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where is the lattice energy (i.e., the molar internal energy change), is the lattice enthalpy, and the change of molar volume due to the formation of the lattice. Since the molar volume of the solid is much smaller than that of the gases, Δ V m < 0 {\displaystyle \Delta V_{m}<0} .
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 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 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 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.
Mixture of polymers and solvent on a lattice. Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing.
For a lattice, the Helmholtz free energy F in the quasi-harmonic approximation is (,) = + (,) (,)where E lat is the static internal lattice energy, U vib is the internal vibrational energy of the lattice, or the energy of the phonon system, T is the absolute temperature, V is the volume and S is the entropy due to the vibrational degrees of freedom.
The proper calculation of electrostatic lattice constants has to consider the crystallographic point groups of ionic lattice sites; for instance, dipole moments may only arise on polar lattice sites, i. e. exhibiting a C 1, C 1h, C n or C nv site symmetry (n = 2, 3, 4 or 6). [11]