The undercooling and nucleation of Al4Mn alloy have been investigated by containerless solidification in a 1.2 m long drop tube, where molten droplets of the alloy solidified in the vacuum. Droplets in various sizes were collected at the bottom of the tube. It is found by x‐ray and electron diffractions that besides the orthorhombic Al6Mn and &bgr;‐Mn phases, two approximants of the decagonal quasicrystal, one approximant of the icosahedral quasicrystal and decagonal domains can be observed in the as‐solidified droplets. However, due to the different cooling rate or undercooling in the samples of different sizes, the phases mentioned above will appear in different amounts. The relationship between the phase composition and the sample size is discussed on the basis of the classical nucleation and growth theories. ©1995 American Institute of Physics.