Particle-based methods in materials science

ICMS, 15 South College Street, Edinburgh, EH8 9AA

23-27 July 2018

Organisers

Ken Elder, Oakland University
Christop Ortner, University of Warwick
Tim Schulze, University of Tennessee

Mathematics and computation have long played a central role in materials science, with efforts increasingly focused on the nanoscale. This workshop will bring together experts focusing on coarse-grained, particle-based methods for simulating the growth and evolution of materials that incorporate atomistic length scales. In recent years there has been extensive development in a diverse collection of such methods, including accelerated molecular dynamics, classical density functional theory, phase field crystal, kinetic Monte Carlo and quasicontinuum methods. Each of these methods attempts to incorporate the discrete nature of crystalline lattices and the defects and dislocations inherent in such systems on length and time scales much larger than atomic vibration times and length scales. These efforts are interdisciplinary, with individuals from mathematics, physics, chemistry and engineering working in these areas. There is a special challenge when trying to encourage interaction between researchers in different disciplines. One of the primary aims of this workshop is to overcome such barriers. To this end, speakers will give an accessible introduction to their approaches in addition to highlighting the cutting edge advances in their field. A specific goal of the meeting is that each participant will come away with knowledge of and an increased appreciation for work in these closely related specialties.

This workshop has been co-funded by the  ERC Starting Grant 335120 Multiscale Modelling of Crystalline Defects.

Arrangements

PARTICIPATION

Invitations were sent out by ICMS in March 2018. 

VENUE

The workshop will be held at ICMS, 15 South College Street, Edinburgh, EH8 9AA

TALKS AND AUDIO/VISUAL EQUIPMENT

All talks will be held in the Newhaven Lecture Theatre.  The lecture theatre has a built in computer, data projector, and visualiser/document camera.  In addition, there are two blackboards.  The projector and one board may be used simultaneously.  We advise Speakers that, where possible, you bring your talk on a memory stick/USB to put onto our computer in advance of your session - either at the start of the day or during coffee/lunch breaks.   ICMS staff can help with this.   It is possible for you to use your own laptops but it is then your own responsibility to ensure that resolutions are changed on the laptops if necessary (ICMS will not change the resolution on our equipment).   If you use a Mac we expect you to bring your own adaptor. 

UK VISAS

If you are travelling from outside of the UK you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one.

TRAVEL

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.

A taxi directly from the airport will cost approximately 20.00 to 25.00 GBP to the city centre for a one-way journey.    

There is also a bus service direct from the airport to the city centre which will cost 4.50 GBP single or 7.50 GBP return - the Airlink 100.  This is a frequent service (every 10 minutes during peak times) and will bring you close to Waverley Railway Station, only a short walk to the workshop venue.

Lothian buses charge £1.70 for a single, £4.00 for a day ticket. Please note that the exact fare is required and no change is given.

If travelling by train, please note that Edinburgh has several railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street.  If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge.

Programme

Monday 23 July

08:45-09:30

Registration in the Chapterhouse, Level 1

09:30-09:45

Welcome/opening remarks

09:45-10:30

Art Voter (Los Alamos National Laboraory)        
Recent developments in accelerated molecular dynamics methods

10:30-11:00

Tea/Coffee in the Chapterhouse, Level 1

11:00-11:45

Tim Schulze (University of Tennessee)        
Lattice and off-lattice kinetic Monte Carlo

11:45-12:30

Christoph Ortner (University of Warwick)        
To follow

12:30-14:00

Lunch provided in the Chapterhouse, Level 1

14:00-14:45

Ken Elder (Oakland University)        
Modelling microstructure formation using phase field crystal models

14:45-15:30

Jim Evans (Iowa State University)        
Stochastic particle-level modeling of coarsening: Cluster diffusion and coalescence on surfaces

15:30-16:00

Tea/Coffee in the Chapterhouse, Level 1

16:00-16:45

Ben Goddard (University of Edinburgh)        
Dynamic density functional theory: modelling, numerics and analysis

