Unit cell zinc blende lattice

The compound MX has a density of 2.1 g/cnf and a cubic unit cell with a lattice parameter of 0.57 nm. The atomic weights of M and X are. respectively, 28.5 and 30g/mol. Based on this information, which of the following structures is (are) possible NaCl, CsCl, or zinc blende Justify your choices. 

The zinc blende lattice Is named after its parent compound, ZnS. Zinc sulfide also exists in a different structure known as the wurtzite lattice. Molecules that can exist in more than one type of crystalline form exhibit polymorphism. The wurtzite lattice is comprised of one type of ion forming a hexagonal closest-packed unit cell, with the other type of ion occupying half of the tetrahedral holes. The following molecules can assume the wurtzite lattice ZnO, ZnS, ZnSe, ZnTe, BeO, Agl, CdS, MnS, SiC, AIN, and NH4F. Both types of lattices consist of corner-shared tetrahedrons, but the tetrahedrons in wurtzite are canted in alternating layers. 

To date, inorganic materials have been used in most semiconductor applications. The most studied and technologically important inorganic semiconductors have the diamond (e.g.. Si) or zinc-blende (e.g., Ga As) crystal structure. Figure 1 shows the zinc-blende crystal structure and the corresponding BrOouin zone. (The symbols label special symmetry points in the zone.) The structure is based on an fee lattice with two atoms per unit cell. The diamond crystal structure is the same as the zinc-blende structure, except that the two atoms in the unit cell are the same for diamond, whereas they are different for zinc blende. The Brillouin zones are the same for the two structures, but for the diamond structure, there is an additional inversion symmetry operator. 

Real crystal lattices are made from atoms, atomic or molecular entities associated with lattice points of the BLs or of their combinations. For instance, when they are centred at the lattice points of a fee BL, entities of two same atoms lying along the diagonal of the unit cell of this BL and separated by one quarter of this diagonal generate the diamond structure (when the two atoms are different, the structure generated is that of sphalerite, also called zinc-blende). 

Zinc blende has face centered cubic lattice in Zn atoms and again face centred lattice in S atoms. The coordinates of Zn atoms and S atoms in a unit cell are... 

VA Fig. 5.19 (a) A typical representation of the diamond lattice, (b) Reorientation of the network shown in (a) provides a representation that can be compared with the unit cell of zinc blende (Figure 5.18b) the atom labels correspond to those in diagram (a). This lattice is also adopted by Si, Ge and a-Sn. (c) The unit cell of P-cristobalite, Si02 colour code Si, purple O, red. 

The sodium chloride (NaCl) and zinc blende (ZnS) structures are based on a face-centered cubic lattice. In both structures the anions sit on the lattice points that lie on the corners and faces of the unit cell, but the two-atom motif is slightly different for the two structures. In NaCl the Na ions are displaced from the Cl ions along the edge of the unit cell, whereas in ZnS the Zn ions are displaced from the ions along the... 

Piezoelectricity is a physical effect exhibited by crystals that are electrically neutral, but that do not have a center of reflective symmetry in crystal structure. The essential property of a point of reflective symmetry is that for each atomic position in the crystal lattice there is a matching atomic position at a point that is directly opposite the first with respect to the point of symmetry this second position is at a same distance from the point of symmetry as the first. For example, the face-centered cubic structure has a point of reflective symmetry at the geometrical center of the unit cell whereas the cubic zinc blende structure does not have a center of symmetry. 

Sphalerite or zinc blende is the chief ore of ZnS. ZnS as well as many of the III-V and II-VI compound semiconductors such as GaAs form a diamond-like stmeture with one type of atom on the fee lattice sites and the other type of atom on every other tetrahedral site. The space group is F43wx (the d-glide plane symmetry in diamond is lost by the fact that different atoms occupy the interstitial sites). Since there are four atoms on the lattice points of the fee unit cell, the stoichiometry is maintained if half of the eight tetrahedral sites are occupied by the second atom. For these systems, the double stacking described above would have different atoms in doubled layers, i.e., A(Zn) A (S) B(Zn) B (S) C(Zn) C (S), etc. This type of structure is the same as shown in Figure 5.9 if the black spots are... 

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