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# Water Enhancement of Si Self-Diffusion in Wadsleyite

Dmitry Druzhbin, Hongzhan Fei, Jialong Hao, Chi Zhang, Yangting Lin, Ralf

Dohmen, Tomoo Katsura

► To cite this version:

Dmitry Druzhbin, Hongzhan Fei, Jialong Hao, Chi Zhang, Yangting Lin, et al.. Water Enhancement of Si Self-Diffusion in Wadsleyite. Journal of Geophysical Research: Solid Earth, 2022, 127 (3), pp.e2021JB023440. 10.1029/2021JB023440. hal-05074781

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https://cnrs.hal.science/hal-05074781v1

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Distributed under a Creative Commons Attribution 4.0 International License
JGR Solid Earth

RESEARCH ARTICLE

10.1029/2021JB023440

**Key Points:**

* Silicon self-diffusion in wadsleyite is enhanced by water incorporation with an exponent of $0.8 \pm 0.1$

* Silicon self-diffusion in wadsleyite is nearly isotropic, and has an activation energy of $270 \pm 40$ kJ/mol

* Viscosity contrast between plume and surrounding mantle is controlled by water and temperature, which may affect the plume shape evolution

**Correspondence to:**

H. Fei,

Hongzhan.fei@uni-bayreuth.de

**Citation:**

Druzhbin, D., Fei, H., Hao, J., Zhang, C., Lin, Y., Dohmen, R., & Katsura, T. (2022). Water enhancement of Si self-diffusion in wadsleyite. *Journal of Geophysical Research: Solid Earth*, 127, e2021JB023440. https://doi.org/10.1029/2021JB023440

Received 18 OCT 2021

Accepted 24 FEB 2022

**Author Contributions:**

**Conceptualization:** Dmitry Druzhbin, Hongzhan Fei, Tomoo Katsura

**Data curation:** Dmitry Druzhbin, Hongzhan Fei

**Formal analysis:** Dmitry Druzhbin, Jialong Hao, Chi Zhang, Yangting Lin, Ralf Dohmen

**Funding acquisition:** Tomoo Katsura

**Investigation:** Dmitry Druzhbin, Jialong Hao, Chi Zhang, Yangting Lin, Ralf Dohmen

**Methodology:** Dmitry Druzhbin, Tomoo Katsura

**Supervision:** Hongzhan Fei, Tomoo Katsura

**Validation:** Dmitry Druzhbin

**Visualization:** Dmitry Druzhbin, Hongzhan Fei

**Writing – original draft:** Hongzhan Fei

**Writing – review & editing:** Hongzhan Fei, Tomoo Katsura

© 2022. The Authors.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Water Enhancement of Si Self-Diffusion in Wadsleyite

Dmitry Druzhbin¹,², Hongzhan Fei¹ D, Jialong Hao³, Chi Zhang³ D, Yangting Lin³ D, Ralf Dohmen⁴, and Tomoo Katsura¹,⁵

¹Bayerisches Geoinstitut, University of Bayreuth, Bayreuth, Germany, ²European Synchrotron Radiation Facility (ESRF), Grenoble, France, ³Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China, ⁴Institute of Geology, Mineralogy and Geophysics, Ruhr-Universität Bochum, Bochum, Germany, ⁵Center for High Pressure Science and Technology Advanced Research, Beijing, China

**Abstract** We investigated the H₂O-content dependence of Si self-diffusion coefficient in Fe-free wadsleyite using multi-anvil experiments at pressures of 19–20 GPa, temperatures of 1573–1873 K, and H₂O-content ranging from ~10 to 5,300 wt. ppm by the isotopic thin-film diffusion-couple method. The ²⁹Si-doped diffusion profiles were measured by nanoscale secondary ion mass spectrometry in the depth profiling mode. The H₂O contents in the samples were analyzed by Fourier transformation infrared spectroscopy. The experimental results show a H₂O enhancement of Si diffusion coefficient with a H₂O content exponent of $0.8 \pm 0.1$. The activation enthalpy was found to be 270 ± 40 kJ/mol. The diffusion coefficients in the [100], [010], and [001] directions are indistinguishable. The temperature and H₂O-content dependences of Si diffusion indicate that H₂O incorporation dramatically reduces the rheological strength of wadsleyite, whereas temperature has a relatively small effect. The viscosity in the mantle transition zone could be significantly reduced by H₂O incorporation in wadsleyite. The viscosity contrast between mantle plumes and surroundings may control the evolution of plume shapes at 410–660 km depths.

**Plain Language Summary** Water incorporation in nominally anhydrous minerals may dramatically affect their physical and chemical properties by introducing additional point defects as hydroxyl in the crystal structures. In particular, the atomic diffusivity in minerals, which is controlled by the concentrations of point defects, could be enhanced, therefore, the diffusion-controlled properties such as rheology could be affected by water incorporation. Because the mantle transition zone is considered to be water-rich, we investigated the effect of water on silicon self-diffusion rate in wadsleyite, which is the dominant mineral in the upper part of mantle transition zone at 410–520 km depth. The experimental results show that water-rich (1.0 wt.% H₂O) wadsleyite is rheologically more than 2.4 orders of magnitude weaker than water-poor (less than 10 wt. ppm) conditions. Therefore, the mantle transition zone is significantly weakened by water incorporation. The viscosity contrast between plumes and surrounding mantle may control the evolution of plume shapes at mantle transition zone depths.

# 1. Introduction

The mantle transition zone located at 410–660 km depth plays a critical role in geodynamics and geochemical evolutions of the mantle. For example, the subducted slabs could stagnate at the bottom of the transition zone (Fukao et al., 2009), preventing the material transportation from the Earth's surface to the deep mantle. Dehydration melting layers can be produced at the 410 and 660-km discontinuities (Revenaugh & Sipkin, 1994; Schmandt et al., 2014). Shallow-originated hotspots can be formed in the mantle transition zone (Kuritani et al., 2019). Moreover, the plume shapes could be controlled by the viscosity contrast between the upwelling flows and the surrounding mantle (Condie, 2016).

A vital feature of the mantle transition zone is that its dominant minerals, wadsleyite and ringwoodite, can dissolve more than 1 wt.% H₂O in their crystal structures as hydroxyl (e.g., Demouchy et al., 2005; Druzhbin et al., 2021; Fei & Katsura, 2020a, 2021; Kohlstedt et al., 1996; Litasov et al., 2011; Sun et al., 2018). Therefore, the transition zone is expected to be H₂O-enriched in contrast to the relatively dry upper and lower mantle, as demonstrated by the H₂O-rich ringwoodite inclusion (Pearson et al., 2014), mineral viscosity (Fei et al., 2017), and electrical conductivity analysis (e.g., Dai & Karato, 2009; Huang et al., 2005; Karato, 2011; Kelbert et al., 2009; Manthilake et al., 2009). Because H₂O incorporation may affect the rheological properties of minerals (e.g., Costa & Chakraborty, 2008; Fei et al., 2017, 2013; Hustoft et al., 2013; Kohlstedt, 2006; Shimojuku et al., 2010),
understanding the role of H₂O on the rheology of wadsleyite and ringwoodite is essential for investigating of geodynamics in the deep mantle.

