earth mantle,1) and are also present as major phases in ...
Transcript of earth mantle,1) and are also present as major phases in ...
Physics Reports of Kumamoto University, Vol. 13, No. 2 (2010) 293
Ab initio Molecular-Dynamics Study of Structural and Electronic
Properties of Liquid MgSiO3 under Pressure
RyoYOSHIMURA、Satoshi OHMURA and Fuyuki SHIMOJO
Department of Physics, Kumamoto University, Kumamoto 860-8555
(Received September 30, 2010)
The structural and electronic properties of liquid MgSiC>3 under pressure are investigated
by ab initio molecular-dynamics simulations. At ambient pressure, most Si atoms have the
same coordination even in the liquid state as in the crystalline phase, i.e., each Si atom
is bonded to two bridging oxygens twofold-coordinated to Si, and two nonbridging oxygens
onefold-coordinated to Si. It is found that the structural defects, such as fivefold- or threefold-
coordinated Si atoms, are always formed with the rearrangement of Si-0 covalent bonds in the
atomic diffusion processes. The population analysis clarifies that maximum of the diffusivity
in the pressure dependence is originated from the increasing of the number of defects undercompression.
§1. Introduction
The structural and dynamic properties of liquid silicates have been attracted
the interest of many scientists because of the importance in the earth's mantle. In
addition, the magnesium-rich silicate minerals are the primary constituents of the
earth mantle,1) and are also present as major phases in chondrite meteorites andinterplanetary dust.2)'3)
In ambient conditions, crystalline magnesium silicate (MgSiOa) has a SiC>4 tetra-
hedral unit in which each silicon atom is coordinated to four oxygen atoms with
single bonds.4) A high-pressure phase appears at a pressure of about 25 GPa undercompression. There is a SiC>6 octahedral unit in this structure. Each Mg atom is
coordinated to 12 oxygens with bond lengths ranging from 2.014 to 3.12 A and O-
Mg-0 angles ranging from 52.19° to 70.89°.5) The ideal value of an O-Mg-0 angle
for a regular MgOi2 polyhedron is 60°. The small variations in the Si-0 distances
and the small deviation of the O-Si-0 angles from 90° (88.5° - 91.5°) show that the
SiO6 octahedron is much more regular than the MgOi2 polyhedron.
Since it would be difficult to clarify the diffusion mechanism in liquid MgSiC>3
experimentally, theoretical studies would be needed. However, only a few theoretical
studies of atomic diffusion have been reported so far,6) while their crystalline phases
have been extensively investigated.7) Molecular dynamics (MD) simulations6) withempirical interatomic potentials have been used for the diffusion mechanism of oxy
gen ions in Me2OSi02 (Me = Li, Na, K, Cs) melts at 2000 K. Although effects of
alkali ions have been examined on the structure of transient complexes temporarily
formed in alkali silicate systems, the effects of electronic properties are still unclear.
In this paper, we carry out ab initio MD simulations of liquid MgSiC>3 under
pressure. We obtain the atomic forces quantum mechanically from the electronic-
structure calculations. The purpose of our study is to clarify the microscopic mech-
294 R. Yoshimura, S. Ohmura and F. Shimojo
Table I. Pressure P, temperature T and number density p used in this study.
P (GPa)
0.1
9.5
21.1
48.9
97.8
149.1
198.2
T(K)
2500
2900
3300
4500
5500
6000
7000
9 (A"3)
0.068
0.086
0.099
0.113
0.132
0.146
0.156
anism of atomic diffusion in the liquid state from first principles. We are unaware of
investigations of the diffusion mechanism in liquid silicates based on first-principles
theories though some first principles studies of liquid MgSiC>3 under pressure have
already been reported.8)'9) We discuss how Si-0 bonds are exchanged, accompanying the diffusion of atoms in detail. Such findings are important not only for
imderstanding the equilibrium properties of liquid MgSiC>3 but also for properties of
basic liquids in the earth's mantle.
§2. Method of calculation
In our MD simulations, a system of 120 (24 Mg + 24 Si + 720) atoms in a
cubic supercell is used under periodic boundary conditions. The equations of mo
tion for atoms are solved via an explicit reversible integrator10) with a time step
of At = 1.2 fe. The atomic forces are obtained from the electronic states cal
culated by the projector-augmented-wave method11)'12) within the framework of
density-functional theory. The generalized gradient approximation13) is used for
the exchange-correlation energy. The plane wave cutoff energies are 30 and 250 Ry
for the electronic psedo-wave-functions and the pseudo-charge-density, respectively.
The energy functional is minimized using an iterative scheme.14)'15) Projector func
tions are generated for the 3s, 3p and 3d states of Mg and Si, and the 2s and 2p
states of O.
For each pressure (0 - 200 GPa), the temperature is set to be the melting point
plus about 500 K. To determine the density of the liquid state under compression,
constant-pressure MD simulation16) is performed for 2.4 ps at given pressure. The
static and diffusion properties are investigated by MD simulations in the canonical
ensemble.17)'18)
§3. Results and discussion
3.1. Structure factor
Figure 1 shows the pressure dependence of the structure factor of liquid MgSiC>3.
