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Mineral Physics is one of the three branchesof geophysics (the others being geodynamics
and seismology) [1]. It involves the
application of physics, chemistry and
material science techniques in order to
understand and predict the fundamental
behavior of materials where the Earth and
other planets are composed [2]. Hence, italso provides solutions to large scale
problems in Earth and planetary sciences [2].
What is Mineral Physics?
Importance of Studying
the DisciplineIt provides information that are essential in
interpreting observational data from many of
the disciplines in the Earth Sciences,
including geodynamics, seismology,
geochemistry, petrology, geomagnetism,
planetary sciences, material science and
climate studies, as illustrated on the
following figure [3].
Contents
• Definition of MineralPhysics
• Relation to other
Earth Sciences
• The Discipline
• List of Material’s
Properties
• Investigation of Elastic
Property
• The Earth’s Radial
Structure
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MineralPhysics and the
Petrology
Planetary
Science Seismology
ClimaGeochemistry
Geodynamics
Geomagnetism
Material
cience
hase Equilibria
nd Phase Deformation
Interior Chemistry,
Partitioning and Diffusion
Electromagnetic and Iron Alloy
Properties
Thermal and Rheological
Properties
Elastic and Inelastic PropertiesChemistry and Physics of
nteriors, and Impact Processes
perhard
d Novel
aterials
Volatile,
Degassin
Retention
other disciplines of Earth Science
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All of the natural sciences devote a
great deal of their focus on
processes that occur on the Earth’s
surface [3]. Our understanding of
these processes can be enriched by
insight into how the Earth’s surface
and atmosphere have developed
and continue to evolve over time
[3]. Much of this evolution is the
result of surface manifestation of
deep Earth phenomena. Mineral
Physics helps us understand the
properties of materials that are
involved in deep Earth Phenomena
such as [3]:
Propagation of Seismic Waves
Earth’s Gravitational Field
Earth’s Magnetic Field
Plate Tectonics
Mantle Convection
Eruptions of Kimberlites
Volcanism
Hot Spots
Evolution of the Earth’s Interior
Release of Gases from the
Earth’s Interior into the
Atmosphere
It also focuses on the properties o
materials that may make the
economically useful. Some of thes
properties are [3]:
Superconductivity
Optical Properties
Magnetic Properties
Potential for Generating, Storing
Conducting, and Releasing
Energy
Potential Information Storage
Chemical Properties
Material’s property is an intensiv
often quantitative, property of som
material [4]. A property is may be
constant or may be a function of on
or more independent variables, suc
as temperature and pressure [4
However, materials properties ofte
vary to some degree according to th
direction in the material in whic
they are measured, a conditio
referred to anisotropy [4]. Some o
the material’s properties were als
used in relevant equations to predi
the attributes of a system a priori [4
The Discipline
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List of Material’
Properties
Acoustic Properties
Acoustical Absorption
Speed of Sound
Atomic Properties
Atomic Mass
Atomic Number (pure elements)Atomic Weight (individual
isotopes or mixtures of isotopes
of a given element)
Chemical Properties
Corrosion Resistance
HygroscopypH
Reactivity
Specific Internal Surface Area
Surface Energy
Surface Tension
Electrical propertiesDielectric constant
Dielectric strength
Electrical conductivity
Permittivity
Piezoelectric constants
Seebeck coefficient
Environmental properties
Embodied energy
Embodied water
Magnetic properties
Curie temperature
DiamagnetismHysteresis
Permeability
Manufacturing properties
Castability
Extruding temperature and
pressureMachinability rating
Machining speeds and feeds
Mechanical properties
Bulk modulus)
Coefficient of
Coefficient of restitutionCompressive strength
Creep
Ductility
Fatigue limit
Flexural Modulus
Flexural Strength
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Fracture toughness
Hardness
Plasticity
Poisson’s ratio
Resilience
Shear modulusShear strain
Shear strength
Specific modulus
Specific strength
Specific weigth
Surface toughness
Tensile strengthYield strength
Young’s modulus
Optical properties
Absorbance
Birefringence
ColorLuminosity
Photosensitivity
Reflectivity
Refractive index
Scattering
Transmittance
Radiological properties
Neutron crosssection
Specific activity
Thermal properties
Auto-ignition temperature
Binary phase diagram
Boiling point
Coefficient of thermal
expansion
Critical temperature
Curie pointEmissivity
Eutectic point
Flammability
Flash point
Glass transition temperature
Heat of fusion
Heat of vaporizationInversion temperature
Melting point
Phase diagram
Pyrophoricity
Seebeck coefficient
Solidus
Specific heatThermal conductivity
Thermal diffusivity
Thermal expansion
Triple point
Vapor pressure
Vicat softening point
Most of the properties
were reliably measured by
standardized test methods
and equipments [4]:
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If we are to utilize the rich source of information on velocit
variations in Earth’s interior to infer basic properties such a
composition and temperature, it requires knowledge of the elasti
properties of Earth materials and so, we need instruments tha
could achieve high P/T levels similar to the levels inside and at the
deep-Earth [2].
