What determines the crystal structure of an ionic solid?

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.

How do tetrahedral and octahedral holes differ in ionic crystals?

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.

Why does sodium chloride have a coordination number of six?

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.

What is the zinc blende structure and how does it form?

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.

How does the fluorite structure accommodate unequal numbers of cations and anions?

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.

Why does caesium chloride have a different structure than sodium chloride?

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.

What role does cation-to-anion ratio play in determining ionic crystal structure?

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.

11.16

Ionic Crystal Structures

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Ionic solids typically are closely packed in a crystal lattice. However, the charges and sizes of the ions greatly influence their packing configuration, leading to significant variation in crystal structure and coordination number.

For example, caesium chloride, where both ions are of similar sizes, resembles a primitive cubic lattice of chloride anions with caesium cations in the centers. The caesium chloride unit cell is assigned one chloride anion and one caesium cation.

Each caesium ion is surrounded by eight chloride ions and vice versa, giving both caesium and chloride coordination numbers of eight.

Sodium chloride resembles a face-centered cubic lattice of chloride anions with the smaller sodium cations occupying the spaces between the anions.

The difference in ionic radii results in each sodium cation interacting with only six chloride anions and vice versa, with four chloride anions and four sodium cations assigned to the unit cell. This is often referred to as the rock salt structure.

Zinc sulfide has an even greater difference in ionic radii than that of sodium chloride, leading to the zinc blende structure. Although the sulfide arrangement resembles a face-centered cubic lattice, the zinc cations are located within tetrahedra of sulfide anions, leading to a coordination number of four.

Only half of all possible tetrahedral ‘holes’ are occupied by zinc cations, leaving the rest empty. The unit cell has four sulfide anions and four zinc cations.

The proportion of cations to anions also affects which structure an ionic solid adopts. Calcium fluoride, which has one cation and two anions, exhibits the fluorite structure.

Here, the cations are arranged in a face-centered cubic lattice with the anions occupying all tetrahedral holes. The unit cell has four calcium cations, each with a coordination number of eight, and eight fluoride anions, each with a coordination number of four.

The antifluorite structure is exhibited by compounds like sodium oxide, which has two cations and one anion. Here, the anions are arranged in a face-centered cubic lattice with cations occupying the eight tetrahedral holes.

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Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is…