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Interfaces in SolidsInterfaces in Solids
MATERIALS SCIENCEMATERIALS SCIENCE&&
ENGINEERING ENGINEERING
Anandh Subramaniam & Kantesh Balani
Materials Science and Engineering (MSE)
Indian Institute of Technology, Kanpur- 208016
Email: [email protected], URL: home.iitk.ac.in/~anandh
AN INTRODUCTORY E-BOOKAN INTRODUCTORY E-BOOK
Part of
http://home.iitk.ac.in/~anandh/E-book.htmhttp://home.iitk.ac.in/~anandh/E-book.htm
A Learner’s GuideA Learner’s GuideA Learner’s GuideA Learner’s Guide
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 mismatchCoherency 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
80 Å
240 Å
FILM
SUBSTRATE
SYMMETRY LINE EDGE
80 Å
240 Å
FILM
SUBSTRATE
SYMMETRY LINE EDGE
FILM
SUBSTRATE
SYMMETRY LINE EDGE
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)Ge0.5Si0.5 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 <110>
Low angle tilt grain boundary
22
Sin
h
b
b
2h2
~h
btan
h
bBook
No visible Grain Boundary
2.761 Å
Fourier filtered image
Dislocation structures at the Grain boundary
~8º TILT BOUNDARY IN SrTiO3 POLYCRYSTAL
Twins
Type of boundary Energy (J/m2)
Surface ~ 0.89
Grain boundary ~0.85
Twin Boundary~ 0.63
0.498 (Cu)
Stacking Fault0.08 (Cu)
0.2 (Al)
Comparison of Energy of Various 2D Defects
Metal SurfaceSolid/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 1140 - 625 120 ~200
Copper 1750 177 646 44 73
Iron 1950 204 780 190 -
Tin 680 54.5 - - -
Comparison of Interfacial Energies of Various 2D Defects
External surface of the crystal
External surfaces have energy related to the number of bonds brokenat the surface
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 1.4 1.65
2
E . n . nγ bbaSurface Energy/
unit area (J/m2)
No. of atoms/ unit area
No. of bonds broken/ unit area
Bond energy / bond
As two surfaces are created / bond broken