There are several instruments and techniques that were used tha
could attain high pressure and temperature for measuring th
elastic property [2]. And one of them is the high stati
compression [2].
Piston Cylinder ApparatusIn its simplest form, a sample is placed in a steel or WC cylinder,
and is compressed by pistons that advance into the two ends of
the cylinder [2]. The sample volume at high pressure is measuredby the area of the piston, and the force applied to the piston is
used to calculate the pressure [2]. It achieves high pressures
using the principle of pressure amplification: converting a small
load on a large piston to a relatively large load on a small piston
[8]. The uniaxial pressure is then distributed (quasihydrostatically)
over the sample through deformation of the assembly materials
[8]. The nominal pressure in an experiment is can be calculatefrom the amplification of the oil pressure through the reduction
in area over which it is applied, but every component has a
characteristic yield stress, consequently the nominal pressure is
different from the effective one [8]. Thus, the friction between
the piston and cylinder, as well as other frictional effects, need to
be accounted for in calculating an accurate pressure [2].
Creating High PressureHigh static compressions are investigated using Piston Cylinder
Apparatus, Diamond Anvil Cells and Multi Anvil Cells.
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Multi Anvil Devices
These devices can hold much larger sample volumes,
approximately 1mm or larger, it can also provide relativelyuniform heating of a sample, and can accommodate a
thermocouple inside the sample chamber [2]. Pressures of about
28 GPa (equivalent to depths of 840 km), and temperatures above
2300 °C, it can be attained using WC anvils and a lanthanum
chromite furnace. The apparatus is very bulky and cannot achieve
pressures like those in the diamond anvil cell (below), but it can
handle much larger samples that can be quenched and examinedafter the experiment [2]. Recently, sintered diamond anvils have
been developed for this type of press that can reach pressures of
90 GPa (2700 km depth) [2]. The pressure achievable with this
apparatus depends on the truncation area of the inner-stage
cubes, with smaller truncations yielding greater pressures [2].
Diamond Anvil CellsThe diamond anvil cell is a small table-top device for
concentrating pressure [2]. It can compress a small (submillimeter
sized) piece of material to extreme pressures, which can exceed
3,000,000 atmospheres (300 GPa) [2]. This is beyond the
pressures at the center of the Earth [2]. The concentration of
pressure at the tip of the diamonds is possible because of their
hardness, while their transparency and high thermal conductivity
allow a variety of probes can be used to examine the state of the
sample [2]. Pressure is most often measured indirectly via the
fluorescence wavelength of ruby, which are strongly pressure
dependent [2]. The simplicity of the diamond-anvil pressure cell
makes it a highly versatile device for a wide variety of
spectroscopic studies, not only of the bulk modulus but also
phase relations and a host of other properties [2].
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Figure 1 A modern piston
cylinder apparatus, wherein
hydrostatic pressure is
transmitted to the sample by
argon gas [2].
Figure 2 Motorized level
-arm DAC assembly and
the Be gasket [2].
Figure 3 Diagram of a single-
stage pressure device with six
anvils compressing the sample
assembly along the directions
of the faces on a cube [2].
Piston Cylinder Apparatus
Diamond Anvil Cell
Multi Anvil Devices
High Static Compressions Devices
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For high temperature measurements there are different heating
materials that were used for DAC and Multianvil Devices. DAC
made used of the following heat sources [2]:
Radiation from the X-ray Diffraction (XRD) measured by
electrical resistance coils external to DAC.
High-power Infrared lasers, and
Liquid nitrogen or helium flow cryostat.
