Matter, Materials, Crystal Structure
and Bonding
Chris J. Pickard
Why should a theorist care?
Where the atoms are determines what they do
Where the atoms can be determines what we can do
Overview of Structure and Bonding
Atoms and Elements
Non-crystalline materials
Crystalline materials
Bonding and cohesion
Atoms and Elements
Molecules
Naphalene
Molecules are finite collections of covalently bonded atoms
They vary from diatomic molecules, to massive proteins
Polymers
Polyethylene (or polythene)
Polymers are long chain molecules,often with a carbon backbone(sometimes silicon)
The repeat unit, or monomer, isrepeated and joined together manytimes
The chemical formula for polyethyleneis (CH2)N
Many properties depend simply on N
Nanoparticles
Silver Nanoparticle
Nanoparticles range in size from 1 100 nm and can contain from 10 to100,000 atoms
Their properties are not necessarilythe same as the bulk material
The physical, mechanical, electronic,magnetic, optical and chemicalproperties can all differ
Nanostructures
(9,9) armchair nanotube
More complex structure thannanoparticles
Might be designed, and often selfassembled
Nanotechnology is a very hot topic,with strong technological promises fornanoelectronics etc.
Amorphous Solids
Amorphous Carbon
Amorphous solids have no long rangeorder
The are disordered, and the kind ofdisorder is structural as opposed tocompositional
In this example both sp3 and sp2
bonding is found
Can have a variety of electronic andmechanical properties
Order in randomness
A silica glass
The atomic positions are rarelyentirely random
The structural constraints imposesome order on the randomness
The result is short range order,without long range order
This order can be probedexperimentally
The radial distribution function
0 2 4 6r (Angstrom)
0
5
10
15
Rad
ial d
istr
ibut
ion
func
tion
The RDF is the probability density offinding particle i at a given distancefrom particle j:
Gi,j =N
i6=j (r |ri rj|)
Can be measured in scatteringexperiments (X-ray, neutron)
For a crystalline solid this would justbe a set of delta spikes . . .
Crystalline solids
A crystal is a homogeneous solid with a regularly repeating atomic arrangement
The majority of the solid state physicists theoretical tools have been developedfor dealing with crystals
Most current scientific questions concern non ideal crystals (or structures thatare simply not crystalline)
Our tools are still useful . . .
Ionic crystals
Halite (NaCl)
The Alkali Halides are typical ioniccrystals
Can only exist for compounds(different elements)
Are electronic wide band gapinsulators
Are of technological importance fortheir optical properties
Pure Metal
Aluminium
The pure form of the majority ofthe elements in the periodic table aremetallic
Metals conduct electricity freely, andreflect light
Many pure metals are soft, buttransition metals are harder
Alloys
Ordered metallic alloy
Alloys are mixtures of elements, notexclusively metallic and can be eitherordered or disordered
The properties depend dramaticallyon the composition, and history ofthe alloy
Understanding alloying is ofimmense economic and technologicalimportance
Covalent Crystals
Diamond
The strong directional covalent bondslead to mechanically strong crystals
Covalent crystals are less wellinsulating than ionic crystal
Carbon can form a range of differentcovalent bonds, in this case sp3
Graphite
Bernal Graphite
The graphene sheets are purely sp2
covalently bonded
Graphite can exist in different phases,according to the stacking
Bernal graphite (structure found byJ. D. Bernal in 1924) has an. . . ABABABA. . . stacking
Graphite is a semi-metal (a non-zeroDOS at the Fermi level)
Semiconductors
Gallium Arsenide (GaAs)
Semiconductors are still less insulatingthan ionic crystals
Band-gaps range from a fraction of anelectron volt, to several
They can be doped to control theelectronic properties
They are the basis of thesemiconductor industry
Zeolites
Ferrierite
Built up from SiO4 tetrahedral units
Like the flexible hybridisation ofcarbon, these units allow manystructural possibilities
Zeolites are open silicates
They are industrially important ascatalysts
Minerals
Amphibole
Minerals are materials found naturallyin the earth
Many are silicate based (again, on theSiO4 tetrahedra)
The structures can be very complex,contain many atomic species, anddepend on the geological history ofthe sample
A wide range of properties
High Temperature Superconductors
YBa2Cu3O7
YBCO is a complex layered metaloxide
It is in the Perovskite structure
YBCO superconducts at 92K
Oxidation state of CuO planesand chains control superconductingproperties
Molecular crystals
Solid cubane
Molecules play the role of atoms toform molecular crystals
At non-zero temperature, themolecules will be in often complexmotion
Molecular crystals can be organicnon-linear optical materials, andother electronic properties are oftechnological interest
Cubic Ice
Cubic water ice (H2O)
Water ice is another form of molecularcrystal
Held together by directional, butweak, hydrogen bonds
The H2O molecule can vibrate, buthave less freedom to rotate
Molecular crystal with hydrogen bonds
Indigo
Many organic molecules (pigmentslike Indigo, or drug molecules) are heldtogether by both hydrogen bonds, andeven weaker van der Waals bonds
There can be very many possiblepolymorphs
The physical properties of the crystalwill depend on the exact polymorphpresent
Bonding
The energy of a collection of atoms is often lower if they are close
The atoms stick together
In specific ways, depending on the nature of the atoms and their neighbours
This bonding can be classified as Covalent, Ionic, Mixed, Metallic, Molecularand Hydrogen Bonding
Of course, in reality there is a continuum
Covalent Bonding
Diamond
The atoms involved in a covalent bondcan be said to be sharing valenceelectrons so as to attain a magicaloctet
Visually, this expresses itself as asignificant charge density between theatoms
Covalent bonds are strong, gettingstronger (and shorter) the moreelectrons that are shared
Ionic Bonding
Halite (NaCl)
The electrons are not shared and thereis a concentration of charge density onthe more electronegative ion
The ion that donates electronsbecomes positively charged (cations),and the receiving electron negativelycharged (anions)
The bond is due to the electrostaticinteraction between the oppositelycharged ions, and non-directional
Mixed Ionic Covalent Bonding
III-V Semiconductor (GaAs)
The ionicity is weaker, due to thecloser electro-negativity of the atoms,but still present
There is an increase in charge densitybetween bonded atoms
The bond has both covalent andionic character, and the bonding isdirectional
Metallic Bonding
Aluminium
The electrons are shared across theentire solid, and are delocalised : anextreme version of covalent bonding
The more electrons shared, thestronger the metallic bonding: Mghas a higher melting point than Na
The bonding is non directional, canhave a covalent character, and resultsin close packed solids
Hydrogen Bonding
Cubic water ice (H2O)
Weak directional bonds due tothe electrostatic attraction of polarmolecules (or permanent dipoleswithin molecules)
These permanent dipoles are due todifferences in electronegativity
Hydrogen is unusual: it cannot fullyionise (first ionisation potential toohigh), but also can form only onecovalent bond
Van der Waals Bonding
Solid cubane
Weak non-directional bonds due tothe electrostatic attraction betweenfluctuating dipoles
Always present, but only dominatesif all other bonds are saturated orimpossible
The charge density between van derWaals bonded elements is verysmall
Cohesive Energy
2 4 6 8 10 12 14 16 18 20Lattice Parameter (Angstrom)
-1250
-1200
-1150
-1100
-1050
Tot
al E
nerg
y (e
V)
The total energy of diamond withlattice parameter
See Chapter 20 of Ashcroft andMermin for a more (slightly more ...)quantitative approach
To do a proper job, you really needto use a first principles QM basedapproach
See the lecture courses of Drs.Molteni and Towler next term
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