Heat capacity Schottky anomaly

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. 

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... 

Deenadas et al. (69) reported the heat capacity of NdAl2. This shows superimposition of a Schottky-type heat capacity excess over the normal X-type anomaly. Magnetization measurements (6S) on single crystals of NdAl2 in three crystallographic directions in fields up to 350kG and neutron inelastic scattering experiments (70) yielded consistent crystal field parameters (A (r4) = 40K and A (r6> = - 12K). 

The heat capacity behavior of PrNi2 confirms that it becomes a Van Vleck paramagnet at low temperatures (65). It exhibits no X-type thermal anomaly expected if there is magnetic ordering only a Schottky-type heat capacity excess is observed. This is a consequence of the thermal population of the higher crystal field states. 

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 ... 

For example, proper accoimting of electronic excitation influences the thermal characteristic result obtained from the measurement of low-temperature heat capacity in a temperature range from dose to 0 K up to 350 K. Although these studies were largely direded at the determination of the heat capacity C° 298) and entropy S°(298) values at standard temperature (298.15 K), they were also concerned with proving the existence of contributions to the heat capacity (as well as, entropy) of lanthanide compounds induced by exdtation of electronic states. Significant and distinctive changes in C (298) and S°(298) values were foimd for most lanthanide compounds. That is, the existence of the so-called Schottky anomaly in thermal parameters was established. 

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