Debye temperature, definition

In 1926, Bjerrum [137] used Debye-Hiickel theory to describe ion association and took into account the interaction of ions within a short range. He introduced an ion-pair concept, gave a definition of ion pairs as neutral species formed by electrostatic attraction between oppositely charged ions in solution, and showed how ion-pair formation was dependent on the ions size (radius of ions), solvent (dielectric constant), and temperature. 

The accuracy and usefulness of these relationships is dependent on the mathematical definition of/ . This coefficient is estimated from various modifications of the Debye-Hiickel equation [23,44,45] [Eqs. (13-17) Section 2.2.5]. The definition given by Eq. (1) is certified by British Standard no. 2586 (a revision of Br. Std. no. 1647) to be accurate to 0.02 pH imit in the temperature region 0 to 95 °C. The British Standard [60] is stated [45] to be "consistent in nearly all respects with the NBS conventional scale "... 

As we have previously shown [5], there is also a definite relationship between the Debye characteristic temperature and the heat of activation of diffusion U, etc. However, an analysis of the experimental curves of the specific heat as a function of temperature shows that, for all bodies, including those whose specific heat is more or less satisfactorily described by the Debye equation, the characteristic temperature of the whole crystal is essentially a function of temperature (Fig.3). In addition, it is observed that the greater the deviation of the curve of from the horizontal straight line, the more the temperature dependence of the specific heat deviates from the Debye law. Despite the fact that the temperature dependence of the specific heat is comparatively insensitive to the form of the phonon spectrum, an evaluation of the trend of the specific heat curves already indicates that the vibration spectrum of ion vibrations in real solids differs essentially from the Debye law. 

In the SmC liquid crystals, the primary order parameter is the director tilt and not the spontaneous polarization. The polarization, therefore, is often called secondary-order parameter, and the SmC materials are called improper ferroelectrics. The main reason for this is the weakness of the dipole-dipole interactions in the molecules. The polar order can be estimated by the ratio of the actual spontaneous polarization and which is the value that would appear when complete polar order is assumed. From its definition, the polarization is the density of the molecular dipoles. Assuming molecular dipoles of 3 Debye ( 10 Cm) and typical molecular weight of 300 g, density of about 1 g/cm = 10 kg/m, we get that in 1 m we have 6 10 molecules, which would give Po 2 W C/m = 2000nC/cm. For a SmC with Pg <100 nC/cnP, this means that less than 5% of the dipoles are ordered in one direction. For this reason, in the first approximation the polarization is proportional to the tilt angle. This relation, indeed, is found to be true for materials with moderate or low polarization. However, for materials with large polarization, like Pg 500 nC/cm, the dipole-dipole interaction becomes considerable, and the proportionality is not true. The deviation is more pronounced at lower temperatures, when the dipole-dipole... 

The semi-log plots in FIGURES 6 and 7 show the temperature dependence of the relaxation frequencies for the two compounds. The Debye behaviour of the isotropic phase with the expected Arrhenius temperature dependence is quite evident in the oriented phases instead the temperature dependence of the two relaxation times is clearly non-linear on a log scale, thus preventing the definition of an activation energy for the relaxation processes involved. In TABLE 1 we have... 

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