Lattice-dynamics and thermal-conductivity calculations were performed using the supercell finite-differences approach implemented in the Phonopy and Phono3py packages. The second-order (harmonic) force constants were computed in a 4 × 2 × 4 expansion of the CTO unit cell (640 atoms), and 4 × 4 × 4 expansions of the STO and BTO primitive unit cells (640/320 atoms). Atom-projected phonon density of states (PDoS) curves were computed by interpolating the phonon frequencies onto regular Γ-centred q q q-point grids with 12 × 12 × 12 subdivisions using the linear tetrahedron method for Brillouinzone integration. Phonon dispersions were obtained by evaluating the frequencies at strings of q q q points passing through the highsymmetry points in the respective Brillouin zones. Non-analytical corrections to the dynamical matrices at q q q → Γ were included using the approach in Ref. using Born effective-charge tensors Z Z Z * and high-frequency dielectric constants ε ε ε ∞ computed us- Atom colours: Ca -blue; Sr -yellow; Ba -orange; Ti -grey; O -green. These images were prepared using the VESTA software. ing the density-functional perturbation theory (DFPT) routines in VASP. The third-order (anharmonic) force constants were computed in a 2 × 1 × 2 expansion of the CTO unit cell (80 atoms) and 2 × 2 × 2 expansions of the STO and BTO primitive cells (80/135 atoms). The lattice thermal conductivities were then computed within the single-mode relaxation-time approximation (SM-RTA) by combining the second-and third-order force constants to obtain modal heat capacities C λ , group velocities ν ν ν λ and lifetimes τ λ on uniform Γ-centered 8 × 8 × 8 q q q-point sampling meshes. This mesh was chosen based on explicit testing to converge the average of the three diagonal components of the κ κ κ latt tensors, κ ave , to within 5% of the values obtained with larger sampling meshes. Electronic transport calculations were performed using the AMSET code. Accurate band gaps E g were obtained using non self-consistent calculations with the HSE06 hybrid functional, where a single-point energy calculation with PBE 51 is performed to obtain a set of Kohn-Sham orbitals and the band energies recalculated with HSE06 without updating the orbitals. Uniform band-structure calculations were then performed with PBEsol and denser 8 × 8 × 4, 10 × 10 × 6 and 8 × 8 × 8 k k k-point meshes for CTO, STO and BTO, respectively, and the bandgaps increased to the HSE06 values using appropriate scissors operators. These meshes were further interpolated to a ∼30 × higher density when calculating the transport properties.