Ab initio study of the structure and relative stability of MgSiO
4
H
2
polymorphs at high
pressures and temperatures
Natalia V. Solomatova
1,
*
,
‡
, Razvan Caracas
1,2
, Luca Bindi
3,4,
†, and Paul D. Asimow
5
1
CNRS, Ecole Normale Supérieure de Lyon, Laboratoire de Géologie de Lyon LGLTPE UMR5276, Centre Blaise Pascal,
46 allée d’Italie Lyon 69364, France
2
The Center for Earth Evolution and Dynamics (CEED), University of Oslo, Blindern, Oslo, Norway
3
Dipartimento di Scienze della Terra, Università degli Studi di Firenze,Via G. La Pira 4, I-50121 Firenze, Italy
4
C.N.R., Istituto di Geoscienze e Georisorse, Sezione di Firenze, Via G. La Pira 4, I-50121 Firenze, Italy
5
Division of Geological & Planetary Sciences, Caltech, Pasadena, California 91125, U.S.A.
Abstract
Using particle swarm optimization with density functional theory, we identify the positions of
hydrogen in a hypothetical Mg-end-member of phase egg (MgSiO
4
H
2
) and predict the most stable
crystal structures with MgSiO
4
H
2
stoichiometry at pressures between 0 and 300
GPa. The particle
swarm optimization method consistently and systematically identifies phase H as the energetically most
stable structure in the pressure range 10–300
GPa at 0
K. Phase Mg-egg has a slightly higher energy
compared to phase H at all relevant pressures, such that the energy difference nearly plateaus at high
pressures; however, the combined effects of temperature and chemical substitutions may decrease or
even reverse the energy difference between the two structures. We find a new MgSiO
4
H
2
phase with
the
P
4
3
2
1
2 space group that has topological similarities to phase Mg-egg and is energetically preferred
to phase H at 0–10
GPa and 0
K. We compute the free energies for phase Mg-egg, phase
P
4
3
2
1
2, and
phase H at 0–30
GPa within the quasi-harmonic approximation and find that the effect of temperature
is relatively small. At 1800
K, the stability field of phase
P
4
3
2
1
2 relative to the other polymorphs
increases to 0–14
GPa, while pure phase Mg-egg remains energetically unfavorable at all pressures.
Simulated X-ray diffraction patterns and Raman spectra are provided for the three phases. Additionally,
the crystallographic information for two metastable polymorphs with the
P
1 space group is provided.
Our results have implications for the deep hydrogen cycle in that we identify two novel potential carrier
phases for hydrogen in the mantles of terrestrial planets and assess their stability relative to phase H.
We determine that further experimental and computational investigation of an extended compositional
space remains necessary to establish the most stable dense hydrated silicate phases.
Keywords:
Ab initio, global hydrogen cycle, dense hydrous magnesium silicates, lower mantle,
high pressure, phase egg, phase H; Physics and Chemistry of Earth’s Deep Mantle and Core
Introduction
The water content of the Earth’s mantle is poorly constrained.
In addition to its significance for planetary habitability when it
resides in surface reservoirs, water that remains in the interior
may lower the melting temperature of rocks (Gaetani and Grove
1998
), enhance the rate of phase transitions (Kubo et al.
1998
),
change the position of phase boundaries (Wood
1995
), lower
the mantle’s viscosity (Mei and Kohlstedt
2000
), affect mantle
dynamics (Nakagawa et al.
2015
), and facilitate element transport
(Kogiso et al.
1997
). Improving our knowledge of the budget and
history of hydrogen depends on knowing its storage and transport
mechanisms, as well as its original sources. Although most of
the common hydrous phases observed at near-surface condi
-
tions decompose at mantle pressures and temperatures, there are
several potential reservoir phases. In the upper mantle, “water”
may be present at low concentrations in nominally anhydrous
phases, such as olivine, garnet, and pyroxene and, in the transi
-
tion zone, wadsleyite and ringwoodite (Gasparik
1993
; Inoue
et al.
1995
; Smyth and Kawamoto
1997
; Pearson et al.
2014
).
Mineralogists have also identified a range of so-called dense
hydrous magnesium silicates, such as phase D [MgSi
2
O
4
(OH)
2
]
and superhydrous B [Mg
12
Si
4
O
19
(OH)
2
], that may survive dehydra
-
tion reactions in subduction zones and therefore serve as efficient
transport vectors for water through the upper mantle and perhaps
into the lower mantle. In addition to water recycled at subduction
zones, if primordial water has persisted throughout Earth’s his
-
tory, it must have also resided in some host phases. Numerical
models have suggested that an early terrestrial global magma
ocean may have retained substantial H
2
O in the silicate melt,
given the solubility beneath a thick, CO
2
-dominated atmosphere
(Gaillard and Scaillet
2014
; Bower et al.
2019
; Solomatova et al.
2021). Upon crystallization of the magma ocean, a portion of that
American Mineralogist, Volume 107, pages 781–789, 2022
0003-004X/22/0005–781$05.00/
D
OI: https://doi.org/10.2138/am-2021-7937
781
* E-mail:
nsolomat@gmail.com
†
Orcid 0000-0003-1168-7306
‡ Special collection papers can be found online at
http://www.minsocam.org/MSA/
AmMin/special-collections.html
.
Open access:
Article available to all readers online.
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SOLOMATOVA ET AL.: STRUCTURE AND STABILITY OF MGSIO
4
H
2
POLYMORPHS
782
American Mineralogist, vol. 107, 2022
dissolved water budget may have become incorporated into dense
hydrous magnesium silicates. Thus, to improve our understanding
of both the current state and evolution of Earth’s lower mantle,
it is necessary to quantify its water budget and characterize the
possible phases that may or may not exist at those pressures and
temperatures. Note that one may equally well discuss the budget
of hydrogen; given the ready availability of oxygen throughout
the mantle and surface reservoirs of Earth, hydrogen and water
are interchangeable when discussing inventories.
Several dense hydrous magnesium silicate phases have been
suggested as possible carriers of hydrogen in the mantle. In
subduction zones, serpentine (the product of lower-temperature,
near-surface alteration of peridotite minerals) decomposes into
a mixture of phase A, enstatite, and fluid. Subsequent reactions
of hydrous magnesium silicate phases with increasing depth
depend on the water content (Ohtani et al.
2000
) and also,
most likely, on temperature, chemistry, and oxidation state. In
wet regions of the transition zone, the major hydrogen-bearing
phases are likely hydrous wadsleyite, hydrous ringwoodite, and
superhydrous phase B. At the top of the lower mantle, phase D
becomes the dominant water carrier. It was previously assumed
that all hydrous phases decompose beyond ~45
GPa (Shieh et al.
1998
). However, it has recently been proposed that polymorphs
of MgSiO
4
H
2
may be important carriers of water in the lower
mantle at pressures exceeding 45
GPa (Tsuchiya
2013
; Nishi et
al.
2014
; Bindi et al.
2014
; Panero and Caracas
2017
,
2020
). One
such polymorph, phase H, topologically equivalent to
δ
-AlOOH,
was experimentally found to exist at pressures of 35–60
GPa and
temperatures below ~1500
K (Ohtani et al.
2014
). In agreement
with the experiments, a computational study predicts that phase
H exists up to 60
GPa at 1000
K, decomposing into bridgmanite
+ ice VII at higher pressures (Tsuchiya and Umemoto
2019
).
Another new phase, Mg-bearing phase egg [note that phase egg
sensu stricto is a polymorph of AlSiO
3
OH (eggleton et al.
