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Dr. S. M. Condren
Chapter 15
The Liquid State, The Solid State, and Modern Materials
Dr. S. M. Condren
Properties of Liquids
surface tension - A property of liquids arising from unbalanced molecular cohesive forces at or near the surface
Dr. S. M. Condren
Properties of Liquids
surface tension
capillary action - phenomenon in which the surface of a liquid is elevated or depressed when it comes in contact with a solid
Dr. S. M. Condren
Properties of Liquidssurface tension
capillary action
viscosity
– resistance of a fluid to flow
– resistance acts against the motion of any solid object through the fluid, and also against motion of the fluid itself past stationary obstacles
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Compared to the average energy, those molecules which escape the surface of a liquid are
lower in energy
same energy
higher in energy
Dr. S. M. Condren
Phase Changes
Evaporation
phase change from liquid to gas
Condensation
phase change from gas to liquid
Dr. S. M. Condren
Vapor Pressure vs. Temperature
p vs. t(oC)
exponential function as t increases, p increases
Dr. S. M. Condren
Dr. S. M. Condren
Pressure vs. Temperature
0
200
400
600
800
1000
1200
0 20 40 60 80 100 120
Temperature, C
Va
po
r P
ress
ure
, to
rr
Dr. S. M. Condren
ln P vs 1/T
0.5
1
1.5
2
2.5
3
0.0025 0.0027 0.0029 0.0031 0.0033 0.0035 0.0037 0.0039
1/T, 1/K
ln P
Dr. S. M. Condren
Vapor Pressure vs. Temperature
Clausius-Clapeyron Equation
ln(P2/P1)=(Hvap/R)(1/T1 - 1/T2)
Dr. S. M. Condren
Properties of Liquidsboiling point
• the temperature at which its vapor pressure is equal to the local atmospheric pressure
normal boiling point
• the temperature at which its vapor pressure is equal to one atmospheric pressure
Dr. S. M. Condren
Properties of Liquids
liquid-vapor equilibirum
• both liquid and vapor of the liquid present in the same container uder stable conditions
vapor pressure
• The pressure exerted by a vapor in equilibrium with its solid or liquid phase.
Dr. S. M. Condren
Properties of Liquids
enthalpy of vaporization - The amount of heat required to convert a unit mass of a liquid at its boiling point into vapor without an increase in temperature.
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Phase Changes
Melting
phase change from solid to liquid
Freezing
phase change from liquid to solid
melting point(freezing point)
temperature at which a liquid congeals into the solid state at a given pressure
Dr. S. M. Condren
Dr. S. M. Condren
Phase Changes
Melting and Freezing
enthalpy of fusion - heat absorbed by the substance in changing its state without raising its temperature
Dr. S. M. Condren
Dr. S. M. Condren
Phase ChangesLiquid Crystals
• substance that behaves like both a liquid and a solid
• by applying a small electric field, certain liquid crystal substances gain the ability to rotate polarized light. These types of liquid crystals are used to construct displays used in digital watches, calculators, miniature television sets, portable computers, and other items
Dr. S. M. Condren
Dr. S. M. Condren
Phase Diagram - General
P
T
Solid
Gas
Liquid
1 atm mpnbp
triple point
critical point
x sublimation point
x x
Dr. S. M. Condren
Phase Diagrams
label axes
label phase regions
label: triple point
critical point
melting point
boiling point
sublimation point
Dr. S. M. Condren
Critical Point
• The temperature and pressure at which the liquid and gaseous phases of a pure stable substance become identical.
• The critical temperature of a gas is the maximum temperature at which the gas can be liquefied; the critical pressure is the pressure necessary to liquefy the gas at the critical temperature.
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Solids
• Crystals
• X-ray Diffraction
• Bragg's Law
Dr. S. M. Condren
Solids
Crystals - A homogenous solid formed by a repeating, three-dimensional pattern of atoms, ions, or molecules and having fixed distances between constituent parts.
Dr. S. M. Condren
SolidsX-ray Diffraction - When an X-ray beam
bombards a crystal, the atomic structure of the crystal causes the beam to scatter in a specific pattern. This phenomenon, known as X-ray diffraction, occurs when the wavelength of the X rays and the distances between atoms in the crystal are of similar magnitude.
Dr. S. M. Condren
Solids
Bragg's Law - The fundamental law of x-ray crystallography, n = 2dsin, where n is an integer, is the wavelength of a beam of x-rays incident on a crystal with lattice planes separated by distance d, and is the Bragg angle.
[After Sir William Henry Bragg and Sir William Lawrence Bragg.]
Dr. S. M. Condren
Structure Determination
High Voltage
X-Ray DiffractionX-ray Tube
Lead Screen
X-ray Beam
Crystal
Photographic Plate
Projection Screen
Visible Light Laser 35mm slide
Optical Transforms
L
X
Dr. S. M. Condren
Diffraction Conditions
Solid State Resources CD-ROM
Movies
Chapter 4
Dr. S. M. Condren
Diffraction ConditionsFraunhofer diffraction Bragg diffraction
For constructive interference, d sin = n
For constructive interference, 2(d sin ) = n
}d
d }}
d
d sin
}
}d
d sin d sin
Dr. S. M. Condren
Solids
Bragg's Law
n = 2d sinwhere n => order of diffraction
=> X-ray wavelength
d => spacing between layers
of atom
=> angle of diffraction
Dr. S. M. Condren
EXAMPLE
What is the spacing between copper atoms if X-ray radiation of wavelength 1.54diffracts in the second order at 58.42°?
n = 2 = 1.54A = 58.42° d = ?
