Chapter 4: Imperfections (Defects) in Solids ISSUES TO ADDRESS... What types of defects exist in solids? How do defects affect material properties? Can the number and type of defects be varied and controlled? Chapter 4-1
Types of Imperfections (or Defects) in Crystals NO perfect crystals in reality: defects or imperfection always exist Many of materials properties are determined or influenced by defects Point (0D) defects Linear/line (1D) defects Area/planar (2D) defects Volume (3D) defects Vacancy Interstitial atoms Substitutional atoms Dislocations Grain boundaries, Surfaces Interfaces Foreign inclusions Voids 2 Chapter 4 -
Point Defect: Vacancy & Interstitials Vacancies: -vacant atomic sites in a structure. -very common (10-4 near melting point) distortion of planes Vacancy Interstitials: -"extra" atoms positioned between atomic sites. Self interstitial rare, i.e., extremely low concentration Impurity atom interstitial common: e.g., C or H in Fe Self-interstitials (very rare) distortion of planes Impurity atom interstitials (common) Chapter 4-3
Equilibrium Concentration of Vacancies Vacancies need extra energy to form (to break bonds between neighboring atoms) Equilibrium concentration for vacancy varies with temperature: Activation energy # density of vacany (heat of formation (v for vacancy here) of vacancy, in unit Lattice site density Each lattice site is a potential vacancy site N v N = exp Q v kt Boltzmann's constant (1.38 x 10-23 J/K) (8.62 x 10-5 ev/k) of kj/mol or J per vacancy) Temperature Chapter 4-4
Nv N Change of Vacancy Concentration with Temperature Vacancy concentration increases exponentially with T exponential dependence! T vacancy concentration N v N = exp Q v kt If known N v vs T, activation energy Q V could be measured Nv ln N slope -Qv /k 1/T Chapter 4-5
Example: Estimating Vacancy Number/Concentration Estimate the total number of vacancies within 1 cubic meter (1m 3 ) of Cu at 1000 C under equilibrium condition if knowing r = 8.4 g/cm 3 A Cu = 63.5 g/mol Q v = 0.9 ev/atom N A = 6.02 x 10 23 N v N = exp Q v kt 0.9 ev/atom = 2.7 x 10-4 atoms/mol 1273 K 8.62 x 10 N -5 ev/atom-k For 1 m 3, N = r 1 m 3 A = 8.0 x 10 28 atoms (sites) A Cu Answer: total number of vacancies in 1m 3 Cu at 1000C Nv = (2.7 x 10-4 )(8.0 x 10 28 ) sites = 2.2 x 10 25 vacancies Chapter 4-6
Observing Vacancy Movement Low energy electron microscope view of a (110) surface of NiAl Increasing temperature causes surface island to grow (expand). Why? The equilibrium vacancy concentration increases via atom motion from the crystal inside to the surface, where they join the island. Island grows/shrinks to maintain equil. vancancy conc. in the bulk. Click once on image to start animation Reprinted with permission from Nature (K.F. McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies in Solids and the Stability of Surface Morphology", Nature, Vol. 412, pp. 622-625 (2001). Image is 5.75 mm by 5.75 mm.) Copyright (2001) Macmillan Publishers, Ltd. Chapter 4-7
Applications Example when vacancies are desirable: Oxygen sensor at high temperature: vacancies help ion conduction and sensing Example when vacancies are undesirable: Voiding of materials at high temperatures Chapter 4-8
Point Defect: Impurity Atoms in Solids Two outcomes if impurity atom (B) is added to host (A): (Uniform) Solid solution of B in A (i.e., random distribution of point defects) Solute (atom) OR Solvent (matrix) Substitutional solid solution. Solute atom has similar size (e.g., Cu in Ni) Interstitial solid solution Solute atom usually much smaller (e.g., C or N in Fe) Solid solution of B in A plus particles of a new compound (in some systems with with higher concentration of B in A) Second phase particle -- different composition -- often different structure. Chapter 4-9
Impurity Atoms in Solids (2) Conditions for forming substitutional solid solution (S.S.) with high solubility: W. Hume Rothery Rule (empirical) 1. r (atomic radius) < 15% 2. Proximity in periodic table, i.e., similar electronegativities 3. Same crystal structure 4. Same or similar valence Chapter 4-10
Impurity Atoms in Solids (3) Application of Hume Rothery rules for Solid Solutions When forming solid solutions of Zn in Cu Ni in Cu Which metal (Zn or Ni) has higher solubility in Cu and why? Ni has higher solubility in Cu due to Ni has i) same Table on p. 118, Callister & Rethwisch 8e. crystal structure, ii) very close radius, iii) very close electronegativity, and iv) same valence as Cu. Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivity Cu 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2 Chapter 4-11
Applications Examples when impurity atoms are desirable Controlled doping of Si with P or B for semiconductor Alloying Zn with Cu to improve mechanical properties Examples when impurity atoms are undesirable Fe or Ni contaminants in Si wafer Chapter 4-12
Line (1D)/Linear Defects Dislocations One-dimensional defects around which atoms are misaligned Two basic types Edge dislocation Screw dislocation Chapter 4-13
1D Defect - Edge Dislocation Edge dislocation: extra half-plane of atoms inserted in a crystal structure b perpendicular ( ) to dislocation line Fig. 4.3, Callister & Rethwisch 8e. Chapter 4-14
