Determining the translational and internal temperatures of isolated metal clusters: A comprehensive approach based on molecular-beam-deflection experiments

Abstract

An approach to translational, rotational, and vibrational temperatures of small metal clusters (${\mathrm{Ga}}_{M}{\mathrm{Sn}}_{N}, M=0,1$ and $N=6--16$) in a molecular beam from a cryogenically cooled laser vaporization source is presented. The velocity distribution in the molecular beam is measured with a mechanical shutter at a fixed photoionization delay which gives an estimate of the lower bound of the translational temperature ${T}_{\text{trans}}$. These values of ${T}_{\text{trans}}$ are found to be considerably smaller than the corresponding nozzle temperatures ${T}_{\text{nozzle}}=16--300\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The rotational temperature ${T}_{\text{rot}}$ is estimated from the comparison of an electric deflection experiment with molecular dynamics simulations and from magnetic deflection experiments to be in the range ${T}_{\text{rot}}=5--20\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for ${T}_{\text{nozzle}}=16\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The vibrational temperature ${T}_{\text{vib}}$ is studied by comparing magnetic deflection experiments with a microscopic model based on avoided level crossings between vibrational, rotational, and Zeeman energy levels. For ${T}_{\text{nozzle}}\ensuremath{\ge}50\phantom{\rule{0.16em}{0ex}}\mathrm{K}, {T}_{\text{vib}}\ensuremath{\approx}{T}_{\text{nozzle}}$ is observed, while for lower temperatures, ${T}_{\text{vib}}>{T}_{\text{nozzle}}$. Thus, ${T}_{\text{trans}}\ensuremath{\le}{T}_{\text{rot}}<{T}_{\text{vib}}$ is found at least for $N=11,12$ and the lowest nozzle temperature of 16 K.