16:45-17:30

Simiso Mkhonta (University of Swaziland)        
Emergence of disordered hyperuniform systems in random pinning potentials

17:30-18:30

Informal wine reception in the Chapterhouse, Level 1

 

Tuesday 24 July

09:00-09:45

Peter Voorhees (Northwestern University)        
The phase field method: crystal structures and facets

09:45-10:30

Charalambos Makridakis (University of Sussex)        
Formulation and analysis of discontinuous interface atomistic - continuum coupling methods

10:30-11:00

Tea/Coffee in the Chapterhouse, Level 1

11:00-11:45

Danny Perez (Los Alamos National Laboraory)        
To follow

11:45-12:30

Laszlo Granasy (Wigner Research Centre for Physics)        
Nucleation modes and polycrystalline growth in a hydrodynamic phase-field crystal model

12:30-14:00

Lunch provided in the Chapterhouse, Level 1

14:00-14:45

Gideon Simpson (Drexel University)        
To follow

14:45-15:30

Dmitri Schebarchov (Victoria University of Wellington)        
To follow

15:30-16:00

Tea/Coffee in the Chapterhouse, Level 1

16:00-16:45

Andrew Archer (Loughborough University)
To follow

16:45-17:30

Marco Salvalaglio (Technische Universität Dresden)
Coarse-grained, three-dimensional modeling of defect networks by the amplitude expansion of the phase field crystal model

 

Wednesday 25 July

09:00-09:45

Gabor Csanyi (University of Cambridge)        
The new dawn of force fields

09:45-10:30

Abhijit Chatterjee (Indian Institute of Technology Bombay)        
Temperature programmed molecular dynamics: theory and applications

10:30-11:00

Tea/Coffee in the Chapterhouse, Level 1

11:00-11:45

Zhi-Feng Huang ( Wayne State University)        
Continuum field modeling of crystalline microstructures: length scales and bond-angle control

11:45-12:30

Thomas Hudson (University of Warwick)        
A rigorous approach to describing the mobility of screw dislocations

12:30

Free afternoon

 

Thursday 26 July

09:00-09:45

Tapio Ala-Nissila (Aalto  & Loughborough University)        
Multiscale modelling of graphene from nano to micron scales with the phase-field crystal model

09:45-10:30

Genevieve Dusson (University of Warwick)
To follow

10:30-11:00

Tea/Coffee in the Chapterhouse, Level 1

11:00-11:45

Steve Wise (University of Tennessee)        
Some numerical methods for and numerical analyses of phase field crystal models

11:45-12:30

Doaa Taha (University of Michigan)        
To follow

12:30-14:00

Lunch provided in the Chapterhouse, Level 1

14:00-14:45

Stela Makri (University of Warwick)        
A preconditioning scheme for minimum energy path finding methods

14:45-15:30

Tony Lelievre (Ecole des Ponts)
Metastability: a journey from stochastic processes to semiclassical analysis

15:30-16:00

Tea/Coffee in the Chapterhouse, Level 1

16:00-16:45

Arunima Singh (Arizona State University)
A density-functional theory-based approach for aqueous stability of materials

16:45-17:30

TBC (Institution)        
Title

19:00

Workshop dinner  19:00 at Blonde Restaurant, 71-75 St. Leonard’s St, Edinburgh EH8 9QR

 

Friday 27 July

09:00-09:45

David Wales (University of Cambridge)        
Exploring energy landscapes: molecules, nanodevices and condensed matter

09:45-10:30

Rainer Backofen (Technical University of Dresden)        
Modelling and control of grain boundaries by the phase field crystal approach

10:30-11:00

Tea/Coffee in the Chapterhouse, Level 1

11:00-11:45

Huajie Chen (Beijing Normal University)        
QM/MM methods for crystalline defect

11:45-12:30

Lei Zhang (Shanghai Jiao Tong University)        
A priori and a posteriori error estimates for multiscale coupling methods

