37
Introduction to high-pressure Introduction to high-pressure science science Przemyslaw Dera Przemyslaw Dera Center for Advanced Radiation Sources Center for Advanced Radiation Sources The University of Chicago The University of Chicago Argonne National Laboratory Argonne National Laboratory Advanced Photon Source Advanced Photon Source NATO Science for Peace and Security Program Advanced Study Institute International School on High Pressure Crystallography Erice, Italy, June 4-14, 2009

Introduction to high-pressure science

  • Upload
    apu

  • View
    46

  • Download
    2

Embed Size (px)

DESCRIPTION

Introduction to high-pressure science. Przemyslaw Dera Center for Advanced Radiation Sources The University of Chicago Argonne National Laboratory Advanced Photon Source. NATO Science for Peace and Security Program Advanced Study Institute - PowerPoint PPT Presentation

Citation preview

Page 1: Introduction to high-pressure science

Introduction to high-pressure scienceIntroduction to high-pressure science

Przemyslaw DeraPrzemyslaw DeraCenter for Advanced Radiation SourcesCenter for Advanced Radiation SourcesThe University of Chicago The University of Chicago Argonne National Laboratory Argonne National Laboratory Advanced Photon SourceAdvanced Photon Source

NATO Science for Peace and Security ProgramAdvanced Study InstituteInternational School on High Pressure CrystallographyErice, Italy, June 4-14, 2009

Page 2: Introduction to high-pressure science

Why High Pressure?Why High Pressure?

Pressure spans in the visible universe over Pressure spans in the visible universe over 60 orders 60 orders of magnitudeof magnitude, from the non-equilibrium pressure of , from the non-equilibrium pressure of hydrogen in intergalactic space, to the kinds of pressure hydrogen in intergalactic space, to the kinds of pressure encountered within neutron stars. encountered within neutron stars.

It provides unique possibility to It provides unique possibility to control structure and control structure and propertiesproperties of materials, dramatically of materials, dramatically alter electronic alter electronic propertiesproperties, , break existing, or form new chemical break existing, or form new chemical bondsbonds, by reaching , by reaching compressions in excess of an compressions in excess of an order of magnitudeorder of magnitude for molecular materials. for molecular materials.

The free energy change associated with this degree of The free energy change associated with this degree of compression can be in the order of compression can be in the order of 10 eV10 eV, exceeding , exceeding the strength of the strongest molecular bonds. the strength of the strongest molecular bonds.

The pressure induced changes in chemical affinities The pressure induced changes in chemical affinities can significantly can significantly alter reactivity of elements and alter reactivity of elements and compoundscompounds, opening door to synthesis of new classes , opening door to synthesis of new classes of materials. of materials.

“Scientists around the world are now racing to harness the power of yet another of nature’s forces - the force of high pressure. (…)They have subjected ordinary sand to tons of pressure to shed light on the extinction of the dinosaurs. (…) They have used high pressure to transform any carbon-rich material, from road tar to peanut butter, into the most prized of gems - diamonds.”

Robert Hazen, 1993“The New Alchemists. Breaking through the barriers of high pressure.”

Page 3: Introduction to high-pressure science

What is pressure?What is pressure?

Pressure (scalar)

P=F/A

F - normal forceA – area on which the force acts

Stress (tensor)

- stress tensor components - strain tensor componentsC – elastic compliances

12

13

23

33

22

11

661111111111

115511111111

111144111111

111111331111

111111112211

161514131211

12

13

23

33

22

11

CCCCCC

CCCCCC

CCCCCC

CCCCCC

CCCCCC

CCCCCC

Page 4: Introduction to high-pressure science

When is pressure high?When is pressure high?

No

n e

qu

ilib

riu

m "

pre

ss

ure

" o

f h

yd

rog

en

ga

s in

inte

rga

lac

tic

s

pa

ce

.

Pre

ss

ure

in in

terp

lan

eta

ry s

pa

ce

Be

st

va

cu

um

ac

hie

ve

d

in la

bo

rato

ry.

Pre

ss

ure

of

str

on

g s

un

ligh

t a

t s

urf

ac

e o

f E

art

h.

Be

st

va

cu

um

att

ain

ab

le w

ith

m

ec

ha

nic

al p

um

p.

Va

po

ur

pre

ss

ure

of

wa

ter

at

trip

le p

oin

t o

f w

ate

r.

