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THE addition of a heterogeneous nucleus can result in the generation of the isotropic structure of crystal grains.[1] During casting, the grain refiner is added to molten metal and acts as the heterogeneous nucleus.[2] When the grain refiner is added during directional solidification, directionally solidified microstructure changes from an anisotropic columnar crystal to an isotropic equiaxed crystal, because the equiaxed grains can nucleate from the refiner at the site where the columnar grains normally appear.[3] Materials that have good lattice registry with the metal matrix act as more effective heterogeneous nuclei because of a simple crystallographic theory.[4] To evaluate the lattice registry of the heterogeneous nucleus with an asymmetric crystal structure, the disregistry

SHUNYA YAMAMOTO and NAOKI DATE are with the Graduate School of Fundamental Science and Engineering, Waseda University, Tokyo, 169-8555 Japan. Contact e-mail: [email protected] YUHI MORI is with the Graduate School of Fundamental Science and Engineering, Waseda University and also now with the National Institute for Materials Science, Ibaraki, 305-0047 Japan. SHINSUKE SUZUKI is with the Graduate School of Fundamental Science and Engineering, Waseda University and also with the Kagami Memorial Research Institute of Materials Science and Technology, Waseda University, Tokyo, 162-0051 Japan. YOSHIMI WATANABE is with the Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, 4668555 Japan. SHIZUKA NAKANO and NAOKO SATO are with the National Institute of Advanced Industrial Science and Technology, Ibaraki, 305-8564 Japan. Manuscript submitted January 18, 2019. Article published online May 9, 2019 3174—VOLUME 50A, JULY 2019

model of two-dimensional lattices (plane disregistry d) is often used. However, the physical meaning of this model is unclear. Therefore, the parameter M is used,[5] which is defined as 2 M ¼ e21 þ e22 þ e1 e2 : 3

½1

The symbols e1 and e2 are the principal misfit strains on the interface between the matrix material and heterogeneous nucleus in two directions. The parameter M is approximately proportional to the elastic strain energy caused by misfit strains around the interface. A crystallographic orientation relationship with small M values can easily appear. Therefore, the material with small M values can work as an effective heterogeneous nucleus. Ti6Al4V is one of the most widely used titanium alloys. It is applied as a biomaterial[6] or raw material for additive manufacturing.[7] Therefore, the method whereby the grain structure of Ti6Al4V products is controlled from anisotropic to isotropic by adding the heterogeneous nucleus can be applied in many industrial fields. Considering the parameter M, TiC is suitable as the heterogeneous nucleus for Ti6Al4V (M: 12.0 9 103).[8] Previous studies on grain refiners clarified that some materials act as the heterogeneous nucleus in Al alloys,[9,10] but did not clarify the suitable materials and amount for the heterogeneous nucleus in a directionally solidifi