Ionic crystals, heat capacity

The most direct effect of defects on tire properties of a material usually derive from altered ionic conductivity and diffusion properties. So-called superionic conductors materials which have an ionic conductivity comparable to that of molten salts. This h conductivity is due to the presence of defects, which can be introduced thermally or the presence of impurities. Diffusion affects important processes such as corrosion z catalysis. The specific heat capacity is also affected near the melting temperature the h capacity of a defective material is higher than for the equivalent ideal crystal. This refle the fact that the creation of defects is enthalpically unfavourable but is more than comp sated for by the increase in entropy, so leading to an overall decrease in the free energy... 

The phase behavior of ionic liquids can be complicated. Some are crystalline at low temperatures and show a sharp transition from crystal to liquid state (a true melting point) as the temperature is raised, but others exist as a glass at low temperatures and convert to a liquid at the glass-liquid transition temperature, denoted by a small change in heat capacity. Still others are glasses at very low temperatures, transform to crystals as the temperature is raised, and finally become liquid at a still higher temperature. See Reference 3 for a discussion of the types of phase behavior. 

The lattice contributions to the heat capacities of molten GdQ2 and TbCl2 were obtained on the assumption of their linear dependence upon the ionic radius. This estimate was made because it was accepted in this work that gadolinium and terbium dihalides have SrBr2-type structures with CN = 8. The smoothed crystal radii of Eu +, Gd +, Tb and E)y used in our calculations were taken from Chervonnyi and Chervormaya (2005c). 

Microscopic ionic volumes of RTILs, the sums of the constituent 20 cations and 20 anions Vj = v+ + v, were calculated by several theoretical methods according to Preiss et al. [49] and compared with the crystal volumes obtained from x-ray diffraction (Table 2.4). It was then shown that several physical properties were linear with these microscopic volumes the molar volume V, the isobaric expansibility ap, the molar heat capacity Cp, the (logarithm of) the viscosity In , and the (logarithm of) the molar conductivity InA all these obey the relation a + bv. ... 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

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