The zinc blende crystal structure is one that may be generated from close- packed planes of anions. (a) Will the stacking sequence for this structure be FCC or HCP? Why? (b) Will cations fill tetrahedral or octahedral poitions? Why? (c) What fraction of the positions will be bccupied?

The face-centered cubic (FCC) lattice plays a pivotal role in the structure of many crystalline solids, including the zinc blende structure. In an FCC lattice, each unit cell is shaped like a cube with atoms located at all corners and the centers of all the cube faces. The defining characteristic of this arrangement is its packing efficiency, which maximizes the use of space within the crystal.

In the context of the zinc blende structure, the anions (typically the larger ions in the structure) occupy these positions, creating a lattice that is highly symmetrical and dense. The FCC lattice has a particular stacking sequence labeled as ABCABC... where each layer is offset, providing no direct vertical alignment between atoms in successive layers. This contrasts with the hexagonal close-packed (HCP) arrangement, which has an ABAB... stacking sequence, with every other layer directly aligned.

The FCC structure’s arrangement leads to multiple interstitial sites – small spaces between the anions where cations can reside.

Within the FCC lattice, there are two primary types of interstitial sites where cations can be found: tetrahedral and octahedral. Tetrahedral sites are formed by four anions arranged at the corners of a tetrahedron. Each FCC lattice has eight such sites. These sites are smaller than octahedral sites, which are formed by six anions at the corners of an octahedron, and of which there are four in every FCC unit cell.

In the specific case of the zinc blende structure, cations occupy half of the available tetrahedral sites. This arrangement occurs because each cation is bonded to four anions, forming a perfect tetrahedron and maintaining charge neutrality in the crystal. This selective occupation of tetrahedral sites is central to the unique properties of zinc blende, as it leads to an orderly and consistent pattern throughout the crystal.

The coordination number in crystal structures refers to the number of immediate neighbor atoms that each atom has. It is a crucial parameter that affects both the physical and chemical properties of the material. In the FCC lattice structure, the coordination number is 12 for the atoms at the face-centered and corner positions; this means each atom is surrounded by 12 equidistant neighbors.

In contrast, within the zinc blende structure, the anions and cations have different coordination numbers due to the tetrahedral site occupation. Each anion is surrounded by four cations, giving it a coordination number of 4, which reflects its occupancy of tetrahedral sites. Likewise, each cation has a coordination number of 4 since it's bonded to four anions at the vertices of a tetrahedron. This lower coordination number is distinct for tetrahedrally bonded materials and influences properties such as bond angles and bond strength.