  We present a phase field model of solidification which includes the effects
of the crystalline orientation in the solid phase. This model describes grain
boundaries as well as solid-liquid boundaries within a unified framework. With
an appropriate choice of coupling of the phase field variable to the gradient
of the crystalline orientation variable in the free energy, we find that high
angle boundaries undergo a premelting transition. As the melting temperature is
approached from below, low angle grain boundaries remain narrow. The width of
the liquid layer at high angle grain boundaries diverges logarithmically. In
addition, for some choices of model coupling, there may be a discontinuous jump
in the width of the fluid layer as function of temperature.

Materials Science