ENS167 Chapter 5 Imperfections in Solids PDF

ENS167 Fundamentals of Materials Science and Engineering William D. Callister Jr. CHAPTER 5 IMPERFECTIONS IN SOLIDS Maria Cristina P. Vegafria 2D representation of a perfect single crystal Schematic drawing of a poly-crystal with...

ENS167 Fundamentals of Materials Science and Engineering William D. Callister Jr. CHAPTER 5 IMPERFECTIONS IN SOLIDS Maria Cristina P. Vegafria 2D representation of a perfect single crystal Schematic drawing of a poly-crystal with many defects by Helmut Föll, University of Kiel, Germany.  Defects in Solids 0D Point defects – atoms missing or in irregular places in the lattice Vacancies Interstitials Impurities, weight and atomic composition 1D Linear Defects/ Dislocations – groups of atoms in irregular positions Edge Dislocation Screw Dislocations 2D Planar Defects – the interfaces between the homogeneous regions of the material External Surfaces Grain boundaries -Tilt -Twist 3D Bulk or Volume Defects – extended defects (pores, cracks) Atomic vibrations  Defects in Solids Defects have a profound impact on Processing determines the defects the properties of materials Thermomechanical Processing a metallurgical process that combines mechanical or plastic deformation process like compression or forging, rolling etc. with thermal processes like heat treatment, water quenching, heating and cooling at various rates into a single process Point Defects (1) vacancy (2) self-interstitial (3) interstitial impurity (4,5) substitutional impurities Vacancy - a lattice position that is vacant because the atom is missing Interstitial - an atom that occupies a place outside the normal lattice position. - may be the same type of atom as the others (self interstitial) or an impurity interstitial atom Point Defects (2) self-interstitial (3) interstitial impurity Self-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 cm3 at room T). Point Defects (3) interstitial impurity (4,5) substitutional impurities Impurities atoms which are different from the host May be intentional or unintentional All real solids are impure. Very pure metals - 99.9999% -one impurity per 106 atoms Examples: - Carbon added in small amounts to iron makes steel, which is stronger than pure iron - Boron added to silicon (p-type doping) change its electrical properties  Point Defects (4,5) substitutional impurities Impurities Examples: - Carbon added in small amounts to iron makes steel, which is stronger than pure iron - Boron or phosphorous added to silicon (doping) change its electrical properties Assignment: 1. How doping works? 2. Explain the difference between n-type and p-type semiconductors  Point Defects Schematic representations of cation and anion vacancies and a cation interstitial  Point Defects Electroneutrality the state that exists when there are equal numbers of positive and negative charges from the ions defects in ceramics do not occur alone  Point Defects The ratio of cations to anions is not altered by the formation of either a Frenkel or a Schottky defect Frenkel Defect involves a cation–vacancy and a cation–interstitial pair Schottky Defect a cation vacancy–anion vacancy pair  Point Defects Stoichiometry a state for ionic compounds wherein there is the exact ratio of cations to anions as predicted by the chemical formula If no other defects are present, the material is said to be stoichiometric. A ceramic compound is nonstoichiometric if there is any deviation from the exact ratio of cations to anions. - occurs for some ceramic materials in which two valence (or ionic) states exist for one of the ion types  Point Defects Schematic representation of an Fe2+ vacancy in FeO that results from the formation of two Fe3+ ions. The crystal is no longer stoichiometric because there is one more O ion than Fe ion; however, the crystal remains electrically neutral.  Point Defects Example: If electroneutrality is to be preserved, what point defects are possible in NaCl when a Ca2+ substitutes for an Na+ ion? How many of these defects exist for every Ca2+ ion? Answer: Replacement of an Na+ by a Ca2+ ion introduces one extra positive charge. Electroneutrality is maintained when either a single positive charge is eliminated or another single negative charge is added. Removal of a positive charge is accomplished by the formation of one Na+ vacancy. Alternatively, a Cl- interstitial will supply an additional negative charge, negating the effect of each Ca2+ ion. However, the formation of this defect is highly unlikely.  Solid Solutions made of a host (the solvent or matrix) which dissolves the minor component (solute) The ability to dissolve is called solubility. Solvent: in an alloy, the element or compound present in greater amount Solute: in an alloy, the element or compound present in lesser amount Solid Solution: homogeneous crystal structure is maintained contains randomly dispersed impurities (substitutional or interstitial) Second Phase: As solute atoms are added, new compounds / structures are formed, or solute forms local precipitates.  