Ionic compounds lattice defects

In pure and stoichiometric compounds, intrinsic defects are formed for energetic reasons. Intrinsic ionic conduction, or creation of thermal vacancies by Frenkel, ie, vacancy plus interstitial lattice defects, or by Schottky, cation and anion vacancies, mechanisms can be expressed in terms of an equilibrium constant and, therefore, as a free energy for the formation of defects, If the ion is to jump into a normally occupied lattice site, a term for... 

Fig. 3-12. Lattice defects and ion levels of ionic compound AB (a) ionnation of a pair of ion vacancy and interstitial ion, (b) A ion levels in ionic crystals. Va = A ion vacancy A] = intoatitial A ion Oa. = A ion level = unitary A ion level at lattice sites ...

Fig. 3 -13. (a) A ion levels at the surface and in the interior of ionic compound AB, and (b) concentration profile of lattice defects in a surface space charge layer since the energy scales of occupied and vacant ion levels are opposite to each other, ion vacancies accumulate and interstitial ions deplete in the space charge layer giving excess A ions on the surface. 

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. 

Before introducing experimental results for crystals grown by these methods, we shall consider the possible crystal defects of GaAs for a better understanding of experimental results. It is expected that at higher P, vacancies of Ga lattice sites or interstitial As may occur and at lower Pas vacancies of As or interstitial Ga may occur. Because GaAs is considered to be an ionic compound Ga-As, these defects at higher Pas act as donors (n-type) and those at lower P 1S act as acceptors (p-type). As shown below, the experimental results are not so simple. 

Intrinsic point defects are deviations from the ideal structure caused by displacement or removal of lattice atoms [106,107], Possible intrinsic defects are vacancies, interstitials, and antisites. In ZnO these are denoted as Vzn and Vo, Zn and 0 , and as Zno and Ozn, respectively. There are also combinations of defects like neutral Schottky (cation and anion vacancy) and Frenkel (cation vacancy and cation interstitial) pairs, which are abundant in ionic compounds like alkali-metal halides [106,107], As a rule of thumb, the energy to create a defect depends on the difference in charge between the defect and the lattice site occupied by the defect, e.g., in ZnO a vacancy or an interstitial can carry a charge of 2 while an antisite can have a charge of 4. This makes vacancies and interstitials more likely in polar compounds and antisite defects less important [108-110]. On the contrary, antisite defects are more important in more covalently bonded compounds like the III-V semiconductors (see e.g., [Ill] and references therein). 

The II-VI compounds have a larger ionicity than the III-V compounds, and it was first assumed that most of the residual donors and acceptors were due to the lattice defects like the anion and cation vacancies (Vn and VVi) and to group-II and group)-VI interstitial atoms, but it was later found that in most cases, group-1 and group)-V impurities were involved [118]. In some of these compounds, Li occupies a group-II site, where it is an acceptor, but it can also be present in the interstitial form, leading to self-compensation. 

Ionic conduction may dominate the electrical behavior of materials with small electronic conductivity, and its study is useful in the investigation of lattice defects and decomposition mechanisms. In order to establish that conduction takes place by the motion of ions and not of electrons or holes, one can compare the transport of charge with the transport of mass plated out on electrodes in contact with the sample. In practice, this approach is not always feasible because of the very low conductivities associated with ionic motion. When ionic conductivity is suspected one usually attempts to vary the concentration of defects by introducing impurities. For example, for cation conduction in monovalent ionic compounds, addition of divalent cations should enhance the conductivity, since the vacancies produced (in order to ensure charge compensation) lead to enhanced diffusion of the monovalent cation. (The diffusion of a vacancy in one direction is equivalent to the diffusion of an ion in the opposite direction). 

When metals react with gases, the main corrosion products are ionic compounds that can be stoichiometric or nonstoichiometric. Generally, only defect ions (ion condnctors) arise in stoichiometric componnds snch as silver chloride (AgCl) and NaCl. Four border cases of imperfections are possible When cation vacancies in the lattice and cations at interstitial lattice sites are found in an undisturbed anion lattice, the cations are mobile. Alternatively, the anions are mobile. In compounds with anion and cation vacancies, both can migrate, as they can when an equal number of cations and anions are present at interstitial lattice sites. 

