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Electronic Structure of
Material Grain Boundaries and Interfaces
A. Stability of Silver
Ultra-Thin Films on GaAs (110)
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(a) Motivation
- Ag/GaAs (110)
- Two-step deposition:
- Deposit Ag on to chilled substrate ~100K. (Ag
Nanoclusters form)
- Slowly anneal to RT (300 K)
- Film morphology dependent on amount of Ag deposited:
- Ag Thickness < 15 Å → Islands
- Ag Thickness = 15 Å → Flat film
- Ag Thickness > 15 Å → Rough film
- Ag has different preferential thickness on different
substrates
- Ag/GaP (110) ~ 17 Å
- Ag/GaAs (110) ~ 15 Å
- Ag/GaSb (110) ~ 6 Å
- Why is this interesting?
- Practical → Device contacts
- Scientific → Self assembly
- Uses → Method used to grow buffer layers for Fe on
GaAs
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(b) Methodology
- One model that attempts to explain the preferential
stability of some metal films is the Electronic
Growth Model (EGM).
- Density functional theory (DFT) within the CASTEP
program:
- GGA-PW91
- ultrasoft pseudopotentials
- K.E. cutoff 340 eV
- k-point spacing:
- 0.10 Å-1 (initial)
0.05 Å-1 (to evaluate E)
- Tolerances:
- DE = 5x10-6 eV/atom
- DFRMS = 0.100 eV/Å
- DDRMS = 0.001 Å
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Convergence of the
total energy for GaAs as a function of kinetic energy cutoff. FFT grid
is 36×36×36 and lattice parameters are fixed at
experimental values of 5.635 Å.
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(c) Results
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i) Optimizing the Unit Cell
- The 1×5 near coincident size lattice (NCSL)
unit cell is strain free, but is too large to handle computationally.
- An approximate unit cell is needed to calculate
properties of multilayer systems.
- Calculated adhesion
energies of approximate unit cells are dependent on lateral
interactions.
- The 1×2 NCSL provides the best combination
of accuracy and affordability.
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(d) Conclusions
- In the EGM simple calculations are performed to determine
the stability of the metallic overlayer.
- First principles calculations on Ag/GaAs show the
importance of accounting for the resulting structural changes caused by
- the presence of the interface
- the overlayers response to the surrounding electronic
structure
- Both quantities act to strain the overlayer from ideal
positions.
- These structural changes are not accounted for in simple
electron gas models of metals.
B. Doped and Pristine Cubic-ZrO2 Tilt Grain Boundaries
(a) Motivation
- Impurity and point defect segregation to ionic grain boundaries and surfaces is known to influence the physical properties of ceramic materials.
- Characterization of these defects is essential to tailor metal oxides for technological applications.
- Ab initio calculations can help us better understand the driving forces that lead to point defect segregation in metal oxides.
(b) Computational Details
- Density functional theory
- Local density approximation (LDA)
- Nonlocal, norm-conserving pseudopotentials and plane wave expansions with kinetic energy cutoffs of 600 eV
| Lattice Parameter (Å) | LDA-600 eV cutoff | LDA-800 eV cutoff | LDA-1000 eV cutoff | GGA-600 eV cutoff | Expt. data |
| Lattice constant | 5.15 | 5.15 | 5.16 | 5.16 | 5.09 |
| Zr-O length | 2.23 | 2.23 | 2.24 | 2.24 | 2.21 |
| Zr-Zr length | 3.64 | 3.64 | 3.65 | 3.65 | 3.60 |
| Energy/ZrO2 (eV) | 956.39 | 959.52 | 961.13 | 961.07 | |
(c) Calculations
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i) Grain Boundary Energies
| Model | Number of atoms | Grain boundary energy
(eV/Å2) | Grain boundary energy
(relaxed)
(eV/Å2) |
| 1 |  | 144 | 0.4738±0.0014 | |
| 2 |  | 132 | 0.2199±0.0013 | |
| 3 |  | 132 | 0.3791±0.0013 | 0.0449±0.0013 |
| 4 |  | 132 | 0.3894±0.0013 | |
| 5 |  | 132 | 0.2302±0.0013 | ?0.0449±0.0013 |
ii) Segregation of Y to Relaxed ZrO2 Σ5(310)/[001] Tilt Grain Boundary
Esegregation = (EYGB - EY0) - (EGB - E0)
| Substitution Site | Segregation Energy
(eV/atom) |
| Site A | -9.87 |
| Site B | -13.78 |
| Site C | -4.30 |
| Site D | -9.28 |
| Site E | -0.08 |
(d) Conclusions
- The O-terminated Ni(111)/ZrO2(100) interface is more stable then the Zr-terminated interface according to our preliminary first principles calculations. We are working to complete these preliminary calculations and consider the effect of Y3+ doping on the results.
- Five pristine ZrO2 grain boundary model structures are examined and the most energetically favorable models are determined.
- Lowest energy models relax to the same structure that agrees well with experimental Z-contrast image data.
- Segregation energies at the grain boundaries after Y3+ doping are also determined and a preferred doping site with the lowest segregation energy is identified.
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