Pre

ss

ure

ins

ide

lig

ht

bu

lb

Atm

os

ph

eri

c p

res

su

re a

t s

ea

lev

el

Pe

ak

pre

ss

ure

of

fis

t o

n c

on

cre

ted

uri

ng

ka

rate

str

ike

Pre

ss

ure

at

gre

ate

st

de

pth

s in

o

ce

an

s

Hig

he

st

pre

ss

ure

att

ain

ab

le in

la

bo

rato

ry b

efo

re d

iam

on

d a

nv

il c

ell

Hig

he

st

pre

ss

ure

ac

hie

ve

d

wit

h d

iam

on

d a

nv

il c

ell

Pre

ss

ure

at

ce

ntr

e o

f s

un

Pre

ss

ure

at

ce

ntr

e o

f re

d-g

ian

t s

tar

Pre

ss

ure

at

ce

ntr

e o

f n

eu

tro

n s

tar

-40

-30

-20

-10

0

10

20

30

log

(p)

Range of pressure in the Universe

Pressure scale:

1GPaSample size <0.3mmSample thickness<0.1mmMost proteins denaturate

10 GPaSample size <0.05mmSample thickness<0.05mmAll subtances solidify

100 GPaSample size <0.01mmSample thickness<0.005mmAll “organics” amorphize

364329 136 24 0

1969

1979

1989

Page 5: Introduction to high-pressure science

Multidisciplinary science of high pressureMultidisciplinary science of high pressure

Physics Physics ChemistryChemistry GeophysicsGeophysics Materials science and engineeringMaterials science and engineering BiologyBiology Energy science Energy science

(energy storage, fuels, high energy density materials, explosives, shock physics)(energy storage, fuels, high energy density materials, explosives, shock physics)

Common groundCommon ground PhysicsPhysics

Interatomic interaction potentials Interatomic interaction potentials Thermodynamic driving forces of transformationsThermodynamic driving forces of transformations

ChemistryChemistry Hydrostatic vs. osmoticHydrostatic vs. osmotic Chemical potentialsChemical potentials ReactionsReactions

Page 6: Introduction to high-pressure science

High-pressure phenomenaHigh-pressure phenomena

Structural phase transitionsStructural phase transitions ReconstructiveReconstructive DisplaciveDisplacive Order-disorderOrder-disorder

Electronic transitionsElectronic transitions Metal-insulatorMetal-insulator High-spin low-spinHigh-spin low-spin SuperconductivitySuperconductivity

Magnetic transitionsMagnetic transitions MeltingMelting AmorphisationAmorphisation Chemical transformationsChemical transformations

OsmoticOsmotic Chemical reactionsChemical reactions

Continuous changes in the physical propertiesContinuous changes in the physical properties

Page 7: Introduction to high-pressure science

Touch of historyTouch of history

Page 8: Introduction to high-pressure science

Percy W. Bridgman (1882-1961) Percy W. Bridgman (1882-1961) Harvard UniversityHarvard University

He has carried out extensive investigations on the properties of matter at pressures up to 10 GPa including a study of the volume compressibility, electric and thermal conductivity, tensile strength and viscosity of more than 100 different compounds.

He found it necessary to design his own experimental equipment, including static and dynamic seals for fluids in excess of 3 GPa utilizing his original recognition of the principle of "unsupported area"

The mushroom shaped piece (a) is free to move in the socket piece (e) with variations of pressure. The area of its stem is the unsupported area. The soft packing (c) is squeezed in the annulus between the socket piece (e) and the mushroom head (a) to pressure slightly in excess of the system pressure (P). The triangular shaped cross sectional pieces of bronze (b) move to prevent extrusion of the soft packing. The packing is self-sealing to approximately 3 GPa.

1946 Nobel Prize in Physics forhis work on the physics of high pressure

Bridgman, P. W. 1911. Water, in the liquid and five solid forms, under pressure. Proc. Am. Acad. Arts Sci. 47:441-558. McMillan (2005) Nature Materials, 4, 715

Page 9: Introduction to high-pressure science

Charles Weir, Alvin van Valkenburg, Gasper J. Piermarini National Bureau of Standards (now NIST)

1959 Opposed anvil geometry DAC1964 metal foil gasketing techniquePioneered single-crystal XRDPioneered high pressure studies of molecular materials

Crystal of benzene grown from liquid Piermarini (2001) J. Res. NIST, 106, 889

Page 10: Introduction to high-pressure science

In 1928 Bernal predicted that all matter should ultimately become metallic at sufficient pressure, as the forced overlap of electron orbitals induces electron delocalization.

