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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.
Each is by definition the wavevector of a plane wave in the Fourier series of a spatial function which periodicity follows the crystal lattice (e.g., the function representing the electronic density of the crystal), wavefronts of each plane wave in the Fourier series is perpendicular to the plane wave's wavevector , and these wavefronts are ...
Vectors and planes in a crystal lattice are described by the three-value Miller index notation. This syntax uses the indices h, k, and â„“ as directional parameters. [4] By definition, the syntax (hkâ„“) denotes a plane that intercepts the three points a 1 /h, a 2 /k, and a 3 /â„“, or some multiple thereof. That is, the Miller indices are ...
The Born–Mayer equation is an equation that is used to calculate the lattice energy of a crystalline ionic compound.It is a refinement of the Born–Landé equation by using an improved repulsion term.
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 energy of such a state can lie either at the band edge or within the band gap. If the energy is within the band gap, the state is a surface state localized at one end of the lattice, but if the energy is at the band edge, the state is delocalized across the lattice.
A completely distributive lattice L is called the free completely distributive lattice over a poset C if and only if there is an order embedding: such that for every completely distributive lattice M and monotonic function:, there is a unique complete homomorphism: satisfying =.