⇦Chinese Physics Letters, 2017, Vol. 34, No. 10, Article code 108301⇨ Hydrogen-Bond Symmetrization of $\delta$-AlOOH * Duan Kang(康端)1, Ye-Xin Feng(冯页新)2, Ying Yuan(袁颖)3, Qi-Jun Ye(叶麒俊)3, Feng Zhu(朱峰)1, Hao-Yan Huo(霍浩岩)3, Xin-Zheng Li(李新征)3**, Xiang Wu(巫翔)4** Affiliations 1Key Laboratory of Orogenic Belts and Crustal Evolution (Ministry of Education), School of Earth and Space Sciences, Peking University, Beijing 100871 2School of Physics and Electronics, Hunan University, Changsha 410081 3School of Physics and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871 4State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan 430074 Received 12 June 2017 ^*Supported by the National Natural Science Foundation of China under Grant Nos U1232204, 41473056, 11422431 and 11634001, the National Key Research and Development Program of China under Grant No 2016YFA0300901, and the National Basic Research Program of China under Grant No 2013CB934600.
^**Corresponding author. Email: wuxiang@cug.edu.cn; xzli@pku.edu.cn Citation Text: Kang D, Feng Y X, Yuan Y, Ye Q J and Zhu F et al 2017 Chin. Phys. Lett. 34 108301 Abstract The $\delta$-AlOOH can transport water into the deep mantle along cold subducting slab geotherm. We investigate the hydrogen-bond symmetrization behavior of $\delta$-AlOOH under the relevant pressure-temperature condition of the lower mantle using ab initio molecular dynamics (MD). The static symmetrization pressure of 30.0 GPa can be reduced to 17.0 GPa at 300 K by finite-temperature ($T$) statistics, closer to the experimental observation of $\sim $10.0 GPa. The symmetrization pressure obtained by MD simulation is related to $T$ by $P\,({\rm GPa})=13.9\,({\rm GPa})+0.01\,({\rm GPa/K})\times T\,({\rm K})$. We conclude that $\delta$-AlOOH in the lower mantle exists with symmetric hydrogen bond from its birthplace, or someplace slightly deeper, to the core-mantle boundary (CMB) along cold subducting slab geotherm. The bulk modulus decreases with $T$ and increases anomalously upon symmetrization: $K_{0}\,({\rm GPa})=181\,({\rm GPa})-0.013\,({\rm GPa/K})\times T\,({\rm K})$ for $\delta$-AlOOH with asymmetric hydrogen bond, and $K_{0}\,({\rm GPa})=216\,({\rm GPa})-0.013\,({\rm GPa/K})\times T\,({\rm K})$ for $\delta$-AlOOH with symmetric hydrogen bond. Our results provide an important insight into the existent form and properties of $\delta$-AlOOH in the lower mantle. DOI:10.1088/0256-307X/34/10/108301 PACS:83.10.Rs, 83.10.Tv, 64.30.Jk © 2017 Chinese Physics Society Article Text Water plays an important role in the evolution of Earth because it changes the physical properties of mantle materials, including the melting temperature, viscosity, and diffusion rate.[1] Most of the hydrous phases, such as the superhydrous phase B, phase D and phase E, decompose and dehydrate above the deep lower mantle due to the high temperature.[1] However, phase $\delta$ ($\delta$-AlOOH), phase H (MgSiO$_{4}$H$_{2}$) and their solid solution ($\delta$-AlOOH-MgSiO$_{4}$H$_{2}$) can be stable down to the CMB below subduction zone.