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Solids

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Title: Solids


1
Chapter 16
  • Solids

2
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.

3
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.

4
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

5
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.

6
 Structure of Metals
  • Simple Cubic
  • (????)
  • Hexagonal Closest Packed (HCP)
  • (??????)
  • Face-Centered Cubic (FCC)
  • (????)
  • Body-Centered Cubic (BCC)
  • (????)

7
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.

8
  • 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.

9
  • 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.

10
ABABA.. packing sequence of the hcp structure
ABCABC.. packing sequence of the fcc structure
11
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12
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.

13
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.

14
  • 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.

15
c 4r(2/3)1/2
b2r
a2r
16
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17
An actual STM image of a Ni surface. Note the
hexagonal arrangement of atoms. This image is the
property of IBM Corporation.
18
Fcc structure
  • The ..ABCABC.. packing sequence of the fcc
  • structure gives rise to a three-dimensional
  • structure with cubic symmetry.

19
FCC structure
20
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22
  • Coordination Numbers (CN)12
  • Net number of spheres in unit cell
    (81/8)(61/2)4

23
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.

24
BCC structure
25
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26
  • Coordination Numbers (CN)8
  • Net number of spheres in unit cell
    (81/8)(11)2

27
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28
Packing Efficiency
  • For a FCC structure
  • For a BCC structure

29
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.

30
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

31
g120o
a90o
c 4r(2/3)1/2
b90o
b2r
a2r
32
X-Ray Analysis of Solids
33
Bragg equation nl2dsinq
34
X-ray crystal diffraction
35
X-ray power diffraction
Cu(111)
Cu(100)
36
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.

37
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.

38
  • 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.

39
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40
  • 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.

41
Electron sea model
42
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43
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44
Empty MOs
Filled MOs
45
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46
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.

47
Metal Alloys
  • Definition A substance that contains a mixture
    of elements and has metallic properties.
  • Substitutional alloy
  • Interstitial alloy

48
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.

49
Vacancy Diffusion
Atomic migration by a mechanism of
vacancy migration. Materials flow (the atom) is
opposite the vacancy flow direction.
50
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.

51
Interstitial diffusion
Requires small impurity atoms (e.g. C, H, O) to
fit into interstices in host.
52
Cu/Zn alloy Substitutional alloy
Fe/C alloy Interstitial alloy
53
Covalent crystalsNetwork Atomic Solids Carbon
?60
????
54
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55
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56
TEM micrographs of SWNTs
57
Superconductivity
  • Electrical resistance is zero.
  • No wasted heat energy
  • 1911 mercury-4 K
  • Niobium alloy 23 K
  • High-temperature superconductor-perovskites
  • YBa2Cu3Ox (x6.527)

58
Kelvins Highest knownsuperconducting temperatures
59
The structure of quartz
60
Examples of silicate anions, all of which are
based on SiO44- tetrahedra
61
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62
Two-dimensional reprentations of (a) a quartz
crystal and (b) a quartz glass.
63
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.

64
Intrinsic Semiconductor
65
Silicon Energy Bands
66
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.

67
The addition of penta-valent impurities such as
Sb, As or P contribute free electrons, greatly
increasing the conductivity of the intrinsic
semiconductor.
68
The addition of trivalent impurities such as B,
Al or Ga to an intrinsic semiconductor creates
deficiencies of valence electrons, called
"holes".
69
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70
Ionic Solid
  • Stable
  • High melting substance
  • Held by the strong electrostatic forces that
    exists between oppositely charged ions.

71
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72
Octahedral Hole
  • An octahedral hole lies at the center of six
    equidistant spheres whose centers define an
    octahedron.

73
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.
74
Tetrahedral Holes
  • A tetrahedral hole lies at the center of four
    spheres whose centers form a tetrahedron.

75
In a closest packed structure, a tetrahedral hole
has a radius that is 0.225 times the radius of
the packed spheres.
76
Cubic Holes
77
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79
Structure of Actual Ionic Solid
80
The Structure of Alkai Halides
81
Lattice DefectsPoint Defects
  • Schottky defects A crystal with missing
    particles
  • Frenkel defect Crystals in which particles have
    migrated to nonstandard positions.

82
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