The most direct approach to understand the mineral rheology in the Earth's mantle is deformation experiments. However, sample dehydration in the open system makes it difficult to control the H₂O contents in a deformation experiment under high-pressure and high-temperature conditions. Hence, investigating the effect of H₂O on the rheological properties is challenging. The majority of the deformation studies on wadsleyite and ringwoodite were thus performed by experiments under nominally dry conditions (e.g., Farla et al., 2015; Kawa-zoe et al., 2010, 2011, 2013, 2016; Nishihara, Tinker et al., 2008) and by numerical modeling (e.g., Ritterbex et al., 2015, 2020). Although Hustoft et al. (2013) observed H₂O weakening of wadsleyite and ringwoodite by deformation experiments, the H₂O contents in the samples were not well controlled, as they pointed out. Thus, the H₂O effect has not been determined quantitatively.

Due to the difficulty of deformation experiments under hydrous conditions, a rather indirect method was adopted in Fei et al. (2017), that is, the H₂O effect on dislocation mobility in ringwoodite was determined based on dislocation recovery experiments, in which the samples were embedded in a closed system and therefore the H₂O contents were well controlled. By this technique, a H₂O content exponent of 1.1 ± 0.1 was obtained for the dislocation mobility in ringwoodite. Namely, H₂O has a large effect on the rheology of ringwoodite.

For wadsleyite, Shimojuku et al. (2004, 2009, 2010) adopted another indirect method. They determined the Si self-diffusion coefficients in samples with various H₂O contents by means of the isotope diffusion couple method using secondary ion mass spectroscopy (SIMS). They found that the diffusion coefficients in the samples with 10–140 wt. ppm H₂O (350–500 wt. ppm before diffusion experiments) are about half an order of magnitude higher than those with 20–60 wt. ppm H₂O (20–40 wt. ppm before diffusion), indicating a H₂O weakening of wadsleyite because the creep rate of silicate minerals is controlled by diffusion of the slowest species, which is Si in wadsleyite (Kubo et al., 2004; Shimojuku et al., 2004, 2009, 2010; Zhang et al., 2021). Nevertheless, because of the limited range of H₂O content in Shimojuku et al. (2004, 2009, 2010), they could not obtain a H₂O content exponent. Thus, the magnitude of H₂O effect on wadsleyite rheology is still unknown. Additionally, their diffusion coefficients (Shimojuku et al., 2004, 2009, 2010) were obtained from polycrystalline samples, which does not allow to identify diffusion anisotropy. The polycrystalline may also enlarge the sample surface roughness (Mullins, 1958), which in turn affects the depth resolution of the SIMS profiles (e.g., Dohmen, Becker, et al., 2002; Fei et al., 2012, 2013, 2014).

In this study, we systematically measured the Si self-diffusion coefficients in wadsleyite single crystals as a function of H₂O content from 10 to 5,300 wt. ppm at pressures of 19–20 GPa and temperatures of 1573–1873 K along the [100], [010], and [001] crystallographic axes. To reduce the surface roughness effect in SIMS analysis, the diffusion profiles were measured using a nanoscale SIMS (NanoSIMS), by which more smooth area can be analyzed by reducing the crater sizes.

## 2. Experimental and Analytical Procedures

### 2.1. Synthesis of Wadsleyite Single Crystals

Fe-free wadsleyite single crystals were synthesized at high-pressure and high temperature conditions by multi-anvil experiments using Mg₂SiO₄ forsterite powder ground from a single crystal of forsterite (Oxide Co., Japan). The impurities of the single crystal were ~80 and 82 wt. ppm of Ir and Fe, respectively, as described in Fei et al. (2012). The forsterite powder was sealed in platinum capsules with inner and outer diameters of 1.6 and 2.0 mm, respectively, by arc-welding. The adhesive moisture in the powder acted as the H₂O source. Each capsule was placed into an MgO sleeve in a LaCrO₃ heater with a ZrO₂ thermal insulator. A Cr₂O₃-doped MgO octahedron with edge lengths of 18 mm was used as the pressure medium (18/8 standard assembly at Bayerisches Geoinstitut, University of Bayreuth). The assembly was compressed to 21 GPa by eight pieces of tungsten carbide anvils with 8-mm truncation edge lengths, followed by annealing at a temperature of 2050 K for 2–5 hr monitored by a W/Re (D-type) thermocouple. Afterwards, the assembly was quenched to room temperature by switching off the heating power, and decompressed to ambient pressure for more than 15 hr. Finally, inclusion- and crack-free wadsleyite single crystals with 100–1,000 µm grain sizes were picked up from the sample capsules.
<figure><img src="image_4.png" /><figcaption>**Figure 1.** 18/8 multi-anvil cell assembly (left) and capsule design (right) used for diffusion experiments in this study. The thin-film coated wadsleyite single crystals faced to a diamond single crystal were embedded in gold powder within the gold capsule. The same cell assembly design but with forsterite powder within a platinum capsule was used for sample synthesis experiments.</figcaption></figure>

## 2.2. Diffusion Experiments

The wadsleyite single crystals were oriented along the [100], [010], and [001] crystallographic axes using a single-crystal X-ray diffractometer. They were mechanically polished on the crystallographic planes using diamond powder until no scratches were recognized, and then chemically polished using an alkaline colloidal silica solution for 2–7 hr. Finally, the surface topography (hereafter defined as one standard deviation of the surface topography) was less than 3 nm. The polished surfaces were deposited with an amorphous film of 500–1,000 nm thickness produced by pulsed laser ablation on a 29Si-enriched Mg₂SiO₄ target using the pulsed laser deposition system at the Ruhr-University Bochum (Dohmen, Chakraborty, et al., 2002).

To protect the thin film from mechanical damage during compression, the thin-film-coated surfaces were faced on a diamond single crystal (Figure 1), which had a topography of less than 5 nm. The thin-film-coated wadsleyite sample with the diamond crystal, together with enstatite powder at the back side of the sample to buffer the SiO₂ activity, were embedded in gold powder and welded in a gold capsule with a 2.0-mm outer diameter and 1.6-mm inner diameter. The capsule was loaded into the same cell assembly as that for the single-crystal synthesis (Figure 1), and annealed at 19–20 GPa and 1573–1873 K for 0–600 min.

