Solids

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Chapter 16

• Solids

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Types of SolidsCrystalline solids

• 1. Shows a sharp melting point.
• 2. Have a regular, ordered structure composing of
  identical repeating units having the same
  orientation throughout the crystal.

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Types of Crystalline solids

• Metallic crystals- are composed of bonded
• metal atoms example are Na, Cu, Fe, and
• alloys.
• Covalent crystals-consisted of an infinite
• network of atoms held together by covalent
• bonds, no individual molecules being present.
• Example are dismond, graphite, SiC and SiO2.

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Types of Crystalline solids

• Molecular crystals-are composed of individual
• molecules. Example are Ar, CO2 and H2O
• Ionic crystals-consisted of an array of positive
• and negative ions example are NaCl, MgO,
• CaCl2 and KNO3

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Types of SolidsAmorphous solids

• 1. An amorphous solid does not have a
• characteristic crystals shape.
• 2. When heated, it softens and melts over a wide
  temperature range.

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 Structure of Metals

• Simple Cubic
• (????)
• Hexagonal Closest Packed (HCP)
• (??????)
• Face-Centered Cubic (FCC)
• (????)
• Body-Centered Cubic (BCC)
• (????)

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Closest Packing hcp and fcc

• The hcp and fcc structures are closely related
• they are both based upon stacking layers of
• atoms, where the atoms are arranged in a close-
• packed hexagonal manner within the individual
• layer.

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• The atoms of the next layer of the structure
• will preferentially sit in some of the hollows
• in the first layer - this gives the closest
  approach
• of atoms in the two layers and thereby
• maximizes the cohesive interaction.

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• When it comes to deciding where the next
• layer of atoms should be positioned there are
• two choices - these differ only in the relative
• positions of atoms in the 1st and 3rd layers.

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ABABA.. packing sequence of the hcp structure
ABCABC.. packing sequence of the fcc structure
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Closest Packing hcp and fcc

• These hcp and fcc structures share common
• features
• (a) The atoms are close packed
• (b) Each atom has 12 nearest neighbours.

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Hcp structure

• The ..ABABA.. packing sequence of the hcp
• structure gives rise to a three-dimensional unit
• cell structure whose symmetry is more
• immediately related to that of the hexagonally-
• close packed layers from which it is built.

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• The unit cell for the hexagonal closest-packed
  structure has a diamond-shaped or hexagonal base
  with sides of equal length.
• The volume is the product of the area of the base
  and the height of the cell.

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c 4r(2/3)1/2
b2r
a2r
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An actual STM image of a Ni surface. Note the
hexagonal arrangement of atoms. This image is the
property of IBM Corporation.
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Fcc structure

• The ..ABCABC.. packing sequence of the fcc
• structure gives rise to a three-dimensional
• structure with cubic symmetry.

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FCC structure
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• Coordination Numbers (CN)12
• Net number of spheres in unit cell
  (81/8)(61/2)4

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Bcc structure

• The bcc structure has very little in common with
  the fcc structure - except the cubic nature of
  the unit cell. Most importantly, it differs from
  the hcp and fcc structures in that it is not a
  close-packed structure.
• The structure of the alkali metals are
  cheracterized by a bcc unit cell.

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BCC structure
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• Coordination Numbers (CN)8
• Net number of spheres in unit cell
  (81/8)(11)2

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Packing Efficiency

• For a FCC structure

• For a BCC structure

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Packing Efficiency of HCP Structure

• The unit cell is characterized by three lengths
  (a, b, c) and three angles (a, b, g).
• The quantities a and b are the lengths of the
  sides of the base of the cell and g is the angle
  between these two sides.
• The quantity c is the height of the unit cell.
• The angles a and b describe the angles between
  the base and the vertical sides of the unit cell.
  

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Packing Efficiency of HCP Structure

• In the hexagonal closest-packed structure, a b
  2r and c 4(2/3)1/2r, where r is the atomic
  radius of the atom.
• a b 90o and g 120o
• The volume of the hexagonal unit cell
• V 8(2)1/2r3

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g120o
a90o
c 4r(2/3)1/2
b90o
b2r
a2r
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X-Ray Analysis of Solids
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Bragg equation nl2dsinq
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X-ray crystal diffraction
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X-ray power diffraction
Cu(111)
Cu(100)
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Band Theory

• Consider a molecule with two atomic orbitals. The
  result must be that two molecular orbitals will
  be formed from these atomic orbitals one bonding
  and one anti-bonding, separated by a certain
  energy.

