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The lattice energy of an ionic compound depends strongly upon the charges of the ions that comprise the solid, which must attract or repel one another via Coulomb's Law. More subtly, the relative and absolute sizes of the ions influence Δ H l a t t i c e {\displaystyle \Delta H_{lattice}} .
The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound.In 1918 [1] Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term.
z + = charge number of cation; z − = charge number of anion; e = elementary charge, 1.6022 × 10 −19 C; ε 0 = permittivity of free space 4 π ε 0 = 1.112 × 10 −10 C 2 /(J·m) r 0 = distance to closest ion; ρ = a constant dependent on the compressibility of the crystal; 30 pm works well for all alkali metal halides
The macroscopic energy equation for infinitesimal volume used in heat transfer analysis is [6] = +, ˙, where q is heat flux vector, −ρc p (∂T/∂t) is temporal change of internal energy (ρ is density, c p is specific heat capacity at constant pressure, T is temperature and t is time), and ˙ is the energy conversion to and from thermal ...
The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%. Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known.
The energies of these states match the energy bands of the infinite system. [6] For each band gap, there is one additional state. The energies of these states depend on the point of termination but not on the length . [6] The energy of such a state can lie either at the band edge or within the band gap.
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In solid state physics, a surface phonon is the quantum of a lattice vibration mode associated with a solid surface. Similar to the ordinary lattice vibrations in a bulk solid (whose quanta are simply called phonons), the nature of surface vibrations depends on details of periodicity and symmetry of a crystal structure. Surface vibrations are ...