IR Features of Hydrous Mg 2 SiO 4 -Ringwoodite, Unannealed and Annealed at 200–600 ◦ C and 1 atm, with Implications to Hydrogen Defects and Water-Coupled Cation Disorder

: Three batches of Mg 2 SiO 4 -ringwoodites (Mg-Rw) with di ﬀ erent water contents ( C H2O = ~1019(238), 5500(229) and 16,307(1219) ppm) were synthesized by using conventional high- P experimental techniques. Thirteen thin sections with di ﬀ erent thicknesses (~14–113 µ m) for water-related IR peaks using unpolarized infrared spectra at ambient P - T conditions, to the observation of 15 IR peaks at ~3682, 3407, 3348, 3278, 3100, 2849, 2660, 2556, 2448, 1352, 1347, 1307, 1282, 1194 and 1186 cm − 1 . These IR peaks suggest multiple types of hydrogen defects in hydrous Mg-Rw. We have attributed the IR peaks at ~3680, 3650–3000 and 3000–2000 cm − 1 , respectively, to the hydrogen defects [ V Si (OH) 4 ], [ V Mg (OH) 2 Mg Si Si Mg ] and [ V Mg (OH) 2 ]. Combining these IR features with the chemical characteristics of hydrous Rw, we have revealed that the hydrogen defects [ V Mg (OH) 2 Mg Si Si Mg ] are dominant in hydrous Rw at high P - T conditions, and the defects [ V Si (OH) 4 ] and [ V Mg (OH) 2 ] play negligible roles. Extensive IR measurements were performed on seven thin sections annealed for several times at T of 200–600 ◦ C and quickly quenched to room T . They display many signiﬁcant variations, including an absorption enhancement of the peak at ~3680 cm − 1 , two new peaks occurring at ~3510 and 3461 cm − 1 , remarkable intensiﬁcations of the peaks at ~3405 and 3345 cm − 1 and signiﬁcant absorption reductions of the peaks at ~2500 cm − 1 . These phenomena imply signiﬁcant hydrogen migration among di ﬀ erent at high T . From the IR spectra obtained for hydrous Rw both unannealed and annealed at high T , further disproportional e ﬀ ects on the unit-cell volume and thermal expansivity. Z.S., preparing the thin sections, collecting the infrared spectra and preparing drafts of the ﬁgures; H.F., conducting the high- P synthesizing experiments and interpreting the results. W.Y., collecting and interpreting the IR data. Y.M., discussing and interpreting the results. Y.Y., discussing and interpreting the results.


Introduction
It has been widely accepted that ringwoodite (Rw; (Mg,Fe) 2 SiO 4 with a molar Mg/(Mg + Fe) ratio close to~0.9, crystallizing in the spinel structure), with a volume fraction up to~60%, is the major where ε is the molar absorption coefficient. Clearly, for the weakly light-absorbing water species (with small ε), its IR signals can be observed only at high water content or with very thick crystal plate. Under either condition, however, the IR signals of those strongly light-absorbing water species may be already oversaturated, and thus, hard to be correctly observed. This means that crystal plates with a range of appropriate thicknesses should be prepared and investigated in order to obtain a full appreciation of the infrared features of water in Rw. Thirdly, the water content in Rw is usually high and its infrared signals are exceedingly intense, so that crystal plates with thickness down to a few microns may be required for a good infrared spectroscopic observation [67]. This is certainly a hard task to accomplish, especially with those tiny crystals from high-P experiments.
To fully assess the infrared spectroscopic features of water in Rw, we have firstly carried out three high-P experiments to synthesize large Mg 2 SiO 4 -Rw (Mg-Rw) crystals with different amounts of water. The water contents have been determined as 1019(238), 5500(229) and 16,307(1219) ppm (more details presented later), and the crystals have been accordingly named as low-H 2 O Mg-Rw, intermediate-H 2 O Mg-Rw and high-H 2 O Mg-Rw, respectively. We have secondly performed systematic infrared spectroscopic analyses on (1) a series of thin sections prepared from the high-H 2 O Mg-Rw crystals, with the thickness ranging from~14 to 64 µm, (2) a series of thin sections prepared from the low-H 2 O Mg-Rw crystals, with the thickness ranging from~15 to 113 µm and (3) a series of thin sections prepared from the intemediate-H 2 O Mg-Rw crystals, with the thickness varying little (from 52 to 69 µm). We have thirdly annealed at different T (~200-600 • C) for different durations, mainly those thin sections made from the intermediate-H 2 O Mg-Rw crystals, then quickly quenched them to room T and immediately characterized them using infrared spectroscopy. We have also examined these annealed thin sections using a micro-Raman system. With these data, we can fully appreciate the IR features of water in the Mg-Rw crystals, both as-received from conventional high-P synthesizing experiments and as further annealed to different T at 1 atm. It has been found that a large number of differences exist among the IR spectra obtained for hydrous Rw unannealed and annealed at high T. In addition, we have directly observed some of the IR features for the SiO 4 structural units in the Mg-Rw, and derived a method for estimating the thickness of the Mg-Rw thin section.

Synthesizing Mg-Rw Crystals at High P
Three synthesizing high-P experiments, Run 1584, Run 1589 and Run 4753, were conducted at the Bayerisches Geoinstitut, Germany. In these experiments, Pt capsule with starting material loaded was placed into an MgO sleeve, which was in turn placed into a LaCrO 3 furnace surrounded by a ZrO 2 thermal insulator. The standard 18/11 cell assembly at the Bayerisches Geoinstitut, with a Cr 2 O 3 -doped MgO octahedron as pressure medium, was used to generate high P. A W 97 Re 3 -W 75 Re 25 thermocouple was used to measure and control the experimental T. The cell assembly was first compressed to a targeted P at ambient T by employing eight tungsten carbide cubes (truncated edge lengths of 11 mm), and then heated up to a targeted T with a rate of~100 • C/min. After being maintained for a desired amount of heating time at the targeted T, the experiment was quenched to room T by cutting off the heating power and afterwards decompressed to ambient P over~15 h.
Run 1584 was conducted under nominally dry condition, with a P of~22 GPa, a T of 1700 • C and a heating time of 2 h. Its starting material was forsterite single crystals, mixed with some fine CsCl powder. With a direct phase transformation from forsterite to Mg-Rw, this experiment yielded very pure Mg-Rw crystals, with the grain sizes in the range of~150-300 µm. The H 2 O content (C H2O ) has been determined as~1019(238) ppm by using unpolarized transmission infrared spectroscopy (more details later). The Mg-Rw crystals have been named as low-H 2 O Mg-Rw in this study.
Run 1589 was also carried out under nominally dry condition, with a P of~22 GPa, a T of 1700 • C and a heating time of 2 h. Its starting material was forsterite powder, mixed with fine powders of potassium carbonate and magnesium carbonate. This experiment yielded very pure Mg-Rw crystals, with grain sizes in the range of~150-300 µm. The C H2O has been determined as~5500(229) ppm. The Mg-Rw crystals have been named as intermediate-H 2 O Mg-Rw in this study.
Run 4753 was run under wet condition, with a P of~23 GPa, a T of 1500 • C and a heating time of 5 h. Its starting material was a mixture made of MgO, Mg(OH) 2 and SiO 2 powders (with an equivalent water content of~15 wt%). This experiment produced one mega Mg-Rw crystal (up to~1000 µm), some melt and a trace amount of MgSiO 3 -perovskite. The C H2O of the Mg-Rw crystal has been determined as~16,307(1219) ppm. The Mg-Rw crystal has been named as high-H 2 O Mg-Rw in this study.

Preparing Single-Crystal Thin Sections
Clear and fracture-free Mg-Rw crystals from the high-P experimental products were handpicked under an optical microscope, and processed to generate nominally parallel-sided, stand-alone, doubly-polished single-crystal thin sections for later annealing experiments and IR measurements. We followed the general preparation procedure described in Liu et al. [66] and He et al. [68]. The Mg-Rw crystals were firstly mounted to glass slides with crystal-bond by using a hot plate running at~145 • C, secondly manually ground and slowly reduced under an optical microscope to the desired thicknesses by using a series of silicon carbide abrasive sandpaper and thirdly polished well to generate scratch-free surfaces. The resulting thin sections were then immersed in acetone for 15 min to remove the crystal-bond, washed repeatedly in anhydrous ethanol and deionized water and dried in a drying oven at 110 • C.
The relatively small crystal size of the Mg-Rw presented an obstacle for the preparation of really parallel thin sections and usually led to wedged crystal plates. The thickness of the crystal plates was consequently estimated with two methods: one was a direct thickness measurement by using a micrometer (termed as D m hereafter) and the other was an indirect thickness calculation by using the integrated IR absorption in the range of~1850-1500 cm −1 . The IR peaks in this wavenumber range are the combination bands/overtones of the SiO 4 structure units [62], and the absorption can be used to accurately constrain the thickness of the sample precisely at the analyzing spot (discussed further below). In rare cases, interference fringes occurred in the IR spectra acquired from truly parallel thin sections; the thickness could be determined with a third method, as detailed later.

Annealing Single-Crystal Thin Sections at 1 atm
All thin sections prepared from the intermediate-H 2 O Mg-Rw crystals, plus one made from a low-H 2 O Mg-Rw crystal, were annealed at various T for various amounts of time by using a heating platform (Model DB-C600 with a heating capability up to~650 • C). The annealing T varied from 200 to 600 • C. Each thin section was placed in a small thin-walled Pt boat (10 × 10 × 5 mm 3 in size), which was in turn positioned at the hot spot of the heating platform. The uncertainty of the annealing T was presumably less than~5 degrees. After annealed for a desired amount of time, the Pt boat was quickly removed from the heating platform, placed on a large piece of stainless steel plate, and cooled to room T in open air. The whole process might take less than~10 s. The annealed thin section was then picked up under an optical microscope, transported and analyzed by an IR spectrometer. After finishing the IR analyses, the thin section was reannealed and reanalyzed. This experimental procedure might be repeated for several times.

Unpolarized Transmission IR Measurements
The single-crystal thin sections, without or with certain annealing at certain T and 1 atm, were placed on a clean BaF 2 sample holder and subsequently probed at ambient P-T conditions by using a Nicolet iN10 MX IR Microscope installed at the High-Pressure Laboratory of Peking University [65,66]. Unpolarized transmission IR spectra were collected for the data range of 4000-675 cm −1 . In these measurements, we used a high-energy Ever-Glo™ infrared source, a standard KBr beam splitter and an MCT detector that was cooled by liquid N 2 . We chose an aperture size of 40 × 40 µm 2 . We performed 512 scans in every individual analysis and set the spectroscopic resolution as 4 cm −1 , both for the background and for the sample. The IR spectra were processed either by using the OMNIC 8.2 software or by using the Peakfit v4.12 software.

Unpolarized Raman Spectroscopic Characterizations
After completing the IR analyses, some annealed Mg-Rw thin sections were characterized at ambient P-T conditions by using a confocal micro-Raman system in a back-scattering geometry (Renishaw inVia Reflex system) [10,69]. Unpolarized Raman spectrum was collected from 1350 to 100 cm −1 . A 532 nm laser with an emission power of~50 mW and a 50× long-distance objective were used in all analyses. Other analytical conditions were~1 µm light spot, 1 cm −1 spectral resolution and 20 successive scans for every analysis (10 s for each scan).