1978
)],
was synthesized at 24
GPa and 1673
K, suggesting that it may
also be a potential carrier of hydrogen at lower mantle conditions
(Bindi et al.
2020
). The Al-end-member of phase egg decomposes
to
δ
-AlOOH + SiO
2
stishovite below ~1500
K and to Al
2
SiO
4
(OH)
2
phase D + Al
2
O
3
corundum + SiO
2
stishovite above ~1500
K at
pressures of about 17–24
GPa (Fukuyama et al. 2017). However,
the fate of Mg-bearing phase egg is yet to be determined. Here we
explore the structure and relative stability of the Mg-end-member
of phase egg in the context of various polymorphs of MgSiO
4
H
2
using computational methods.
Computational methods
The Crystal Structure AnaLYsis by Particle Swarm Optimization (CALYPSO)
package (Wang et al.
2012
) seeks optimal structures by minimizing enthalpy dur
-
ing structural evolution by particle swarm optimization. Structural relaxation and
enthalpy calculations are conducted with external optimization codes, which may be
based either on density functional theory or interatomic pair potentials. In this study,
the CALYPSO method was used for two purposes: (1) to determine the hydrogen
positions in the hypothetical Mg-end-member of phase egg (Bindi et al.
2020
) and
(2) to search for any other energetically stable crystal structures with MgSiO
4
H
2
stoichiometry at pressures between 0 and 300
GPa. Structures were optimized with
density functional theory using the VASP package (Kresse and Furthmüller
1996
).
The first-generation structures were produced randomly; then, half of each subsequent
generation was generated through particle swarm optimization and the other half was
generated randomly. Each calculation consisted of about 40–60 generations with a
population size of 30 structures per generation. To determine the hydrogen posi
-
tions in the Mg-end-member of phase egg (hereafter, “phase Mg-egg”), the atomic
positions of magnesium, silicon, and oxygen were fixed to the positions determined
from single-crystal X-ray diffraction experiments (Bindi et al.
2020
). The hydrogen
atoms were then inserted into the structure either randomly or through particle swarm
optimization, after which the structures were completely relaxed with VASP, allowing
for all atoms to reach their equilibrium positions. The search was repeated eight times
at pressures between 18 and 26
GPa to ensure reproducibility and self-consistency.
To search for additional energetically stable structures with MgSiO
4
H
2
stoichiometry,
we conducted a full structure search with no pre-defined atomic positions at pressures
of 0, 5, 10, 15, 20, 80, 135, 200, and 300
GPa, varying the number of formula units
per unit cell from
Z
=
1 to
Z
=
4.
Ab initio calculations were performed using the projector-augmented wave
(PAW) method (Blöchl
1994
) implemented in VASP. The generalized gradient
approximation (GGA) (Perdew et al.
1996
) was used to approximate the exchange
correlation terms. A plane-wave energy cut-off of 600
eV was used to ensure excellent
convergence in volume and total energy (Online Material
s
1
Fig. OM1), and a k-point
grid of <0.04
Å
−1
was required to refine the transition pressures. The convergence
criteria for electronic self-consistency and ionic relaxation loop were set to 10
−5
and
10
−4
eV, respectively. We ensured that forces acting on all relaxed atoms were less than
0.01
eV/
Å
. As discussed below, we found phase Mg-egg, phase H, a new low-energy
structure with space group
P
4
3
2
1
2, and two additional metastable but competitive
candidate structures. These five structures were relaxed between 0 and 140
GPa to
compare their relative stabilities. It is possible that, with certain cation substitutions,
the competing candidate phases may be observed experimentally. Hence, all the
studied structures, including those found to be metastable in the pure system, are
provided in the Online Materials crystallographic information file (CIF
1
). X-ray dif
-
fraction patterns were simulated in the VESTA program (Momma and Izumi 2008).
The PAW method with the GGA approximation has successfully predicted the
physical and elastic properties of a wide range of geological materials, including
dense hydrous silicates (Li et al.
2006
; Panero and Caracas
2017
,
2020
; Caracas and
Panero
2017
), silicate perovskites (Jung and Oganov
2005
; Stixrude et al.
2007
),
pyroxenes (Yu et al.
2010
), and carbonates (Oganov et al.
2008
; Arapan and Ahuja
2010
; Solomatova and Asimow
2017
). The GGA approximation is known to slightly
underestimate cohesive energies, resulting in the underestimation of bulk moduli and
overestimation of volumes and phase transition pressures. While the experimentally
synthesized phase H is characterized by disordered hydrogen atoms occupying half
the 4
g
positions (Bindi et al.
2014
), in our density functional theory calculations, the
hydrogen positions are ordered, which reduces the symmetry from the experimentally
determined orthorhombic
Pnnm
space group
to the monoclinic
Pm
space group
.
In
comparison, phase δ-AlOOH, the topologically equivalent structure to phase H, is
characterized by ordered hydrogen at ambient pressure and undergoes an order-to-
disorder transition at ~10
GPa, which results in an increase in symmetry from the
P
2
1
nm
to
Pnnm
space group and a change in compressional behavior (Sano-Furukawa
et al.
2009
,
2018
; Kuribayashi et al.
2014
; Ohira et al.
2019
).
We compare the calculated lattice parameters, unit-cell volumes, and bond
lengths of phase H to those experimentally measured by Bindi et al. (
2014
). Despite
the difference in space groups between the computationally and experimentally
studied phase H, we find that the GGA approximation overestimates lattice param
-
eters by 0.2–1.4% and unit-cell volume by 1.8% (Online Materials
1
Table OM1),
while the O-H bond lengths are overestimated by about 3% (Online Materials
1
Table OM2). We compare the equation of state parameters that result from fitting
a Birch-Murnaghan equation of state to calculations covering the same pressure
interval as in situ experimental volume data on phase H (Nishi et al.
2018
), finding
that the GGA method underestimates the bulk modulus by about 5–7% (Online
Materials
1
Table OM3). The higher degree of compressibility can be attributed to
the lower symmetry of the structure and difference in hydrogen ordering. Although
experiments have not yet constrained the hydrogen bond symmetrization pressure in
phase H, previous simulations on AlOOH find that the PAW method with the GGA
approximation overestimates the phase transition pressure of α-AlOOH to δ-AlOOH
by <1
GPa (Li et al.
2006
).
The method of lattice dynamics within the quasi-harmonic approximation was
implemented using the finite-displacement method in the PHONOPY package (Togo
and Tanaka
2015
) to calculate the vibrational zero-point energies and thermal effects
on the relative phase stabilities of the three most stable phases (i.e., phase Mg-egg,
phase H, and the newly found
P
4
3
2
1
2 phase) at 0–30
GPa. Supercells of 1
×
2
×
1 (64
atoms), 2
×
2
×
3 (96 atoms), and 2
×
2
×
1 (128 atoms) were created for phase Mg-egg,
phase H and phase
P
4
3
2
1
2, respectively, which proved to be sufficiently large for an
energy convergence of about 10
−4
to 10
−5
eV/atom. Each supercell contains one atomic
displacement with a magnitude of 0.01
Å
and the number of supercells used for each
phase depends on the space group (ranging between 16 and 48 calculations per phase
at each pressure). Force constants were calculated for each displaced supercell using
VASP. The convergence criterion for the ionic relaxation was decreased to 10
−7
eV
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SOLOMATOVA ET AL.: STRUCTURE AND STABILITY OF MGSIO
4
H
2
POLYMORPHS
783
American Mineralogist, vol. 107, 2022
for the geometric relaxation of the undisplaced cells, and the convergence criterion
for electronic self-consistency was decreased to 10
−8
eV for all calculations related
to the zero-point energy and thermal calculations. The resulting force constants were
then used to calculate phonon-related properties (i.e., the zero-point energy and
vibrational Helmholtz free energy at finite temperature), from which we derived the
Gibbs free energies as a function of pressure and temperature.
