Figure 1

(a) EELS spectra acquired at the center of bubbles of different size (thick lines) and corresponding fit of the Pd plasmon (thin lines). (b) Subtracted He signal. The shift of the He $K$-line for bubbles of different size is obvious. Note that bubble B8 in Fig. 2 seems to be empty (the mean He signal is very close to zero). In this case, the analysis of the subtracted spectrum indicates that the adopted background subtraction does not introduce significant artifacts on the He signal.Reuse & Permissions

Figure 2

Maps extracted from a spectrum-image of a selected area of the sample. (a) Bright field image of the analyzed area. Bubbles showing He signal are evidenced. (b) Helium chemical map. (c) Map of the He density inside the He filled bubbles. (d) Map of the energy shift of the He $K$-line. The reference energy is chosen as that of the atomic He (21.218 eV).Reuse & Permissions

Figure 3

(a) Experimental relation between energy shift and measured density. Empty squares represent uncorrected density value; linear fit law: $\Delta E=(0.044\pm 0.007)n+(0.07\pm 0.18)$. Filled square represent density value corrected by surface effects; linear fit law: $\Delta E=(0.037\pm 0.004)n+(0.08\pm 0.10)$. Error bars correspond the standard deviation calculated on the selection of pixels of the density map, and therefore are large for small bubbles having a bad statistics. (b) Experimental relation between pressure and the inverse of the bubble radius. Empty circles are deduced from uncorrected density values; linear fit law: $P=(0.6\pm 0.2)\times 1/R+(0.04\pm 0.05)$. Filled circles account for surface effects; linear fit law: $P=(1.0\pm 0.4)\times 1/R+(0.002\pm 0.083)$. The theoretical linear relation for elastic deformation of the ${\mathrm{Pd}}_{90}{\mathrm{Pt}}_{10}$ matrix is also displayed. Error bars are estimated by calculating the variation of the equation of state in the density range defined by the corresponding density error bars. Error bars for corrected values (not shown) are identical to those for uncorrected values.Reuse & Permissions

Figure 4

Experimental profiles of the estimated density ( filled circles) and of the blueshift of the He $K$-line (filled squares) as a function of the mean local thickness $d$. Data are extracted from a spectrum image of $40\times 40$ pixels (spatial sampling of 0.5 nm), acquired on a bubble of 19.5 nm diameter. For comparison, the corresponding simulated profiles of the He $K$ line density (empty circles) and energy position (empty square) are also displayed.Reuse & Permissions