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Interfaces in Solids. Coherent without strain. Matching spacing but with different crystal structure . Same crystal structure (& lattice spacing) but different composition. Schematics of strain free coherent interfaces. Coherent strained. Region with Tensile Stresses. Interface.
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Coherent without strain Matching spacing but with different crystal structure Same crystal structure (& lattice spacing) but different composition Schematics of strain free coherent interfaces
Coherent strained Region with Tensile Stresses Interface Compressively stressed region Coherent interface with a small lattice mismatch Coherency stresses develop in the adjoining crystals
Schematic showing a coherent precipitate and the origin of coherency strains
Semi-Coherent • 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 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)
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)Ge0.5Si0.5 FILM ON Si SUBSTRATE for a film of larger lattice parameter Zoomed region near the edge dislocation MPa
Variation of Grain boundary energy with misorientation for symmetric tilt boundaries in Al with rotation axis parallel to <110>
b 2h Book
No visible Grain Boundary 2.761 Å Fourier filtered image Dislocation structures at the Grain boundary ~8º TILT BOUNDARY IN SrTiO3 POLYCRYSTAL
External surface of the crystal • External surfaces have energy related to the number of bonds broken at the surface No. of atoms/ unit area Surface Energy/unit area (J/m2) No. of bonds broken/ unit area Bond energy / bond As two surfaces are created / bond broken