We adapt the recent derivation of a long-wave evolution equation for a solid-liquid interface undergoing directional solidification near the limit of absolute stability to the case of a symmetric model that includes solid diffusion. The stability of steady and spatially periodic solutions are investigated and it is found that these cellular solutions are subject to an oscillatory instability with twice the wavenumber of the underlying pattern. We discuss this instability in the context of experiments on the directional solidification of nematic liquid crystals.

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