Heat Schottky anomaly

In metallic compounds, optical methods cannot be used to determine the crystal-field levels. The determination of crystal field levels in such compounds has been reviewed by Fulde (1979) and is only mentioned here. These are primarily based on measurements of the magnetic susceptibility, magnetization in high magnetic field, specific heat (Schottky anomaly), Mossbauer effect, electron paramagnetic resonance, and inelastic neutron scattering. 

This behaviour is characteristic of any two-state system, and the maximum in the heat capacity is called a Schottky 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. 

An example of magnetic contributions to the specific heat is reported in Fig. 3.9 that shows the specific heat of FeCl24H20, drawn from data of ref. [35,36]. Here the Schottky anomaly, having its maximum at 3K, could be clearly resolved from the lattice specific heat as well as from the sharp peak at 1K, which is due to a transition to antiferromagnetic order (lambda peak). 

Let us examine the data of the third measurement on the metallized wafer. There are two contributions to the heat capacity, a linear contribution and a spurious one. The spurious contribution may be interpreted as the high temperature side of a Schottky anomaly. In this hypothesis, the heat capacity per unit volume of the metallized wafer may be... 

As such, nuclear contributions to the heat capacity due to the interaction between germanium crystalline electric field gradients and the quadrupole moments of boron nuclei could account for the observed onset of the Schottky anomaly. 

Also, the heat capacity is affected by the axial ZFS parameter and, in excess of the lattice contribution, it shows a Schottky anomaly as modeled in Fig. 2. In the zero magnetic field the isofield heat capacity Ch collapses to the usual Cp and stays isotropic. 

The excess contribution is due to the distribution of the valence electrons over the energy levels, and includes the splitting of the ground term by the crystalline electric field (Stark effect) and is called the Schottky heat capacity or Schottky anomaly. It can be calculated from... 

Schottky anomaly is determined from the difference between an RY compound and LaX or LuX compound. Then the crystal field parameters are deduced from the Schottky anomaly data. The accuracy of the method is limited by spin-phonon interactions and exchange effects in rare earth ions which affect the Schottky effect, ft is used to find crystal field parameters, W, x which fit the specific heat data as shown in Fig. 8.4. The figure refers to a plot of C/Rq vs. T for TmAF [19]. 

The cluster compounds [Ag6M4Pi2]Gc6 with = Ge, Sn show at low temperatures a valence fluctuation of the inner core Ag6" +, which can be seen in the elastic behavior " and vibrational anharmonicity as well as in the measurements of the specific heat. The valence fluctuations generate a pronounced schottky anomaly, which can be emphasized more clearly by the comparison and therefore possible normalisation of cluster compounds. 

The diaracteristics of the two-levd system is that x(T) and u(T) tend towards a saturation-value with increasing temperature, and pass through a point of inflection. As a result, the heat capacity initially increases with temperature, but decreases as the temperature increases further (cf. Fig. 2.1). The heat capacity passes through a maximum, the so-called Schottky anomaly, at a temperature of ... 

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.

Fig. 69. The 5f-derived specific heat of URUjSij, AC, as a function of temperature (on a logarithmic scale) (Renker et al. 1987b). Thick line shows Schottky anomaly for doublet-doublet CF system with a sphtting of kg 75 K. Thin line is guide to the eye.

U. Kohler, R. Demchyna, S. Paschen, U. Schwarz, F. Steglich, Schottky anomaly in the low-temperature specific heat of Bag.j,EUj,Ge43n3. Physica B 378-380, 263 (2006)... 

Fig. 63. Left panel Complete B-T phase diagram (Maple et al., 2002) with SC regime and region of field induced order parameter which is presumably of antiferroquadrupolar (AFQ) type. Data are obtained from resistivity (p), magnetization (M), specific heat (C) and thermal expansion (o ) measurements. Right panel High magnetic field phase diagram (Aoki et al., 2003) with upper part of AFQ phase (full squares) and line of high field Schottky anomaly from the Fi-Fs crossing. The inset shows calculation for tetrahedral CEF model.

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