Grain Boundary Properties: Energy (L21) - Materials Science and ...

20
Force Balance Equations/
Herring Equations
• The Herring equations[(1951). Surface tension as a motivation
for sintering. The Physics of Powder Metallurgy. New York,
McGraw-Hill Book Co.: 143-179] are force balance equations at
a TJ. They rely on a local equilibrium in terms of free energy.
• A virtual displacement, δr, of the TJ (L in the figure) results in no
change in free energy.
• See also: Kinderlehrer D and Liu C, Mathematical Models and
Methods in Applied Sciences, (2001) 11 713-729; Kinderlehrer,
D., Lee, J., Livshits, I., and Ta'asan, S. (2004) Mesoscale
simulation of grain growth, in Continuum Scale Simulation of
Engineering Materials, (Raabe, D. et al., eds),Wiley-VCH
Verlag, Weinheim, Chap. 16, 361-372