Quantifying Water Content of Mg-Rw
Rw is an optically isotropic mineral. Its water content can be quantified by using the following equation, which is merely another form of the Beer-Lambert law: where C H2O is the concentration of H 2 O in weight (ppm), A tot is the total integrated absorption, which is calculated as three times the integrated absorption (cm −1 ) in an unpolarized IR spectrum, d is the thickness of the crystal thin section (cm), ρ is the Rw density (g/cm 3 ) and ε tot is the total integrated molar absorption coefficient (L·mol −1 ·cm −2 ). For quantifying the water contents of our Mg-Rw, we used ρ = 3.527 g/cm 3 from Ye et al. (for the Mg-Rw with~0.76 wt% H 2 O) [23], and ε tot = 118,500(5000) L·mol −1 ·cm −2 from Bolfan-Casanova et al. [56]. We integrated the unpolarized IR spectrum in the energy range 3730-2000 cm −1 to derive the integrated absorption, which was in turn multiplied by 3 to obtain the total integrated absorption [56]. Eventually, we have obtained 1019(238), 5500(229) and 16,307(1219) ppm H 2 O for the Mg-Rw crystals from Run 1584, Run 1589 and Run 4753, respectively.

Results and Discussions
The details and results of the ambient unpolarized IR measurements performed on the thin sections prepared from the Mg-Rw crystals, as generated from our conventional high-P experiments, are listed in Table 1. The details and results of the ambient unpolarized IR measurements performed on those successively annealed and quickly quenched Mg-Rw thin sections are listed in Table 2. The infrared spectrum has been numbered as Run #-Crystal #-Spectrum # (e.g., 1584-01-01 in Table 1), with the first term representing a high-P experiment (Run 1584 here), the second term representing a thin section made from an Mg-Rw crystal from that experiment (01 here) and the third term representing an infrared spectrum taken from that thin section (01 here). In total, 13 thin sections were prepared and 56 infrared spectra were collected. In most cases, multiple infrared spectra were taken at different spots of one thin section, annealed or unannealed (Tables 1 and 2). The IR features for water in the Mg-Rw demonstrated by these ambient IR spectra are summarized and compared in Table 3.   (4)). d This thin section has an unusually low water content; however, this does not affect our IR spectroscopic analysis.  --------3120  --2540  -------B00/H892  45/0.78  3695  --------3120  ---2455 1347  Figure 1 shows some IR spectra (~2100-700 cm −1 ) taking from some thin sections with various thicknesses made from some high-H 2 O and low-H 2 O Mg-Rw crystals. The independent variables there are the thickness and the H 2 O content. We have arranged the spectra according to the measured thickness, with D m increasing from the top spectrum (~14 µm) to the bottom spectrum (~113 µm), so that we could readily observe positive correlations between the thicknesses and the absorptions for those IR peaks unrelated to the hydrogen defects. For those IR peaks relevant to the hydrogen defects, any such correlations should be generally masked by the fluctuation of the water content.
Minerals 2020, 10, 499 9 of 32 Figure 1 shows some IR spectra (~2100-700 cm −1 ) taking from some thin sections with various thicknesses made from some high-H2O and low-H2O Mg-Rw crystals. The independent variables there are the thickness and the H2O content. We have arranged the spectra according to the measured thickness, with D-m increasing from the top spectrum (~14 μm) to the bottom spectrum (~113 μm), so that we could readily observe positive correlations between the thicknesses and the absorptions for those IR peaks unrelated to the hydrogen defects. For those IR peaks relevant to the hydrogen defects, any such correlations should be generally masked by the fluctuation of the water content. The IR spectra were taken from some thin sections made from high-H2O Mg-Rw (Run 4753) and low-H2O Mg-Rw (Run 1584). The IR # is followed by the measured thickness of the thin section (D-m in parentheses). Tmin stands for the minimum percentage of the transmitted light for the segment ~1150-700 cm −1 . The only expected fundamental at ~830 cm −1 is denoted by the thick broken line.

