The number densities of hematite crystals, N_XL  = 8.7 ± 2 × 10 ⁵  mm ⁻³ , are orders of magnitude larger than the BNDs (Fig.  3 ): about 2 orders of magnitude in the 1,000 kPa/s series, and up to 4 orders of magnitude in the 27.8 kPa/s series. .

As the bubbles in our samples are 10–100 times larger than the hematite crystals (Fig.  3 ), we have no direct insight into the shape of the substrates on which bubbles nucleated.

In our experiments, N was not controlled by N_XL for two reasons: (1) the numbers of bubbles are two orders of magnitude smaller than the numbers of crystals in the 1,000 kPa/s series ( N_XL  = 8.7 ± 2 × 10 ⁵  mm ⁻³ ; Figs.  2 , 3 ), and four orders of magnitude smaller in the 27.8 kPa/s series and (2) as the number density of crystals is the same in the two series, a control of N by N_XL cannot account for the strong correlation between N and $$ \left| {\left.