Global Focus on Knowledge 2005 Global Focus on Knowledge 2005 Science of MatterScience of Matter

Science of Materials Science of Materials －－Origin and ApplicationOrigin and Application－－

Lecture 6~9Lecture 6~9

Characteristics of Matter

November 21, 2005Global Focus on Knowledge 2005 Science of Matter

The University of Tokyo, The University of Tokyo, The Institute For Solid The Institute For Solid

State PhysicsState PhysicsYasuhiro IyeYasuhiro Iye

The figures, photos and moving images with ‡ marks attached belong to their copyright holders. Reusing or reproducing them is prohibited unless permission is obtained directly from such copyright holders.

Lecture OutlookLecture OutlookLecture 1Lecture 1 Dr. Masatoshi Dr. Masatoshi KoshibaKoshiba ““The Creation of MatterThe Creation of Matter””Lecture 2Lecture 2--55 Dr. Katsuhiko SatoDr. Katsuhiko Sato

““The Birth of MatterThe Birth of Matter-- Elementary Particles, Atoms, and the Elementary Particles, Atoms, and the UniverseUniverse””

Lecture 6Lecture 6--99 Dr. Iye Yasuhiro Dr. Iye Yasuhiro ““Characteristics of MatterCharacteristics of Matter””Lecture 6Lecture 6 What is SolidWhat is Solid--state Physics?state Physics?Lecture 7 Lecture 7 Quantum Mechanics and Artificial MaterialsQuantum Mechanics and Artificial Materials-- HighHigh--tech tech

and the Stateand the State--ofof--thethe-- art Physicsart PhysicsLecture 8Lecture 8 Atom Control and Quantum ControlAtom Control and Quantum Control

---- NanoNano--science and Quantum Information science and Quantum Information

Lecture 9Lecture 9 Diverse Matter and Physical Properties Diverse Matter and Physical Properties

Lecture 10Lecture 10--1313 Dr. Hiroshi Komiyama Dr. Hiroshi Komiyama ““ The Production and Application of The Production and Application of MatterMatter””

Lecture 6 What is Condensed Matter Physics? Lecture 7 Quantum Mechanics and Artificial Materials

-- High-tech and the State-of-the-art PhysicsLecture 8 Atom Control and Quantum Control

--Nano-science and Quantum Information Lecture 9 Diverse Matter and Physical Properties

November 21, 2005University Lecture

Science of Matter

The University of Tokyo, The University of Tokyo, The Institute For Solid The Institute For Solid

State PhysicsState PhysicsYasuhiro IyeYasuhiro Iye

TodayToday’’s Topicss Topics- Stories about size and extent- Modern civilization and physics- Condensed matter physics is the field of physics,- Quantum mechanics and atomic structure- Existing forms of matter- Agglutination mechanism and crystal structure of atoms.

・・・・・・・・・・

１2800kｍ

１ ｍ １０3 ｍ １０6 ｍ １０18ｍ１０12ｍ １０24ｍ

Macroscopic ScaleMacroscopic Scale

１ｋｍ １０００ ｋｍ 1 cosmological unit1 light year

End of U

niverse

‡

出典：http://www.solarviews.com/eng/homepage.htm

Microscopic Scale

１ ｍ１０-3 ｍ１０-9 ｍ１０-12 ｍ １０-6 ｍ

１ ｐｍ

Picometer１ ｎｍ

Nanometer１ μｍ

Micrometer(Micron)

１ ｍｍ

MillimeterNeedle hole and hum

an hair

Wavelength of visible light

Size of atomic nucleus

Size of atom

Virus

O-157

Bacteria

Planck scale１０-35ｍ １０-32ｍ １０-21ｍ １０-18ｍ

The grand unified scale

Electroweak unification scale

‡

Modern Civilization and Modern Civilization and PhysicsPhysics

Personal computer

ComputerComputer

Behavior of electrons in semiconductors:

Condensed matter physics is based on

quantum mechanics.

Memory Storage Memory Storage Magnetic hard disk

Recording digital information as magnetizing directions of magnetic substances.

