*3.2. Crystal Structures*

The space group of coesite is *C*2/*c*, and SiO4 tetrahedra form an infinite three-dimensional framework of a (*b*-unique) monoclinic structure (Figure 2). There are a total of two Si sites (Si1 and Si2) and five O sites (special O1 and O2 sites, as well as general O3, O4, and O5 ones) in the lattice. The refined crystal structures in this study are consistent with the previous studies [10,39–43]. The measured unit-cell volumes of the B-doped (R663), B,Al-doped (R694 and R712), and Al-doped (R749) samples differ −0.15%, −0.3 to about −0.4%, and +0.1%, away from that for the Si-pure one (R503), respectively, while such differences are significantly larger than the experimental uncertainty from single-crystal XRD. Hence, even a few hundred ppm concentrations of B and Al trace elements could have noticeable impact on the volume of coesite, and a similar phenomenon was also noted by Koch-Müller et al. [25].

**Figure 2.** Crystal structure of coesite sketched on the basis of the structure refinement for the sample R503 in this study. The smaller (at centers of tetrahedra) and larger balls represent Si and O atoms, respectively.

To further investigate any B and Al effects on the internal structure of coesite, we conducted structure refinements on these five synthetic samples. The calculated bond lengths and angles are listed in Table 4, using the software package XTALDRAW [44]. As compared with the Si-pure sample (R503), the B-doped (R663) and B,Al-doped (R694 and R712) ones exhibit significantly shorter Si1–O4 and Si1–O5 bond lengths, while the Al-doped one (R749) shows noticeably longer Si2–O4 and Si2–O5 bond lengths, which are generally consistent with the order of cation sizes of B3<sup>+</sup> < Si4<sup>+</sup> < Al3<sup>+</sup>. The Si2–O3 bond length for R503 is longer than those for other samples. In addition, there are no significant differences for the O–Si–O bond angles among these samples. Hence, we proposed that the B3<sup>+</sup> cations may concentrate in the smaller Si1 tetrahedra, while the Al3<sup>+</sup> cations would prefer the larger Si2 tetrahedra. The B,Al-coupled substitution seems to collapse the lattice structure even more, as compared with the case with only B substitution in coesite.


**Table 4.** Bond lengths (Å), bond angles (◦), and polyhedral volumes (Å3).
