1Introduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering1“Crystals are like people, it is the defects in them which tend to make them interesting!”- Colin Humphreys.• Defects in Solids¾ 0D, Point defects9 vacancies9 interstitials9 impurities, weight and atomic composition¾ 1D, Dislocations9 edge9 screw¾ 2D, Grain boundaries9 tilt9 twist¾ 3D, Bulk or Volume defects¾ Atomic vibrations4.9 - 4.10 Microscopy & Grain size determination –Not Covered / Not TestedChapter OutlineIntroduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering2Real crystals are never perfect, there are always defectsSchematic drawing of a poly-crystal with many defects by Helmut Föll, University of Kiel, Germany. Defects – Introduction (I)2Introduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering3Defects – Introduction (II)Defects have a profound impact on the macroscopic properties of materialsBonding+ Structure+ DefectsPropertiesIntroduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering4CompositionBonding Crystal StructureThermomechanicalProcessingMicrostructureDefects – Introduction (III)The processing determines the defectsdefects introduction and manipulation3Introduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering5Types of DefectsDefects may be classified into four categories depending on their dimension:¾ 0D, Point defects: atoms missing or in irregular places in the lattice (vacancies, interstitials, impurities)¾ 1D, Linear defects: groups of atoms in irregular positions (e.g. screw and edge dislocations)¾ 2D, Planar defects: the interfaces between homogeneous regions of the material (grain boundaries, external surfaces)¾ 3D, Volume defects: extended defects (pores, cracks)Introduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering6Point defects: vacancies & self-interstitialsSelf-interstitialsVacancyVacancy - a lattice position that is vacant because the atom is missing.Interstitial - an atom that occupies a place outside the normal lattice position. It may be the same type of atom as the others (self interstitial) or an impurity interstitial atom.4Introduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering7The equilibrium number of vacancies formed as a result of thermal vibrations may be calculated from thermodynamics:How many vacancies are there?where Nsis the number of regular lattice sites, kBis theBoltzmann constant, Qvis the energy needed to form a vacant lattice site in a perfect crystal, and T the temperature in Kelvin (note, not inoCoroF).Using this equation we can estimate that at room temperature in copper there is one vacancy per 1015lattice atoms, whereas at high temperature, just below the melting point there is one vacancy for every 10,000 atoms.Note, that the above equation gives the lower end estimation of the number of vacancies, a large numbers of additional (non-equilibrium) vacancies can be introduced in a growth process or as a result of further treatment (plastic deformation, quenchingfrom high temperature to the ambient one, etc.)−=TkQexpNNBvsvIntroduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering8Let’s estimate the number of vacancies in Cu at room TThe Boltzmann’s constant kB= 1.38 × 10-23 J/atom-K = 8.62 × 10-5eV/atom-KThe temperature in Kelvin T = 27oC + 273 = 300 K. kBT = 300 K × 8.62 × 10-5eV/K = 0.026 eVThe energy for vacancy formation Qv= 0.9 eV/atomThe number of regular lattice sites Ns= NAρ/AcuNA= 6.023 × 1023atoms/molρ = 8.4 g/cm3Acu= 63.5 g/mol−=TkQexpNNBvsv()322323scmatoms108molg5.63cmg4.8molatoms10023.6N ×=××==−×=atomeV026.0atomeV9.0expcmatoms108N322v37cmvacancies104.7 ×=5Introduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering9OBSERVING EQUIL. VACANCY CONC.• Low energy electron microscope view of a (110) surface of NiAl.• Increasing T causes surface island ofatoms to grow.• Why?The equil. vacancy conc. increases via atom motion from the crystalto the surface, where they join the island.Reprinted with permission from Nature (K.F. McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies inSolids and the Stability of Surface Morphology",Nature, Vol. 412, pp. 622-625 (2001). Image is5.75 µm by 5.75 µm.) Copyright (2001) Macmillan Publishers, Ltd.Introduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering10Self-interstitials in metals introduce large distortions in the surrounding lattice ⇒ the energy of self-interstitial formation is ~ 3 times larger as compared to vacancies (Qi~ 3×Qv) ⇒ equilibrium concentration of self-interstitials is very low (less than one self-interstitial per cm3at room T).Self-interstitials12345Other point defects: self-interstitials, impuritiesSchematic representation of different point defects:(1) vacancy;(2) self-interstitial;(3) interstitial impurity;(4,5) substitutional impuritiesThe arrows show the local stresses introduced by the point defects.6Introduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering11ImpuritiesImpurities - atoms which are different from the host¾ All real solids are impure. Very pure metals 99.9999% - one impurity per 106atoms ¾ May be intentional or unintentionalExamples: carbon added in small amounts to iron makes steel, which is stronger than pure iron. Boron added to silicon change its electrical properties.¾ Alloys - deliberate mixtures of metalsExample: sterling silver is 92.5% silver – 7.5% copper alloy. Stronger than pure silver.Introduction To Materials Science, Chapter 4, Imperfections in solidsUniversity of Tennessee, Dept. of Materials Science and Engineering12Solid SolutionsSolid solutions are made of a host (the