Semiconductor memoryFlash memoryFerroelectric memory

CD-ROM/DVD

Using laser reflection differences against irregularities on the recording surface.

Radio (High Frequency) and Radio (High Frequency) and Optical CommunicationOptical Communication

Mobile phone

Satellite communicationSatellite broadcasting

Optical fiber

High mobility transistorHEMT Luminescent diode

Semiconductor laser

Internet

Next generation CS

CS prototype(Skyperfect TV)

Common receptor

Broadcast station

East longitude

Two-way service

•Online shopping•Music and image download•Home banking

GPSGPS（（Global Positioning System) Global Positioning System) NavigationNavigation

In order to achieve satisfactory functioning of GPS, correction for general and special relativity is required.

24 stationary satellites have been launched.

These satellites trace the location of the target by triangulation.

Accurate timing is essential. An atomic clock is deployed in satellites.

CERN

Figure removed due to copyright restrictions

In Elementary Particle and In Elementary Particle and Cosmology Research Cosmology Research

Subaru telescopeCCD cameras

Super KamiokandePhotomultiplier tubes

In StateIn State--ofof--thethe--art Medical Serviceart Medical ServiceMRI (Magnetic Resonance Imaging)

MEG (magnetoencephalogram) andSQUID (superconducting quantum interference device) detect weak magnetic signals.

CERN

Figure removed due to copyright restrictions

In Everyday LifeIn Everyday Life

Liquid crystals, e.g., displays.Liquid crystals, e.g., displays.High strength fibers, e.g., for tennis rackets.High strength fibers, e.g., for tennis rackets.Gels, e.g., paper diapers.Gels, e.g., paper diapers.Fuel cellsFuel cellsSolar power generationSolar power generationPhotoPhoto--catalystscatalysts・・・・・・・・・・

Condensed Matter Physics is Condensed Matter Physics is the Field of Physicsthe Field of Physics

Matter and MaterialsMatter and Materials

Matter: A substance that occupies space-time.Material: The substance of which something is

composed.

Solid State PhysicsCondensed Matter Physics

Materials Science Materials Engineering

The Notion of Condensed Matter The Notion of Condensed Matter PhysicsPhysics

It is intellectual curiosity that drives us to want to learn It is intellectual curiosity that drives us to want to learn more about the properties of matter and their more about the properties of matter and their correlation with the foundation of physics. correlation with the foundation of physics. ⇒⇒ The viewpoint of matter is organized. The viewpoint of matter is organized.

We further understand and utilize matter to cultivate and We further understand and utilize matter to cultivate and control useful functions.control useful functions.⇒⇒ Applied physicsApplied physics

CuriosityCuriosity--Driven ResearchDriven ResearchMissionMission--Oriented ResearchOriented Research

The Notion of Condensed Matter The Notion of Condensed Matter PhysicsPhysics

It is a game of catch of the concepts between condensed It is a game of catch of the concepts between condensed matter physics and elementary particle and nuclear matter physics and elementary particle and nuclear physics. physics.

Phase transition: Spontaneous symmetry breaking.Phase transition: Spontaneous symmetry breaking.NambuNambu--Goldstone modeGoldstone mode

Asymptotic freedom,Asymptotic freedom,topological excitation, and quantum phase.topological excitation, and quantum phase.・・・・・・・・・・・・・・・・・・

The Hierarchical Structure of the The Hierarchical Structure of the Physical WorldPhysical World

Macroscopic scaleMicroscopic scale1 mm

1020 atoms

0.3 ｎm

Solid crystal

Atomic arrangement

Atom(atomic nucleus

and electron)

Large scale energy Small scale energy

Condensed Matter PhysicsCondensed Matter PhysicsThe field of study that deals with the diverse physical The field of study that deals with the diverse physical properties of matter based on the understanding of physical properties of matter based on the understanding of physical principles. principles. CharacteristicsCharacteristics

ExperimentalExperimental ((⇔⇔Astrophysics and planetary geophysics)Astrophysics and planetary geophysics)Small scienceSmall science ((⇔⇔Big science)Big science)Chemistry, applied physics, Chemistry, applied physics, …… , and life science?, and life science?

