A pure crystallogeometrical approach is proposed for predicting orientation relationships, habit planes and atomic structures of the interfaces between phases, which is applicable to systems of low-symmetry phases and epitaxial thin film growth. The suggested models are verified with the example of epitaxial growth of -,and -FeSi 2 silicide thin films on silicon substrates. The density of near-coincidence sites is shown to have a decisive role in the determination of epitaxial thin film orientation and explains the superior quality of -FeSi 2 thin grown on Si(111) over Si(001) substrates despite larger lattice misfits. Ideal conjunctions for interfaces between the silicide phases are predicted and this allows for utilization of a thin buffer -FeSi 2 layer for oriented growth of -FeSi 2 nanostructures on Si(001). The thermal expansion coefficients are obtained within quasi-harmonic approximation from the DFT calculations to study the influence of temperature on the lattice strains in the derived interfaces. Faster decrease of misfits at the -FeSi 2 (001)||Si(001) interface compared to -FeSi 2 (001)||Si(001) elucidates the origins of temperature-driven change of the phase growing on silicon substrates. The proposed approach guides from bulk phase unit cells to the construction of the interface atomic structures and appears to be a powerful tool for the prediction of interfaces between arbitrary phases for subsequent theoretical investigation and epitaxial film synthesis. M. A. Visotin et al. -, -, -FeSi 2 and Si phases 471 research papers Acta Cryst. (2020). B76, 469-482 M. A. Visotin et al. -, -, -FeSi 2 and Si phases 473 research papers Acta Cryst. (2020). B76, 469-482 M. A. Visotin et al. -, -, -FeSi 2 and Si phases 479 Figure 6Temperature dependence of interface strain" " for different silicon||silicide and silicide||silicide ORs from Table 1. research papers Acta Cryst. (2020). B76, 469-482 M. A. Visotin et al. -, -, -FeSi 2 and Si phases 481