CONDENSED MATTER: the SOLID STATE We learned in the last few - - PowerPoint PPT Presentation

We learned in the last few sections about the great mysteries of the universe & how it is made. We now turn to a discussion of the collective properties of matter, bew ildering in their variety – ranging from simple atoms to the overw helming complexity of living systems. The energy range over w hich matter can exist in condensed (ie., solid or liquid) form is enormous – up 10 10K in the centre of neutron stars. Thus most matter in the universe is condensed. One of the miracles that w e w ant to understand is – how is it that so much order & structure has emerged since the universe began? How is it that an inanimate universe governed by simple law s could have generated such complexity (including life)? We begin our story by looking at HARD MATTER - the solid state. Solids exist because of bonds that can form betw een atoms (or at very high pressures, betw een nucleons). These bonds are entirely a result of quantum mechanics. The almost limitless structures that form in Nature result from the directionality of these bonds, & from various quantum coherence effects betw een groups of atoms. Solid-state physics has been central to high-tech for over 60 years. In recent years our ability to manipulate and control the structure of materials at the molecular scale has led to new nanotechnologies

CONDENSED MATTER: the SOLID STATE

PCES 5.38

Above: Some of the electronic states in an atom. We see the probability density for one electron, for 4 different states.

With the discovery of Quantum Mechanics the old dream of Democritus was realised- the existence & structure of atoms is an immediate consequence of the quantum rules, for electrons moving in the field of the

• nucleus. Different atomic ‘shapes’ come

from the different shaped electron clouds, having ‘lobes’ (called ‘atomic orbitals’) of increased probability in certain directions.

How then do w e get elements? Pauli exclusion – no 2 electrons can occupy the same state, so each set of ‘lobes’ fills up, & w hen all are full, the atom begins filling a new ‘shell’ of similar orbitals further from the nucleus. Thus w e get a ‘repeating pattern’ of atoms, depicted in the periodic table. 2 elements in the same vertical column have the same set of

• ccupied outer orbitals, & hence

similar chemical properties

ATOMIC STRUCTURE: The Elements

PCES 5.39

THE CHEMICAL BOND: Sharing of electrons

Quantum Mechanics explains chemical bonding. As we saw, in QM we can form states which are superpositions (ie., sums) of different states- allowing them to spread in space, which lowers their kinetic energy (this is clear from the uncertainty principle). Electrons then spread between atoms by tunneling, & lower their

• energy. Chemical bonding is just this quantum-mechanical sharing of
• electrons. The electron wave-functions ‘lobes’ come off the atoms in

certain directions- these are the bond directions. Note- the electron clouds repel each other at short distances, because of the exclusion principle, which stops electron states from overlapping in space (they also repel each other when they are further apart, because of the Coulomb interaction between like charges). These repulsions are what make matter HARD.

interaction energy between 2 atoms.

We can put some numbers to this, in We can put some numbers to this, in a nice illustration of the uncert a nice illustration of the uncertai ainty principl nty principle. Suppos

• e. Suppose we have

e we have an electron of mass an electron of mass m, and , and its wave- its wave-fun unction in ction incr creases its sp eases its spread ad fr from

• m r

to to R . Wh . What are the kinetic at are the kinetic energies of these 2 states? According energies of these 2 states? According to the uncertainty principle we have to the uncertainty principle we have Energy before spreading: Energy before spreading: Er = Energy after spreading: Energy after spreading: ER = Because Because R > r R > r, the electr , the electron lowers its energy by spreadin

• n lowers its energy by spreading out –

g out – it is then t is then S SHAR ARED between the atoms. ED between the atoms. h2

• 2mr

2mr2

• h2

2m 2mR2

PCES 5.40 A covalent ‘sigma’ chemical bond, in ethane (C2 H6 ).

CONDENSED MATTER: BONDS MOLECULES

The C-60 molecule (the ‘buckyball’) Caffeine Serotonin

Chemical bonds lead to an a Chemical bonds lead to an amazing array of structures. mazing array of structures. Only the noble gases (He, Ne, Only the noble gases (He, Ne, Ar, etc.) find it hard to Ar, etc.) find it hard to bond with other atoms – bond with other atoms – their heir shells are already full. shells are already full.

