Transcript Solids and Surfaces - Foord @ chem.ox.ac.uk

Solids and Surfaces
Prof. John Foord
Eight lectures
3rd year PTCL ‘core’
(for more (!), see PTCL option 1
“Interfaces” in HT )
What is the interest in
“Solids”?
• “Solids” are an important application of
chemistry e.g.
– Structural; steel, concrete, glass, plastics
etc. etc.
– Functional; semiconductors,
superconductors, magnetic, optical,
coatings, sensors etc. etc.
The properties of solids are
controlled by the chemical
bonding
• Strength, hardness,
melting point etc.
• Electrical properties
• Optical and Magnetic
• Changes with
temperature and
pressure
Crown jewels
“Great Star of
Africa” 530 Carats
Solid Surfaces
•Adhesion and
coatings
•Functional solid
state devices
•Nanotechnology
•Electrochemistry
•Detergent Action
•Catalysis
•Corrosion
Etc. Etc.
Aims of the course
1. Understanding some properties of
solids in a physical chemical
framework.
{Revision of some statistical mechanics}
2. An introduction to surface chemistry
•
Chemistry at the solid-gas interface
{Foundations for PTCL Option 1}
Books (Solids)
• Solid state inorganic texts, West etc.
• Smart and Moore, “Solid State
Chemistry”
• Mandl, “Statistical Physics”
• Elliott, “The Physics and Chemistry of
Solids”
Solids
1. Heat capacity of solids
– Solids possess a significant heat capacity
even at low T
– Must have a different origin to the that for
gases, which mainly stems from
translation and rotation at room T
– Lattice vibrations
– [Electronic excitations in metals]
Early ideas - Dulong and Petit
• C for many monatomic solids is around
3R
[Aside: for a gas Cp-Cv = R ; for a solid
the two heat capacities are virtually
identical since solids have small
expansion effects]
• Each atom is
vibrating in the
x,y,z direction
• From energy
equipartition
expect C= 3R
• Deviations at low
T later ascribed to
“quantum” effects
Element
Cp
Element
Cp
Al
24.4
S
22.7
Au
25.4
Si
19.9
Cu
24.5
C
6.1
(diamond)
Formal model - Einstein theory
for a pure monatomic solid
• Assume each atom in the
solid vibrates
independently in three
independent directions
x,y,z
• So that there are 3NAvo
oscillators…
• ..and they will all have the
same frequency
• Assume the vibrations are
harmonic
• Reminder about stat. mechs
 lnq 
U  NkT 

 T 
where
E i 
 m ol. partition function
q   gi exp
kT 

i
2
and

C  U
 heat capacity

T
• For a single oscillator


E i  v + 1 h or w.r.t. zero point energy (easier)
2
E i  vh v = 0,1,2 .......
qvib  e

0hv
kT
e
hv
kT
e
1
hv 

1 e kT 


2hv
kT
 .....
• And need the differential of q w.r.t. T


hv
q 1
where x  e
and dx   2 x
1 x
dT kT 
q  1 dx  1  hv x




2
2
2
T 1 x  dT  1 x  kT 
hv
kT
So we know what q and its differential is.
We can now get the energy
 lnq 



q
2  1 




U  NkT 
 3N AvokT
 q  T 
 T 
2
substitute in the previous expressions
for q and the different ial gives
hv 

3N Avo hve kT  3N hv



Avo 
U
 hv
hv
1 e kT
e kT 1
• And finally differentiate U w.r.t. to T to
get the heat capacity.
1
hv hv kt
C  3N Avohv
e
2
2
hv

e kt 1
 kT




hv
2 
 hv 
e kt 
 3N Avok  
2 
hv
kT  
e kt 1
 
 

E
 E 2 e T
 3R 
 T    E 2
e T 1


where  E  hv /k
Notes
• Qualitatively works
quite well
• Hi T  3R
(Dulong/Petit)
Lo T 0
• Different crystals are
reflected by differing
Einstein T (masses
and bond strengths)