Dipole lattice energy

TABLE 1 Dipole lattice energy of the hydroquinone clathrate com-... 

Values for the partial charges of atoms can be derived from quantum mechanical calculations, from the molecular dipole moments and from rotation-vibration spectra. However, often they are not well known. If the contribution of the Coulomb energy cannot be calculated precisely, no reliable lattice energy calculations are possible. 

Qualitatively, the dipole-dipole interactions between the macro-molecular chains and the halide salt compensate for the lattice energy of the halide crystal and tend to decrease the interactions existing in the glass between the oxide macroanions. This decrease is probably the reason for the significant drop in the glass transition temperature resulting from the addition of a halide salt (Reggiani et al, 1978). Furthermore this type of reaction is consistent with the fact that dissolution of a halide salt in a vitreous solvent requires the existence of ionic bonds provided by a network modifier. 

Table 5.37 Lattice energy terms for C2/c pyroxenes. Values in kJ/mole. bhf = energy of Born-Haber-Fayans thermochemical cycle U- = lattice energy Ec = coulombic energy = repulsive energy Edd = dipole-dipole interactions E q = dipole quadrupole interactions =...

Hirshfeld and Mirsky (1979) evaluated the relative contributions to the lattice energy for the crystal structures of acetylene, carbon dioxide, and cyanogen, using theoretical charge distributions. Local charge, dipole and quadrupole moments are used in the evaluation of the electrostatic interactions. When the unit cell dimensions are allowed to vary, inclusion of the electrostatic forces causes an appreciable contraction of the cell. In this study, the contributions of the electrostatic and van der Waals interactions to the lattice energy are found to be of comparable magnitude. 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

LATTICE ENERGIES MADELUNG, REPULSION, DISPERSION, DIPOLE-DIPOLE, AND OTHERS... 

Ionic solids are only soluble in extremely polar solvents, due to dipole-dipole interactions between component ions and the solvent. Since the lattice energy of the crystal must be overcome in this process, the solvation of the ions (i.e., formation of [(H20) Na]+) represents a significant exothermic process that is the driving force for this to occur. 

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