## 2.3. Diffusion Profile Analysis

The diffusion profiles were measured using Cameca NanoSIMS 50 L installed at the Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing. A primary beam of 100 pA Cs⁺ were used to scan the 10 × 10 µm² area to acquire the ion image of 28Si and 29Si in multi-collection mode. To avoid the edge effect from the SIMS craters, only the 28Si and 29Si intensity data from the central region of each crater with 2.5 × 2.5 µm² area were used to calculate the diffusion profiles (Figure 2).

The intensities of 29Si and 28Si were obtained as a function of sputtering time by the NanoSIMS. The depth of each SIMS crater was subsequently determined by a 3D-Nanofocus microscope at the University of Bayreuth. The time data in the SIMS analysis was converted to depth by assuming a constant sputtering rate for each crater. The 29Si/(29Si + 28Si) ratios were thus obtained as a function of depth (Figure 3).

The diffusion coefficients were obtained by fitting the diffusion profiles to the error function,

$$c(x) = c_0 + \frac{c_1 - c_0}{2} \left( \text{erf} \frac{h - x}{\sqrt{4D'_{\text{Si}} t}} + \text{erf} \frac{h + x}{\sqrt{4D'_{\text{Si}} t}} \right) \quad (1)$$
<figure><img src="image_5.png" /><figcaption>**Figure 2.** An example of secondary ion mass spectroscopy crater (1753). <sup>29</sup>Si and <sup>28</sup>Si intensity data from the center region of the crater with about 2.5 × 2.5 µm<sup>2</sup> area were used for diffusion profile analysis.</figcaption></figure>

where $c(x)$ is the <sup>29</sup>Si/(<sup>29</sup>Si + <sup>28</sup>Si) ratio at depth $x$, $c_0$ and $c_1$ are the initial <sup>29</sup>Si/(<sup>29</sup>Si + <sup>28</sup>Si) ratios in the substrate and thin film, respectively, $h$ is the position of the boundary between the thin film and substrate from the surface, $t$ is the annealing time, and $D'_{Si}$ is the apparent Si diffusion coefficient.

## 2.4. Topography Effect

The high-temperature annealing increases the sample surface roughness due to the crystallization of the thin films. The rough surfaces would broaden the diffusion profiles, causing overestimating the diffusion profiles

<figure><img src="image_6.png" /><figcaption>**Figure 3.** Examples of diffusion profiles obtained in run 1596 and 1753 at 1873 K with annealing durations of 0 (0-time run) and 10 min, respectively.</figcaption></figure>
<caption>**Table 1**</caption>

A List of Run Conditions, C<sub>H2O</sub> in the Samples Before and After Diffusion, Topography (σ, One Standard Deviation of the Topography) at the Bottom of Secondary Ion Mass Spectroscopy Craters, and Si Diffusion Coefficients

<table><thead><tr><th>Run. No.</th><th>T (K)</th><th>t (min)</th><th>Axis</th><th>C<sub>H2O</sub> (wt.ppm)<sup>b</sup></th><th>C<sub>H2O</sub> (wt.ppm)<sup>c</sup></th><th>C<sub>H2O</sub> (wt.ppm)<sup>d</sup></th><th>σ (nm)</th><th>D<sub>Si</sub> (m<sup>2</sup>/s)</th></tr></thead><tbody><tr><td>1695</td><td>1873</td><td>600</td><td>[100]</td><td>&lt;10 (10)</td><td>&lt;10 (10)</td><td>&lt;30</td><td>52 (13)</td><td>8.3 (3.1) × 10<sup>-19</sup></td></tr><tr><td>1753-1</td><td>1873</td><td>10</td><td>[100]</td><td>553 (82)</td><td>520 (77)</td><td></td><td>13 (5)</td><td>8.7 (0.9) × 10<sup>-18</sup></td></tr><tr><td>1753-2</td><td>1873</td><td>10</td><td>[100]</td><td>553 (82)</td><td>520 (77)</td><td></td><td>34 (16)</td><td>1.9 (0.1) × 10<sup>-17</sup></td></tr><tr><td>1514</td><td>1873</td><td>100</td><td>[100]</td><td>291 (34)</td><td>274 (32)</td><td>315 (9)</td><td>26 (28)</td><td>9.4 (0.9) × 10<sup>-18</sup></td></tr><tr><td>1814-61</td><td>1673</td><td>30</td><td>[100]</td><td>1,982 (237)</td><td>1,864 (223)</td><td></td><td>22 (5)</td><td>4.3 (0.4) × 10<sup>-18</sup></td></tr><tr><td>1814-62</td><td>1673</td><td>30</td><td>[100]</td><td>1,982 (237)</td><td>1,864 (223)</td><td></td><td>16 (6)</td><td>1.5 (0.2) × 10<sup>-18</sup></td></tr><tr><td>1886</td><td>1873</td><td>600</td><td>[010]</td><td>44 (9)</td><td>50 (10)</td><td>&lt;30</td><td>50 (14)</td><td>3.0 (0.3) × 10<sup>-18</sup></td></tr><tr><td>1890</td><td>1873</td><td>600</td><td>[010]</td><td>23 (3)</td><td>26 (3)</td><td>&lt;30</td><td>41 (17)</td><td>1.1 (1.5) × 10<sup>-18</sup></td></tr><tr><td>1742-1</td><td>1873</td><td>15</td><td>[010]</td><td>1,136 (159)</td><td>1,282 (180)</td><td></td><td>33 (26)</td><td>1.0 (0.1) × 10<sup>-17</sup></td></tr><tr><td>1742-3</td><td>1873</td><td>15</td><td>[010]</td><td>1,136 (159)</td><td>1,282 (180)</td><td></td><td>39 (1)</td><td>2.6 (1.1) × 10<sup>-17</sup></td></tr><tr><td>1777-1</td><td>1873</td><td>20</td><td>[010]</td><td>2,634 (378)</td><td>2,973 (427)</td><td>1,710 (234)</td><td>25 (6)</td><td>5.1 (1.0) × 10<sup>-17</sup></td></tr><tr><td>1777-2</td><td>1873</td><td>20</td><td>[010]</td><td>2,634 (378)</td><td>2,973 (427)</td><td>1,710 (234)</td><td>57 (10)</td><td>1.8 (0.2) × 10<sup>-17</sup></td></tr><tr><td>1801</td><td>1873</td><td>30</td><td>[010]</td><td>2,581 (302)</td><td>2,913 (341)</td><td></td><td>7 (1)</td><td>7.7 (0.5) × 10<sup>-17</sup></td></tr><tr><td>1827-1</td><td>1773</td><td>20</td><td>[010]</td><td>1,802 (227)</td><td>2,034 (256)</td><td></td><td>13 (2)</td><td>4.3 (0.1) × 10<sup>-17</sup></td></tr><tr><td>1827-2</td><td>1773</td><td>20</td><td>[010]</td><td>1,802 (227)</td><td>2,034 (256)</td><td></td><td>14 (3)</td><td>3.8 (0.1) × 10<sup>-17</sup></td></tr><tr><td>1826</td><td>1773</td><td>60</td><td>[010]</td><td>5,028 (650)</td><td>5,675 (734)</td><td>6,591 (127)</td><td>9 (1)</td><td>3.6 (0.3) × 10<sup>-17</sup></td></tr><tr><td>1906</td><td>1673</td><td>600</td><td>[010]</td><td>2,197 (318)</td><td>2,480 (359)</td><td></td><td>35 (22)</td><td>8.9 (1.0) × 10<sup>-18</sup></td></tr><tr><td>1765-2</td><td>1873</td><td>15</td><td>[001]</td><td>2,541 (322)</td><td>4,032 (511)</td><td>2,573 (76)</td><td>16 (8)</td><td>3.6 (0.2) × 10<sup>-17</sup></td></tr><tr><td>1765-3</td><td>1873</td><td>15</td><td>[001]</td><td>2,541 (322)</td><td>4,032 (511)</td><td>2,573 (76)</td><td>16 (5)</td><td>3.2 (0.2) × 10<sup>-17</sup></td></tr><tr><td>1757</td><td>1873</td><td>10</td><td>[001]</td><td>2,460 (573)</td><td>3,903 (908)</td><td></td><td>51 (17)</td><td>8.7 (0.6) × 10<sup>-17</sup></td></tr><tr><td>1773-1</td><td>1773<sup>a</sup></td><td>15</td><td>[001]</td><td>1,583 (245)</td><td>2,512 (388)</td><td></td><td>19 (8)</td><td>1.0 (0.2) × 10<sup>-17</sup></td></tr><tr><td>1773-2</td><td>1773<sup>a</sup></td><td>15</td><td>[001]</td><td>1,583 (245)</td><td>2,512 (388)</td><td></td><td>32 (10)</td><td>2.4 (0.1) × 10<sup>-17</sup></td></tr><tr><td>1814-81</td><td>1673</td><td>30</td><td>[001]</td><td>1,562 (196)</td><td>2,478 (312)</td><td>1,710 (234)</td><td>3 (1)</td><td>1.3 (0.1) × 10<sup>-18</sup></td></tr><tr><td>1802-1</td><td>1673</td><td>60</td><td>[001]</td><td>5,301 (764)</td><td>8,411 (1,212)</td><td>6,591 (127)</td><td>28 (12)</td><td>2.6 (0.1) × 10<sup>-17</sup></td></tr><tr><td>1802-2</td><td>1673</td><td>60</td><td>[001]</td><td>5,301 (764)</td><td>8,411 (1,212)</td><td>6,591 (127)</td><td>28 (10)</td><td>2.4 (0.1) × 10<sup>-17</sup></td></tr><tr><td>1817</td><td>1573</td><td>150</td><td>[001]</td><td>2,448 (443)</td><td>3,884 (688)</td><td></td><td>35 (8)</td><td>1.6 (0.2) × 10<sup>-18</sup></td></tr></tbody></table>

