High-throughput Simulations of Using MD Jacob Wilkins University of York jacob.wilkins@york.ac.uk Mar 2018
Outline 1 2 3 4 5
What are shock-waves? are pressure-waves moving through material faster than sound. System has no time to relax and dissipate energy. The shock is made of 3 major parts: Unshocked Region which the shock has not yet reached. Shock Front Region which is currently under shock. Post-shock rarefaction Region through which the shock has passed.
Why are shock-waves important? occur frequently in nature. Useful probes of extreme systems. Useful in development of new materials. Useful in materials properties testing.
Why do we need simulations? happen quickly. Shock-wave experiments can be expensive. Shock-wave experiments can be dangerous.
What is it? Modified equations of motion for shock state. Based on Hugoniot-Rankine jump conditions Equation of state for shocked system. Applies friction or acceleration to atoms to get correct energy. E 2 E 1 = 1 2 (P 2 + P 1 ) (V 1 V 2 ) (1) Hugoniot-Rankine Equation
Implementation Implemented as a Nosé-Hoover integrator. Requires coupling (χ) to the system motion. Coupling related to vibrational modes of compressed state. Can be done as a single compression, steady compression or with extra terms to modulate pressure. ṗ i = F i χp i (2) χ i = E 2 E 1 1 2 (P 2 + P 1 ) (V 1 V 2 ) (3) Modification to the EoM at each step
In summary + Equilibrate system to Hugoniot of system. + Implemented like a thermostat. + Doesn t need large simulation cell. + Can obtain relaxation information. - Only simulates system at shock-front. - Lose transitional states. - Require prior knowledge of system.
Simulation developments Ab initio much better in static cell. Though static compression exists... Difficult to predict pressure of given compression. Difficult to predict coupling at given compression. Need to estimate at these. Bad estimate = Wasted calculation 4500 4000 3500 Temperature (K) 3000 2500 2000 1500 1000 500 0 0 2000 4000 6000 8000 10000 12000 14000 16000 Time (fs)
Build upon a series of static compression measurements. Predict compression for next target pressure. Use curvature to estimate coupling of next system. Completely automate generation of Hugoniot profile. 16000 14000 12000 Temperature (K) 10000 8000 6000 4000 2000 0 0 30 60 90 120 150 180 210 Time (fs/10^3)
Pressure Curve Pressure (GPa) 100 80 60 40 20 0 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 Compression (V/V0) 500 atom Lennard-Jones simulation using the predictor-corrector method
Temperature Curve Temperature (K/10^3) 25 20 15 10 5 0 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 Compression (V/V0) 500 atom Lennard-Jones simulation using the predictor-corrector method
Hugoniot Temperature (K/10^3) 25 20 15 10 5 0 0 10 20 30 40 50 60 70 80 90 100 Pressure (GPa) 500 atom Lennard-Jones simulation using the predictor-corrector method
What can we get? All sorts of properties of the shocked states: Relaxation geometries Grüneisen parameter Shear and bulk moduli Structural defect formation
Use to find shocked state of materials. Measure system states at each step and use curvature to estimate coupling of next system. Completely automates generation of Hugoniot profile. Reference: : B Maillet, J et al. (2001). Uniaxial : A method for atomistic simulations of shocked materials. doi:10.1103/physreve.63.016121.