“perfect crystals?”
DESCRIPTION
“Perfect Crystals?”. A Little Thermo Free Energies & Entropy Defects in a “Perfect” Crystal Atoms Vibrating in a Well Diffusion Hopping Concentration Gradients HW #4 Due 2/11/03 Exam #1 Date Change to Thurs. 2/27 from Thurs. 3/6. Thursday, Feb. 4, 2003. - PowerPoint PPT PresentationTRANSCRIPT
“Perfect Crystals?”
• A Little Thermo– Free Energies & Entropy
• Defects in a “Perfect” Crystal Atoms Vibrating in a Well
• Diffusion– Hopping– Concentration Gradients
• HW #4 Due 2/11/03• Exam #1 Date Change to Thurs. 2/27 from
Thurs. 3/6
Thursday,Feb. 4, 2003
MATS275: MATS275: INTRODUCTION TO INTRODUCTION TO
MATERIALS SCIENCEMATERIALS SCIENCE
Crystal Structures
• BCC• FCC• HCP• CsCl• NaCl• Diamond Cubic• Zinc Blende• Fluorite (CaF2)• Crystobalite (SiO2)
• Ice (snowflakes)
Defects
• Zero Dimensional– Vacancies
– Interstitials
– Impurities
• One Dimensional– Dislocations
• Two Dimensional– Planar
• Three Dimensional– Amorphous Mat’ls
Zero Dimensional Defects
These are in order of prevalence in nature from most to least
• V: Vacancy• S: Substitutional Atom• I: Interstitial atom• J: Self-Interstitial atom
These can also be divided into intrinsic defects (native to the material) and extrinsic defects (other atoms than the lattice)
V
s
J
I
Clean Si (111) - 7 x 7reconstruction
Si surface reacted with Br2
(top layer stripped away, Br terminated surface)
Courtesy: J.J. Boland, UNC Dept. of Chemistry
A Little Thermo
• Reaction– Spontaneous if G<0– Exothermic if H<0
G = H - T S
Gibb’s Free Energy
Enthalpy
Entropy
kTH
TS
kTH
kTG
CeeeK
At Equilibrium
kT
ENn D
i exp
and note that ni / N is the concentration of defects. (N is the total number of lattice
sites) So we can write this expression:
kT
E
N
nc Die exp
where ce is the equilibrium concentration.
Vacancies
• The vacancy activation energy for VAl in Aluminum is 0.76 eV. At 400°C, the fraction of Al sites that are vacant is 2.29 x 10-5. What fraction are vacant at 660°C?
241110292C
eN
nCCe
N
n
Al
V
K673
11604eV7605
Al
eVK
kTH
kTH
.exp..
4K933
11604eV760108282411Ce
N
n eVK
kTH
.exp.
.
Aluminum Vacancy Concentration
0.E+00
1.E-04
2.E-04
3.E-04
4.E-04
5.E-04
6.E-04
7.E-04
8.E-04
9.E-04
0 200 400 600 800 1000
Temperature (K)
[V]/
[Al]
mp Al ~ 940 K
Aluminum Vacancy Concentration
1E-1911E-1811E-1711E-1611E-1511E-1411E-1311E-1211E-1111E-101
1E-911E-811E-711E-611E-511E-411E-311E-211E-11
0.1
0 0.01 0.02 0.03 0.04 0.05 0.06
1/T
ln([
V]/
[Al]
)
Impurities
• Add a different atom to the lattice– Form a solid solution
• INTERSTITIAL• RANDOM• ORDERED
Ex) AuCu3 - at T<390°C Cu occupies face centers of FCC, above that Cu and Au are randomly distributed
SUBSTITUTIONAL
Liquid Solutions: Molecular Mixing
H2O Molecule (Solvent)
C2H5OH Molecule (Solute)
Water Alcohol
Mixing on the Molecular Scale
Hume-Rothery Rules
• What can be substitutional?– Atomic size difference <15%– Same crystal structure– Similar electronegativities– Same valence
• EXAMPLE - Cu and Ni– rCu=0.128nm, rNi=0.125 (2.3% diff)
– both fcc
– ENCu=1.90, ENNi=1.91
– Valences: Cu +1 +2, Ni +2
ImpuritiesIonic Materials
• Put Cd in AgCl– Cd wants to be +2, Ag is +1...
Cl2
AgAgClAg ClCdVClAgCd
+2
-1
T Dependence of D
1.E-27
1.E-25
1.E-23
1.E-21
1.E-19
1.E-17
1.E-15
1.E-13
1.E-11
1.E-09
1.E-07
1.E-05
1.E-03
1.E-01
4.0E-04 6.0E-04 8.0E-04 1.0E-03 1.2E-03 1.4E-03
1/T
ln(D
)
H in Fe
C in Fe
Fe in Fe
Al in Al2O3
O in Al2O3