The Cu-Zn alloy has widely used as electric contact material on the micro-electronic device, automotive connectors, electric machine and electronic instrument, etc. The Cu-Zn alloys has widely used as electric contact material on the micro-electronic device, automotive connectors, electric machine and electronic instrument, etc. Materials were used application to electrical contact are usually constituted of a copper-zinc alloys interesting for its excellent electrical conductivity and an inexpensive materials cost.

because the ZnO are hexagonal crystal. If crystal planes in hexagonal systems are indexed using Miller indices, then crystallographically equivalent planes have indices which appear dissimilar, so they make 4 parameter Miller-Bravais lattice to be easier to understand. you can find some documents to learn how to change three coordinate system to 4 coordinate system. :D

Low-energy electron diffraction, X-ray photoelectron spectroscopy and synchrotron-radiation-excited angle-resolved photoelectron spectroscopy have been used to characterize Cu-oxide overlayers on the Zn-terminated ZnO(0 0 0 1) surface. Deposition of Cu on the ZnO(0 0 0 1)–Zn surface results in the formation of Cu clusters with (1 1 1) top terraces. Oxidation of these clusters by annealing at 650 K in O2 atmosphere (1.3 × 10−4 Pa) leads to an ordered Cu2O overlayer with (1 1 1) orientation. Good crystallinity of the Cu2O(1 1 1) overlayer is proved by energy dispersion of one of Cu2O valence bands. The Cu2O(1 1 1) film exhibits a strong p-type semiconducting nature with the valence band maximum (VBM) of 0.1 eV below the Fermi level. The VBM of ZnO at the Cu2O(1 1 1)/ZnO(0 0 0 1)–Zn interface is estimated to be 2.4 eV, yielding the valence-band offset of 2.3 eV.

Refer to Any good solid state physics book (may be Aschroft -Mermin or Kittel) for Indexing system for Hexagonal, wurtzite struture. 

The Miller-Bravais indexing (hkil) has - as written above - some advantages to recognize symmetry-equivalent planes, like for highest cubic symmetry. There you simply can permutate indices (be careful, it only works for m-3m).

(hkil) and and (hkl) use the same h,k,l and i = -(h+k)

e.g. it is difficult to (124) recognize which planes are equivalent. With Miller-Bravai it is easy:

(12- 34), (-3124), (2-314), (21-34), (1-324), (-3214)

(12- 3-4), (-312-4), (2-31-4), (21-3-4), (1-32-4), (-321-4)

 (-1-2 34), (3-1-24), (-23-14), (-2-134), (-13-24), (3-2-14)

 (-1-2 3-4), (3-1-2-4), (-23-1-4), (-2-13-4), (-13-2-4), (3-2-1-4)

compared to (hkl) - simply delete i it looks really weird :-)

(124), (-314), (2-34), (214), (1-34), (-324)

(123-4), (-31-4), (2-3-4), (21-4), (1-3-4), (-32-4)

 (-1-2 4), (3-14), (-234), (-2-14), (-134), (3-24)

 (-1-2-4), (3-1-4), (-23-4), (-2-1-4), (-13-4), (3-2-4)

Finally it only more convenient. I myself often prefer (hkl).

Be careful with lattice directions [uvtw] and [uvw]. The rules are different and more complicated, although very interesting is that (hki0) and [uvt0] are parallel to each other. This is not the case for (hk0) and [uv0]. 

Refer to the theory in the Wurzite structure.Solid State Physics by Kittel is the best in this.

Beacuase of the hexagonal wurtzite structure of the ZnO.The indexing is slightly different.