Ionic structures: rock salt, zinc blende, antifluorite, CsCl and rutile

Ionic structures are close-packed anions with cations in the holes

Intuition

Think of big balls in a crate with small balls tucked into the gaps. The big ones are the anions, the small ones the cations. Which gaps you fill, and how many, decides the crystal.

Using the table from the previous page, each structure is a choice of packing (ccp or hcp) and which holes are filled. Coordination numbers are written cation first, anion second.

Exam detail

Test 1 asks for structural descriptions of various ionic lattices. Know packing, filled holes, coordination and space group for each of these.

The five structures

Rock salt, NaCl. ccp Cl$^-$ anions with Na$^+$ in all octahedral holes. Space group Fm$\bar{3}$m, where F means face-centred. Coordination is 6:6. The lecture shows it as close-packed, as ClNa$_6$ octahedra and as NaCl$_6$ octahedra.

Zinc blende, ZnS. ccp S$^{2-}$ anions with Zn$^{2+}$ in half of the tetrahedral holes. Coordination 4:4. Space group F$\bar{4}$3m.

Antifluorite, Li$_2$O. ccp O$^{2-}$ anions with Li$^+$ in all the tetrahedral holes. Coordination 4:8. Space group Fm$\bar{3}$m.

Caesium chloride, CsCl. Two interpenetrating simple cubic cells, not ccp. Coordination 8:8. Space group Pm$\bar{3}$m.

Rutile, TiO$_2$. A distorted hcp array of anions with half of the octahedral sites occupied by cations. Ti$^{4+}$ sits in a body-centred tetragonal cell, and O$^{2-}$ has local trigonal planar geometry. Coordination 6:3. Space group P4$_2$/mnm. Usually drawn as a primitive cell.

Compare

Coordination (cation:anion)

6:6 rock salt. 4:4 zinc blende. 4:8 antifluorite. 8:8 CsCl. 6:3 rutile.

Structures

Zinc blende and antifluorite both fill tetrahedral holes: half of them, or all of them.

The formula comes from counting the shared atoms

Try it: worked example

Find the formula of the rock-salt unit cell by counting atoms.

Show answer and steps

AnswerNa4Cl4, which reduces to NaCl.

1. Na sits at the 8 corners (each shared by 8 cells) and 6 face centres (each shared by 2 cells): $8 \times \tfrac{1}{8} + 6 \times \tfrac{1}{2} = 1 + 3 = 4$.
2. Cl sits at the 12 edge centres (each shared by 4 cells) and 1 body centre (not shared): $12 \times \tfrac{1}{4} + 1 \times 1 = 3 + 1 = 4$.
3. The cell holds Na$_4$Cl$_4$, so the empirical formula is NaCl.

Fractional coordinates locate the atoms in the cell

The lecture gives four atom positions for each of the worksheet cells. These are numbered positions on the slide diagrams, not the full list of atoms.

• Rock salt. Na at $(0,0,0)$, $(\tfrac12,0,0)$, $(\tfrac12,0,\tfrac12)$, $(1,\tfrac12,\tfrac12)$, as listed on the slide.
• Zinc blende. 1 $(0,0,0)$, 2 $(\tfrac12,\tfrac12,0)$, 3 $(\tfrac12,\tfrac12,1)$, 4 $(\tfrac34,\tfrac14,\tfrac14)$.
• Antifluorite. 1 $(0,0,0)$, 2 $(\tfrac12,\tfrac12,0)$, 3 $(\tfrac12,0,\tfrac12)$, 4 $(\tfrac34,\tfrac14,\tfrac14)$.
• CsCl. 1 $(1,0,0)$, 2 $(\tfrac12,\tfrac12,\tfrac12)$, 3 $(1,0,1)$, 4 $(1,1,1)$.
• Rutile. Approximate: 1 $(\sim0.3,\sim0.7,0)$, 2 $(\tfrac12,\tfrac12,\tfrac12)$, 3 $(\sim0.8,\sim0.8,\tfrac12)$, 4 $(\sim0.7,\sim0.3,1)$.

Optional aside

These coordinates are the slide’s worksheet answers. The labels on the slide pictures decide which atom each number refers to, and those pictures were not transcribed. Use the slide to see which atom is which. The Na position list on the rock-salt slide also looks inconsistent with a face-centred cell, so check it against the picture.

Pitfall

Coordination numbers read cation first. The 6:3 for rutile means each Ti has six O neighbours and each O has three Ti.