Confirmation Confirmation Comparison between experiments and theoryComparison between experiments and theoryHypothesis and demonstration, i.e., a game of catch. Hypothesis and demonstration, i.e., a game of catch.

Useful propertiesUseful properties ⇒⇒ applicationapplicationConstruction of matter viewpoint. Construction of matter viewpoint.

The World View of PhysicsThe World View of Physics

ReductionismThe behaviors of a system that belong to a particular hierarchy can be explained by more-simply-reduced hierarchy of principles.

The fundamental constituent of all force ⇒ The ultimate theory

Emergent propertiesInteraction of many-body systems: phase transition.

E.g., superconductivity and the life process.More is different.

(P.W.Anderson)

What Condensed Matter Physics Is What Condensed Matter Physics Is Concerned WithConcerned With

Solid bodies (monocrystals and polycrystals).Disturbed crystals (impure and defective types).Amorphous, glass, liquids, and quasi-crystals.Fine particles and cluster.Surface and interface.Artificial crystals (superlattice) and nano-structures.Soft matter (polymers, liquid crystals, and gels).Atomic gases (Bose condensate)

Properties of MatterProperties of MatterStructural propertiesStructural properties (Crystal structure and the (Crystal structure and the disturbance)disturbance)

Solid, liquid, and glass.Solid, liquid, and glass.Mechanical propertiesMechanical properties (Compressibility, elasticity (Compressibility, elasticity modulus, and plasticity)modulus, and plasticity)

Diamonds and iron and steel are hard while gold is soft. Glass Diamonds and iron and steel are hard while gold is soft. Glass is hard but brittle.is hard but brittle.

Thermal propertiesThermal properties (Melting point, boiling point, (Melting point, boiling point, specific heat, and thermal conductivity)specific heat, and thermal conductivity)

Copper has high thermal conductivity while stainless steel has Copper has high thermal conductivity while stainless steel has low thermal conductivity.low thermal conductivity.

Properties of MatterProperties of MatterElectrical properties Electrical properties (Electric conductivity, dielectric (Electric conductivity, dielectric constant, and superconductivity)constant, and superconductivity)

Metal, insulators, and semiconductorsMetal, insulators, and semiconductorsFerroelectricsFerroelectricsSuperconductorsSuperconductors

Magnetic propertiesMagnetic properties (Susceptibility and magnetization)(Susceptibility and magnetization)Ferromagnetic body: How does iron become magnetized?Ferromagnetic body: How does iron become magnetized?

Optical propertiesOptical properties (Optical spectrum, transmittance, and (Optical spectrum, transmittance, and reflectivity)reflectivity)

The color of gemstones and metallic lusterThe color of gemstones and metallic lusterLuminescence (lightLuminescence (light--emitting diodes and semiconductor lasersemitting diodes and semiconductor lasers

Matter and the Physical Environment Matter and the Physical Environment

The environment, outer field, and The environment, outer field, and perturbation where matter is placed.perturbation where matter is placed.

TemperatureTemperaturePressure and stressPressure and stressElectric fieldElectric fieldMagnetic fieldMagnetic fieldInteraction with light (electromagnetic Interaction with light (electromagnetic waves)waves)Sample sizesSample sizes

Quantum Mechanics and Quantum Mechanics and Atomic StructureAtomic Structure

Major Players in Condensed Matter PhysicsMajor Players in Condensed Matter PhysicsThe players The players ((““ElementaryElementary”” particles)particles)

ElectronsElectronsAtomic Nucleus (protons + neutrons)Atomic Nucleus (protons + neutrons)

Atoms and moleculesAtoms and moleculesIonIon

The forces that act among The forces that act among ““elementaryelementary”” particles: particles: electromagnetic interaction.electromagnetic interaction.

