Slide 1

Polycrystalline materialMetastable equilibriumGrain boundary migrationGrain growth and Recrystallization

Electron backscattered diffraction (EBSDGrain boundaries are region of higher energySo, well annealed polycrystalline material is always in metastable equilibrium

Balance of grain-boundary tensions for a grain-boundary interaction in metastable equilibriumMetastable EquilibriumIf GB energy is same (independent of orientation) then

Migration of GBs thermal activationFor complete metastable equilibrium the surface tension must also balance over all the boundary facesAny curved boundary is acted by a force towards its centre of curvature

In real metallurgical materials The boundaries have net curvature in one direction Therefore inherently unstable and migrate towards their centre of curvature

Planar (6 GBs) metastable equilibriumConcave inwards (< 6 GBs) Shrink > 6 GBs - Grow

Effect of the pressure difference caused by curved boundary is to create a difference in free energy (G) or chemical potential () that drives the atom across the boundary

Driving force for migrationPulling force per unit area of boundary

Free energy difference due to boundary curvatureGrain growth Difference in dislocation strain energy between the two grainsRecrystallization

Moving boundary velocity

Mobility of GB

Lead alloyed with tinCoherent twin boundary are almost immobile

Effect of solute In general special boundaries are more mobile than random GBs. This is because solute preferentially segregate to random grain boundaries (more open structure) Due to solute dragKinetics of grain growthDriving force for grain growth is to reduce total no. of grains thereby increase the mean grain diameter

Experimentally it is found

n = 0.5, for pure metals at very high temperaturesn usually less than 0.5,due to solute drag effect

Force due to solute dragForce due to GB curvatureEffect of particles on GB migrationMaximum grain size in presence of particle is given by

Vol. fraction of particlesmean radius of particles

TimeTo retard grain growth large volume fraction of very small particles are required