Application of M\"{o}ssbauer effect to study subnanometer harmonic displacements in a thin solid

We measure subnanometer displacements of thin samples vibrated by piezotransducer. Samples contain $^{57}$Fe nuclei, which are exposed to 14.4 keV $\gamma$-radiation. Vibration produces sidebands from a single absorption line of the sample. The sideband intensities depend on the vibration amplitude and its distribution along the sample. We developed a model of this distribution, which adequately describes the spectra of powder and stainless steel (SS) absorbers. We propose to filter $\gamma$-radiation through a small hole in the mask, placed before the absorber. In this case only a small spot of the vibrated absorber is observed. We found for SS foil that nuclei, exposed to $\gamma$-radiation in this small spot, vibrate with almost the same amplitudes whose difference does not exceed a few picometers.