Alloys Alloys - deliberate mixtures of metals Example: sterling silver - 92.5% silver , 7.5% copper alloy - stronger than pure silver Gold Alloys  Substitutional Solid Solutions Factors for high solubility: Atomic size factor - atoms need to “fit” ⇒ solute and solvent atomic radii should be within ~ 15% Crystal structures of solute and solvent should be the same Electronegativities of solute and solvent should be comparable (otherwise new inter-metallic phases are encouraged) Generally more solute goes into solution when it has higher valency than solvent  Interstitial Solid Solutions Interstitial solid solution of C in α-Fe. The C atom is small enough to fit, after introducing some strain into the BCC lattice. Factors for high solubility: For fcc, bcc, hcp structures - the voids (or interstices) between the host atoms are relatively small ⇒ atomic radius of solute should be significantly less than solvent Normally, max. solute concentration ≤ 10%, (2% for C-Fe)  Composition/Concentration Composition can be expressed in weight percent - useful when making the solution atom percent - useful when trying to understand the material at the atomic level  Composition/Concentration Weight percent (wt %): -weight of a particular element relative to the total alloy weight. Atom percent (at %): -number of moles (atoms) of a particular element relative to the total number of moles (atoms) in alloy. where : m1 and m2 – weight in grams of elements 1 and 2 respectively nm1 = m1/A1 nm2 = m2/A2 A1 - atomic weight of element 1  Linear Defects Dislocations the interatomic bonds are significantly distorted only in the immediate vicinity of the dislocation line. This area is called the dislocation core. create small elastic deformations of the lattice at large distances  Linear Defects Burgers Vector – Description of Dislocations Burgers vector b - describes the size and the direction of the main lattice distortion caused by a dislocation Dislocations showing Burgers vector directed perpendicular to the dislocation line. These dislocations are called Edge Dislocations.  Linear Defects Screw Dislocation a second basic type of dislocation parallel to the direction in which the crystal is being displaced (Burgers vector is parallel to the dislocation line) (a) A screw dislocation within a crystal. (b) The screw dislocation in (a) as viewed from above. The dislocation line extends along line AB.  Linear Defects Screw and Edge Dislocation Schematic representation of a dislocation that has edge, screw, and mixed character. (b) Top view, where open circles denote atom positions above the slip plane. Solid circles, atom positions below. At point A, the dislocation is pure screw, while at point B, it is pure edge. For regions in between where there is curvature in the dislocation line, the character is mixed edge and screw.  Linear Defects Mixed/Partial Dislocations To add to the complexity of real defect structures, dislocation are often split in "partial“ dislocations that have their cores spread out over a larger area.  Planar/Interfacial Defects External Surfaces Surface atoms have unsatisfied atomic bonds, and higher energies than the bulk atoms ⇒ Surface energy, γ (J/m2) Surface areas tend to minimize (e.g. liquid drop) Solid surfaces can “reconstruct” to satisfy atomic bonds at surfaces. Grain Boundaries Polycrystalline material - comprised of many small crystals or grains The grains have different crystallographic orientation. There exist atomic mismatch within the regions where grains meet. These regions are called grain boundaries.  Grain Boundaries High and Low Angle Grain Boundaries  Grain Boundaries Tilt and Twist Grain Boundaries Low angle grain boundary - an array of aligned edge dislocations. This type of grain boundary is called tilt boundary (consider joint of two wedges). Twist boundary - the boundary region consisting of arrays of screw dislocations (consider joint of two halves of a cube and twist an angle around the cross section normal)  Grain Boundaries Tilt and Twist Grain Boundaries Low angle grain boundary - an array of aligned edge dislocations. This type of grain boundary is called tilt boundary (consider joint of two wedges) Twist boundary - the boundary region consisting of arrays of screw dislocations (consider joint of two halves of a cube and twist an angle around the cross section normal) Grain Boundaries Twin Boundaries Low-energy twin boundaries with mirrored atomic positions across boundary may be produced by deformation of materials. This gives rise to shape memory metals, which can recover their original shape if heated to a high temperature. Shape-memory alloys are twinned and when deformed they untwin. At high temperature the alloy returns back to the original twin configuration and restore the original shape.  Grain Boundaries Electron Microscopy Dislocations in Nickel High-resolution Transmission (the dark lines and loops), Electron Microscope image of a tilt transmission electron grain boundary in aluminum microscopy image  Bulk/Volume Defects Pores - greatly affect optical, thermal, mechanical properties Cracks - greatly affect mechanical properties Foreign Inclusions - greatly affect electrical, mechanical, optical properties A cluster of microcracks in a melanin granule irradiated by a short laser pulse  Atomic Vibrations Heat causes atoms to vibrate Vibration amplitude increases with temperature Melting occurs when vibrations are sufficient to rupture bonds The vibrational and rotational transitions of Atomic vibrations in crystals the CO2 molecule which is the basis of CO2 laser