Fundamentals, Combinations/Overtones, Thickness Estimates and Water Quantifications
The spectra shown in Figure 1 can be roughly divided into three segments, segment ~1850-1500 cm −1 , segment ~1500-1150 cm −1 and segment ~1150-700 cm −1 . In segment ~1850-1500 cm −1 , there are likely two IR peaks at ~1741 and 1603 cm −1 , with their intensities generally positively correlating with the thickness of the thin sections. They are the combination bands/overtones of the SiO4 structure units in Mg-Rw, as suggested by Bolfan-Casanova et al. [49] and Chamorro Pérez et al. [51]. In the segment ~1500-1150 cm −1 , there are at least four IR peaks at ~1348, 1305, 1280 and 1185 cm −1 (more discussion later), with their intensities erratically correlating with the thickness. Hence, we attribute them to the hydrogen defects in Mg-Rw, as suggested by Bolfan-Casanova et al. [49] and Chamorro Pérez et al. [51]. In the segment ~1150-700 cm −1 , there are potentially many IR peaks with different origins [62]. For the purpose of convenience, we choose to loosely and collectively name them as the fundamentals of the SiO4 structure units in Mg-Rw, although only one fundamental should be expected in this wavenumber range [41,71].
The fundamentals in the segment ~1150-700 cm −1 seem poorly resolved still. Similar to quartz [68], coesite [66] and olivine [65], these vibrational modes in Mg-Rw are very light-absorbing, so that the infrared light has been completely blocked for any thin section with thickness > ~40 μm ( Figure  1). For the thicker thin sections, the minimum percentage of the transmitted light (Tmin) is constantly ~2%-3%, which is definitely an artifact, as discussed by He et al. [68]. When the thickness of the thin sections becomes smaller, the Tmin starts to increase, and the true absorption peaks start to emerge and overall change from a nominally round IR feature to an absorption platform (generally wider than ~200 wavenumbers). From the high-H2O Mg-Rw thin sections, the maximum Tmin observed is The spectra shown in Figure 1 can be roughly divided into three segments, segment~1850-1500 cm −1 , segment~1500-1150 cm −1 and segment~1150-700 cm −1 . In segment~1850-1500 cm −1 , there are likely two IR peaks at~1741 and 1603 cm −1 , with their intensities generally positively correlating with the thickness of the thin sections. They are the combination bands/overtones of the SiO 4 structure units in Mg-Rw, as suggested by Bolfan-Casanova et al. [49] and Chamorro Pérez et al. [51]. In the segment 1500-1150 cm −1 , there are at least four IR peaks at~1348, 1305, 1280 and 1185 cm −1 (more discussion later), with their intensities erratically correlating with the thickness. Hence, we attribute them to the hydrogen defects in Mg-Rw, as suggested by Bolfan-Casanova et al. [49] and Chamorro Pérez et al. [51]. In the segment~1150-700 cm −1 , there are potentially many IR peaks with different origins [62]. For the purpose of convenience, we choose to loosely and collectively name them as the fundamentals of the SiO 4 structure units in Mg-Rw, although only one fundamental should be expected in this wavenumber range [41,71].
The fundamentals in the segment~1150-700 cm −1 seem poorly resolved still. Similar to quartz [68], coesite [66] and olivine [65], these vibrational modes in Mg-Rw are very light-absorbing, so that the infrared light has been completely blocked for any thin section with thickness >~40 µm ( Figure 1). For the thicker thin sections, the minimum percentage of the transmitted light (T min ) is constantlỹ 2%-3%, which is definitely an artifact, as discussed by He et al. [68]. When the thickness of the thin sections becomes smaller, the T min starts to increase, and the true absorption peaks start to emerge and overall change from a nominally round IR feature to an absorption platform (generally wider than 200 wavenumbers). From the high-H 2 O Mg-Rw thin sections, the maximum T min observed is~9.6% (4753-05-01; D m = 14 µm). We believe that this IR spectrum is generally reliable, on the basis of the consistent appearance of the absorption platform in the IR spectra acquired from the thin sections with D m <~40 µm. In contrast, the IR spectra from the low-H 2 O Mg-Rw are rather different, in terms of the shape of the absorption feature and the T min . For example, the spectrum 1584-03-03 collected from the low-H 2 O Mg-Rw thin section with D m = 15 µm seems much comparable to the IR spectrum 1584-01-01 from the low-H 2 O Mg-Rw thin section with D m = 113 µm, rather than similar to the IR spectrum 4753-05-01 from the high-H 2 O Mg-Rw thin section with D m = 14 µm (Figure 1). This strongly implies that the H 2 O content in Mg-Rw has important influence on the fundamentals. The Mg-Rw crystals from Run 1584 have a much lower H 2 O content than those from Run 4753 (1019(238) vs. 16,307(1219) ppm), so that their hydrogarnet substitution, Si 4+ + 4O 2− ↔ [4] (Si) + 4OH − should be much lower [39][40][41][42]45], and their SiO 4 structure units causing the absorption features in the segment 1150-700 cm −1 are correspondingly more abundant.
The fundamentals in the segment~1150-700 cm −1 were previously investigated by a few studies. Akaogi et al. [72] carried out an IR study using a nominally H 2 O-free Mg-Rw powder sample admixed with some KBr (Rw:KBr = 3:250 in weight). However, they did not report the experimental details such as the particle size of the Mg-Rw and the thickness of the probed KBr disc, so that the amount of the Mg-Rw probed by the IR beam was unknown. Hofmeister and Mao [62] collected some absorption data from a nominally H 2 O-free Mg-Rw single-crystal sample, and observed a severe peak intensity saturation (as shown in their Figure 7). The thickness of their crystal plate was not reported, but has been calculated here as~146 µm using the interference fringes around~1100 cm −1 . The used equation in the calculation is: where D c1 is the calculated thickness (cm) of the thin section, n the refractive index of Rw (1.708 for nominally anhydrous Mg-Rw; Binns [73]; Inoue et al. [14]) and ν the wavelength (cm −1 ) of the interference fringes. Both Akaogi et al. [72] and Hofmeister and Mao [62] reported a round IR feature in the energy range~1150-700 cm −1 , which is very similar to what we have observed with our thick thin sections. The results are, thus, highly questionable. Furthermore, Chamorro Pérez et al. [51] and Koch-Müller et al. [74], respectively, investigated the IR features of water-rich Mg-Rw (~1.0-1.7 wt% H 2 O) and water-poor Rw (<~0.61 wt% H 2 O) up to~30 GPa, and reported some high-P data for the fundamentals in the corresponding energy range~1150-700 cm −1 at ambient P. The initial thickness of the sample (with 1.7 wt% H 2 O) in Load 1 of Chamorro Pérez et al. [51] was just 26 µm, and the observed IR feature at all P was an absorption platform with a width >~200 wavenumbers, which is similar to what we have observed from the high-H 2 O Mg-Rw thin sections with D m <~40 µm. The exact thickness of the samples in Koch-Müller et al. [74] was not released. Luckily enough, some of the reported IR spectra display interference fringes around~1500 cm −1 , which can be used to estimate the sample thickness by resorting to Equation (3). For the two series of compression experiments with the MA-120 Rw (0.6 wt% H 2 O), respectively in an annealed argon pressure medium and in an unannealed argon pressure medium, our estimated sample thickness is~41 µm at 0.1 GPa and~34 µm at 13.3 GPa for the former, and~27.5 µm at 0.2 GPa, 26.7 µm at 12 GPa and 25.0 µm at 31.7 GPa for the latter. All the observed IR features did not show broad absorption platforms, similar to our observations made either with the thick thin sections (D m >~40 µm) prepared from the high-H 2 O Mg-Rw or with the thin sections (D m ≥~15 µm) prepared from the low-H 2 O Mg-Rw. It follows that the fundamentals in the energy range~1150-700 cm −1 are generally known for water-rich Mg-Rw, but still unclear for dry or water-poor Mg-Rw.
To quantify the H 2 O contents in our Mg-Rw, accurate thickness estimation is critical. The common absence of interference fringes in the IR spectra both in the literature and in this study suggests that thin sections prepared from tiny crystals tend to be wedged to some extent. As a result, any direct thickness measurement with a micrometer should often yield a maximum value for the entire thin section, which may be significantly larger than the exact sample thickness at the analyzing spot of the IR beam. It is then desirable to develop a method which can be used to calculate the sample thickness directly from an IR spectrum. Apparently, the Mg-Rw IR features in the segment~1850-1500 cm −1 ( Figure 1) can fulfill this duty. Figure 2 plots the integrated absorption data against the measured thickness data for our thin sections ( Table 1). Assuming that the six IR spectra, from 1584-01-01 to 1584-01-06, have well sampled our thickest Mg-Rw thin section (D m = 113 µm), and collecting the data with the highest absorption among them (i.e., the maximum sample thickness and the highest absorption) to the origin (i.e., 0 sample and 0 absorption), we arrive at the following equation: where A is in cm −1 and D c2 is in µm. Theoretically, Equation (4) is equal to Equation (1), with the constant 1.0707 approximating ε SiO4 × C SiO4 . Our assumption is obviously justified because nearly all data, with only a few exceptions at very small thin section thickness, are plotted to the right of the straight line dictated by Equation (4), matching the expectation that D m should be often larger than D c2 . Furthermore, Equation (4)  1500 cm −1 (Figure 1) can fulfill this duty. Figure 2 plots the integrated absorption data against the measured thickness data for our thin sections ( Table 1). Assuming that the six IR spectra, from 1584-01-01 to 1584-01-06, have well sampled our thickest Mg-Rw thin section (D-m = 113 μm), and collecting the data with the highest absorption among them (i.e., the maximum sample thickness and the highest absorption) to the origin (i.e., 0 sample and 0 absorption), we arrive at the following equation: where A is in cm −1 and D-c2 is in μm. Theoretically, Equation (4) is equal to Equation (1), with the constant 1.0707 approximating εSiO4 × CSiO4. Our assumption is obviously justified because nearly all data, with only a few exceptions at very small thin section thickness, are plotted to the right of the straight line dictated by Equation (4), matching the expectation that D-m should be often larger than D-c2. Furthermore, Equation (4) seems applicable to Mg-Rw with different amounts of H2O, since Figure 2 displays no apparent correlation between the deviation of the experimental data from the straight line and the H2O content. Even more, Equation (4) should be largely applicable to Rw with different amounts of iron, since the IR features in the segment ~1850-1500 cm −1 are directly related to the SiO4 structure units only. The accuracy of Equation (4) has been independently verified, as shown in Figure 3. Our IR spectra 4753-05-01, taken from a thin section with D-m = 14 μm, and 1584-03-01, obtained from a thin section with D-m = 15 μm, display the IR features in the segment ~1850-1500 cm −1 and some interference fringes around ~2150 cm −1 (shown later), so that both Equation (3) and Equation (4) can be simultaneously applied to them. In both cases, we have obtained essentially identical results, D-c1 = 14.0 μm and D-c2 = 14.6 μm for the former, and D-c1 = 22.5 μm and D-c2 = 21.6 μm for the latter. Equation (3) is a well-known and standard formula for calculating the thickness of parallel thin sections [75,76], a point that can also be illustrated by the data of Rw with different H2O and Fe contents, as summarized in Figure 3. Consequently, Equation (4) should have a wide application, both to parallel thin sections and to wedged thin sections, and its verification is thus very meaningful. The accuracy of Equation (4) has been independently verified, as shown in Figure 3. Our IR spectra 4753-05-01, taken from a thin section with D m = 14 µm, and 1584-03-01, obtained from a thin section with D m = 15 µm, display the IR features in the segment~1850-1500 cm −1 and some interference fringes around~2150 cm −1 (shown later), so that both Equation (3) and Equation (4) can be simultaneously applied to them. In both cases, we have obtained essentially identical results, D c1 = 14.0 µm and D c2 = 14.6 µm for the former, and D c1 = 22.5 µm and D c2 = 21.6 µm for the latter. Equation (3) is a well-known and standard formula for calculating the thickness of parallel thin sections [75,76], a point that can also be illustrated by the data of Rw with different H 2 O and Fe contents, as summarized in Figure 3. Consequently, Equation (4) should have a wide application, both to parallel thin sections and to wedged thin sections, and its verification is thus very meaningful.  Table 1  . Ignoring the small effect of water [14], the refractory index of Rw with different Fe contents has been estimated according to Binns [73].
The H2O contents of the Mg-Rw crystals calculated with the D-c2 values are compared to those calculated with the D-m values in Figure 4. As expected, the former are much less scattered than the latter, and are thus better. Removing two abnormal IR analyses, 1584-03-01 and 1589-03-01 (Table 1), we have accordingly determined the water contents of the Mg-Rw in Run 1584, Run 1589 and Run 4753 as 1019(238), 5500(229) and 16,307(1219) ppm, respectively. The abnormal H2O content estimated from 1584-03-01 may be caused by a combined influence of the low H2O content and the apparent interference fringes (shown later). However, reason for the abnormal H2O content estimated from 1589-03-01 is unclear.   Table 1  Bolfan-Casanova et al. [49] (1936, with D m = 45(5) µm and D c1 = 37.3 µm). Ignoring the small effect of water [14], the refractory index of Rw with different Fe contents has been estimated according to Binns [73].
The H 2 O contents of the Mg-Rw crystals calculated with the D c2 values are compared to those calculated with the D m values in Figure 4. As expected, the former are much less scattered than the latter, and are thus better. Removing two abnormal IR analyses, 1584-03-01 and 1589-03-01 (Table 1) Table 1  . Ignoring the small effect of water [14], the refractory index of Rw with different Fe contents has been estimated according to Binns [73].
The H2O contents of the Mg-Rw crystals calculated with the D-c2 values are compared to those calculated with the D-m values in Figure 4. As expected, the former are much less scattered than the latter, and are thus better. Removing two abnormal IR analyses, 1584-03-01 and 1589-03-01 (Table 1), we have accordingly determined the water contents of the Mg-Rw in Run 1584, Run 1589 and Run 4753 as 1019(238), 5500(229) and 16,307(1219) ppm, respectively. The abnormal H2O content estimated from 1584-03-01 may be caused by a combined influence of the low H2O content and the apparent interference fringes (shown later). However, reason for the abnormal H2O content estimated from 1589-03-01 is unclear.

IR Peaks for Water in Mg-Rw without Anealing
Rw has a cubic spinel structure (space group Fd3m), which has only one distinct site for each element [79]. Oxygens appear as a cubic close packing array, Si cations occupy one eighth of the tetrahedral sites (T-sites; 8a), and Mg and/or Fe cations take half of the octahedral sites (M-sites; 16d). There is another octahedral site (16c) in the spinel structure, which is usually vacant (vacant M-sites). According to theoretical investigations [39][40][41][42], hydrogen atoms may enter all the T-sites and M-sites (filled or not) to significant amounts, resulting in many IR peaks. Cation disordering on the T-sites and M-sites may further complicate the IR features [43,44,52]. Figure 5 shows the infrared spectra (4000-1000 cm −1 ) taken from the high-H 2 O Mg-Rw thin sections with D m = 14-64 µm (C H2O = 16,307(1219) ppm). Mainly, there are five sets of IR peaks occurring in the energy ranges of~3750-3620,~3620-2700,~2700-2300,~1850-1500 and~1500-1150 cm −1 . Peak Set I, appearing in the energy range of~3750-3620 cm −1 , contains a relatively weak and broad feature centering at~3682 cm −1 . This broad feature was previously observed in the IR spectra for water-rich Rw [12,28,49,51,56], but hardly detected in those for water-poor Rw [12,28,49,53,56]. Following Blanchard et al. [40], Li et al. [41] and Mrosko et al. [52], we attribute this weak peak to the hydrogens on the T-sites. Peak Set II, appearing in the energy range of~3620-2700 cm −1 , is nominally made of one intense and broad peak centering at~3118 cm −1 . It is the major water peak that was usually observed and commonly assigned to the hydrogens on the M-sites [40,41,52]. Peak Set III, appearing in the energy range of~2700-2300 cm −1 , may contain three weak peaks at~2663, 2538 and 2445 cm −1 . Whether they are related to any hydrogen or not has been a controversial issue, but will be resolved later in this study. Peak Set IV, appearing in the energy range of~1850-1500 cm −1 , may have two peaks at~1734 and 1601 cm −1 . They are not related to any hydrogen, as previously discussed (Figure 1). Peak Set V, appearing in the energy range of~1500-1150 cm −1 , is generally composed of three water-related peaks at~1347, 1281 and 1186 cm −1 [49]. As shown later, there may be some more weak and hidden IR peaks though. For the energy interval~2300-1850 cm −1 , there is no apparent IR peak intrinsic to Rw, so that it is the ideal wavenumber range to display the interference fringes, as exampled by the spectrum 4753-05-01 ( Figure 5).
Minerals 2020, 10, 499 13 of 32 represent water contents derived with calculated crystal plate thickness (D-c2), with the former showing more scattering.