The Raman spectra were computed as a function of pressure within the density
functional perturbation theory (Baroni and Resta
1986
; Baroni et al.
2001
; Gonze et
al.
2005
), as implemented in ABINIT (Veithen et al.
2005
; Gonze et al.
2002
,
2009
).
We used the relaxed structures obtained with VASP, with norm-conserving pseudo
-
potentials and a k-point grid density of ~0.04
Å
−1
. The simulations use parameters
similar to those employed to obtain the Raman spectra for minerals in the WURM
database (Caracas and Bobocioiu
2011
), which give reliable results for both anhy
-
drous (McKeown et al.
2010
) and hydrous minerals (Bobocioiu and Caracas
2014
).
Results
Structure searches
We identified the positions of the hydrogen atoms in the
Mg-end-member of phase egg with the
P
2
1
/
n
space group using
constrained structure searches with the particle swarm optimiza
-
tion method (Fig. 1; Online Materials
1
CIF). In phase Mg-egg
(MgSiO
4
H
2
), half of the hydrogen positions are equivalent to those
of Al-end-member phase egg (AlSiO
4
H) (eggleton et al.
1978
;
Schmidt et al.
1998
; Schulze et al.
2018
). We looked specifically
at the question of whether the Mg-egg structure contains H
2
O
groups; according to our results, it does not—every hydrogen
atom is separately bonded with a single oxygen atom. With the full
structure of phase Mg-egg identified, it is possible to compare the
relative energy to its polymorph, phase H (Tsuchiya
2013
; Nishi et
al.
2014
; Bindi et al.
2014
). At 0
K, phase H is preferred to phase
Mg-egg between 2.5
GPa and to at least 300
GPa, the maximum
pressure explored with CALYPSO in this study.
Our structure search identified two energetically stable crystal
structures with MgSiO
4
H
2
stoichiometry in the pressure range
from 0 to 300
GPa. At pressures between 0 and 10
GPa, the
newly discovered structure with the
P
4
3
2
1
2 space group is the
energetically preferred phase (Fig. 2). The
P
4
3
2
1
2 phase has topo
-
logical similarities to
P
2
1
/
n
Mg-egg. In Mg-egg, every two MgO
6
polyhedra share edges, resulting in Mg
2
O
10
dimers, which are all
interconnected through their corners. Additionally, each Mg
2
O
10
dimer shares four edges with two SiO
6
octahedra and two corners
with another two SiO
6
octahedra. In the
P
4
3
2
1
2 phase, the MgO
6
octahedra share only corners with each other; every two MgO
6
octahedra are at an acute angle of 56
°
(i.e., “dimer precursors”).
Each MgO
6
octahedron shares an edge with a SiO
4
tetrahedron
and three corners with three SiO
4
tetrahedra. Evidently, the
P
4
3
2
1
2
Figure 1.
Crystal structures of (
a
) phase H with the
Pm
space group (reduced symmetry from
Pnnm
due to cation ordering); (
b
) phase Mg-egg
(the Mg-end-member of phase egg); (
c
) the newly identified phase with the
P
4
3
2
1
2 space group; (
d
) the newly identified
P
1-a phase; and (
e
) the
newly identified
P
1-b phase. Figures were produced in VESTA (Momma and Izumi 2008). The structures are represented with magnesium polyhedra
(orange), silicon polyhedra (blue), oxygen atoms (red), and hydrogen atoms (white).
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SOLOMATOVA ET AL.: STRUCTURE AND STABILITY OF MGSIO
4
H
2
POLYMORPHS
784
American Mineralogist, vol. 107, 2022
phase is a more open, less dense structure than Mg-egg. We provide
simulated X-ray diffraction patterns of phase H, phase Mg-egg
and phase
P
4
3
2
1
2 at 0
GPa (Fig. 3).
Two additional triclinic phases with the
P
1 space group were
discovered at low pressure. Although the energy differences are
small, both triclinic structures have slightly higher energies than
the
P
4
3
2
1
2 phase at all pressures explored in this study. Due to the
possibility that relative energies may change at high temperature
and with chemical substitutions, we provide the structures of the
two
P
1 phases, hereafter referred to as
P
1-a and
P
1-b (Fig. 1). The
two
P
1 phases are characterized by corner-sharing SiO
4
tetrahedra
and MgO
6
octahedra with H
2
O groups attached to the elongated
axes (
P
1-a) or short axes (
P
1-b) of the MgO
6
octahedra (Fig. 1).
At all pressures examined between 10 and 300
GPa, the par
-
ticle swarm optimization method consistently and systematically
identifies phase H as the energetically most stable structure. Phase
Mg-egg has a slightly higher energy compared to phase H between
2.5 and 300
GPa; the energy difference between the two phases
nearly plateaus at roughly 60
meV/atom at lower-mantle pressures
(Fig. 2). This implies that the molar volumes of Mg-egg and phase
H are similar and converge toward the same value, whereas
P
4
3
2
1
2,
P
1-a, and
P
1-b are all much less dense. Hence, it is possible, given
changes in relative energies due to temperature or chemistry, that
phase Mg-egg could become energetically favorable relative to
phase H at pressures of Earth’s lower mantle or the mantles of
super-Earth exoplanets.
Standard density functional theory calculations do not include
the kinetic energy corresponding to zero-point motion. The
zero-point motion is larger for light elements such as hydrogen
(Matsushita and Matsubara
1982
; Natoli et al. 1993; Rivera et al.
2008
), affecting the nature of hydrogen bonds and the structure of
ice polymorphs (Benoit et al.
1998
; Herrero and Ramírez
2011
),
such that zero-point energy may be significant for dense hydrous
silicate phases (Tsuchiya et al.
2005
). We investigated this effect
for the MgSiO
4
H
2
polymorphs, and we find that the zero-point
energy corrections are small, e.g., ~1.5
meV/atom. The resulting
Gibbs free energy differences are 0.5–14
meV/atom, which results
in <1
GPa differences in phase transition pressures, and so do not
affect the relative phase stabilities (Fig. 2 inset).
We applied the quasi-harmonic approximation to estimate the
Gibbs free energies of phase H, phase Mg-egg, and phase
P
4
3
2
1
2
along an isotherm at 1800
K, the approximate temperature of the
deep upper mantle and transition zone. We find that the thermal
effects are relatively small and do not change the sequence of
stable MgSiO
4
H
2
polymorphs with pressure. The stable energy
crossover between phase
P
4
3
2
1
2 and phase H shifts from 10
GPa
(0
K) to 14
GPa (1800
K), while the metastable energy crossover
between phase Mg-egg and phase H shifts from 2.5
GPa (0
K)
to 9
GPa (1800
K). However, phase Mg-egg remains energeti
-
cally disfavored relative to other polymorphs at all pressures and
temperatures considered.
Equations of state
The pressure-volume results of our calculations for phase
Mg-egg, phase
P
4
3
2
1
2, and phase H were fitted with finite-strain
equations of state (Fig. 4). The graph of reduced pressure (
F
) vs.
Eulerian finite strain (
f
) reveals the level of Taylor expansion
necessary to accurately fit equation-of-state data (Angel
2000
).
