Imperfections, Defects and Diffusion

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1 Imperfections, Defects and Diffusion Lattice Defects Week5 Material Sciences and Engineering MatE271 1 Goals for the Unit I. Recognize various imperfections in crystals (Chapter 4) - Point imperfections - Impurities - Line, surface and bulk imperfections II. Define various diffusion mechanisms (Chapter 5) III. Identify factors controlling diffusion processes Material Sciences and Engineering MatE271 Week 5 2

2 Defects in Materials - Why study defects? - Types of defects - How are defects introduced - Diffusion in materials Material Sciences and Engineering MatE271 Week 5 3 Types of Defects o Point defects (composition) Vacancies Interstitials (missing atoms) (extra atoms) Impurities (unwelcome segregation) o Extensive chemical changes - Solid solutions - Not a defect in intentional alloying or doping o Line defects (1-dimensional) (Deformation) dislocations - in metals Material Sciences and Engineering MatE271 Week 5 4

3 Types of Defects, cont. o Interfacial defects (2-dimensional) (Properties) - surfaces - both interior (pore walls) and exterior (surface of material) - interfaces -(grain boundaries) o Bulk-Volume defects (3-dimensional) - cracks, foreign inclusions, other phases (including pores). Material Sciences and Engineering MatE271 Week 5 5 Point Defects in Metals Self Interstitial Interstitial Impurity Vacancy Substitutional Impurity Material Sciences and Engineering MatE271 Week 5 6

4 Point defects o Vacancy An empty atomic site o Interstitial An atom somewhere other than an atomic site - Self-interstitial - Impurity interstitial o Substitutional impurity Some foreign species on an atomic site Material Sciences and Engineering MatE271 Week 5 7 How are point defects introduced? - Some types are thermally generated - Direct result of thermal vibration of the atomic array - The concentration of thermally-produced defects increases exponentially with increasing temperature Hint: Equilibrium number of vacancies N v, for a material N v = N exp [-Q v /kt] N = total number of atomic sites Qv = activation energy to form a vacancy, ev k = Boltzmann s constant (8.62 x 10-5 ev/atom-k) T = Temperature (K) Material Sciences and Engineering MatE271 Week 5 8 aterial Sciences and Engineering,

5 How are point defects introduced? How are point defects introduced? 1. Added solutes (impurities or dopants) ordered or disordered solid solution How do they get uniformly distributed? 2. Stoichiometry changes (cation/anion ratio changes) e.g., ZrO 2-δ, Fe 1-δ O (δ~ 0.05) How is uniform composition accomplished? (Stoichiometric: State in an ionic compound in which there is an exact ratio of cations to anions as predicted by the chemical formula.) Material Sciences and Engineering MatE271 Week 5 9 Point Defects in Ceramics Schottky defect (anion and cation vacancies) Frenkel defect (cation vacancy + cation interstitial) Anion Vacancy Cation Vacancy Material Sciences and Engineering MatE271 Week 5 10 aterial Sciences and Engineering,

6 Point Defects in Ceramics Interstitial Cation Impurity Substitutional Cation Impurity Substitutional Anion Impurity Anion impurity Interstitial (not shown) Material Sciences and Engineering MatE271 Week 5 11 Solid Solution All solids have some degree of impurities dissolved in them - Unintentional - called impurities - Intentional - called dopants or alloying additives Solute and solvent - Solvent (present in greatest amount) - Solute (present in minor concentration) Material Sciences and Engineering MatE271 Week 5 12 aterial Sciences and Engineering,

Hume-Rothery Rules Complete mutual solid solubility will occur between two metals if: - Less than 15% difference in atomic radii - Both have the same crystal structure in pure form - Both have

7 Hume-Rothery Rules Complete mutual solid solubility will occur between two metals if: - Less than 15% difference in atomic radii - Both have the same crystal structure in pure form - Both have similar electronegativities - Both have the same valence The more deviation, the less the solubility Can also be applied roughly in simple ceramics Material Sciences and Engineering MatE271 Week 5 13 Solution of ~30 at% Cu dissolved in solid Ni(substitutional solid solution) Ni Cu Material Sciences and Engineering MatE271 Week 5 14

8 Disordered (normal) and ordered solid solution Expected gold or Copper atom position Disorderd AuCu 3 (Above 380 o C) Gold atom Copper atom Ordered AuCu 3 (Below 380 o C) correction Material Sciences and Engineering MatE271 Week 5 15 Interstitial solid solution C atom dissolve interstitially at type position In BCC structure of α-fe For α-fe, r interstitial = nm r carbon =0.077 nm Material Sciences and Engineering MatE271 Week 5 16

