Structures of Solids
 Crystalline solids: well-ordered, rigid, long-range order
    The molecules, atoms or ions occupy specific positions.  
                      Examples: quartz, salt, sugar.
    Tend to melt at specific temperatures, because crystalline
        solids have a narrow range of intermolecular forces. 
        The shattering of crystalline materials produces
        fragments having the same shape and structural
        characteristics of the orginal sample.
 
 Amorphous solids: molecules, atoms or ions which do NOT
        have an orderly arrangement.  Examples:rubber,glass.
    Tend to soften & melt over a range of temperatures,
        because amorphous solids have variable
        intermolecular forces.  The shattering of a glass
        produces irregularly shaped pieces with curved edges
        and irregular angles.  When you heat sulfur or rubber,
        these soften and melt over a broad range of
        temperatures.
 

Unit Cells
 Crystals have an ordered, repeating structure.
 The smallest repeating unit in a crystal is a unit cell.
 The unit cell is the smallest unit with all the symmetry of
        the entire crystal.
 Three-dimensional stacking of the unit cells is the
            crystal lattice.

There are three types of cubic unit cells; (there are many
        other systems).

1. Primitive cubic: atoms at the CORNERS of a simple cube;
        each atom is shared by 8 unit cells;

     Z =  # of atoms per cell =
     Z =  8 corners/cell x (1/8) atom/corner = 1 atom/cell

2. Body-centered cubic (bcc): atoms at the CORNERS of a
        cube plus one in the CENTER of the body of the cube;
        the corner atoms are shared by 8 unit cells, and the
        center atom is completely enclosed in one unit cell;

     Z = # atoms per cell = (8 x 1/8) + 1 = 2 atoms/cell

3. Face-centered cubic (fcc): atoms at the CORNERS of a
        cube plus one atom in the CENTER OF EACH FACE of
        the cube;  the corner atoms are shared by 8 unit cells,
        the face atoms are shared by 2 unit cells; 

   Z = # atoms per cell =(8 x 1/8)+(6 x 1/2)=4 atoms/cell

The Crystal Structure of Sodium Chloride:
      Face-centered cubic lattice (fcc).
      There are two equivalent ways of defining the unit cell:
  1. Cl^- (larger) ions at the corners of the cell, or
  2. Na⁺ (smaller) ions at the corners of the cell.

 The cation:anion ratio in a unit cell is the same as that for
      the crystal.
   In NaCl, each unit cell contains the same number of Na⁺
      and Cl^- ions.

    Note that the unit cell for CaCl₂ needs twice as many
        Cl^-  ions as Ca²⁺ ions.

    There are two possible choices for the third layer of
        spheres:
   1. Third layer eclipses the first (ABABABAB arrangement).
        This is  called        hexagonal close packing (hcp).

   2. Third layer is in a different position relative to the first
           (ABCABCABC arrangement).  This is called    
            cubic close packing (ccp); this ends up to be
            identical to face-centered cubic (fcc).

 
Coordination number:  the number of spheres directly
       surrounding a central sphere.

    In simple cubic, the coordination number is 6.

    In bcc, the coordination number is 8.

    In fcc, the coordination number is 12. 
 
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X-Ray Diffraction:
 When waves are passed through a narrow slit, they are
        diffracted.
 When waves are passed through a diffraction grating
    (many narrow slits in parallel), they interact to form a
    diffraction pattern (areas of light and dark bands).
 Efficient diffraction occurs when the wavelength of light
    is close to the size of the slits.
 The spacing between layers in a crystal is 2-20 Angstroms,
    which is the wavelength range for X-rays.

Bonding in Solids:
There are four types of solids:

1. Molecular (formed from molecules, i.e., C₁₀H₁₈O₃, C₆H₆)
        usually soft with low melting points and poor
        conductivity of electricity (melting pt. of C₆H₆ = 5.5^oC).

2. Covalent network (formed from covalently-bonded giant
        rigid networks, i.e., SiC, diamond) - very hard with
        very high melting points, and not freely mobile,
        therefore, usually poor conductors of heat & electricity;
        diamond is an exception and jewelers use the high
        conduction of heat to distinguish real diamonds from
        fakes.

  3. Ions (formed from anions & cations, i.e., NaCl) - hard,
        brittle, high melting points and poor conductors of
        electricity & heat .

4. Metallic (formed from metal atoms, i.e., Ag) - soft or
        hard, wide range of melting points, good conductivity
        of electricity & heat, malleable and ductile.

Molecular Solids:
 Intermolecular forces: dipole-dipole, London dispersion
        and H-bonds.
 These relatively weak intermolecular forces give rise to
        low melting points.
 Room temperature gases and liquids usually form
        molecular solids at low temperature.
 Efficient packing of molecules is important (since they
        are not regular spheres).    Examples:  C₆H_6, CO_2, N₂
 

Covalent-Network Solids:
 Atoms held together in large networks.
         Examples: diamond, graphite, quartz (SiO₂),
                 silicon carbide (SiC), and boron nitride (BN).
     In diamond:
          Each C atom has a coordination number of 4; each C
          atom is tetrahedral; there is a 3-dimensional array of
          atoms; diamond is hard, and has a very high melting
          point (3550^oC)!

     In graphite:
          Each C atom is arranged in a planar hexagonal ring;
          layers of interconnected rings are placed on top of
          each other; the distance between C atoms is close to
          that in benzene (142 pm vs. 139.5 pm in benzene);
          the distance between layers is large (341 pm);
          electrons move in delocalized orbitals (good
          conductor of electricity).  Sheets slide over one
          another easily; therefore, good lubricant.
 

Ionic Solids:
 Ions (spherical) held together by electrostatic forces of
          attraction.
    The higher the charge (Q) and the smaller the distance
          (d) between the ions, the stronger the ionic bond. 
          There are some simple classifications for ionic lattice
          types:

     NaCl Structure:
          Each ion has a coordination number of 6.
         Face-centered cubic lattice (fcc).
          Cation to anion ratio is 1:1.
          Examples: LiF, KCl, AgCl and CaO.

     CsCl Structure:
         Cs⁺ has a coordination number of 8.
         Different from the NaCl structure (Cs⁺ is larger than
                Na⁺ and is located in the center of the cell).
        Primitive cubic (even though it LOOKS like bcc!).
         Remember:  bcc has to have same atom (ion) at
         center as at the corners.   Cation to anion ratio is 1:1.
 

     Zinc-Blende Structure:
         Typical example ZnS.
         S^2- ions adopt a fcc arrangement.
         Zn²⁺ ions have a coordination number of 4.
         The S^2- ions are placed in a tetrahedron around
            the Zn²⁺ ions.  Another example: CuCl.
 

     Fluorite Structure:
         Typical example CaF₂.
         Ca²⁺ ions in a fcc arrangement.
         There are twice as many F^- as Ca²⁺ ions in each
            unit cell.  Examples: BaCl₂, PbF₂.
 

Metallic Solids:
 Metallic solids have metal atoms in hcp (hexagonal
        close pack), fcc (face centered cubic) or
        bcc (body-centered cubic) arrangements.
   Coordination number for each atom is either 8 or 12.
   Problem: the bonding is too strong for London dispersion
        and there are not enough electrons for covalent bonds.
   Resolution: the metal nuclei "float" in a sea of electrons.
   Therefore, metals conduct electricity, because the
        electrons are delocalized and are mobile.

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