Six alloys were directionally solidified at low growth speeds (1-5 mu m s(-1)) under a weak transverse magnetic field (<= 0.5 T). The results show that the application of a weak transverse magnetic field significantly modified the solidification structure. Indeed, it was found that, along with the refinement of cells/dendrites, the magnetic field caused the deformation of liquid solid interfaces, extensive segregations (i.e., freckles and channels) in the mushy zone, and a change in the mushy zone length. Further, in situ monitoring of the initial transient of the directional solidification was carried out by means of synchrotron X-ray radiography. It was observed that dendrite fragments and equiaxed grains were moved approximately along the direction perpendicular to the magnetic field. This result shows that a thermoelectric magnetic force (TEMF) acted on the liquid or the solid during directional solidification under a weak magnetic field. The TEMF during directional solidification under a transverse magnetic field was investigated numerically. The results reveal that a unidirectional TEMF acted on the solid and induced thermoelectric magnetic convection (TEMC) in the liquid. Modification of the solidification structure under a weak magnetic field is attributed to TEMC-driven heat transfer and interdendritic solute transport and TEMF-driven motion of dendrite fragments.