12:30

Close of workshop

 

Abstracts

Tapio Ala-Nissilä
Multiscale modelling of graphene from nano to micron scales with the phase-field crystal model
Over the last few years novel two-dimensional materials and nanoscopically thin heteroepitaxial overlayers have attracted intense attention due to their unusual properties and important technological applications. Many physical properties of these systems such as thermal conductivity and electrical transport are intimately coupled to the large scale mechanical and structural properties of the materials. However, modeling such properties is a formidable challenge due to a wide span of length and time scales involved. In this talk, I will review recent significant progress in structural multi-scale modeling of two dimensional materials and thin heteroepitaxial overlayers [1], and graphene in particular [2], based to a large extent on the Phase Field Crystal (PFC) model combined with standard microscopic modeling methods (classical Molecular Dynamics and Quantum Density Functional Theory). The PFC framework allows one to reach diffusive time scales for structural relaxation of the materials at the atomic scale, which facilitates quantitative characterisation of domain walls, dislocations, grain boundaries, and strain-driven self-organisation up to almost micron length scales. This allows one to study e.g. thermal conduction and electrical transport in realistic multi-grain systems [3].

References:
1. K. R. Elder et al,. Phys. Rev. Lett. vol. 108, 226102 (2012); Phys. Rev. B vol. 88, 075423 (2013); J. Chem. Phys. 144, 174703 (2016).
2. P. Hirvonen et al., Phys. Rev. B 94, 035414 (2016).
3. Z. Fan et al., Phys. Rev. B vol. 95, 144309 (2017); Nano Lett. 7b172 (2017); K. Azizi et al., Carbon 125, 384 (2017).

Andrew Archer
To follow
To follow

Rainer  Backofen
Modelling and control of grain boundaries by the phase field crystal approach
To follow

Abhijit Chatterjee
Temperature programmed molecular dynamics: theory and applications
Temperature programmed molecular dynamics (TPMD) method is a recently developed rare event acceleration scheme. TPMD can be used to efficiently study the long timescale dynamics of a material system. A situation commonly encountered in several complex materials is that the system remains trapped for long periods of time in a collection of potential basins in the energy landscape, called a superbasin. Transitions between superbasin states can be rare at molecular dynamics timescales, however, escapes from the superbasin involving larger activation barriers are even rarer. Often, it is the latter type of moves that are of interest when long timescales of seconds and beyond need to be accessed. TPMD method employs a temperature program with state-constrained molecular dynamics calculations that allows transitions of interest to happen more frequently. Separation of timescales is exploited for identifying the superbasin and selecting a superbasin escape for a move. Using TPMD method one can accurately study superbasin-to-superbasin transitions while disregarding low-barrier pathways that have been traditionally difficult to handle with rare-event simulations. I will describe some of the other key features of the TPMD method such as estimation of Arrhenius parameters for kinetic pathways. Application of the technique to various materials problems will be discussed.

Huajie Chen
QM/MM methods for crystalline defect
We develop and analyze QM/MM (quantum/classic) hybrid methods for crystalline defects within the context of the tight-binding model. QM/MM methods employ accurate quantum mechanics (QM) models only in regions of interest (defects) and switch to computationally cheaper interatomic potential molecular mechanics (MM) models to describe the crystalline bulk. We propose new energy-based and force-based QM/MM methods, building on two principles: (i) locality of the QM model; and (ii) constructing the MM model as an explicit and controllable approximation of the QM model. This approach enables us to rigorously establish convergence rates in terms of the size of the QM region. This is a joint work with Christoph Ortner.

