# Solids

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```					                     Solids
• Solids have “resistance” to changes in both
shape and volume
• Solids can be Crystalline or Amorphous
• Crystals are solids that consist of a periodic
array of atoms, ions, or molecules
– If this periodicity is preserved over “large”
(macroscopic) distances the solid has “Long-
range Order”
• Amorphous solids do not have Long-Range
Order
– Short Range Order
Solids
• Crystals Solids:          • Amorphous solids:
– Short-range Order            – ~Short-range Order
– Long-range Order             – No Long-range Order
Crystals
• The periodic array of atoms, ions, or
molecules that form the solids is called
Crystal Structure
• Crystal Structure = Space (Crystal) Lattice
+ Basis
– Space (Crystal) Lattice is a regular periodic
arrangement of points in space, and is purely
mathematical abstraction
– Crystal Structure is formed by “putting” the
identical atoms (group of atoms) in the points
of the space lattice
– This group of atoms is the Basis
Crystal Structure and
Classification of Solids
Crystals
Crystal Structure = Space Lattice + Basis
Solids
• Different solids can have the
same geometrical arrangements
of atoms
– Properties are determined by
crystal structure, i.e. both crystal
lattice and basis are important
• Example:
– Si, Diamond (C), GaAs, ZnSe have
the same geometry
– Si and C (Diamond) Form
“Diamond Structure”
– GaAs or ZnSe form a structure
called “Zinc Blende”

http://www.neubert.net/Crystals/CRYStruc.html
Solids
• Different arrangements of atoms (even the same
atoms) give different properties

Single layer is graphene
Solid Models: Close-Packed Spheres
• Most atoms or ions forming solids have spherical
symmetry
• Considering the atoms or ions as solid spheres we
can imagine crystals as closely packed spheres
Classification of Solids
• Since we know the structure of atoms that
form solids, we can classify them via the
type of bonds that hold solids together
– In this case we say that we classify solids
according to the nature of bonding
– There are four classes of solids:
•metallic, ionic, covalent, and molecular
– All the forces holding solids together have
electrostatic origin
General Considerations
• There must be an attractive force
– An apparent candidate is the Coulomb Force
1 q1q2
F
4 0 r 2
– Here r is a distance between atoms (ions) forming a solid
• What stops atoms (ions) from getting closer than they
do?
– When ions are very close to each other, other forces arise.
These are the so-called short-range repulsive forces, due
to rearrangement of electrons as nuclei approach
• Equilibrium distance, r0, is point at which energy is at
a minimum, forces are balanced
General Considerations
Ionic Solids
• Ionic crystals consist of the negative and positive
ions, attracted to each other
– Electron from one of the atoms removed and transferred
to another: NaCl, AgBr, KCl

– When the crystal is formed excess heat is generated
Crystalline Structure of NaCl
Ionic Solids
• Let’s find the energy required to transfer an electron
from Na to Cl and then to form a NaCl molecule
– To remove an electron from Na (ionize the atom) one
needs to “spend” 5.14eV (compare with the ionization
energy of a hydrogen atom?)

Na + 5.14eV  Na+ + e-
– When a Cl atom captures an electron, 3.62eV of energy is
released

Cl + e-  Cl- + 3.62eV
Ionic Solids
• In solid, Na+ and Cl- are brought together at the
distance r0  2.51Å [Å = 10-10m = 0.1nm]
– The total energy is lowered due to the Coulomb
attraction
1 e2
•                   The results is -5.73 eV
4 0 r
• Thus when a NaCl “molecular unit” of NaCl solid
is formed the following occurs
Na + 5.14eV  Na+ + e-
Cl + e-  Cl- + 3.62 eV
Cl- + Na+  NaCl + 5.73 eV
Na + Cl  NaCl + 4.21 eV
Ionic Solids
• The energy gain for NaCl solid is ~ 4.21 eV per
NaCl pair
– This is the energy required to break an NaCl
molecule and restore neutral Na and Cl atoms
• This energy is huge (in 1 cm3):
4.21×1.6×10-19 (Joules per pair) × 3 × 1022
(pairs) = 20200 Joules
– To more accurately calculate the total
electrostatic energy, need to calculate
interaction of each ion with all other ions in
the crystal
Ionic Solids
• In ionic crystals all electrons are bound to
the ions: There are no free electrons!!!

– Thus most ionic crystals are insulators
• There are ionic conductors, where ions, and
not electrons conduct: Example: AgI
Covalent Solids
• The covalent bond is usually formed from two
electrons, one from each atom participating in the
bonding: These electrons are shared by the atoms
– Quantum Mechanics is required to calculate binding
energies
– The probability of finding electrons forming the bond
between the two atoms is high
– Covalent bonds are very strong and directional
Covalent Solids
• In general, since there are no free electrons, these
crystals are insulators or semiconductors
Crystalline Structure of Diamond
Compare
• Covalent Solids

• Ionic Solids
Mixed Bonding Solids
• The electrons forming the covalent bond tend to be
localized in the region between the two atoms
• If the atoms elements forming the covalent solid
are different
– e.g., Zn & Se for ZnSe then the electrons a localized
closer to one of the atoms (with higher electron affinity)
• We say that the bond is partially covalent and
partially ionic
Metallic Bond
• Metals may be seen as collections of stationary
ions surrounded by a sea of electrons
– Can be viewed as limit of covalent bonding, when
electrons are shared by all the ions in the crystal
– The metallic bond is not directional
Molecular Solids

• Very weak bonding: Dipole-Dipole Interaction

U
r6

• Liquid Crystals, Ice
– low melting temperatures
Classification of Solids by
Conductivity
• Another way of classifying solids, in
addition to (a) crystal structure and (b)
type of bonds between atoms is (c)
electrical conductivity
• Conductors
• Insulators
• Semiconductors

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