Fig. 2.

Fast Fourier transform (FFT) spectra and quality factors $Q_{\mathrm{br}}$ of Au nanoplate vibrations on Lacey carbon films. a Thickness-dependent breathing mode vibrations. b Quality factors $Q_{\mathrm{br}}$ for the different nanoplates. The average quality factor is 180 ± 26, where the error is the standard deviation. For comparison, $Q_{\mathrm{br}}$ is 10 ± 3 for Au nanoplates on glass substrates. The solid line on top of the shaded area corresponds to mechanical vibration quality factor $Q=k_{\mathrm{B}}{T}_{\mathrm{room}}∕h{f}_{\mathrm{br}}$. Note that the quality factors were retrieved by fitting to Eq. (1), not from the FFT analysis