[2-4] The properties of $\delta$-AlOOH under conditions of high temperature and high pressure can inform discussions of the water content and distribution in the lower mantle. The hydroxyl group (OH) in hydrous phases is weakly attracted to a neighboring oxygen atom on the opposite site, presenting an asymmetric O-H$\cdots$O configuration under ambient conditions,[5] where the potential surface along the two neighboring atoms is double-well and the hydrogen atom is bound to one neighboring oxygen atom. With the increasing pressure, the potential barrier between the two neighboring atoms becomes so low that the H atoms' zero-point energy can wash it out. In this case, H atoms distribute broadly and flatly in a unimodal centering at the midpoint between the two nearest O atoms, and the hydrogen bond presents a symmetric configuration. When pressure increases further, the potential surface may finally change to a single well, with the hydrogen atom centered perfectly between its two neighboring atoms.[6-8] This process, defined as pressure-induced hydrogen-bond symmetrization, has been described by both experiments and first-principles calculations for ice,[9,10] $\alpha$-FeOOH,[11] $\varepsilon$-FeOOH[12] and $\delta$-AlOOH.[13-15] Hydrogen-bond symmetrization produces significant effects on the properties of the hosts, such as an increase in elasticity.[5,16] Additionally, hydrogen-bond symmetrization is coupled with the spin transition of Fe$^{3+}$, i.e., the hydrogen-bond symmetrization can assist in ferric spin collapse. In turn, the ferric spin collapse would accelerate the symmetrization in the case of FeOOH.[11,12] The $\delta$-AlOOH, formed at the top of the lower mantle from the decomposition of phase Egg,[17] is the high-pressure polymorph of $\alpha$- and $\gamma$-AlOOH.[13] The properties of $\delta$-AlOOH have been examined and discussed by several groups.[13-15] Some experimental evidence, such as the abnormalities observed in the shift of vibrational peaks and the change of axial compressibility under high pressure, indicates that $\delta$-AlOOH undergoes an asymmetric-to-symmetric transition of hydrogen bonds at approximately 10.0 GPa and at room temperature. However, this critical pressure for the hydrogen-bond symmetrization of $\delta$-AlOOH is calculated by first principles to be approximately 30.0 GPa.[13,16,18] Thus a considerable gap of 20.0 GPa exists compared with the experimentally measured values. The most likely reason for this discrepancy is that previous calculations were based on static calculations and did not take into account the thermal vibration effects and quantum effects, which can affect the symmetrization pressure. Molecular dynamics simulation is a successful method to take into account of thermal vibration effects, and has been widely applied to the investigations of many materials.[19-23] Bronstein et al.[24] have recently performed standard MD simulations taking account of thermal vibrational effects and quantum thermal bath (QTB) MD taking account of thermal vibrational and nuclear quantum effects on $\delta$-AlOOH at 300 K. Here we performed a series of standard MD simulations for $\delta$-AlOOH at high pressures and 300, 1000, 1500 and 2000 K. To our knowledge, this is the first high-temperature MD report on $\delta$-AlOOH. We have obtained the relationship between the symmetrization pressure of $\delta$-AlOOH and temperature.

Fig. 1. Crystal structures of $\delta$-AlOOH. (a) The hydrogen bond is asymmetric. (b) The hydrogen bond is symmetric.