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Band Theory

• If this is expanded to a molecule with three
  atoms, assuming 1 atomic orbital for each, then
  the result must be that 3 molecular orbitals will
  be formed.

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• Now , let's take it to 10 atoms. This will
  produce 10 molecular orbitals 5 bonding and 5
  anti-bonding. As the number of molecular orbitals
  increases, the energy difference between the
  lowest bonding and the highest anti-bondig
  increases, while the space between each
  individual orbital decreases.

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• Consider a metal with an infinite number of
  atoms. This will form an infinite number of
  molecular orbitals so close together they blur
  into one another forming a band.

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Electron sea model
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Empty MOs
Filled MOs
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Fermi Level/ Fermi Energy

• At absolute zero, electrons pack into the lowest
  available energy states and build up a "Fermi
  sea" of electron energy states. The top of that
  "Fermi sea" of electrons is called the Fermi
  energy or Fermi level.
• The Fermi level is the surface of that sea at
  absolute zero where no electrons will have enough
  energy to rise above the surface.

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Metal Alloys

• Definition A substance that contains a mixture
  of elements and has metallic properties.
• Substitutional alloy
• Interstitial alloy

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Substitutional alloy

• Definition Some of the host metal atoms are
  replaced by other metal atoms of similar size.
• Vacancy Diffusion Vacancy diffusion involves the
  migration of an atom from a typical lattice
  position to a vacancy lattice site.

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Vacancy Diffusion
Atomic migration by a mechanism of
vacancy migration. Materials flow (the atom) is
opposite the vacancy flow direction.
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Interstitial alloy

• Definition The solute metal atoms occupy holes
  in the close-packed structure of the solvent
  metal.
• Interstitial diffusion Interstitial diffusion
  involves the movement of an atom from a typical
  lattice position to an empty space between the
  lattice atoms called interstitial site.

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Interstitial diffusion
Requires small impurity atoms (e.g. C, H, O) to
fit into interstices in host.
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Cu/Zn alloy Substitutional alloy
Fe/C alloy Interstitial alloy
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Covalent crystalsNetwork Atomic Solids Carbon
?60
????
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TEM micrographs of SWNTs
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Superconductivity

• Electrical resistance is zero.
• No wasted heat energy
• 1911 mercury-4 K
• Niobium alloy 23 K
• High-temperature superconductor-perovskites
• YBa2Cu3Ox (x6.527)

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Kelvins Highest knownsuperconducting temperatures
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The structure of quartz
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Examples of silicate anions, all of which are
based on SiO44- tetrahedra
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Two-dimensional reprentations of (a) a quartz
crystal and (b) a quartz glass.
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Semiconductors

• A silicon crystal at any temperature above
  absolute zero temperature, there is a finite
  probability that a few electron can cross the gap
  at 25oC.
• The lattice will be knocked loose from its
  position, leaving behind an electron deficiency
  called a hole".
• At high temperature, more energy is available to
  excite electrons into the conduction band.

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Intrinsic Semiconductor
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Silicon Energy Bands
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The Doped Semiconductors

• The addition of a small percentage of foreign
  atoms in the regular crystal lattice of silicon
  or germanium produces dramatic changes in their
  electrical properties, producing n-type and
  p-type semiconductors.

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The addition of penta-valent impurities such as
Sb, As or P contribute free electrons, greatly
increasing the conductivity of the intrinsic
semiconductor.
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The addition of trivalent impurities such as B,
Al or Ga to an intrinsic semiconductor creates
deficiencies of valence electrons, called
"holes".
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Ionic Solid

• Stable
• High melting substance
• Held by the strong electrostatic forces that
  exists between oppositely charged ions.

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Octahedral Hole

• An octahedral hole lies at the center of six
  equidistant spheres whose centers define an
  octahedron.

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This result shows that an octahedral hole in a
closest packed structure has a radius that is
0.414 times the radius of the packed spheres.
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Tetrahedral Holes

• A tetrahedral hole lies at the center of four
  spheres whose centers form a tetrahedron.

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In a closest packed structure, a tetrahedral hole
has a radius that is 0.225 times the radius of
the packed spheres.
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Cubic Holes
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Structure of Actual Ionic Solid
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The Structure of Alkai Halides
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Lattice DefectsPoint Defects

• Schottky defects A crystal with missing
  particles
• Frenkel defect Crystals in which particles have
  migrated to nonstandard positions.

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