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Droplets of Ag60Sb34Cu6 ternary alloy within the diameter range of 60-800 μm were rapidly solidified by means of drop tube containerless processing, and the solidification mechanism is analyzed. With a decrease in droplet size, the cooling rate increases from 57 to 5.8×104 K/s. The maximum undercooling is determined to be 180 K (0.23TL) and the microstructure of primary ε(Ag3Sb) dendrite refines drastically until homogenous equiaxed dendrite forms. Experimental results indicate that (ε+Ag) pseudobinary eutectic cannot form under high undercooling conditions and the solubility of Ag in primary ε phase increases as undercooling increases. Based on thermal analysis and crystal growth morphology, it is found that this alloy is solidified in two ways corresponding to different undercooling levels.