Interstitial atoms lattice defects, elements

Another type of lattice defect for elements is interstitial atoms, in which an atom is transferred from a regular lattice point to an interstitial position, normally unoccupied by an atom. Consider a crystal which has N atoms sited on regular lattice points and N, atoms sited on interstitial lattice points (the number of interstitial lattice points is A, which is fixed by the crystal structure under consideration), by a similar calculation, the free energy increment from the ideal crystal is expressed as... 

Since irregular structure elements (point defects) such as interstitial atoms (ions) or vacancies must exist in a crystal lattice in order to allow the regular structure elements to move, two sorts of activation energies have to be supplied from a heat reservoir for transport and reaction. First, the energy to break bonds in the crystal... 

Chemical solid state processes are dependent upon the mobility of the individual atomic structure elements. In a solid which is in thermal equilibrium, this mobility is normally attained by the exchange of atoms (ions) with vacant lattice sites (i.e., vacancies). Vacancies are point defects which exist in well defined concentrations in thermal equilibrium, as do other kinds of point defects such as interstitial atoms. We refer to them as irregular structure elements. Kinetic parameters such as rate constants and transport coefficients are thus directly related to the number and kind of irregular structure elements (point defects) or, in more general terms, to atomic disorder. A quantitative kinetic theory therefore requires a quantitative understanding of the behavior of point defects as a function of the (local) thermodynamic parameters of the system (such as T, P, and composition, i.e., the fraction of chemical components). This understanding is provided by statistical thermodynamics and has been cast in a useful form for application to solid state chemical kinetics as the so-called point defect thermodynamics. 

Defects in crystalline solids occur for structural reasons, because the atoms (or ions) are not arranged ideally in the crystal when all the lattice sites are occupied, and for chemical reasons, because inorganic compounds may deviate from the fixed composition determined by the valence of the atoms. There are different types of structural defects in a crystalline solid which are normally classified into three groups (1) point defects, (2) line defects, and (3) planar defects. Point defects are associated with one lattice point and its immediate vicinity. They include missing atoms or vacancies, interstitial atoms occupying the interstices between atoms, and substitutional atoms sitting on sites that would normally be occupied by another type of atom. These point defects are illustrated in Fig. 7.2 for an elemental solid (e.g., a pure metal). The point defects that are formed in pure crystals (i.e., vacancies and interstitials) are sometimes referred to as intrinsic or native defects. 

The active elements that can be served as catalysts for anunonia synthesis are found in IVB to VIII groups, which form interstitial nitrides. Metal lattices are expanded due to the fact that nitrogen atom occupies the lattice defect positions. Because the interstitial nitrides are similar to metals, they are called metalhc nitrides. 

Apart from lattice vacancies, most real carbides, nitrides and materials produced from them contain another type of lattice defect namely impurities, both interstitial and substitutional. These impurities may result in quite critical changes in properties of such phases, see the reviews of Samsonov, Upadkhaya and Neshpor (1974), Alyamovsky, Zainulin and Shveikin (1981) and Shveikin et al (1984). Moreover, doping of the compounds with atoms of other elements is one of the most direct and frequently used ways of changing the characteristics of initial phases and is extensively used in the synthesis of new materials with an improved set of technological parameters. For these reasons studies of the electronic properties of doped refractory phases and alloys have received a lot of attention in the last few years. 

Theoretical studies of diffusion aim to predict the distribution profile of an exposed substrate given the known process parameters of concentration, temperature, crystal orientation, dopant properties, etc. On an atomic level, diffusion of a dopant in a siUcon crystal is caused by the movement of the introduced element that is allowed by the available vacancies or defects in the crystal. Both host atoms and impurity atoms can enter vacancies. Movement of a host atom from one lattice site to a vacancy is called self-diffusion. The same movement by a dopant is called impurity diffusion. If an atom does not form a covalent bond with siUcon, the atom can occupy in interstitial site and then subsequently displace a lattice-site atom. This latter movement is beheved to be the dominant mechanism for diffusion of the common dopant atoms, P, B, As, and Sb (26). 

The notion of point defects in an otherwise perfect crystal dates from the classical papers by Frenkel88 and by Schottky and Wagner.75 86 The perfect lattice is thermodynamically unstable with respect to a lattice in which a certain number of atoms are removed from normal lattice sites to the surface (vacancy disorder) or in which a certain number of atoms are transferred from the surface to interstitial positions inside the crystal (interstitial disorder). These forms of disorder can occur in many elemental solids and compounds. The formation of equal numbers of vacant lattice sites in both M and X sublattices of a compound M0Xft is called Schottky disorder. In compounds in which M and X occupy different sublattices in the perfect crystal there is also the possibility of antistructure disorder in which small numbers of M and X atoms are interchanged. These three sorts of disorder can be combined to give three hybrid types of disorder in crystalline compounds. The most important of these is Frenkel disorder, in which equal numbers of vacancies and interstitials of the same kind of atom are formed in a compound. The possibility of Schottky-antistructure disorder (in which a vacancy is formed by... 

Point defects are imperfections in the actual crystalline architecture as compared to the ideal lattice in which each atom site is filled with the appropriate element. They can influence properties at extremely low levels (ppb or ppm). Typical point defects include crystal sites with missing atoms (vacancies), atoms positioned in sites that are not filled by the crystal structure in question (interstitials), crystal sites containing impurity atoms (dopants), and cations with different oxidation states. Because mass. 

Substitution of a dopant for an element of the perfect crystal leads to a distortion of the perfect lattice from which electrons can scatter. If that substitutional dopant is ionized, the electric field of that ion adds to the scattering. Impurities located at interstitial sites (i.e., between atoms in the normal lattice sites) also disrupt the perfect crystal and lead to scattering sites. Crystal defects (e.g., a missing atom) disrupt the perfect crystal and appears as a scattering site in the free space seen by the electron. In useful semiconductor crystals, the density of such scattering sites is small relative to the density of sihcon atoms. As a result, removal of the silicon atoms through use of the effective mass leaves a somewhat sparsely populated space of scattering sites. 

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