1 / 30

Metadynamics for Simulating Crystal Nucleation

17/04/2007 Long Timescale Workshop. Outline. Why study crystal nucleation? The timescale problemSimulation methodsBrute force molecular dynamicsUmbrella sampling Monte-Carlo methodsLong timescale methods and metadynamics Application of metadynamics to nucleationLennard-Jones crystallisatio

cassius
Download Presentation

Metadynamics for Simulating Crystal Nucleation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. 17/04/2007 Long Timescale Workshop Metadynamics for Simulating Crystal Nucleation David Quigley University of Warwick

    2. 17/04/2007 Long Timescale Workshop Outline Why study crystal nucleation? The timescale problem Simulation methods Brute force molecular dynamics Umbrella sampling Monte-Carlo methods Long timescale methods and metadynamics Application of metadynamics to nucleation Lennard-Jones crystallisation revisited Ice nucleation Calcium Carbonate Future Work

    3. 17/04/2007 Long Timescale Workshop Why study crystal nucleation? Fundamental Interest Nucleation mechanisms Metastability Industrial Gas hydrate formation Limescale Biomineralisation Templating Self Assembly

    4. 17/04/2007 Long Timescale Workshop Freezing Questions Is the structure nucleated consistent with the Ostwald step rule? Aggregation of crystallites? What are the free-energy barriers to nucleation of each crystal phase? How does this vary with temperature/pressure? System size effects?

    5. 17/04/2007 Long Timescale Workshop Nucleation Barrier Assumptions Nucleus is spherical Nucleus adopts crystal structure of the bulk solid Sharp interface between solid and liquid

    6. 17/04/2007 Long Timescale Workshop Simulation of freezing Experimental nucleation rates vary from O(101) – O(106) nuclei per cm3 per second. Consider a simulation cell of 10,000 water molecules. At best expect 1 nucleation event every 1012 seconds if at freezing temperature. Can simulate 500 ns at best using molecular simulation. Approach 1: Heavily supercool to reduce timescale. Magnitude of ?? increases rapidly below melting temperature. Lower energy barrier and smaller critical nucleus. Approach 2: Insertion of a nucleation ‘seed’ Estimate critical nucleus size from bulk free-energy calculations and/or experiment. Must assume structure of the critical nucleus.

    7. 17/04/2007 Long Timescale Workshop Examples

    8. 17/04/2007 Long Timescale Workshop Umbrella Sampling Methods Monte-Carlo method first applied to soft spheres by van Duijneveldt and Frenkel. [J.Chem.Phys 99 4655 – 4668 (1992)] Crystallisation characterised by one or more reaction co-ordinates or order parameters. Free-energy profile along the reaction pathway can be reconstructed from the umbrella sampling. Applied to Lennard-Jones fluid, hard-sphere colloids, water, N2 ,CO2, NaCl and various metals.

    9. 17/04/2007 Long Timescale Workshop Metadynamics [Laio & Parrinello P.N.A.S. 99 12562 (2002)] Characterise system by collective variables (order parameters) l = (l1,l2l3….lM) which describe the state of the system. Derivative of the free-energy w.r.t. l is ; evaluated via MD or MC. “Thermodynamic force” acting on the order parameters is : Augment Ftherm with history dependent potential Vaug(l1,l2l3….lM). Pushes the system away from previously visited l. Grow a bias potential to overcome energy barriers. Pushed into rare configurations to overcome entropic barriers. -Vaug provides a running estimate of the free-energy surface.

    10. 17/04/2007 Long Timescale Workshop Lennard-Jones Freezing Simple well studied pair-potential model, often used to benchmark methods. Phase diagram and free-energy are well known and parameterised. Stable phase is HCP/FCC, BCC phase closest in free-energy to liquid. Test of the Ostwald step rule.

