Software Platforms for Electronic/Atomistic/Mesoscopic Modeling: Status and Perspectives
- 397 Downloads
Predicting engineering properties of materials prior to their synthesis enables the integration of their design into the overall engineering process. In this context, the present article discusses the foundation and requirements of software platforms for predicting materials properties through modeling and simulation at the electronic, atomistic, and mesoscopic levels, addressing functionality, verification, validation, robustness, ease of use, interoperability, support, and related criteria. Based on these requirements, an assessment is made of the current state revealing two critical points in the large-scale industrial deployment of atomistic modeling, namely (i) the ability to describe multicomponent systems and to compute their structural and functional properties with sufficient accuracy and (ii) the expertise needed for translating complex engineering problems into viable modeling strategies and deriving results of direct value for the engineering process. Progress with these challenges is undeniable, as illustrated here by examples from structural and functional materials including metal alloys, polymers, battery materials, and fluids. Perspectives on the evolution of modeling software platforms show the need for fundamental research to improve the predictive power of models as well as coordination and support actions to accelerate industrial deployment.
KeywordsIntegrated computational materials engineering (ICME) Materials modeling Software Interoperability Industrial deployment Metal alloys Polymers Batteries Fluids
We are witnessing the dawn of a Golden Age of integrated computational materials engineering (ICME). The confluence of five main factors is creating this unprecedented situation, namely (i) theoretical physics and chemistry have established a solid scientific foundation in the form of classical mechanics, electrodynamics, statistical thermodynamics, and quantum mechanics; (ii) computer hardware with astounding performance has become readily affordable; (iii) advanced software systems are enabling unprecedented productivity while the tools for software development are constantly improving; (iv) today’s communication technologies enable instantaneous and global collaboration as well as access to a daunting wealth of data; and, last but not the least, (v) the potential economic impact of this technology has aroused the interest of industry around the globe, thus driving the accelerated transition from academic research to practical applications.
There are also important modeling applications in the field of raw natural materials. These materials can be either minerals (e.g., rocks, ores, clay) or organic (e.g., wood, coal, kerogen, asphalt). They are used or processed by important industrial sectors including oil and gas, building materials, metallurgy, energy, and chemistry. Understanding the properties of these materials is required for the design of safe and economic processes in these branches. Due to their complexity, they are particularly challenging for modeling, but substantial progress is already being made.
At present, simulations based on classical mechanics, fluid dynamics, and electrodynamics are well established R&D tools in the design of components and systems, leading to better products, reduced development time, and lower experimental costs. The benefits are evident such as safer and better cars, highly efficient airplanes and turbines, and a myriad of electronic products. However, the materials property data required for these macroscopic simulations are for the most part taken from experiment. Hence, the introduction of new materials hinges on experimental synthesis and characterization, which are often slow and expensive bottlenecks.
While experiments will always be needed, the capability of computing properties of materials prior to their synthesis radically changes this picture. This is a wonderful situation, but the reality of predicting the properties of a material at a level of accuracy and reliability to be useful in an engineering process is challenging. Successes are emerging, but it is fair to say that the technological readiness level of electronic and atomistic software, which is a fundamental part of ICME, leaves ample opportunities for improvement.
It is the purpose of the present paper to review the current state of software platforms, which enable materials property predictions based on a combination of electronic structure methods, atomistic simulation tools using interatomic potentials or forcefields, and mesoscopic modeling tools. In the following, this combination will be referred to as “e/a/m.” The focus here is on approaches based on fundamental physical concepts such as Schrödinger’s equation and statistical thermodynamics. One needs to keep in mind that in practice, empirical methods such as quantitative structure-property relationships (QSPR), data mining, and machine learning play an important role. In fact, these approaches can be very effective if used in combination with physical equation-based predictive methods.
Historically, the methods shown in Fig. 2 have been developed by different groups, initially mostly in academic research groups, government laboratories, and in some cases by industrial research organizations such as Bell Labs and the research centers of IBM in Yorktown Heights and Rüschlikon. The work by different research groups in physics, chemistry, materials science, and biology, and the different focus, assumptions, and approximations used in describing various materials and properties have resulted in a fragmentation of this field, which persists to the present day.