Both Mg-egg and
P
4
3
2
1
2 phases show concave-down parabolic
curves in
F
-
f
space that call for the use of the fourth-order Birch-
Murnaghan equations of state (Fig. 4 inset). The situation for phase
H is complex; the
Pm
structure of phase H undergoes a second-
order phase transition to the
P
2/
m
structure at about 30
GPa due
to H-O bond symmetrization (Tsuchiya and Mookherjee
2015
;
Lv et al.
2017
). The phase transition is subtle in pressure-volume
space but manifests as a clear break in slope at
f
=
0.05 in the
F
-
f
Figure 2.
The Gibbs free energy difference between candidate
MgSiO
4
H
2
polymorphs with respect to phase H at 0
K, without the
contribution of zero-point energy. Here at 0
K the Gibbs free energy is
equivalent to the enthalpy. The inset shows the Gibbs free energies of
phase Mg-egg (blue) and phase
P
4
3
2
1
2 (red) relative to phase H without
the addition of the zero-point energy (solid circles; equivalent to the main
figure), with the addition of the zero-point energy (open circles) and at
1800
K as calculated from the quasi-harmonic approximation (QHA)
(solid squares). The change in slope in the energy difference between
25 and 30
GPa is due to the hydrogen bond symmetrization in phase H.
Figure 3.
(
a
) Simulated X-ray diffraction patterns at 0
GPa for
phase H (black), Mg-egg (blue), and the newly identified phase with
the
P
4
3
2
1
2 space group (red).
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SOLOMATOVA ET AL.: STRUCTURE AND STABILITY OF MGSIO
4
H
2
POLYMORPHS
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American Mineralogist, vol. 107, 2022
plot. The linearity of the low-pressure region warrants the use of
a third-order Birch-Murnaghan equation of state between 0 and
25
GPa, while the concave-down behavior of the high-pressure
region warrants the use of a fourth-order Birch-Murnaghan equa
-
tion of state between 35 and 140
GPa. Phase H experimentally
synthesized at 1273
K and studied at 300
K has
Pnnm
symmetry
(Bindi et al.
2014
), with disordered hydrogen occupying half the
4
g
positions and octahedral sites occupied equally by magnesium
and silicon. On the other hand, in 0
K density functional theory
studies, phase H becomes ordered, which reduces the symmetry
to
Pm
. The lowest-energy ordering of the sites was chosen for
the purpose of this study, such that the hydrogen positions cor
-
respond to the “hydrogen off-centered 1” (HOC1) arrangement
in
δ-
AlOOH (Tsuchiya et al.
2002
, 2008).
In the resulting monoclinic structure of phase H, the calcu
-
lated results of density functional theory relaxation indicate a
second-order transition at about 30
GPa from a
Pm
space group
with asymmetric hydrogen positions to a
P
2/
m
structure with
symmetrized hydrogen bonds, in agreement with previous density
functional theory calculations (Tsuchiya
2013
); the
Pm
and
P
2/
m
structures are otherwise topologically equivalent (Tsuchiya and
Mookherjee
2015
). Bond symmetrization has been experimentally
observed in δ-AlOOH at ~18
GPa through neutron diffraction
(Sano-Furukawa et al.
2018
) and in phase D at ~40
GPa through
anomalous axial and volumetric compression (Shinmei et al.
2008
; Hushur et al.
2011
). In phase D, bond symmetrization was
experimentally observed at ~40
GPa through anomalous axial and
volumetric compression (Shinmei et al.
2008
; Hushur et al.
2011
).
Bond switching (O-H···O to O···H-O) was observed in the Al-egg
phase (AlSiO
3
OH) at 14
GPa using a combination of IR spectros
-
copy and single-crystal X-ray diffraction (Liu et al.
2021
). We do
not observe bond switching in the Mg-egg phase; the additional
hydrogen atoms prevent the occurrence of bond switching since the
potential recipient oxygen atom is already bonded to a hydrogen
atom. Meanwhile, the additional hydrogen atoms in the Mg-egg
structure relative to the Al-egg structure do not experience bond
switching due to the different local environment.
The symmetrization of the O-H bonds in phase H results in
an increase in the zero-pressure bulk modulus
K
0T
from 133(1)
to 174(4) GPa and a decrease in the zero-pressure unit-cell vol
-
umes
V
0
from 7.41(1) to 7.25(2) Å
3
/atom
(Table 1). The results
of an X-ray diffraction study on phase H at 0 and 35–60
GPa
are consistent with a change in compressibility at 30
GPa due to
bond symmetrization (Nishi et al.
2018
); however, more detailed
experimental studies at pressures corresponding to the onset of
bond symmetrization are needed. In comparison to phase H, we
find that phase Mg-egg is more compressible with a bulk modulus
of 113(1) GPa, consistent with convergence between the volumes
of phases H and Mg-egg at high pressure and the leveling-off
of the energy difference between them. Phase
P
4
3
2
1
2 has the
lowest bulk modulus, 76(1) GPa, and the largest initial volume,
9.08(1) Å
3
/atom, indicating that it is a low-pressure phase that is
not expected to exist at lower-mantle pressures. Previous density
functional theory calculations on phase H predict bulk moduli of
151.9 and 185.8
GPa and volumes of 7.34 and 7.20 Å
3
/atom
for the
asymmetric and symmetric hydrogen bond structures, respectively
(Tsuchiya
2013
). The differences in the fitted equations of state
parameters for phase H between this study and Tsuchiya (
2013
)
are consistent with expectations for the comparison of density
functional theory calculations with core electron treated with norm-
conserving pseudopotentials (Tsuchiya
2013
) and with the PAW
method (this study). We confirmed this by relaxing the reported
unit cell of Tsuchiya (
2013
) with the PAW method, resulting in an
increase of the unit-cell volume from 7.34 to 7.41 Å
3
/atom
and an
increase in the
γ
angle from 93.25
°
to 93.31
°
.
Raman vibrational modes
We provide the simulated Raman spectra of phase H, phase
Mg-egg and phase
P
4
3
2
1
2 at 0–40
GPa (Fig. 5). The spectra are
computed for static structures, the main contribution of the an
-
harmonicity being the broadening of the peaks. The vibrational
frequencies of Raman bands are systematically related to features
of the O-H bonds in the studied phases. The stretching frequencies
of the O-H bonds depend on both O···O distance and H-O-O angle
in the O-H···O bond environment (Hofmeister et al.
1999
); an
Figure 4.
The pressure-volume data for the newly identified phase
P
4
3
2
1
2 (red; largest volume), phase Mg-egg (blue; intermediate volume),
and phase H (black; lowest volume). A third-order Birch-Murnaghan
equation of state was fitted to the pressure-volume data of phase H between
0 and 25
GPa where the ordered phase H exists in the
Pm
space group,
exhibits non-symmetrical hydrogen bonds and is characterized by a linear
trend of the normalized pressure as a function of Eulerian strain (dashed
black curve). A fourth-order Birch-Murnaghan equation of state was fitted
to the pressure-volume data of phase H between 35 and 140
GPa where
phase H exists in the
P
2/
m
space group, exhibits symmetrical hydrogen
bonds and is characterized by a parabolic trend of the normalized pressure
as a function of Eulerian strain (solid black curve). Fourth-order Birch-
Murnaghan equations of state were fitted to the pressure-volume data of
phase
P
4
3
2
1
2 and phase Mg-egg at 0–140
GPa.
T
able
1.