Light (electromagnetic wave) Light (electromagnetic wave) photon.photon.

kg 1091.0C 1060.1

30

19

−

−

×=

×=

eme

enp mmm 1840≈≈

sJ1062.6 34 ⋅×= −hνh

Energy ScaleEnergy Scale22 smkgJ =Energy unit: Joules

nm1240cm8070

Hz 1042.2eV1

1

14

=↔=↔

×=↔=

λννν

-

c

h

The oscillation frequency, wave number, wavelength of the photon with energy １eV.

J106.1 eV1C106.1

19

19

−

−

×=

×=eElectron volts

seV 1013.4sJ1062.6

15

34

⋅×=

⋅×=−

−hPlanck constant is

2

21 mv

Kinetic energy

Quantum MechanicsQuantum Mechanics

sJ1005.12

34 ⋅×== −

πh

h2

2

2

2

2

22

22

),,(),,()(2

zyx

zyxEzyxrVm

∂∂

+∂∂

+∂∂

≡∇

=⎟⎟⎠

⎞⎜⎜⎝

⎛+∇− ψψh

Schroedinger’s equation

),,( zyxψWave function

EEnergy level

2),,( zyxψ

Probability distribution of particles

Hydrogen AtomsHydrogen Atoms

)()(42 0

22

2

rErr

em

ψψπε

=⎥⎦

⎤⎢⎣

⎡−∇−

h

Proton+e

Electron-e

Bohr radius

nm053.042

20

0 ==me

a hπε

Rydberg constant

eV 6.1324

12

42

0

=⎟⎟⎠

⎞⎜⎜⎝

⎛=

h

meRyπε

Coulomb potential

n=1

n=2n=3

ｒ0

E

rerV

0

2

4)(

πε−=

Ry

02anr

n=

Bound state: discrete energy level

Ryn

En 2

1−=

Spectrum of Hydrogen AtomsSpectrum of Hydrogen Atoms

hν ⎟⎠⎞

⎜⎝⎛ −=

−=

22

11nm

Ry

EEh mnν

2nRyEn −=

Hz 1055.4 14×=νnm 659=λ

eV 89.1365

31

21

22

==

⎟⎠⎞

⎜⎝⎛ −=−

Ry

RyEE mn

Balmer series(m=2)

0

2

14

4

12

s dp fE (eV)

1s

2s 2p

3s 3p 3d4f4d4p4s

Energy Level of Hydrogen AtomsEnergy Level of Hydrogen Atoms

2

2

2

2

2

22

22

),,(),,()(2

zyx

zyxzyxrVm

∂∂

+∂∂

+∂∂

≡∇

=⎟⎟⎠

⎞⎜⎜⎝

⎛+∇− ψεψh

),()(),,( φθφθψ YrRr =

2

2

2222

22

sin1sin

sin11

φθθθ

θθ ∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

≡∇rrr

rrr

Spherically symmetry potential

m=-2

m=0

m=1

m=-1

m=2

m=-3

m=3

)exp()(cos),( φθφθ imPY ml

ml ∝

Angular momentum quantum number

)12(,1,,,2,1,0

+−−==

llllml

L

L

Principle quantum number L,1, += lln

σ,,, mlnSpin quantum number 1±=σ

Angles in the Atomic Angles in the Atomic WavefunctionWavefunction)exp()(cos),( φθφθ imPY m

lm

l ∝

s px py pz

dyz dzx dxy dx2-y2 d3z2-r2

Electron Energy Level of Atoms

Many-electron atoms: Atomic nuclei that possess electric charges +Ze and Z electrons.Electrons received at the energy level are assigned by the fermions ⇒ （n, l, m,σ）

Atomic nucleus

+Ze-e

-e -e

-e

1622 )3()2()2()1(:Na spss

Na： Z=11

H

Li

Na

K

Rb

Cs

Fr

Sc

Y

La

Ac

Be

Mg

Ca

Sr

Ba

Ra

Ti

Zr

Hf

V

Nb

Ta

Cr

Mo

W

Mn

Tc

Re

Fe

Ru

Os

Co

Rh

Ir

Ni

Pd

Pr

Cu

Ag

Au

Zn

Cd

Hg

B

Al

Ga

In

Tl

C

Si

Ge

Sn

Pb

N

P

As

Sb

Bi

O

S

Se

Te

Po

F

Cl

Br

I

At

Ne

Ar

Kr

Xe

Rn

He

Ce NdPr Pm Sm Eu Gd Tb Dy Ho Er

Th UPa Np Pu Am Cm Bk Cf Es Fm

Tm

Md

Yb

No

Lu

Lw

Ru Ha

1s

4d

4f

2s

3s

4s

2p

3p

4p3d

5s5p

6s6p 5d

7s

Method of Filling the Electron Energy LevelMethod of Filling the Electron Energy Level

