  By introducing a new topology, a representation formula of the Gamma limit of
the Kobayashi-Warren-Carter energy is given in a multi-dimensional domain. A
key step is to study the Gamma limit of a single-well Modica-Mortola
functional. The convergence introduced here is called the sliced graph
convergence, which is finer than conventional $L^1$ convergence, and the
problem is reduced to a one-dimensional setting by a slicing argument.
