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Computer simulation of disordered structures and nanosystems: An atomic-scale view
Solid State Sciences 12 (2010) 155–156
Contents lists available at ScienceDirect
Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie
Editorial
Computer simulation of disordered structures and nanosystems: An atomic-scale view a b s t r a c t This paper reviews the motivations underlying the organization of the 2008 EMRS Symposium ‘‘Morphology and dynamics of nanostructures and disordered systems via atomic-scale modelling’’ and provides an overview of the main results contained in the nine papers composing the present special issue. We underline the use of molecular dynamics as a main tool to describe structural evolution for systems escaping a precise experimental determination of their atomic configurations (nanostructures and disordered networks). Ó 2010 Elsevier Masson SAS. All rights reserved.
Modelling materials with the purpose of achieving quantitative power of prediction is a longstanding goal of theoretical condensed matter physics and chemistry. In this respect, certain classes of materials have more to gain from approaches in which atomic structures are accurately and reliably determined, both at room temperature and when thermal evolution is taken into account. This is the case of relatively small, isolated systems (hereafter to be intended as nanosystems and/or nanostructures, that could be also found in interaction with a substrate), and of disordered materials, such as liquids and glasses. In both cases, the collection of direct information about microscopic structures stemming from spectroscopy data appears unfeasible, many experimental methods relying on a wealth of interpretation steps not always supported by stringent facts. Historically, the first goal of atomic-scale simulations (a special emphasis being placed in this context on molecular dynamics) was to provide a qualitative, complementary view of microscopic structures and mechanisms of atomic (molecular) motion. Such approaches bypassed the complexity of chemical bonding, to mimic realistic behaviors via ad hoc models. By and large, two effects were reproduced: the repulsion among atoms at very short distances and some form of attraction accounting for bulk cohesion. This scheme was able to characterize at the atomic-scale macroscopic effects such as melting, glass formation, long-range diffusion and stabilization of extended defects (grain boundaries, dislocations). However, the corresponding values of the physical parameters (temperature, pressure) at which the phenomena were observed had, most often, little in common with those recorded in laboratory materials. Quite soon, it appeared clear that simulating condensed matter systems by relying on ’’toy models’’ had more to do with statistical mechanics than with materials science. From the conceptual point of view, the quest for a realistic modelling of materials was boosted over the past three decades 1293-2558/$ – see front matter Ó 2010 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2010.01.016
by two main methodological advances. On the one hand, continuous work has been undertaken to improve the performances of interatomic potentials, by incorporating in their analytical expression many-body forces, polarization effects and parameter fitting on electronic structure calculations. On the other hand, a description of the interatomic forces explicitly taking into account the electronic structure was made available, its only limits being the available computational power, and the accuracy of the electronic structure framework. The collection of papers presented at the EMRS Fall Meeting 2008 ‘‘Morphology and dynamics of nanostructures and disordered materials via atomic-scale modelling’’ is a representative and instructive series of examples of what can be achieved today on a computer, to model disordered materials and nanostructures, including nanostructural-based solid state assemblies. As the title of symposium suggests, the authors have relied on models based on interatomic interactions (either empirically constructed, i.e. classical molecular dynamics (CMD), or based on an explicit account of their electronic structure, i.e. first-principles molecular dynamics (FPMD)). In their work on the transition from wurtzite to the rock salt structure in CdSe, Bealing et al. provide an interesting comparison between a standard CMD approach, where the sample is overpressurized to overcome kinetic barriers, and the metadynamics approach, in which the use of a history-dependent potential forces the system out of local minima. In addition to the physical description of a solid-solid structural transformation, this contribution highlights a methodological advance (the metadynamics) allowing, to overcome the intrinsic time–scale limitations of conventional molecular dynamics. Turning to disordered systems and to the issue of short range order, CMD has been applied to the case of pressure effects in undercooled liquid copper by Celino et al. Here the idea is to analyze the way copper atoms arrange themselves when a liquid
156
Editorial / Solid State Sciences 12 (2010) 155–156
structure becomes configurationally arrested, this kinetic effect being further modified by the presence of an external pressure. This work shows that the pressure increases the probability to find atomic bonds with icosahedral symmetry. In the above examples, CMD allows to tackle issues related to structural organization and phase transitions that are beyond the reach of FPMD, due to its prohibitive computational cost, in terms of memory and CPU time. The question arises about the price that one can afford to pay on the side of a reliable description of bonding. This point is raised in the contribution by Soulairol and Cleri, devoted to the study of Si nanocrystal embedded in an amorphous silica matrix. Here the main issue is the continuous switching of Si atoms from an ideally covalent Si–Si interaction, to a largely ionic character when interacting with oxygen. The presence of very short Si–O bonds prompted the authors to the observation that fine details of chemical bonding (as the appearance of Si–O double bonds) cannot be accounted