High-pressure transformations from insulator to metal were first observed in iodine, silicon, germanium, and other elements by Drickamer et al.

In 1936 came up with hypothesis that a phase transition in olivine might be the cause of discontinuities in the observed in the earthquake travel times.

Worked on the description of the structure of liquid water.

John D. Bernal (1901-1971), Cambridge University

Page 11: Introduction to high-pressure science

A. Francis Birch (1903-1992) Harvard University

In 1952 he published a well-known paper where he demonstrated that the Earth mantle is mainly composed of silicate minerals, the upper and lower mantle are separated by a thin transition zone associated with silicate phase transitions, and the inner and outer core are alloys of crystalline and molten iron.

"Unwary readers should take warning that ordinary language undergoes modification to a high-pressure form when applied to the interior of the Earth. A few examples of equivalents follow:"

In 1947, he adapted the isothermal Murnaghan equation of state, which had been developed for infinitesimal strain, for Eulerian finite strain, developing what is now known as the Birch-Murnaghan equation of state.

In 1961, Birch published two papers on compressional wave velocities establishing a linear relation (now called Birch's law) of the compressional wave velocity Vp of rocks and minerals of a constant average atomic weight with density ρ.

High Pressure Form Ordinary MeaningCertain DubiousUndoubtedly PerhapsPositive proof Vague suggestionUnanswerable argument Trivial objectionPure iron Uncertain mixture of all the elements

Page 12: Introduction to high-pressure science

William A. Bassett Cornel University

First deterimination of high-pressure phase of ironFirst observation of phase transition from spinel to lower mantle phasesCo-inventor of the laser-heating method and spectroscopic temperature measurementDesign of the Merrill-Bassett DAC

Page 13: Introduction to high-pressure science

Larry W. Finger and Robert M. Hazen, Carnegie Institution

• Automated and optimized single-crystal XRD experiments in DAC

• Determined compression mechanisms of ~100 minerals up to pressure reachable in Merrill-Bassett DAC.

• Formulated foundations of the comparative crystal chemistry in p-T-X space.

Page 14: Introduction to high-pressure science

Strategies for success in high-pressure scienceStrategies for success in high-pressure science

High pressure research is to a large extent an exploratory experimental discipline, in High pressure research is to a large extent an exploratory experimental discipline, in which many extraordinary discoveries come by surprise. A which many extraordinary discoveries come by surprise. A wise strategy for the wise strategy for the explorationexploration is usually the key to success. is usually the key to success.

Mastering a single technique and improvement/optimization of it to the “state of the Mastering a single technique and improvement/optimization of it to the “state of the art” level provides a high-pressure researcher with a unique vehicle for this art” level provides a high-pressure researcher with a unique vehicle for this exploration. exploration.

Seek additional information from complementary methods once an interesting Seek additional information from complementary methods once an interesting phenomenon has been identified. phenomenon has been identified.

Page 15: Introduction to high-pressure science

Major experimental and theoretical methodsMajor experimental and theoretical methods

X-ray and neutron diffractionX-ray and neutron diffraction

X-ray absorption spectroscopy

Raman and IR spectroscopy

Optical absorption spectroscopy

X-ray emission spectroscopy

X-ray Raman spectroscopy

Conventional and synchrotron Mossbauer spectroscopy

Inelastic scattering

Brillouin spectroscopy and ultrasonic measurements

Magnetic susceptibility measurements

Electrical conductivity measurements

Page 16: Introduction to high-pressure science

Mineral PhysicsMineral Physics Properties of earth-forming minerals at geo-Properties of earth-forming minerals at geo-relevant conditionsrelevant conditions Phase transitions in earth forming mineralsPhase transitions in earth forming minerals Melting relationsMelting relations Element partitioningElement partitioning Shock metamorphismShock metamorphism RheologyRheology

Page 17: Introduction to high-pressure science

Murakami et al. (2004) Science, 304, 855Oganov and Ono (2004) Nature 430, 445

Wentzcovitch et al. (2006) PNAS, 103, 543

Post-perovskite story• MgSiO3 perovskite is thought to be one of the principal mineral phases present in the upper part of Earth lower mantle.• For many ears it was assumed that pv either remains stable in its original structure or decomposes into oxides as p and T progress along the geotherm.• Resent studies demonstrate that most of perovskite structures transform into ppv at high pT conditions.• ppv exhibits physical properties markedly different from pv.

