Intrinsic Point Defects

The microstmcture and imperfection content of coatings produced by atomistic deposition processes can be varied over a very wide range to produce stmctures and properties similar to or totally different from bulk processed materials. In the latter case, the deposited materials may have high intrinsic stress, high point-defect concentration, extremely fine grain size, oriented microstmcture, metastable phases, incorporated impurities, and macro-and microporosity. AH of these may affect the physical, chemical, and mechanical properties of the coating. 

It is not necessary for a compound to depart from stoichiometry in order to contain point defects such as vacant sites on the cation sub-lattice. All compounds contain such iirndirsic defects even at the precisely stoichiometric ratio. The Schottky defects, in which an equal number of vacant sites are present on both cation and anion sub-lattices, may occur at a given tempe-ramre in such a large concentration drat die effects of small departures from stoichiometry are masked. Thus, in MnOi+ it is thought that the intrinsic concentration of defects (Mn + ions) is so large that when there are only small departures from stoichiometry, the additional concentration of Mn + ions which arises from these deparmres is negligibly small. The non-stoichiometry then varies as in this region. When the departure from non-stoichio-... 

All of these point defects are intrinsic to the heterogeneous solid, and cirise due to the presence of both cation and anion sub-lattices. The factors responsible for their formation are entropy effects (stacking faults) and impurity effects. At the present time, the highest-purity materials available stiU contain about 0.1 part per billion of various impurities, yet are 99.9999999 % pure. Such a solid will still contain about IQi impurity atoms per mole. So it is safe to say that all solids contain impurity atoms, and that it is unlikely that we shall ever be able to obtain a solid which is completdy pure and does not contain defects. 

A considerable body of scientific work has been accomplished in the past to define and characterize point defects. One major reason is that sometimes, the energy of a point defect can be calculated. In others, the charge-compensation within the solid becomes apparent. In many cases, if one deliberately adds an Impurity to a compound to modify its physical properties, the charge-compensation, intrinsic to the defect formed, can be predicted. We are now ready to describe these defects in terms of their energy and to present equations describing their equilibria. One way to do this is to use a "Plane-Net". This is simply a two-dimensional representation which uses symbols to replace the spherical images that we used above to represent the atoms (ions) in the structure. 

Intrinsic Defects The simplest crystalline defects involve single or pairs of atoms or ions and are therefore known as point defects. Two main types of point defect have been identified Schottky defects and Frenkel defects. A Schottky defect consists of a pair of vacant sites a cation vacancy and an anion vacancy. A Schottky defect is... 

Chapter 2) and cannot be eliminated from the solid. They are called intrinsic point defects. This residual population is also temperature dependent, and, as treated later (Chapter 2), heating at progressively higher temperature increases the number of defects present. 

Intrinsic point defects are always present in a crystal as an inescapable property of the solid. For this to be so the intrinsic defect must be stable from a thermodynamic point of view. In this chapter the consequences of this thermodynamic aspect will be considered in more detail. 

Movement through the body of a solid is called volume, lattice, or bulk diffusion. In a gas or liquid, bulk diffusion is usually the same in all directions and the material is described as isotropic. This is also true in amorphous or glassy solids and in cubic crystals. In all other crystals, the rate of bulk diffusion depends upon the direction taken and is anisotropic. Bulk diffusion through a perfect single crystal is dominated by point defects, with both impurity and intrinsic defect populations playing a part. 

The compound will be stoichiometric, with an exact composition of MX10ooo when the number of metal vacancies is equal to the number of nonmetal vacancies. At the same time, the number of electrons and holes will be equal. In an inorganic compound, which is an insulator or poor semiconductor with a fairly large band-gap, the number of point defects is greater than the number of intrinsic electrons or holes. To illustrate the procedure, suppose that the values for the equilibrium constants describing Schottky disorder, Ks, and intrinsic electron and hole numbers, Kc, are... 

The papers of Wagner and Schottky contained the first statistical treatment of defect-containing crystals. The point defects were assumed to form an ideal solution in the sense that they are supposed not to interact with each other. The equilibrium number of intrinsic point defects was found by minimizing the Gibbs free energy with respect to the numbers of defects at constant pressure, temperature, and chemical composition. The equilibrium between the crystal of a binary compound and its components was recognized to be a statistical one instead of being uniquely fixed. 

Once the cluster expansion of the partition function has been made the remaining thermodynamic functions can be obtained as cluster expansions by taking suitable derivatives. Of particular interest are the expressions for the equilibrium concentrations of intrinsic point defects for the various types of lattice disorder. Since the partition function is a function of Nx, N2, V, and T, it is convenient for the derivation of these expressions to introduce defect chemical potentials for each of the species in the set (Nj + N2) defined, by analogy with ordinary Gibbs chemical potentials (cf. Section I), by the relation... 

FIGURE 5.1 Schematic illustration of intrinsic point defects in a crystal of composition MX (a) Schottky pair, (b) perfect crystal, and (c) Frenkel pair. 

The importance of interactions amongst point defects, at even fairly low defect concentrations, was recognized several years ago. Although one has to take into account the actual defect structure and modifications of short-range order to be able to describe the properties of solids fully, it has been found useful to represent all the processes involved in the intrinsic defect equilibria in a crystal (with a low concentration of defects), as well as its equilibrium with its external environment, by a set of coupled quasichemical reactions. These equilibrium reactions are then handled by the law of mass action. The free energy and equilibrium constants for each process can be obtained if we know the enthalpies and entropies of the reactions from theory or... 

---