The solid and dashed lines display the X-ray and neutron structure factors, Sx(k)
and Sn(fc), respectively. Sx(fc) is obtained from the partial structure factors 5Q^(fc),
shown in Fig. 2, with the X-ray scattering factors, and Sn(k) is calculated from
Structural and Electronic Properties of Liquid MgSiOs 295
Sap{k) with the neutron-scattering lengths. At pressures below 10 GPa, clear peaks
exist at about k = 2.0 and 4.4 A""1 in the profiles of Sx{k) and Sn(k). Note that theoverall profile of Sx(k) at 0 GPa is consistent with the experimental Sx(k) of the
vitreous state.19) While only <Sn(A;) has another peak at 3.0 A""1 at lower pressures,the corresponding peak grows in Sx(k) at higher pressures. With increasing pressure,
the peak at about A; = 2.0 A"1 in both Sx(k) and Sn(k). A remarkable featureexhibited in Sx(k) and Sn(k) is the small peak at about A; = 1.2 A"1 at 0 GPa,
which means that the spatial correlation exists on an intermediate distance ~ 6 A.
This peak disappears under pressure.
3-
— X-ray(simulation, liquid)
--- Neutron(simulation, liquid)
• X-ray(experiment, glass)
200 GPa (+6.0)— Mg-Mg
- Si-Si
oo 110
1(
— Mg-Si
- Mg-0
_(b)- si-o_
~J\i'
0 2 4 6 8 10 0 2 4 6 8 10
Fig. 1. Pressure dependence of the total struc- Fig. 2. Pressure dependence of the partial struc
() (d) Sture factors Sap(k). (a) 5m8m8 (solid),
(dashed) and Soo (dotted), (b) SMgSi (solid),
SMgo (dashed) and Ssio (dotted).
ture factors. The solid and dashed lines indi-
cate the X-ray and neutron structure factors,
Sx(fc) and Sn(fc), respectively. The open cir-
cles at 0 GPa are the experimental values for
glass MgSiO3. The curves are shifted verti
cally as indicated by the figures in parenthe
ses.
Figure 2 shows the Ashcroft-Langreth partial structure factors Sap(k). The pres
sure dependence of the profiles of Sx(k) and Sn(k) is well understood from Sap{k).
At 0 GPa, Ssisi(fc) has Peaks at about k = 1.2 A"1, which gives the correspondingpeak in Sx(k) and Sn(k). At lower pressures, SMgMg(fc), SSiSi(*0 ^d Soo(k) havethe peak at about k = 2.3 A"1. Because of the cancellation due to the existence
296 R. Yoshimura, S. Ohmura and F. Shimojo
of a negative dip in Sugo(k) and Ssio(*0> no clear Peak appears in Sx(k) aroimdk = 2.3 A"1. With increasing pressure, all peaks shift to larger k in SMgMg(*0>SsiSi(fc) and Soo(k), whereas the negative dip changes only a little in SMgo(fc) and
Ssio{k). Therefore, the peaks of Sx(k) and Sn(k) grow at the corresponding k when
the pressure increases. At higher pressure, the main peak of SuSMg(k) is as high as
that of SsiSi(k).
3.2. Diffusivity
The diffusion coefficients Da for a = Mg, Si, and 0 atoms are defined as
(3.1)
where r»(*) is the position of the i-th atom at time t. Figure 3 shows Da as a
function of pressure. Whereas Ds» Do and DMg have maxima at 50 GPa, DMg has
a minimum at 20 GPa. While DMg has larger values than Do under pressures up to
about 10 GPa, Do becomes comparable with £>Mg at about 20 GPa.
P (GPa)
Fig. 3. Pressure dependence of the diffusion coefficients Da for a = Mg (circles), Si (squares) and
O (diamonds) atoms.
3.3. Mechanism of atomic diffusion
It is found, from the distribution of coordination numbers, that Si atoms are
mainly coordinated to four O atoms; two O atoms bridge two adjacent Si atoms,
and the other two O atoms are coordinated to only one Si atom, as in the crystalline
phase even though atoms diffuse in the liquid state. However, it is unclear how Si-0
bonds are exchanged with the diffusion of atoms in the liquid state while retaining
the covalent bonds. To clarify the mechanism of atomic diffusion, we investigate the
time evolution of the bonding nature by utilizing population analysis. The bond-
overlap population Ojj(t), which gives a semiquantitative estimate of the strength of
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§4.Suxnmary
Th燈mi心roscopicmechanismof誠0m正diHilfii⑪ninliquidMgSiO3hH遇beeninPvBstigat⑧dbya6鈍雄。moIBcul渉dynami⑪s急imnl鉱ions,IthasbeenconfirmBdthat,evmintheliqUidstate,siliconatom;ar心predominantly蝿urliDldPm0rdmatedtoh必tematomswithsinglB⑪OvalBntbondsat⑬mbientconditions,asinthGcryst錨llinBandvitreougstates.Wもh誠巴fbundthatth⑬reappearsastru⑯tumlde比ctwh心nevcratDmicdiHilsionoccursn心compani⑧dwiththecovalent-bondexchangesoThBfbrm針tiDnm垣(、h麺i釘nofsuchdefbctstructurehasbeendiscussdind巳tailusingthCtimB
Structural and Electronic Properties of Liquid MgSiO^ 299
evolution of the bond-overlap populations between atoms. The number of structural
defects increases gradually with compression. Therefore, atomic diffusion events re
lated to overcoordinated Si occur easily. As a result, Dsi and Do increase up to 50
GPa.
Acknowledgments
The authors thank Research Institute for Information Technology, Kyushu Uni
versity for the use of facilities. The computation was also carried out using the
computer facilities at the Supercomputer Center, Institute for Solid State Physics,
University of Tokyo.
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