*3.3. Lattice Vibrations and Grüneisen Parameters* γ*iP*

The Raman spectra measured at ambient condition (in the frequency range up to 1200 cm−1) are shown in Figure 3 for these synthetic samples. The fitted peak positions are listed in Table S2, and the vibrational bands at 521 cm−<sup>1</sup> are always detected with most intensity. The Raman spectra are essentially the same among these coesite samples, while the most noticeable difference is that for the Al-doped samples (R694, R712, and R749). The intensities of the Raman modes at 151 and 178 cm−<sup>1</sup> are relatively stronger and even comparable to the one at 119 cm<sup>−</sup>1, as compared with those for the Al-free samples (R503 and R663). There are a total of 33 Raman-active modes (16 Ag(R) + 17 Bg(R)) as well as 36 IR-active modes (18 Au(IR) + 18 Bu(IR)) predicted for coesite [16,17], while fewer peaks are detected in this Raman measurement.

**Figure 3.** Raman spectra obtained at ambient condition for these synthetic coesite samples.

Next, we carried out in-situ high-temperature Raman experiments on the Si-pure (R503), B-doped (R663), Al-doped (R749), and B,Al-doped (R712) samples, as well as low-temperature measurement on R503. The representative Raman spectra for R503 at various temperatures are shown in Figure 4A as an example, while the high-*T* spectra for other coesite samples are deposited in the supplementary Figure S1 (See Supplementary Materials). The R503 sample was heated up to the temperature of 1500 K, and no phase transition was detected throughout the heating procedure. Although the signals got weaker and the background radiation became stronger especially at high temperatures above 1300 K, most of the Raman peaks could still be distinguished and fitted at the high temperatures. Another spectrum was recorded when the temperature was quenched to room temperature, and no clear shifts were observed among these Raman bands compared with those before heating (Figure 4B). Meanwhile, Bourova et al. [11] superheated a coesite sample to the temperature of 1776 K (at ambient pressure), which was 900 K higher than the predicted metastable melting point [45], and the coesite sample remained stable without any significant phase transition, melting, or amorphization. On the other hand, Liu et al. [19] reported amorphization of a hydrous coesite sample at a relatively low temperature of 1473 K. (See Supplementary Materials).

**Figure 4.** (**A**) Selected Raman spectra for the sample of R503 at various temperatures; (**B**) comparison of the Raman spectra taken before and after heating.

Variation of these Raman-active modes for R503 is plotted as a function of temperature in Figure 5A–C, and the data points at low temperatures are in consistence with those at high temperatures (Figures S2–S4 for R663, R712, and R749, individually). All these bands systematically shift to a lower frequency at elevated temperature, and linear regression was fitted to each mode with the negative slopes (δν*i*/δ*T*) (at *P* = 0 GPa) (Table S2). The values of (δν*i*/δ*T*)*<sup>P</sup>* are typically in the range of −0.01 to about <sup>−</sup>0.03 (cm−1·K−1) for the modes below 350 cm−<sup>1</sup> or above 700 cm−1, while <sup>−</sup>0.002 to about <sup>−</sup>0.007 (cm−1·K<sup>−</sup>1) for the ones in the range from 350 to 700 cm−1. Our result is essentially in agreement with the previous high-temperature Raman studies on SiO2-pure coesite [17,46].

**Figure 5.** Variation of the frequencies for the Raman-active modes (R503) with temperature, in the frequency ranges of (**A**) 0–400 cm<sup>−</sup>1, (**B**) 400–800 cm<sup>−</sup>1, and (**C**) 800–1200 cm<sup>−</sup>1. Linear regression is fitted for each dataset.

The isobaric mode Grüneisen parameter (γ*iP*) is defined as

$$\gamma\_{iP} = -\frac{1}{\alpha \cdot v\_i} \cdot \left(\frac{\partial v\_i}{\partial T}\right)\_P \tag{3}$$

where <sup>α</sup> is the averaged volumetric thermal expansion coefficient (<sup>α</sup> <sup>=</sup> 8.4 <sup>×</sup> <sup>10</sup>−<sup>6</sup> <sup>K</sup>−<sup>1</sup> for coesite [11]). The calculated γ*iP* parameters are shown in Figure 6A for the samples of R503, R663, R712, and R749. The Raman-active modes above 400 cm−<sup>1</sup> are mostly associated with the internal bending and stretching vibrations of SiO4 tetrahedra linked in a three-dimensional framework for coesite [17,19,47]. The corresponding γ*iP* parameters (1.4–3.2) are systematically larger than those internal modes (0–1.4) for isolated SiO4 units as in forsterite (Mg-pure olivine) [48,49] and pyrope garnet [50], as well as a one-dimensional Si2O6 chain as in enstatite (MgSiO3-orthorpyroxene) [51], which are the most abundant minerals in the upper mantle above 410-km seismic discontinuity. Although the magnitudes of the (δν*i*/δ*T*)*<sup>P</sup>* slopes are similar among these studies, the thermal expansion coefficient for coesite [11] is much smaller as compared with these silicate minerals [52–54]. On the other hand, for the bands below 350 cm<sup>−</sup>1, which are typically attributed to the external vibrations of SiO4 tetrahedra in coesite, the values of γ*iP* Grüneisen parameters are distributed in a much wider value range from −5 to 20.

Next, the differences of the γ*iP* parameters among the samples of R663, R712, R749, and R503 (reference) are plotted in Figure 6B. The most significant difference is that in the frequency range below 350 cm<sup>−</sup>1, the γ*iP* parameters for the Al-doped samples (R712 and R749) are systematically lower than those for the Al-free ones (R503 and R663), while no such differences are observed above 400 cm−1. When the Al3<sup>+</sup> cations take the place of Si4<sup>+</sup> in the tetrahedra, the thermal response of the enlarged tetrahedra units could get hindered to some extent at high temperature, while the smaller B3<sup>+</sup> cations do not show such an effect on the external vibrations of the tetrahedra units in coesite.

**Figure 6.** (**A**) The isobaric mode Grüneisen parameters (γ*iP*) for the synthetic samples of R503, R663, R712, and R749; (**B**) comparison among the γ*iP* parameters with the ones for the sample R503 set as reference.
