Schottky anomalies

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. 

Broad maxima in Cm versus T (the so-called Schottky anomalies) frequently indicate partially populated discrete levels that are separated by an energy difference AE in the range of knT. For a simple two-level system, the maximum occurs at B niax 0.42A/i. Phase transitions, for example, transitions between a long-range ordered ferromagnetic phase and a paramagnetic phase, produce a characteristic peak in Cm versus T graphs. 

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. 

Calorimetric measurements on Schottky anomalies are reviewed elsewhere [50]. 

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 ... 

Au = 2.55 kJ/moI q = 6 and L = 11. As the tendency to aggregation increases, the Schottky anomaly assumes more and more the shape of a comparatively clearly defined, but diffuse transformation... 

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