While the Multianvil Devices uses graphite, LaCrO3, composite of
TiC pdiamond, and metals of high melting point such as Pt, Ta, andRe [2]. Among them, the graphite heater works excellently to
higher than 2500 K at pressures up to 11 GPa, but, at still higher
pressures, partial transformation of graphite into diamond
prevents to serve as a heating material [2]. Maximum attainable
temperatures by using various heating materials depend on shape,
size, and configuration of the thermal insulator in the sample
assembly, and those are typically 1900, 2000, 2700, and 2900 K forPt, Ta, Re, and LaCrO3, respectively [2]
Creating High Temperature
Figure 4 Left bottom, schematic
of a laser –heated DAC. Top left,
photomicrograph showing the
Mg0.6Fe0.4SiO3 orthopyroxene
sample (En60) in a transparent
graphite ring in Be gasket at 130
Gpa before heating; top right,during laser heating to 1800 K
[2].
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The most remarkable and informative feature of Earth’s radial
structure is that it is not smooth and the variations of seismic
wave velocities with depth is broken up at several depths by
rapid changes in physical properties [2]. These are generally
referred to as discontinuities, although in all probability, they
represent regions where physical properties change very rapidly
over a finite depth interval. Each discontinuity is associated with
a mean depth, a range of depth due to topography on the
discontinuity, and a contrast in physical properties, most directly
the impedance contrast [2],
Where ρ is the density and V is either the shear or longitudinal-
wave velocity and ∆ represents the difference across the
discontinuity [2]. For isochemical changes in physical properties
that follow Birch’s law, the velocity contrast is approximately
two-thirds of the impedance contrast for S-waves andapproximately three-fourths for P-waves [2].
Birch’s Law: The changes in density produced by compression or
by replacing a mineral by an ‘‘analog’’ compound of same mean
atomic mass but of different chemical composition, causes the
same change in elastic wave velocity.
Discontinuities are important because they tie seismological
observations to the Earth’s thermal and chemical state in an
unusually precise and rich way [2]. Many discontinuities in the
mantle occur at depths that correspond closely to the pressure
of phase transformations that are known from experiments to
occur in plausible mantle bulk compositions [2].
The Earth’s Radial Structure
(1)
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The pressure at which the phase transformation occurs
generally depends on temperature via the Claussius-Clapeyron
relation (slope of the phase boundary) [7].
Where T t is the temperature of transition at pressure P, while
∆V is the volume change and ∆S is the change in entropy [7].
This relation was derived from the total differential change in
Gibbs free energy G, expressing the equilibrium between solid
and liquid at the melting point; assuming that when a small
volume element of the solid changes to liquid then G is equal
tends to be zero [7].
Here VL, SL, and VS, SS are the specific volume and entropy per
unit mass of the liquid and solid respectively.
Hence, the mean depth of a discontinuity then anchors the
geotherm [2]. Lateral variations in the depth of the discontinuity
constrain lateral variations in temperature [2].
Figure 5 Phase
proportions and
geotherm at the
transition zone
and the upper
mantle [2].
(2)
(3)
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Phase transformation also influence mantle dynamics [2]. The
extent to which a phase transformation alters dynamics scales
with the phase buoyancy parameter,
Where γ is the Clapeyron slope, g is the acceleration due to
gravity, α is the thermal expansitivity, and h is the depth of the
mantle [2]. Phase transformation with negative Clapeyron
slopes, such as the perovskite forming reaction tend to impede
radial mass transfer, while those with positive Clapeyron slopes,
such as the olivine to wadsleyite transformation, tend to
encourage it [2]. In application to Earth’s mantle, the phase
buoyancy parameter must be generalized to account for the factthat only a fraction of the mantle undergoes the phase
transformation (i.e., 50-60% in the case of the olivine to
wadsleyite transition), and that nearly all phase transformation
are at least diviriant and occur over a finite range of depth [2].
Phase transformation also depends sensitively on bulk
composition, which means that the Earth’s discontinuitystructure also contains mantle chemistry [2]. However, not all
discontinuities can be explained by phase transformations [2]. In
some cases, no phase transformations occur near the
appropriate depth. In others, phase transformations do occur,
but the change in physical properties caused by the transition is
far too subtle to explain the seismic signal [2]. Rapid variation
with depth in chemical composition, the pattern or strength ofanisotropy, or in the magnitude of attenuation and dispersion
may also cause discontinuities [2].
Discontinuities are can be observe through seismological Earth
models that typically use velocity-depth profiles and an
equation of state relating density to (adiabatic) bulk modulus to
(4)
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obtain density, pressure and elastic moduli profiles [7]. The
Earth is divided into radially symmetrical shells separated by
convenient seismological discontinuities, of which the principal
are situated at depths of 400, 670, 2890 and 5150 km,
corresponding to the seismic boundaries between uppermost
mantle and transition zone, upper and lower mantle, mantle
and core, and outer and inner core, respectively [7]. In this
section we are only dealing with Preliminary Reference Earth
Model (PREM) seismological model (Dziewonsky and Anderson,
1981).