for within a CMD framework, and would require a DFT-based approach. The dilemma between the less accurate CMD large–scale simulations, and the predictive power of the FPMD approach, clearly limited in both the space and the temporal scale, is one of the open issues of modern computational material science, the present collection of papers providing some stimulating examples. Along these lines, the paper by Jafar and Goyhenex focuses on the complexity inherent in the modelling of metallic bonding for the case of surfaces. A standard tight-binding potential based on the second moment approximation cannot adequately model such defects as stacking faults at surfaces of fcc materials. This means that a higher accuracy in the electronic structure is needed to recover meaningful stacking fault energies. In particular, the paper points out that sp-d hybridization has to be taken into account in order to differentiate hcp and fcc stacking. In this context, the use of order N DFT schemes for metals appears promising and should be pursued. In the case of lithium and sodium tetrasilicate glasses, CMD and FPMD have been used in combination (contribution by Ispas et al.). CMD was employed to produce glassy structures, to be used as starting configurations for FPMD. FPMD allows the direct calculation of NMR spectra, to be compared with experiments. The extraction of structural information from CMD trajectories and their use as starting configurations for FPMD calculations makes sense in this case, since the interatomic potentials are able to reproduce quite correctly essential features of bonding, such as the coordination and the angle distributions. This stems from the predominant ionic character of bonding in this compounds, for which modelling with point-like charges can be taken as realistic. On the contrary, this statement does not hold for the case of chalcogenides systems, where the balance between ionic and covalent contributions is far from trivial. A prototypical phase change material (GeSb2Te4) is investigated by a full FPMD approach in the paper by Raty et al. A simulation box of 168 atoms turns out to be sufficiently large to characterize the amorphous phase and its electronic structure, featuring a non-negligible gap and sp3 hybridization. As a further demonstration of the predictive power of FPMD in the area of disordered materials, the amorphous phase of GeSe2 is taken as a benchmark system to probe the performances of exchange-correlation functionals of DFT (see the paper by Massobrio et al.). Exchangecorrelation schemes which enhance the ionic character of bonding
are found to provide a better picture of deviations from chemical order in this tetrahedral network (homopolar bonds, coordinations different from the tetrahedral one). Overall, FPMD appears as the method of choice for any structural study in which the complexity of bonding invalidates simpler approaches, provided the maximum affordable system sizes are large enough to capture the relevant physical processes. The above selection of papers, derived from the presentations given at the EMRS Fall Meeting 2008 "Morphology and dynamics of nanostructures and disordered materials via atomic-scale modelling", is completed by two contributions less directly linked to the main scope of the meeting. In the first one, Radchenko et al. exploit a kinetic model to describe metal-doped graphene. In the second one, by Lo´pez et al., the effect of electromagnetic fields and pressure is studied in quantum wells. In summary, it is useful to recall a few facts concerning the meeting as a whole. The main result was to make possible the gathering of computational scientists belonging to different communities (materials science, condensed matter physics and chemistry, inorganic chemistry and biology) using atomic-scale computational tools, most of all molecular dynamics. Participants have become aware that the realistic simulation of complex systems, over time intervals encompassing a few ns, has become a reality, due to a combination of methodological advances and increased computational power. Also, awareness of the richness of the techniques available to extend the time scales of the simulations is one of the additional outcomes. By comparing several approaches having in common the acceleration of the dynamical events, a full list of choices has been made available to the users, each specific implementation being adapted to a particular issue. In this context, the impact of linearly–scaling electronic structure methods on future developments appears to increase at a rapid pace. Overall, an upcoming scenario of the evolution of computation for the years to come can now be sketched, combining linearly–scaling methods, accelerated dynamics for rare events, and increasingly reliable descriptions of the chemical bonding. Accordingly, as a promising consequence, future directions in the field of molecular dynamics simulations will be more and more adapted to solve a series of problems common to different scientific areas, with continuous feedback among researchers active in different disciplines. Carlo Massobrio Institut de Physique et de Chimie des Mate´riaux de Strasbourg, 23 rue du Loess, BP43, F-67034 Strasbourg Cedex 2, France Fabrizio Cleri Institut d’Electronique, Microe´lectronique et Nanotechnologie, Universite´ de Lille I, F-59652 Villeneuve d’Ascq, France Rafal Kozubski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Krakow, Poland 11 January 2010
Contents lists available at ScienceDirect
Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie
Editorial
Computer simulation of disordered structures and nanosystems: An atomic-scale view a b s t r a c t This paper reviews the motivations underlying the organization of the 2008 EMRS Symposium ‘‘Morphology and dynamics of nanostructures and disordered systems via atomic-scale modelling’’ and provides an overview of the main results contained in the nine papers composing the present special issue. We underline the use of molecular dynamics as a main tool to describe structural evolution for systems escaping a precise experimental determination of their atomic configurations (nanostructures and disordered networks). Ó 2010 Elsevier Masson SAS. All rights reserved.