Gabor Csanyi
The new dawn of force fields
To follow

Genevieve Dusson
To follow
To follow

Ken Elder
Modelling microstructure formation using phase field crystal models
To follow

Jim Evans
Stochastic particle-level modeling of coarsening: Cluster diffusion and coalescence on surfaces
Stochastic particle-level lattice-gas models have enabled detailed characterization of the formation of non-equilibrium distributions of islands (also described as nanoclusters) during submonolayer deposition on flat surfaces [1], as well as their subsequent coarsening [2]. For island formation, fundamental open questions remain regarding the size distribution and spatial distribution of islands (the latter including tessellation of the surface into capture zones surrounding islands [3]). Post-deposition coarsening reduces the number of islands and increases their mean size, thereby evolving the system to equilibrium. This process can occur either via Ostwald Ripening (where small islands dissolve) or via Smoluchoswki Ripening (i.e., diffusion [4] and coalescence [5] of islands). We focus on the latter processes where both diffusion and coalescence are mediated of periphery diffusion (PD) of atoms around the edge of the cluster. We utilize both tailored models and ab-initio based models to describe the relevant PD kinetics. For the size-dependence of cluster diffusion, we find remarkably rich behavior on the nanoscale (with nucleation-mediated and facile branches of diffusion, strong oscillations in size) giving way to macroscopic behavior described by continuum Langevin theory.

Ben Goddard
Dynamic density functional theory: modelling, numerics and analysisIn recent years, a number of dynamic density functional theories (DDFTs) have been developed to describe colloid particle dynamics. These DDFTs aim to overcome the high-dimensionality of systems with large numbers of particles by reducing to the dynamics of the one-body density, described by a PDE in only three spatial dimensions, independent of the number of particles. The standard derivations start from stochastic equations of motion, but there are fundamental differences in the underlying assumptions in each DDFT. I will begin by giving an overview of some DDFTs, highlighting the assumptions and range of applicability. Particular attention will be given to the inclusion of inertia and hydrodynamic interactions, both of which strongly influence non-equilibrium properties of the system. I will then demonstrate the very good agreement with the underlying stochastic dynamics for a wide range of systems, including confined systems with hydrodynamic interactions. If time allows, I will also discuss an accurate and efficient pseudospectral numerical code that we have developed, as well as the passage to Smoluchowski-like and Navier-Stokes-like equations in appropriate limits.
Joint work with Serafim Kalliadasis, Greg Pavliotis, and Andreas Nold

Laszlo Granasy
Nucleation modes and polycrystalline growth in a hydrodynamic phase-field crystal model
Nucleation of solid phases in undercooled liquids is investigated using a hydrodynamic model of solidification based on combining the phase-field crystal model with fluctuating nonlinear hydrodynamics [1,2]. Structural aspects of homogeneous and heterogeneous nucleation will be addressed, including growth front nucleation mechanisms that lead to the formation of differently oriented grains at the solidification front in highly non-equilibrium liquids. It is predicted that even in simple liquids, amorphous precursor structures may assist crystal nucleation. It will be shown furthermore that new orientation may form at the perimeter of growing crystals by two mechanisms: via
(i) incorporating dislocations into the crystalline phase during rapid solidification, and
(ii) the interference of extended density waves ahead of the crystallization front observed in the vicinity of the stability limit of the liquid.
Joint work with Frigyes Podmaniczky and Gyula I. Tóth.
[1] G.I. Tóth et al. J. Phys.: Condens. Matter. 26, 055001 (2014).
[2] F. Podmaniczky et al. Phys. Rev. E. 95, 052801 (2017).

Zhi-Feng Huang
Continuum field modeling of crystalline microstructures: length scales and bond-angle control
The coarse-graining, density-field based continuum theories have been proven efficient in modeling complex material systems, particularly those involving multiple spatial and temporal scales. There are some fundamental but challenging issues that remain to be resolved, two of which will be discussed in this talk based on the phase field crystal type method:
(i) how to systematically model and control the interparticle bond orientation in a continuum description, and
(ii) how to address the coupling among microscopic and mesoscopic length scales.

