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Crystals with obvious flat faces are called euhedral crystals, while those lacking defined faces are called anhedral crystals. For example, consider a cubic cell of dimension 3.52 Å. As the entire crystal consists of repeating unit cells, this definition is sufficient to represent the entire crystal. The growth of epitaxial films can be done by a number of methods including molecular beam epitaxy, atomic layer epitaxy, and chemical vapor deposition, all of which will be described later.Table \(\PageIndex{1}\) shows the various crystal systems, while Figure \(\PageIndex{1}\) shows the 14 Bravais lattices. As the film gets thicker and thicker, it will try to relieve the strain in the film, which could include the loss of epitaxy of the growth of dislocations. In contrast, common coordination numbers in the solid state are 3, 4, 6, 8, and 12. In epitaxial growth, there is a precise crystal orientation of the film in relation to the substrate. A number of inter-atomic distances may be calculated for any material with a zinc blende unit cell using the lattice parameter (a).An interstitial impurity occurs when an extra atom is positioned in a lattice site that should be vacant in an ideal structure (Figure \(\PageIndex{13}\) b).Since all the adjacent lattice sites are filled the additional atom will have to squeeze itself into the interstitial site, resulting in distortion of the lattice and alteration in the local electronic behavior of the structure. In both fcc and hcp cells most of the space within these atoms lies within two different sites known as octahedral sites and tetrahedral sites. These usually have the units of Angstroms and relate to the distance in each direction between the origin of the cell and the atom. This system also includes body-centered orthorhombic, base-centered orthorhombic, and face-centered orthorhombic (Figure \(\PageIndex{1}\).However, it should be noted that these formulae do not necessarily apply when the ratio a/c is different from the ideal value of 1.632.The hexagonal close packed cell is a derivative of the hexagonal Bravais lattice system (Figure \(\PageIndex{6}\) with the addition of an atom inside the unit cell at the coordinates (1/3,2/3,1/2). Any impurity element that is incorporated during crystal growth can occupy a lattice site. The arrangement of atoms, ions, or molecules in a crystal. Figure \(\PageIndex{13}\) summarizes various classes of native point defects, however, they may be divided into two general classes; defects with the wrong number of atoms (deficiency or surplus) and defects where the identity of the atoms is incorrect.Antisite defects are a particular form of substitution defect, and are unique to compound semiconductors. Within the unit cell, the atomic arrangement is expressed using coordinates. Crystals have been studied using x-rays, which excite signals from the atoms. It can also form amorphous ice.There was an error. In both fcc and hcp lattices each of the atoms have a coordination number of 12.The most efficient way for equal sized spheres to be packed in two dimensions is shown in Figure \(\PageIndex{4}\), in which it can be seen that each sphere (the dark gray shaded sphere) is surrounded by, and is in contact with, six other spheres (the light gray spheres in Figure \(\PageIndex{4}\). For example, zinc selenide (zinc blende, a = 5.668 Å) is readily grown on gallium arsenide (zinc blende, a = 5.653 Å).

Determination of the packing fraction is accomplished by calculating the number of whole spheres per unit cell (2 in hcp), the volume occupied by these spheres, and a comparison with the total volume of a unit cell. This is demonstrated in Figure \(\PageIndex{5}\). If a crystal is formed of ions, the compound can be described as an ionic lattice.

Individual Miller indices are given in parentheses (hkl), while braces {hkl} are placed around the indices of a family of planes. This concept requires that the atoms (ions) are arranged so as to have the maximum density. Antisite defects involve fitting into a lattice site atoms of a different size than the rest of the lattice, and therefore this often results in a localized distortion of the lattice.
Crystal structure. In the structure drawn, all of the particles (yellow) are the same.
Depending on the impurity, substitution defects can greatly distort the lattice and/or alter the electronic structure. Since face centered cubic or fcc is more commonly used in preference to cubic close packed (ccp) in describing the structures, the former will be used throughout this text.\[ Na-Cl\ =\ \frac{a}{2} \approx 0.5 a \label{4} \]Many crystal structures can be described using the concept of close packing. An example of an amorphous solid is glass, which may resemble a crystal when faceted, yet isn't one.Carbon can form diamond (cubic lattice) and graphite (hexagonal lattice. For good quality epitaxy, this should be less than 1%. In the hexagonal close packed system, the tetrahedral sites are at (0,0,3/8) and (1/3,2/3,7/8), and the octahedral sites are at (1/3,1/3,1/4) and all symmetry equivalent positions.\[ Na-Na \ =\ Cl-Cl \ =\ \frac{a}{\sqrt{2}} \approx 0.707\ a \label{5} \]The mineral chalcopyrite CuFeS2 is the archetype of this structure.