PCES 5.41

Th The benzen e benzene e mo molecule forms lecule forms ‘p ‘pi- i-bond bonds’ s’ (left), wi (left), with a Q th a QM s superpo perposition of ion of the 2 states sho the 2 states shown above right n above right A tungste A tungsten-based

• based

mo molecular co lecular comp mplex lex Fo Formatio rmation of ethylene (C n of ethylene (C2 H4 ) vi ) via s a sigma- a- and p and pi-bond

• bonding

Almost any structure Almost any structure can be formed but can be formed but most of them are not stable. On earth, both in most of them are not stable. On earth, both in Nature and in industry Nature and in industry, metallic complexes , metallic complexes (metals bon (metals bonded with lighter ed with lighter elemen elements) ar ts) are v e very

• important. Many of them p
• important. Many of them play a key role in living

lay a key role in living

• rganisms –
• rganisms –
• thers are highly poisonous. M
• thers are highly poisonous. Most of
• st of

them dissociate in water (ie., they dissolve) them dissociate in water (ie., they dissolve) By far the most complex structures are formed By far the most complex structures are formed by by carbon bonds – carbon bonds – these ar hese are very strong e very strong & s & so huge huge molecular structures can form wi molecular structures can form with them. The covalent sharing of th them. The covalent sharing of electrons between C atoms can take electrons between C atoms can take various geometries, depending various geometries, depending

• n which orbitals
• n which orbitals
• verlap to shar
• verlap to share electrons

e electrons (the most common are (the most common are ‘sigma’ ‘sigma’ and ‘pi’ and ‘pi’ bonds). One can also have bonds). One can also have quantum-mechanical superp quantum-mechanical superposition of

• sition of

diff different bon ent bond ar arrangements, as in ben angements, as in benzen ene. e.

Hence the subject of ‘Organic Chemistry’ (the chemistry of C-based molecules). The chemistry of molecules involving C rings is called ‘aromatic chemistry’, w ith some v important players (see Figs.).

CONDENSED MATTER: Crystals

TOP: The basic ‘unit cell’ structure, of Si & O atoms, repeated in quartz. BOTTOM: structure

• f water ice, made

from H2 O units. Haematite crystals ( Fe2 O3 ) Iron pyrite ( FeS ) ; ‘fool’s gold’. Epsomite crystals

Hundreds of different basic patterns Hundreds of different basic patterns are possible, giving a large variety of are possible, giving a large variety of natural cr natural crystals made fr ystals made from different

• m different

atomic sub-units. Their strength and atomic sub-units. Their strength and hardnes hardness depe depends e nds entire tirely o ly on t that of t t of the bonds between the atoms. Th bonds between the atoms. Thus diamond is ver us diamond is very hard hard (depending on strong (depending on strong inter-Carbon bonds), but graphite is inter-Carbon bonds), but graphite is made fr made from Carbon planes which are

• m Carbon planes which are
• nly
• nly

weakly coupled to each other weakly coupled to each other- so they so they easily slide acr easily slide across one anoth ss one another. One can . One can convert graphite to diamon convert graphite to diamond by applyi d by applying pressure ng pressure & heat, & make many other & heat, & make many other Carbo Carbon-based st

• based structures (eg.

ructures (eg. the ‘buckyball’, C-60, on the ‘buckyball’, C-60, on pag page 5.41). One e 5.41). One ca can a n also ma so make ‘ ke ‘molecul

• lecular crysta

ar crystals’ ls’

• f

f molecules, held molecules, held together together b by weaker weaker bonds between the bonds between the molecules. molecules. Obviously one can make repetitive Obviously one can make repetitive patterns b patterns by assembling many atoms assembling many atoms

• f t
• f the sa

same ki me kind. d.

PCES 5.42

It is rare in Nature to find large cr It is rare in Nature to find large crystals – ystals – but we are sur but we are surrounded by aggregates of

• unded by aggregates of

different micr different microcystals. These polycr

• cystals. These polycrystalline

ystalline amalgams are known as r amalgams are known as rocks. cks.

CONDENSED MATTER: Structure of ‘Hard’ Solids

Most hard objects are not macroscopic crystals! At the microscopic level we have many kinds of structure. For example: (i) Many microcrystals, which fit together, withdislocations & defects between them. Heating a ‘polycrystal’ ‘anneals’ it- the defects move out, leaving a single crystal. Defects are formed when a crystal is strongly strained. (ii) We can have defects everywhere, with atomic bonds oriented in random

• directions. The system has to melt to get

rid of such extensive disorder. Such systems, called ‘glasses’ (eg., window glass), form if a crystal solidifies too fast. One can freeze defects by adding impurities, preventing plastic deformation, & making the material strong- eg. steel. (iii) One can have ‘Quantum Solids’, in which the atoms or defects can tunnel quite rapidly. These solids can still change their configurations even at absolute zero.

