Guide to files / folders in this data entry: 1. "Heat_Capacity" 2. "LFA_diffusivity" 3. "Machine_learning_data" 4. "Powder_diffraction_patterns" 5. "Probe_structures" Data used to construct the convex hulls used in this work. Contains two folders, for the Y-Ba-Ti-O and Y-Sr-Ti-O phase fields. Each folder contains folders labelled 1 to n, where n is the number of compositions at which probe structures were calculated, along with a folder labelled "ICSD_structures". The numbered folders each contain the structures generated by MC-EMMA (YBaTiO) or FUSE (YSrTiO) as optimised with density functional theory, with the lowest energy structure used for the convex hull and an empty text file, to denote the composition of the set of probe structures. ICSD_structures contains the previously known materials which were used in creating the convex hull. Additoinally each of the YBaTiO_hull and YSrTiO_hull folders contains a file "hull.csv" which contains the convex hull computed in this work. 6. "Raman" 7. "SEM" 8. "Thermal_conductivity" 9. CIFs This folder contains the powder crystallographic information files (CIFs) for the commensurate approximant and modulated solutions for Ba10Y6Ti4O27 refined against the I11 data. 10. Property Calculations for Ba10Y6Ti4O27 This folder contains the VASP files used in the phonon calculations in thie work