The eutectic LiF−LiYF 4 has been solidified by Bridgman and micro-pulling down (mPD) at pulling rates from 4 to 300 mm/h. The microstructure changes from a coupled, interpenetrated-like one to macrofaceted colonies composed of an approximately triangular arrangement of LiF fibers inside the LiYF 4 matrix as the pulling rate increases. The cross-over pulling rate is around 3 times larger for the mPD method, corresponding to its larger solidification gradient. The crystallographic growth direction of the matrix phase was found using EBSD. Effective medium estimations of the THz permittivity of the composite predict around the interphase phonon-polariton resonance (wavelength around 17.5 µm) a small permittivity hyperbolic behavior specific of the ordered composite that is tolerant to different relative orientations. Water etching of polished crosssections constitutes a very simple procedure to generate surface micro-holes of predefined size in the LiYF 4 matrix.