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One of the less desirable aspects of fusion-based additive manufacturing is the propensity for coarse columnar grain structures crossing build layers to form. This paper initially attempts to explain the reason for the formation of columnar grain structures in terms of the high thermal gradients typically observed during solidification and the alloy compositions that are typically used which promote epitaxial growth. Successful approaches to the grain refinement of titanium alloys using alloying elements that produce constitutional supercooling are discussed along with the difficulty with nucleant additions. Much of the grain-refining technology already used in aluminium casting is shown to also be applicable to additive manufacturing, although the novelty of the effective use of nanoparticles as nucleants is highlighted. It is also shown that for other alloy systems for which there is a lack of grain-refining technology using …