as described previously (e.g., Dohmen, Becker, et al., 2002; Fei et al., 2012, 2013, 2014). The sample surface in this study also became very rough even by the protection using diamond single crystals. It was therefore frequently difficult to find an area on the sample surface with topography of less than 100 nm in an 80 × 80 µm² area, which was the typical crater size in previous studies using SIMS Cameca-3f or Cameca-6f (e.g., Costa & Chakraborty, 2008; Fei et al., 2012, 2013; Shimojuku et al., 2004, 2009, 2010). Areas with less than 100 nm topography were generally limited to 20 × 20 µm². Such small crater sizes with high mass resolutions were achieved by using a NanoSIMS. By reducing the crater size to 10 × 10 µm², the surface topography within the craters was suppressed to less than 60 nm, and mostly less than 40 nm, as listed in Table 1.

Additionally, we performed zero-time runs, in which the samples were heated to the target temperature and then quenched immediately. The nominal diffusion profiles in the samples from zero-time runs were analyzed by NanoSIMS as well (Figure 3). The nominal diffusion lengths (L) in these runs were found to be a linear function of surface topography (σ), which agrees well with that determined by Fei et al. (2012) (Figure 4). The D'$_{Si}$ in the real diffusion experiments obtained from Equation 1 was thus corrected using the following linear relationship (Ganguly et al., 1988),

<footnote><sup>a</sup>Temperature estimated from the power-temperature relationship from other runs. <sup>b</sup>C<sub>H2O</sub> based on unpolarized Fourier transformation infrared spectroscopy analysis with infrared light parallel to [100], [010], or [001] following the axes for Si diffusion. <sup>c</sup>C<sub>H2O</sub> after orientation correction using the C<sub>H2O</sub> with **E**//[100], **E**//[010], and **E**//[001] polarizations reported in Jacobsen et al. (2005). <sup>d</sup>C<sub>H2O</sub> before diffusion annealing (with random orientation).</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Linear relationship between nominal diffusion length (L) in zero-time runs and the standard deviation of surface topography (σ) in the secondary ion mass spectroscopy crater. The data points obtained in this study using Cameca NanoSIMS agree well with those obtained in Fei et al. (2012) using Cameca IMS-6f.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Examples of Fourier transformation infrared spectroscopy (FTIR) spectra in the recovered samples after baseline correction and thickness normalization to 1 cm. The spectra agree well with typical FTIR spectra of wadsleyite with strong absorptions at 3,320 and 3,357 cm⁻¹, and relatively weak absorptions at 3,579 and 3,265 cm⁻¹.</figcaption></figure>

$$4D_{Si}t = 4D'_{Si}t - L^2(\sigma) \quad (2)$$

where D_Si is the Si diffusion coefficient after the correction. The Equation 2 covers the corrections of the SIMS convolution effect (depth resolution of SIMS), diffusion during heating up to the target temperature, and the relatively small contribution by the surface topography.

## 2.5. FT-IR Spectroscopy

The H₂O content in each recovered sample was determined by unpolarized Fourier transformation infrared spectroscopy (FTIR) using a Bruker IFS 120 high-resolution spectrometer coupled with a Bruker IR microscope. One or two hundred scans were accumulated for each spectrum at a resolution of 2 cm⁻¹ with infrared light parallel to [100], [010], or [001] following the polished planes for diffusion experiments (Table 1). Examples of the spectra are given in Figure 5.

