Point Defects in Stoichiometric Compounds

What point defects are vital for the operation of Lil pacemaker batteries  

What is the basis of atomistic simulation calculations of point defect formation energies  

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. 

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Non-stoichiometry is a very important property of actinide dioxides. Small departures from stoichiometric compositions, are due to point-defects in anion sublattice (vacancies for AnOa-x and interstitials for An02+x )- A lattice defect is a point perturbation of the periodicity of the perfect solid and, in an ionic picture, it constitutes a point charge with respect to the lattice, since it is a point of accumulation of electrons or electron holes. This point charge must be compensated, in order to preserve electroneutrality of the total lattice. Actinide ions having usually two or more oxidation states within a narrow range of stability, the neutralization of the point charges is achieved through a Redox process, i.e. oxidation or reduction of the cation. This is in fact the main reason for the existence of non-stoichiometry. In this respect, actinide compounds are similar to transition metals oxides and to some lanthanide dioxides. 

In this chapter, we discuss classical non-stoichiometry derived from various kinds of point defects. To derive the phase rule, which is indispensable for the understanding of non-stoichiometry, the key points of thermodynamics are reviewed, and then the relationship between the phase rule, Gibbs free energy, and non-stoichiometry is discussed. The concentrations of point defects in thermal equilibrium for many types of defect structure are calculated by simple statistical thermodynamics. In Section 1.4 examples of non-stoichiometric compounds are shown referred to published papers. 

As mentioned above, the non-stoichiometric compounds originate from the existence of point defects in crystals. Let us consider a crystal consisting of mono-atoms. In ideal crystals of elements, atoms occupy the lattice points regularly. In real crystals, on the other hand, various kinds of point defects can exist in thermodynamic equilibrium. First, we shall consider vacancies , which are empty regular lattice points. Consider a crystal composed of one element which has N atoms sited on regular lattice points and vacancies,... 

Chapter 1 deals with classical non-stoichiometric compounds. By classical, the author means that the basic concept of the phase stability has been well established from a thermodynamical point of view, and does not mean that research in this field has been fully completed. In these compounds the origin of non-stoichiometry is point defects . In the first half of the chapter, the fundamental relation between point defects and non-stoichiometry is described in detail, based on (statistical) thermodynamics, and in the second half various examples, referred to the original papers, are shown. 

We have discussed point defects in elements (A) and in nearly stoichiometric compounds having narrow ranges of homogeneity. Let us extend this discussion to the point defect thermodynamics of alloys and nonmetallic solid solutions. This topic is of particular interest in view of the kinetics of transport processes in those solid solutions which predominate in metallurgy and ceramics. Diffusion processes are governed by the concentrations and mobilities of point defects and, although in inhomogeneous crystals the components may not be in equilibrium, point defects are normally very close to local equilibrium. 

When the composition of a crystal is defined by a distinct chemical formula e.g., Si02), it is known as a stoichiometric compound. If the composition of the crystal is altered upon doping or thermal treatment, the resulting solid may deviate from the original chemical formula, forming a nonstoichiometric solid. Nonstoichiometry and the existence of point defects in a solid are often closely related. For instance, the formation of x anion vacancies per each quartz unit cell will result in the nonstoichiometric compound Si02-x ... 

For a non-stolchiometrlc crystal, the concentration of each point defect, in each conjugate pair, is no longer equal. If there is an excess of Vm, , or Xx, then the compound will have a surplus of X (or deficiency of M, which is the same thing) over the ideal stoichiometric composition. This is called a positive deviation firom stoichiometry. Conversely, for a negative deviation, there will be an excess of Vx, Mi, or Mm. This explains the plus and minus in equation 2.6.9. In terms of the above given defects, 6 may be expressed as shown in the following Table ... 

We have already covered, albeit briefly, non-ionized stoichiometric and non-ionlzed non-stoichlometric intrinsic-defect compounds. Let us now consider the ionization of defects in these compounds. In the MXs compound, if we remove some of the X-atoms to form Vx, the electrons from the removed X-atom (or from the bond holding the X-atom in the crystal) are left behind for charge compensation reasons. At low temperatures, these electrons are localized near the vacancy but become dissociated from the point defect at higher temperatures. They become free to move through the crystal, and we say that the intrinsic defect has become ionized. We can write the following equations for this mechanism ... 

In view of the many types of point defects that may be formed in inorganic compounds and that each type of defect may have varying effective charge, numerous defect reactions may in principle be formulated. In the following, a few simple cases will be treated as examples. First, we will consider defect stmcture situations in stoichiometric compounds (Schottky, Frenkel and intrinsic electronic disorders) and then defect structure situations in nonstoichiometric oxides will be illustrated. Finally, examples of defect reactions involving foreign elements will be considered. 

As described in the previous chapter, the defect structures in stoichiometric compounds contain equivalent concentrations of negatively and positively charged point defects. These are formed as a result of internal equilibria in the crystal and do not involve reactions with the surroundings. For this reason the defect stmctures in stoichiometric compounds are also termed internal disorder. 

The relation between x and p in non-stoichiometric compounds was analyzed based on statistical thermodynamics of point defects in a previous report (Kosuge, 1993) and eq.(7) was derived. 

J. B. Lightstone and G. G. Libowitz, Interaction between point defects in non-stoichiometric compounds, J. Phys. Chem. Solids 1025-1036 (1969). 

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-... 

Compounds are made up of atoms of more than one chemical element. The point defects that can occur in pure compounds parallel those that occur in monatomic materials, but there is an added complication in this case concerning the composition of the material. In this chapter discussion is confined to the situation in which the composition of the crystal is (virtually) fixed. Such solids are called stoichiometric compounds. (The situations that arise when the composition is allowed to vary are considered in Chapter 4 and throughout much of the rest of this book. This latter type of solid is called a nonstoichiometric compound.) The composition problem can be illustrated with respect to a simple compound such as sodium chloride. 

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