Crystal-Air surfaceInterphase boundaryGrain boundaryTwin BoundaryStacking FaultsCrystal BoundaryCrystal-CrystalLow angleHigh angle

ExternalHomophaseHeteropaseTwin BoundaryStacking FaultsGrain boundaryInternalLow angleHigh angleRotationMirrorTranslation(From lecture notes of Dr. Rajesh Prasad)

HomophaseLow angleHigh angleBased on axisBased on angle of rotationBased on Lattice ModelsTwistTiltMixedSpecialRandomCSLBased on Geometry of the Boundary planeCurvedFacetedMixed

HeteropaseCoherentSemi-coherentIncoherent

Surface Imperfections 2D in a mathematical sense The region of distortion is ~ few atomic diameters in thickness

External surface of the crystal External surfaces have energy related to the number of bonds broken at the surfaceSurface Energy/ unit area (J/m2)No. of atoms/ unit areaNo. of bonds broken/ unit areaBond energy / bondAs two surfaces are created / bond broken

Surface free energies of some crystals (J/m2)NaClLiFCaF2MgOSiAgFeAuCu0.300.340.451.21.241.141.41.41.65

Interphase boundaryGrain boundary

Grain Boundary The grain boundary region may be distorted with atoms belonging to neither crystal The thickness may be of the order of few atomic diameters The crystal orientation changes abruptly at the grain boundary In an low angle boundary the orientation difference is < 10 In the low angle boundary the distortion is not so drastic as the high-angle boundary can be described as an array of dislocations Grain boundary energy is responsible for grain growth on heating ~ (>0.5Tm) Large grains grow at the expense of smaller ones The average no. of nearest neighbours for an atom in the grain boundary of a close packed crystal is 11

Grain boundaries in SrTiO3

Type of boundaryEnergy (J/m2)Grain boundary between BCC crystals0.89Grain boundary between FCC crystals0.85Interface between BCC and FCC crystals0.63

Low angle grain boundaries (misorientation < 10)TILTAn array of edge dislocationsTWISTAn array of screw dislocationsTwo extremes Rotation axis lies on the boundary plane Rotation axis lies to the boundary plane

Low angle tilt grain boundary

b2hBook

~8 TILT BOUNDARY IN SrTiO3 POLYCRYSTAL

Twin Boundary The atomic arrangement on one side of the twin boundary is related to the other side by a symmetry operation (usually a mirror) Twin boundaries usually occur in pairs such that the orientation difference introduced by one is restored by the other The region between the regions is called the twinned regionAnnealing twins (formed during recrystallization)Deformation twins (formed during plastic deformation)Twin

Twin boundary in Fe doped SrTiO3 bicrystals (artificially prepared) [1] S. Hutt, O. Kienzle, F. Ernst and M. Rhle, Z Metallkd, 92 (2001) 2Twin planeMirror relatedvariantsHigh-resolution micrograph

Stacking Fault Error in the sequence of stacking atomic planes Stacking fault Defined by a shift vectorABC ABC ABC ABCABC AB AB ABCFCC stackingFCC stacking with a stacking faultThin region of HCP type of stacking In above the number of nearest neighbours remains the same but next-nearest neighbours are different than that in FCC Stacking fault energy ~ 0.01 0.05 J/m2 Stacking fault in HCP can lead to thin region of FCC kind of stacking

Comparison of Energy of Various 2D Defects

Type of boundaryEnergy (J/m2)Surface~ 0.89Grain boundary~0.85Twin Boundary~ 0.63 0.498 (Cu)Stacking Fault0.08 (Cu)0.2 (Al)

Comparison of Interfacial Energies of Various 2D Defects

MetalSurfaceSolid/ LiquidGrain BoundaryTwin BoundaryStacking Fault(J/m2)Gold1370132364~1055Silver1140126790-17Platinum13102401000196~95Nickel1860255690-~400Aluminium1140-625120~200Copper17501776464473Iron1950204780190-Tin68054.5---