**2. Experimental method**

The samples were prepared by a conventional solid-state reaction method. The raw materials were powders of K2CO3, Na2CO3, Li2CO3, Nb2O5, CaCO3, TiO2, BaCO3, ZrO2, Co3O4, Fe2O3, and ZnO with a purity of more than 99%. Here, K1–*x*Na*x*N, NTK, and BZ refer to (K1– *<sup>x</sup>*Na*x*)0.86Ca0.04Li0.02Nb0.85O3–δ, K0.85Ti0.85Nb1.15O5, and BaZrO3, respectively. At the outset, hygro‐ scopic powders of K2CO3, Na2CO3, and Li2CO3 were dried in an oven at 150°C for 2 h to ensure accurate weighing. The masses of K1–*x*Na*x*N, NTK, and BZ corresponding to their respective composition formulas were weighted out, after which the materials, were calcined at 930°C in air for 4 h.

The calcined powders were again weighed assuming the chemical formula 0.92K1–*x*Na*x*N– 0.047NTK–0.023BZ–0.0017Co3O4–0.002Fe2O3–0.005ZnO (*x* = 0.51) and 0.910K1–*x*Na*x*N– 0.042NTK–0.036BZ–0.0016Co3O4–0.0025Fe2O3–0.0069ZnO (*x* = 0.33, 0.42, 0.50, 0.56, 0.58, 0.61, 0.67, 0.71, and 0.75).

The weighed powders were mixed with a ball mill for 15 h and then re-calcined at 930°C in air for 4 h. The dispersant and binder were added to the calcined powder, and the mixture was ball-milled for 15 h. The slurry was filtered through a 25 μm mesh sieve and dried, and the dried powder was classified with a 250 μm mesh sieve. The classified powders were pressed into discs under a uniaxial pressure of 200 kg/cm2 . The samples were sintered in air at 1150°C for 4 h, following which they were polished and silver electrodes were painted onto both surfaces of the samples. The samples used for electrical properties measurements were 35 mm in diameter and 2 mm in thick for *x* = 0.51, and 15 mm in diameter and 1 mm in thick for *x* = 0.33, 0.42, 0.50, 0.56, 0.58, 0.61, 0.67, 0.71, and 0.75 for the planar and thickness vibration modes. For the transverse-, longitudinal-, and shear-vibration mode, the samples dimensions were, 23 × 3 × 0.15 mm, 2.2 mm in diameter and 8 mm in thick, and 7 × 2 × 0.2 mm, respectively. The samples were polarized for 30 min in silicone oil under an electric field of 6 kV/mm at 80°C.

The piezoelectric properties of 1-day-old samples were measured using the resonance– antiresonance method with Hewlett-Packard 4194A impedance analyzer. The mechanical characteristics of 3 × 4 × 40 mm were evaluated according to the Japan Industrial Standard R 1607.

XRD samples were prepared by grinding particles with a 10 μm initial diameter in a Si3N4 mortar. The resulting fine powder was sealed in a 0.3 mm diameter Lindemann glass capillary. XRD measurements were done at the BL19B2 beam line of SPring-8 synchrotron, which is equipped with a Debye–Scherrer camera. The incident X-ray wavelength was estimated to be 0.69948 Å by calibration with a standard CeO<sup>2</sup> specimen. The crystal structure was analyzed by Rietveld refinement with the help of the RIETAN-2000 code [30]. The profile parameters were refined using the split-type Pearson VII function [31], and partial profile relaxation was applied to the diffraction peaks from the domain-wall planes. The values reported by Waas‐ maier and Kirfel [32] were used to correct for dispersion.

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) data were acquired using a PHI TRIFT V nano TOF with a 30 keV Bi3 ++ primary ion source in pulsed mode. For each spectrum, the area analyzed is 50 × 50 μm. The mass resolution (m/Δm) typically exceeds 4000 for the (m/ z) 27 peaks in the positive ion spectra. Positive ion spectra were mass calibrated using CH3 + , C2H5 + , and C3H7 + fragments.

For TEM analysis, the samples were cut into 3 mm in diameter discs, polished to a thickness of approximately 50 μm and dimpled to approximately 10 μm thick at the disc center. The specimens were prepared by ion milling with 2–4 keV Ar ions incident at an angle of 4° with respect to the normal to the sample surface. High-resolution TEM observations were made using a TOPCOM EM-002B TEM equipped with an energy dispersive X-ray spectrometer (EDS) with a 200 keV accelerating voltage. To acquire the SAD patterns, we used a 200 nm diameter aperture.
