Аннотация:This paper focuses on the quantitative analysis towards the search for suitable lattice-matched substrates, acceptable fluxes for liquid phase epitaxy (LPE) of Yb:YAB thin films. Various inorganic crystals and their solid solutions have been considered as potential substrates. First of all, the structural data were analysed for oxides, silicates, borates, molybdates, tungstates, tantalates and niobates. This analysis was based on the existing structural and physico-chemical database for inorganic oxide compounds. The epitaxial relations were examined for some crystallographic orientations of the Yb:YAB epicrystal and most preferable substrates. Generally, quality of thin films mostly depends on the interfacial energy during heteroepitaxial growth. The film can be grown by two-dimensional, when the lattice mismatch between film and substrate material is relatively small. In the case of the thickness of the epilayer is thinner than the critical thickness, lattice strain generated by misfit is elastically accumulated within the growth layer, and an interfacial layer is formed. If the film thickness exceeds the critical thickness, the introduction of misfit dislocations is energetically favoured rather than the elastic accumulations of misfit strain, and the dislocation relieves some of the strain.