Strachan_MD - Molecular dynamics modeling of thermal...

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Molecular dynamics modeling of thermal Molecular dynamics modeling of thermal and mechanical properties and mechanical properties Alejandro Strachan School of Materials Engineering Purdue University strachan@purdue.edu
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Materials at molecular scales Materials at molecular scales Molecular materials Ceramics Metals
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Materials properties charts Materials properties charts Materials look very different Materials properties vary by many orders of magnitude Composition/chemistry Microstructure A variety of mechanisms govern materials behavior Materials Selection in Mechanical Design (3rd edition) by MF Ashby, Butterworth Heinemann, 2005
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Multiscale Multiscale modeling of materials modeling of materials L e n g t h T i m e nanometer mm picosec. nanosec. microsec femtosec. Molecular dynamics micron Mesoscale meters second Quantum Mechanics Macroscale Electrons Atoms Mesoparticles Elements •Understand the molecular level origins of materials behavior Predict the behavior of materials from first principles •Help design new materials or devices with improved performance
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Molecular dynamics Molecular dynamics Explicitly solve the dynamics of all atoms of the material of interest Newton’s equations of motion with forces obtained from the inter-atomic potential
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MD: structure of an MD code MD: structure of an MD code Initial conditions [r i (0), v i (0)] Calculate forces at current time [F i (t)] from r i (t) Integrate equations of motion r(t) _ r(t+ Δ t) v(t) _ v(t+ Δ t) t_t+ Δ t Save properties Done? End Y No Output file
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MD: integrating the equations of motion MD: integrating the equations of motion ( ) () ( ) ( ) ( ) 4 3 2 4 3 2 6 1 2 1 6 1 2 1 t t t r t t r t t r t r t t r t t t r t t r t t r t r t t r i i i i i i i i i i Δ Ο + Δ Δ + Δ = Δ Δ Ο + Δ + Δ + Δ + = Δ + & & & & & & & & & & & & Taylor expansion of positions with time The Verlet algorithm
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MD: thermodynamic ensembles MD: thermodynamic ensembles i i i i i
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Strachan_MD - Molecular dynamics modeling of thermal...

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