    11. 17/04/2007 Long Timescale Workshop Order parameter Q6 Steinhardt order parameter [ Steinhardt et al. Phys.Rev.B. 28 784 – 805 (1983) ]

    12. 17/04/2007 Long Timescale Workshop Where to look? Aiming to simulate 10% or weaker supercooling. Understand trends in nucleation across the supercooled region. Influence of density of structure of crystallites? Systematic study of system size effects?

    13. 17/04/2007 Long Timescale Workshop Cluster Formation

    14. 17/04/2007 Long Timescale Workshop Nucleation and Growth

    15. 17/04/2007 Long Timescale Workshop Cluster Analysis Define a local vector where runs over only the separations between particle i and its nearest neighbours. Two particles i and j are connected if i.e. if ‘bonds’ align. A particle with 8 or more connections is part of a cluster. Clusters can then be identified and subjected to local optimisation. Crystal structure can then be assigned to each particle based on local order parameters.

    16. 17/04/2007 Long Timescale Workshop Aggregation?

    17. 17/04/2007 Long Timescale Workshop Cluster Sizes

    18. 17/04/2007 Long Timescale Workshop BCC or FCC?

    19. 17/04/2007 Long Timescale Workshop Internal structure of nucleus

    20. 17/04/2007 Long Timescale Workshop Energy Barriers Refine metadynamics estimate of ? G with umbrella sampling. Use metadynamics configurations to initialise umbrella sampling in each window. Expected system size dependence on barrier height.

    21. 17/04/2007 Long Timescale Workshop Localising Cluster Growth Biasing Q6 does not prefer growth of one large vs many small clusters – potentially unphysical. Bias w.r.t. size of largest cluster? Shown to reduce size of critical nucleus in LJ system. Identify largest cluster in general system? [ten Wolde et al Faraday Discuss. 104, 93-110] Restrict bias to a spatial region? Used successfully in studies of N2 and CO2. [Leyssale et al, J.Chem.Phys 122, 104510 (2005)]

    22. 17/04/2007 Long Timescale Workshop TIP4P Water Simple rigid-body model of water. Lennard-Jones site on oxygen + three charge sites.

    23. 17/04/2007 Long Timescale Workshop Ice Freezing

    24. 17/04/2007 Long Timescale Workshop Order Parameters Work of Radhakrishnan and Trout suggests that Q6 combined with a tetrahedral order parameter ? can describe the nucleation of ice I. j and k run over the four nearest neighbours of i. ? = 0.95 for Ice1h at 200 K ? = 0.63 for water at 300 K No calculations have yet located an Ice 1 minima, but reach order-parameter values of ices 2 and 3.

    25. 17/04/2007 Long Timescale Workshop Relevent Ice Phases

    26. 17/04/2007 Long Timescale Workshop Water Progress Extending cluster analysis to recognise ice 2 and 3. Parallel tempering options to accelerate sampling. Localising cluster growth as with Lennard-Jones systems. Further calculations in progress.

    27. 17/04/2007 Long Timescale Workshop Calcium Carbonate Aiming to simulate nucleation of calcite from solution in organic environment. Using potentials developed within the consortium. Currently testing metadynamics implementation on nucleation of CaCO3 nanoparticles and bulk.

    28. 17/04/2007 Long Timescale Workshop Metastable phases

    29. 17/04/2007 Long Timescale Workshop Order Parameters A combination of Q4 order parameters for Ca-Ca and Ca-O bonds describes the orientational order. Calcite crystallisation simulations are in progress.

    30. 17/04/2007 Long Timescale Workshop Future Work Extend metadynamics implementation within DLPOLY code. Lennard-Jones systems Nucleation rates. Bigger systems! Water Tuning history dependent potential. Nucleation of other ice phases. Gas hydrate nucleation. Nucleation at surfaces. Calcium carbonate Phase boundary calculation. Nucleation from solution. Presence of egg-shell proteins?

    31. 17/04/2007 Long Timescale Workshop Thanks University of Warwick Mark Rodger Mike Allen University of Sheffield John Harding Colin Freeman

More Related