The H₂O contents in the samples were calculated using the Beer-Lambert law,

$$C_{H2O} = 10^6 \times \int \frac{3H(v)M_{H2O}}{\varepsilon \tau \rho} dv \quad (3)$$

where C_H₂O is the H₂O content in wt. ppm, H(v) is the infrared absorption at wavenumber v, M_H₂O is the molar weight of H₂O (18.02 g/mol), ε is the absorption coefficient (ε = 69,000 ± 7,000 L mol⁻¹ cm⁻² for Fe-free wadsleyite determined by Bolfan-Casanova et al., 2018), τ is the sample thickness, and ρ is the density (ρ ≈ 3,500 g L⁻¹ under hydrous conditions [Jacobsen et al., 2005]). After background subtraction, the integration was performed in the range of 3,000–4,000 cm⁻¹. It is noted that the infrared spectra of wadsleyite is anisotropic (Jacobsen et al., 2005), thus, C_H₂O based on unpolarized FTIR spectra obtained on the particular planes may cause biases. Therefore, the C_H₂O values were corrected using the ratio of C_H₂O with E// [100], E// [100], and E// [100] polarizations given in Jacobsen et al. (2005) in addition to those without orientation correction as shown in Table 1.

Because the sample surrounding (gold) cannot absorb any H₂O, the C_H₂O in the samples did not vary significantly, that is, within a factor of 1.5 (Table 1), which is acceptable in log scale by considering the experimental uncertainty (Figure 6). Additionally, proton diffusion in wadsleyite is extremely fast (10⁻⁹.⁵–10⁻¹⁰.⁵ m²/s at 1573–1873 K) (Sun et al., 2018), the H₂O in wadsleyite should reach equilibrium within 1 min. Therefore, the C_H₂O measured in the recovered samples should represent the C_H₂O condition during diffusion annealing.

## 3. Experimental Results

The experimental results show that D_Si increases systematically by about two orders of magnitude with increasing C_H₂O from ~10 to 5,300 wt. ppm (Figure 6). On the other hand, D_Si increases by about 1.5 orders of magnitude with increasing temperature from 1573 to 1873 K (Figure 7). The D_Si show indistinguishable values in the [100], [010], and [001] directions, indicating no detectable anisotropy of Si diffusion in wadsleyite (Figures 6 and 7).

The data points are fitted to the Arrhenius equation with the H₂O content factor,
<figure><img src="image_9.png" /><figcaption>**Figure 6.** H₂O content dependence of Si diffusion coefficient in wadsleyite at 1873 K along [100], [010], and [001] directions. (a). Based on C<sub>H₂O</sub> without orientation correction. (b). Based on C<sub>H₂O</sub> with orientation correction. The dash lines are fitting curves of [010] and [001] data points. The thick gray line is fitting of all the data points.</figcaption></figure>

$$D_{\text{Si}} = D_0(C_{\text{H}_2\text{O}})^r \exp\left(-\frac{\Delta H}{RT}\right) \quad (4)$$

where D₀ is the pre-exponential factor, r is the C<sub>H₂O</sub> exponent, ΔH is the activation enthalpy, R is the gas constant, and T is the absolute temperature. The least squares fitting yields D₀ = 10⁻¹¹.⁵ ± 1.¹ m²/s, r = 0.8 ± 0.1, and ΔH = 270 ± 40 kJ/mol, by assuming r independent from T. The fitting of r based on C<sub>H₂O</sub> without and with orientation correction do not show meaningful difference (r = 0.82 ± 0.12 and 0.77 ± 0.11, respectively, as shown in Figure 6).
<figure><img src="image_10.png" /></figure>

**Figure 7.** Temperature dependence of Si diffusion coefficient in wadsleyite along [100], [010], and [001] directions. The data points from this study are adjusted to a H₂O content of 3,000 and 3,001 wt. ppm using the C₉₀₀-exponent of *r* = 0.8. The data points from Shimojuku et al. (2004, 2009; 2010) were obtained from polycrystalline samples with H₂O content of 10–140 wt. ppm. The dash lines are fitting curves of [100], [010], and [001] data points, respectively. The black line is fitting of all the data points.

# 4. Discussions

## 4.1. H₂O Content and Temperature Dependences of D<sub>Si</sub>

As mentioned in the introduction, the C<sub>H2O</sub> exponent for Si diffusion in wadsleyite was not quantitatively determined previously. In the present study, the H₂O enhancement of Si diffusion in wadsleyite is quantitatively determined with a C<sub>H2O</sub> exponent of *r* = 0.8 ± 0.1 (Figure 6). It indicates that H₂O incorporation significantly enhances Si diffusion in wadsleyite, which is a strong contrast to the Si diffusion in its low-pressure polymorph, olivine (*r* = 0.32 ± 0.07 [Fei et al., 2013]), and contrast to the Mg diffusion (D<sub>Mg</sub>) in wadsleyite (*r* = 0.3 ± 0.1 [Zhang et al., 2021]).

The temperature dependence of D<sub>Si</sub> determined in this study is comparable with those reported previously (Shimojuku et al., 2004, 2009; 2010). However, the absolute values of D<sub>Si</sub> in this study are higher (Figure 7), that is, D<sub>Si</sub> from this study after C<sub>H2O</sub> adjusting to 1 wt. ppm using the C<sub>H2O</sub> exponent of 0.8 is comparable with those reported in Shimojuku et al. (2004, 2009, 2010) with 10–140 wt. ppm (Figure 7). This discrepancy could be caused by multiple reasons, (a) polycrystalline samples were used in Shimojuku et al. (2004, 2009, 2010), which may potentially enlarge the uncertainties because √4D<sub>Si</sub>t and c₀ in Equation 1 are less constrained in fitting due to the contributions of grain-boundary diffusion (e.g., Figure 4 in Shimojuku et al., 2010); (b) the surface topography in Shimojuku et al. (2004, 2009, 2010) are 40–300 nm, which is comparable with their reported √4D<sub>Si</sub>t. Namely, the lattice diffusion is partially hidden by topography; (c) the actual Si activity could be systematically different although both Shimojuku et al. (2004, 2009, 2010) and this study are buffered by SiO₂; (d) the actual temperature in the cell assemblies of this study and Shimojuku et al. (2004, 2009, 2010) could be systematically different although both are self-consistent. However, all of those causes should not affect the C<sub>H2O</sub> exponent for D<sub>Si</sub> determined in this study.

