Orthorhombic CaFe2O4-structured (Cf) Na-rich aluminous silicate (space group Pbnm) is a major mineral of metabasaltic rocks at lower mantle conditions and can, therefore, significantly affect the physical properties of subducted oceanic crusts. We attempted to synthesize single crystals of Cf-type phases in the systems NaAlSiO4, NaAlSiO4-MgAl2O4, NaAlSiO4-MgAl2O4-Fe3O4, and NaAlSiO4-MgAl2O4-Fe3O4-H2O at 23-26 GPa and 1100-2200 degrees C. Under dry conditions, single crystals of Cf-type phase up to 100-150 mu m in size were recovered from 23 GPa and 2000-2200 degrees C. Single-crystal X-ray diffraction and composition analyses suggest that the synthesized Cf-type phases have a few percent of vacancies in the eightfold-coordinated site with Na, Mg, and Fe2+ and partially disordered Al and Si in the octahedral sites. Iron-bearing Cf-type phases have 32-34% Fe3+ that is hosted both in the octahedral sites and in the eightfold-coordinated site. In NaAlSiO4-MgAl2O4-Fe3O4-H2O system, no formation of Cf-type phase was observed at 24 GPa and 1100-2000 degrees C due to the formation of hydrous Na-rich melt and Al-rich oxides or hydroxides, suggesting the possible absence of Cf-type phase in the hydrous basaltic crust. The single-crystal syntheses of Cf-type phases will be useful for investigating their physical properties, potentially improving models of lower mantle structure and dynamics.