The instabilities of a fluid layer of a binary alloy, cooled from above and consequently frozen at bottom, are considered. The released light material at the freezing interface is diffused by pressure and composition gradients. As a result of a small cooling rate and a large thermal diffusivity, the thermal effect is inefficient, compared with the compositional one, for driving a possible convection. Cellular convective modes of long and short wavelengths,; requiring 1 < R < 1 + S + qa(2)/Q, and morphological mode of short wavelength, requiring R > 1 + S + qa(2)/Q, are found. As Schmidt number P-L --> infinity, the instabilities set in stationarily at the marginal state. Nonlinear analysis of cellular convective modes of long wavelengths shows that finite amplitudes of disturbances just past the marginal state behave like (R - R(c))(1/2). Subcritical instabilities are possible for cellular convective modes other than rolls.