(emd)平衡分子动力学计算热导率课件
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V olz/Chen
114 (Tersoff)
Dong/Sankey/M yles
λ (exp)
2190
Anthony et al.
130 (natural)
Capinski/Maris/ et al
62 (natural)
Slack/Glassbrenner
* λ: units of W/m/K • Good agreement with previous theoretical calculations. • Reasonable agreement with experiment -- trends are correct. • Ratio λ(12C) / λ(Cnatural) = 1.4 in agreement with experiment.
• Can compute λ by MD or BTE • One option is NEMD (non-equilibrium), but …
• NEMD requires large temperature gradients • boundary condition issues at interfaces • Instead pursue Green-Kubo approach: • Fluctuation-Dissipation theorem:
Results: C, Si, Ge
Material C C, natural
Si
Ge
λ (calc) 1390 990
180
80
λ (calc) 1200 (Brenner)
Che/Cagin/Deng/Goddard
840 (Brenner)
Che/Cagin/Deng/Goddard
230 (Stillinger-Weber)
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Summary
• Demonstrated modification of existing software to compute thermal conductivities using a GreenKubo approach. • Evaluated several convergence schemes. • Obtained preliminary results for diamond-like materials in agreement with previous theoretical models and experiment.
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Lattice Contribution to Thermal Conductivity
Goals / General Approach:
Principal goal is the optimization of thermoelectric figure of merit ZT.
Applied Cluster Computing Technologies Group
Convergence of auto-correlation function
Convergence requires a large number of ensembles: tens of ns required…
Ansatz:
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Results: λ(N)
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Applied Cluster Computing Technologies Group
Motivation: Thermoelectrics
• Goal: Optimize ZT (efficiency)
• engineering of phonon & electronic energy dispersions
First principles electronic structure
Figure of Merit
Parameter fitting (Genetic Algorithm)
Tight binding calculation
Boltzmann Transport Equation Green Kubo formalism
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Evaluation of heat current
Symmetrized Tersoff:
CMDF Workshop, Caltech, 05.08.23
Modeling thermal conductivity: a Green-Kubo approach
Fabiano Oyafuso, Paul von Allmen, Markus Bühler
Jet Propulsion Laboratory Pasadena, CA
CMDF Workshop, Caltech, 05.08.23
Focus of this work is on lattice contribution, κph
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Motivation: Optimization of ZT
Status:
• Derived analytic expression for heat flux for Tersoff potential.
• Implemented heat flux calculation in IMD (ITAP) code and integrated output thereof into separate code to compute thermal conductivity.
/FWFSUIFMFTT DPOWFSHFODFPGJOUFHSBM NBZTUJMMCFTMPXPSXPSTF OPUXFMM CFIBWFE
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
• Computed λ for diamond structures (C,Si,Ge).
Implementation:
• Modified pre-existing software, ITAP: www.itap.physik.uni-stuttgart.de/~imd
• Two options: numerical/analytic differentiation compute heat flux.
• Validate code by computing λ for C, Si, Ge • Compute λ for various bulk materials (e.g. Bi2Te3) • Generalize to simple nanostructures.
Technical Approach:
Conductivity calculation: three approaches
• Three approaches:
• Direct integration • Fit frequency dependent thermal conductivity to single relaxation time approximation (Volz/Chen). • Fit autocorrelation function directly to a small set of relaxation times (Che et al.)
Modified IMD code • compute j(t) and save to binary file
Postprocessing Module • compute heat auto correlation function • integrate to compute thermal conductivHale Waihona Puke Baiduty
Electronic contribution: - Seebeck coefficient - Electrical conductivity - Thermal conductivity
Lattice contribution: - Thermal conductivity
Boltzmann Transport Equation Green Kubo formalism First principles Force Fields
Funding: DARPA
Applied Cluster Computing Technologies Group
Outline
• Motivation -- thermoelectrics • Theory • Implementation • Preliminary results
CMDF Workshop, Caltech, 05.08.23
114 (Tersoff)
Dong/Sankey/M yles
λ (exp)
2190
Anthony et al.
