Analysis of Solidified Structure Constituted with Dendrites by Using Solid Analytical Geometry

Solidified structure near the chill zone is complex, since the growth directions of dendrites are not in accordance with the observed plane. Many lines, which are called ghost lines, can be observed in the solidified structure. The ghost lines have been analyzed applying the solid analytical geometry. Dendrite of cubic metals has been simplified with rod as a dendrite trunk and four plates with the same thickness. In order to characterize the solidified pattern, angles of ghost lines (η and ξ) are chosen and calculated using θ, φ and β, which are the important parameters to indicate the dendrite orientation in the space. The calculated results have been confirmed by the experimental results solidified unidirectionally of Al–20mass%Cu alloy. It has been found that the spacing or thickness of ghost lines may be the useful parameters to characterize the spatial array of dendrites with respect to the plane for observation.