Interfaces in SolidsInterfaces in Solids

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