130 (natural)
Capinski/Maris/ et al
62 (natural)
Slack/Glassbrenner
* λ: units of W/m/K • Good agreement with previous theoretical calculations. • Reasonable agreement with experiment -- trends are correct. • Ratio λ(12C) / λ(Cnatural) = 1.4 in agreement with experiment.
• Can compute λ by MD or BTE • One option is NEMD (non-equilibrium), but …
• NEMD requires large temperature gradients • boundary condition issues at interfaces • Instead pursue Green-Kubo approach: • Fluctuation-Dissipation theorem:
Results: C, Si, Ge
Material C C, natural
Si
Ge
λ (calc) 1390 990
180
80
λ (calc) 1200 (Brenner)
Che/Cagin/Deng/Goddard
840 (Brenner)
Che/Cagin/Deng/Goddard
230 (Stillinger-Weber)
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Summary
• Demonstrated modification of existing software to compute thermal conductivities using a GreenKubo approach. • Evaluated several convergence schemes. • Obtained preliminary results for diamond-like materials in agreement with previous theoretical models and experiment.
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Lattice Contribution to Thermal Conductivity
Goals / General Approach:
Principal goal is the optimization of thermoelectric figure of merit ZT.
Applied Cluster Computing Technologies Group
Convergence of auto-correlation function
Convergence requires a large number of ensembles: tens of ns required…
Ansatz:
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Results: λ(N)
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Applied Cluster Computing Technologies Group
Motivation: Thermoelectrics
• Goal: Optimize ZT (efficiency)
• engineering of phonon & electronic energy dispersions
First principles electronic structure
Figure of Merit
Parameter fitting (Genetic Algorithm)
Tight binding calculation
Boltzmann Transport Equation Green Kubo formalism
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Evaluation of heat current
Symmetrized Tersoff:
CMDF Workshop, Caltech, 05.08.23
Modeling thermal conductivity: a Green-Kubo approach
Fabiano Oyafuso, Paul von Allmen, Markus Bühler
Jet Propulsion Laboratory Pasadena, CA
CMDF Workshop, Caltech, 05.08.23
Focus of this work is on lattice contribution, κph
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
Motivation: Optimization of ZT
Status:
• Derived analytic expression for heat flux for Tersoff potential.
• Implemented heat flux calculation in IMD (ITAP) code and integrated output thereof into separate code to compute thermal conductivity.
/FWFSUIFMFTT DPOWFSHFODFPGJOUFHSBM NBZTUJMMCFTMPXPSXPSTF OPUXFMM CFIBWFE
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
CMDF Workshop, Caltech, 05.08.23
Applied Cluster Computing Technologies Group
• Computed λ for diamond structures (C,Si,Ge).
Implementation:
• Modified pre-existing software, ITAP: www.itap.physik.uni-stuttgart.de/~imd
• Two options: numerical/analytic differentiation compute heat flux.
• Validate code by computing λ for C, Si, Ge • Compute λ for various bulk materials (e.g. Bi2Te3) • Generalize to simple nanostructures.
Technical Approach:
Conductivity calculation: three approaches
• Three approaches:
• Direct integration • Fit frequency dependent thermal conductivity to single relaxation time approximation (Volz/Chen). • Fit autocorrelation function directly to a small set of relaxation times (Che et al.)
Modified IMD code • compute j(t) and save to binary file
Postprocessing Module • compute heat auto correlation function • integrate to compute thermal conductivHale Waihona Puke Baiduty
Electronic contribution: - Seebeck coefficient - Electrical conductivity - Thermal conductivity
Lattice contribution: - Thermal conductivity
Boltzmann Transport Equation Green Kubo formalism First principles Force Fields
Funding: DARPA
Applied Cluster Computing Technologies Group
Outline
• Motivation -- thermoelectrics • Theory • Implementation • Preliminary results
CMDF Workshop, Caltech, 05.08.23