Interfaces in Solids
Coherent without strain Schematics of strain free coherent interfaces Same crystal structure (& lattice spacing) but different composition Matching spacing but with different crystal structure
Coherent strained Coherent interface with a small lattice mismatch Coherency stresses develop in the adjoining crystals Interface Compressively stressed region Region with Tensile Stresses
Schematic showing a coherent precipitate and the origin of coherency strains
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
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
Incoherent
Precipitates with mixed type interfaces
Grain Boundaries
Variation of Grain boundary energy with misorientation for symmetric tilt boundaries in Al with rotation axis parallel to
Low angle tilt grain boundary
bb 2h Book
No visible Grain Boundary Å Fourier filtered image Dislocation structures at the Grain boundary ~8º TILT BOUNDARY IN SrTiO 3 POLYCRYSTAL
Twins
Type of boundaryEnergy (J/m 2 ) Surface~ 0.89 Grain boundary~0.85 Twin Boundary ~ (Cu) Stacking Fault 0.08 (Cu) 0.2 (Al) Comparison of Energy of Various 2D Defects
MetalSurface Solid/ Liquid Grain Boundary Twin Boundary Stacking Fault (J/m 2 ) Gold ~1055 Silver Platinum ~95 Nickel ~400 Aluminium ~200 Copper Iron Tin Comparison of Interfacial Energies of Various 2D Defects
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 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