*3.4. OH-Stretching Modes at High Temperature*

The selected high-temperature FTIR spectra for R503 are shown in Figure 7A in the temperature range up to 1150 K (Figure S5 for other coesite samples). The IR signal became weaker and broader at a higher temperature, which might be caused by rapid proton hopping between adjacent O atoms [55,56], as well as a black body radiation effect. Above 700 K, the broadened OH-stretching modes of *v*1, *v*2a,b, and *v*<sup>3</sup> (in the frequency range of 3450–3600 cm−1) merge to be a broad hump and could not be distinguished from each other. The weak and discrete *v*<sup>4</sup> band (around 3300 cm<sup>−</sup>1) vanishes very quickly and cannot be detected above 500 K. Another FTIR spectrum was collected when quenched to room temperature, and all these four OH-stretching bands could be clearly identified at the same positions as before heating (Figure 7B). The integrated absorbance for all these OH modes is about 80% of that before heating, and then 20% of the OH groups in the sample could be dehydrated during the heating procedure up to 1150 K. On the other hand, 30–40% dehydration was also observed for

other samples at temperatures of up to 1000–1100 K, by comparing the integrated IR absorbance of the OH-stretching modes before and after heating. Meanwhile, Liu et al. [19] also conducted high-*T* FTIR measurement on hydrous coesite, and they observed noticeable dehydration above 870 K as well as completed dehydration at the temperature of 1473 K. In addition, we also conducted reflectance FTIR measurements [56,57] on these coesite samples. Nevertheless, due to the low water contents, the signals are significantly weaker as compared with those collected in the transmission method at ambient condition, and the OH bands could not be observed in the reflectance IR spectra above 500 K.

**Figure 7.** (**A**) Representative spectra for the sample of R503 at elevated temperatures; (**B**) comparison of the OH-stretching bands measured before and after heating.

Variations of the OH bands with temperature are plotted in Figure 8A–D for samples R503, R663, R694, and R749. Throughout the high-*T* measurments, the modes of *v*2a,b, *v*3, as well as *v*<sup>6</sup> (for B-doped samples of R663 and R712) were observed to show a 'blue-shift' with a slope (δν*i*/δ*T*)*<sup>P</sup>* of +0.01 to about <sup>+</sup>0.20 cm−1·K<sup>−</sup>1, whereas a slight 'red shift' is detected for the *<sup>v</sup>*<sup>1</sup> mode (at a high frequency of around

3600 cm−1) with a temperature derivative of –0.08 to about –0.20 cm−1·K−1. Above 600–700 K, these OH vibrations cannot be distinguished from each other, and the broad hump is observed to gradually move to a higher frequency at a higher temperature, with a temperature dependence of +0.05 to about <sup>+</sup>0.09 cm−1·K<sup>−</sup>1. In addition, the *<sup>v</sup>*<sup>4</sup> mode also shows a 'blue shift' with temperature increasing to below 500 K.

**Figure 8.** The frequencies of the OH-stretching modes as a function of temperature for the samples of (**A**) R503, (**B**) R663, (**C**) R694, and (**D**) R749. Linear regression lines are fitted (Table S3), and the vertical error bars represent the full-width of half maximum for each OH-stretching mode.

The OH-stretching modes observed in this study (in the frequency range above 3300 cm−<sup>1</sup> with O...O distance of >2.74 cm−1) should be attributed to protonation outside SiO4 tetrahedra with the OH bonds pointing away from the centers of the tetrahedra [24–26]. The oxygen anion, that belong to different SiO4 tetrahedra, may try to get away from each other during the thermal expansion and relaxation procedure at high temperature (i.e., the O...O distance between tetrahedra becomes larger). Consequently, we observe a 'blue shift' for most of the OH-stretching bands in the high-temperature FTIR measurements. On the other hand, Koch-Müller et al. [25] reported that some other OH-stretching modes (*v*7, *v*8, *v*9, and *v*<sup>10</sup> in the wavenumber range of 3370–3470 cm<sup>−</sup>1) shift to higher frequencies at a high pressure of up to 10 GPa.
