Sodium Debye temperature

The free energy due to harmonic lattice vibrations (or equivalently the Debye temperature) is approximately the same for bcc, fee, and hep structures but with a significant tendency for the bcc value to be a few percent lower. The more open bcc structure has a transverse phonon mode with a particularly low frequency which causes a more rapid decrease in the free energy with temperature. On cooling, sodium and lithium transform partially from bcc to hep at very low temperatures (0.1-0.2 Tm). Calcium, strontium, beryllium, and thallium transform to a bcc phase at high temperatures (0.66-0.98 Tm) when there is a considerable anharmonic contribution to the free energy. 

Figure 5.6 Isomer shifts (relative to sodium nitroprusside) as a function of temperature in the Debye model, along with measurements on a-FeOOH (adapted from [11]).

As an illustrative example taken from Russel et al. (1989), let us consider a 0.01 molar solution of sodium chloride in contact with a surface charged at a density of 5 x 10 negative charges per square meter at room temperature, 298°K. Equation (2-52) gives /c = 3 nm. The dimensionless surface potential exfJkrtT. obtained from Eq. (2-45), is —5.21, and Eqs. (2-46) and (2-49) give respectively the exact and the Debye-Huckel approximations for the potential as a function of distance from the surface. The results are plotted in Fig. 2-13. Note that since — s/ ks T > 1, the Debye-Huckel approximation is... 

For example, Marshall and Slusher (1966) made a detailed evaluation of the solubility of ealeium sulphate in aqueous sodium chloride solution, and suggested that variations in the ion solubility product could be described, for ionic strengths up to around 2 M at temperatures from 0 to 100 °C, by adding another term in an extended Debye Hiickel expression. Above 2 M and below 25 °C, however, further correction factors had to be applied, the abnormal behaviour being attributed to an increase in the complexity of the structure of water under these circumstances. Enthalpies and entropies of solution and specific heat capacity were also reported as functions of ionic strength and temperature. 

---