## 4.2. Defect Chemistry Model

Comparison of the C<sub>H2O</sub> exponent for D<sub>Si</sub> in wadsleyite with its lower-pressure polymorph, olivine, shows that, H₂O incorporation dramatically enhances the Si diffusion in wadsleyite (*r* = 0.8 ± 0.1 determined in this study), but only slightly in olivine (*r* = 0.32 ± 0.07 [Fei et al., 2013]). In contrast, the D<sub>Mg</sub> in olivine is significantly enhanced
<table><caption>**Table 2**
$f_{H2O}$ Exponents for Defect Concentrations Under Various Charge Neutrality Conditions</caption><thead><tr><th>Charge neutrality</th><th>[Fe<sub>Mg</sub>•]</th><th>[V<sub>Mg</sub>'']</th><th>[H<sub>Mg</sub>']</th><th>[(2H)<sub>Mg</sub>×]</th><th>[V<sub>Si</sub>'''']</th><th>[H<sub>Si</sub>'''']</th><th>[(2H)<sub>Si</sub>''']</th><th>[(3H)<sub>Si</sub>']</th><th>[(4H)<sub>Si</sub>×]</th></tr></thead><tbody><tr><td>[Fe<sub>Mg</sub>•] = 2[V<sub>Mg</sub>'']</td><td>0</td><td>0</td><td>1/2</td><td>1</td><td>0</td><td>1/2</td><td>1</td><td>3/2</td><td>2</td></tr><tr><td>[(OH)<sub>O</sub>•] = 2[V<sub>Mg</sub>'']</td><td>-1/6</td><td>1/3</td><td>2/3</td><td>1</td><td>2/3</td><td>1</td><td>4/3</td><td>5/3</td><td>2</td></tr><tr><td>[Fe<sub>Mg</sub>•] = [H<sub>Mg</sub>]</td><td>1/4</td><td>-1/2</td><td>1/4</td><td>1</td><td>-1</td><td>-1/4</td><td>1/2</td><td>5/4</td><td>2</td></tr><tr><td>[(OH)<sub>O</sub>•] = [H<sub>Mg</sub>]</td><td>0</td><td>0</td><td>1/2</td><td>1</td><td>0</td><td>1/2</td><td>1</td><td>3/2</td><td>2</td></tr><tr><td>[(OH)<sub>O</sub>•] = 4[V<sub>Si</sub>'''']</td><td>-1/10</td><td>1/5</td><td>3/5</td><td>1</td><td>2/5</td><td>4/5</td><td>6/5</td><td>8/5</td><td>2</td></tr><tr><td>[(OH)<sub>O</sub>•] = 3[H<sub>Si</sub>'''']</td><td>0</td><td>0</td><td>1/2</td><td>1</td><td>0</td><td>1/2</td><td>1</td><td>3/2</td><td>2</td></tr><tr><td>[(OH)<sub>O</sub>•] = 2[(2H)<sub>Si</sub>''']</td><td>1/6</td><td>-1/3</td><td>1/3</td><td>1</td><td>-2/3</td><td>0</td><td>2/3</td><td>4/3</td><td>2</td></tr><tr><td>[(OH)<sub>O</sub>•] = [(3H)<sub>Si</sub>']</td><td>1/2</td><td>-1</td><td>0</td><td>1</td><td>-2</td><td>-1</td><td>0</td><td>1</td><td>2</td></tr></tbody></table>

*Note.* The $C_{H2O}$ is proportional to $f_{H2O}$ if protons are primarily held by the defects which has an $f_{H2O}$ exponent of 1. The exponent values are calculated following Kohlstedt (2006).

by H₂O incorporation ($r = 1.2 \pm 0.2$ for $D_{Mg}$ [Fei et al., 2018], $r = 0.9 \pm 0.3$ for $D_{Fe-Mg}$ [Fe-Mg interdiffusion, Hier-Majumder et al., 2005]), whereas that in wadsleyite has very small $C_{H2O}$ dependence ($r = 0.3 \pm 0.1$ for $D_{Fe-Mg}$ [Zhang et al., 2021]) (Table 2). For the higher-pressure form, ringwoodite, If the $C_{H2O}$ exponent for $D_{Si}$ in ringwoodite is equal to that of the dislocation mobility ($r = 1.1 \pm 0.1$) (Fei et al., 2017), the $C_{H2O}$ exponent for $D_{Si}$ of wadsleyite is slightly smaller than that of ringwoodite. On the other hand, the $D_{Fe-Mg}$ in ringwoodite has an $C_{H2O}$ exponent of $0.25 \pm 0.03$ (Zhang et al., 2019), which is comparable with that in wadsleyite (Zhang et al., 2021) and much smaller than that in olivine (Fei et al., 2018). Below we discuss the defect chemistry of the three polymorphs individually to interpret the different $C_{H2O}$ exponents for $D_{Si}$ and $D_{Mg}$.

The Si and Mg diffusion occur by migration of Si and Mg ions from regular sites to neighboring vacant sites by the vacancy diffusion mechanism. Therefore, $D_{Si}$ and $D_{Mg}$ should be proportional to the concentrations of the corresponding rate-limiting defects, that is, $D_{Si} \propto [V_{Si}]$, $D_{Mg} \propto [V_{Mg}]$ (here $V_{Si}$ and $V_{Mg}$, respectively, are defects related to Si and Mg that are hydrated or unhydrated). Thus, the $C_{H2O}$ exponents for $D_{Si}$ and $D_{Mg}$ can be understood by the $C_{H2O}$ exponents (and H₂O fugacity [$f_{H2O}$] exponents) for defect concentrations under hydrous conditions.

Protons are incorporated into wadsleyite primarily by substituting the Mg sites, where one Mg ion is replaced by two protons (e.g., Demouchy et al., 2005; Druzhbin et al., 2021; Fei & Katsura, 2021; Litasov et al., 2011; Purevjav et al., 2016), leading to much higher defect concentrations on the Mg sites than the Si sites. The primary hydration reaction is,

$$ \mathrm{Mg}_{\mathrm{Mg}}^{\times} + 2\mathrm{O}_{\mathrm{O}}^{\times} + \mathrm{H}_{2}\mathrm{O} = \{\mathrm{V}_{\mathrm{Mg}}^{\prime\prime} - 2(\mathrm{OH})_{\mathrm{O}}^{\bullet}\}^{\times} + \mathrm{MgO} \quad (5) $$

where the defect association $\{V_{Mg}'' - 2(OH)_O\cdot\}^\times$ is equivalent with $(2H)_{Mg}^\times$. The dominance of this hydration reaction leads to $C_{H2O} \propto f_{H2O}$ (Kohlstedt, 2006).

