Aluminium-silicon alloys in the composition range 12 to 16 wt. % silicon have been frozen unidirectionally over a range of rates from ca. 0.3 to 30 $\mu$ m/s and with imposed temperature gradients ranging from 0.35 to ca. 40 $^\circ$C/mm. The detailed morphology and crystallography of silicon in these alloys are described and the various structures are rationalized in terms of the variables, composition, freezing rate and temperature gradient. Three growth processes are distinguished in which (A) massive silicon crystals grow at a planar aluminium front by a relatively long range diffusion process: (B) short range diffusion occurs at the growth front between silicon crystals which develop a preferred $\langle$100$\rangle$ fibre texture; and (C) silicon crystals are more or less heavily twinned and grow by steady or fluctuating short-range diffusion processes. There do not appear to be any preferred epitaxial orientations between the phases. Similarities are noted between the microstructures of eutectic alloys in the systems AI-Si and Ag-Si, and it is shown that in chilled or 'modified' alloys the silicon occurs in an irregular fibrous form rather than as isolated globules. The mechanisms are discussed for (I) the growth kinetics of silicon, (II) the transition from a long-range to a short-range diffusion process, (III) steady-state, and (IV) non-steady-state growth processes, and (V) repeated nucleation of silicon crystals from the liquid.