Birch-Murnaghan equation-of-state parameters for calcu
-
lated MgSiO
4
H
2
polymorphs
Phase
V
0
/Atom (Å
3
)
K
0
(GPa)
K
0
’
K
0
” ( G Pa
–1
)
Phase H (
Pm
)
7.41(1)
133(1) 5.3(1)
–
Phase H (
P
2/
m
)
7.25(2)
174(4)
4.6(2) –0.04(1)
Phase Mg-egg (
P
2
1
/
n
) 7.70(1)
113(1)
5.9(1)
–0.12(1)
P
4
3
2
1
2
9.08(1)
76(1)
5.6(1)
–0.16(1)
Notes
: The pressure-volume data of phase H with the
Pm
and
P
2/
m
space groups
were fitted in the pressure range of 0–25 and 35–140
GPa, respectively. Both
structures of phase H are topologically equivalent to the phase H reported in
Bindi et al. (
2014
); phase H with the
Pm
space group is the ordered version of
phase H with the
Pnnm
space group, whereas phase H with
P
2/
m
symmetry is
characterized by the symmetrization of the O-H bonds above ~30
GPa.
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SOLOMATOVA ET AL.: STRUCTURE AND STABILITY OF MGSIO
4
H
2
POLYMORPHS
786
American Mineralogist, vol. 107, 2022
H-O-O angle of 0
°
corresponds to a linear O-H
...
O arrangement.
Generally, larger O···O distances and H-O-O angles are expected
to result in higher O-H stretching frequencies.
In the phase H structure, there are two types of O-H bonds,
which are both oriented toward hydrogen-free oxygen atoms. The
O-H···O bond environments are characterized by very small H-O-
O angles of 1.0
°
(H1-O3-O1) and 2.3
°
(H2-O2-O4) and moder
-
ate O···O distances of 2.58
Å
(O3···O1) and 2.51
Å
(O2···O4)
at 0
GPa (Figs. 6a and 7). The restricted O-H environment in
phase H results in low frequencies of the O-H stretching modes
of about 2380 and 2425
cm
−1
(Fig. 5a). By 20
GPa, the environ
-
ment becomes even more restrictive with H-O-O angles of 0.2
°
(H1-O3-O1) and 0.7
°
(H2-O2-O4) and O···O distances of 2.41
Å
(O3···O1) and 2.39
Å
(O2···O4), decreasing the intensity of the
O-H stretching modes and shifting them to 1570 and 1750
cm
−1
.
By 30
GPa, the phase H structure achieves bond symmetrization
and the OH-stretching modes shift to 1550
and 1710
cm
−1
with
intensities that are several orders of magnitude lower and so are not
visible in Figure 5a. All calculated Raman vibrational modes and
O-H···O bond environment information can be found in Online
Materials
1
datasets 1 and 2, respectively.
Phase Mg-egg is characterized by two types of O-H···O bond
environments. The first type of O-H bonds are oriented toward
a hydrogen-free oxygen atom with an H1-O1-O3 angle of 5.1
°
and an O1···O3 distance of 2.45
Å
, while the second type of O-H
bonds are oriented toward a hydrogen-bonded oxygen atom with
an H2-O4-O1 angle of 13.5
°
and an O1···O4 distance of 2.89
Å
at 0
GPa (Fig. 6b). The more restricted local environment of the
first type of O-H bonds results in a lower frequency stretching
vibration compared to the second type. The calculated Raman
spectrum for phase Mg-egg at 0
GPa shows vibrational modes at
~2850 and ~3475
cm
−1
(Fig. 5b), corresponding to the first and
second type of O-H bonds, respectively. With increasing pressure,
the O-H distances and H-O-O angles steadily decrease, resulting in
a gradual shift of the O-H stretching modes to lower frequencies.
Unlike phase H and phase Mg-egg, phase
P
4
3
2
1
2 contains only one
Figure 5.
Simulated Raman spectra with 25
cm
−1
of broadening for (
a
) phase H, (
b
) Mg-egg, and (
c
) the newly identified phase with the
P
4
3
2
1
2
space group at 0, 10, 20, 30, and 40
GPa. The progressive pressure-induced O-H···O bond stiffening is observed in phase H through the decrease
in intensity and shift to lower wavenumbers of the OH symmetric stretching modes. When calculating the intensities, the wavelength of the laser
source and temperature were set to 19
636 cm
–1
and 300 K, respectively.
Figure 6.
The ambient-pressure O-H···O bond environments in (
a
)
phase H with the
Pm
space group (reduced symmetry from
Pnnm
due
to cation ordering), (
b
) phase Mg-egg (the Mg-end-member of phase
egg), and (
c
) the newly identified phase with the
P
4
3
2
1
2 space group.
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SOLOMATOVA ET AL.: STRUCTURE AND STABILITY OF MGSIO
4
H
2
POLYMORPHS
787
American Mineralogist, vol. 107, 2022
type of O-H bond. In phase
P
4
3
2
1
2, the O-H bonds are all oriented
toward hydrogen-free oxygen atoms at an H1-O2-O1 angle of 6.6
°
and an O1···O2 distance of 2.75
Å
at 0
GPa (Fig. 6c), resulting in
intermediate vibrational frequencies at ~3000
cm
−1
(Fig. 5c). With
increasing pressure, the O1···O2 distance and H1-O2-O1 angle
decrease, shifting the O-H stretching modes to lower frequencies.
An experimental study on δ-AlOOH, the topologically equiva
-
lent structure to phase H, found that the O-H stretching modes
exist between 2100 and 2700
cm
−1
at 0
GPa (Ohtani et al.
2001
).
With ab initio calculations, Tsuchiya et al. (2008)
found that the
O-H stretching modes range from 2000 to 2700
cm
−1
and that the
number and frequency of the vibrational modes depend on the
degree of hydrogen disorder and the O···O distances. It is also
likely that the local environment of hydrogen would be affected by
the chemistry of the mineral phase. Our predicted O-H vibrational
frequencies of 2380–2425
cm
−1
for Mg-end-member phase H exist
within the range of frequencies observed in δ-AlOOH. Density
functional perturbation theory calculations from Lv et al. (
2017
)
on phase H using the CASTEP software package (Segall et al.
2002
) produce very similar Raman spectra to those of this study
(Online Materials
1
Fig. OM2). The low O-H stretching vibrational
frequencies observed in phase H and δ-AlOOH are characteristic
of constrained O-H environments. Previous computational and
experimental studies have reported similarly anomalous low O-H
stretching frequencies in other hydrous phases: ~2000
cm
−1
for ice
X extrapolated to 25
GPa (Caracas
2008
), ~2700
cm
−1
for ice VII
at 25
GPa (Hernandez and Caracas
2018
), and 2500–3000
cm
−1
for dimer acids at ambient pressure (Chen et al.
2017
), where the
O-H environments are highly constrained.
Discussion
In this study, simulations based on the particle swarm
optimization method, density functional theory, and the quasi-
harmonic approximation were used to (1) identify the positions
of hydrogen in phase Mg-egg, (2) identify additional candidate
MgSiO
4
H
2
structures, and (3) examine the effect of temperature
on relative phase stabilities. Identifying the atomic coordinates
of the hydrogen atoms in phase Mg-egg is fundamental to char
-
acterizing its structure and will facilitate future experimental
and computational studies; despite the addition of H necessary
to charge-balance the substitution of Mg for Al in phase egg,
the structure does not develop H
2
O groups. We find that pure
end-member Mg-egg does not have a stability field in the range
of 0–300
GPa and 0–1800
K. With particle swarm optimization,
we identified three other candidate MgSiO
4
H
2
polymorphs: two
structures with the
P
1 space group that is never energetically
favored relative to other polymorphs and a structure with the
P
4
3
2
1
2 space group that is preferred over phase H at 0–14
GPa at
1800
K. It is possible that phase
P
4
3
2
1
2 may be stable at certain
low-pressure conditions within the Earth’s mantle, particularly
in subducting slabs just before reaching the transition zone.