A certain fraction of $(2H)_{Mg}^\times$ may dissociate to $(OH)_O\cdot$, $V_{Mg}''$, and $H_{Mg}'$ (e.g., Kohlstedt, 2006; Kohlstedt & Hansen, 2015) as,

$$ (2H)_{Mg}^{\times} \equiv \{V_{Mg}'' - 2(OH)_O\cdot\}^{\times} = H_{Mg}' + (OH)_O\cdot \quad (6) $$

$$ (H)_{Mg}' \equiv \{V_{Mg}'' - (OH)_O\cdot\}^{\prime} = V_{Mg}'' + (OH)_O\cdot \quad (7) $$

Under these circumstances, the charge neutrality conditions in Fe-free hydrous wadsleyite is expected to be maintained by $[(OH)_O\cdot] = 2[V_{Mg}'']$ or $[(OH)_O\cdot] = [H_{Mg}']$ (e.g., Fei & Katsura, 2016; Kohlstedt, 2006). With each charge neutrality conditions, the concentrations of different defects increase or decrease by increasing $f_{H2O}$ with different exponents (Table 2).
The current $C_{H2O}$ exponent of $r = 0.8 \pm 0.1$ for $D_{Si}$ in Fe-free wadsleyite suggests that Si diffusion is controlled by either $(2H)_{Si}''$ with the charge neutrality condition of $[(OH)_{O}^{\bullet}] = [H_{Mg}']$ $[(2H)_{Si}'''] \propto C_{H2O}^{-1}$ shown in Table 2) or by $V_{Si}'''$ or $H_{Si}'''$ with the charge neutrality condition of $[(OH)_{O}^{\bullet}] = 2[V_{Mg}']$ $[V_{Si}''''] \propto C_{H2O}^{2/3}[H_{Si}''''] \propto C_{H2O}^{-1}$, Table 2). In other words $(3H)_{Si}'$ and $(4H)_{Si}^{\times}$ are unlikely to dominate Si diffusion in Fe-free wadsleyite because they will result in much larger $C_{H2O}$ exponents ($\ge 3/2$, Table 2).

In Fe-bearing wadsleyite, Nishihara, Shinmei, Karato (2008) suggested a charge neutrality condition of $[Fe_{Mg}^{\bullet}] = [H_{Mg}']$. This condition leads to the $C_{H2O}$ exponents of 1/4 for both $[H_{Mg}']$ and $[Fe_{Mg}^{\bullet}]$, explaining the $H_2O$ exponent of $r = 0.3 \pm 0.1$ for $D_{Fe-Mg}$ reported by Zhang et al. (2021). If $V_{Si}'''$ or $H_{Si}'''$ dominated Si diffusion, $D_{Si}$ would have a negative $C_{H2O}$ dependence (Table 2), which is against the water-weakening of Fe-bearing wadsleyite (Hustoft et al., 2013). Thus, $V_{Si}'''$ and $H_{Si}'''$ are excluded as the dominant species for Si diffusion in Fe-bearing wadsleyite. Therefore, if we assume the same Si diffusion mechanism in Fe-bearing and Fe-free wadsleyite, $D_{Si}$ is most likely controlled by migration of $(2H)_{Si}''$.

Fe-bearing hydrous ringwoodite has a $C_{H2O}$ exponent of $r = 0.25 \pm 0.03$ for $D_{Fe-Mg}$ (Zhang et al., 2019), indicating the charge neutrality condition of $[Fe_{Mg}^{\bullet}] = [H_{Mg}']$. Therefore, the $r = 1.1 \pm 0.1$ for $D_{Si}$ inferred from dislocation annihilation rate in Fe-bearing ringwoodite (Fei et al., 2017) suggests a $(3H)_{Si}'$-controlled Si diffusion mechanism because $[(3H)_{Si}'] \propto C_{H2O}^{5/4}$. The $V_{Si}'''$, $H_{Si}'''$, $(2H)_{Si}'$, and $(4H)_{Si}^{\times}$ are all unlikely because of their much smaller ($r \le 1/2$) or larger ($r = 2$) $C_{H2O}$ exponents (Table 2).

In olivine, proton incorporation occurs by substituting the Si sites with the reaction $Si_{Si}^{\times} + 4O_{O}^{\times} + 2H_2O = V_{Si}''' + 4(OH)_O^{\bullet} + SiO_2$ (e.g., Fei & Katsura, 2020b). Therefore, the charge neutrality condition could be maintained by $V_{Si}'''$ and $(OH)_O^{\bullet}$ (Table 2). The $r = 0.32 \pm 0.07$ for $D_{Si}$ and $r = 0.9-1.2$ for $D_{Mg}$ in olivine (Fei et al., 2013, 2018; Hier-Majumder et al., 2005) suggest that Si and Mg diffusion are most likely controlled by $V_{Si}'''$ and $(2H)_{Mg}^{\times}$, respectively, under the charge neutrality condition of $[(OH)_{O}^{\bullet}] = 4[V_{Si}''']$ because of $[V_{Si}''''] \propto C_{H2O}^{2/5}$ and $[(2H)_{Mg}^{\times}] \propto C_{H2O}^{-1}$ (Table 2) by assuming $C_{H2O} \propto f_{H2O}$ (Kohlstedt et al., 1996; Zhao et al., 2004). However, depending on the dominant defects for holding protons, $C_{H2O}$ and $f_{H2O}$ may not follow a linear relationship (Otsuka & Karato, 2011), thus, the $C_{H2O}$ exponents for $D_{Si}$ and $D_{Mg}$ may not equal the $f_{H2O}$ exponents for $[V_{Si}]$ and $[V_{Mg}]$. For example, if protons are held primarily by $(2H)_{Si}'$ and the charge neutrality condition is $[(OH)_O^{\bullet}] = 4[V_{Si}'''']$, we have $C_{H2O} \propto [(2H)_{Si}'] \propto f_{H2O}^{6/5}$, thus, $D_{Si} \propto [V_{Si}''''] \propto f_{H2O}^{2/5} \propto C_{H2O}^{1/3}$ (Table 2), which also agree with the experimental results. To better constrain the Si diffusion mechanism in hydrous olivine, precise $f_{H2O}$ and $C_{H2O}$ relationship is required.

