Kinetics of Thermal Grain Boundary Grooving for Changing Dihedral Angles

In his classic paper on thermal grain boundary grooving Mullins [W.W. Mullins, J. Appl. Physics 28, 333 (1957)] assumes that the dihedral angle at the groove root remains constant and predicts that the groove width and depth grow αt^0.25. Here, we derive models describing groove growth while the dihedral angle changes. In our grooving experiments with tungsten at 1350 °C in which the dihedral angle decreased, the growth exponent for the groove depth reached values as high as 0.44 while the growth exponent for the width decreased slightly from Mullins' value of 0.25. Hence groove width data alone are not sufficient for verifying Mullins' growth law unless the dihedral angle is constant. The observed changes in the dihedral angle are used as an input for numerical simulations. With the simulations we are able to extract the surface diffusion constants. Atomic force microscope observations of groove widths and depths in tungsten are in excellent agreement with the simulations.