Bending a crystal creates ‘fault lines’ (defects, dislocations), & then polycrystals. Heating then anneals out the dislocations. The atomic structure

• f a glass

How ever by far the most complex solids are those formed by assembling large molecules together, making ‘soft matter’ – see next section

PCES 5.43

ELECTRONS in SOLIDS: Metals & Insulators

Wha What s stops the electrons in a

• ps the electrons in a

solid from spreading over solid from spreading over the the whole solid? As th whole solid? As they spread ey spread, , electron cl electron clouds s

• uds start to overlap,

art to overlap, & 2 things happen: & 2 things happen: (i) electro (i) electrons are fo s are forced rced into into different s different states by the Pauli ates by the Pauli principle – principle – stopping them from topping them from

• verlapping too much in space.
• verlapping too much in space.

(ii) electrons (ii) electrons that get too cl that get too close to each

• se to each other repel each
• ther repel each other –
• ther –

the Coulomb repulsion he Coulomb repulsion between lik tween like charges. This also stops th e charges. This also stops them from clos em from closely overlapping in space. ely overlapping in space. We can now We can now understand rstand the dif the differenc rence b e between tween metals ( tals (where electrons here electrons spread over the spread over the whole system in d whole system in delocalised localised stat states- es- so metals

• metals cond

conduct electricity), & insulators (wh uct electricity), & insulators (where re electrons are bound to the atoms). In metals th electrons are bound to the atoms). In metals the e electrons electrons do spread out, but to avoid do spread out, but to avoid each each

• ther they
• ther they go into wave-

go into wave-lik like states with dif e states with different rent wavelengths wavelengths & energies – energies – the set he set of all

• f all thes

these sta e states & es & their different energies is ca their different energies is called an ‘energy band’. If lled an ‘energy band’. If an energy an energy b band is only p nd is only partly full, then it is easy to rtly full, then it is easy to move electrons move electrons from from one s

• ne state to another, and we

ate to another, and we have a conductor. In insulators, electrons can only have a conductor. In insulators, electrons can only move by jumping f move by jumping from localised

• m localised

atomic states to a atomic states to a higher energy band, w higher energy band, which hich takes a lot of energy. takes a lot of energy.

LEFT: The energy levels of 2 atoms as they approach. CENTRE: The levels of 5 atoms forced to approach each other. RIGHT: The levels of very many atoms approaching each other. The filling of states up to the Fermi energy in 2 bands of a conductor, insulator, &

• semiconductor. Filled states are in red, empty
• nes in green.

PCES 5.44

SOLID-STATE ELECTRONICS

In modern times a technology of ‘quantum devices’ has developed, depending on our understanding of electron states in solids. The first major development was the transistor, & now we have thousands of devices ranging from solid-state lasers to electronic computers. Computers work by transferring electrons around- to make them faster one needs smaller components. Computing history is a story of component size reduction- which still has far to go.

1st transistor (1949) Oppenheimer, von Neumann, & the Los Alamos computer RIGHT: a Pentium 2 chip, containing 5 million processing elements BELOW: rise in computing speed, 1972-2007 PCES 5.45

CONDENSED MATTER: Solid Surfaces

In the last 20 yrs a new technique has allowed physicists to look at & manipulate matter at the atomic scale on solid

• surfaces. The STM

(Scanning Tunneling Microscope) is a very sharp needle which moves across a surface, only a few Angstroms above it. Electrons quantum tunnel between the two, & by measuring the electric current we look directly at the electronic clouds on the surface. One sees not only the structure of the electrons localised around atoms, but also the wavelike patterns of itinerant electrons moving across the surface.. The STM’s can also be used to drag or pick up atoms, to make surface structures- such as the famous ‘quantum corral’. The STM is one of the important tools used in the modern technology of ‘nanoscience’, ie, making nm-sized structures.

STM tip (human hair ~ 100 μm thick) Surface of Cu using STM A ‘quantum corral’, with Co atoms on a Cu surface. Surface of Be, near an atomic ‘edge’.