Our simulations were performed using the plane wave-based density-functional theory (DFT) code Vienna ab-initio simulation package (VASP).[25,26] Projector-augmented wave potentials along with a 750 eV plane-wave cut-off energy were employed in both static calculations and standard MD calculations. In the static calculations, an 8-atom unit cell was calculated with the Perdew–Burke–Ernzerhof (PBE) exchange-correlation function[27] using a ($5\times5\times8$) Monkhorst–Pack grid to sample the Brillouin zone. Two structure candidates were employed, i.e., the structure with asymmetric hydrogen bond, possessing the $P2_{1}nm$ space group, and the structure with symmetric hydrogen bond, possessing the $Pnnm$ space group (Fig. 1, Table S1). Higher cut-off energies and denser Monkhorst–Pack grids have slight significance. Based on the optimized structures from static calculations, supercells containing 64 atoms were adopted in the MD calculations, in which we used a ($2\times2\times4$) Monkhorst–Pack grid. We performed isothermal–isobaric molecular dynamics (NPT-MD) (constant pressure and temperature) simulations at 300, 1000, 1500 and 2000 K. All of the pressures used in the present study are real statistical pressures. Each MD simulation at a finite temperature and pressure was run for 11000 steps using a step of 1 fs, and the final 10000 steps (10 ps) were included in the analysis. Under the 0 GPa and 0 K condition, $R_{\rm O-H}$ is 1.040 Å and $R_{\rm O\cdots H}$ is 1.510 Å, presenting an asymmetric hydrogen bond. With increasing pressure, $R_{\rm O-H}$ increases while $R_{\rm O\cdots H}$ decreases almost linearly (Fig. 2(a)). At 25.0 GPa, the hydrogen bond is still asymmetric (1.159 Å for $R_{\rm O-H}$ and 1.223 Å for $R_{\rm O\cdots H}$). However, at 30.0 GPa, $R_{\rm O-H}$ and $R_{\rm O\cdots H}$ reach almost the same length, with a difference of 0.001 Å, and $R_{\rm O-H}$ becomes $1/2R_{\rm OO}$ (the nearest neighboring O$\cdots$O distance), indicating that the hydrogen atom is located at the center between the two oxygen atoms (the inset of Fig. 2(a)). Thus we propose that $\delta$-AlOOH undergoes an asymmetric-to-symmetric transition of the hydrogen bond at 30.0 GPa and 0 K, in agreement with the previous results.[16,18] Figure 2(b) shows that the $a/c$ and $b/c$ ratios of $\delta$-AlOOH with asymmetric hydrogen bond decrease below 25.0 GPa and increase above 25.0 GPa, in agreement with those observed experimentally (Fig. 2(b)),[14] except for the critical pressures (expt. $\sim$10.0 GPa; theor. $\sim$30.0 GPa). Placed on the plane composed of the $a$ and $b$ axes, the asymmetric hydrogen bond is easily compressed, while the symmetric bond is difficult to compress due to its increased strength.[28] As a result, the $a$ and $b$ axes are more compressible than the $c$ axis in $\delta$-AlOOH with asymmetric hydrogen bond but less compressible in $\delta$-AlOOH with symmetric hydrogen bond.

Fig. 2. (a) O-H and O$\cdots$H distances in $\delta$-AlOOH at different pressures calculated at 0 K. The evolution of $R_{\rm O-H}$ as a function of $R_{\rm OO}$ is displayed as an inset in this figure. The dots are placed every 5.0 GPa from 0 GPa, except for the 29.0 GPa point. The dashed line has the relationship of $R_{\rm O-H}=1/2R_{\rm OO}$, indicating the symmetrization. (b) The $a/c$ and $b/c$ ratios versus pressure in $\delta$-AlOOH. The green solid and green dashed lines, respectively, represent the results of $\delta$-AlOOH with asymmetric hydrogen bond and $\delta$-AlOOH with symmetric hydrogen bond in the present study. The red solid and red dashed lines indicate the theoretical results in the literature.[16] The magenta and purple open circles represent the experimental results by Sano-Furukawa et al.[14] and the wine open diamonds represent the experimental results by Kuribayashi et al.[29]

To understand in detail the evolution of the hydrogen atom probability distribution ($P$) at high-pressure and high-temperature, we plot it as a function of the hydrogen-atom transfer coordinate along the hydrogen bond ($\delta$) and the corresponding O$\cdots$O distance ($R_{\rm OO}$) at different pressures and temperatures in Fig. 3, and the additional figures are shown in Fig. S1 in supplementary materials. The parameter $\delta$ is defined for each hydrogen atom as its transfer coordinate along the hydrogen bond. This coordinate is the difference between the distances of this hydrogen atom to the two oxygen atoms at the ends of this hydrogen bond. When the coordinate is zero, the hydrogen is shared by two oxygen atoms and remains in the center of the hydrogen bond. When the coordinate is large in magnitude on both the positive and negative sides, the hydrogen is bound to one oxygen atom. Asymmetric structures are reflected by the double-peak distributions, indicative of larger probabilities that hydrogen atoms will stay away from the center, whereas single-peak distributions represent symmetric structures, in which hydrogen atoms are located at the center of the two nearest oxygen atoms.[30]

Fig. 3. The hydrogen atom probability distribution functions $P(\delta,R_{\rm OO})$, as a function of the hydrogen atom position relative to the midpoint of the two nearest oxygen atoms ($\delta$) and the distance between the two nearest oxygen atoms ($R_{\rm OO}$) in MD simulations at 300, 1000 and 1500 K. The distribution functions are smoothed for presentation and symmetrized about $\delta= 0$ Å.