Page 18: Introduction to high-pressure science

Extraterrestrial minerals and shock metamorphismExtraterrestrial minerals and shock metamorphism

Post-stishovite polymorph of silica

Sharp et al. (1999) Sciecne, 284, 1511Dubrovinskaya et al. (2001) Eur. J. Mineral. 13, 479Dera et al (2003) Am. Mineral., 87, 1018El Gorezy (2008) Eur. J. Mineral. 20, 523

Barringer crater, AZ

Meteorite name Shergotty Location Found Shergotty, India Date Found August 25, 1865Mass (g) ~5,000Type Shergottite (SNC)Radiometric age (x109 years) 0.16±0.01

Page 19: Introduction to high-pressure science

Materials science and Materials science and engineeringengineering

New technological materials synthesis New technological materials synthesis Tuning materials propertiesTuning materials properties Stress/strain relationsStress/strain relations Materials stability limitsMaterials stability limits

Page 20: Introduction to high-pressure science

Tuning materials properties: Ferroelectric PbTiO3 and pressure-induced morphotropic transition

Ahart (2008) Nature, 451, 545

• Piezoelectric materials exhibit a morphotropic phase boundary associated with symmetry lowering and maximization of electromechanical properties.• Morphotropic transitions are usually triggered by change in composition.• In PbTiO3 morthotropic transition was demonstrated to occur as a function of pressure at low temperature.

Page 21: Introduction to high-pressure science

High p-T synthesis of platinum nitrideGregoryanz et al. (2004) Nature Matrials, 3, 294

High p-T synthesis of indium nitrideCrowhurst et al. (2006) Science, 311, 1275

Synthesis of noble metal nitrides from elements

Page 22: Introduction to high-pressure science

ChemistryChemistry

Solid-state reactionsSolid-state reactions Changes of chemical potentialsChanges of chemical potentials Osmotic reactionsOsmotic reactions High-pressure polymerizationHigh-pressure polymerization

Page 23: Introduction to high-pressure science

Bonding changes in high-pressure phase of oxygen

• Oxygen is the only diatomic molecule that has a magnetic moment.• Solid oxygen becomes metallic at pressure close to 100 GPa.• Epsilon or “red” oxygen was discovered by Nicol et al. (1979), Chem. Phys. Lett. 68, 49• Space group and tentative model were proposed by Johnson et al. 1993, J. Appl. Cryst. 26, 320• Correct model of the crystal structure of epsilon oxygen exhibiting occurrence of (O2)4 molecular units was determined by Lundegaard et al. (2006) Nature, 443, 201

Page 24: Introduction to high-pressure science

Co2

Infrared spectra show formation of single bondsAmorphous phase of CO2 (carbonia)Santoro et al. (2006) Nature, 441, 857

Bonding changes in CO2

Page 25: Introduction to high-pressure science

PhysicsPhysics

Structural phase transitionsStructural phase transitions Electronic and magnetic transitionsElectronic and magnetic transitions Response to pressure in continuous Response to pressure in continuous compression regime compression regime

Page 26: Introduction to high-pressure science

Mott-Hubbard transition in FeMott-Hubbard transition in Fe22OO33

p [GPa]

0 20 40 60 80

V [

A3]

200

220

240

260

280

300

320

Rozenberg et al. 2002 (Ar)Liu et al. 2002 (Ar)Staun Olsen 1991 EOS (alc.)This paperBirch_Murnaghan EOS fit

X Data

0 10 20 30 40 50 60

Y D

ata

2.62

2.64

2.66

2.68

2.70

2.72

2.74

Badro et al. (2002) PRL 89, 205504

Pasternak et al. (1999) PRL 82, 4663

Page 27: Introduction to high-pressure science

Corundum structure Rh2O3-II structure

Page 28: Introduction to high-pressure science

H-bond symmetrization in iceH-bond symmetrization in ice

Hydrogen bond symmetrization in phase DTsuchiya et al. (2005) Am. Mineral. 90, 44-49

Hydrogen bond symmetrization in H2O iceGoncharov et al. (1996) Science, 273, 218-220