PCES 5.46

PCES 5.47

NANOSCIENCE: New Quantum Structures

PCES 5.48

Th The n new ew t tech chniq nique ues of s of ‘nanofab ‘nanofabri ricat cation’

• n’

are re on

• ne of
• f t

the he main main fact factors

• rs

behind nano behind nanoscience. It is likely

• science. It is likely that in the next 20-30 yrs this will

that in the next 20-30 yrs this will revolutio revolutionise ise large parts o arge parts of technolo technology. gy. The nano he nanoscale scale is defined by the nanometer s defined by the nanometer; ; 1 nm is 1 nm is 10 10-9

• 9
• m. A
• m. An idea o

idea of different length different length sc scales appears o ales appears on the previous page (recall the previous page (recall that 1 Angs that 1 Angstrom = 0.1 nm is the size of a small trom = 0.1 nm is the size of a small atom). Using the techniques of nanofabrication it atom). Using the techniques of nanofabrication it is no is now possible to make structures down to the w possible to make structures down to the atomic atomic sc

• scale. These techniques are called ‘top
• ale. These techniques are called ‘top-down’
• down’

nanoengineering nanoengineering tools – tools – controll controlled by us. d by us.

At scales o At scales of 10-100 nm one can make stru f 10-100 nm one can make structures ctures by ‘electr ‘electron b beam lith am lithogr

• graphy’

y’, usin , using v g very fin fine beams of high-energy electr beams of high-energy electrons to cut metals &

• ns to cut metals &

semic semicond nductor tors into sp into speci ecific sh

• shapes. On
• apes. One c

e can n Make nanoelectronic Make nanoelectronic cir circuits with uits with these – these – more more recently these circuits ha recently these circuits have been connected using ve been connected using ‘Carbo ‘Carbon na n nano notubes’, w tubes’, which ich are only 1 nm in diameter are only 1 nm in diameter, , but extremely strong – but extremely strong – they hey can b n be made mm in length made mm in length.

Using STM’s, one can mak Using STM’s, one can make Atomic siz Atomic size structures structures – as as seen at right. seen at right.

nanofabricat nanofabricated Au wir ed Au wire se semiconduc conductor Nano tor Nanoto towers wers ‘Kenj ‘Kenji’ (Japa Japanese for ato nese for atom) m) written w tten with Co a th Co atoms o s on C Cu ABOVE: A Carbon nanotube ABOVE: A Carbon nanotube cappe capped at d at both ends by buck both ends by buckyba yball sectio

• tions. The
• s. The

diameter is roug ameter is roughly 1 n hly 1 nm Cross-sectio Cross-section of n of Aa Aaca carb rbon

• n

na nano notube tube Nano Nanotube tube on A

• n Au alectro

alectrodes es Nano Nanotube tube on A

• n Au alectro

alectrodes es

NANOSCIENCE: Molecular Engineering

PCES 5.49

Another appr Another approach to design of

• ach to design of

nanosystems nanosystems is ‘bottom-up’, is ‘bottom-up’, ie., starting with existing ie., starting with existing na nanoscale noscale

• bj
• bjects.

ects. Such objects are typically Such objects are typically molecular molecular, an and in instead stead of

• f

bei being m g made by ma de by man usi n using g top-d top-down methods, they ar

• wn methods, they are

e the product of chemistry. the product of chemistry. The simplest such molecules The simplest such molecules have metallic co metallic cores, an s, and can b can be assemb assembled in led in man many ways. ways. Currently they are used where pi Currently they are used where pinp npoint deliv

• int delivery o
• f the metals

the metals is required (eg., for is required (eg., for medical applications). medical applications). A much greater A much greater range range of applications is envisaged for organ

• f applications is envisaged for organic

ic

• molecules. These can range from the
• molecules. These can range from the

quite bizar quite bizarre (such as nanoscale e (such as nanoscale mecha echani nical devices – cal devices – the he na nanocar nocar sho hown above is an example), to wn above is an example), to possible molecular electronics devices. A major disc possible molecular electronics devices. A major discovery of the

• very of the

1980’s was 980’s was of conducti

• f conducting organic

ng organic molecules – molecules – in principle this opens th n principle this opens the way to electronic cir e way to electronic circuitry at uitry at the nanoscale the nanoscale level, using conducti level, using conducting polymer chains as quantum ng polymer chains as quantum wir

• wires. S

Some o me of the possibilities f the possibilities now being discussed are now being discussed are shown shown here. N

• here. Note that to make

te that to make these is hard, & needs ‘top-down’ these is hard, & needs ‘top-down’ appr approaches

• aches

A ‘ A ‘nan anoc

• car

ar’ with ith ch chemical mak emical makeup up shown at top. It can ro n at top. It can roll a acro ross a go ss a gold s surfa rface e – STM TM experi experiments ments c can trac an track i k its m s motio tion Metallic clus Metallic cluster mo ter molecule, with Au:P lecule, with Au:Pd core DNA chain connecting 2 Au electro DNA chain connecting 2 Au electrodes es Gating circ Gating circuit uit usin using a g aroma

• matic

ic c chain ain st struct ructur ure