Effect of radiative cooling on the size-dependent stability of small boron clusters

The mass spectrum of cationic boron clusters, ${{\mathrm{B}}_N}^{+}$ ($N=5-20$), after photoexcitation demonstrates that radiative cooling is an important, though often neglected, process in determining the relative stability of small and isolated particles. The observed intensities in mass spectra suggest that ${{\mathrm{B}}_5}^{+},{{\mathrm{B}}_{11}}^{+},{{\mathrm{B}}_{13}}^{+}$, and ${{\mathrm{B}}_{15}}^{+}$ are particularly stable clusters, consistent with density-functional theory calculations. Quantitative agreement, however, is only obtained if radiative cooling is included in the analysis. All clusters are found to radiate on microsecond timescales, suggesting recurrent fluorescence as the dominant photon emission process.

Figure 1

Distribution of ${{\mathrm{B}}_N}^{+}$ clusters produced by photofragmentation of neutral species using a focused VUV laser (157 nm). The blue lines are used to visualize the intensity patterns of prompt (quasi-instantaneous) fragments. The prompt ${{\mathrm{B}}_{15}}^{+}$ cluster is marked in the figure, together with its metastable fragments ${{\mathrm{B}}_{14}}^{+}$ and ${{\mathrm{B}}_{13}}^{+}$ produced by monomer and dimer evaporation, respectively.

Figure 2

Monomer (black squares) and dimer (red circles) metastable fractions, extracted from the mass spectrum of Fig. 1.

Figure 3

(a) The metastable fraction $M_N$ versus $\ln \left(t_2/t_1\right)$ for three boron clusters: ${{\mathrm{B}}_9}^{+},{{\mathrm{B}}_{14}}^{+}$, and ${{\mathrm{B}}_{17}}^{+}$. The negative intercept with the ordinate axis shows the presence of radiative cooling. (b) Rates of photon emission of ${{\mathrm{B}}_N}^{+}$ clusters, extracted by fitting Eq. (2) to measured $M_N$ versus $\mathrm{\Delta }t$ curves.

Figure 4

Ratio of dissociation energies extracted from the metastable fractions after photofragmentation. The analysis with and without radiative cooling is presented, together with the values calculated in Ref. [22]. The inset shows a close-up of the figure. Error bars include propagation from the fitting errors of $k_p$ and assuming a 5% uncertainty on the determination of flight times $t_1$ and $t_2$, and a similar value for the frequency factor $\omega$.