H HeLi Be B C N O F Ne

MgNa Al Si P S Cl ArK Ca Sc Ti V Cr M

nFe Co Ni Cu ZnGa Ge Se Br KrAs

Rb

Many-electron atoms

Electron Energy Level in Atoms

The shell structure assigned by the value of n

n=1 2×1 = 2 n=2 2×(1+3) = 8n=3 2×(1+3+5) =18

The number of atoms with completely occupied shells 2, 10, 18, 36･･･are energy stable.

Each electron is received at the energy level that are assigned by the fermions ⇒ （n, l, m,σ）

Noble gas (inert gas) atom:He, Ne, Ar，Kr，and Xe.

Electron Energy Level in Atoms

Electrons in the outermost shell are the most Electrons in the outermost shell are the most important in affecting the physical properties of important in affecting the physical properties of matter because the electrons can be dropped into matter because the electrons can be dropped into lower orbits. lower orbits. ⇒⇒ Valence electronsValence electrons

The atoms that have similar electron configuration in The atoms that have similar electron configuration in the outermost shells represent similar chemical the outermost shells represent similar chemical properties.properties.⇒⇒ Periodic table of the elementsPeriodic table of the elements

Periodic Table of the ElementsPeriodic Table of the ElementsPeriodic Table of the Elements

Nonmetals

Noble gasesTransition metals

Alkali metals and other metals

Metalloids

Although, there is greater Although, there is greater coulombiccoulombic attraction involved with the attraction involved with the atoms of greater atoms of greater Z, Z, there will also be a greater number of electrons there will also be a greater number of electrons around the atoms thus, the electron energy of the outermost shelaround the atoms thus, the electron energy of the outermost shell will l will be obtained as approximately a few be obtained as approximately a few eVeV energy level.energy level.

Electron Energy Level in Atoms

The energy scale of condensed matter physics is between a few eV and meV.

Dry battery is 1.5V.Electromotive force due to the exchange of atoms.

Rhodopsin: the light receptor protein in the retina. Has an energy level equivalent to that of visible light.

Laser pointer Two dry batteries ３VRed light ～1.5eV，Green light ～2.5eV

Existing Forms of MatterExisting Forms of Matter

Types of MatterTypes of MatterThere are roughly 100 types of single-elements.(Carbon, for example, has many different existing forms.)

Seven Types of CarbonSeven Types of Carbon

Graphite

C70

Carbon nanotubes

Carbon peapod

C60 fullerene

Carbon atoms can form a variety of materials.

Diamond

Amorphous carbon

Types of MatterTypes of MatterThere are roughly 100 types of single-elements.(Carbon, for example, has many different existing forms.)

There are variety of the combinations when compound such as NaCl and the alloy such as Pb1-xSnx are considered.

When three-dimension compounds and four-dimension compounds, and more,… are further considered, then there would be an infinite possibility for various types of matter⇒ search and development of matter and materials.

We hope to design and create the particular matter that we want ⇒Material design (computational material science)

Existing Forms of Matter Existing Forms of Matter

Vapor

Liquid

Solid

Temperature

Plasma

Energy versus entropy

Ordered state

Disordered state

Phase transition

Lowest possible energy

Greatest possible freedom

Interacting many-particle system

Phase TransitionPhase Transition

0=TAbsolute zero point：ferromagnetic phase.

Ordered state

cTT >

High temperature：paramagnetic phase.

Disordered state

Spin： magnetic momentum(micro-magnet)

The spins will try to be parallel or antiparallel.