Page 29: Introduction to high-pressure science

BiologyBiology Thermodynamic limits of life and habitability Possible role of high pressure environments in the origins of life on Earth Response (stress and adaptation) of organisms and biomolecules to high pressure Understanding extremophiles The “mechanics” of enzyme molecules

Page 30: Introduction to high-pressure science

High pressure crystallography and biology

Extremely barophilic bacteria isolated from the Mariana Trench, Chal lenger Deep, at a Depth of 11,000 Meters Kato et al. (1998) Appl. Envir. Microbiol., 64, 1510

Daniel et al. (2006) Chem. Soc. Rev., 35, 858

Page 31: Introduction to high-pressure science

Food preparation technologyFood preparation technology

Wort, as well as end-processing beer from barley can be pressurized and different parameters related to the beer quality were measured to assess the influence of High Pressure Treatment (HPT). Bitterness, iso-a-acids, and total a-acids were reduced in wort after applying high pressures. Foam, haze and chill haze, and saturated ammonium sulphate precipitation limit were increased in beer with high pressures. There is a chance for the industrial application of HPT to reduce wort bitterness. The foaming characteristics and the colloidal stability of beer can also be enhanced with this treatment [Perez-Lamela et al. (2004) Deutsche Lebensmittel-Rundschau, 100, 53 ].

• High pressure (HP) treatment causes unique effects on proteins and other food components that could be advantageously used in the dairy industry. Although commercial application of HP technology is currently limited to the processing of guacamole, oysters, juices and fruit jams and jellies, this technology offers potential to be applied in cheese manufacture. • Pressurization of milk causes conformational changes of milk proteins. On the one hand, HP treatment decreases the size and increases the number of naturally occurring casein micelles, thus, depending on treatment temperature. Denaturation occurs reversibly at pressure treatments below 200MPa, however, at higher pressures irreversible denaturation increases with increasing pressure. • HP treatment technology offers the advantage of shortening ripening times in cheese making [San Martin-Gonzalez et al., 2004, IFT Annual Meeting, Las Vegas ].

Hendrick and Knorr Eds. (2002) “Ultra High Pressure Treatment of Food Engineering” Kluwer Academic/Plenum Publishers

Page 32: Introduction to high-pressure science

Medical applicationsMedical applications

Hyperbaric oxygen therapyHyperbaric oxygen therapyTypical pressure used is 1.5 barTypical pressure used is 1.5 bar

Several therapeutic principles are uses in HBOT:Several therapeutic principles are uses in HBOT: The increased overall pressure is of therapeutic value when The increased overall pressure is of therapeutic value when HBOT is used in the treatment of decompression sickness and air HBOT is used in the treatment of decompression sickness and air embolism. embolism. For many other conditions HBOT drastically increases partial For many other conditions HBOT drastically increases partial pressure of oxygen in the tissues of the body. A related effect is pressure of oxygen in the tissues of the body. A related effect is the increased oxygen transport capacity of the blood plasma. the increased oxygen transport capacity of the blood plasma.

High-pressure Neurological Syndrome High-pressure neurological syndrome (HPNS) is a condition encountered in diving beyond a depth of 100 m. Manifestations include headache, tremor, myoclonus, neuropsychiatric disturbances and EEG changes. Convulsions are seen only in experimental animals. Most of the changes are reversible on surfacing but some such as memory disturbances may linger on for long periods

Gill and Bell “Hyperbaric oxygen: its uses, mechanisms of action and outcomes” (2004) QJM. 97, 385

Talpalar “High pressure neurological syndrome” (2007) Rev. Neurol. 45, 631

Page 33: Introduction to high-pressure science

Role of crystallography in high pressure scienceRole of crystallography in high pressure science

Modern crystallography is defined much broader than just diffraction experiments, it Modern crystallography is defined much broader than just diffraction experiments, it includes many scattering and spectroscopy techniques, as well as theoretical includes many scattering and spectroscopy techniques, as well as theoretical modeling approaches. modeling approaches.

Crystallographic techniques are used not only to study the structure of crystalline Crystallographic techniques are used not only to study the structure of crystalline solids, but apply also to amorphous substances, liquids, thin films, etc.solids, but apply also to amorphous substances, liquids, thin films, etc.

Crystallographic experiments and simulations provide the link between the micro-Crystallographic experiments and simulations provide the link between the micro-world of atoms and interatomic interaction and macro-world of physical properties and world of atoms and interatomic interaction and macro-world of physical properties and chemical transformations.chemical transformations.