The observed values entering the model at figure 7 are travel
times of P and S body waves with a period of 1s and the period
of free oscillations, together with the attenuation factors [7]. It
can be observed that for an increasing density the wave
velocities experience a rapid change more especially on the
location of discontinuities, it can be seen that the attenuation
largely affects most specially wave velocities at the 660 km
discontinuity. It can also be observed a large discontinuity at the
2890 km that defines the boundaries of the mantle and core [7].
Figure 6 Calculated dens
and elastic wave velociti
for different geotherms f
pyrolite like compositio
with (a) 3% Al2O3 and (
5% Al2O3 [2].
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F i g u r e
7 P R E M m o d e l : S e
i s m i c v e l o c i t i e s a n d d
e n s i t y p r o f i l e ( l e f t )
a n d E a r t h s d e p t h w h e r e d
i s c o n t i n u i t i e s a r e r e c
o r d e d ( r i g h t ) [ 7 ] .
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The two largest discontinuities in the mantle occur at 410 and 660
km depth [2]. These have been explained by phase
transformations from olivine to its high pressure polymorph
wadsleyite for the 410 and from ringwoodite, the next highest
pressure olivine polymorph, to the assemblage perovskite plus
periclase for the 660 according to the reaction [2],
Mg4SiO4 (ringwoodite) = MgSiO3 (majorite) + MgO ( periclase) (5)
Recent studies have indicated complexity in the structure at the
660 km [2]. In relatively cold mantle, the transition is preceded by
[2],
MgSiO3 (akimotoite) = MgSiO3 ( perovskite) (6)
while in hot mantle the amount of ringwoodite is diminished
prior to the transition via [2],
Mg4SiO4 (ringwoodite) = MgSiO3 (majorite) + MgO ( periclase) (7)
In cold and hot mantle, the reactions will be followed by a further
reaction [2]:
MgSiO3 (majorite) = MgSiO3 ( perovskite) (8)
The sequence of reactions (5) and (6) should produce a ‘doubled’
660 in which a single velocity jump is replaced by two that areclosely spaced in depth and of similar magnitude [2]. There is
some seismological evidence for this doubling in some locations.
[2] The relative importance of reactions (5) –(8) will also depend
on the bulk composition, particularly the Al content. Below 660 is
a steep velocity gradient that may be considered a continuation
of the transition zone [2].
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At the transition zone it is also observed that the width of the
discontinuity is found to increase with decreasing temperature
which would affect the visibility of transition [2]. The transition i
also sensitive to water content as wadsleyite appears to have a
much higher solubility than olivine although more recent result
suggest that water partitioning between these two phases, andthe influence of water on the form of the 410, is not as large as
previously assumed [2]. Portions of the mantle are found to have
broad and nonlinear 410 discontinuities, consistent with th
anticipated effects of water enrichment [2]. In some locations, the
410 is overlain by low velocity patches that have been interpreted
as regions of partial melt, perhaps associated with wate
enrichment [2]. These patches appear to be associated withsubduction zones, suggesting the slab as a possible source o
water [2]. Other interpretations involving much more pervasive
fluxing of water through the transition zone have also bee
advanced, although it has been argued that this scenario i
inconsistent with the thermodynamics of water-enhanced mantle
melting [2].
References
[1] Tao Sun and Dong-Bo Zhang, et.al. Computational Mineral Physics. Blue Water Annual Report, pp. 58-60.
Date Retrieved: November 30, 2015
[2] Dr. G. David Price, Treatise on Geophysics, Vol. 2 - Mineral Physics. University College London, pp. 1-#
[3] Teaching Mineral Physics Across the Curriculum. Website: http://serc.carleton.edu. Date Retrieved:
November 30, 2015
[4] List of Materials Properties. Website: https://en.wikipedia.org. Date Retrieved: December 10, 2015
[5] C. M. R. Fowler. The Solid Earth, An Introduction to Global Geophysics. Cambridge University Press, page100
[6] Michael Wysession. Grand Challenges for Seismology: Relevance to Mineral Physics. Compres, Long Range
Science Plan for Seismology Workshop, 2008. Powerpoint Presentation Retrieved Last: December 10, 2015
[7] Jean-Paul Poirier. Introduction to the Physics of the Earth’s Interior 2nd Edition. Cambridge University Press,
pp. 115 and 245
[8] Piston Cylinder Apparatus. Website: https://en.wikipedia.org. Date Retrieved: December 10, 2015