Measurement and analysis of grain boundary grooving by volume diffusion

Experimental measurements of isothermal grain boundary grooving by volume diffusion are carried out for Sn bicrystals in the Sn-Pb system near the eutectic temperature. The dimensions of the groove increase with a temporal exponent of 1/3, and measurement of the associated rate constant allows the determination of the product of the liquid diffusion coefficient D and the capillarity length Gamma associated with the interfacial free energy of the crystal-melt interface. The small-slope theory of Mullins is generalized to the entire range of dihedral angles by using a boundary integral formulation of the associated free boundary problem, and excellent agreement with experimental groove shapes is obtained. By using the diffusivity measured by Jordon and Hunt, the present measured values of Gamma are found to agree to within 5 percent with the values obtained from experiments by Gunduz and Hunt on grain boundary grooving in a temperature gradient.