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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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posted:1/21/2012
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