mineral physics module

7/21/2019 Mineral Physics Module

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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



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



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



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



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]:



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.



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].



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



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].



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)



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)



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)



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].



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 ] .



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].



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

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