The oscillatory instability of convection in a binary liquid-mixture with negative Soret effects coupling Benard convection and solidification is investigated when the temperature of the upper boundary is below the freezing point of the two-component system. Complete rejection of the lean component from the solid into the liquid phase is assumed. The Soret coefficient and the coefficients of thermal and solutal expansion depend strongly on the local concentration in the liquid and, consequently, on the thickness of the solidified layer. Linear stability analysis for typical ethanol-water mixtures demonstrates that the variation of concentration is a dominant effect in the destabilization of the conductive state.