Imperfections: Good or Bad? Structural imperfections (defects) Compositional imperfections (impurities)

Transcription

1 Imperfections: Good or Bad? Structural imperfections (defects) Compositional imperfections (impurities) 1

2 Structural Imperfections A perfect crystal has the lowest internal energy E Above absolute zero at constant volume, the system responds by minimizing the free energy F = E - TS, where T is the absolute temperature and S entropy 2

3 Structural Imperfections 3

4 Compositional Imperfections Impurities always present in materials Without impurities, semiconductor devices and advanced engineering materials not possible Si devices cannot function without lowlevel impurities Silver not useable as utensils without addition of copper 4

5 Solid Solutions Consider addition of Ni into Cu (both FCC) Ni atoms occupy Cu sites Substitutional solid solution Rules of miscibility Atomic size Crystal structure Electronegativity (Valence) 5

6 Ni/Cu Atomic size: nm vs nm Crystal structure: both FCC Electronegativity: 1.91 vs 1.90 Valence: both +2 Fully miscible 6

7 Zn/Cu Atomic size: nm vs nm Crystal structure: HCP vs FCC Electronegativity: 1.65 vs 1.90 Valence: both +2 Cu can only dissolve 38 at. % Zn 7

8 Two Types of Solid Solutions Substitutional - impurity or solute atoms occupying regular lattice sites, e.g., Ni in Cu Interstitial - impurity or solute atoms occupying holes between lattice sites, e.g., C in Fe Applicable for small atoms, e.g., C Low solubility 8

9 Intrinsic Point Defects Interstitials Vacancies, produced by thermal excitation N = N exp Q v v kt energetic particle bombardment, e.g., neutron irradiation in a nuclear reactor 9

10 Frenkel and Schottky Defects 10

11 Point Defects in Ionic Crystals Consider the following 3 situations: 1. Generation of a cation (+ve) vacancy in stoichiometric NaCl 2. Loss of oxygen from TiO 2 3. Introduction of oxygen in NaCl 11

12 Line Defects Edge Dislocations Screw Dislocations 12

13 Edge Dislocation Inserting an extra half-plane of atoms into the crystal! 13

14 Edge Dislocation Formed by having an extra half-plane of atoms One part under compression, one part under tension Scavenger of impurity atoms (Cottrell atmosphere) Important in controlling plastic deformation 14

15 Motion of Dislocation under Shear Stress 15

16 Screw Dislocation 16

17 Grain Boundaries Transition regions between grains More open structure Segregation of impurity atoms Obstacles against dislocation motion, transport of electrons and lattice vibrations (charge and heat) 17

18 Precipitates Addition of C to Fe forms Fe 3 C Addition of Cu to Al forms various CuAl intermetallic compounds These form precipitates that are harder than the matrix, improving mechanical properties 18

19 Atomic Diffusion Without defects such as vacancies or interstitals, atomic diffusion would have been very slow, and useful engineering materials could not have been produced Diffusion as a musical chair process, facilitated by atoms jumping into adjacent vacancies or interstitial sites. 19

20 Atomic Diffusion Jumping out of vacancies or interstitials requires the breaking of bonds Correlation between activation energy for diffusion and bond energy, e.g., Al: activation energy for diffusion = 165 kj/mole; melting point = 660 C Mo: activation energy for diffusion = 460 kj/mole; melting point = 2600 C 20

21 Fick s Laws 1st Law 2nd Law J = D dc dx C t = D 2 C x 2 where D is the diffusion constant or diffusivity D = D o exp Q k B T 21

22 Activation Energy for Diffusion Correlates with bond strength Depends on the openness of the diffusion path compared with atomic size, e.g. C in BCC iron (900K): Q = m 2 /s C in FCC iron (900K): Q = m 2 /s Grain boundaries more open --> smaller Q Surface diffusion fastest 22

23 Activation Energy for Diffusion Diffusion aided by other factors Electrical currents - electromigration Additional vacancies Stress gradient 23

24 Diffusion Profile for a 1D Concentration Step " C x C o C s C o = 1 erf x 2 Dt " # $ % 24

25 Error Function erf (z) = 2 π z 0 exp( y 2 )dy & 25

26 Diffusion Distance x RMS = 2Dt 26

27 Example: Case Hardening Diffuse carbon into steel surface to increase surface hardness (hard case) Gas carburizing or plasma carburizing using a carbon-containing gas Typical carbon concentration in the % range Surface concentration C s controlled by gas pressure 27

28 Example: Impurity Diffusion into Silicon Diffuse impurity atoms into silicon to change electrical properties Concentration in the ppm range Impurity atoms usually introduced in the form of hydrides, e.g. use PH 3 to introduce P Surface concentration controlled by pressure of dopant gas molecules 28

29 Diffusion in Biological Systems Diffusion of small molecules such as oxygen, carbon dioxide, water and ethanol through cell membranes - passive diffusion (based on concentration gradient) Major component of cell membrane is the phospholipid double layer Molecules dissolve in the phospholipid double layer and diffuse across the cell membrane, e.g., osmosis 29

30 Facilitated Diffusion Certain biochemical processes require diffusion of species not soluble in the phospholipid double layer, or opposite to concentration gradient Diffusion of ions, charged molecules (e.g., amino acids), or large polar molecules (e.g., sugar molecules) across cell membrane - facilitated diffusion 30

31 Facilitated Diffusion '!!! "! 31

32 Facilitated Diffusion! '!! ( ) ( )! 32

33 Ion Channels Important for transmission of nerve impulses Fast diffusion ions/sec For membrane thickness of 10 nm, this corresponds to a diffusivity of m 2 /sec at 37 C As a comparison, diffusion of C in steel is about m 2 /sec at ~1000 C 33