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Atomistic Simulation &Energy Research Group
Vibrationally Accurate Interatomic PotentialsAndrew Rohskopf
Advisor: Asegun Henry
Massachusetts Institute of Technology
Department of Mechanical Engineering
Tuesday, August 20, 2019
Atomistic Simulation &Energy Research Group
Modes (Phonons) & MD Simulations
2
0
0Q Q t dt
mod ,1 mod ,2 mod ,3e e e
QHeat flux
Thermal conductivity
Mode 1 Mode 2 Mode 3
Atomistic Simulation &Energy Research Group
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Vibrational Modes & Heat Transfer
Aids heat transfer Inhibits heat transfer
https://lifestyleremodeling.com
Gifs courtesy of Freddy DeAngelis
Atomistic Simulation &Energy Research Group
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Modes at Interfaces
Interface
Extended Modes
Partially Extended Modes
Isolated Modes
Interfacial Modes
Gifs courtesy of Kiarash Gordiz
Z. J. Liu, T. et al, Monolithic Integration of Algan/Gan Hemt on Led by Mocvd, IEEE Electron Device Letters, 35, 330-332 (2014).
Atomistic Simulation &Energy Research Group
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Modes & Energy Conversion
B. Yu et al, Enhancement of Thermoelectric Properties by Modulation-Doping in Silicon Germanium Alloy Nanocomposites, Nano letters, 12, 2077-2082 (2012).
Thermoelectric generator
Gifs courtesy of Hamid Seyf
Atomistic Simulation &Energy Research Group
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Modes Make Things Happen
MD @ T=300KMD @ T=300K + energy input to
a few selected modesLi
P
O
Ge
Movies courtesy of Kiarash Gordiz
Atomistic Simulation &Energy Research Group
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Phonon Theory
i i ij jj
mu K u equilibrium
i i iu x x
Fre
qu
en
cy
Wave-vector k
Phonon DispersionMass X Acceleration = Harmonic Force
Atomistic Simulation &Energy Research Group Taylor Expansion Potential
8W.Weber, Phys. Rev .B 15, 4789 (1977).
Silicon Phonon Dispersion
1 1
2 3!ij i j ijk i j kij ijk
E K u u K u u u
2
iji j
EK
u u
3
ijki j k
EK
u u u
equilibriumi i iu x x
Wave vector
Atomistic Simulation &Energy Research Group Current Potentials
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Silicon Phonon Dispersion
Wave vector
Tersoff, J. J. P. R. B. 38, 9902 (1988). Tersoff, J. J. P. R. B. 39, 5566 (1989). Tersoff, J. J. P. r. l. 64, 1757 (1990). Munetoh, S., et al. 39, 334-339 (2007). Stillinger, F. H. & Weber, T. A. J. P. r. B. 31, 5262 Lee, Y. & Hwang, G. S. J. P. R. B. 85, 125204 (2012). Justo, J et al. F. S. J. P. r. B. 58, 2539 (1998). Jiang, C et al. I. J. P. R. B. 86, 144118 (2012). Van Duin, A. C. et al. 107, 3803-3811 (2003). Bartók, A. P. et al. J. P. r. l. 104, 136403 (2010).W.Weber, Phys. Rev .B 15, 4789 (1977).
Silicon Thermal Conductivity
Atomistic Simulation &Energy Research Group
The “Phonon Potential”
1
2 ij i j anharmonicij
K EuE u
10
Morse
3-body
2
1 2 31 expE r
2 3
1 0 2 0E SNAP
0 k kk
E B
https://github.com/rohskopf
har nh mm a ar FF F
anharmF
harmF
Atomistic Simulation &Energy Research Group Silicon
11
2 2
1 2 3 4 0
11 exp
2 ij i jij
E K u u r
Harmonic part fitwith least squares
Anharmonic part fit with genetic algorithm
https://github.com/rohskopf
Atomistic Simulation &Energy Research Group
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50 % force error
Blue: DFT force
Red: Potential force
DFT potential
DFT
Error F -F
F
Atomistic Simulation &Energy Research Group
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3 % force error
Blue: DFT force
Red: Potential force
DFT potential
DFT
Error F -F
F
Atomistic Simulation &Energy Research Group Silicon
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1 % error
2 2
1 2 3 4 0
11 exp
2 ij i jij
E K u u r Dispersion Thermal Conductivity
Atomistic Simulation &Energy Research Group Germanium
15
2 2
1 2 3 4 0
11 exp
2 ij i jij
E K u u r
3 % error
Thermal ConductivityDispersion
Atomistic Simulation &Energy Research Group Gallium Arsenide
16
2 2
1 2 3 4 0
11 exp
2 ij i jij
E K u u r
6 % error
Dispersion Thermal Conductivity
Atomistic Simulation &Energy Research Group Gallium Nitride
17
(SNAP)0
1
2 ij i j k kij k
E K u u B
10 % error
Dispersion Thermal Conductivity
Atomistic Simulation &Energy Research Group
Conclusion
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A Rohskopf, H Seyf, K Gordiz, T Tadano, A Henry. "Empirical interatomic potentials optimized for phonon properties." NPJ Computational Materials 3 (2017)
M Muraleedharan, A Rohskopf, V Yang, A Henry. “Phonon optimized interatomic potential for aluminum.” AIP Advances 7 (2018)
A Rohskopf, S Wyant, A Henry. “Fast and accurate empirical interatomic potentials for describing thermal vibrations”. In progress
OPEN-SOURCEhttps://github.com/rohskopf
1
2 ij i j anharmonicij
E K u u E