We start our discussion with the results at 300 K. At 5.0 GPa, the hydrogen-atom distribution is clearly double-peak, corresponding to an asymmetric structure (Fig. 3(a)). This asymmetric feature weakens upon increasing pressure, and the distribution finally becomes single-peak, which indicates a symmetric structure. The estimation of symmetrization pressure can be improved quantitatively by applying Landau's second-order phase-transition theory, where we plot the probability distribution function of the hydrogen atom as a function of $\delta$ using $P=A\delta^{4}+B\delta^{2}+C$. When the quadratic coefficient $B$ equals zero, the system is at the second-order phase-transition point. Table S3 and Fig. S1b show that 17.0 GPa is the phase-transition pressure for $\delta$-AlOOH at 300 K, as zero falls within the 95% confidence interval of the quadratic coefficient $B$. Bronstein et al.[24] reported that the hydrogen bond in $\delta$-AlOOH symmetrizes at around 15–20 GPa in standard molecular dynamics, in good agreement with our results. At 1000, 1500 and 2000 K, the hydrogen-atom distributions change upon compression in a similar manner to those at 300 K, except that the symmetrization pressure is $\sim$25.0 GPa at 1000 K (Figs. 3(l) and S1e), $\sim$29.9 GPa at 1500 K (Figs. 3(t) and S1h) and $\sim$34.9 GPa at 2000 K (Fig. S1k). The details of determining the distribution shape and transition pressure at 300–2000 K are demonstrated in the supplementary materials (Fig. S1, Tables S2–S6, Texts S1 and S2). It can be seen that the symmetrization pressure of $\delta$-AlOOH depends positively on temperature according to the following relationship: $P\,({\rm GPa})=13.9\,({\rm GPa})+0.01\,({\rm GPa/K})\times T\,({\rm K})$. When temperature further increases, two scenarios exist. In the case that $\delta$-AlOOH possesses asymmetric hydrogen bond at low temperature, the increase of thermal uncertainty results in larger hydrogen-atom distribution probabilities at smaller $R_{\rm OO}$. The system thus becomes less asymmetric, and this effect can be seen by comparing the 5.0 GPa results at 300, 1000 and 1500 K. However, when the hydrogen bond in $\delta$-AlOOH is already symmetric at a low temperature, the increase of thermal uncertainty results in larger hydrogen-atom distribution probabilities at larger $R_{\rm OO}$. Consequently, the system becomes less symmetric under increasing temperature, and the $\sim$20.0 GPa results at 300, 1000 and 1500 K is an example confirming this effect. Moreover, this is the main reason for the fact that the symmetrization pressure of $\delta$-AlOOH increases with temperature. The calculated isothermal zero-pressure bulk moduli ($K_{0}$) of $\delta$-AlOOH with asymmetric or symmetric hydrogen bond at different temperatures that were found by fitting the Birch–Murnaghan equation of state[31] are listed in Table 1. When $K'_{0}$ is 5.0, the theoretical $K_{0}$ values at 0 K for $\delta$-AlOOH with asymmetric hydrogen bond based on DFT calculated in the previous study[16] and in the present study are 167 GPa and 159 GPa, respectively. When $K'_{0}$ is 4.3, the DFT $K_{0}$ values at 0 K for $\delta$-AlOOH with symmetric hydrogen bond calculated in the previous study[16] and in the present study are 205 GPa and 199 GPa, respectively. Therefore, our calculated 0 K DFT $K_{0}$ values are close to those calculated in the previous study.