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Interfaces in Solids

MATERIALS SCIENCE & ENGINEERING . Part of . A Learner’s Guide. AN INTRODUCTORY E-BOOK. Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh.

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Interfaces in Solids

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  1. MATERIALS SCIENCE & ENGINEERING Part of A Learner’s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email:anandh@iitk.ac.in, URL:home.iitk.ac.in/~anandh http://home.iitk.ac.in/~anandh/E-book.htm Interfaces in Solids

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

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

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

  5. 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)

  6. 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

  7. Incoherent

  8. Precipitates with mixed type interfaces

  9. Grain Boundaries

  10. Variation of Grain boundary energy with misorientation for symmetric tilt boundaries in Al with rotation axis parallel to <110>

  11. Low angle tilt grain boundary

  12. b 2h Book

  13. No visible Grain Boundary 2.761 Å Fourier filtered image Dislocation structures at the Grain boundary ~8º TILT BOUNDARY IN SrTiO3 POLYCRYSTAL

  14. Twins

  15. Comparison of Energy of Various 2D Defects

  16. Comparison of Interfacial Energies of Various 2D Defects

  17. 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

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