FeO (altervalent cation - vacancy charge compensation) O 2- cation vacancies Fe 3+ Fe 2+

9 Solution of NiO in MgO (cations of same valence) O 2- Ni 2+ Mg 2+ Random substitutional solid solution Material Sciences and Engineering MatE271 Week 5 17 Solution of Fe 2 O 3 in FeO (altervalent cation - vacancy charge compensation) O 2- cation vacancies Fe 3+ Fe 2+ Vacancy Material Sciences and Engineering MatE271 Week 5 18 aterial Sciences and Engineering,

Line Defects: Dislocation in Metals Responsible for large mechanical deformation in crystalline solids -Linear (one dimensional) defect around which some of the atoms are misaligned Material Sciences

10 Line Defects: Dislocation in Metals Responsible for large mechanical deformation in crystalline solids -Linear (one dimensional) defect around which some of the atoms are misaligned Material Sciences and Engineering MatE271 Week 5 19 Types of Dislocations - Edge Dislocation: A portion of an extra plane of atoms - Screw Dislocation: Helical atomic displacement around a line extending through the crystal - Mixed Dislocation: Some edge, some screw nature Material Sciences and Engineering MatE271 Week 5 20

11 Edge Dislocation Material Sciences and Engineering MatE271 Week 5 21 Burgers vector Perfect crystal b dislocated crystal b-represents the magnitude of the structural defect Material Sciences and Engineering MatE271 Week 5 22

12 Screw Dislocation Material Sciences and Engineering MatE271 Week 5 23 Mixed Dislocation Material Sciences and Engineering MatE271 Week 5 24

13 Why are Dislocations Important? The motion of dislocations is the principle mechanism whereby metals deform Material Sciences and Engineering MatE271 Week 5 25 Why? Energy, Energy, Energy! o Lower energy than breaking all bonds in a plane at once Material Sciences and Engineering MatE271 Week 5 26

Shear occurs by dislocation movement producing permanent (plastic) deformation by slip Textbook ch6, pp 212-218 Slip plane Direction of

14 Shear occurs by dislocation movement producing permanent (plastic) deformation by slip Textbook ch6, pp Slip plane Direction of dislocation movement Material Sciences and Engineering MatE271 Week 5 27 Edge Dislocation Motion - 3D Material Sciences and Engineering MatE271 Week 5 28

15 Slip occurs along densely packed directions on densely packed planes Material Sciences and Engineering MatE271 Week 5 29 pp 215 (Plane)[Direction] pairs designate slip systems (e.g., in FCC and HCP) Material Sciences and Engineering MatE271 Week 5 30

16 Dislocation movement and ductility A large number of independent slip systems are required for good ductility in polycrystalline materials so grains can deform to accommodate their neighboring grains Common in many metal structures (esp. bcc and fcc) Dislocations are very complex in ceramic structures This and complications of like charged ions encountering each other during slip make dislocation movement almost impossible in ceramics Therefore ceramics are not ductile, they are brittle Material Sciences and Engineering MatE271 Week 5 31 Impediments to easy dislocation movement Impurity atoms ( solute hardening ) Intersection with other dislocations (entanglement) ( work hardening ) Grain boundaries (dislocations pile up ) Small dispersed inclusions ( precipitation hardening ) All of these affect ductility and yield strength of a metals Material Sciences and Engineering MatE271 Week 5 32

17 Grain boundaries and other dislocations impede the movement of dislocations causing hardening Dislocations Material Sciences and Engineering MatE271 Week D Defects Twin boundaries Grain boundaries Surfaces Material Sciences and Engineering MatE271 Week 5 34

18 Twinning is common in some materials Material Sciences and Engineering MatE271 Week 5 35 Small angle grain boundaries can be thought of as arrays of dislocations Material Sciences and Engineering MatE271 Week 5 36

19 Some details of surface structure Material Sciences and Engineering MatE271 Week 5 37 Material Science Investigative Techniques Microscopy Optical microscope surface microstructure (~ 1µm) Scanning electron microscope (SEM) Surface microstructure, analytical chemistry (~ nm) Transmission electron microscope resolve the atomic structure from a very thin foil (30 A o ), (~1 A o ) Atomic force microscope 3D surface topography, electrical, magnetic scanning (~1 nm) Material Sciences and Engineering MatE271 Week 5 38

20 Reading Assignment Shackelford 2001(5 th Ed) Read Chapter 4, pp , Read ahead Chapter 5, pp Material Sciences and Engineering MatE271 Week 5 39

Defects and Diffusion

Defects and Diffusion Goals for the Unit Recognize various imperfections in crystals Point imperfections Impurities Line, surface and bulk imperfections Define various diffusion mechanisms Identify factors