Under high temperatures, the spins tend to

direction randomly.

Energy and EntropyEnergy and EntropyThe lowest energy state (ground state) can be obtained under the absolute zero point.

Under a finite temperature（T > 0）, the condition of the state is determined by the balance between energy E and entropy S .

TSEF −=Free energy (F = E-TS) is the lowest state.

The crystal state where atoms are orderly aligned.The magnetic ordering state where a moment is lined in order.

The phase transition from the ordered state to the disordered state occurs at a particular temperature (critical temperature).

Solid ⇔ Liquid(Anti)Ferromagnetic phase ⇔ Paramagnetic phase

Thermal EnergyThermal EnergyJ/K1038.1 23

B−×=k

Boltzmann constant

K 11600eV1B =↔= TTk

meV25K 300 B =↔= TkT

Temperature T

Room temperature

Thermal energy TkB

The Agglutination Mechanism and The Agglutination Mechanism and the Crystal Structure of Atomsthe Crystal Structure of Atoms

Crystal StructureCrystal StructureWhat types of atomic arrangement would have the lowest energy?

What happens when a box is occupied with many rigid spheres?Packing problem

Close-packed structureFilling factor 74%

Face-centered cubic lattice(fcc)

Hexagonal close-packed lattice(hcp)

How Do We Study the Periodic How Do We Study the Periodic Order of Atoms?Order of Atoms?

Diffraction

Electron beam and neutron beam diffractions are used.

q

Interatomic space～0.3 nm ⇔ ～X-ray wavelengthλθ nd =sin

Optical path differenceIn phase

Antiphase

Diffraction of light

Crystal Structure AnalysisCrystal Structure Analysis

λθ nd =sin2Four-circle X-ray diffractometer

2qq

qd

Incident wave Reflected wave

Bragg condition

Atom Bonding ForcesAtom Bonding Forces

Interatomic interactionVan der Waal bondingIon bondingCovalent bondingMetallic bondingHydrogen bonding

The attraction between atoms forms a condensed state (solid and liquid).

Various types of interatomic forces represent particular crystal structures

Noble Gas CrystalNoble Gas Crystal

Interatomic potential

Rigid body repulsion Van der Waal attraction

Close-packed structureFace centered cubic lattice (ｆｃｃ)

Ne，Ar、Kr, Xe

What about He？Quantum liquid

Energy

Interatomic distance

Ion BondsIon Bonds

NaCl type CsCl type

The coulombicattraction between cation and anion.

Na+

Cl-

Li Be B C N O F Ne

Na Mg Al Si P S Cl Ar

H He

K Ca Ga Ge As Se Br Kr

Metallic BondsMetallic Bonds

The cation is occupied in the negatively charged moving electron bed.

1622 )3()2()2()1(:Na spss

Na+Valence electron

-e

+ ++ +

+ ++ +

+ ++ +

+ ++ +

Li Be B C N O F Ne

Na Mg Al Si P S Cl Ar

H He

K Ca Ga Ge As Se Br Kr

Covalent BondsCovalent BondsHydrogen atom： H2

+e-e

+e-e

+e +e

+e +e

Bond orbital

Antibonding orbital

Molecular orbital

Covalent BondsCovalent Bonds

Diamond structure

Graphite (black lead)

Lamellar crystalStrong covalent bond is seen inside the layers, while weak Van derWaals bonding holds between the layers.

⇒ easy to split

C，Si，Ge

Li Be B C N O F Ne

Na Mg Al Si P S Cl Ar

H He

K Ca Ga Ge As Se Br Kr

Aphaleritestructure

ＧａＡｓ，ＩｎＰ

Hydrogen BondsHydrogen BondsWater molecule

Ice crystal

Hydrogen bond

Covalent bond

Hydrogen bonds play a very important role in

biomolecules.DNA

SummarySummary

• Stories about size and extent• Modern civilization and physics• Condensed matter physics; sub-field of physics• Quantum mechanics and atomic structure• Existing forms of matter• Agglutination mechanism and crystal structure of atoms