However, note that this study is restricted to the relative
stability
of phases with MgSiO
4
H
2
stoichiometry only. In particular, we
have not examined the effects of decomposition into less hydrous
Figure 7.
The O···O distances (
a
), O-H bond lengths (
b
), H-O-O bond angles (
c
), and the ratio between the O-H bond length and the O···H
distance (
d
) for phase H (black), phase Mg-egg (blue), and the newly identified phase with the
P
4
3
2
1
2 space group (red). Previous ab initio calculations
on phase H using norm-conserving pseudopotentials are shown with gray diamonds (Tsuchiya
2013
) and gray squares (Lv et al.
2017
). At 40
GPa,
the results of Tsuchiya (
2013
) and this study are equivalent. Experimental results of Bindi et al. (
2014
) for phase H are shown with gray triangles.
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SOLOMATOVA ET AL.: STRUCTURE AND STABILITY OF MGSIO
4
H
2
POLYMORPHS
788
American Mineralogist, vol. 107, 2022
Mg-silicates and free H
2
O, due to the complex nature of the
phase diagram of H
2
O and the sensitivity of computed physical
and thermodynamic properties of H
2
O to various parameters of
density functional theory models (e.g., representation of Van
der Waals forces, flavor of pseudopotentials, the inclusion of
zero-point motions, and inherent anharmonicity). A thorough
density functional theory study of the decomposition of hydrous
magnesium silicates into ice and anhydrous magnesium silicates
has been performed (Tsuchiya
2013
), predicting that phase H
would be stable at 30–52
GPa at 0
K and 50–52
GPa at 1600
K
(corresponding to a cold geotherm), decomposing above about
1900
K. Considering that phase Mg-egg and phase
P
4
3
2
1
2 are
both less stable than phase H above ~15
GPa, it is unlikely that
the Mg-end-members of these phases would exist at any depth
in the mantle. Furthermore, the relative stability of phase H may
increase at high temperatures due to the configurational entropy
from the disordering of Mg and Si on the octahedral sites.
Although pure phase Mg-egg is never favored relative to
its polymorphs at the conditions explored in this study, chemi
-
cal substitutions may decrease the energy difference between
phase Mg-egg and phase H. Indeed, an (Mg,Al)-bearing phase
egg solid solution was successfully synthesized and recovered
from high-pressure experiments likely to have approached equi
-
librium. The observed synthetic composition was found to be
Al
0.65
Mg
0.35
SiO
4
H
1.35
(Bindi et al.
2020
). The presence of aluminum
in MgSiO
4
H
2
may significantly alter the relative phase stabilities
and their high-pressure behavior. It is thus possible that (Mg,Al)-
bearing phase egg is thermodynamically favored over (Mg,Al)-
bearing phase H or the assemblage of Mg-end-member phase H
and Al-end-member phase egg under some natural conditions. Ad
-
ditional calculations are needed to examine the effect of aluminum
substitution on the relative stability of the MgSiO
4
H
2
polymorphs.
Implications
Dense hydrous magnesium silicate phases are important
hydrogen carriers and/or reservoirs of hydrogen in the deep
mantle, affecting the melting temperature of surrounding rocks,
changing phase relations, and affecting mantle dynamics. The
sequence of hydrous phases that exist in the mantle depends
on the local geotherm, water content, and overall chemistry
(Ohtani et al.
2000
). Here we have examined the polymorphs
of the end-member MgSiO
4
H
2
. We confirm that phase H is the
preferred crystal structure with the MgSiO
4
H
2
stoichiometry at
pressures corresponding to the Earth’s transition zone and entire
lower mantle. In fact, phase H continues to be the preferred poly
-
morph of MgSiO
4
H
2
to at least 300
GPa, indicating that it may
be a candidate phase in water-bearing exoplanetary interiors if
other hydrous magnesium silicate assemblages are not favored.
Although we found that the Mg-end-member of phase egg is
never energetically favorable relative to its polymorphs and phase
P
4
3
2
1
2 is likely unstable relative to multiphase assemblages, it
is possible that certain chemistries and water contents would
favor them with respect to decomposition products and other
dense hydrous magnesium silicate phases. Further investigations
into the compositional space of dense hydrated silicates, e.g.,
the relative stabilities of solid solutions of phases egg, H, and
P
4
3
2
1
2 along the MgSiO
4
H
2
-AlSiO
3
(OH) join, are necessary to
resolve these questions.
Funding
This research was supported in part by the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation program (grant
agreement no. 681818–IMPACT to R.C.). We acknowledge access to the Irene
supercomputer through the PRACE computing grant no. RA4947 and the PSMN
center of ENS Lyon.
References cited
Angel, R.J. (2000) Equations of state. Reviews in Mineralogy and Geochemistry, 41,
35–59.
Arapan, S., and Ahuja, R. (2010) High-pressure phase transformations in carbonates.
Physical Review B, 82, 184115.
Baroni, S., and Resta, R. (1986) Ab initio calculation of the low-frequency Raman
cross section in silicon. Physical Review B, Condensed Matter, 33, 5969–5971.
Baroni, S., de Gironcoli, S., Dal Corso, A., and Giannozzi, P. (2001) Phonons and
related crystal properties from density-functional perturbation theory. Reviews of
Modern Physics, 73, 515–562.
Benoit, M., Marx, D., and Parrinello, M. (1998) Tunnelling and zero-point motion in
high-pressure ice. Nature, 392, 258–261.
Bindi, L., Nishi, M., Tsuchiya, J., and Irifune, T. (2014) Crystal chemistry of dense
hydrous magnesium silicates: The structure of phase H, MgSiH
2
O
4
, synthesized at
45 GPa and 1000 ºC. American Mineralogist, 99, 1802–1805.
Bindi, L., Bendeliani, A., Bobrov, A., Matrosova, E., and Irifune, T. (2020) Incorporation
of Mg in phase egg, AlSiO
3
OH: Toward a new polymorph of phase H, MgSiH
2
O
4
,
a carrier of water in the deep mantle. American Mineralogist, 105, 132–135.
Blöchl, P.E. (1994) Projector augmented-wave method. Physical Review B, Condensed
Matter, 50, 17953–17979.
Bobocioiu, E., and Caracas, R. (2014) Stability and spectroscopy of Mg sulfate miner
-
als: Role of hydration on sulfur isotope partitioning. American Mineralogist, 99,
1216–1220.
Bower, D.J., Kitzmann, D., Wolf, A.S., Sanan, P., Dorn, C., and Oza, A.V. (2019)
Linking the evolution of terrestrial interiors and an early outgassed atmosphere to
astrophysical observations. Astronomy & Astrophysics, 631, A103.
Caracas, R. (2008) Dynamical instabilities of ice X. Physical Review Letters, 101,
085502.
Caracas, R., and Bobocioiu, E. (2011) The WURM project—a freely available web-
based repository of computed physical data for minerals. American Mineralogist,
96, 437–444.
Caracas, R., and Panero, W.R. (2017) Hydrogen mobility in transition zone silicates.
Progress in Earth and Planetary Science, 4, 9.
