Transcript High-Efficiency, Scalable Solar Cells of Earth

3.40/22.71
Summary of 10/23/2012
Sergio Castellanos
Mechanical Engineering Department
Massachusetts Institute of Technology, Cambridge, MA (USA)
Stress-Strain
σ
A
 Constitutive Relations:
 Strength [A]
 Ductility [B]
 Toughness [C]
C
B
σ
ε
 Upon unloading
 εtotal = εplastic + εelastic
 I.e. Springback
E [Pa]
εplastic εelastic
ε
 Hysteresis Loop.- Dissipation
converts useful mechanical
energy into heat.
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Inelastic Processes
• Fracture
Periodic
Slip Displacement
Total Metal-Metal Coordination remains
constant
Potential
Energy (V)
Potential
Energy (V)
• Plasticity
• Phase
Transformatio
n
Non-Periodic
V”=0
Cleavage
Opening
One-off dissipation mechanism
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Inelastic Processes in Metals
 Easier to follow the path of plasticity (sustainable dissipation)
 Fracture toughness: Resistance against crack propagation
Metallic
Ionic
Covalent
Material
KIC-Max [MPa/m0.5]
Cu
107
Ag
105
Fe
150
Ni
150
W
150
SiC
5.1
B-Si3N4
10
TiC
3
MgO
2.8
NaCl
0.19
S. Ogata and J. Li “Toughness scale from first principles” J. Appl. Phys. 106, 113534 (2009)
3
Inelastic Processes in Metals
 Easier to follow the path of plasticity (sustainable dissipation)
 Fracture toughness: Resistance against crack propagation
•

K IC
˜
K
1
B  6
B=Bulk Modulus
G=Shear Modulus
Ω=Cell Volume
• KIC function of:
- Bonding energy
- Ideal strength
- Bandgap
- Ionicity
Shear Weak = Energy  Dislocation Spread =
KIC
S. Ogata and J. Li “Toughness scale from first principles” J. Appl. Phys. 106, (2009) 113534
4
Flow in the presence of Diffusion: Creep
Input
Output
σ
…
ε
ε(t-to)
σo
εo
to
t
to
t
 Different stages on Creep:
1.
2.
3.
Progression towards steady state flow (s.s. dislocation density – gen.)
Static recovery counterbalances new dislocation generation
Terminal failure (e.g. necking in tension test)
5
Deformation-Mechanism Map
Frost, Harold Jefferson, and M. F. Ashby. "Deformation-mechanism maps: The plasticity and creep of metals and
ceramics.” Pergamon Press, Oxford, UK (1982).
6
Deformation-Mechanism Map
Limit on Ideal Shear Strength
Low T plasticity by dislocation glide
and twinning
Displacive
Limited by:
Discrete obstacles
Lattice Friction
Mixed
Diffusional
Power Law by Glide / Glide + Climb
Limited by:
Glide processes
Lattice-Diffusion controlled climb
Core-Diffusion controlled climb
Breakdown
Harper-Dorn
Dynamic Recristallization
Diffusional Flow
Limited by:
Lattice-Diffusion (Nabarro-Herring)
GB Diffusion (Coble)
Interface-reaction controlled
Frost, Harold Jefferson, and M. F. Ashby. "Deformation-mechanism maps: The plasticity and creep of metals and
ceramics.” Pergamon Press, Oxford, UK (1982).
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Diffusional
Coble
(Surface)
•Does not involve
dislocations.
Nabarro-Herring
(Lattice)
• Through bulk or
along free surfaces
, Low T
Dsurface>>Dbulk
, High T
Dsurface comparable Dbulk
-
[1] Image from http://en.wikipedia.org/wiki/Frank_Nabarro
[2] Image from http://news.stanford.edu/news/2009/july27/herring-physics-obit-073109.html
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[3] Brown, L.M. “Frank Reginald Nunes Nabarro MBE” Biographical Memoirs of Fellows of the Royal Society (2009)
Hall-Petch: Smaller is Stronger
Copper
M.A. Meyers et al. “Mechanical Properties of nanocrystalline materials” Progress in Materials Science 51 (2006),
427-556 9
Surface Dislocation Nucleation
 Nucleation Stress
value computed
 Transition
predicted from
collective
dislocation
dynamics to
signle dislocation
nucleation
 Geomtry = Long
Range Elastic
Interaction
(Corner/Image)
T. Zhu et al. “Temperature and Strain-Rate Dependence of Surface Dislocation Nucleation” PRL 100, (2008) 025502
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Ultra-Strength Materials
 crit 
 elastic
 shear _ ideal
G

10
10
1

 1%
100
 This implies that properties
(thermal conductivity,
transmittance, etc) can be
modified while in the elastic
regime.
Elastic-Strain Engineering
Hydrostatic: phase transformation
(Ppty)
d(Ppty)   
0


[1]
[1] Yanming Ma et al. “Transparent Dense Sodium” Nature 458, (2009) 182
[2] Images from ti-fr.com, nutritionresearchcenter.org
DoE
(Taguchi
)
[2]
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Elastic-Strain Engineering
E
M Γ K M
Synthesize
• Graphene
• Carbon Nanotubes
• Bulk Nanocrystals
Strain and
Measure Force
• AFM
Measure
Strain
• Synchrotron
• In-situ TEM
Numerical
Prediction
• DFT
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Cool (or Hot?) Application: Photovoltaics
[1]
Challenges:
- Thermalization Losses
- Non-Absorption Losses
[1] Image: http://en.wikibooks.org/wiki/Microtechnology/Semiconductors
[2] Ji Feng et al. “Strain-Engineered Artificial Atom as a Broad-Spectrum Solar Energy Funnel” Nature (2012)
Accepted
[2]
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