n = 2d sin
d = (n)/2sin = (2*1.54A)/(2*sin(58.42°))
= 1.54A/0.852 = 1.81
Dr. S. M. Condren
Dr. S. M. Condren
Ionic Solids
cations and anions form the points in the 3-D structure
• NaCl
Dr. S. M. Condren
Metallic Solids
atoms of the metal form the 3-D points in the structure
• iron
• copper
Dr. S. M. Condren
Molecular Solids
molecules form point in the 3-D structure
• sugar
Dr. S. M. Condren
Network Covalent Solids
atoms covalently bonded to the surrounding atoms in a 3-D network
• diamond
• quartz
Dr. S. M. Condren
Lattice and Units Cells
Lattices
7 types
4 most common types: cubic
orthorhombic
monoclinic
triclinic
Dr. S. M. Condren
Unit Cells?
Dr. S. M. Condren
Which are Unit Cells?
Dr. S. M. Condren
Unit Cells of Metals
cubic: a = b = c
= = = 90°
simple cubic (primitive cubic) atoms only at corners of cube
body centered cubic (BCC) atoms at the corners and at the center of the body.
face-centered cubic (FCC) atoms at the corners and at the center of all 6 faces, same as cubic close-packed.
Dr. S. M. Condren
Dr. S. M. Condren
Structures of Metallic Elements
Ru
H
Li
Na
K
Rb
Cs
Fr
Be
Mg
Ca
Sr
Ba
Ra
Sc
Y
La
Ac
Ti
Zr
Hf
V
Nb
Ta
Cr
Mo
W
Mn
Tc
Re
Fe
Os
Co
Ir
Rh
Ni
Pd
Pt
Cu
Ag
Au
Zn
Cd
Hg
B
Al
Ga
In
Tl
C
Si
Ge
Sn
Pb
N
P
As
Sb
Bi
O
S
Se
Te
Po
F
Cl
Br
I
At
Ne
Ar
Kr
Xe
Rn
He
Primitive Cubic
Body Centered Cubic
Cubic close packing(Face centered cubic)
Hexagonal close packing
Dr. S. M. Condren
Number of Atoms per Unit Cell
- atoms at corner of unit cell count 1/8
- atoms at center of a face count 1/2
- atoms at center of the body count 1
Dr. S. M. Condren
Dr. S. M. Condren
Primitive Cubic
use of an orange to show why only 1/8 atom at corners of a unit cell
Solid State Resources CD-ROM
Chapter 3
Movie Orange Slicing
Dr. S. M. Condren
Number of Atoms per Unit Cell
primitive cubic => 8(1/8) = 1
BCC => 8(1/8) + 1 = 2
FCC => 8(1/8) + 6(1/2) = 4
Dr. S. M. Condren
Combinations of ElementsElement Combination Likely Structure
Nonmetal and nonmetal Discrete moleculeCO2, PCl3, NO
Metal and metal Extended (alloys)CuZn (brass), NiTi
Metal and nonmetal Extended (salts)NaCl, ZnS, CaTiO3
Dr. S. M. Condren
Unit Cells of Compounds
cubic: a = b = c
= = = 90°
face-centered cubic (FCC) =>NaCl, LiCl, ZnS(zinc blend, S ions in FCC with Zn ions in tetrahedral holes)
Dr. S. M. Condren
Dr. S. M. Condren
NaCl Stoichiometry
8 corners X 18 12 edges X
14
6 faces X 12 1 center X 1
---------------- ----------------4 Cl- ions 4 Na+ ions
z=0, 1 z=1/2
NaCl has 1:1 stoichiometry!
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Why is CsCl not
body-centered cubic (BCC)?
Dr. S. M. Condren
Unit Cells of Compounds
orthorhombic: abc
= = = 90°
monoclinic: a b c
= = 90°
> 90°
triclinic: ab c
90°
Dr. S. M. Condren
EXAMPLE
Metallic gold crystallizes in the face-centered cubic lattice. The length of the cubic unit cell is 4.070A. What is the closest distance between gold atoms?
a = 4.070 r = ? closest distance = 2r
Dr. S. M. Condren
Face-Centered-Cubic Unit Cell
df = face diagonal
r = radius of atom
df = 4r
a = edge
a2 + a2 = df2
2a2 = (4r)2
r = (a*21/2 )/4
Dr. S. M. Condren
EXAMPLEMetallic gold crystallizes in the face-centered cubic lattice. The length of the cubic unit cell is 4.070A. What is the closest distance between gold atoms?
a = 4.070A r = ? closest distance = 2r
4r = a21/2 => r = a21/2/4
r = (4.070A*1.414)/4 = 1.44A
closest distance = 2(1.44A) = 2.88A
Dr. S. M. Condren
Molecular Substances
Common Properties
- nonconductors of electricity when pure
- insoluble in water but soluble in non-polar solvents
- volatile, appreciable vapor pressure at room temperature
- low melting and boiling points
Dr. S. M. Condren
Metals
Common Properties
– Nonvolatile.
– Insoluble in water and other common solvents.
Dr. S. M. Condren
Dr. S. M. Condren
Network Covalent Substances
graphite => sp2 hybrid C, planar
Dr. S. M. Condren
Dr. S. M. Condren
Network Covalent Substances
diamond => sp3 hybrid C, 3D
Dr. S. M. Condren
Dr. S. M. Condren
Network Covalent Substances
silicon dioxide => sp3 Si, 4 O around each
Si
=> sp3 O, 4 Si around each
Si
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Amorphous Solids (Glasses)
• lacking definite form
• no long range ordering in the structure