[16] With $K'_{0}$ fixed at 4, the 300 K $K_{0}$ obtained by our simulations for $\delta$-AlOOH with asymmetric hydrogen bond is 171 GPa, 19 GPa greater than the 300 K $K_{0}$ obtained in experiments ($K_{0}=152$ GPa);[14] the 300 K $K_{0}$ by our MD simulations for $\delta$-AlOOH with symmetric hydrogen bond is 196 GPa, 23 GPa smaller than the experimental one obtained by Sano-Furukawa et al.[14] (Fig. 4). When $K'_{0}$ is 3.7, $K_{0}$ at 300 K for $\delta$-AlOOH with symmetric hydrogen bond calculated by our MD data ($K_{0}=203$ GPa) is 13 GPa greater than the data $K_{0}=190$ GPa obtained experimentally by Mashino et al.[32] Additionally, using the 300 K experimental pressure and volume data,[14] we have calculated $K_{0}$ to be 226 GPa with $K'_{0}$ being 3.7. It can be seen that the 300 K experimental $K_{0}$ for $\delta$-AlOOH with symmtric hydrogen bond by Sano-Furukawa et al.[14] and Mashino et al.[32] have a 36 GPa discrepancy. Despite the discrepancies for $K_{0}$ calculated by our 300 K MD data with those reported by previous experiments, our calculated 300 K $K_{0}$ for $\delta$-AlOOH with symmetric hydrogen bond lies between the 300 K experimental $K_{0}$ values reported by Sano-Furukawa et al.[14] and Mashino et al.[32]

**Table 1.** Zero-pressure bulk moduli, pressure derivatives and zero-pressure volumes of $\delta$-AlOOH.
Temperature,	$\delta$-AlOOH with asymmetric hydrogen bond				$\delta$-AlOOH with symmetric hydrogen bond
Method	$K_{0}$ (GPa)	$K'_{0}$	$V_{0}$ (Å$^{3}$)	Pressure (GPa)	$K_{0}$ (GPa)	$K'_{0}$	$V_{0}$ (Å$^{3}$)	Pressure (GPa)
0 K, DFT$^{\rm a}$	173	4.0	57.76	5.0$\sim $30.0	212	4.0	56.71	35.0$\sim $55.0
0 K, DFT$^{\rm a}$	159	5.0	57.92	5.0$\sim $30.0	199	4.3	56.96	35.0$\sim $55.0
0 K, DFT[16]	167	5.0	58.61	0$\sim $30	205	4.3	57.57	30$\sim $60
300 K, MD$^{\rm a}$	171	4.0	58.09	5.0$\sim $15.0	196	4.0	57.60	20.0$\sim $35.0
300 K, MD$^{\rm a}$					203	3.7	57.48	20.0$\sim $35.0
300 K, exp.[14]	152	4.0	56.408	0$\sim $10	219	4.0	55.47	10$\sim $63.5
300 K, exp.[32]					190	3.7	56.374
300 K, exp.[14]					226	3.7	55.392	10$\sim $63.5
1000 K, MD$^{\rm a}$	159	4.0	59.75	5.0$\sim $20.0	175	4.0	59.25	25.0$\sim $45.0
1500 K, MD$^{\rm a}$	149	4.0	61.06	9.9$\sim $27.9	168	4.0	60.25	34.9$\sim $49.9
2000 K, MD$^{\rm a}$					160	4.0	61.30	34.9$\sim $55.9
$^{\rm a}$This work.

Fig. 4. The value of $K_{0}$ for $\delta$-AlOOH with asymmetric or symmetric hydrogen bond as a function of temperature, with $K'_{0}=4$. The experimental $K_{0}$ are derived with $K'_{0}$ being fixed to 4.[14] For $\delta$-AlOOH with asymmetric hydrogen bond (purple line) $K_{0}\,({\rm GPa})=181\,({\rm GPa})-0.013\,({\rm GPa/K})\times T\,({\rm K})$; for $\delta$-AlOOH with symmetric hydrogen bond (red line) $K_{0}\,({\rm GPa})=216\,({\rm GPa})-0.013\,({\rm GPa/K})\times T\,({\rm K})$.