IR Peaks for Water in Mg-Rw without Anealing
Rw has a cubic spinel structure (space group Fd3 ̅ m), which has only one distinct site for each element [79]. Oxygens appear as a cubic close packing array, Si cations occupy one eighth of the tetrahedral sites (T-sites; 8a), and Mg and/or Fe cations take half of the octahedral sites (M-sites; 16d). There is another octahedral site (16c) in the spinel structure, which is usually vacant (vacant M-sites). According to theoretical investigations [39][40][41][42], hydrogen atoms may enter all the T-sites and M-sites (filled or not) to significant amounts, resulting in many IR peaks. Cation disordering on the T-sites and M-sites may further complicate the IR features [43,44,52]. Figure 5 shows the infrared spectra (4000-1000 cm −1 ) taken from the high-H2O Mg-Rw thin sections with D-m = 14-64 μm (C-H2O = 16,307(1219) ppm). Mainly, there are five sets of IR peaks occurring in the energy ranges of ~3750-3620, ~3620-2700, ~2700-2300, ~1850-1500 and ~1500-1150 cm −1 . Peak Set I, appearing in the energy range of ~3750-3620 cm −1 , contains a relatively weak and broad feature centering at ~3682 cm −1 . This broad feature was previously observed in the IR spectra for water-rich Rw [12,28,49,51,56], but hardly detected in those for water-poor Rw [12,28,49,53,56]. Following Blanchard et al. [40], Li et al. [41] and Mrosko et al. [52], we attribute this weak peak to the hydrogens on the T-sites. Peak Set II, appearing in the energy range of ~3620-2700 cm −1 , is nominally made of one intense and broad peak centering at ~3118 cm −1 . It is the major water peak that was usually observed and commonly assigned to the hydrogens on the M-sites [40,41,52]. Peak Set III, appearing in the energy range of ~2700-2300 cm −1 , may contain three weak peaks at ~2663, 2538 and 2445 cm −1 . Whether they are related to any hydrogen or not has been a controversial issue, but will be resolved later in this study. Peak Set IV, appearing in the energy range of ~1850-1500 cm −1 , may have two peaks at ~1734 and 1601 cm −1 . They are not related to any hydrogen, as previously discussed ( Figure 1). Peak Set V, appearing in the energy range of ~1500-1150 cm −1 , is generally composed of three water-related peaks at ~1347, 1281 and 1186 cm −1 [49]. As shown later, there may be some more weak and hidden IR peaks though. For the energy interval ~2300-1850 cm −1 , there is no apparent IR peak intrinsic to Rw, so that it is the ideal wavenumber range to display the interference fringes, as exampled by the spectrum 4753-05-01 ( Figure 5). Typical unpolarized IR spectra taken on four crystal plates made from the high-H2O Mg-Rw in Run 4753. The IR # is followed by the measured thickness of the crystal plate (D-m in parentheses). Note the interference fringes around ~2150 cm −1 in the spectrum 4753-05-01, which can be used to calculate the thickness. Figure 6 shows the infrared spectra (4000-1000 cm −1 ) taken from the low-H2O Mg-Rw thin sections with D-m = 15-113 μm (C-H2O = 1019(238) ppm). As we can see, the weak and broad feature in Peak Set I (~3750-3620 cm −1 ) previously observed for the high-H2O Mg-Rw is now gone and Note the interference fringes around~2150 cm −1 in the spectrum 4753-05-01, which can be used to calculate the thickness. Figure 6 shows the infrared spectra (4000-1000 cm −1 ) taken from the low-H 2 O Mg-Rw thin sections with D m = 15-113 µm (C H2O = 1019(238) ppm). As we can see, the weak and broad feature in Peak Set I (~3750-3620 cm −1 ) previously observed for the high-H 2 O Mg-Rw is now gone and completely replaced by a large number of tiny peaks (highlighted by the broken square), whose intensities are highly similar to those tiny peaks at >~3750 cm −1 . The low-H 2 O Mg-Rw thus likely has a negligible amount of hydrogen on its T-sites, as suggested by Ye et al. [23]. The intense and broad peak in Peak Set II (~3620-2700 cm −1 ) is still there, but centers at~3088 cm −1 , with two new peaks appearing at 3278 and 2845 cm −1 . In addition, those peaks at~2960 and 2918 cm −1 should belong to the acetone residues [80]. The three weak peaks in Peak Set III (~2700-2300 cm −1 ) are still there, with slightly different peak positions though (at~2670, 2554 and 2454 cm −1 ). Similarly, the two water-irrelevant peaks in Peak Set IV (~1850-1500 cm −1 ) remain, but appear at~1734 and 1614 cm −1 . Peak Set V (1500-1150 cm −1 ) now has much more component peaks, with one group of sharp peaks at~1356, 1304 and 1189 cm −1 and another group of weak and broad peaks at~1388, 1258, 1237 and 1211 cm −1 . We assign the former to the hydrogen defects in Mg-Rw and the latter as the combinations/overtones. Additionally, note the interference fringes around~2150 cm −1 in the spectrum 1584-03-01. completely replaced by a large number of tiny peaks (highlighted by the broken square), whose intensities are highly similar to those tiny peaks at > ~3750 cm −1 . The low-H2O Mg-Rw thus likely has a negligible amount of hydrogen on its T-sites, as suggested by Ye et al. [23]. The intense and broad peak in Peak Set II (~3620-2700 cm −1 ) is still there, but centers at ~3088 cm −1 , with two new peaks appearing at ~3278 and 2845 cm −1 . In addition, those peaks at ~2960 and 2918 cm −1 should belong to the acetone residues [80]. The three weak peaks in Peak Set III (~2700-2300 cm −1 ) are still there, with slightly different peak positions though (at ~2670, 2554 and 2454 cm −1 ). Similarly, the two waterirrelevant peaks in Peak Set IV (~1850-1500 cm −1 ) remain, but appear at ~1734 and 1614 cm −1 . Peak Set V (1500-1150 cm −1 ) now has much more component peaks, with one group of sharp peaks at ~1356, 1304 and 1189 cm −1 and another group of weak and broad peaks at ~1388, 1258, 1237 and 1211 cm −1 .
We assign the former to the hydrogen defects in Mg-Rw and the latter as the combinations/overtones. Additionally, note the interference fringes around ~2150 cm −1 in the spectrum 1584-03-01. Collectively, Figure 5, Figure 6 and Figure 7 have suggested the following 15 water peaks for our Mg-Rw synthesized with conventional high-P experimental techniques (Table 3)  wavenumber, say ~1190 cm −1 . Furthermore, the peak at ~1381 cm −1 in the spectrum 1584-01-01 is extremely broad, suggesting multiple peak components (Figure 1). Indeed, there is a minor water peak at ~1356 cm −1 (Figure 6) or at ~1352 cm −1 (Figure 7). Consequently, we have assigned these three small peaks at ~1356, 1305 and 1190 cm −1 as water peaks. Since there are different types of hydrogen defects in Rw, it is possible that these peaks might just represent other types of hydrogen defects, whose IR signals can be clearly observed, with only Rw having appropriate amounts of water.  Collectively, Figures 5-7 have suggested the following 15 water peaks for our Mg-Rw synthesized with conventional high-P experimental techniques (Table 3) There have been some debates on the relationship between the IR peaks of Peak Set V (from 1500 to 1150 cm −1 ) and the water in Rw. Bolfan-Casanova et al. [49] compared the IR features of one nominally dry polycrystalline sample and two water-rich Mg-Rw crystal plates (~7500-7800 ppm H 2 O), and concluded that the peaks at~1347, 1286 and 1191 cm −1 should be considered as in-plane X-OH bending vibrations since they only occurred in the IR spectra of the water-rich Mg-Rw. Their conclusion was supported by Chamorro Pérez et al. [51], in which an Mg-Rw with an even higher H 2 O content (~17,000 ppm) was investigated. Hofmeister and Mao [62], however, interpreted the IR features from~1500 to 1150 cm −1 as combinations of the first-order overtones of the Si-O stretching, O-Si-O bending and translation of octahedral and tetrahedral cations while they investigated a very water-poor Mg-Rw [23,79]. Here, we have observed two groups of IR peaks with distinctly different features, as shown in Figure 1 Figure 5). More interestingly, a peak at~1305 cm −1 can be clearly observed for the low-H 2 O Mg-Rw (e.g., 1584-01-01 in Figure 1), and can be vaguely detected as a shoulder on the high wavenumber side of the strong but generally broad water-related peak at~1280 cm −1 in the IR spectrum 4753-01-01 ( Figure 1). Similar to the peak at~1280 cm −1 , the water-related peak at~1185 cm −1 in the IR spectrum 4753-01-01 is also very broad, and might contain two components, with the major one at~1185 cm −1 and the minor one presumably at a slightly higher wavenumber, say~1190 cm −1 . Furthermore, the peak at~1381 cm −1 in the spectrum 1584-01-01 is extremely broad, suggesting multiple peak components (Figure 1). Indeed, there is a minor water peak at~1356 cm −1 (Figure 6) or at~1352 cm −1 (Figure 7). Consequently, we have assigned these three small peaks at~1356, 1305 and 1190 cm −1 as water peaks. Since there are different types of hydrogen defects in Rw, it is possible that these peaks might just represent other types of hydrogen defects, whose IR signals can be clearly observed, with only Rw having appropriate amounts of water.
The IR peak at~1604 cm −1 is worthy of a few words. Following Bolfan-Casanova et al. [49] and Chamorro Pérez et al. [51], we have already interpreted it as a combination band/overtone of the SiO 4 structure units in Rw. An IR peak at similar energies is usually observed for water-rich silicate glasses [76,81] and some hydrous minerals such as lawsonite [82], and attributed to the bending vibration of water molecules. Rw seemingly has no water molecules in its structure.
There have been intense discussions on the nature of the IR peaks at~2550 cm −1 . Bolfan-Casanova et al. [49], Chamorro Pérez et al. [51] and Bolfan-Casanova et al. [56] treated them as the first-order overtones of the X-OH bending vibrations occurring in the energy range of~1500-1150 cm −1 , whereas Hofmeister and Mao [62] and Thomas et al. [38] interpreted them as the second-order overtones and combinations of the Si-O vibrations. The same IR spectra shown in Figure 1 are shown for a different energy range in Figure 8. On one hand, there is no positive correlation between the intensities of the peaks at~2656, 2551 and 2453 cm −1 and the thickness of the thin sections, suggesting that these peaks are not the second-order overtones and combinations of the Si-O vibrations. On the other hand, the much high intensity of these peaks for the high-H 2 O Rw than for the low-H 2 O Rw straightforwardly indicates their relations to water. If these peaks were the second-order overtones and combinations of the Si-O vibrations, their intensities should be about one tenth of the intensities of the first-order overtones/combinations appearing at~1850-1500 cm −1 [83], which is clearly not the case ( Figure 5). Furthermore, the assignment of these water peaks at~2550 cm −1 as the first-order overtones of the X-OH bending vibrations occurring in the energy range of~1500-1150 cm −1 [49,51,56] is also not supported by our data. These peaks are just too intense (Figures 5 and 6). Therefore, we tend to believe that these water peaks might have some special relations to the quench process of the high-P experiments. Indeed, Mrosko et al. [52] observed their almost complete disappearance at~500 • C but reappearance at room T. The IR peak at ~1604 cm −1 is worthy of a few words. Following Bolfan-Casanova et al. [49] and Chamorro Pérez et al. [51], we have already interpreted it as a combination band/overtone of the SiO4 structure units in Rw. An IR peak at similar energies is usually observed for water-rich silicate glasses [76,81] and some hydrous minerals such as lawsonite [82], and attributed to the bending vibration of water molecules. Rw seemingly has no water molecules in its structure.
There have been intense discussions on the nature of the IR peaks at ~2550 cm −1 . Bolfan-Casanova et al. [49], Chamorro Pérez et al. [51] and Bolfan-Casanova et al. [56] treated them as the first-order overtones of the X-OH bending vibrations occurring in the energy range of ~1500-1150 cm −1 , whereas Hofmeister and Mao [62] and Thomas et al. [38] interpreted them as the second-order overtones and combinations of the Si-O vibrations. The same IR spectra shown in Figure 1 are shown for a different energy range in Figure 8. On one hand, there is no positive correlation between the intensities of the peaks at ~2656, 2551 and 2453 cm −1 and the thickness of the thin sections, suggesting that these peaks are not the second-order overtones and combinations of the Si-O vibrations. On the other hand, the much high intensity of these peaks for the high-H2O Rw than for the low-H2O Rw straightforwardly indicates their relations to water. If these peaks were the second-order overtones and combinations of the Si-O vibrations, their intensities should be about one tenth of the intensities of the first-order overtones/combinations appearing at ~1850-1500 cm −1 [83], which is clearly not the case ( Figure 5). Furthermore, the assignment of these water peaks at ~2550 cm −1 as the first-order overtones of the X-OH bending vibrations occurring in the energy range of ~1500-1150 cm −1 [49,51,56] is also not supported by our data. These peaks are just too intense ( Figure 5 and Figure 6). Therefore, we tend to believe that these water peaks might have some special relations to the quench process of the high-P experiments. Indeed, Mrosko et al. [52] observed their almost complete disappearance at ~500 °C but reappearance at room T. There has not been any doubt on the relations between the water in Rw and the IR peaks of Peak Set II (from ~3620 to 2700 cm −1 ) and Peak Set I (from ~3750 to 3620 cm −1 ). For Peak Set II, two more weak and broad water peaks were observed at ~3598 and 3568 cm −1 , respectively, by Ye et al. [23] and Thomas et al. [38]. Based on the IR measurement [23], and the Raman measurement and proton- There has not been any doubt on the relations between the water in Rw and the IR peaks of Peak Set II (from~3620 to 2700 cm −1 ) and Peak Set I (from~3750 to 3620 cm −1 ). For Peak Set II, two more weak and broad water peaks were observed at~3598 and 3568 cm −1 , respectively, by Ye et al. [23] and Thomas et al. [38]. Based on the IR measurement [23], and the Raman measurement and proton-proton scattering measurement [38], the investigated Mg-Rw SZ0820 mostly contained~1.77(35) wt% H 2 O, similar to our high-H 2 O Mg-Rw (~1.63(12)%). The thickness of the thin sections was either~30 µm [23] or 84 µm [38], generally in the thickness range of our thin sections (Table 1). Since we do not observe these two peaks in our IR spectra ( Figure 5), and since Panero et al. [53] did not observe them in the IR spectra taking from the Mg-Rw SZ0820 (thickness = 25 µm), the identity of these two peaks may be problematic and require further investigation (Table 3). For Peak Set II, most studies, ours included, usually suggest one weak and broad IR peak at~3680 cm −1 , but Bolfan-Casanova et al. [56] reveals two peaks at~3733 and 3687 cm −1 . were, respectively, annealed at 350, 400, 450, 500, 550 and 600 • C. For each of these six thin sections, the annealing experiment was successively carried out for two-five times with an annealing duration of usually 15 min (Table 2). It should be noted that all these six thin sections have much similar thickness, ranging from 52-69 µm, so that their IR spectra can be generally directly compared to examine the effects of annealing T and duration.

