Kinetics of Thermal Grain Boundary Grooving for Changing Dihedral Angles

Abstract

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 αt0.25. 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.

Thermal grain boundary grooving with anisotropic surface free energy in three dimensions

“…As discussed in Ref. [2], a time-varying dihedral angle may be caused by a time-varying surface free energy or a time-varying grain boundary free energy. The model and simulation presented here apply directly to the cases of a changing dihedral angle caused by time-varying grain boundary energy.…”

“…The only modification would be to input a time-varying dihedral angle instead of a fixed-degree angle in the boundary condition of the model and simulation. In the cases of a changing dihedral angle caused by a time-varying surface free energy, a slight modification to the evolution equation, similar to that for the isotropic case [2], is needed in addition to the input of a time-varying dihedral angle. As in Ref.…”

“…It can be used to determine material properties such as surface energy, grain boundary energy or diffusion coefficient [1,2]. The study of the anisotropic thermal grain boundary grooving has potentially significant applications in the manufacture of high-temperature (coated) superconductor tapes and thin films, since the material used there is usually highly anisotropic.…”

Transport processes at quartz–water interfaces: constraints from hydrothermal grooving experiments

“…The geometry of the groove is sensitive to these extensions but general features of the Mullins' theory are mostly maintained while the absolute grooving kinetics are altered. When multicomponent diffusion (Dhalenne et al, 1979;Klinger, 2002) takes place or time dependence of interface energies is involved (Zhang et al, 2002), the growth exponent n may change considerably. Table 1.…”

“…This anticipated reorientation should rather yield an increase in the grooveroot angle with time. Alternatively, evolution in grain boundary/surface energy ratio due to segregation impurity, for example, has been invoked as an explanation for the change in the groove-root angle with time (Zhang et al, 2002). Also, the blunting effect of grain-boundary migration on root angles (Dillon and Rohrer, 2009) might contribute to the evolution.…”