Unit cell wurtzite lattice

Fig. 4.12 (a) CdSe wurtzite unit cell (b) schematic illustration of a hexagonal (wurtzite) CdSe basal plane on a (111) section of the gold lattice, emphasizing the 2 3 lattice match. Note the [111] Au//(0001)CdSe orientation, with the CdSe a-directions aligned along the (llO)Au. The outlined rhombus indicates the projection of a CdSe unit cell. (Adapted from [112])... 

An enormous range of properties is found in oxides. The most successful and most widely used substrate for GaN to date is sapphire, AI2O3. Except for wurtzite materials, few of the unit cells in these materials match with GaN, but it is usually useful to think of these systems as having a close-packed nitrogen lattice in GaN matching to a near close-packed oxygen lattice in the oxide. 

The high temperature modification of ZnAl2S4 was described by Hahn and Frank (12) as being of the wurtzite type, with a disordered distribution of the three metal atoms and one gap on the four sites of the metal lattice. Recently, it has been shown (5) that this compound has a superstructure of wurtzite with an orthorhombic unit cell. The unit cell of ZnAl2S4 is actually monoclinic with a ft angle of 90°. Its space group is Pm—C1S. The parameters of the unit cell... 

William B. Pearson (1921-2005) developed a shorthand system for denoting alloy and intermetallic structure types (Pearson, 1967). It is now widely used for ionic and covalent solids, as well. The Pearson symbol consists of a small letter that denotes the crystal system, followed by a capital letter to identify the space lattice. To these a number is added that is equal to the number of atoms in the unit cell. Thus, the Pearson symbol for wurtzite (hexagonal, space group PS mc), which has four atoms in the unit ceU, is hPA. Similarly, the symbol for sodium chloride (cubic, space group Fm3m), with eight atoms in the unit cell, is cF8. 

The crystal structure for this complex lattice (wurtzite structure) is shown in Figure 2.15. This is best described as an hep lattice of sulfide ions, with zinc ions occupying one-half of the available tetrahedral interstitial sites. For this lattice, there are two units of ZnS per unit cell ... 

Figure 2.15. Model of the wurtzite (ZnS) crystal structure. The framework is based oir air hep lattice of anions (yellow the unit cell consists of A and B ions) with zinc ions occupying tetrahedral interstitial sites (white, labeled as X and Y ions).

Wurtzite ZnO structure with four atoms in the unit cell has a total of 12 phonon modes (one longitudinal acoustic (LA), two transverse acoustic (TA), three longitudinal optical (LO), and six transverse optical (TO) branches). The optical phonons at the r point of the Brillouin zone in their irreducible representation belong to Ai and Ei branches that are both Raman and infrared active, the two nonpolar 2 branches are only Raman active, and the Bi branches are inactive (silent modes). Furthermore, the Ai and Ei modes are each spht into LO and TO components with different frequencies. For the Ai and Ei mode lattice vibrations, the atoms move parallel and perpendicular to the c-axis, respectively. On the other hand, 2 modes are due to the vibration of only the Zn sublattice ( 2-low) or O sublattice ( 2-high). The expected Raman peaks for bulk ZnO are at 101 cm ( 2-low), 380 cm (Ai-TO), 407 cm ( i-TO), 437 cm ( 2-high), and 583 cm ( j-LO). 

Other Metal Sulphides. A survey of lattice data and structure types of 40 compounds of the type Cu2ABS4, where A = Mn, Fe, Co, Ni, Zn, Cd, or Hg and B = Si, Ge, or Sn, has shown that three tetrahedral structure types, differing in symmetry and unit-cell size, exist.254 All of the compounds were found to adopt one of the following structure types the stannite structure, an orthorhombic superstructure of wurtzite, or a hitherto unknown structure based on slightly distorted sphalerite cells of tetragonal, orthorhombic, or monoclinic symmetry. 

This method was used to calculate the nearest distance (uq/c) between the A1 and the N ions along the c axis from the measured values of the square of the structure amplitude. We found (Fig. 2) that Uj/c = 0.386 0.001 and that It was independent of temperature (within the limits of the experimental error). Jeffrey et al. [1] reported 0.385 for this parameter. If all the shortest atomic spacings were equal and c/a = 1.600, we should obtain Uq/c = 0.380, whereas in the case of a perfect wurtzite structure (c/a = 1.633) we should have 0.375. Hence, we concluded that the ions located within tetrahedra in tiie aluminum nitride lattice were displaced somewhat toward the base of the unit cell. The shortest distance between the Al and the... 

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. 

Fig.3 7. a) Unit cell and primitive translation vectors of the hexagonal lattice. The Figure also shows the structure of 3-AgI (Wurtzite structure) ( ) Ag-ions, ( ) I-ions, (====) Ag-I bonds ions number 1 to 4 belong to the unit cell, b) Brillouin zone of the hexagonal lattice [3.5]... 

Figure 13.3 Schematic illustration for the sublattice sites. The parameter a and c refer c stalline unit cell of the hexagonal wurtzite to the hexagonal lattice constants of the structure. The large gray spheres represent wurtzite structure. On the right side, the A...

In the first case, along the direction of the diagonal of the cubic cell, there is a sequence ABC of identical unit slabs ( minimal sandwiches ), each composed of two superimposed triangular nets of Zn and S atoms, respectively. The thickness of the slabs, which include the Zn and S atom nets, is 0.25 of the lattice period along the superimposition direction (that is along the cubic cell diagonal aj3). It is (0.25,3 X 541) pm = 234 pm. In the wurtzite structure there is a sequence BC of similar slabs formed by sandwiches of the same triangular nets of Zn and S atoms. Their thickness is —0.37 X c = 0.37 X 626.1pm = 232 pm). 

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