The near-field evanescent microwave microscope is based on a coaxial transmission line resonator with a silver-plated tungsten tip protruding through an end-wall aperture. The sensor is used to measure local dielectric properties of thin-film YBa2Cu3O7−δ deposited on three different SrTiO3 bi-crystal substrates having mismatch grain boundary angles of 3°, 6°, and 12°. The measurements in the superconducting state are below critical temperature at T = 79.4 K. The dielectric property of the superconductor within the near field of the tip frustrates the electric field and measurably changes the transmission line's resonant frequency. The shift of the resonator's frequency is measured as a function of tip–sample separation and associated changes in quality factor (ΔQ) image scans of the thin film are presented. A quantitative relationship between the real and imaginary parts of the local dielectric constant and the frequency shift using the method of images is established. The comparison between experimental data and theory based on this method is given and discussed. Raman measurements of the intergranular strain within the YBa2Cu3O7−δ thin film deposited on each SrTiO3 substrate in the region of the bi-crystal junction showed excellent correlation between grain boundary mismatch and induced grain boundary strain. Compressive strains normal to the aaxis (i.e. tensile strains normal to the b axis) were detected across the grain boundary. The magnitude of induced strain as well as its spread away from the grain boundary increased as the mismatch angle increased.
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