly occurs at such a low temperature that other contributions to the total heat capacity are still small, and hence, the Schottky anomaly shows up. Even in compounds like Eu(OH)i where the excited electronic states are only several hundred wavenumbers above the ground state, the Schottky maximum occurs at temperatures where the total heat capacity curve is dominated by the vibrational modes of the solid, and a peak is not apparent in the measured heat capacity. In compounds where the electronic and lattice heat capacity contributions can be separated, calorimetric measurements of the heat capacity can provide a useful check on the accuracy of spectroscopic measurements of electronic energy levels. 

Fig. 26. High-temperature specific heat of three Kondo eompounds with an abnormal Schottky anomaly, after de Boer et al. (1985) and Felten (1987). The continuous curve is a Schottky contribution for a F-j-Fg thermal promotion.

Fig. 16. Temperature dependence of 4f-derived specific heat, C, and entropy in units of the gas constant, SJR, for (a) CeRu j Gcj and (b) CeCu GCj (Felten et al. 1987). Solid curves in upper parts show Schottky anomalies corresponding to the CF splitting of Ce given in the text.

Since the magnetic interaction parameter a is of order 0.1 K, the associated Schottky anomaly in the Cp versus T curve will peak at around this temperature. Thus, for Tb, Ho and Tm we find that even in the analysis above 0.1 K we must include an estimate of the nuclear contribution (see table 5.2). 

---