Modelling materials with the purpose of achieving quantitative power of prediction is a longstanding goal of theoretical condensed matter physics and chemistry. In this respect, certain classes of materials have more to gain from approaches in which atomic structures are accurately and reliably determined, both at room temperature and when thermal evolution is taken into account. This is the case of relatively small, isolated systems (hereafter to be intended as nanosystems and/or nanostructures, that could be also found in interaction with a substrate), and of disordered materials, such as liquids and glasses. In both cases, the collection of direct information about microscopic structures stemming from spectroscopy data appears unfeasible, many experimental methods relying on a wealth of interpretation steps not always supported by stringent facts. Historically, the first goal of atomic-scale simulations (a special emphasis being placed in this context on molecular dynamics) was to provide a qualitative, complementary view of microscopic structures and mechanisms of atomic (molecular) motion. Such approaches bypassed the complexity of chemical bonding, to mimic realistic behaviors via ad hoc models. By and large, two effects were reproduced: the repulsion among atoms at very short distances and some form of attraction accounting for bulk cohesion. This scheme was able to characterize at the atomic-scale macroscopic effects such as melting, glass formation, long-range diffusion and stabilization of extended defects (grain boundaries, dislocations). However, the corresponding values of the physical parameters (temperature, pressure) at which the phenomena were observed had, most often, little in common with those recorded in laboratory materials. Quite soon, it appeared clear that simulating condensed matter systems by relying on ’’toy models’’ had more to do with statistical mechanics than with materials science. From the conceptual point of view, the quest for a realistic modelling of materials was boosted over the past three decades 1293-2558/$ – see front matter Ó 2010 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2010.01.016
by two main methodological advances. On the one hand, continuous work has been undertaken to improve the performances of interatomic potentials, by incorporating in their analytical expression many-body forces, polarization effects and parameter fitting on electronic structure calculations. On the other hand, a description of the interatomic forces explicitly taking into account the electronic structure was made available, its only limits being the available computational power, and the accuracy of the electronic structure framework. The collection of papers presented at the EMRS Fall Meeting 2008 ‘‘Morphology and dynamics of nanostructures and disordered materials via atomic-scale modelling’’ is a representative and instructive series of examples of what can be achieved today on a computer, to model disordered materials and nanostructures, including nanostructural-based solid state assemblies. As the title of symposium suggests, the authors have relied on models based on interatomic interactions (either empirically constructed, i.e. classical molecular dynamics (CMD), or based on an explicit account of their electronic structure, i.e. first-principles molecular dynamics (FPMD)). In their work on the transition from wurtzite to the rock salt structure in CdSe, Bealing et al. provide an interesting comparison between a standard CMD approach, where the sample is overpressurized to overcome kinetic barriers, and the metadynamics approach, in which the use of a history-dependent potential forces the system out of local minima. In addition to the physical description of a solid-solid structural transformation, this contribution highlights a methodological advance (the metadynamics) allowing, to overcome the intrinsic time–scale limitations of conventional molecular dynamics. Turning to disordered systems and to the issue of short range order, CMD has been applied to the case of pressure effects in undercooled liquid copper by Celino et al. Here the idea is to analyze the way copper atoms arrange themselves when a liquid
156
Editorial / Solid State Sciences 12 (2010) 155–156
structure becomes configurationally arrested, this kinetic effect being further modified by the presence of an external pressure. This work shows that the pressure increases the probability to find atomic bonds with icosahedral symmetry. In the above examples, CMD allows to tackle issues related to structural organization and phase transitions that are beyond the reach of FPMD, due to its prohibitive computational cost, in terms of memory and CPU time. The question arises about the price that one can afford to pay on the side of a reliable description of bonding. This point is raised in the contribution by Soulairol and Cleri, devoted to the study of Si nanocrystal embedded in an amorphous silica matrix. Here the main issue is the continuous switching of Si atoms from an ideally covalent Si–Si interaction, to a largely ionic character when interacting with oxygen. The presence of very short Si–O bonds prompted the authors to the observation that fine details of chemical bonding (as the appearance of Si–O double bonds) cannot be accounted for within a CMD framework, and would require a DFT-based approach. The dilemma