![]() Radius to anion radius is 0.414 (r +/r - or radius ratio). Using the Pythagorean theorem, the optimum ratio of cation Using geometry, we can work out the ideal Interstitial space available for a cation to fit between the six anions. The dashed circle represents the anions below and above the plane. The diagram below shows four spheres represent some anions ofĪ part of a cubic layer. The packing arrangement adopted by an ionic compound is determined by the comparative sizes of the ions.Ĭonsider a lattice in which the anions assume a cubic array. For MgCl 2 the lattice mustīe an array of chloride anions with only half that number of magnesium ion. The cation to anion ratio must reflect the stoichiometry of the compound.Usually in the packingĪrrangement, the cation is just large enough to allow te anions to surround it without touching one another. ![]() Ions try to surround themselves with as many ions of opposite charge as closely as possible.Ions are assumed to be charged, incompressible, nonpolarizable spheres.The smaller cations reside in the holes between In most ionic compounds, the anions are much larger than the cations, and it is theĪnions which form the crystal array. Structure when repeated is called a unit cell. The simplest arrangement of spheres, which will reproduce the entire crystal Layer,is placed over the holes not covered from the first layer, the arrangement is called If the third layer of spheres instead of being placed over the hole of the second Over the base layer, the hexagonal close-packed array is obtained.Įach sphere has a coordination number of twelve. If a third layer is placed over the holes of the second layer so it is superimposed over Over all the holes in the first layer - only half of the holes can be covered. The second hexagonal layer over the first, it is physically impossible for spheres to be placed In this arrangement the holes between spheres are smaller than in the cubic arrangement. Which each each sphere is surrounded by six neighbors in the plane. In this arrangement, each sphere is touched by four atoms above andįour atoms below its plane giving a coordination number of eight.Īnother arrangement has a base layer of spheres organized in a hexagonal arrangement in This is a more compact arrangement than the Successive layers are added in the same fashion. The third layer of spheres are placed over Spheres over the holes (or interstices) of the base layer. Touched by six neighboring spheres giving it a coordination number of six.Īn alternative packing arrangement can be obtained by placing the second layer of Touched by four other atoms in its own plane plus one atom above and one below. Type of array is known as simple cubic packing. Layers of spheres are then added directly over the spheres of the layer below. The simplest arrangement is one in which the spheres in the base are packed side by side. The easiest way to picture such an array is to arrange one layer of spheres and then place The concept of crystal packing assumes that the ions are hard spheres. In an ionic solid, the ions are packed together into a repeating array called a crystal lattice.
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