Chen, C., Yang, S., Liu, L., Xie, H., Liu, H., Zhu, L., and Xu, X. (2017) A green one-step
fabrication of superhydrophobic metallic surfaces of aluminum and zinc. Journal
of Alloys and Compounds, 711, 506–513.
eggleton, R.A., Boland, J.N., and Ringwood, A.E. (1978) High pressure synthesis of
a new aluminium silicate: Al
5
Si
5
O
17
(OH). Geochemical Journal, 12, 191–194.
Fukuyama, K., Ohtani, E., Shibazaki, Y., Kagi, H., and Suzuki, A. (2017) Stability field
of phase egg, AlSiO
3
OH at high pressure and high temperature: Possible water
reservoir in mantle transition zone. Journal of Mineralogical and Petrological
Sciences, 112, 31–35.
Gaetani, G.A., and Grove, T.L. (1998) The influence of water on melting of mantle
peridotite. Contributions to Mineralogy and Petrology, 131, 323–346.
Gaillard, F., and Scaillet, B. (2014) A theoretical framework for volcanic degassing
chemistry in a comparative planetology perspective and implications for planetary
atmospheres. Earth and Planetary Science Letters, 403, 307–316.
Gasparik, T. (1993) The role of volatiles in the transition zone. Journal of Geophysical
Research: Solid Earth, 98, 4287–4299.
Gonze, X., Beuken, J.M., Caracas, R., Detraux, F., Fuchs, M., Rignanese, G.M., Sindic,
L., Verstraete, M., Zerah, G., Jollet, F., and others (2002) First-principles computa
-
tion of material properties: the ABINIT software project. Computational Materials
Science, 25, 478–492.
Gonze, X., Rignanese, G.-M., and Caracas, R. (2005) First-principles studies of the
lattice dynamics of crystals, and related properties. Zeitschrift Für Kristallogra
-
phie—Crystalline Materials, 220, 458–472.
Gonze, X., Amadon, B., Anglade, P.-M., Beuken, J.-M., Bottin, F., Boulanger, P.,
Bruneval, F., Caliste, D., Caracas, R., Côté, M., and others (2009) ABINIT: First-
principles approach to material and nanosystem properties. Computer Physics
Communications, 180, 2582–2615.
Hernandez, J.A., and Caracas, R. (2018) Proton dynamics and the phase diagram of
dense water ice. The Journal of Chemical Physics, 148, 214501.
Herrero, C.P., and Ramírez, R. (2011) Isotope effects in ice Ih: A path-integral simulation.
The Journal of Chemical Physics, 134, 094510.
Hofmeister, A.M., Cynn, H., Burnley, P.C., and Meade, C. (1999) Vibrational spectra of
dense, hydrous magnesium silicates at high pressure: Importance of the hydrogen
bond angle. American Mineralogist, 84, 454–464.
Hushur, A., Manghnani, M.H., Smyth, J.R., Williams, Q., Hellebrand, E., Lonappan, D.,
Ye, Y., Dera, P., and Frost, D.J. (2011) Hydrogen bond symmetrization and equation
of state of phase D. Journal of Geophysical Research, 116.
Inoue, T., Yurimoto, H., and Kudoh, Y. (1995) Hydrous modified spinel, Mg
1.75
SiH
0.5
O
4
:
Downloaded from http://pubs.geoscienceworld.org/msa/ammin/article-pdf/107/5/781/5596803/am-2021-7937.pdf
by California Inst of Technology user
on 04 May 2022
SOLOMATOVA ET AL.: STRUCTURE AND STABILITY OF MGSIO
4
H
2
POLYMORPHS
789
American Mineralogist, vol. 107, 2022
a new water reservoir in the mantle transition region. Geophysical Research Let
-
ters, 22, 117–120.
Jung, D.Y., and Oganov, A.R. (2005) Ab initio study of the high-pressure behavior of
CaSiO
3
perovskite. Physics and Chemistry of Minerals, 32, 146–153.
Kogiso, T., Tatsumi, Y., and Nakano, S. (1997) Trace element transport during dehydra
-
tion processes in the subducted oceanic crust: 1. Experiments and implications for
the origin of ocean island basalts. Earth and Planetary Science Letters, 148, 193–205.
Kresse, G., and Furthmüller, J. (1996) Efficiency of ab-initio total energy calculations for
metals and semiconductors using a plane-wave basis set. Computational Materials
Science, 6, 15–50.
Kubo, T., Ohtani, E., Kato, T., Shinmei, T., and Fujino, K. (1998) Effects of water on the
α-β transformation kinetics in San Carlos olivine. Science, 281, 85–87.
Kuribayashi, T., Sano-Furukawa, A., and Nagase, T. (2014) Observation of pressure-
induced phase transition of δ-AlOOH by using single-crystal synchrotron X-ray
diffraction method. Physics and Chemistry of Minerals, 41, 303–312.
Li, S., Ahuja, R., and Johansson, B. (2006) The elastic and optical properties of the high-
pressure hydrous phase δ-AlOOH. Solid State Communications, 137, 101–106.
Liu, Y., Huang, R., Wu, Y., Zhang, D., Zhang, J., and Wu, X. (2021) Thermal equation
of state of phase egg (AlSiO
3
OH): Implications for hydrous phases in the deep
earth. Contributions to Mineralogy and Petrology, 176, 1–10.
Lv, C.J., Liu, L., Gao, Y., Liu, H., Yi, L., Zhuang, C.Q., Li, Y., and Du, J.G. (2017)
Structural, elastic, and vibrational properties of phase H: A first-principles simula
-
tion. Chinese Physics B, 26, 067401.
Matsushita, E., and Matsubara, T. (1982) Note on isotope effect in hydrogen bonded
crystals. Progress of Theoretical Physics, 67, 1–19.
McKeown, D., Bell, M.I., and Caracas, R. (2010) Theoretical determination of the Raman
spectra of single-crystal forsterite (Mg
2
SiO
4
). American Mineralogist, 95, 980–986.
Mei, S., and Kohlstedt, D.L. (2000) Influence of water on plastic deformation of olivine
aggregates: 2. Dislocation creep regime. Journal of Geophysical Research: Solid
Earth, 105, 21471–21481.
Momma, K., and Izumi, F. (2008) VESTA: A three-dimensional visualization system for
electronic and structural analysis. Journal of Applied Crystallography, 41, 653–658.
Nakagawa, T., Nakakuki, T., and Iwamori, H. (2015) Water circulation and global
mantle dynamics: Insight from numerical modeling. Geochemistry, Geophysics,
Geosystems, 16, 1449–1464.
Natoli, V., Martin, R.M., and Ceperley, D.M. (1993) Crystal structure of atomic hydrogen.
Physical Review Letters, 70, 1952.
Nishi, M., Irifune, T., Tsuchiya, J., Tange, Y., Nishihara, Y., Fujino, K., and Higo, Y.
(2014) Stability of hydrous silicate at high pressures and water transport to the deep
lower mantle. Nature Geoscience, 7, 224–227.
Nishi, M., Tsuchiya, J., Arimoto, T., Kakizawa, S., Kunimoto, T., Tange, Y., Higo, Y.,
and Irifune, T. (2018) Thermal equation of state of MgSiO
4
H
2
phase H determined
by in situ X-ray diffraction and a multianvil apparatus. Physics and Chemistry of
Minerals, 45, 995–1001.
Oganov, A.R., Ono, S., Ma, Y., Glass, C.W., and Garcia, A. (2008) Novel high-pressure
structures of MgCO
3
, CaCO
3
and CO
2
and their role in Earth’s lower mantle. Earth
and Planetary Science Letters, 273, 38–47.