1D Defect - Screw Dislocation Screw Dislocation spiral planar ramp resulting from shear deformation b parallel ( ) to dislocation line Screw Dislocation Dislocation line Burgers vector b (a) Adapted from Fig. 4.4, Callister & Rethwisch 8e. b (b) Chapter 4-15
In VMSE: VMSE: Screw Dislocation a region of crystal containing a dislocation can be rotated in 3D dislocation motion may be animated Front View VMSE Screen Shots Top View Chapter 4-16
Edge, Screw, and Mixed Dislocations Mixed Edge Adapted from Fig. 4.5, Callister & Rethwisch 8e. Screw Chapter 4-17
Observation of Dislocations Dislocations are visible in transmission electron microscope (TEM) Fig. 4.6, Callister & Rethwisch 8e. Chapter 4-18
Application Examples when linear defects (dislocations) are desirable Strain hardening of materials: dislocations help improve mechanical strength of metals Examples when linear defects are undesirable Dislocation in polycrystalline Si for solar cell wafers: dislocations cause degradation of carrier lifetime and decrease solar cell efficiency Chapter 4-19
Planar (2D) Defects in Solids (1) Grain Boundaries Regions between individual crystals or grains Transition from lattice of one ordered region to that of another Slightly disordered Lower packing density in grain boundaries Higher mobility Higher chemical reactivity Adapted from Fig. 4.7, Callister & Rethwisch 8e. Chapter 4-20
Planar (2D) Defects in Solids (2) Chapter 4-21
Additional Planar (2D) Defects in Solids (3) Twin boundary (plane) A special grain boundary with a reflection of atom positions across the twin plane. Adapted from Fig. 4.9, Callister & Rethwisch 8e. Stacking faults For FCC metals an error in ABCABC packing sequence Ex: ABCABABC Chapter 4-22
Application Examples when we want planar defects (e.g., grain boundary) Grain size reduction for improved mechanical properties Examples when planar defects are unwanted Grain boundary in polycrystalline Si for solar cell wafers decrease carrier lifetime and resulting solar cell efficiency Chapter 4-23
Microscopic Examination Techniques Crystallites (grains) and defects (e.g., grain boundaries). Vary considerably in size. Can be quite large (~mm or larger). ex: Large single crystal of quartz, diamond, or Si ex: Metal light post or garbage can - see the individual grains Can be quite small (~μm or smaller) necessary to observe with a microscope. Chapter 4-24
Optical Microscopy Based on visible light (wavelength of 0.4-0.7 μm) Up to 2000x magnification. Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal orientation. Adapted from Fig. 4.13(b) and (c), Callister & Rethwisch 8e. (Fig. 4.13(c) is courtesy of J.E. Burke, General Electric Co.) crystallographic planes Micrograph of brass (a Cu-Zn alloy) after etching 0.75mm Chapter 4-25
Optical Microscopy (2) Grain boundaries... are imperfections, are more susceptible to etching, may be revealed as dark lines, change in crystal orientation across boundary. (a) Fe-Cr alloy polished surface surface groove grain boundary Adapted from Fig. 4.14(a) and (b), Callister & Rethwisch 8e. (Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].) (b) Chapter 4-26
Electron Microscopy Electrons Wavelengths can be as short as ~3 pm (0.003 nm) Atomic resolution (~0.1 nm) possible (10 6 times!) Electron beam focused by magnetic lenses. On surface - Scanning electron microscope (SEM) Through bulk Transmission electron microscope (TEM) SEM TEM Chapter 4-27
Scanning Probe Microscopy (SPM) Even atoms can be arranged and imaged! Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright 1995. Carbon monoxide molecules arranged on a platinum (111) surface. Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word atom. Chapter 4-28
Summary Point, Line, and Planar defects exist in solids. The number and type of defects can be varied and controlled (e.g., T controls vacancy conc.) Defects affect material properties Defects may be desirable or undesirable depending on materials and specific application Chapter 4-29
Homework Statement confirming reading of chapter 4 Callister 8ed 4.1, 4.4 (c only), 4.29(a) Chapter 4-30
Calister 8ed, 4.1 Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 327 C (600 K). Assume an energy for vacancy formation of 0.55 ev/atom Chapter 4 -
Callister 8ed, 4.4(c) Below, atomic radius, crystal structure, electronegativity, and the most common valence are tabulated, for several elements; for those that are nonmetals, only atomic radii are indicated. Which of these elements would you expect to form the following with copper: (a) substitutional solid solution with complete solubility; (b) substitutional solid solution with incomplete solubility; (c) An interstitial solid solution Element Atomic Radius (nm) Crystal Structure Electronegativi ty Valence Cu 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Pt 0.1387 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2 Chapter 4 -
Calister 8ed, 4.29(a) 4.29 (a) For a given material, would you expect the surface energy to be greater than, the same as, or less than the grain boundary energy? Why? Chapter 4 -