W/o crystallographic characterization (atomistic model) most high-pressure W/o crystallographic characterization (atomistic model) most high-pressure phenomena can only be understood at a descriptive level.phenomena can only be understood at a descriptive level.

Page 34: Introduction to high-pressure science

Central facilities for high-pressure researchCentral facilities for high-pressure research

USAUSA Argonne National Laboratory, APS (Chicago, IL)Argonne National Laboratory, APS (Chicago, IL) Brookhaven National Laboratory, NSLS (Brookhaven, NY)Brookhaven National Laboratory, NSLS (Brookhaven, NY) Lawrence Berkley National Laboratory, ALS (Berkley, CA)Lawrence Berkley National Laboratory, ALS (Berkley, CA) CHESS (Ithaca, NY)CHESS (Ithaca, NY) Oak Ridge National Laboratory, SNS (Oak Ridge, TN)Oak Ridge National Laboratory, SNS (Oak Ridge, TN)

UKUK DiamondDiamond DaresburyDaresbury ISISISIS

JapanJapan SPRING-8 SPRING-8 Photon FactoryPhoton Factory

GermanyGermany DESY/HASYLAB (Hamburg)DESY/HASYLAB (Hamburg)

FranceFrance ESRF (Grenoble)ESRF (Grenoble) ILL (Grenoble)ILL (Grenoble) Soleil (Paris)Soleil (Paris)

RussiaRussia DubnaDubna

Page 35: Introduction to high-pressure science

High-pressure community organizationsHigh-pressure community organizations

European High Pressure Research Group (EHPRG) European High Pressure Research Group (EHPRG)

www.ehprg.orgwww.ehprg.org Established in 1963Established in 1963 EHPRG awardEHPRG award Organizes annual meeting, often combined with AIRAPTOrganizes annual meeting, often combined with AIRAPT

International Association for the Advancement of High Pressure Science and Technology International Association for the Advancement of High Pressure Science and Technology (AIRAPT)(AIRAPT)

www.ct.infn.it/airaptwww.ct.infn.it/airapt// Established in 1965, grew out of the Community of Gordon Research Conferences on Research at High Established in 1965, grew out of the Community of Gordon Research Conferences on Research at High

pressurepressure organizes biennal conferences often combined with EHPRGorganizes biennal conferences often combined with EHPRG Awards Bridgman AwardAwards Bridgman Award

International Union of Crystallography Commission on High-PressureInternational Union of Crystallography Commission on High-Pressure www.iucr.org/iucr/commissions/chp.htmlwww.iucr.org/iucr/commissions/chp.html

Established in 1987Established in 1987 Organizes annual workshops and high-pressure focus sessions at International Crystallographic CongressOrganizes annual workshops and high-pressure focus sessions at International Crystallographic Congress

Consortium for Materials Research in Earth Sciences (COMPRES) Consortium for Materials Research in Earth Sciences (COMPRES)

www.compres.uswww.compres.us Established in 2001 by a grant from National Science Foundation Established in 2001 by a grant from National Science Foundation Coordinates and maintains high-pressure synchrotron beamlines in USACoordinates and maintains high-pressure synchrotron beamlines in USA Organizes annual meetingOrganizes annual meeting

Page 36: Introduction to high-pressure science

Future Future

from first explorers to colonizationfrom first explorers to colonization

High pressure science receives increasing recognition and interest from High pressure science receives increasing recognition and interest from funding agencies and management of central facilities.funding agencies and management of central facilities.

Excellent advanced experimental tools and methods are now available for Excellent advanced experimental tools and methods are now available for the general community at central facilities.the general community at central facilities.

Extending the limits of experimental techniques (pressure, temperature, Extending the limits of experimental techniques (pressure, temperature, magnetic field).magnetic field).

Extending high-pressure crystallographic techniques to time-resolved Extending high-pressure crystallographic techniques to time-resolved domain.domain.

Extending the subjects of investigation to more complex materials.Extending the subjects of investigation to more complex materials. Increasing real technological applications of high-pressure discoveries.Increasing real technological applications of high-pressure discoveries.

Page 37: Introduction to high-pressure science

AcknowledgementsAcknowledgements

Very special thanks to Lodovico Riva Di San Severino, Paola Spadon, John Irvin and Elena Pappinutto

and all the lecturersThey made this school possible!!!