For the first issue we construct an angle-adjustable density field formulation to simultaneously incorporate the micro-scale interparticle bond-angle anisotropy and the global-scale rotational invariance of material systems. This is achieved by making use of a decades-old mathematical concept/theorem of isotropic Cartesian tensor, and via the complete expansion of particle direct correlation functions particularly that of four-point correlation. Various 2D and 3D crystalline phases are modeled by this generic approach, which also shows the capability of continuous bond angle control and tuning. For the second issue of length scale coupling, it is addressed through a sample system of alloy liquid-solid interface and the development of a nonadiabatic amplitude equation formulation. The interface lattice pinning effect during material growth and effects of compositional stress on anisotropic interfacial properties are identified, as a result of meso-micro and meso-meso scale couplings.

Tom Hudson
A rigorous approach to describing the mobility of screw dislocations
Discrete Dislocation Dynamics (DDD) is a phenomenological modelling and simulation technique used to study plasticity in crystalline solids on length- and timescales inaccessible with molecular dynamics. In this talk, I will present some mathematical results demonstrating that in certain parameter regimes, forms of DDD for screw dislocations can be derived from a microscopic stochastic model.

Tony Lelievre
Metastability: a journey from stochastic processes to semiclassical analysis
A stochastic process is metastable if it stays for a very long period of time in a region of the phase space (called a metastable region) before going to another metastable region, where it again remains trapped. Such processes naturally appear in many applications, metastability being related to a two time scale mechanism: the small time scale corresponds to the vibration period within the metastable regions and the large time scale is associated with the transitions between metastable states. For example, in molecular dynamics, the metastable regions are typically associated with the atomic conformations of a molecule (or an ensemble of molecules), and one is actually interested in simulating and studying the transitions between these conformations.

In this talk, I will explain how the exit events from a metastable state can be studied using an eigenvalue problem for a differential operator. This point of view is useful to build very efficient algorithms to simulate metastable stochastic processes (using in particular parallel architectures). It also gives a new way to prove the Eyring-Kramers laws and to justify the parametrization of an underlying Markov chain (Markov state model), using techniques form semiclassical analysis.
Reference: https://arxiv.org/abs/1706.08728

Stela Makri
A preconditioning scheme for minimum energy path finding methods
In transition state theory, the study of thermally activated transitions between energy minima is achieved by finding transition paths connecting the minima. These paths provide information on the energy barrier and reaction rates of the system without going through long and expensive simulations. To find them, current techniques use steepest descent-like minimisation to relax a discretised initial guess. However, steepest descent typically gives slow convergence rates in the presence of ill-conditioned potentials. In this talk I will be discussing how to reduce the condition number of the potential of an arbitrary system and improve the convergence speed and robustness of transition path finding methods, using a preconditioning scheme. Our key assumption is that the cost of constructing a preconditioner is much smaller than the cost of computing the potential; for density functional theory the cost of single point evaluations is much more expensive than the computation of a preconditioner and thus the proposed approach improves computing times significantly. We have developed a preconditioning scheme, where the preconditioner acts as a coordinate transformation of the discrete images along the path to aid the ill-conditioning in the transverse direction and a preconditioning scheme that considers the interactions between the images is currently in development. Finally, we are working towards a preconditioning scheme for finding energy barriers in hybrid quantum mechanical – molecular mechanical models.

Charalambos Makridakis
Formulation and analysis of discontinuous interface atomistic - continuum coupling methods

To follow

Simiso K. Mkhonta
Emergence of disordered hyperuniform systems in random pinning potentials
To follow

Christoph Ortner
To follow
To follow

Danny Perez
To follow
To follow

Marco Salvalaglio
Coarse-grained, three-dimensional modeling of defect networks by the amplitude expansion of the phase field crystal model
To follow

