Chapter 5. Imperfections in Solids 5-1 Introduction For a crystalline solid we have assumed that perfect order exists throughout the material on an atomic scale. However, such an idealized solid does not exist. All contain large numbers of various defects or imperfections. The influence of the imperfections is not always adverse. Specific characteristics are fashioned by the introduction of the controlled amount or number of particular defect. Classification of crystalline imperfection : according to the geometry and dimensionality of the defect. Point defect: associated with one or two atomic positions Linear defect: one dimensional defect Interfacial defect or boundaries: two dimensional defect Impurities in solid: as point defect 李榮和

5-2 Point Defects in Metals Vacancy (or vacant lattice site) The simplest of the point defects. One normally occupied from which an atom is missing All crystalline solids contain vacancies and, in fact, it is not possible to create such a material that is free of theses defect. The presence of vacancies increases the entropy (the randomness) of the crystal. 李榮和

The equilibrium number of vacancies N  : increase with temperature N  = N exp (-Q  / kT) N: total number of atomic sites Q  : energy required for the formation of a vacancy K: Boltzmann’s constant (1.38x J/atom-K or 8.62x10 -5 eV/atom-K) For most metals, the fraction of vacancies N  /N just below the melting temperature is on the order of One lattice site out of will be empty. 李榮和

A self-interstitial is an atom from the crystal that is crowed into an interstitial site, a small void space that under ordinary circumstances ( 環境 ) is not occupied In metals, a self-interstitial introduces relatively large distortions ( 扭曲 ) in the surrounding lattice Because the atom is substantially larger than the interstitial position in which it is situated The formation of this defect is not highly probable, exist in very small concentration, which are significantly low than the vacancies. Self-interstitial ( 自格隙 ) 李榮和

5-3 Point Defect in Ceramics NaCl: Na or Cl both exist in interstitials and vacancies (Cl in interstitial site is highly improbable) The anion is relative large, and to fit into a small interstitial position, substantial strains on the surrounding ions must be introduced. 李榮和

Fig 5.3 Frenkel and Schottky Defects in Ionic Solids Because the atoms exist as charged ions, when defect structures are considered, conditions of electro-neutrality must be maintained Frenkel Defect: defect involves a cation-vacancy and a cation- interstitial pair. (A cation leaving its normal position and moving into an interstitial site) Schottky Defect ( 蕭特基缺陷 ): a cation vacancy-anion vacancy pair (removing one cation and one anion from the interior of the crystal and then placing them both at an external surface) 李榮和

Stoichiometry ( 化學計量 ) : Defined as a state for ionic compounds wherein there is the exact ratio of cations to anions as predicted by the chemical formula. (Ex: NaCl: 1:1) Nonstoichiometry ( 非化學計量 ): EX: Fe 1-X O May occur for some cermic materials in which two valence or ionic states exist for one of the ion types (Fe 2+ or Fe 3+ ) Electro-neutrality and Nonstoichiometry ( O 多一個 ) 李榮和

5.4 Impurities in Solids Impurities in Metal Impurity or foreign atoms will always be present and some will exist as crystalline point defect. It is difficult to refine metals to a purity in excess of %. (10 22 – impurity atoms will be present in one cubic meter of material) Alloys: Sterling ( 英幣 ) Silver: Silver/Cu: 92.5% / 7.5% (Silver: Highly corrosion resistant, Cu: mechanical strength) The addition of impurity atoms to a metal will result in the formation of a solid solution and/ or a new second phase, depending on the kinds of impurity, their concentrations, and the temperature of the alloy. Solvent and solute 李榮和

Solid Solutions ( 固溶體 ) A solid solution forms when, as the solute atoms are added to the host materials, the crystal structure is maintained, a no new structures are formed. A solid solution is also compositionally homogeneous; the impurity atoms are randomly and uniformly dispersed within the solid Impurity Point Defect in Solid Solution: Substitutional ( 置換 ) or Interstitial ( 格隙 ) Substitutional : Solute or impurity atoms replace or substitute for the host atoms. 李榮和

There are several features of the solute and solvent atoms that determine the degree to which the former dissolves in the latter ( 溶質溶於溶劑程 度之影響因素 ) 1.Atomic size factor: Appreciable quantities of a solute may be accommodated ( 收容 ) in this type of solid solution only when the difference in atomic radii between the two atom types is less than about +/- 15 %. Otherwise the solute atoms will create substantial lattice distortions and a new phase will form. 2.Crystal structure: For appreciable solid solubility ( 固態溶解度 ) the crystal structures for metals of both atom types must be the same. 3.Electro-negativity: The more electropositive one element and the more electronegative the other, the greater is the likelihood that they will form an intermetallic compound ( 金屬化合物 ) instead of a substitutional solid solution ( 置換式固溶體 ). 4.Valences: Other factors being equal, a metal will have more of a tendency to dissolve another metal of higher valency than one of a lower valency. 李榮和

A substitutional solid solution ( 置換式固溶體 ): Copper-Nickel ( 銅 - 鎳 ) 1. These two elements are completely soluble in one another at all proportions. 2. The atomic raddi: copper : nm, Nickel: nm 3. Both have the FCC crystal structure. 4. Electronegative: copper : 1.9, Nickel: Valences: Copper: +1 (sometime +2), Nickel: +2 A interstitial solid solution ( 插入式固溶體 ) 1.Impurity atoms fill the voids or interstices among the host atoms. 2.For metallic materials that have relatively high atomic packing factors, these interstitial positions are relatively small. 3.The atomic diameter of an interstitial impurity must be substantially small than that of the host atoms. 4.Normally, the maximum allowable concentration of interstitial impurity is low (<10%). 5.Even very small impurity atoms are ordinarily larger than the interstitial sites, and as a consequence they introduce some lattice strains on the adjacent host atoms. 6.Carbon forms an interstitial solid solution when added to iron. The maximum concentration of carbon is about 2 % (The atomic radius of carbon atom is much smaller than that of iron: nm versus nm) 李榮和

Impurity in Ceramics Impurity can form solid solution in ceramic material Solid solution of both substitutional and interstitial types For interstitial impurity : the ionic radius of the impurity must be relatively small in comparison to the anion. For substitutional impurity (cation or anion): 1.A substitutional impurity will substitute for the host ion to which it is most similar in an electrical sense. 2.For NaCl: Ca 2+ and O 2- ions would most likely substitute for Na + and Cl - ions, respectively. 3.To achieve any appreciable solid solubility of substituting impurity atoms, the ionic size and charge must be very nearly the same as those of one of the host ions. 李榮和

4. For an impurity ion having a charge different from the host ion for which it substitutes, the crystal must compensate ( 補償 ) for this difference in charge so that electro-neutrality is maintained with the solid. One way this is accomplished is by the formation of lattice defects – vacancies or interstitials of both ion types, as discussed above. 李榮和