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

PCES 5.38 CONDENSED MATTER: the SOLID STATE 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 10 K 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

PCES 5.39 ATOMIC STRUCTURE: The Elements 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. Above: Some of the electronic states in an atom. We see the probability density for one electron, for 4 different states. 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 occupied outer orbitals, & hence similar chemical properties

PCES 5.40 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 interaction energy certain directions- these between 2 atoms. 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. A covalent ‘sigma’ chemical bond, in ethane (C 2 H 6 ). 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 om r to R to . What are the kinetic . Wh at are the kinetic energies of these 2 states? According to the uncertainty principle we have energies of these 2 states? According to the uncertainty principle we have h 2 h 2 ----------- ----------- Energy before spreading: Energy before spreading: E r = ----------- ----------- Energy after spreading: E R Energy after spreading: = 2mr 2mr 2 2mR 2 2m Because R > r Because R > r, the electr , the electron lowers its energy by spreadin on lowers its energy by spreading out – g out – it is then t is then S SHAR ARED between the atoms. ED between the atoms.

PCES 5.41 CONDENSED MATTER : BONDS � MOLECULES Chemical bonds lead to an amazing array of structures. Chemical bonds lead to an a mazing array of structures. Only the noble gases (He, Ne, Ar, etc.) find it hard to Only the noble gases (He, Ne, Ar, etc.) find it hard to bond with other atoms – bond with other atoms – their heir shells are already full. shells are already full. Formatio Fo rmation of ethylene (C n of ethylene (C 2 H 4 ) 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, metallic complexes Nature and in industry , 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 organisms – organisms – others are highly poisonous. M others are highly poisonous. Most of ost of them dissociate in water (ie., they dissolve) them dissociate in water (ie., they dissolve) A tungsten-based A tungste -based By far the most complex structures are formed By far the most complex structures are formed mo molecular co lecular comp mplex lex by carbon bonds – by carbon bonds – these ar hese are very strong e very strong & s & so huge huge molecular structures can form with them. The covalent sharing of molecular structures can form wi th them. The covalent sharing of electrons between C atoms can take electrons between C atoms can take various geometries, depending various geometries, depending Th The benzen e benzene e on which orbitals on which orbitals overlap to shar overlap to share electrons e electrons (the most common are (the most common are mo molecule forms lecule forms ‘sigma’ ‘sigma’ and ‘pi’ and ‘pi’ bonds). One can also have bonds). One can also have ‘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 quantum-mechanical superposition of quantum-mechanical superp osition 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 The C-60 molecule some v important players (see Figs.). (the ‘buckyball’) Caffeine Serotonin

PCES 5.42 CONDENSED MATTER: Crystals Obviously one can make repetitive Obviously one can make repetitive patterns by assembling many atoms patterns b assembling many atoms of t of the sa same ki me kind. d. 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 om different atomic sub-units. Their strength and atomic sub-units. Their strength and Iron pyrite ( FeS ) ; ‘fool’s gold’. hardnes hardness depe depends e nds entire tirely o ly on t that of t t of the bonds between the atoms. Thus diamond is ver bonds between the atoms. Th us diamond is very hard hard (depending on strong (depending on strong inter-Carbon bonds), but graphite is made fr inter-Carbon bonds), but graphite is made from Carbon planes which are om Carbon planes which are only only 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 Carbon-based st Carbo -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 olecular crysta ar crystals’ ls’ of f TOP: The basic ‘unit molecules, held molecules, held cell’ structure, of Si together together b by weaker weaker & O atoms, repeated in quartz. bonds between the bonds between the BOTTOM: structure molecules. molecules. of water ice, made from H 2 O units. It is rare in Nature to find large crystals – It is rare in Nature to find large cr ystals – but we are surrounded by aggregates of but we are sur ounded by aggregates of different micr different microcystals. These polycr cystals. These polycrystalline ystalline amalgams are known as r amalgams are known as rocks. cks. Haematite crystals ( Fe 2 O 3 ) Epsomite crystals