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  2. Lattice constant - Wikipedia

    en.wikipedia.org/wiki/Lattice_constant

    Unit cell definition using parallelepiped with lengths a, b, c and angles between the sides given by α, β, γ [1]. A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal.

  3. Born–Landé equation - Wikipedia

    en.wikipedia.org/wiki/Born–Landé_equation

    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.

  4. Kapustinskii equation - Wikipedia

    en.wikipedia.org/wiki/Kapustinskii_equation

    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.

  5. Crystal structure - Wikipedia

    en.wikipedia.org/wiki/Crystal_structure

    The lengths of principal axes/edges, of unit cell and angles between them are lattice constants, also called lattice parameters or cell parameters. The symmetry properties of crystal are described by the concept of space groups. [1] All possible symmetric arrangements of particles in three-dimensional space may be described by 230 space groups.

  6. Gauss circle problem - Wikipedia

    en.wikipedia.org/wiki/Gauss_circle_problem

    Another generalization is to calculate the number of coprime integer solutions , to the inequality m 2 + n 2 ≤ r 2 . {\displaystyle m^{2}+n^{2}\leq r^{2}.\,} This problem is known as the primitive circle problem , as it involves searching for primitive solutions to the original circle problem. [ 9 ]

  7. Scherrer equation - Wikipedia

    en.wikipedia.org/wiki/Scherrer_Equation

    Just as in 1D, the FWHM varies as the inverse of the characteristic size. For example, for a spherical crystallite with a cubic lattice, [2] the factor of 5.56 simply becomes 6.96, when the size is the diameter D, i.e., the diameter of a spherical nanocrystal is related to the peak FWHM by

  8. Born–Mayer equation - Wikipedia

    en.wikipedia.org/wiki/Born–Mayer_equation

    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.

  9. Lattice energy - Wikipedia

    en.wikipedia.org/wiki/Lattice_energy

    The concept of lattice energy was originally applied to the formation of compounds with structures like rocksalt and sphalerite where the ions occupy high-symmetry crystal lattice sites. In the case of NaCl, lattice energy is the energy change of the reaction Na + (g) + Cl − (g) → NaCl (s) which amounts to −786 kJ/mol. [2]