*3.1. Hydration and B*/*Al Concentrations*

The representative FTIR spectra for these synthetic coesite samples at ambient condition are shown in Figure 1. Four OH-stretching bands of *v*<sup>1</sup> (3572 cm−1), *v*2a,b (3522 cm−1), *v*<sup>3</sup> (3458 cm−1), and *v*<sup>4</sup> (3300 cm<sup>−</sup>1) are detected for all these synthetic samples, which are independent of presence of B or Al. The mode *v*<sup>6</sup> (3500 cm−1) is clearly observed with most absorbance for the B-doped samples (R663, R694, R712), as compared to the B-free samples (R503 and R749), which is caused by B-substitution in coesite (Si4<sup>+</sup> = B3<sup>+</sup> + H+) [25]. It should be noted that the B concentrations in this study are much higher than those synthesized in Koch-Müller et al. [25] (BR01-03), and the *v*<sup>6</sup> absorbance is consequently significantly stronger than that for *v*2a,b.

The total H2O content in coesite (*C*H2O, wt%) can be calculated on the basis of Lambert–Beer law [24]:

$$\mathcal{C}\_{\text{H2O}} = \frac{1.8 \times A\_i}{\rho \times \varepsilon\_i \times d'} \tag{1}$$

where ρ is density (2.93 g/cm3), *d* is the thickness of sample (cm−1), while ε*<sup>i</sup>* is the integrated molar absorption coefficient for H2O, which was calibrated to be 190000 <sup>±</sup> 30000 L·mol−1·cm−<sup>2</sup> for coesite [24]. The integrated absorbance *Ai* in the wavenumber range from *v*<sup>1</sup> to *v*<sup>2</sup> is expressed as

$$A\_{\bar{l}} = \int\_{v\_1}^{v\_2} \log\left(\frac{I\_0}{I}\right) \cdot dv \tag{2}$$

where *I*<sup>0</sup> and *I* are the intensities of incoming and transmitted radiation, respectively. For each coesite sample, several unoriented crystal pieces were selected and polished for FTIR measurement at room temperature, and similar *Iv*3/*Iv*<sup>1</sup> and *Iv*2/*Iv*<sup>1</sup> intensity ratios are observed among these FTIR spectra. The averaged hydration concentrations are listed in Table 1 with statistical uncertainties.

**Figure 1.** Representative FTIR spectra obtained at ambient conditions with the OH-stretching bands noted.

The hydration concentrations in these synthetic samples show a general trend: R663 (B-doped) > R503 (B,Al-free) > R694/R712 (B,Al-doped) > R749 (Al-doped). This observation can be satisfactorily interpreted as results of different incorporation mechanisms between B and Al in coesite. The predominant B-substitution mechanism in coesite should be an electrostatically coupled substitution Si4<sup>+</sup> = B3<sup>+</sup> + H<sup>+</sup> [25], which could increase hydration solubility, as compared with the Si-pure sample R503. In contrast, most of Al cations were incorporated into the internal structure of coesite by causing oxygen vacancies (2Si4<sup>+</sup> = 2Al3<sup>+</sup> + OV), which is similar to the Al-substitution mechanism in stishovite [36,37]. Such Al-corporation may have an effect of reducing water solubility in coesite, according to the estimated water content in the sample R749. In the case of R749, the atomic concentration ratio of Al:H reaches more than 24:1, while in the B,Al-doped samples (R694 and R712), the sums of B and Al atomic concentrations are still four or five times of that for hydrogen. In addition, we also tried to collect Raman spectra on these samples in the similar frequency range of 3200–3700 cm<sup>−</sup>1, but no OH-stretching modes were detected due to the low water concentrations (no more than 60 ppmw).

The magnitudes of the B/106Si and Al/106Si concentrations in this study are about one order of magnitude higher than those (BR01, BR02, BR03, and BRcal2) from Koch-Müller et al. [25], whereas the magnitudes of the measured water contents from both studies are in the same range (H/106Si in a few hundred atomic ppm). The synthetic conditions (including pressure, temperature, heating duration, as well as excessive B and Al in the starting materials) are similar or comparable for both studies, while the main difference is that the Ni:NiO buffer was adopted in Koch-Müller et al. [25] to control water (oxygen) fugacity. However, it should be also noted that Deon et al. [26] also synthesized a coesite sample with 1600 atomic ppm B (B/106Si) and 900 atomic ppm H (H/106Si), both of which are even higher than those in our sample R663, at a *P-T* condition of 9.1 GPa and 1673 K.

Hence, the B and Al solubilities in coesite at high *P*-*T* conditions still need to be carefully examined, and the effect of oxygen fugacity should also be taken into consideration. What is more important, Koch-Müller et al. [25] measured B and Al concentrations by ion microprobe [38], whereas we used fs-LA–ICP-MS in this study, as well as EPMA to cross check the Al content in the sample R749. Hence, discrepancies between different analytical methods in different laboratories should also be considered.
