Geoscience Reference
In-Depth Information
7
Ab Initio
Mineralogical Model of the
Earth's Lower Mantle
TAKU TSUCHIYA
1
AND KENJI KAWAI
2
1
Geodynamics Research Center, Ehime University, Matsuyama, Ehime, Japan
2
Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo, Japan
Summary
7.1
Introduction
Recent progress in theoretical mineral physics
based on the
ab initio
quantum mechanical com-
putation method has been dramatic in conjunc-
tion with the rapid advancement of computer
technologies. It is now possible to predict sta-
bility and several physical properties of complex
minerals quantitatively with uncertainties that
are comparable to or even smaller than those
attached in experimental data. Especially, calcu-
lation of high-pressure elasticity of minerals is of
particular geophysical interest, since this allows
us to construct a priori mineralogical models of
the deep Earth through direct comparisons be-
tween the calculated seismic velocities and the
actual Earth's values. In the present chapter,
we briefly review recent progress in studying
high-pressure elasticity of lower mantle miner-
als including silicates, oxides, and some hydrous
phases, then summarize current knowledge on
the aggregate elasticity of representative lithology
closely related to the mantle and slab materials.
Our analyses indicate that the pyrolitic compo-
sition can describe the Earth's properties quite
well in terms of density, P and S wave velocity,
and bulk sound velocity. The overall agreements
are better than those expected in more silicic
compositions. Computations also suggest that cu-
mulated basaltic piles are unsuitable to explain
the LLSVP.
Progress in computational mineral physics based
on the
ab initio
quantum mechanical calculation
method has been dramatic in the last decade in
conjunction with the rapid advancement of com-
puter technologies. While the classical molecu-
lar simulations required an empirical treatment
on the interatomic model potentials, which en-
tirely rely on available experimental data and are
often oversimplified, the quantum mechanical
Hamiltonian of many-body electron systems can
be efficiently and quantitatively evaluated even
without any empirical treatment on the basis
of the density functional theory (DFT) (Hohen-
berg & Kohn, 1964; Kohn & Sham, 1965). Practical
calculations of minerals having complex crystal
structures can be achieved by combining various
methods and techniques developed following the
DFT. As a result of such advancement in the
ab initio
techniques, it is now possible to pre-
dict stability and several physical properties, in-
cluding elasticity, thermodynamic and electronic
properties, of materials under high-pressure quan-
titatively with uncertainties that are comparable
to or even less than those found in experimental
data. Especially, reliable determination of high-
P
,
T
elasticity, which is still quite difficult experi-
mentally in the Earth's lower mantle condition,
is of significant geophysical importance, because
this allows us to construct mineralogical models
