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

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

6. 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)

7. 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

8. Incoherent

11. Precipitates with mixed type interfaces

12. Grain Boundaries

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

15. Low angle tilt grain boundary

16. b 2h
Book

17. ~8º TILT BOUNDARY IN SrTiO3 POLYCRYSTAL
No visible Grain Boundary
2.761 Å
Fourier filtered image
Dislocation structures at the Grain boundary

19. Twins

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

22. 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

24. 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