### 4.3. Isotropic Si Diffusivity in Mantle Minerals

As shown in Figures 6 and 7, the $D_{Si}$ in wadsleyite is found to be isotropic under both $H_2O$-poor and $H_2O$-rich conditions. The least squares fitting of data points for each crystallographic axis suggest an apparent maximum anisotropy factor of about three at 1500–1600°C (Figure 7), but this apparent value is caused by the scattering of [010] data points. The actual anisotropy is expected to be much smaller than three. The nearly isotropic Si diffusion is also the case of other mantle minerals including olivine (Costa & Chakraborty, 2008), bridgmanite (Xu et al., 2011), quartz, and feldspar (Cherniak, 2003). Although small anisotropy is reported in stishovite (Shatskiy et al., 2010), its magnitude of anisotropy is within experimental uncertainty as well. In contrast, the Mg diffusion in olivine is found to be anisotropic (Chakraborty et al., 1994).

It is known that self-diffusion in a crystal occurs by hopping of the diffusing species driven by thermal vibrations. The probabilities of successful hops along various crystallographic directions, which are related to the frequencies and activation barriers of the thermal vibrations, control the diffusion anisotropy. In the case of Mg diffusion, the activation barrier is related to the distances between two Mg ions, therefore, the diffusion anisotropy is correlated to the distances (e.g., Brodholt, 1997). In the case of Si, the activation barrier is primarily controlled by the local environment, that is, limited by the escape of a Si ion from the closely packed $SiO_4$ tetrahedron regardless of diffusion direction. Hence, the diffusion coefficient is nearly isotropic.

### 4.4. H₂O-Induced Viscosity Reduction in the Mantle Transition Zone

Because the viscosity of silicate minerals is considered to be inversely proportional to the diffusion coefficient of Si, the $H_2O$ enhancement of $D_{Si}$ will induce the reduction of viscosity. Using the $C_{H2O}$ exponent of 0.8, the
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Relative viscosity ($\eta \propto 1/D_{Si}$) in the transition zone and plumes at various H₂O content and temperature conditions. The temperature in the plumes is assumed to be 200–500 K higher ($\Delta T$) than normal geotherm (Katsura et al., 2010). The pressure dependence of $D_{Si}$ is assumed to be the same as olivine (Fei et al., 2012). MTZ: mantle transition zone.</figcaption></figure>

viscosity of H₂O-rich wadsleyite ($C_{H2O} \sim 1.0$ wt.%, H₂O-saturated wadsleyite at mantle transition zone temperature [Fei & Katsura, 2021]) is by 1.6 orders of magnitude lower than H₂O-poor wadsleyite ($C_{H2O} \sim 0.01$ wt.%) (Figure 8). On the other hand, although the $C_{H2O}$ exponent for $D_{Si}$ in ringwoodite is unknown, it can be estimated to be $r \approx 1.1$ based on the H₂O dependence of dislocation-annihilation rate in ringwoodite (Fei et al., 2017). Therefore, the H₂O incorporation dramatically reduces the viscosity of both wadsleyite and ringwoodite, the dominant minerals in the upper (410–520 km depth) and lower (520–660 km depth) part of mantle transition zone, respectively (Figure 8).

### 4.5. Evolution of Plumes in the Mantle Transition Zone

Seismic observations of the 60 plumes (e.g., Zhao, 2007) indicate that the mantle transition zone induces enigmatic evolutions of the plumes when crossing the 410–660 km layer. Some plumes such as Iceland, Hainan, and Galapagos are accelerated and narrowed in the mantle transition zone, whereas some others such as Hawaii, East Australia are broadened or curved. The cause of such enigmatic evolutions is unknown.

The plume shape is controlled by the viscosity contrast between the upwelling flow and materials in the surrounding mantle (Condie, 2016). When the plume has a lower viscosity than the surrounding mantle, it will appear like a mushroom with a broad head and may be curved by the horizontal flow

driven by plate tectonics. On the other hand, when the plume has a higher viscosity than the surroundings, it will rise straightly with its original thickness or could be slightly narrowed because of cooling of the plume edges by the surroundings. Therefore, the viscosity contrast of wadsleyite (and ringwoodite) between the plumes and the surrounding mantle may provide an answer for the origin of the mystical evolution of plumes in the mantle transition zone.

Combining the H₂O and temperature effects on Si diffusion coefficient in wadsleyite determined in this study, the viscosity contrast between the plume and surrounding mantle in the transition zone can be evaluated with various temperature and H₂O content conditions. As shown in Figure 8, if the plume has a low H₂O content ($C_{H2O} = 0.01$ wt.%) and relatively low temperature [$\Delta T = +200$ K, that is, 200 K higher than normal geotherm (Katsura et al., 2010), the plume viscosity will be higher than a H₂O-rich mantle transition zone by about one order of magnitude. In contrast, when the plume has either high temperature ($\Delta T = +500$ K) or high H₂O content ($C_{H2O} = 1.0$ wt.%), the viscosity will be significantly reduced and become comparable or even lower than a H₂O-rich transition zone. However, if the mantle transition zone is H₂O-poor, the plume viscosity will be always lower than the surrounding mantle because $\Delta T > 0$ (Figure 8).

Most of the plumes are originated from the deep lower mantle (Condie, 2016; Zhao, 2007). Therefore, they should be H₂O-poor because of the dry lower mantle (Hirschmann, 2006; Liu et al., 2021). On the other hand, the mantle transition zone is demonstrated to be H₂O-rich at least locally (Kelbert et al., 2009; Pearson et al., 2014) or even globally (Fei et al., 2017). Thus, the plumes with a relatively low-temperature (still higher than the transition zone, e.g., $\Delta T = +200$ K in Figure 8) are expected to be accelerated and narrowed because of it has higher viscosity than the transition zone. On the other hand, the plumes that are broadened or curved in the mantle transition zone are expected to have either relatively high temperature (e.g., $\Delta T \ge +500$ K) or locally dry surrounding mantle.

In case of either narrowed or broadened in the mantle transition zone, eventually, the upwelling flows will reach the 410-km depth boundary between the transition zone and upper mantle. Because the upper mantle has low H₂O content (~100 wt. ppm), the plumes will have lower viscosity than the surrounding mantle and therefore been broadened just beneath 410-km depth. It explains the inverted-triangle-shape of the narrowed plumes such as Iceland, Galapagos, Hainan, and San Felix near the 410-km depth boundary (Zhao, 2007).
## Acknowledgments

We appreciate H. Fischer for the preparation of high-pressure cell assembly, R. Njul for sample polishing, and Dr. Jianchao Zhang for assistance in SIMS analysis. We also appreciate two anonymous reviewers for helpful comments. This work is financially supported by the Deutsche Forschungsgemeinschaft to T. Katsura (KA3434/7-1, KA3434/8-1) and the annual budget of Bayerisches Geoinstitut to H. Fei. Open access funding enabled and organized by Projekt DEAL.

## Data Availability Statement

The SIMS and FTIR data for this paper are given in Zenodo (https://doi.org/10.5281/zenodo.6265716).

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