1. Interfaces in Solids

2. Coherent without strain Schematics of strain free coherent interfaces Same crystal structure (& lattice spacing) but different composition Matching spacing but with different crystal structure

3. Coherent strained Coherent interface with a small lattice mismatch Coherency stresses develop in the adjoining crystals Interface Compressively stressed region Region with Tensile Stresses

4. Schematic showing a coherent precipitate and the origin of coherency strains

6. Semi-Coherent Schematic showing a Semi-coherent interface: A series of edge dislocations at a spacing of D partially relax the misfit strain at the interface (this can be thought of as the interface breaking up into regions with registry and those with dislocations)  Semicoherent interfaces have an array of dislocations which partially relax the misfit strains arising from the lattice mismatch across the interface between the two materials

7. Zoomed region near the edge dislocation MPa Stress state of an semi-coherent interface Dislocation stress fields partly relax the coherency stresses Compressively strained film and substrate in tension (away from the dislocation line) Ge 0.5 Si 0.5 FILM ON Si SUBSTRATE for a film of larger lattice parameter

8. Incoherent

11. Precipitates with mixed type interfaces

12. Grain Boundaries

13. Variation of Grain boundary energy with misorientation for symmetric tilt boundaries in Al with rotation axis parallel to

15. Low angle tilt grain boundary

16. bb 2h Book

17. No visible Grain Boundary 2.761 Å Fourier filtered image Dislocation structures at the Grain boundary ~8º TILT BOUNDARY IN SrTiO 3 POLYCRYSTAL

19. Twins

20. Type of boundaryEnergy (J/m 2 ) Surface~ 0.89 Grain boundary~0.85 Twin Boundary ~ 0.63 0.498 (Cu) Stacking Fault 0.08 (Cu) 0.2 (Al) Comparison of Energy of Various 2D Defects

22. MetalSurface Solid/ Liquid Grain Boundary Twin Boundary Stacking Fault (J/m 2 ) Gold1370132364~1055 Silver1140126790-17 Platinum13102401000196~95 Nickel1860255690-~400 Aluminium1140-625120~200 Copper17501776464473 Iron1950204780190- Tin68054.5--- Comparison of Interfacial Energies of Various 2D Defects

24. External surface of the crystal  External surfaces have energy related to the number of bonds broken at the surface Surface free energies of some crystals (J/m 2 ) NaClLiFCaF 2 MgOSiAgFeAuCu 0.300.340.451.21.241.141.4 1.65 Surface Energy/ unit area (J/m 2 ) No. of atoms/ unit area No. of bonds broken/ unit area Bond energy / bond As two surfaces are created / bond broken