Multiscale modeling of materials with atomic scale resolution using phase-field-crystal methods (MULTIMAT)
CECAM-HQ-EPFL, Lausanne, Switzerland
One of the main challenges in the research in physics and materials sciences, and especially in the field of complex and advanced functional materials is the ability to understand, predict, and control material properties and functionality. These materials include both solid state (such as metallic alloys, ferroelectrics, ferromagnets, and semiconductor nanostructures) and soft matter systems (such as colloids, liquid crystals, foams, and microemulsions). These materials can exist under equilibrium or non-equilibrium conditions, with spatially and topologically complicated structures and defects, involve a variety of spatial and temporal scales, and also coupling with growth and processing conditions. Most of the current computational modeling methods focus on specific scales ranging from particle-based atomistic (classical or quantum-mechanical) to continuum-hydrodynamic levels and span multiple disciplines including physical, chemical, mathematical, and materials sciences. However, such approaches usually encounter a common problem: How to simultaneously address and bridge the complicated microscopic material details with the much larger length and time scales of experimental relevance in terms of material properties and functionality? A specific example would be the elastic and plastic deformations during either nanostructure formation or alloy processing. The understanding of such deformations requires detailed information of the crystalline microstructures, while the corresponding outcome of structural, mechanical, electromagnetic, or transport properties usually involves mesoscopic or larger length scales on diffusive time scales.
The main purpose of the MULTIMAT workshop is to bring together the leading experts in the field of multiscale materials modeling within the context of focusing on novel mesoscale approaches that simultaneously incorporate atomic scale resolution and mesoscopic-macroscopic scales. The main topic will be the recently developed Phase Field Crystal (PFC) model [1,2] and related methods, which incorporate microscopic and atomic-level structural details into a mesoscopic continuum theory and address diffusive time scales that are of experimental relevance. This modeling framework thus naturally provides the bridging between different scales, and is appealing as compared to conventional atomistic techniques in terms of computational requirements and costs, and to traditional continuum methods in terms of the ability to capture microscopic details and insights into formation of complex structures across mesoscopic scales. The PFC methodology has been developing very rapidly since its emergence about 10 years ago, and it has been successfully applied to the study of a wide range of material systems including nanoscale, structural, and energy materials, for both solid and soft matter (for a recent review, see Ref. ). Some topics related to the PFC methods were discussed in a previous CECAM workshop in 2009 (“Classical density functional theory methods in soft and hard matter”, organized by M. Haataja, H. Löwen and L. Granasy , which was a great success and has subsequently stimulated a plethora of further research in this realm. The success of the meeting is documented in a special issue of the Journal of Physics: Condensed Matter 22 (2010), which contains the proceeding publications. Since then significant progress has been made, although many challenges still remain, as will be further described below. Therefore, it would be very timely to bring together experts in this field, from different disciplines such as physics, engineering, materials science, chemistry, and mathematics, to assess the current state of the field and to discuss and exchange ideas about recent advances and remaining challenges. The timing for this workshop is optimal, considering the explosive increase in the application of the PFC methodology and the large number of students and postdocs who are currently working on this problem. Thus, we expect that the MULTIMAT workshop will serve as an important educational tool for future generation of scientists.
There will be a special focus in MULTIMAT on both analytic and computational developments in the field, and applications related to the dynamics of defects in materials. Specifically, the following topics will be addressed in this workshop:
• Studies of structural properties and dynamics in complex materials. These are among the most explored topics for PFC applications, including nanostructure formation and growth (e.g., quantum dots [4,5]), eutectic/dendritic [2,6] or colloidal  solidification (see e.g., Fig. 1), grain nucleation and growth [6,8], structural phase transformations , compositional domain formation , phase segregation [2,6], formation, melting, and critical dynamics of topological defects such as dislocations and grain boundaries [11-14], glass formation , surface and interface properties , commensurate/incommensurate transitions and driven response in pinned layers , modeling of atomistically this strained overlayers , foam dynamics , phase behavior of liquid crystals , the Kirkendall effect , etc.. Despite many successful examples, many important issues still remain open. For solid materials, examples include the complex coupling between alloy composition inhomogeneity and defect dynamics, interaction among topological defects, transition between continuous and nucleated growth modes of nanostructures, among many others. For soft matter, there are a variety of problems and open challenges as well. These range from the heterogeneous nucleation of colloidal crystals in complex environments, to interfacial kinetics and to the formation and growth of binary crystals. In particular, liquid crystalline phases have been the focus of recent applications of the PFC models . There is an emerging need to apply these extended PFC models to various nonequilibrium situations of liquid crystals such as relaxational dynamics, nucleation and growth of nematic, smectic, columnar and plastic crystalline phases. Moreover the PFC model itself needs further generalization to colloidal particles with arbitrary shapes. An exciting recent development is the application to supported graphene overlayers, which facilitates large-scale studies of strained graphene .
