Surface energy ionic compounds

Sum rule for oscillator strengths, 102, 11 If Superconductivity high-temperature, 455 transition temperature, 399 Superionic conductors, 316 Surface dipoles, 399ff, 425ff Surface energy ionic compounds, 336 semiconductors, 230ff simple metals, 401f Surface tension, 233 Surface states... 

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. 

The above considerations are borne out experimentally on most rocksalt ionic compounds. For example, when magnesium metal is burned, the tiny MgO smoke particles that are formed are almost perfect cubes (see Fig. 2.4 in Ref. 1). The need to form a non-polar surface and to maximize the ligand coordination of surface ions makes the (100) surface energy much lower than that of other possible surfaces in the rocksalt structure. This is also manifest in the cubic shape of grains of table salt, NaCl. The (110) surface of MgO, whose ions are only four-fold coordinated, is also much less stable than the (100) surface [24]. 

Vacancy mechanism (Figure 8.3B). The movement of adjacent atoms occurs to an unoccupied site (vacancy) because of the surface energy difference between them. The lathee distortion caused by the movement of a neighboring atom through the vacancy is lower than that predicted by the interstitial mechanism. This mechanism is well known and is often used to describe him formation on metals, metal alloys, ionic compounds, and oxides. 

Dielectric continuum models such as the Generalized Born Solvent Accessible Surface Area (GB/SA) model are, in conjunction with force fields, excellent tools for fast and reliable calculations of hydration energies and solvent effects on, e.g., conformational equilibria and ligand-receptor interactions. The performance for neutral solutes is very good, whereas calculations on ionic compounds are currently more problematic. A solution to these problems most probably requires force fields that include polarization effects. For optimal accuracy of calculations using a dielectric continuum model, it is a clear advantage if the model is parameterized for the particular force field used. 

The results can be rationalized within the Levin-Mark model [55], which has been developed for the study of the energies of surface states in highly ionic compounds. The energy gap for ions in the bulk, Eb, is taken to be the lowest energy needed for the transfer of electron density from an anion ji/ to a distant cation If A is the electron affinity of the anion and 1 the ionization energy of the cation, Eb is given by... 

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... 

From the (limited) data in Table 22.2, is there a trend for the relationship between the surface energy of ionic compounds and the magnitudes of the charges on the ions ... 

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