Chapter 5 Imperfections in SolidsLecturer: Shenhua SONGOutline Point defects1. Point defects in metals 2. Point defects in ceramics Linear defects Dislocations Plane defectsExternal surfacesGrain boundariesTwin boundariesStacking faultsPhase boundaries Volume defectsPores, cracks, inclusions, and second phasesPoint Defects Point Defects in Metals (1)1. Vacancies and Interstitials (self-interstitials) Thermal equilibrium vacancies and interstitials Quenching-induced non- equilibrium vacancies and interstitials Irradiation-induced non- equilibrium vacancies and interrstitials Deformation-induced non- equilibrium vacancies Frenkel pair: vacancy + interstitialSchottky defect: moving an atom to the surface produces a vacancyPoint Defects Point Defects in Metals (2)Formation leading to an increase of internal energy free energy increase (G = H - TS, H=U+PV, U - H - G )Formation leading to an increase of entropy (randomness) free energy decreaseAt a given temperature, there must be a concentration of point defects at which the free energy of the system has a minimum value. Why there is a thermal equilibrium concentration for vacancies or interstitials (self-interstitials)Point Defects Point Defects in Metals (3)Derivation of equilibrium vacancy concentration where Hv is the increase in enthalpy per mole of vacancies introduced (the vacancy formation energy)The increase in enthalpy for introducing Xv mole of vacancies in one mole of material (Xv: the mole fraction of vacancies):The increase in entropy:where Sv is the increase in thermal entropy per mole of vacancies introducedThe increase in the free energy of the system due to the vacancy formation:G = H - T SPoint Defects Point Defects in Metals (4)The molar free energy of the crystal containing Xv mole of vacancies:where GA is the molar free energy of the vacancy-free crystalThe equilibrium concentration of vacancies can be calculated by the condition:Point Defects Point Defects in Metals (5)Or(G = H - T S)is in units of the mole fraction and can also be represented by= Nv/Nwhere Nv is the number of vacancies at equilibrium for a certain amount of material and N is the total number of atomic sitesPoint Defects Point Defects in Metals (6)3 for most metalse.g. iron (Fe): Hv is 1.4 eV per atom, the melting points is 1808K (1535oC), the equilibrium vacancy concentration is= 3.810-4For most metals, the value near the melting point is in the range of 10-3 to 10-4Point Defects Point Defects in Metals (7)For interstitials (self-interstitials)HI is very high and is usually higher than 3 eV for most metals leading to a very small equilibrium concentration (negligible) In thermal conditions, we do not care about interstitials. However, under irradiation, the interstitials are main point defects (migration energy is low)Point Defects Point Defects in Metals (8)2. Impurities A pure metal composed of only one type of atom is impossible in reality. It is difficult to refine metals to a purity of 99.99999% There is always some level of impurity or foreign atoms in a metal, leading to the formation of an alloy Alloys solid solutions and intermetallics Concept: solvent the matrix or host; solute minor component, e.g. Al-2.5%Cu alloyPoint Defects Point Defects in Metals (9)Point Defects Point Defects in Metals (10) Solid solutions Composed of two or more elements The crystal structure of the alloy phase is the same as that for one of the forming elements (e.g. Al-0.5%Cu) Good comprehensive mechanical properties Intermetallics Composed of two or more elements The crystal structure of the alloy phase is different from that for any forming element (e.g. Al2Cu) Poor comprehensive mechanical propertiesPoint Defects Point Defects in Metals (11) Classification of solid solutions(1) Substitutional solid solution solute atoms replace some solvent atoms (host atoms) (2) Interstitial solid solution solute atoms occupy the interstices Atomic size factor: =|(rsolute-rsolvent)|/rsolvent, if 15%, a considerable quantity of solute may be dissolved in the solvent Crystal structure: For high solid solubility, the crystal structures must be the same for the two components (e.g. Cu- Ni alloy) Electronegativity: the larger the difference of the two elements in electronegativity, the more likely they form an intermetallic compound instead of a solid solution. Only when the difference is less than 0.4, the formation of an appreciable solid solution is possible Valences: if other factors are equal, a solute dissolves more in a lower valence solvent than in a higher valence solvent Point Defects Point Defects in Metals (12) Factors affecting the formation of a substitutional solid solutionPoint Defects Point Defects in Metals (13)Atomic radius: Cu-0.128 nm, Ni-0.125, =2.3%Crystal structure: both FCCElectronegativity: Cu-1.