A high-throughput investigation of local epitaxy (called combinatorial substrate epitaxy) was carried out on Ca$_2$MnO$_4$ Ruddlesden-Popper thin films of six thicknesses (from 20 to 400 nm), all deposited on isostructural polycrystalline Sr$_2$TiO$_
4$ substrates. Electron backscatter diffraction revealed grain-over-grain local epitaxial growth for all films, resulting in a single orientation relationship ($OR$) for each substrate-film grain pair. Two preferred epitaxial $ORs$ accounted for more than 90 % of all ORs on 300 different microcrystals, based on analyzing 50 grain pairs for each thickness. The unit cell over unit cell $OR$ ([100][001]$_{film}$ $parallel$ [100][001]$_{substrate}$, or $OR1$) accounted for approximately 30 % of each film. The $OR$ that accounted for 60 % of each film ([100][001]$_{film}$ $parallel$ [100][010]$_{substrate}$, or $OR2$) corresponds to a rotation from $OR1$ by 90$^{circ}$ about the a-axis. $OR2$ is strongly favored for substrate orientations in the center of the stereographic triangle, and $OR1$ is observed for orientations very close to (001) or to those near the edge connecting (100) and (110). While $OR1$ should be lower in energy, the majority observation of $OR2$ implies kinetic hindrances decrease the frequency of $OR1$. Persistent grain over grain growth and the absence of variations of the $OR$ frequencies with thickness implies that the growth competition is finished within the first few si{ anometer}, and local epitaxy persists thereafter during growth.
The local epitaxial growth of pulsed laser deposited Ca$_2$MnO$_4$ films on polycrystalline spark plasma sintered Sr$_2$TiO$_4$ substrates was investigated to determine phase formation and preferred epitaxial orientation relationships ($ORs$) for iso
structural Ruddlesden-Popper (RP) heteroepitaxy, further developing the high-throughput synthetic approach called Combinatorial Substrate Epitaxy (CSE). Both grazing incidence X-ray diffraction and electron backscatter diffraction (EBSD) patterns of the film and substrate were indexable as single-phase RP-structured compounds. The optimal growth temperature (between 650 $^{circ}$C and 800 $^{circ}$C) was found to be 750 $^{circ}$C using the maximum value of the average image quality (IQ) of the backscattered diffraction patterns. Films grew in a grain-over-grain pattern such that each Ca$_2$MnO$_4$ grain had a single $OR$ with the Sr$_2$TiO$_4$ grain on which it grew. Three primary $ORs$ described 47 out of 49 grain pairs that covered nearly all of RP orientation space. The first $OR$, found for 20 of the 49, was the expected RP unit-cell over RP unit-cell $OR$, expressed as [100][001]$_{film}$||[100][001]$_{sub}$. The other two $ORs$ were essentially rotated from the first by 90$^{circ}$, with one (observed for 17 of 49 pairs) being rotated about the [100] and the other (observed for 10 of 49 pairs) being rotated about the [110] (and not exactly by 90$^{circ}$). These results indicate that only a small number of $ORs$ are needed to describe isostructural RP heteroepitaxy and further demonstrate the potential of CSE in the design and growth of a wide range of complex functional oxides.