Ohtani, E., Mizobata, H., and Yurimoto, H. (2000) Stability of dense hydrous magnesium
silicate phases in the systems Mg
2
SiO
4
-H
2
O and MgSiO
3
-H
2
O at pressures up to
27 GPa. Physics and Chemistry of Minerals, 27, 533–544.
Ohtani, E., Litasov, K., Suzuki, A., and Kondo, T. (2001) Stability field of new hydrous
phase, δ-AlOOH, with implications for water transport into the deep mantle. Geo
-
physical Research Letters, 28, 3991–3993.
Ohtani, E., Amaike, Y., Kamada, S., Sakamaki, T., and Hirao, N. (2014) Stability of
hydrous phase H MgSiO
4
H
2
under lower mantle conditions. Geophysical Research
Letters, 41, 8283–8287.
Ohira, I., Jackson, J.M., Solomatova, N.V., Sturhahn, W., Finkelstein, G.J., Kamada, S.,
Kawazoe, T., Maeda, F., Hirao, N., Nakano, S., and others (2019) Compressional
behavior and spin state of δ-(Al,Fe)OOH at high pressures. American Mineralo
-
gist, 104, 1273–1284.
Panero, W.R., and Caracas, R. (2017) Stability of phase H in the MgSiO
4
H
2
–AlOOH–
SiO
2
system. Earth and Planetary Science Letters, 463, 171–177.
——— (2020) Stability and solid solutions of hydrous alumino-silicates in the Earth’s.
Minerals , 10, 330.
Pearson, D.G., Brenker, F.E., Nestola, F., McNeill, J., Nasdala, L., Hutchison, M.T.,
Matveev, S., Mather, K., Silversmit, G., Schmitz, S., Vekemans, B., and Vincze, L.
(2014) Hydrous mantle transition zone indicated by ringwoodite included within
diamond. Nature, 507, 221–224.
Perdew, J.P., Burke, K., and Ernzerhof, M. (1996) Generalized gradient approximation
made simple. Physical Review Letters, 77, 3865–3868.
Rivera, S.A., Allis, D.G., and Hudson, B.S. (2008) Importance of vibrational zero-point
energy contribution to the relative polymorph energies of hydrogen-bonded species.
Crystal Growth & Design, 8, 3905–3907.
Sano-Furukawa, A., Kagi, H., Nagai, T., Nakano, S., Fukura, S., Ushijima, D., Iizuka,
R., Ohtani, E., and Yagi, T. (2009) Change in compressibility of δ-AlOOH and
δ-AlOOD at high pressure: A study of isotope effect and hydrogen-bond sym
-
metrization. American Mineralogist, 94, 1255–1261.
Sano-Furukawa, A., Hattori, T., Komatsu, K., Kagi, H., Nagai, T., Molaison, J.J., Dos
Santos, A.M., and Tulk, C.A. (2018) Direct observation of symmetrization of
hydrogen bond in δ-AlOOH under mantle conditions using neutron diffraction.
Scientific Reports, 8, 15520–15529.
Schmidt, M.W., Finger, L.W., Angel, R.J., and Dinnebier, R.E. (1998) Synthesis, crystal
structure, and phase relations of AlSiO
3
OH, a high-pressure hydrous phase. Ameri
-
can Mineralogist, 83, 881–888.
Schulze, K., Pamato, M.G., Kurnosov, A., Ballaran, T.B., Glazyrin, K., Pakhomova,
A., and Marquardt, H. (2018) High-pressure single-crystal structural analysis of
AlSiO
3
OH phase egg. American Mineralogist, 103, 1975–1980.
Segall, M.D., Lindan, P.J., Probert, M.A., Pickard, C.J., Hasnip, P.J., Clark, S.J., and
Payne, M.C. (2002) First-principles simulation: ideas, illustrations and the CASTEP
code. Journal of Physics: Condensed Matter, 14, 2717.
Shieh, S.R., Mao, H.K., Hemley, R.J., and Ming, L.C. (1998) Decomposition of phase D
in the lower mantle and the fate of dense hydrous silicates in subducting slabs. Earth
and Planetary Science Letters, 159, 13–23.
Shinmei, T., Irifune, T., Tsuchiya, J., and Funakoshi, K.I. (2008) Phase transition and
compression behavior of phase D up to 46 GPa using multi-anvil apparatus with
sintered diamond anvils. High Pressure Research, 28, 363–373.
Smyth, J.R., and Kawamoto, T. (1997) Wadsleyite II: A new high pressure hydrous phase
in the peridotite-H
2
O system. Earth and Planetary Science Letters, 146, E9–E16.
Solomatova, N.V., and Asimow, P.D. (2017) Ab initio study of the structure and stability
of CaMg(CO
3
)
2
at high pressure. American Mineralogist, 102, 210–215.
Solomatova, N.V., and Caracas, R. (2021) Genesis of a CO
2
-rich and H
2
O-depleted atmo
-
sphere from Earth’s early global magma ocean. Science Advances, 7(41), eabj0406.
Stixrude, L., Lithgow-Bertelloni, C., Kiefer, B., and Fumagalli, P. (2007) Phase stabil
-
ity and shear softening in CaSiO
3
perovskite at high pressure. Physical Review
B, 75, 024108.
Togo, A., and Tanaka, I. (2015) First principles phonon calculations in materials science.
Scripta Materialia, 108, 1–5.
Tsuchiya, J. (2013) First principles prediction of a new high-pressure phase of dense
hydrous magnesium silicates in the lower mantle. Geophysical Research Letters,
40, 4570–4573.
Tsuchiya, J., and Mookherjee, M. (2015) Crystal structure, equation of state, and
elasticity of phase H (MgSiO
4
H
2
) at Earth’s lower mantle pressures. Scientific
Reports, 5, 15534.
Tsuchiya, J., and Umemoto, K. (2019) First-principles determination of the dissocia
-
tion phase boundary of phase H MgSiO
4
H
2
. Geophysical Research Letters, 46,
7333–7336.
Tsuchiya, J., Tsuchiya, T., Tsuneyuki, S., and Yamanaka, T. (2002) First-principles
calculation of a high-pressure hydrous phase, δ-AlOOH. Geophysical Research
Letters, 29, 15-1–15-4.
Tsuchiya, J., Tsuchiya, T., and Tsuneyuki, S. (2005) First-principles study of hydrogen
bond symmetrization of phase D under high pressure. American Mineralogist,
90, 44–49.
Tsuchiya, J., Tsuchiya, T., and Wentzcovitch, R.M. (2008) Vibrational properties of
δ-AlOOH under pressure. American Mineralogist, 93, 477–482.
Veithen, M., Gonze, X., and Ghosez, P. (2005) Non-linear optical susceptibilities,
Raman efficiencies and electrooptic tensors from first-principles density functional
perturbation theory. Physical Review B, 71, 125107.
Wang, Y., Lv, J., Zhu, L., and Ma, Y. (2012) CALYPSO: A method for crystal structure
prediction. Computer Physics Communications, 183, 2063–2070.
Wood, B.J. (1995) July) Storage and recycling of H
2
O and CO
2
in the earth. In AIP
Conference Proceedings, vol. 341, no. 1, pp. 3–21. American Institute of Physics.
Yu, Y.G., Wentzcovitch, R.M., and Angel, R.J. (2010) First-principles study of thermo
-
dynamics and phase transition in low-pressure (
P
2
1
/
c
) and high-pressure (
C
2/
c
)
clinoenstatite MgSiO
3
. Journal of Geophysical Research: Solid Earth, 115.
Manuscript received December 21 2020
Manuscript accepted July 7, 2021
Manuscript handled by Bin Chen
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