Dimtri Schebarchov
To follow
To follow

Tim Schulze
Lattice and off-lattice kinetic Monte Carlo
To follow

Gideon Simpson
To follow

To follow

Arunima Singh
A density-functional theory-based approach for aqueous stability of materials
Aqueous media-based electrochemical processes such as water purification and electrocatalysis routinely operate devices at finite potentials and pH where materials stability is strikingly different from ambient conditions. In this talk I will describe our density-functional theory-based formalism [1] to assess the propensity of materials toward electrochemical stabilization, passivation, or corrosion in aqueous media. This formalism allows us to evaluate the relative Gibbs free energy of arbitrary materials with respect to Pourbaix stable species at any pH, voltage, temperature, and concentration of ions. Benchmarking against 20 stable as well as metastable materials reported in the literature and also our experimental investigation of metastable triclinic-FeVO4, we present quantitative estimates for the relative Gibbs free energy and corresponding aqueous regimes where materials are most likely to be stable, form inert passivating films, or steadily corrode to aqueous species. The implementation of this formalism is freely available via the Materials Project github repository at https://github.com/materialsproject/pymatgen, allowing the programmatic determination of electrochemical stability of arbitrary materials, including the 69,000 materials available through the Materials Project Database.

I will discuss how this ab-inito density-functional theory-based approach can be combined with molecular dynamics simulations to parametrize phenomenological models [2] to determine rate of corrosion, passivation film thickness as a function of time as well as the electronic properties of the passivated films.

[1] Singh, A.K., Zhou, L., Shinde, A., Suram, S.K., Montoya, J.H., Winston, D., Gregoire, J.M. and Persson, K.A., 2017. Electrochemical Stability of Metastable Materials. Chemistry of Materials, 29, 10159−10167 (2017).
[2] Macdonald, D. On the existence of our metals-based civilization. I. Phase-space analysis. Journal of Electrochemical Society, 153 (7), B213− B224 (2016).

Doaa Taha
To follow
To follow

Katsuo Thornton
To follow
To follow

Peter Voorhees
The phase field method: crystal structures and facets
Phase field crystal (PFC) method allows the atomic scale motion and defect formation to be determined on diffusive timescales.  A major challenge with the method is to devise free energy functions that can yield complicated crystal structures. We introduce a phase-field crystal model that creates an array of complex three- and two-dimensional crystal structures via a numerically tractable three-point correlation function. This approach successfully yields energetically stable simple cubic, diamond cubic, simple hexagonal, graphene layers, and CaF2 crystals, as well as the particularly complex and technologically important perovskite crystal structure. Highly anisotropic interfaces play an important role in the development of material microstructure. We examine the capability of the PFC model to quantitatively describe faceted interfaces by coarse graining the PFC model to attain both its complex amplitude formulation, and its corresponding phase field limit. Using this formulation, we find that the model yields Wulff shapes with missing orientations, the transition to missing orientations, and facet formation. We demonstrate, in two dimensions, how the resultant model can be used to study the growth of crystals with varying degrees of anisotropy in the phase-field limit.

Art Voter
Recent developments in accelerated molecular dynamics methods
To follow

David Wales
Exploring energy landscapes: molecules, nanodevices and condensed matter
The potential energy landscape provides a conceptual and computational framework for investigating structure, dynamics and thermodynamics in atomic and molecular science. This talk will summarise new approaches for global optimisation, quantum dynamics, the thermodynamic properties of systems exhibiting broken ergodicity, and rare event dynamics. Applications will be presented that range from prediction and analysis of high-resolution spectra, to coarse-grained models and design principles for self-assembly of mesoscopic structures.

Selected Publications:
 D.J. Wales, Curr. Op. Struct. Biol., 20, 3-10 (2010) 
 D.J. Wales, J. Chem. Phys., 130, 204111 (2009)
 B. Strodel and D.J. Wales, Chem. Phys. Lett., 466, 105-115 (2008)
 D.J. Wales and T.V. Bogdan, J. Phys. Chem. B, 110, 20765-20776 (2006)
 D.J. Wales, Int. Rev. Phys. Chem., 25, 237-282 (2006)

Steven Wise
Some numerical methods for and numerical analyses of phase field crystal models
To follow

Lei Zhang
A priori and a posteriori error estimates for multiscale coupling method
To follow