On the level of ab initio quantum mechanical approaches, theoretical chemists and solid-state physicists pursued different routes for many decades. Many quantum chemists aimed at the most accurate solution of Schrödinger’s equation for small molecules starting from Hartree-Fock theory while theoretical solid-state physicists developed methods based on density functional theory (DFT) [1, 2]. During the past decades, DFT has become a workhorse also for molecular systems while Hartree-Fock-based methods have found their way into solid-state methods. Driven by the quest for higher accuracy and enabled by increasing compute power, we are witnessing today a convergence of these two approaches, for example in the form of hybrid functionals.
Semi-empirical quantum mechanical approaches as implemented in programs such as MOPAC  are extremely useful due to their high computational efficiency and good performance especially for organic and inorganic molecular systems. The use of extensive training sets of experimental data in the parameterization while maintaining key aspects of molecular quantum mechanics are the foundation for the success of this approach. Semi-empirical calculations can be 100 times faster than ab initio calculations, thus offering an interesting approach for high-throughput calculations . Furthermore, semi-empirical methods can be implemented such that the scaling of the computing time is better than N2 while ab initio approaches typically scale with a power of 3 or higher, with N being the number of electrons, although the so-called order-N ab initio methods exist as well.
The modeling and property predictions of liquids  and amorphous materials such as polymers and glasses, as well as simulations of dislocations in metal alloys, may require the sampling of millions of configurations or large systems containing hundreds of thousands of atoms or more. The desire to model such systems has led to the development of forcefield (or force field) methods, a terminology preferably used by chemists [6, 7, 8] or interatomic potentials, preferably used by physicists [9, 10]. Both terms refer to the same concept, namely, the use of relatively simple mathematical expressions such as Morse-type binding curves to describe the interaction between atoms. A major incentive for the development of forcefields was the desire to simulate the interaction of drug molecules with DNA and proteins. Extension of these forcefields to synthetic polymers and organic liquids has enabled the prediction of structural, thermomechanical, and rheological properties with remarkable accuracy. Interatomic potentials have also been successful in describing metallic systems as well as highly ionic materials. However, these approaches are different in character and thus mixed systems such as an interface between a polymer and a metal represent a conceptual dilemma. In this context, it should be pointed out that the Nobel prize for chemistry was awarded to Martin Karplus, Michael Levitt, and Arieh Warshel in 2013 for the “Development of multi-scale models for complex chemical systems.”
The optimization of forcefield parameters using results from ab initio calculations as training set is one method to expand the scope of ab initio methods. Calibrating the forcefield parameters on sensitive quantities such as the experimental density, heat of formation, mechanical properties, or the melting point of a material leads to powerful computational approaches, which can be more accurate than DFT calculations, albeit with a narrower range of applicability, as will be illustrated by the prediction of boiling points of liquids discussed in a later section.
The so-called cluster expansion method [11, 12] offers another possibility to expand the scope of ab initio calculations. In this powerful and elegant method, ab initio calculations are used iteratively to build an expression of the total energy of a system as a function of local arrangements (clusters) of atoms. This expansion reproduces the original DFT values with a fidelity of a few milli-electron-volts (or a few tenths of a kJ mol−1). However, the presence of a lattice is required. Hence, this method is particularly well suited for the simulation of metal alloys.
Kinetic Monte Carlo simulations can describe phenomena on very long time scales and on large systems containing millions of atoms. For example, the dynamic evolution of phase segregation in a metal alloy can be simulated, if the jump rates of elementary diffusion steps are known. Diffusion rates and, more generally, reaction rates can be obtained from ab initio calculations using transition state theory or specific forms of molecular dynamics.
Coarse-graining is yet another possibility within the class of forcefield methods to extend the length and time scales of atomistic simulations. This method can be applied to perform molecular dynamics, Monte Carlo simulations, Brownian dynamics, and dissipative particle dynamics. While conceptually appealing, the construction of accurate coarse-grained models requires substantial insight into the key interaction mechanisms of a material and thus is far from being an automatic process.
This short overview of e/a/m methods gives a glimpse on the contrasting simplifications of the various approaches and the resulting difficulties in integrating these approaches into a unified modeling platform with smooth interoperability among the different approaches as well as connecting such a platform with simulations operating on the continuum level.
To assess the present modeling platforms, we will now discuss the requirements for such a software system. While great progress has been achieved during the past decades, it will also become obvious that in many instances, these requirements are only partially fulfilled, thus leaving room for major improvements.
Status of e/a/m Modeling Platforms
Material modeling platforms serve two closely connected purposes, namely (i) enabling a deeper understanding of mechanisms that lead to a certain behavior of materials, for example stress corrosion cracking, and (ii) predicting properties of materials prior to their synthesis and experimental characterization, for example solid-state electrolytes for Li-ion batteries. Here, we assess the status of e/a/m modeling platforms guided by their key attributes. To this end, we draw on experience in the development of the modeling and simulation platforms Insight II and Discover (Biosym Technologies), Cerius2 (Molecular Simulations, Inc.), Materials Studio (Accelrys), UniChem (Cray Research), and MedeA (Materials Design, Inc.). It should be noted that this selection is based on the direct experience of the authors and is not intended to be exhaustive. A comprehensive compilation of such platform and simulation tools is given by Schmitz and Prahl .
Comprehensive—predictions of all relevant physical and chemical properties for all types of materials such as metals and alloys, semiconductors, and insulators; inorganic and organic materials; crystalline and amorphous phases such as glasses and polymers as well as fluids in liquid and gaseous form.
State-of-the-art—computational materials science is an active research field with new methods emerging at a relentless pace. Users of leading platforms expect the best and most recent methods to be available.
Verified—tests need to show that algorithms are correctly implemented and that programming bugs have been found and corrected. Verification of computer codes need to be repeated after changes are made to the software or when hardware or operating systems change.
Validated—computed properties need to be validated against experimental data with estimation of error bars.
Robust—in the coming age of high-throughput calculations, all simulation programs need to work correctly under a large range of input conditions.
Error recovery and fault tolerance—errors in the computations, whatever their origin might be, must be automatically detected and, if possible, corrected.
Ease of use—time to solution is critical and needs to be minimized; input parameters should be kept to a minimum without undue complexity nor redundancy.
Standardized—computer programs should use standardized procedures to facilitate the exchange of data from simulations performed by different people at different times with different programs.
Ability to create, store, and re-use workflow protocols—providing traceability and reusability are essential requirements for industrial use and quality control.
Well documented—context-dependent documentation of the underlying theory, algorithms, and tutorials are important parts of any good software system.
Computationally efficient—the performance of hardware continues to progress and should be fully utilized by any software platform.
Supported consistently on evolving hardware and operating systems—acquiring the skills to use any software platforms for materials simulations to its fullest capabilities represents an investment of years. This investment needs to be protected by support over many years.
Extensible—theory, algorithms, and software implementations evolve and any sustainable software platform needs to be able to incorporate new capabilities without having to rewrite entire codes.
Portable—scientific software has a longer life cycle than computer hardware and operating systems; software should be written in a form which facilitates portability to new hardware and operating systems.
Interoperable with other software components and platforms—modeling and simulations of materials involve tools from different sources and suppliers; standardization and interoperability are mandatory.
Able to communicate efficiently with public and proprietary databases—modeling and simulations of materials are built on previous knowledge and data; a close integration of existing experimental data with e/a/m simulation platforms sets the stage for powerful materials property mining and optimization.
Tracking of metadata for traceability and re-use—like experimental data, computed results require metadata to make them useful such as input data, computational parameters, date and time, links to input and output files, program version, operating system, time, and operator.
Based on these requirements, the current status is discussed in detail in the following sections.
Current e/a/m platforms address a wide range of materials and properties, as shown in Fig. 3, but the technological readiness level of such property calculations is not uniform. For example, elastic coefficients of crystalline solids and synthetic polymers like cross-linked epoxy resins can be computed with remarkable accuracy and predictive power while the accurate prediction of other properties such as the melting temperature of even some common crystalline materials remains as a major challenge.
Historically, the modeling of different classes of materials has evolved from research efforts of quite different scientific communities. This has led to a range of different theoretical and computational approaches, terminologies, and different units. Thus, there are now modeling methods which address specific materials and properties quite well, but are applicable only to individual systems such as a bulk metal or an organic polymer, but not to an interface between a polymer and a metal.
Fortunately, as computational approaches mature, they tend to become more general, thus allowing broader modeling of complex multi-phase systems. For example, electronic structure methods for solids on the one hand and quantum chemistry methods for molecules on the other hand have been developed for well over half a century by different research groups. The solid-state community pursued density functional theory (using Rydberg atomic units or eV) while quantum chemists built on Hartree-Fock methods (using Hartree atomic units or kcal mol−1). To further complicate matters, the definition of “mol” could mean mol of atoms, mol of compounds, or mol of simulation boxes. Today, these methods have merged and one can readily compute the interaction of a molecule with a metal surface. Nevertheless, domain-specific computational methods are still predominant presenting a challenge for the practitioner who wants to solve multi-phase and multi-materials problems in a single modeling platform.
Today’s leading e/a/m modeling platforms provide in a single environment access to a comprehensive range of methods including electronic structure methods for solids, surfaces, and molecules as well as forcefield-based methods. These programs are accessible from a single user interface, thus allowing the choice of the most appropriate method for the question or materials property at hand. In addition, there are specialized platforms with a focus on specific properties, for example thermo-physical properties of molecular liquids.
State of the Art
Innovative methods in computational materials science are being developed by an increasing number of research groups around the world. Users of advanced simulation platforms expect to benefit from the best of these developments without undue delay. These could involve, for example, new functionals in DFT methods, new algorithms for highly accurate post-DFT approaches such as the random phase approximation in electronic structure methods , or it could be a new forcefield or a new statistical ensemble. Of course, rapid access to new capabilities competes with other requirements such as validation, robustness, and standardization.
Development and marketing strategies for materials modeling software vary. If the software is intended for a broader user base, then packaging may take precedence over rapid access to the latest and greatest computational methods. Academic sources of software tend to put a high priority on state-of-the-art functionality whereas some commercial software platforms seek a broader user base by providing ease-of-use and automation. Each strategy has its merits and drawbacks and the end-users select the appropriate environment given their needs.
Both scientific and commercial applications of software rely on the correct implementation of algorithms and the absence of programming errors. Verification is a very difficult and time-consuming part of software engineering. Static verification is usually the first step, where the source code is being inspected for aspects such as compliance with the standards of a chosen computer language and the absence of simple typographical errors. Dynamic verification involves the execution of tests where the answer is known from other sources.
When new features are implemented in a software, regression tests are used to verify that existing functionality is preserved. This test is also critical when the software is ported, for example, to new operating systems, but also when new compilers or libraries are used. Non-regression tests are necessary to ensure that improved or new features indeed have the desired effect. Both types of tests are necessary. It is good practice that testing is performed by others than the original code developers.
If a new computational method together with results for specific cases is already published, then a new implementation of such a method should be tested against these earlier results. A recent example is a comparison of DFT results obtained with three different computer codes, namely VASP, GPAW, and Wien2k . This study demonstrated that the variation between the results from these three different implementations vary by an order less than the typical deviation of the computed results from experiment. This example also indicates that verification and validation often go hand in hand.
Validation and Estimation of Error Bars
Practical solutions of many industrial problems do not require the most accurate approaches. However, frequently one needs fast and cost-effective property values with sufficient accuracy and reliability to be used for making engineering decisions. This requirement leads to the need for reliable error estimates, especially for approximate methods. A priori such estimates are very difficult to make. Hence, the assessment by experts are necessary in this case, possibly aided by statistical methods.
Validation of computational approaches and the analysis of uncertainty thus remains a central requirement of e/a/m platforms. Systematic comparison with accurate and reliable experimental data provides the most compelling analysis. However, one should keep in mind that occasionally experimental data are incorrect, for example simply due to typographical transcription errors or due to uncontrolled effects during the measurements. In fact, high-level computations can play a critical role in identifying such errors and deficiencies. Illustrative examples are provided by the realization that the reported elastic constants of sapphire had for many years included an indexing error  and an incorrect feature of the band structure was reported for InAs, a standard III-V semiconductor . In both these instances, the source of the experimental discrepancy was identified based on accurate computation. Industrial research and development experience, which frequently does not immediately emerge in the research literature, indicates that these are far from isolated examples.
In the late twentieth century, when compute power was much more limited and expensive than today, typical modeling efforts entailed in the study of individual or a handful of systems. In this situation, it was quite feasible to monitor the progress of calculations and to adjust computational parameters such as basis sets of quantum mechanical calculations or convergence criteria in geometry optimizations by hand. This is no longer practical in high-throughput calculations on thousands of systems, which are enabled by today’s compute power.
