Intrinsic point defects

Key points: Schottky defects are site vacancies, formed in cation/anion pairs, and Frenkel defects are displaced, interstitial atoms; the structure of a solid influences the type of defect that occurs, with Frenkel defects forming in solids with lower coordination numbers and more covalency and Schottky defects in more ionic materials. The solid-state physicists W. Schottky and J. Frenkel identified two specific types of point defect. A Schottky defect (Fig. 3.53) is a vacancy in an otherwise perfect arrangement of atoms or ions in a structure. That is, it is a point defect in which an atom or ion is missing from its normal site in the structure. The overall stoichiometry of a solid is not affected by the presence of Schottky defects because, to ensure charge balance, the defects occur in pairs in a compound of stoichiometry MX and there are equal numbers of vacancies at cation and anion sites. In solids of different composition, for example MX₂ , the defects must occur with balanced charges, so two anion vacancies must be created for each cation lost. Schottky defects occur at low concentrations in purely ionic solids, such as NaCl; they occur most commonly in structures with high coordination numbers, such as close-packed metals, where the enthalpy penalty of reducing the average coordination number of the remaining atoms (from 12 to 11, for instance) is relatively low.

AFrenkel defect (Fig. 3.54) is a point defect in which an atom or ion has been displaced onto an interstitial site. For example, in silver chloride, which has the rock-salt structure, a small number of Ag ions reside in tetrahedral sites (1). The stoichiometry of the com pound is unchanged when a Frenkel defect forms and it is possible to have Frenkel defects involving either one (M or X displaced) or both (some M and some X interstitials) of the ion types in a binary compound, MX. Thus, the Frenkel defects that occur in, for example, PbF2 involve the displacement of a small number of F ions from their normal sites in the fluorite structure, on the tetrahedral holes in the close-packed Pb2 ion array, to sites that

correspond to the octahedral holes. A useful generalization is that Frenkel defects are most often encountered in structures such as wurtzite and sphalerite in which coordination numbers are low (6 or less) and the more open structure provides sites that can accommodate the interstitial atoms. This is not to say that Frenkel defects are exclusive to such structures; as we have seen, the (8,4)-coordination fluorite structure can accommodate such interstitials although some local repositioning of adjacent anions is required to allow for the presence of the displaced anion. The concentration of Schottky defects varies considerably from one type of compound to the next. The concentration of vacancies is very low in the alkali metal halides, being of the order of 106 cm3 at 130°C. That concentration corresponds to about one defect per 1014 formula units. Conversely, some d-metal oxides, sulfides, and hydrides have very high concentrations of vacancies. An extreme example is the high-temperature form of TiO, which has vacancies on both the cation and anion sites at a concentration corresponding to about one defect per 10 formula units.

Schottky and Frenkel defects are only two of the many possible types of defect. Another type is an atom-interchange or anti-site defect, which consists of an interchanged pair of atoms. This type of defect is common in metal alloys with exchange of neutral atoms. It is expected to be very unfavourable for binary ionic compounds on account of the introduction of strongly repulsive interactions between neighbouring similarly charged ions. For example, a copper/gold alloy of exact overall composition CuAu has extensive disorder at high temperatures, with a significant fraction of Cu and Au atoms interchanged (Fig. 3.55). The interchange of similarly charged species on different sites in ternary and composition ally more complex compounds is common; thus, in spinels (Section 24.8) the partial swap ping of the metal ions between tetrahedral and octahedral sites is often observed. Both Schottky and Frenkel defects are stoichiometry defects in that they do not change the overall composition of the material because the vacancies occur in charge-balanced pairs (Schottky) or each interstitial is derived from one displaced atom or ion (Frenkel, a vacancy-interstitial pair). Similar types of defects, vacancies, and interstitials occur in many inorganic materials and may be balanced by changes in the oxidation number of one component in the system rather than by their creation as charge-balanced pairs. This behaviour, as seen for example in La₂CuO_4.1 with extra interstitial O₂ ions, is discussed more fully in Section 24.8.

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مواضيع ذات صلة

The Fermi level

Densities of states

Band formation by orbital overlap

The conductivities of inorganic solids

Nonstoichiometry

Solubility

Thermal stabilities of ionic solids

The Born–Mayer equation

Structure maps

The radius ratio

Ionic radii

Characteristic structures of ionic solids