Single crystal growth of $BaFe_{12}O_{19}$ by the solid state crystal growth method was attempted. Seed crystals of ${alpha}-Fe_2O_3$ were pressed into pellets of $BaFe_{12}O_{19}$ + 2 wt% $BaCO_3$ and heat-treated at temperatures between $1150^{circ}C$ and $1250^{circ}C$ for up to 100 hours. Instead of single crystal growth taking place on the seed crystal, BaO diffused into the seed crystal and reacted with it to form a polycrystalline reaction layer of $BaFe_{12}O_{19}$. The microstructure, chemical composition and structure of the reaction layer were studied using scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS), x-ray Diffraction (XRD) and micro-Raman scattering and confirmed to be that of $BaFe_{12}O_{19}$. XRD showed that the reaction layer shows a strong degree of orientation in the (h00)/(hk0) planes in the sample sintered at $1200^{circ}C$. $BaFe_{12}O_{19}$ layers with a degree of orientation in the (hk0) planes could also be grown by heat-treating an ${alpha}-Fe_2O_3$ seed crystal buried in $BaCO_3$ powder.