IR Features of Water in low-H 2 O Mg-Rw Annealed at 200, 250 and 300 • C
The IR spectra are summarized in Figure 9. In total, we can observe 10 water peaks at~3297, 3101, 2849, 2664, 2550, 2446, 1353, 1303, 1284 and 1187 cm −1 from these spectra. As the annealing experiments proceed, little change of the water peaks can be easily observed, suggesting limited hydrogen migration among the different crystallographic sites or negligible rearrangement of the O-H dipoles in the Rw structure at 200, 250 and 300 • C. H2O, similar to our high-H2O Mg-Rw (~1.63(12)%). The thickness of the thin sections was either ~30 μm [23] or 84 μm [38], generally in the thickness range of our thin sections (Table 1). Since we do not observe these two peaks in our IR spectra ( Figure 5), and since Panero et al. [53] did not observe them in the IR spectra taking from the Mg-Rw SZ0820 (thickness = 25 μm), the identity of these two peaks may be problematic and require further investigation (Table 3). For Peak Set II, most studies, ours included, usually suggest one weak and broad IR peak at ~3680 cm −1 , but Bolfan-Casanova et al. [56] reveals two peaks at ~3733 and 3687 cm −1 .

IR Features of Water in Annealed Mg-Rw
One low-H2O Mg-Rw thin section (1019(238) ppm H2O) was successively annealed for five times, two times at 200 °C (30 and 60 min, respectively), two times at 250 °C (90 and 30 min, respectively) and one time at 300 °C (60 min). Six intermediate-H2O Mg-Rw thin sections (5500(229) ppm H2O) were, respectively, annealed at 350, 400, 450, 500, 550 and 600 °C. For each of these six thin sections, the annealing experiment was successively carried out for two-five times with an annealing duration of usually 15 min (Table 2). It should be noted that all these six thin sections have much similar thickness, ranging from 52-69 μm, so that their IR spectra can be generally directly compared to examine the effects of annealing T and duration.

IR Features of Water in low-H2O Mg-Rw Annealed at 200, 250 and 300 °C
The IR spectra are summarized in Figure 9. In total, we can observe 10 water peaks at ~3297, 3101, 2849, 2664, 2550, 2446, 1353, 1303, 1284 and 1187 cm −1 from these spectra. As the annealing experiments proceed, little change of the water peaks can be easily observed, suggesting limited hydrogen migration among the different crystallographic sites or negligible rearrangement of the O-H dipoles in the Rw structure at 200, 250 and 300 °C . The IR spectra are summarized in Figure 10a. Largely due to the relatively high water content, three more weak water peaks at ~3684, 3409 and 3345 cm −1 have been observed. In contrary, the peak at ~3297 cm −1 observed for the low-H2O Mg-Rw ( Figure 10) is gone, presumably blocked by the  (30-90 min). The thin section was prepared from a low-H 2 O Mg-Rw (Crystal # 04), synthesized in Run 1584. The IR #, with the Run # and Crystal # omitted, is followed by the annealing T ( • C) and annealing duration (min) in parentheses. As a comparison, the IR spectrum collected before the annealing experiments is also shown.

IR Features of Water in Intermediate-H 2 O Mg-Rw Annealed at 350 • C
The IR spectra are summarized in Figure 10a. Largely due to the relatively high water content, three more weak water peaks at~3684, 3409 and 3345 cm −1 have been observed. In contrary, the peak at~3297 cm −1 observed for the low-H 2 O Mg-Rw ( Figure 10) is gone, presumably blocked by the intensified major water peak at~3101 cm −1 . As the annealing experiments proceed, little change of the water peaks can be easily observed, suggesting limited hydrogen migration among the different crystallographic sites or negligible rearrangement of the O-H dipoles in the Rw structure at 350 • C.
well resolved now. We thus conclude that the hydrogen defects in the Rw at 600 °C are very similar to those at 550 °C and 500 °C .

IR Features of Water in Mg-Rw Annealed at Different T: A Summary
Mg-Rw is metastable at ambient P, and may transit to the isochemical stable phase forsterite if heated for adequate amounts of time at certain T [21,46]. To examine this potential phase transition, the thin sections annealed at 400 and 600 °C (initial CH2O = 5500(229) ppm) have been probed by a Raman spectrometer. The data are shown in Figure 11. Clearly, no any phase transition can be observed for the Mg-Rw thin section annealed at 400 °C for the cumulated annealing time of 75 min. In contrast, a minor fraction of the Mg-Rw thin section annealed at 600 °C for the cumulated annealing time of 30 min may have transited to forsterite, as indicated by the tiny new Raman peak at ~857 cm −1 . Nevertheless, the infrared spectrum 1589-06-03 (Figure 10f), probing both the surface material and the interior material of the thin section, show water peaks completely different to those of forsterite [84][85][86][87], implying a totally negligible amount of phase transition. For the purpose of comparison, the IR spectrum collected for each thin section before the annealing experiments is also shown at the bottom of each graph. It is followed, from the bottom to the top, by the first IR spectrum to the last spectrum taken on the successively annealed thin section. For the experimental details, see Table 2.

IR Features of Water in Intermediate-H 2 O Mg-Rw Annealed at 400 • C
The IR spectra are summarized in Figure 10b. As the annealing experiments proceed, a large number of changes can be observed for the water peaks. Firstly, the weak and broad peak at~3674 cm −1 gradually increases its intensity. Secondly, the main water peak near~3106 cm −1 progressively decreases its intensity and becomes broader, leading to the emergence of one weak water peak at 3251 cm −1 . Thirdly, both the water peaks at~2700-2300 cm −1 and at 1500-1150 cm −1 seem to slowly decrease their intensities. Consequently, there must have been some hydrogen migration among the different crystallographic sites and rearrangement of the O-H dipoles in the Rw structure at 400 • C, with their equilibrium states unclear though.

IR Features of Water in Intermediate-H 2 O Mg-Rw Annealed at 450 • C
As shown in Figure 10c, the changes of the IR features slowly developing at 400 • C happen very fast at 450 • C; with the first annealing experiment at 450 • C, all of them can be readily observed. After completing all five annealing experiments, we can easily tell from the IR spectra that (1) the broad peak at~3663 cm −1 has become very prominent; (2) the usually seen main water peak at~3095 cm −1 has almost completely gone, more minor water peaks have vaguely appeared at~3456, 3352 and 3243 cm −1 and altogether they have formed a very broad IR feature with very low intensity; (3) the water peaks in the range~2700-2300 cm −1 have become hardly detectable; (4) the water peaks at~1349, 1305, 1278 and 1185 cm −1 have achieved much reduction in their intensities, and one additional broad water peak has appeared at~1387 cm −1 . At the annealing T of 450 • C, therefore, there must have been significant hydrogen migrations among the different crystallographic sites and rearrangement of the O-H dipoles in the Rw structure. On the basis of the similarity of the last three or four IR spectra, we believe that a new equilibrium state among the different types of hydrogen defects has been generally established by these annealing experiments.

IR Features of Water in
Intermediate-H 2 O Mg-Rw Annealed at 500 • C As shown in Figure 10d, all the changes observed at 450 • C have been not only reproduced at 500 • C, but also intensified. Clearly, the broad peak at~3663 cm −1 has a larger intensity now. More and better-resolved weak water peaks are observed at~3515, 3453, 3379 and 3292 cm −1 , and altogether, they form a broad but apparent IR feature in the range of~3550-3095 cm −1 . The usually seen main water peak at~3095 cm −1 is completely gone. The water peaks at~2700-2300 cm −1 have turned into a weak and broad feature centering at~2555 cm −1 . For the energy range 1500-1150 cm −1 , we now see three broad features, respectively, at~1382, 1279 and 1191 cm −1 , with the one at~1382 cm −1 dominating. These IR signals may indicate that the initial hydrogen defects in the Mg-Rw as synthesized in and conventionally quenched from high-P experiment have been completely altered by the annealing experiments at 500 • C.  Figure 10f, the annealing experiments at 600 • C well reproduce the results of those annealing experiments at 550 • C and 500 • C. The water peaks at~3510, 3461, 3405 and 3270 cm −1 , once forming a broad feature locating in the energy range of~3550-3095 cm −1 at 550 • C and 500 • C, are well resolved now. We thus conclude that the hydrogen defects in the Rw at 600 • C are very similar to those at 550 • C and 500 • C.

