the wurtzite structure
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The wurtzite structure is the hexagonal twin of zinc blende. Both link every atom tetrahedrally to four of the opposite kind; they differ only in how those tetrahedral layers are stacked. Where zinc blende repeats its layers ABCABC (the cubic rhythm), wurtzite repeats them ABAB (the hexagonal rhythm), giving a crystal with a distinct up-down axis rather than full cubic symmetry.
In packing terms the anions form a hexagonal close-packed array and the cations fill half the tetrahedral holes, again a 4:4 structure, with two formula units in the hexagonal cell. Because the ABAB stacking lacks a centre of symmetry and has a unique polar axis, wurtzite crystals are naturally piezoelectric and pyroelectric: squeeze them and they generate a voltage, heat them and their polarisation shifts.
This structure hosts some of the most important electronic and optical ceramics: aluminium nitride (AlN, a superb electrical insulator that conducts heat well), zinc oxide (ZnO, used in varistors and transparent electronics), gallium nitride (GaN, the blue-LED and power-electronics semiconductor), beryllium oxide, and the 2H polytype of silicon carbide. Honest caveat: because wurtzite and zinc blende differ so little in energy, the same compound can crystallise either way, and the choice is easily nudged by temperature, pressure, or growth conditions.
Gallium nitride, GaN, is wurtzite: an HCP nitrogen array with gallium in half the tetrahedral holes. Its polar wurtzite axis and wide band gap are exactly what make GaN the material of blue and white LEDs and high-power transistors.
HCP anions, cations in half the tetrahedral holes: 4:4, polar.
Wurtzite and zinc blende are polymorphs of the same 4:4 bonding, distinguished only by layer stacking. The wurtzite version lacks inversion symmetry, which is precisely why its crystals are piezoelectric.