• Studies of functional properties and dynamics in engineering and energy materials. There are many open challenging issues and problems for the mesoscale/PFC study in this technologically important area. Efforts on modeling detailed properties of ferroelectrics, ferromagnets, and irradiation effects in alloying nuclear materials that are within the PFC framework and beyond the traditional approaches have just begun. One of the key challenges is the coupling of functional material parameters (such as electric polarization or magnetization) with atomic-level description of elastic and plastic deformation processes.
• Development of PFC framework and computational algorithms. The PFC framework has been continuously developed and extended in a number of directions: 1) The amplitude equation representation has been established for both single-component [23,24] and alloy [6,25] systems, although much work is needed for more complicated material systems such as ferroelectrics, irradiated alloys, or superlattices; 2) The PFC model has been extended to incorporate various types of crystalline symmetries such as fcc, bcc, hcp, diamond, simple cubic, 2D triangular, square, honeycomb and kagome [9,26,22], although further extension to alloy systems is not complete; 3) Some dynamic factors, such as faster time scales associated with mechanical relaxation , have been incorporated in the model. Although the PFC models are much more computationally efficient compared to traditional atomistic techniques, numerically they are still limited by the resolution of small atomic-level length scales and also by the large simulation time steps required in the cases of slow system relaxation. Novel, efficient computational methods are being developed (such as adaptive mesh method  and other new advanced algorithms and schemes ), particularly for large-scale 3D simulations that are compatible to real experimental systems.
• Connection and bridging between different methods and between modeling and experimental results. These include: 1) establishing the connection of PFC models with atomistic methods such as molecular dynamics simulations, and also with the classical density functional theory (DFT) [2,7,19,30] as well as dynamic DFT , for both pure and binary materials; 2) directly connecting the PFC model to classical continuum approaches particularly the traditional phase-field methods, for which the most recent progress shows that the phase field model for binary alloys can be directly derived from the PFC model via amplitude equation expansion , an encouraging result that needs to be extended to more complex materials such as functional materials involving ferroelectricity, ferromagnetism, and irradiation; 3) building the direct linkage between PFC modeling/simulation results and experimental outcome, which is of fundamental and practical importance given that the parameters in the PFC description are mostly phenomenological and hence need explicit connection to experimental data. Some recent research has been driven towards this direction, although several obstacles remain.
We have contacted a number of researchers from various scientific and engineering disciplines who are experts in different aspects of the above topics. Enthusiastic responses have been received from several key scientists in this field. The invited speakers represent 9 different countries, with diverse research background and specialties (including physicists, engineering scientists, and mathematicians). This workshop will provide a nice opportunity for direct interaction, exchange, and possible collaboration between them, in terms of novel modeling methodologies, advanced numerical algorithms, and physics and mechanisms behind complex material phenomena. We also believe that the success of this workshop will highly benefit the research programs of not only all the participants but also other researchers in this field, and importantly, could lead to significant advances within this scientifically and technologically important area of materials science.
For this workshop we will adopt a format which combines regular seminar presentations with a discussion forum in order to foster active debate. More specifically, at the end of every day all speakers of that day will be placed on chairs at the front of the auditorium and face questions from the audience and other “panel” participants, and discuss novel ideas and future developments (i.e., the “Brainstorming” panel discussion). Based on prior experience of the organizers, such a forum very quickly lends itself to a lively debate and exchange of ideas. It also permits more than the usual time at the end of talks and encourages questions from people who need a little more time to digest a presentation before they can ask a good question (often the case for more junior participants).
Tapio Ala-Nissila (Aalto (FI) and Loughborough University (UK)) - Organiser
Hartmut Löwen (University of Duesseldorf) - Organiser
Ken Elder (Oakland University) - Organiser
Zhi-Feng Huang (Wayne State University) - Organiser