1. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 1 “Crystals are like people, it is the defects in them which tend to make them interesting!” - Colin Humphreys. Defects in Solids  0D, Point defects vacancies interstitials impurities, weight and atomic composition  1D, Dislocations edge screw  2D, Grain boundaries tilt twist  3D, Bulk or Volume defects  Atomic vibrations 4.9 - 4.11 Microscopy & Grain size determination – Not Covered / Not Tested Chapter Outline

2. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 2 Real crystals are never perfect, there are always defects Schematic drawing of a poly-crystal with many defects by Helmut Föll, University of Kiel, Germany. Defects – Introduction (I)

3. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 3 Defects – Introduction (II) Defects have a profound impact on the macroscopic properties of materials Bonding + Structure + Defects Properties

4. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 4 Composition BondingCrystal Structure Thermomechanical Processing Microstructure Defects – Introduction (III) Processing determines the defects defect introduction and manipulation

5. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 5 Types of Defects Four categories depending on their dimension  0D, Point defects: atoms missing or in irregular places in the lattice (vacancies, interstitials, impurities)  1D, Linear defects: groups of atoms in irregular positions (e.g. screw and edge dislocations)  2D, Planar defects: interfaces between homogeneous regions of the material (grain boundaries, external surfaces)  3D, Volume defects: extended defects (pores, cracks)

6. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 6 Point defects: vacancies & interstitials Self-interstitials Vacancy Vacancy - lattice position that is vacant because atom is missing. Interstitial - atom that occupies a place outside the normal lattice position. May be same type of atom (self interstitial) or an impurity interstitial.

7. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 7 Equilibrium number of vacancies is due to thermal vibrations How many vacancies? N s = number of regular lattice sites k B = Boltzmann constant Q v = energy to form a vacant lattice site in a perfect crystal T = temperature in Kelvin (note, not in o C or o F). Room temperature in copper: one vacancy per 10 15 atoms. Just below the melting point: one vacancy for every 10,000 atoms. Above lower bound to number of vacancies. Additional (non-equilibrium) vacancies introduced in growth process or treatment (plastic deformation, quenching, etc.)

8. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 8 Estimate number of vacancies in Cu at room T k B = 1.38  10 -23 J/atom-K = 8.62  10 -5 eV/atom-K T = 27 o C + 273 = 300 K. k B T = 300 K  8.62  10 -5 eV/K = 0.026 eV Q v = 0.9 eV/atom N s = N A  /A cu N A = 6.023  10 23 atoms/mol  = 8.4 g/cm 3 A cu = 63.5 g/mol

9. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 9 Large distortions in surrounding lattice  Energy of self-interstitial formation is ~ 3 x larger than for vacancies (Q i ~ 3  Q v )  equilibrium concentration of self- interstitials is very low(< 1/ cm 3 at 300K) Self-interstitials Point defects: self-interstitials, impurities (1) vacancies (2) self-interstitial (3)interstitial impurity (4,5)substitutional impurities Arrows  local stress introduced by defect

10. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 10 Impurities Impurities  atoms which differ from host  All real solids are impure. Very pure metals 99.9999% - one impurity per 10 6 atoms  May be intentional or unintentional Carbon in small amounts in iron makes steel. It is stronger. Boron in silicon change its electrical properties.  Alloys - deliberate mixtures of metals Sterling silver is 92.5% silver – 7.5% copper alloy. Stronger than pure silver.

11. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 11 How Are Impurities Contained in Alloy? Solid solutions Host (Solvent or Matrix) dissolves minor component (Solute). Ability to dissolve is called Solubility.  Solvent: element in greater amount  Solute: element present in lesser amount  Solid Solution: homogeneous maintain crystal structure randomly dispersed impurities (substitutional or interstitial) Second Phase As solute atoms added: new compounds or structures form or solute forms local precipitates Whether addition of impurities results in a solid solution or second phase depends nature of impurities, concentration, temperature and pressure

12. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 12 Substitutional Solid Solutions Factors for high solubility (Solubility limit  maximum that can dissolve)  Atomic size: need to “fit”  solute and solvent atomic radii should be within ~ 15%  Crystal structure: solute and solvent the same  Electronegativities: should be comparable (otherwise new inter-metallic phases favored)  Valency: If solute has higher valency than solvent, generally more goes into solution Ni Cu

13. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 13 Interstitial Solid Solutions Factors for high solubility :  FCC, BCC, HCP: void space between host (matrix) atoms relatively small  atomic radius of solute should be significantly less than solvent  Max. concentration  10%, (2% for C-Fe) Carbon interstitial atom in BCC iron Interstitial solid solution of C in BCC Fe (  phase). C small enough to fit (some strain in BCC lattice).

14. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 14 Composition / Concentration  atom percent (at %): useful in understanding material at atomic level N umber of moles (atoms) of one element relative to total number of moles (atoms) in alloy. 2 component: concentration of element 1 in at. %:  Weight Percent (wt %) Weight of one element relative to total alloy weight 2 components: concentration of element 1 in wt. % n m1 = number density = m’ 1 /A 1 (m’ 1 = weight in grams of 1, A 1 is atomic weight of element 1)

15. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 15 Composition Conversions Weight % to Atomic %: Atomic % to Weight %: Textbook, pp. 71-74

16. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 16 Dislocations = Linear Defects Interatomic bonds significantly distorted in immediate vicinity of dislocation line (Creates small elastic deformations of lattice at large distances.) Dislocations affect mechanical properties Discovery in 1934 by Taylor, Orowan and Polyani marked beginning of our understanding of mechanical properties of materials

17. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 17 Describe Dislocations  Burgers Vector Burgers vector, b, describes size + direction of lattice distortion by a dislocation. Make a circuit around dislocation: go from atom to atom counting the same number of atomic distances in both directions. Vector needed to close loop is b b Burgers vector above directed perpendicular to dislocation line. These are called edge dislocations.

18. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 18 Screw dislocations Screw dislocation: parallel to the direction in which the crystal is being displaced Burgers vector parallel to dislocation line Edge dislocation: Burgers vector perpendicular to dislocation line. Find the Burgers vector of a screw dislocation. How did it get its name?

19. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 19 Interfacial Defects External Surfaces Surface atoms  unsatisfied bonds  higher energies than bulk atoms  Surface energy,  (J/m 2 ) Surface areas try to minimize (e.g. liquid drop) Solid surfaces can “reconstruct” to satisfy atomic bonds at surfaces. Grain Boundaries Polycrystalline: many small crystals or grains. Grains have different crystallographic orientation. Mismatches where grains meet. 1. Surfaces and interfaces are reactive 2. Impurities tend to segregate there. 3. Extra energy associated with interfaces  larger grains tend to grow by diffusion of atoms at expense of smaller grains, minimizing energy.

20. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 20 High and Low Angle Grain Boundaries Misalignments of atomic planes between grains  Distinguish low and high angle grain boundaries

21. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 21 Tilt and Twist Grain Boundaries Tilt boundary  Low angle grain boundary: an array of aligned edge dislocations (like joining two wedges) Twist boundary - boundary region consisting of arrays of screw dislocations (like joining two halves of a cube and twist an angle around the cross section normal) Transmission electron microscope image of a small angle tilt boundary in Si. The red lines mark the edge dislocations, the blue lines indicate the tilt angle

22. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 22 Bulk or Volume Defects  Pores: affect optical, thermal, mechanical properties  Cracks: affect mechanical properties  Foreign inclusions: affect electrical, mechanical, optical properties Cluster of microcracks in a melanin granule irradiated by a short laser pulse. Computer simulation by L. V. Zhigilei and B. J. Garrison.

23. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 23 Atomic Vibrations  Heat causes atoms to vibrate  Vibration amplitude increases with temperature  Melting occurs when vibrations are sufficient to rupture bonds  Vibrational frequency ~ 10 13 Hz  Average atomic energy due to thermal excitation is of order kT

24. Introduction To Materials Science, Chapter 4, Imperfections in solids University of Virginia, Dept. of Materials Science and Engineering 24 Summary  Alloy  Atom percent  Atomic vibration  Boltzmann’s constant  Burgers vector  Composition  Dislocation line  Edge dislocation  Grain size  Imperfection  Interstitial solid solution  Microstructure  Point defect  Screw dislocation  Self-Interstitial  Solid solution  Solubility limit  Solute  Solvent  Substitutional solid solution  Vacancy  Weight percent Understand language and concepts: