Order 1238142: Condensed matter
tutorthammy
Lect-4-bonding.pdf
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Crystal Structure 1
Crystalline Solid
• Crystalline Solid is the solid form of a substance in which the atoms or molecules are arranged in a
definite, repeating pattern in three dimension.
• Single crystals, ideally have a high degree of order, or regular geometric periodicity, throughout the entire
volume of the material.
Crystalline Solids
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Macroscopic form reflects underlying atomic structure
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Crystal Structure 3
Polycrystalline Solid
Polycrystalline
Pyrite form
(Grain)
Polycrystal is a material made up of an aggregate of many small single crystals
(also called crystallites or grains).
Polycrystalline material have a high degree of order over many atomic or molecular
dimensions.
These ordered regions, or single crytal regions, vary in size and orientation wrt one
another.
These regions are called as grains ( domain) and are separated from one another
by grain boundaries. The atomic order can vary from one domain to the next.
The grains are usually 100 nm - 100 microns in diameter. Polycrystals with grains
that are <10 nm in diameter are called nanocrystalline
Crystal Structure 4
Amorphous Solid • Amorphous (Non-crystalline) Solid is composed of randomly
orientated atoms , ions, or molecules that do not form defined patterns or lattice structures.
• Amorphous materials have order only within a few atomic or molecular dimensions.
• Amorphous materials do not have any long-range order, but they have varying degrees of short-range order.
• Examples to amorphous materials include amorphous silicon, plastics, and glasses.
• Amorphous silicon can be used in solar cells and thin film transistors.
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Molecular Crystals
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Formed from C60 or molecules,
Known as “buckyballs”
A molecular lattice of 1·KClO4.
Liquid Crystals & Polymers
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Some properties of liquid,
some of solid
Polymer long chain of atoms
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Bonds between atoms: contents
• bonding in general, attractive and repulsive forces, cohesive energy
• ionic bonding • covalent bonding • metallic bonding • hydrogen bonding and van der Waals bonding • relationship between bonding type and some physical
properties of a solid (in particular melting point)
at the end of this lecture you should understand....
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Bonding in solids: the general idea
• valence electrons (of the outer shell) achieve bonding (like in chemistry)
• decrease in total energy stabilises the solid (the solid’s energy is lower than that of sum of atoms it is made of)
• so the energy gain by the bonding must be higher than the energy it costs to promote electrons from the atomic orbitals
to the electronic states of the solid.
• this energy difference is a measure for the strength of the bond. It is called the cohesive energy.
cohesive energy = energy of atoms - energy of solid
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Repulsive force
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Ionic bonding
• form positive and negative ions (here Na+ and Cl-) • bonding is achieved by electrostatic force and a classical
treatment is (partially) meaningful.
example NaCl (rock salt): cubic structure
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Turning Atoms in Ions
how much energy does it cost?
example: NaCl
ionization energy Na: 5.1 eV
electron affinity Cl: 3.6 eV
net energy cost: (5.1 eV - 3.6 eV) = 1.5 eV per pair
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Ionic bonding
what is the energy gain?
example: NaCl
so the total gain is
5.1 eV - 1.5 eV = 3.6 eV
this amounts to 5.1 eV per pair
potential energy:
= 2.8 Å
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Ionic bonding
but this was just a molecule: what about the
electrostatic energy gain in the solid?
example: NaCl
consider the centre Na ion
energy gain from next 6 Cl:
energy loss from next 12 Na:
next we get 8 more Cl ions and the total energy becomes
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Ionic bonding
example: NaCl
eventually the series converges
and we get (for one ion)
M d
is called the Madelung constant.
It is specific for a given structure.
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Ionic bonding
so the total lattice energy for one mole of NaCl
to count every
pair only once
because there are Na and Cl ions
This gives 861 kJmol -1
. The experiment gives 776 kJmol -1
Note: this is the lattice energy, not the cohesive energy
(the lattice energy minus the energy to turn atoms into ions).
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The covalent bond
• electron configuration: 2 s
and 2 p electrons
• formation of four sp 3
hybrid orbitals as
linear combination
between the s and
three p orbitals
• directional character of p orbitals is also
found in sp 3
orbitals.
e.g. diamond [He] 2s2 2p2
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methane
diamond
The covalent bond: sp 3 bonding
directional character is
maintained and important:
it is found in all solids and
molecules of sp3 bonding
Bonding in most semiconductors
• Tetrahedral (sp3) configuration almost ubiquitous: diamond, Si, Ge, III-V (GaAs, AlAs, InP), II-VI (CdS, CdTe)
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Bonding in most semiconductors
• Tetrahedral (sp3) configuration almost ubiquitous: diamond, Si, Ge, III-V (GaAs, AlAs, InP), II-VI (CdS, CdTe)
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Note: the II/VI or III/V semiconductors may be isoelectronic but in the latter
the bonding is not purely covalent anymore. It is partly ionic.
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• formation of three sp 2
hybrid orbitals as linear combination
between the s and two p orbitals. One p-orbital remains
The covalent bond: sp 2 bonding
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The covalent bond: sp 2 bonding
bucky-balls graphene / graphite
carbon nanotubes
(rolled-up graphene)
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Covalent bonding
• Cohesive energies similar to ionic bonding, in the eV range. • Very directional bonding.
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Metallic bonding
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metals / non-metals
• the boundaries can be disputed • simple metals, transition metals, noble metals
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Metallic bonding (simple metals)
• outer electrons are delocalized and act as “glue” between positively charged ion cores
• generally found for elements with one, two or three valence electrons.
• cohesive energies in the eV range
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• smaller cohesive energies than in ionic crystals • larger ionic radii, e.g. for Na: 3.82 Å (metal) and 1.94 Å (NaCl) • bonding has no directional preference • closed-packed atomic configurations are preferred: best
possible overlap between the orbitals, no “holes” in the
potential
Metallic bonding (simple metals):
more characteristics
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Metallic bonding: why is this so favorable?
kinetic energy (or Hamiltonian for a free particle)
∝ (negative) average curvature of wave function “flatter” wave function -> lower energy
less localization -> smaller p variation
smaller Kinetic Energy Ekin =p
2 /2m
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Transition metals
• 4s and 3d have very similar energies • 4s electrons form delocalized metallic bonds • 3d electrons form more local (covalent-like) bonds • higher cohesive energies
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Bonds between molecules
• molecular solids are very common (but not at RT) • ice • plastic • DNA • what makes molecules bond to each other?
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Bonds between molecules: hydrogen bonds
permanent dipole
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Bonds between molecules: hydrogen bonds
• H is positively charged but also very small: another “real” bond cannot be established without overlap of electron
clouds (in this sense it is too big in this drawing).
• H bonding is important in ice, DNA... but not very strong
Van der Waals Bonding
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Also known as “Fluctuating Dipole Forces, Dispersion Forces,
or Molecular Bonding”
For two atoms/molecules far apart, there is attraction due to van der Waals
forces. Both atoms have a dipole moment which may be zero on average,
but can fluctuate momentarily.
If one atom obtains a momentary dipole moment, p1
the second atom can polarize,
also obtaining a dipole moment p2 to
lower its energy.
As a result, the two atoms will attract each other.
He
e- e-
2
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Bonds between molecules: van der Waals force
• dipole moment caused by fluctuations • this is always present as an attractive force (even between
He atoms as in this case)
• it is very weak and depends on the distance as r-6
E p=αE
attract
polarizability
2
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Bond type and physical properties
Lowest melting temperature: rare-gas solids Ne, Ar, Kr, Xe: only van der
Waals bonding, less than room temperature; then simple metals and noble
metals and finally, transition metals (covalently bonded solids and ionic crystals)
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Summary • We have looked at different types of bonding: ionic,
metallic, covalent, H-bonds, van der Waals bonds.
• In reality, intermediate bonding scenarios are often found.
• We have some ideas about the relation between
the bonding type and the
physical properties
(at least for the melting
point).
Read Table 5.1
of Handout
Types of Bonds in Solids