The defects which disrupt the regular patterns of crystals, can be classified into point defects (zero-dimensional), line defects (1-dimensional), planar (2-dimensional) and bulk defects (3-dimensional). Point defects are imperfections of the crystal lattice having dimensions of the order of the atomic size. The formation of point defects in solids was predicted by Frenkel [40], At high temperatures, the thermal motion of atoms becomes more intensive and some of atoms obtain energies sufficient to leave their lattice sites and occupy interstitial positions. In this case, a vacancy and an interstitial atom, the so-called Frenkel pair, appear simultaneously. A way to create only vacancies has been shown later by Wagner and Schottky [41] atoms leave their lattice sites and occupy free positions on the surface or at internal imperfections of the crystal (voids, grain boundaries, dislocations). Such vacancies are often called Schottky defects (Fig. 6.3). This mechanism dominates in solids with close-packed lattices where the formation of vacancies requires considerably smaller energies than that of interstitials. In ionic compounds also there are defects of two types, Frenkel and Schottky disorder. In the first case there are equal numbers of cation vacancies... 

However, very often there are deviations from this linearity due to a shift of the position of the band edges under illumination or as a consequence of the reaction with the redox system In order to prevent corrosion, compound semiconductors have often been employed in a saturated solution of their ionic components like sulfides in sulfide solutions with the redox system polysulfide/sul-fide or selenides in the redox system polyselenide/selenide. However, it was found that even under these conditions the crystalline semiconductors can decompose and are transformed either into a surface with numerous lattice defects or into a different polycrystalline material. 

To begin with, we can accept the hypothesis that a point defect does not affect the lattice s fundamental vibration frequency, and therefore the term v in relation [3.51] does not depend on the species involved in the quasi-chemical reaction. For ionic compounds, we sometimes choose one anionic vibration frequency and one cationic frequency. Certain authors, such as Mott [MOT 38], opt instead for a half frequency for the defect. We will now examine a few examples, with the vibration frequency being kept constant and unique. 

Electrical methods are veiy sensitive to the properties of solids, especially ionic soUds. Even changes of composition on the ppm level may result in substantial changes in semiconducting properties, such as n-p-type transitions, which may be determined by both electrical conductivity and thermopower. The WF is sensitive to surface properties on an atomic level. This is the reason the electrical methods are finding increasing applications in studies of defect-related properties of materials, based on nonstoichiometric compounds, such as transport properties. Electrical methods have been widely used with high accuracy in studies of nonstoichiometry and related concentrations of lattice defects at elevated temperatures and under gas phase of controlled composition. ... 

Most of the possible combinations of large A cations and smaller B ions, which is needed to form perovskite-type oxides ABO3, had been tried by 1955, as described by F.S. Galasso in his famous book [2] entitled Structure, Properties and Preparation of Perovskite-Type Compounds, published in 1969. This book compiled almost all available data at that time concerning structure, properties, and preparation of perovskite-type compounds. In this book, although lattice defects in the perovskite-type crystal were described, the author did not touch on ionic conduction in the perovskite except for a very brief description of BaTiOs- However, in the 1960s, several pioneering studies on ionic conduction in perovskite-type oxides were performed. 

The ionic defects characteristic of the fluorite lattice are interstitial anions and anion vacancies, and the actinide dioxides provide examples. Thermodynamic data for the uranium oxides show wide ranges of nonstoichiometry at high temperatures and the formation of ordered compounds at low temperatures. Analogous ordered structures are found in the Pa-O system, but not in the Np-O or Pu-O systems. Nonstoichiometric compounds exist between Pu02 and Pu016 at high temperatures, but no intermediate compounds exist at room temperature. The interaction of defects with each other and with metallic ions in the lattice is discussed. 

The free spaces where Ps can form and o-Ps can have a reasonably long lifetime may be extrinsic defects, as just illustrated, or intrinsic defects, such as created when heating a pure solid compound. More generally, they may correspond to the natural voids present in any solid matrix (e.g., "free volume" in polymers, treated elsewhere in this book). Ps can be formed not only in molecular solids, including frozen liquids, but also in a number of ionic solids, even when the open spaces are rather small. For example, Ps is formed in such a highly packed lattice as KC1 [44, 45] where the largest space available corresponds to the tetrahedral sites circumscribed by 4 Cf anions, with a radius of only 0.0845 nm, resulting in an o-Ps lifetime of about 0.65 ns. 

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