between the less accurate CMD large–scale simulations, and the predictive power of the FPMD approach, clearly limited in both the space and the temporal scale, is one of the open issues of modern computational material science, the present collection of papers providing some stimulating examples. Along these lines, the paper by Jafar and Goyhenex focuses on the complexity inherent in the modelling of metallic bonding for the case of surfaces. A standard tight-binding potential based on the second moment approximation cannot adequately model such defects as stacking faults at surfaces of fcc materials. This means that a higher accuracy in the electronic structure is needed to recover meaningful stacking fault energies. In particular, the paper points out that sp-d hybridization has to be taken into account in order to differentiate hcp and fcc stacking. In this context, the use of order N DFT schemes for metals appears promising and should be pursued. In the case of lithium and sodium tetrasilicate glasses, CMD and FPMD have been used in combination (contribution by Ispas et al.). CMD was employed to produce glassy structures, to be used as starting configurations for FPMD. FPMD allows the direct calculation of NMR spectra, to be compared with experiments. The extraction of structural information from CMD trajectories and their use as starting configurations for FPMD calculations makes sense in this case, since the interatomic potentials are able to reproduce quite correctly essential features of bonding, such as the coordination and the angle distributions. This stems from the predominant ionic character of bonding in this compounds, for which modelling with point-like charges can be taken as realistic. On the contrary, this statement does not hold for the case of chalcogenides systems, where the balance between ionic and covalent contributions is far from trivial. A prototypical phase change material (GeSb2Te4) is investigated by a full FPMD approach in the paper by Raty et al. A simulation box of 168 atoms turns out to be sufficiently large to characterize the amorphous phase and its electronic structure, featuring a non-negligible gap and sp3 hybridization. As a further demonstration of the predictive power of FPMD in the area of disordered materials, the amorphous phase of GeSe2 is taken as a benchmark system to probe the performances of exchange-correlation functionals of DFT (see the paper by Massobrio et al.). Exchangecorrelation schemes which enhance the ionic character of bonding
are found to provide a better picture of deviations from chemical order in this tetrahedral network (homopolar bonds, coordinations different from the tetrahedral one). Overall, FPMD appears as the method of choice for any structural study in which the complexity of bonding invalidates simpler approaches, provided the maximum affordable system sizes are large enough to capture the relevant physical processes. The above selection of papers, derived from the presentations given at the EMRS Fall Meeting 2008 "Morphology and dynamics of nanostructures and disordered materials via atomic-scale modelling", is completed by two contributions less directly linked to the main scope of the meeting. In the first one, Radchenko et al. exploit a kinetic model to describe metal-doped graphene. In the second one, by Lo´pez et al., the effect of electromagnetic fields and pressure is studied in quantum wells. In summary, it is useful to recall a few facts concerning the meeting as a whole. The main result was to make possible the gathering of computational scientists belonging to different communities (materials science, condensed matter physics and chemistry, inorganic chemistry and biology) using atomic-scale computational tools, most of all molecular dynamics. Participants have become aware that the realistic simulation of complex systems, over time intervals encompassing a few ns, has become a reality, due to a combination of methodological advances and increased computational power. Also, awareness of the richness of the techniques available to extend the time scales of the simulations is one of the additional outcomes. By comparing several approaches having in common the acceleration of the dynamical events, a full list of choices has been made available to the users, each specific implementation being adapted to a particular issue. In this context, the impact of linearly–scaling electronic structure methods on future developments appears to increase at a rapid pace. Overall, an upcoming scenario of the evolution of computation for the years to come can now be sketched, combining linearly–scaling methods, accelerated dynamics for rare events, and increasingly reliable descriptions of the chemical bonding. Accordingly, as a promising consequence, future directions in the field of molecular dynamics simulations will be more and more adapted to solve a series of problems common to different scientific areas, with continuous feedback among researchers active in different disciplines. Carlo Massobrio Institut de Physique et de Chimie des Mate´riaux de Strasbourg, 23 rue du Loess, BP43, F-67034 Strasbourg Cedex 2, France Fabrizio Cleri Institut d’Electronique, Microe´lectronique et Nanotechnologie, Universite´ de Lille I, F-59652 Villeneuve d’Ascq, France Rafal Kozubski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Krakow, Poland 11 January 2010