Symmetrization behavior induces anomalous increases in the bulk moduli. For example, due to the symmetrization of hydrogen bond, $K_{0}$ increases from 173 GPa to 212 GPa (39 GPa difference, $\sim$23%) at 0 K and increases from 149 GPa to 168 GPa (19 GPa difference, $\sim$13%) at 1500 K, fixing $K'_{0}$ at 4. Additionally, $K_{0}$ decreases with temperature, described by $K_{0}\,({\rm GPa})=181\,({\rm GPa})-0.013\,({\rm GPa/K})\times T\,({\rm K})$ for $\delta$-AlOOH with asymmetric hydrogen bond and $K_{0}\,({\rm GPa})=216\,({\rm GPa})-0.013\,({\rm GPa/K})\times T\,({\rm K})$ for $\delta$-AlOOH with symmetric hydrogen bond (Fig. 4).

Fig. 5. Symmetrization pressure as a function of temperature (red line) along with the mantle geotherm (magenta line)[33] and subducting slab geotherm (purple line).[34] The open red diamonds represent symmetrization pressures at different temperatures. The fitted line represents the function $P\,({\rm GPa})=13.9\,({\rm GPa})+0.01\,({\rm GPa/K})\times T\,({\rm K})$. The error bars are derived from data in Tables S3–S6 and Fig. S3, from which the upper and lower limits of symmetrization pressures can be determined at different temperatures.

Phase Egg (AlSiO$_{3}$OH) decomposes into $\delta$-AlOOH and stishovite at pressures above 23.0 GPa and temperatures below 1473 K.[17] At 1473 K, the symmetrization pressure of the hydrogen bond in $\delta$-AlOOH is estimated to be 28.6 GPa, according to the relationship: $P\,({\rm GPa})=13.9\,({\rm GPa})+0.01\,({\rm GPa/K})\times T\,({\rm K})$. Additionally, nuclear quantum effects would decrease the symmetrization pressure of the hydrogen bond in $\delta$-AlOOH about 5 GPa according to the study by Bronstein et al.[24] As a result, the symmetrization pressure of hydrogen bond in $\delta$-AlOOH is predicted to be around 23.6 GPa, close to the decomposition pressure of phase Egg. Thus we can deduce that $\delta$-AlOOH would be generated with a hydrogen bond that is completely symmetric or close to symmetric at the top of the lower mantle. Despite the variation in the subducting slab temperature caused by many factors, such as its age and the subduction rate,[17] the $dP/dT$ of the cold subducting slab is greater than 0.01 GPa/K,[33,35,36] ensuring that when the cold subducting slab descends, the pressure in the cold subducting slab increases more rapidly than the predicted symmetrization pressure of $\delta$-AlOOH as temperature increases (Fig. 5). Consequently, whenever the hydrogen bond in $\delta$-AlOOH is slightly non-symmetric, it would rapidly become completely symmetric as the cold subducting slab increases in depth. Therefore, $\delta$-AlOOH is predicted to stabilize in symmetric structure from its birthplace or somewhere slightly deeper to the CMB along the cold subducting slabs. In summary, we have examined the behavior of $\delta$-AlOOH using first-principles calculations. A special focus was placed on the influence of finite-temperature statistical effects on the pressure-induced hydrogen-bond symmetrization and bulk modulus. The symmetrization pressure of hydrogen bond in $\delta$-AlOOH is found to be $\sim$17.0 GPa at 300 K and increases with temperature according to the following