Anandh Subramaniam & Kantesh Balani Interfaces in Solids MATERIALS SCIENCE & ENGINEERING 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 AN INTRODUCTORY E-BOOK Part of http://home.iitk.ac.in/~anandh/E-book.htm A Learner’s Guide

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

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 <110>

Low angle tilt grain boundary

b 2h Book

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

Twins

Comparison of Energy of Various 2D Defects Type of boundary Energy (J/m2) Surface ~ 0.89 Grain boundary ~0.85 Twin Boundary ~ 0.63 0.498 (Cu) Stacking Fault 0.08 (Cu) 0.2 (Al)

Comparison of Interfacial Energies of Various 2D Defects Metal Surface Solid/ Liquid Grain Boundary Twin Boundary Stacking Fault (J/m2) Gold 1370 132 364 ~10 55 Silver 1140 126 790 - 17 Platinum 1310 240 1000 196 ~95 Nickel 1860 255 690 ~400 Aluminium 625 120 ~200 Copper 1750 177 646 44 73 Iron 1950 204 780 190 Tin 680 54.5

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 Surface free energies of some crystals (J/m2) NaCl LiF CaF2 MgO Si Ag Fe Au Cu 0.30 0.34 0.45 1.2 1.24 1.14 1.4 1.65