IR Features of Water in Mg-Rw Annealed at Different T: A Summary
Mg-Rw is metastable at ambient P, and may transit to the isochemical stable phase forsterite if heated for adequate amounts of time at certain T [21,46]. To examine this potential phase transition, the thin sections annealed at 400 and 600 • C (initial C H2O = 5500(229) ppm) have been probed by a Raman spectrometer. The data are shown in Figure 11. Clearly, no any phase transition can be observed for the Mg-Rw thin section annealed at 400 • C for the cumulated annealing time of 75 min. In contrast, a minor fraction of the Mg-Rw thin section annealed at 600 • C for the cumulated annealing time of 30 min may have transited to forsterite, as indicated by the tiny new Raman peak at~857 cm −1 . Nevertheless, the infrared spectrum 1589-06-03 (Figure 10f), probing both the surface material and the interior material of the thin section, show water peaks completely different to those of forsterite [84][85][86][87], implying a totally negligible amount of phase transition.   Figure 12. For the annealing temperatures of 350 and 400 °C , water slowly diffused out of the thin sections, and ~25% water had been lost for the cumulated annealing time of 75 min. For the annealing temperatures of 450, 500, 550 and 600 °C , an average of ~60% water seemingly had been lost. At all these temperatures, however, much of the nominal water reduction took place during the first annealing experiment (Figure 10), and was distinctly accompanied by completely new infrared spectra with much higher weighted mean wavenumbers for the water peaks. Since the molar absorption coefficients negatively correlate with the wavenumbers of the water peaks [57,67,[88][89][90], increased mean wavenumbers mean reduced molar absorption coefficients, and underestimated water contents in turn. A quick examination on the infrared spectra shown in Figure 10f has suggested that the change of the weighted mean wavenumbers should be ~350 wavenumbers (from ~3100 to 3450 cm −1 ), implying a ~45% reduction of the molar absorption coefficients [40] and a ~45% underestimation of the water contents. This would suggest that the four trends for the annealing temperatures of 450, 500, 550 and 600 °C shown in Figure 12 should generally overlap with those trends for the annealing temperatures of 400 and 350 °C . The water-losing process thus does not seem strongly affected by T in the T interval of 350-600 °C .
In contrast, distinct differences have been observed for the hydrogen migration processes and rearrangements of the O-H dipoles in the Rw structure at high T and at low T. Our infrared data have clearly suggested that (1) not much happens at annealing T < ~375 °C , and the initial IR features of water usually observed for the Mg-Rw conventionally synthesized in and quenched from high-P experiments do not experience much change; (2) at annealing T > ~375 °C , significant hydrogen migration and rearrangements of the O-H dipoles take place (with slow rates at T < ~425 °C but fast  Figure 12. For the annealing temperatures of 350 and 400 • C, water slowly diffused out of the thin sections, and~25% water had been lost for the cumulated annealing time of 75 min. For the annealing temperatures of 450, 500, 550 and 600 • C, an average of~60% water seemingly had been lost. At all these temperatures, however, much of the nominal water reduction took place during the first annealing experiment (Figure 10), and was distinctly accompanied by completely new infrared spectra with much higher weighted mean wavenumbers for the water peaks. Since the molar absorption coefficients negatively correlate with the wavenumbers of the water peaks [57,67,[88][89][90], increased mean wavenumbers mean reduced molar absorption coefficients, and underestimated water contents in turn. A quick examination on the infrared spectra shown in Figure 10f has suggested that the change of the weighted mean wavenumbers should be~350 wavenumbers (from~3100 to 3450 cm −1 ), implying a~45% reduction of the molar absorption coefficients [40] and ã 45% underestimation of the water contents. This would suggest that the four trends for the annealing temperatures of 450, 500, 550 and 600 • C shown in Figure 12 should generally overlap with those trends for the annealing temperatures of 400 and 350 • C. The water-losing process thus does not seem strongly affected by T in the T interval of 350-600 • C.
bearing Rw by Mrosko et al. [52], the broad feature at ~2550 cm −1 should not have existed at high T, but formed during the quench process. Its much lower absorption observed for the annealed Mg-Rw thin sections than for the unannealed ones agrees with the fact that our room-P quench process proceeded much faster. Therefore, we come to the conclusion that the IR features usually observed on hydrous Rw directly from conventional high-P synthesizing experiments do not exactly reflect the locations of the hydrogen defects at high T.

Hydrogen Defects and Its IR Features in Mg-Rw at High P-T Conditions
The influence of water on the physical and chemical properties of a material is not only dependent on how much water is hosted in the phase, but on how water is incorporated into its structure. In the case of Rw at the P-T conditions of the mantle transition zone, it has been well agreed that water up to ~2.5% can be stored [13][14][15]43], but little agreement has been reached on the hydrogen incorporation mechanisms [39,[43][44][45]51]. Our extensive IR data can shed new lights on the hydrogen defects in Rw.
The hydrogen defects in Rw have been experimentally investigated by a few studies. The singlecrystal X-ray diffraction study of Kudoh et al. [43] suggested the presence of octahedral vacancies and some Mg-Si disorder in the Rw structure. Aided with the correlation between the Mg/Si ratio and water content, Kudoh et al. [43,91] proposed that hydrogen in Rw is mostly incorporated via two mechanisms, Mg = 2H and Mg2Si = 8H, and its possible sites are between the O-O pairs around the octahedra in order to interpret the broad major water peak at ~3160 cm −1 . On the other hand, the In contrast, distinct differences have been observed for the hydrogen migration processes and rearrangements of the O-H dipoles in the Rw structure at high T and at low T. Our infrared data have clearly suggested that (1) not much happens at annealing T <~375 • C, and the initial IR features of water usually observed for the Mg-Rw conventionally synthesized in and quenched from high-P experiments do not experience much change; (2) at annealing T >~375 • C, significant hydrogen migration and rearrangements of the O-H dipoles take place (with slow rates at T <~425 • C but fast rates at T >~425 • C), resulting in the elimination of some initial IR features and the formation of some new IR features ( Figure 10). Additionally, these new IR features are persistent at least up to 600 • C, and mostly quenchable to room T. These observations are in good agreement with Panero et al. [53] and Mrosko et al. [52]. Panero et al. [53] did not observe any major change in the IR features of water in Mg-Rw in their low-T experiments (T < room T), and Mrosko et al. [52] detected significant changes in their high-T experiments (T >~300 • C), with most of the changes quenchable.
Taking into account potential effects of different water contents in Mg-Rw, our annealing experiments reported here may imply the following important changes for the water peaks in Rw at relatively high T (T >~375 • C; Table 3): (1) a significant enhancing of the intensity of the water peak at~3667 cm −1 , (2) two new peaks appearing at~3510 and 3461 cm −1 , which, along with the peaks at 3405, 3345 and~3270 cm −1 , may form a broad new IR feature centering at~3450 cm −1 , (3) the complete disappearance of the conventionally observed major water peak at~3100 cm −1 , (4) merging the IR peaks in the energy range 2700-2300 cm −1 to form a weak and broad feature at~2550 cm −1 and (5) a broad IR feature appearing at~1387 cm −1 . According to the results reported for an annealed Fe-bearing Rw by Mrosko et al. [52], the broad feature at~2550 cm −1 should not have existed at high T, but formed during the quench process. Its much lower absorption observed for the annealed Mg-Rw thin sections than for the unannealed ones agrees with the fact that our room-P quench process proceeded much faster. Therefore, we come to the conclusion that the IR features usually observed on hydrous Rw directly from conventional high-P synthesizing experiments do not exactly reflect the locations of the hydrogen defects at high T.

