Bonding in solidscfs3.tistory.com/upload_control/download.blog?f... · 13 Fermi level ¥N electrons...
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Bonding in solids
Types of solids
• metallic
• ionic
• covalent
• molecular
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Types of Crystals
Metallic Crystals
• Lattice points occupied by metal atoms
• Held together by metallic bonds
• Soft to hard, low to high melting point
• Good conductors of heat and electricity
11.6
Cross Section of a Metallic Crystal
nucleus &
inner shell e-
mobile “sea”
of e-
Types of Crystals
Ionic Crystals
• Lattice points occupied by cations and anions
• Held together by electrostatic attraction
• Hard, brittle, high melting point
• Poor conductor of heat and electricity
CsCl ZnS CaF2
11.6
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Types of Crystals
Covalent Crystals
• Lattice points occupied by atoms
• Held together by covalent bonds
• Hard, high melting point
• Poor conductor of heat and electricity
11.6diamond graphite
carbon
atoms
Types of Crystals
Molecular Crystals
• Lattice points occupied by molecules
• Held together by intermolecular forces
• Soft, low melting point
• Poor conductor of heat and electricity
11.6
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!"# $%:&'( 3)* +"
7
electronic conductors
8
conductor
semiconductor
insulator
metals
electrical conductivity decreases
with increasing temperature,
whereas in semiconductors,
electrical conductivity increases
with increasing temperature.
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band theory of solids
9
formation of a band
10
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overlap of orbitals = band
11
occupation of bands
12
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13
Fermi level
•N electrons for N MO’s
•The hightest occupied MO
PHYS 624: Electronic Band Structure of Solids 14
Is there a Fermi energy of intrinsic Semiconductors?
•If is defined as the energy separating the
highest occupied from the lowest unoccupied level,
then it is not uniquely specified in a solid with an
energy gap, since any energy in the gap meets this
test.
•People nevertheless speak of “the Fermi energy”
on an intrinsic semiconductor. What they mean is
the chemical potential, which is well defined at any
non-zero temperature. As , the chemical
potential of a solid with an energy gap approaches
the energy of the middle of the gap and one
sometimes finds it asserted that this is the “Fermi
energy”. With either the correct of colloquial
definition, does not have a solution in a
solid with a gap, which therefore has no Fermi
surface!
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PHYS 624: Electronic Band Structure of Solids 15
p-type and n-type semiconductors
!PURE
DOPPED"
thermal excitation
• when 2N e- are present, the band is full and it is an insulator at T = 0
• When T>0, there is thermal excitation to form a semiconductor
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P-type, N-type semiconductor
17
dopants can trap electrons
dopants can carry excess electrons
Light Emitting Diode
LED vs. Laser Diode
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• standard enthalpy change accompanying the separation of the species that compose the solid
Lattice enthalpy
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The Solution Process for NaCl
!Hsoln = Step 1 + Step 2 = 788 – 784 = 4 kJ/mol6.7
Born-Haber cycle
crystal structure
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A crystalline solid possesses rigid and long-range order. In a
crystalline solid, atoms, molecules or ions occupy specific
(predictable) positions.
An amorphous solid does not possess a well-defined
arrangement and long-range molecular order.
A unit cell is the basic repeating structural unit of a crystalline
solid.
Unit Cell
lattice
point
Unit cells in 3 dimensions 11.4
At lattice points:
• Atoms
• Molecules
• Ions
11.4
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The identification of crystal
planes - intersection distances
(1a, 1b, infinity c)
(3a, 2b, infinity c)
(-1a, 1b, infinity c)
(infinity a, 1b, infinity c)
Miller indices (hkl)
26
,-. /01 2345-. 678
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11.5
Formation of X-ray
• bremsstrahlung (brake ray)
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Extra distance = BC + CD = 2d sin" = n# (Bragg Equation)11.5
The Bragg Law
glancing angle
X rays of wavelength 0.154 nm are diffracted from a
crystal at an angle of 14.170. Assuming that n = 1,
what is the distance (in pm) between layers in the
crystal?
n# = 2d sin " n = 1 " = 14.170 # = 0.154 nm = 154 pm
d =n
2si
n"
=1 x 154 pm
2 x sin14.17= 77.0 pm
11.5
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William Henry
Bragg
William Lawrence
Bragg
31
Typical X-ray powder diffraction
pattern
32
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Typical Structures
11.4
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Fig. 11.29
11.4
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11.4
Shared by 8
unit cells
Shared by 2
unit cells
11.4
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11.4
1 atom/unit cell
(8 x 1/8 = 1)
2 atoms/unit cell
(8 x 1/8 + 1 = 2)
4 atoms/unit cell
(8 x 1/8 + 6 x 1/2 = 4)
11.4
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When silver crystallizes, it forms face-centered cubic
cells. The unit cell edge length is 409 pm. Calculate
the density of silver.
d = m
VV = a3 = (409 pm)3 = 6.83 x 10-23 cm3
4 atoms/unit cell in a face-centered cubic cell
m = 4 Ag atoms107.9 g
mole Agx
1 mole Ag
6.022 x 1023 atomsx = 7.17 x 10-22 g
d = m
V
7.17 x 10-22 g
6.83 x 10-23 cm3= = 10.5 g/cm3
11.4
ABA vs. ABC packing
42
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hcp vs. ccp
• hexagonal close-packed structure
– ABA
– coordination number 12
• cubic close-packed structure
– ABC
– coordination number 12
43
Structures of ionic crystals
44
6-coordinated rock-salt structure8-coordinated CsCl structure
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Fig. 11.25
Fig. 11.27
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radius-ratio rule
• radius ratio = r(smaller)/r(larger)
• ratio = 0.732
– CsCl structure
• 0.414 < ratio < 0.732
– rock salt structure
– 6 coordination
• ratio < 0.414
– 4 coordination
– ZnS (sphalerite)47
Fig. 11.p460top
High temperatre
superconductor :
HTSC
YBa2Cu3O7 :
123 compound
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amorphous solid
• 9$%: 1; <#
– =;> ?@A BCDE 1;( FG "HI
*"J !"> FGDK L7 MN
– long range OPQR FGS TU
– (V) WH
49
Fig. 11.31
quartz crystal glass
2D structures of SiO2