Dislocations – Linear Defects

1. Dislocations – Linear Defects • Two-dimensional or line defect • Line around which atoms are misaligned – related to slip • Edge dislocation: • extra half-plane of atoms inserted in a crystal structure • Or – think of it as a partially slipped crystal • b to dislocation line • Screw dislocation: • spiral planar ramp resulting from shear deformation • b to dislocation line Burger’s vector, b: measure of lattice distortion or the amount of displacement. Burger’s vector is equal in magnitude to interatomic spacing.

2. Edge Dislocation • This is a crystal that is slipping • Slip has occurred in the direction of slip vector over the area ABCD • Boundary between portion that has slipped and not slipped is AD • AD is the edge dislocation • The Burger’s vector b is • = magnitude to the amount of slip • Is acting in the direction of slip • Note that b is ┴ dislocation line Source: G. Dieter, Mechanical Metallurgy, McGraw Hill, 1986.

3. Dislocations – Linear Defects Edge Dislocation Fig. 4.3, Callister 7e.

4. Motion of Edge Dislocation • Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). • Bonds across the slipping planes are broken and remade in succession. Atomic view of edge dislocation motion from left to right as a crystal is sheared. (Courtesy P.M. Anderson)

5. Dislocations – Linear Defects Screw Dislocation b Dislocation line (b) Burgers vector b (a) Adapted from Fig. 4.4, Callister 7e.

6. Mixed Edge Screw Edge, Screw, and Mixed Dislocations Adapted from Fig. 4.5, Callister 7e.

7. Dislocations – Linear Defects Dislocations are visible in electron micrographs Transmission Electron Micrograph of Titanium Alloy. Dark lines are dislocations. 51450X Adapted from Fig. 4.6, Callister 7e.

8. Interfacial - Planar Defects Surfaces • Atoms do not have the same coordination number • Therefore are in higher energy state • Surface energy, g [=] J/m2 • Materials always try to reduce surface energy – tendency towards spherical shapes

9. nuclei grain structure crystals growing liquid Grain Boundaries – Interfacial Defects Solidification- result of casting of molten material • 2 steps • Nuclei form • Nuclei grow to form crystals – grain structure • Start with a molten material – all liquid • Crystals grow until they meet each other

10. Grain Boundaries Grain Boundaries • regions between crystals • transition from lattice of one region to that of the other • slightly disordered • low density in grain boundaries • high mobility • high diffusivity • high chemical reactivity High energy locations where impurities tend to segregate to

11. Planar Defects in Solids • One case is a twin boundary (plane) • Special kind of grain boundary • Mirror lattice symmetry • Essentially a reflection of atom positions across the twin plane. • Stacking faults • For FCC metals an error in ABCABC packing sequence • Ex: ABCABABC Brass at 60X Figure4.13c Adapted from Fig. 4.9, Callister 7e.

12. Diffusion Diffusion- Mass transport by atomic motion Mechanisms • Gases & Liquids – random (Brownian) motion • Solids – vacancy diffusion or interstitial diffusion

13. Diffusion After some time • Interdiffusion: In an alloy, atoms tend to migrate from regions of high conc. to regions of low conc. Initially Adapted from Figs. 5.1 and 5.2, Callister 7e.

14. Diffusion C C D A A D B B • Self-diffusion: In an elemental solid, atoms also migrate. After some time Label some atoms

15. Diffusion Mechanisms Vacancy Diffusion: • atoms exchange with vacancies • applies to substitutional impurity atoms • rate depends on: --number of vacancies --activation energy to exchange. increasing elapsed time

16. Diffusion Simulation • Simulation of interdiffusion across an interface: • Rate of substitutional diffusion depends on: --vacancy concentration --frequency of jumping. (Courtesy P.M. Anderson)

17. Diffusion Mechanisms Interstitial diffusion – smaller atoms can diffuse between atoms in lattice positions. Adapted from Fig. 5.3 (b), Callister 7e. Which will be faster – vacancy diffusion or interstitial diffusion?

18. Processing Using Diffusion • Case Hardening: • Diffuse carbon atoms into the host iron atoms at the surface. • Use a controlled atmosphere with a specific carbon potential (effective concentration) • Elevated Temperature • Example of interstitial diffusion is a case hardened gear. Result: The higher concentration of C atoms near the surface increases the local hardness of steel.