Hydrogen Defects and Its IR Features in Mg-Rw at High P-T Conditions
The influence of water on the physical and chemical properties of a material is not only dependent on how much water is hosted in the phase, but on how water is incorporated into its structure. In the case of Rw at the P-T conditions of the mantle transition zone, it has been well agreed that water up to 2.5% can be stored [13][14][15]43], but little agreement has been reached on the hydrogen incorporation mechanisms [39,[43][44][45]51]. Our extensive IR data can shed new lights on the hydrogen defects in Rw.
The hydrogen defects in Rw have been experimentally investigated by a few studies. The single-crystal X-ray diffraction study of Kudoh et al. [43] suggested the presence of octahedral vacancies and some Mg-Si disorder in the Rw structure. Aided with the correlation between the Mg/Si ratio and water content, Kudoh et al. [43,91] proposed that hydrogen in Rw is mostly incorporated via two mechanisms, Mg = 2H and Mg 2 Si = 8H, and its possible sites are between the O-O pairs around the octahedra in order to interpret the broad major water peak at~3160 cm −1 . On the other hand, the single-crystal X-ray diffraction study of Smyth et al. [44] concluded that the principle hydration mechanism involves octahedral vacancies and the IR spectrum is consistent with protonation sites around the tetrahedral edges. Chamorro Pérez et al. [51] investigated the room-T IR features up tõ 30 GPa and argued that the major IR peak at~3150 cm −1 should be attributed to the protonation of the tetrahedral edges and the relatively weak IR peak at~3679 cm −1 could be consistent with a partial protonation of the octahedral edges. Stebbins et al. [55] conducted a 29 Si NMR spectroscopic study, and observed some new peaks which cross-polarize very rapidly, indicating very short Si-H distances and the presence of Si-OH, as expected from the Mg = 2H mechanism with the formation of octahedral vacancies. More recently, Purevjav et al. [45] carried out a neutron diffraction study and found that hydrogen exchanges not only with Mg or Fe but also with Si. One major drawback in all these studies is that they were all conducted at ambient T with hydrous Rw synthesized by employing conventional high-P experimental techniques. The samples investigated might have been subject to some quench-related structural modification, a phenomenon well known for the spinel structure [55,92].
Four types of hydrogen defects in Mg-Rw have been theoretically investigated to some degrees, although the number of the cation configurations examined for each type of the hydrogen defects has been limited [39][40][41][42]. . P has a mostly negligible effect on their relative stability, but T might have some impacts, which have not been constrained though [40][41][42].
The populations of these different types of hydrogen defects in the hydrous Rw at high P-T conditions may be faithfully recorded by the variations of the compositions determined on the quenched hydrous Rw. In general, the diffusion reaction in a solid phase is slow, and the conventional quench process of a high-P experiment is not expected to significantly modify the phase composition. Figure 13 shows the most recent and high quality compositional data for the hydrous Rw, along with those for hydrous wadsleyite (Wad), from Bolfan-Casanova et al. [56]. As pointed out by Bolfan-Casanova et al. [56], the net substitution reaction in hydrous Rw is, Mg = 2H, much similar to that in hydrous Wad. Obviously, Figure 13  on the molar absorption coefficients [40], the ratio of the waters ascribed as the hydrogen defects [VSi(OH)4] and [VMg(OH)2MgSiSiMg] is ~0.61, which contradicts with the chemical characteristics of the Rw at high P-T conditions ( Figure 13). This implies that the quench process at high P must have substantially altered the ratio of the hydrogen defects [VSi(OH)4] and [VMg(OH)2MgSiSiMg]. Indeed, the ready conversion between these two types of hydrogen defects has been firmly established in this study ( Figure 10).  [56] (data from experiments 224 and 271 excluded due to typing mistakes). For the purpose of comparison, the data for hydrous wadsleyite (Wad) from Bolfan-Casanova et al. [56] are also plotted. The CH2O contents of these Rw and Wad were obtained via elastic recoil detection analyses.
Rather unfortunately, the hydrogen defects [VMg(OH)2MgSiSiMg] in hydrous Rw have not been well investigated either by experimental techniques or by simulation approaches. Blanchard et al. [40] presents as the only study at this moment. In that study, just three or four cation configurations were relaxed and examined, and only two IR peaks at 3343 and 3004 cm −1 were determined for the hydrogen defects [VMg(OH)2MgSiSiMg]. With the site-exchanging of some Mg and Si cations along with this type of hydrogen defects, however, a much larger number of cation configurations are possible, and many more IR peaks are expected. Furthermore, the site-exchanging process (i.e., cation disordering) is usually T-dependent [92], so that the energetically stable cation configurations may vary with T, and the IR signals may significantly change with T. Indeed, dramatic variations of the IR peaks in the energy range of ~3600-3000 cm −1 have been observed from our hydrous Mg-Rw crystal plates annealed at various T (Figure 10), signifying a dynamic adjustment of the arrangements of the O-H bonds in accordance to the variations of the cation-disorder states at different T.
It is beneficial to explore the influences on the IR features of the quench processes at high P and 1 atm. The quench process at high P may be responsible for the following modifications, (1) the appearance of the IR peak at ~3700 cm −1 , which has been attributed to the hydrogen defects [VSi(OH)4] most non-existing at high P-T conditions, (2) the formation of the conventionally observed major water peak at ~3100 cm −1 by merging most IR peaks (~3600 to 3000 cm −1 ) caused by the dominant hydrogen defects [VMg(OH)2MgSiSiMg] and (3) the appearance of the IR peaks at ~2550 cm −1 , which Figure 13. Effects of different types of hydrogen defects on (Mg + Fe)/Si ratios of Rw with various Mg/Fe ratios. Data are from Bolfan-Casanova et al. [56] (data from experiments 224 and 271 excluded due to typing mistakes). For the purpose of comparison, the data for hydrous wadsleyite (Wad) from Bolfan-Casanova et al. [56] are also plotted. The C H2O contents of these Rw and Wad were obtained via elastic recoil detection analyses.
Our new and extensive ambient-T IR spectra collected from the hydrous Rw, unannealed or annealed at 1 atm, display 11 IR peaks occurring from~3800 to 2000 cm −1 (Table 3). Moreover, for those two weak water peaks at~3598 and 3568 cm −1 , which are presumably detectable with thick and water-rich thin sections only [23,38], 13 IR peaks have been observed for the water in Mg-Rw, strongly indicating the coexistence of different types of hydrogen defects in the Rw structure at 1 atm. We propose that the broad IR peak at~3701-3682 cm −1 should be assigned to the defects [V Si (OH) 4 ] around the tetrahedra, those from~3600 to 3000 cm −1 to the defects [V Mg (OH) 2 Mg Si Si Mg ] around the octahedra and those from~3000 to 2000 cm −1 to the defects [V Mg (OH) 2 ] around the octahedra, following the theoretical predictions of Blanchard et al. [40] and Li et al. [41]. It should be noted that this assignment is in general agreement with the correlations between the O-H stretching frequency (as observed in the IR spectra) and the O-O distance around the hydrogen defects, as established by Nakamoto [93] and Libowitzky [94].  Figure 5), the scenario is more complicated. The IR spectrum 4753-01-01 shows that the ratio of the integrated absorptions for the regions of 3800-3550 cm −1 and 3550-3000 cm −1 is~0.145. Taking into account the effects of the mean wavenumbers of these two IR features (roughly~3700 and 3100 cm −1 , respectively) on the molar absorption coefficients [40], the ratio of the waters ascribed as the hydrogen defects [V Si (OH) 4 ] and [V Mg (OH) 2 Mg Si Si Mg ] is~0.61, which contradicts with the chemical characteristics of the Rw at high P-T conditions ( Figure 13). This implies that the quench process at high P must have substantially altered the ratio of the hydrogen defects [V Si (OH) 4 ] and [V Mg (OH) 2 Mg Si Si Mg ]. Indeed, the ready conversion between these two types of hydrogen defects has been firmly established in this study ( Figure 10).
Rather unfortunately, the hydrogen defects [V Mg (OH) 2 Mg Si Si Mg ] in hydrous Rw have not been well investigated either by experimental techniques or by simulation approaches. Blanchard et al. [40] presents as the only study at this moment. In that study, just three or four cation configurations were relaxed and examined, and only two IR peaks at 3343 and 3004 cm −1 were determined for the hydrogen defects [V Mg (OH) 2 Mg Si Si Mg ]. With the site-exchanging of some Mg and Si cations along with this type of hydrogen defects, however, a much larger number of cation configurations are possible, and many more IR peaks are expected. Furthermore, the site-exchanging process (i.e., cation disordering) is usually T-dependent [92], so that the energetically stable cation configurations may vary with T, and the IR signals may significantly change with T. Indeed, dramatic variations of the IR peaks in the energy range of~3600-3000 cm −1 have been observed from our hydrous Mg-Rw crystal plates annealed at various T (Figure 10), signifying a dynamic adjustment of the arrangements of the O-H bonds in accordance to the variations of the cation-disorder states at different T.
It is beneficial to explore the influences on the IR features of the quench processes at high P and 1 atm. The quench process at high P may be responsible for the following modifications, (1) the appearance of the IR peak at~3700 cm −1 , which has been attributed to the hydrogen defects [V Si (OH) 4 ] most non-existing at high P-T conditions, (2) the formation of the conventionally observed major water peak at~3100 cm −1 by merging most IR peaks (~3600 to 3000 cm −1 ) caused by the dominant hydrogen defects [V Mg (OH) 2 Mg Si Si Mg ] and (3) the appearance of the IR peaks at~2550 cm −1 , which have been attributed to the hydrogen defects [V Mg (OH) 2 ] mostly non-existing in any significant amount at high P-T conditions. The influence on the appearance of the IR peak at~3700 cm −1 may be dependent on the water content of the Rw, being extremely small at low C H2O but relatively large at high C H2O ( Figure 14). As being annealed at high T and 1 atm, the Rw quenched from high-P synthesizing experiments may progressively relax its structure, rearrange the O-H dipoles and attain new equilibrium for the different types of hydrogen defects, which bring forth the changes to the IR features as observed in this study (Figures 10 and 14). These new IR features at high T may be well preserved if the quench process at 1 atm is fast enough. have been attributed to the hydrogen defects [VMg(OH)2] mostly non-existing in any significant amount at high P-T conditions. The influence on the appearance of the IR peak at ~3700 cm −1 may be dependent on the water content of the Rw, being extremely small at low CH2O but relatively large at high CH2O ( Figure 14). As being annealed at high T and 1 atm, the Rw quenched from high-P synthesizing experiments may progressively relax its structure, rearrange the O-H dipoles and attain new equilibrium for the different types of hydrogen defects, which bring forth the changes to the IR features as observed in this study (Figures 10 and 14). These new IR features at high T may be well preserved if the quench process at 1 atm is fast enough. Figure 14. Effects on the broad water peak at ~3700-3660 cm −1 of the quench processes at high P and at 1 atm. For the low-H2O and intermediate-H2O Mg-Rw (Run 1584 and Run 1589, respectively), the quench process at high P did not lead to the formation of a peak at ~3700 cm −1 (black curves). However, for the high-H2O Mg-Rw (Run 4753), it resulted in an apparent water peak with a roughlyweighted mean wavenumber of ~3700 cm −1 (blue curve). The quench process at 1 atm may lead to a good preservation of the high-T IR signals formed by the new equilibrium at the annealing T and 1 atm, as exampled by the broad water peak with a roughly-weighted mean wavenumber of ~3660 cm −1 (red curves).

Water-Coupled Cation Disorder in Mg-Rw and Its Influences
One of the most puzzling issues about the Rw in the mantle transition zone is whether it attains cation-disordering to some degrees. As we mentioned before, Rw crystalizes into the spinel structure, which contains two cation sites, the T-sites and the M-sites. For some spinels with the general chemical formula AB2O4 (e.g., MgAl2O4-Sp), cation disordering, with some of the A and B cations (e.g., Mg and Al cations) exchanging their positions (e.g., some Mg cations usually appearing on the Figure 14. Effects on the broad water peak at~3700-3660 cm −1 of the quench processes at high P and at 1 atm. For the low-H 2 O and intermediate-H 2 O Mg-Rw (Run 1584 and Run 1589, respectively), the quench process at high P did not lead to the formation of a peak at~3700 cm −1 (black curves). However, for the high-H 2 O Mg-Rw (Run 4753), it resulted in an apparent water peak with a roughly-weighted mean wavenumber of~3700 cm −1 (blue curve). The quench process at 1 atm may lead to a good preservation of the high-T IR signals formed by the new equilibrium at the annealing T and 1 atm, as exampled by the broad water peak with a roughly-weighted mean wavenumber of~3660 cm −1 (red curves).

