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The Born–Landé equation above shows that the lattice energy of a compound depends principally on two factors: as the charges on the ions increase, the lattice energy increases (becomes more negative), when ions are closer together the lattice energy increases (becomes more negative)
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.
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.
Here, a A (1-x) B x is the lattice parameter of the solid solution, a A and a B are the lattice parameters of the pure constituents, and x is the molar fraction of B in the solid solution. Vegard's law is seldom perfectly obeyed; often deviations from the linear behavior are observed. A detailed study of such deviations was conducted by King. [3]
This results in typical lattice and free energy differences between polymorphs that are often only a few kJ/mol, very rarely exceeding 10 kJ/mol. [10] Crystal structure prediction methods often locate many possible structures within this small energy range. These small energy differences are challenging to predict reliably without excessive ...
Born–Haber cycles are used primarily as a means of calculating lattice energy (or more precisely enthalpy [note 1]), which cannot otherwise be measured directly. The lattice enthalpy is the enthalpy change involved in the formation of an ionic compound from gaseous ions (an exothermic process ), or sometimes defined as the energy to break the ...
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.
In a one-dimensional lattice the number of reciprocal lattice vectors that determine the bands in an energy interval is limited to two when the energy rises. In two and three dimensional lattices the number of reciprocal lattice vectors that determine the free electron bands () increases more rapidly when the length of the wave vector increases ...