function $P\,({\rm GPa})=13.9\,({\rm GPa})+0.01\,({\rm GPa/K})\times T\,({\rm K})$. It can be predicted that $\delta$-AlOOH stabilizes in the structure with symmetric hydrogen bond from its birthplace or somewhere slightly deeper to the CMB along the cold subducting slabs. The $\delta$-AlOOH bulk modulus increases anomalously by hydrogen-bond symmetrization and decreases with temperature: for $\delta$-AlOOH with asymmetric hydrogen bond $K_{0}\,({\rm GPa})=181.0\,({\rm GPa})-0.013\,({\rm GPa/K})\times T\,({\rm K})$, for $\delta$-AlOOH with symmetric hydrogen bond $K_{0}\,({\rm GPa})=216.0\,({\rm GPa})-0.013\,({\rm GPa/K})\times T\,({\rm K})$, with $K'_{0}$ fixed at 4. References Water in the MantleWater transport into the deep mantle and formation of a hydrous transition zoneThe relation of space-charge and potential gradient to the diurnal system of convection in the lower atmosphereStability of a hydrous Î´-phase, AlOOHâMgSiO2(OH)2, and a mechanism for water transport into the base of lower mantleFirst-principles study of hydrogen bond symmetrization of phase D under high pressureFluid Processes in Subduction ZonesOn the Symmetry of the Hydrogen Bonds in Ice VIIAre Short, Low-Barrier Hydrogen Bonds Unusually Strong?Modulated phases and proton centring in ice observed by X-ray diffraction up to 170âGPaInfrared absorption study of the hydrogen-bond symmetrization in ice to 110 GPaPressure-Induced Hydrogen Bond Symmetrization in Iron OxyhydroxideSymmetrization driven spin transition in Îµ-FeOOH at high pressurePressure-induced Landau-type transition in stishoviteChange in compressibility of Â -AlOOH and Â -AlOOD at high pressure: A study of isotope effect and hydrogen-bond symmetrizationInfrared absorption spectra of Î´-AlOOH and its deuteride at high pressure and implication to pressure response of the hydrogen bondsElastic properties of Î´-AlOOH under pressure: First principles investigationIn situ X-ray observation of decomposition of hydrous aluminum silicate AlSiO3OH and aluminum oxide hydroxide d-AlOOH at high pressure and temperatureVibrational properties of Â -AlOOH under pressureOn the room-temperature phase diagram of high pressure hydrogen: An ab initio molecular dynamics perspective and a diffusion Monte Carlo studyStudy of structural and magnetic properties of Fe ₈₀ P ₉ B ₁₁ amorphous alloy by ab initio molecular dynamic simulationThermal and nuclear quantum effects in the hydrogen bond dynamical symmetrization phase transition of Î´-AlOOHEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setEfficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis setGeneralized Gradient Approximation Made SimpleNeutron diffraction study of Â -AlOOD at high pressure and its implication for symmetrization of the hydrogen bondObservation of pressure-induced phase transition of Î´-AlOOH by using single-crystal synchrotron X-ray diffraction methodQuantum simulation of thermally-driven phase transition and oxygen K-edge x-ray absorption of high-pressure iceFinite Elastic Strain of Cubic CrystalsSound velocities of δ-AlOOH up to core-mantle boundary pressures with implications for the seismic anomalies in the deep mantleThermodynamic parameters in the Earth as determined from seismic profilesPhase transitions of serpentine in the lower mantleOlivine-modified spinelspinel transitions in the system Mg2SiO4-Fe2SiO4: Calorimetric measurements, thermochemical calculation, and geophysical applicationA numerical study of the interaction between the mantle wedge, subducting slab, and overriding plate