Water-Coupled Cation Disorder in Mg-Rw and Its Influences
One of the most puzzling issues about the Rw in the mantle transition zone is whether it attains cation-disordering to some degrees. As we mentioned before, Rw crystalizes into the spinel structure, which contains two cation sites, the T-sites and the M-sites. For some spinels with the general chemical formula AB 2 O 4 (e.g., MgAl 2 O 4 -Sp), cation disordering, with some of the A and B cations (e.g., Mg and Al cations) exchanging their positions (e.g., some Mg cations usually appearing on the T-sites jump to the M-sites and some Al cations commonly docking on the M-sites relocate to the T-sites), has been well observed and intensely investigated [92]. Since cation disorder may significantly modify the physical and chemical properties of the spinel structure [8,9,[95][96][97], it is fundamentally important to examine whether cation-disordering really happens to Rw.
Mg-Rw has been conventionally established as a normal spinel, with all Si cations on the T-sites and all Mg cations on the M-sites (i.e., [4] (Si) [6] (Mg 2 )O 4 ). Its potential cation-disordering process can be adequately described by an inversion parameter, x, which stands for the reduction of the Si cations on the T-sites or the fraction of the Si cations appearing on the M-sites (i.e., [4] (Si 1-x Mg x ) [6] (Mg 2-x Si x )O 4 ). Apparently, x = 0 refers to an Mg-Rw having a normal spinel structure, x = 2/3 an Mg-Rw having a completely disordered spinel structure, and x = 1 an Mg-Rw having an inverse spinel structure. The single-crystal X-ray diffraction study of Sasaki et al. [79] suggested x = 0.2 for their nominally anhydrous Mg-Rw, indicating a partial cation-disordering status. This result, however, is hardly conclusive because of the similarity in the scattering factors of Mg and Si. The single-crystal X-ray diffraction study of Hazen et al. [98], performed with some nominally anhydrous iron-bearing Rw, suggested x =~0.04, indicating a very limited degree of cation-disordering. The 29 Si NMR studies of Stebbins et al. [55,99]  To explain the limited cation-disordering status usually experimentally observed for the Mg-Rw, Liu et al. [10] resorted to the T-quench process at high P which might have severely reordered the cations, and led to the usually observed normal spinel structure. Indeed, there has been trace evidence preserved in a meteoritic Rw grain, with one part of the grain being colorless and indicating an inverse spinel structure whereas the other part being blue and suggesting an undetermined degree of cation disorder [100]. The quick T-quench process experienced by the meteoritic Rw, much faster than in a high-P experiment [101,102], must have helped the preservation of the high-T cation configuration.
The cation disorder issue in anhydrous Rw remains unclear [79,96,98,100], but it is very obvious in hydrous Rw. As the hydrogen defects [V Mg (OH) 2 Mg Si Si Mg ] is dominant in hydrous Rw at the P-T conditions of the mantle transition zone, there must be a water-coupled cation disorder to some degree.
The best way to resolve the cation-disordering issue of the hydrous Rw is presumably to systematically perform in situ high-T single-crystal X-ray diffraction experiments, as done by Ye et al. [22,23]. Thus far, Ye et al. [23] reported the most comprehensive in situ structural analyses of one water-rich Mg-Rw crystal (SZ0820) at T up to~463 • C. They observed an irreversible unit-cell expansion above~313 • C, and proposed that the irreversible unit-cell expansion could be attributed to some hydrogen migration from the M-sites to the T-sites, with the substituted Si cations relocating to nearby empty M-sites (16c). Due to the limited resolution of the single-crystal X-ray diffraction data and lacking high-T IR data, however, the role of the cation-disordering was somewhat uncertain. Our extensive IR data reported in this study can make some semi-quantitative assessment on their proposal.
The crystal used in Ye et al. [23] was synthesized also at the Bayerisches Geoinstitut, Germany, with the P-T conditions (~20 GPa and 1250 • C) similar to our Run 4753 (~23 GPa and 1500 • C). Its water content,~1.77 (35) wt%, is similar to our high-H 2 O Mg-Rw (~1.63(12)%). Using Figure 13, we can estimate its Mg:Si ratio as~1.87 and its chemical formula then as Mg 1.87 SiH 0.26 O 4 . Since the hydrogen defects [V Mg (OH) 2 Mg Si Si Mg ] should be dominant at the synthesizing P-T conditions, its structural formula can be approximated as [4] (Si 0.87 Mg 0.13 ) [6] (Mg 1.74 Si 0.13 H 0.26 )O 4 ), and its inversion parameter x as 0.13. When the synthesizing experiment quenched to room T, some protons might migrate into the T-sites, leading to the formation of the weak IR peak at~3688 cm −1 . If we assume that the synthesizing experiment SZ0820 of Ye et al. [23] and our Run 4753 experienced similar quench processes, we can estimate the amount of protons that migrated. Our IR spectrum 4753-01-01 suggests that the ratio of the water on the T-sites and the M-sites is~0.61. This means~0.67% H 2 O on the T-sites and 1.10% H 2 O on the M-sites of the quenched Mg-Rw from the experiment SZ0820. Accompanying the hydrogen migration, all Mg and Si cations have been completely reordered (i.e., x = 0), as indicated by the single-crystal X-ray diffraction data at room P and T [23].
The size of the water-rich Mg-Rw crystal used in the in-situ single-crystal X-ray diffraction experiments of Ye et al. [23] was~100 × 85 × 70 µm 3 , with its smallest dimension much comparable to the thickness of the thin sections used in our annealing experiments (from 52 to 69 µm). At every experimental T, the data-collecting time was~4 h. According to the IR results of our annealing experiments (Figures 10 and 12), water lost from this crystal should have been minimum at T ≤ 313 • C, but gradually become more important at higher experimental temperatures of 362, 412 and 463 • C. Any sudden and complete dehydration should not be anticipated due to the large size of the crystal and the relative low experimental T. Indeed, no abrupt volume reduction caused by a substantial water-losing had ever been observed by the in situ experiments. The crystal structures at 362, 412 and 463 • C then should be better viewed as partially dehydrated Mg-Rw, with the dehydration extent increasing with T increase. On the base of the water evolution in our annealed thin sections (Figure 12), we may assume that~50% water (likely a low value) was eventually lost after collecting the in situ single-crystal X-ray diffraction data at 463 • C, and then~0.88% H 2 O retained in the quenched crystal. Our IR spectra 1589-05-02 and 1589-06-02 show that the ratio of the integrated absorptions for the regions of~3800-3550 cm −1 and~3550-3000 cm −1 is~0.5. Taking into account the effects of the mean wavenumbers of these two IR features (roughly~3660 and 3450 cm −1 , respectively) on the molar absorption coefficients [40], the ratio of the contents of the water on the T-sites and on the M-sites should be~0.96. This means~0.43% H 2 O on the T-sites and~0.45% H 2 O on the M-sites of the quenched Mg-Rw from the high-T single-crystal X-ray diffraction experiments at room P. Consequently, water on the T-sites and water on the M-sites simultaneously diffused out at high T, requiring no hydrogen migration from the M-sites to the T-sites.
It follows that the irreversible unit-cell expansion observed by Ye et al. [23] is best explained by some Mg-Si cation-disordering triggered by high T, rather than by hydrogen migration from the M-sites to the T-sites. This cation-disordering process in the Mg-Rw is likely slow at low T, but becomes fast at high T, as in the case for the MgAl 2 O 4 -spinel [92]. Due to the very quick quench process in the single-crystal X-ray diffraction experiments at room P, the cation-disorder state achieved at high T can be at least partially preserved, leading to the irreversible unit-cell expansion. Indeed, the structural refinements using the in situ X-ray diffraction data collected at 362, 412 and 463 • C, respectively, suggested x = 0.05(2), x = 0.05(2) and x = 0.07 (2), and those using the X-ray diffraction data collected on the crystal quenched from these temperatures to room T suggested x = 0.04(2), x = 0.06(2) and x = 0.09(2), respectively [23].
One interesting observation pertinent to the Mg-Si cation-disordering at high T reported by Ye et al. [23] is that the relocated Si cations may appear not on the 16d M-sites usually filled by the Mg cations, but on the normally vacant 16c M-sites at (1/2, 1/2, 0). In comparison, Smyth et al. [44] observed a potential partial occupation of the normally vacant T-sites at (5/8, 5/8, 5/8) by Mg cations. These phenomena are very important, and deserve further investigation.
Theoretical results have suggested that the Mg-Si cation-disordering may have great impacts on many physical and chemical properties of the Mg-Rw, e.g., a 12.5% Si-Mg disorder decreasing the seismic velocities by~3%-5% [9,96]. Experimental evidence is lacking though. Here, we can demonstrate a couple of examples. As shown by the solid blue arrow in Figure 15, the effect of the cation disordering on the volume of the partially dehydrated Mg-Rw is very large,~1.1% volume expansion for a~10% cation disorder, which is significantly larger than predicted for anhydrous Mg-Rw by the simplified model of Hazen and Yang ([8]; the broken blue arrow). If one takes into account the influences on the volumes of the various water contents in these structures quenched from 362, 412 and 463 • C, the solid blue arrow then goes steeper, implying an even larger effect. The second example is an exceedingly large effect on the thermal expansivity of the partially dehydrated Mg-Rw [23]. As the fraction of the Si cations on the T-sites reduces at 362, 412 and 463 • C, some Mg cations enter the T-sites, which makes the T-sites much larger and softer, and the tetrahedra expand more easily. This results in a much larger thermal expansivity for the Mg-Rw at these high temperatures, demonstrated by the nearly identical volume expansions for the T intervals of 30-313 • C and 362-463 • C (the black double-headed arrow vs. the red double-headed arrow in Figure 15). If one takes into account the influences on the volumes of the various water contents in these structures at 362, 412 and 463 • C, the red double-headed arrow should extend its length, implying an even larger effect for the cation-disordering process.
Minerals 2020, 10, 499 27 of 32 much slower than the Mg-Si ordering process, similar to the well-investigated Mg-Al order-disorder process in the MgAl2O4 spinel [92]. Therefore, in those experiments with quench-modified Rw performed at relatively low T, say ≤400 °C , the cation-disordering process might have not been successfully triggered, and the results might not be applicable to the Earth. In those experiments performed at relatively high T but with generally limited experimental dwelling time at every T (like that in the sound velocity measurement), the cation-disordering process might have been started, but equilibrated cation distributions might have never been achieved. The measurements then might reflect a mélange of changing Mg-Si order-disorder states of the Rw [8], and the results should be viewed with great caution. Figure 15. Effects of cation disorder on unit-cell volume and thermal expansivity of Mg-Rw. HY99, Hazen and Yang [8]; Y2012, Ye et al. [23]. The numbers along the symbols represent the T (in °C) for the single-crystal X-ray diffraction measurements. The size of the used crystal (SZ0820) was ~100 × 85 × 70 μm 3 , and the initial CH2O was about 1.77%. The X-ray data-collecting time at very T was ~4 h.

Conclusions
1. With extensive IR spectroscopic measurements performed on a large number of thin sections of different thickness and different CH2O, we have found at least up to ~15 IR water peaks for hydrous Mg-Rw quenched from conventional high-P experiments, suggesting multiple types of hydrogen defects in the Rw structure. 2. There are many significant variations in the IR spectra of hydrous Mg-Rw at high T, as observed from thin sections annealed and quickly quenched from different T to room T. The major variations include an absorption enhancement of the peak at ~3680 cm −1 , some new peaks occurring at ~3510 and 3461 cm −1 and significant absorption reductions of the peaks at ~2550 cm − [8]; Y2012, Ye et al. [23]. The numbers along the symbols represent the T (in • C) for the single-crystal X-ray diffraction measurements. The size of the used crystal (SZ0820) was~100 × 85 × 70 µm 3 , and the initial C H2O was about 1.77%. The X-ray data-collecting time at very T was~4 h.
Many experiments have been carried out to investigate the physical properties of Rw (hydrous or anhydrous), with the materials synthesized by conventional high-P techniques. It is highly possible that these materials were severely modified by the quench process, with poor preservations of the cation disorder states once attained at high P-T conditions [10,55,79,99]. Note the large difference between the experimentally determined x value at ambient P-T conditions (~0; Figure 15) and the potential x value (close to~0.13) predicted for the hydrous Mg-Rw with~1.77% H 2 O at high P-T conditions (Figure 13; ignoring any possible effects of the unlike minor hydrogen defects [V Si (OH) 4 ] and [V Mg (OH) 2 ]). It is also highly possible that the Mg-Si disordering process in the Rw is kinetically much slower than the Mg-Si ordering process, similar to the well-investigated Mg-Al order-disorder process in the MgAl 2 O 4 spinel [92]. Therefore, in those experiments with quench-modified Rw performed at relatively low T, say ≤400 • C, the cation-disordering process might have not been successfully triggered, and the results might not be applicable to the Earth. In those experiments performed at relatively high T but with generally limited experimental dwelling time at every T (like that in the sound velocity measurement), the cation-disordering process might have been started, but equilibrated cation distributions might have never been achieved. The measurements then might reflect a mélange of changing Mg-Si order-disorder states of the Rw [8], and the results should be viewed with great caution.