Ионные кристаллические структуры

Two principal factors determine ionic crystal structure: the relative sizes of the ions and the ratio of cations to anions in the compound. Ion size depends on charge magnitude—higher positive charges decrease cation size, while higher negative charges increase anion size. These factors together dictate which holes cations occupy and overall packing arrangement.

Tetrahedral holes form between three anions in one plane and one anion in an adjacent plane, arranged at tetrahedron corners. Octahedral holes form at the center of six anions arranged at octahedron corners. Smaller cations occupy tetrahedral holes, while larger cations occupy octahedral holes, depending on ionic size compatibility.

Sodium chloride exhibits the rock salt structure with a face-centered cubic lattice of chloride anions. The smaller sodium cations occupy octahedral holes between anions, allowing each sodium ion to contact six chloride ions and vice versa. This 1:1 cation-to-anion ratio with size difference produces coordination number six.

Zinc blende structure occurs in zinc sulfide, where sulfide anions form a face-centered cubic lattice and zinc cations occupy tetrahedral holes. The large size difference between ions results in coordination number four. Only half of available tetrahedral holes are filled, leaving the rest empty in this structure.

Fluorite structure, found in compounds like calcium fluoride with a 1:2 cation-to-anion ratio, arranges cations in a face-centered cubic lattice with anions occupying all tetrahedral holes. This arrangement gives calcium cations a coordination number of eight and fluoride anions a coordination number of four.

Caesium chloride has a primitive cubic structure because both ions are similar in size, unlike sodium chloride where size difference is significant. In CsCl, caesium cations occupy cubic holes at the unit cell center, giving both ions a coordination number of eight, whereas NaCl's size difference favors octahedral coordination.

Cation-to-anion ratio determines how many holes can be filled. A 2:1 ratio allows all tetrahedral holes to fill in closest-packed arrays, while a 1:1 ratio fills all octahedral holes. Ratios less than these maxima leave some holes vacant, affecting overall crystal geometry and stability.