[1]	Ohtani E 2005 Elements 1 25
[2]	Ohtani E, Litasov K, Hosoya T, Kubo T and Kondo T 2004 Phys. Earth Planet. Inter. 143 255
[3]	Sano A, Ohtani E, Kondo T, Hirao N, Sakai T, Sata N, Ohishi Y and Kikegawa T 1930 Geophys. Res. Lett. 35 1
[4]	Ohira I, Ohtani E, Sakai T, Miyahara M, Hirao N, Ohishi Y and Nishijima M 2014 Earth Planet. Sci. Lett. 401 12
[5]	Tsuchiya J, Tsuchiya T and Tsuneyuki S 2005 Am. Mineral. 90 44
[6]	Peacock S M 1990 Science 248 329
[7]	Holzapfel W 1972 J. Chem. Phys. 56 712
[8]	Perrin C L 2010 Acc. Chem. Res. 43 1550
[9]	Loubeyre P, Letoullec R, Wolanin E, Hanfland M and Hausermann D 1999 Nature 397 503
[10]	Aoki K, Yamawaki H, Sakashita M and Fujihisa H 1996 Phys. Rev. B 54 15673
[11]	Xu W, Greenberg E, Rozenberg G K, Pasternak M P, Bykova E, Boffa-Ballaran T, Dubrovinsky L, Prakapenka V, Hanfland M, Vekilova O Y, Simak S I and Abrikosov I A 2013 Phys. Rev. Lett. 111 175501
[12]	Gleason A E, Quiroga C E, Suzuki A, Pentcheva R and Mao W L 2013 Earth Planet. Sci. Lett. 379 49
[13]	Tsuchiya J, Tsuchiya T, Tsuneyuki S and Yamanaka T 2002 Geophys. Res. Lett. 29 15-1
[14]	Sano-Furukawa A, Kagi H, Nagai T, Nakano S, Fukura S, Ushijima D, Iizuka R, Ohtani E and Yagi T 2009 Am. Mineral. 94 1255
[15]	Kagi H, Ushijima D, Sano-Furukawa A, Komatsu K, Iizuka R, Nagai T and Nakano S 2010 J. Phys.: Conf. Ser. 215 012052
[16]	Tsuchiya J and Tsuchiya T 2009 Phys. Earth Planet. Inter. 174 122
[17]	Sano A, Ohtani E, Kubo T and Funakoshi K i 2004 J. Phys. Chem. Solids 65 1547
[18]	Tsuchiya J, Tsuchiya T and Wentzcovitch R M 2008 Am. Mineral. 93 477
[19]	Chen J, Ren X G, Li X Z, Alfè D and Wang E G 2014 J. Chem. Phys. 141 024501
[20]	Zhang Q Y, Xie P, Wang X, Yu X W, Shi Z Q and Zhao S H 2016 Chin. Phys. B 25 066102
[21]	Zeng H D, Zhu Z Y, Zhang J D and Cheng X L 2017 Chin. Phys. B 26 056101
[22]	Lin W Q, Xu B, Chen L, Zhou F and Chen J L 2016 Acta Phys. Sin. 65 133102 (in Chinese)
[23]	Zhu L, Wang Y G, Cao C C and Meng Y 2017 Chin. Phys. B 26 067101
[24]	Bronstein Y, Depondt P and Finocchi F 2017 Eur. J. Mineral. 29 385
[25]	Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169
[26]	Kresse G and Furthmüller J 1996 Comput. Mater. Sci. 6 15
[27]	Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[28]	Sano-Furukawa A, Komatsu K, Vanpeteghem C B and Ohtani E 2008 Am. Mineral. 93 1558
[29]	Kuribayashi T, Sano-Furukawa A and Nagase T 2014 Phys. Chem. Miner. 41 303
[30]	Kang D D, Dai J Y, Sun H, Hou Y and Yuan J M 2013 Sci. Rep. 3 3272
[31]	Birch F 1947 Phys. Rev. 71 809
[32]	Mashino I, Murakami M and Ohtani E 2016 J. Geophys. Res. 121 595
[33]	Brown J M and Shankland T J 1981 Geophys. J. Int. 66 579
[34]	Nishi M, Irifune T, Gréaux S, Tange Y and Higo Y 2015 Phys. Earth Planet. Inter. 245 52
[35]	Kirby S H, Stein S, Okal E A and Rubie D C 1996 Rev. Geophys. 34 261
[36]	Eberle M A, Grasset O and Sotin C 2002 Phys. Earth Planet. Inter. 134 191