For this reason, robustness of “compute engines” is becoming a critical aspect of modern simulation platforms. This means that the right choices of computational parameters can no longer be made by hand for each system, but they need to be universal over a large set of systems. Before launching any simulations, the modeling platform needs to assess the formal correctness and consistency of input structures and computational parameters. This includes simple aspects such as avoiding that input structures contain atoms which are unphysically close, but it also can mean that a model of cross-linked polymer with 100,000 atoms does not contain unphysical topologies such as highly strained ring catenation. Leading modeling platforms provide such consistency checks.
Today’s leading quantum mechanical solid-state programs such as VASP are remarkably general in terms of the choice of atoms (from hydrogen to curium) and robust in terms of initial structures in geometry optimizations or ab initio molecular dynamic simulations. The situation is quite different in forcefield-based molecular dynamics and Monte Carlo simulations. While excellent forcefields (in terms of generality and accuracy) for many organic molecules are available, which today’s modeling platforms can assign automatically in a large variety of models such as molecular liquids and polymers, occasionally functional groups or multifunctional molecules are encountered, where some forcefield parameters are missing. This issue is more pronounced when forcefields (or interatomic potentials) are needed to describe inorganic systems and/or systems comprising inorganic and organic matter. For many cases, classical forcefields simply do not exist or transferability of parameters cannot be achieved. Using such forcefields in a blind fashion can then lead to unexpected results or perhaps unmitigated disasters. The fact that a given forcefield is not applicable to a specific system or to a certain property may not be obvious even to the experienced users. No current modeling platform can guarantee robustness in every situation. Rather, the platform should warn the user before launching a simulation, in cases where the initial model of the system(s) or the description of the interatomic interactions may be unphysical.
Another aspect of robustness is the behavior of the modeling platform when the size of the system or the required simulation time exceeds the available computing resources. While it would be desirable that the user is informed about the necessary computing resources prior to launching a simulation, estimating such resource requirements is demanding and today’s modeling platforms usually do not currently offer such a feature.
Robustness of a software system also implies stable behavior under any operating conditions. State-of-the-art modeling platforms involve very complex human/machine interactions as well as asynchronous, non-deterministic inter-process communications, for example between a user interface and tasks running on different computers in a network. Sophisticated software engineering, employing established communication patterns and protocols, make such systems reliable.
Error Detection and Correction, Fault Tolerance
Errors can occur in any modeling step including the building of structural models, the setting of input parameters, lack of convergence in iterative procedures, and numerical instabilities, as well as in the analysis, storage, and retrieval of computed results. Furthermore, today’s highly networked and distributed computing environments are subject to faults due to network problems as well as failures in hardware and operating systems. In the past, when simulations were executed individually, error detections and corrections were possible by human control and intervention. With workflows and high-throughput calculations, this is no longer possible and automated control mechanisms are required. Determining whether a specific simulation was correct or erroneous requires context-dependent information and judgment. Most advanced materials modeling platforms presently leave room for improvement in error handling and fault tolerance.
Ease of Use
The ease of use of a software system can be gauged by the number, rapidity, and visual comfort of steps a user must take to accomplish a task. If the task is simple and well-defined, then the number of steps should be minimal and convenient. If the task is complex, the user should have flexibility in defining the appropriate modeling approach and parameters. In any event, the user interface should be homogeneous in its automation, e.g., in the treatment of single-phase and multi-phase systems or in the treatment of a single system or a large list of systems.
The options for each step should be self-evident to the user and they should be presented in a form and language which is commonly used in the specific discipline. The high degree of specialization in materials science and engineering makes the design of easy-to-use software platforms challenging. However, specialization also implies a narrow focus, which could make it easier to construct protocols involving a small number of steps.
Typically, academic researchers require leading functionality and access to a large range of computational parameters enabling them to push the frontiers of research while industrial materials engineers need well-tested computational protocols and parameter settings to obtain a specific answer rapidly and reliably in the context of an overall engineering project. Few parameters are often a good indicator of mature algorithms and programs.
Software engineers of user interfaces for smartphones are masters in the creation of ergonomic systems, thus setting similarly high expectations for ease of use in other software systems. However, user interface design for a smartphone is subject to very different constraints than those of highly specialized materials modeling platform. The market for smartphones is measured in billions while that for materials modeling software is about five orders of magnitude smaller. The possible investments in user interface design scale accordingly. The functionality of smartphones like making a phone call, taking a picture, or getting directions to a restaurant can be readily defined while ease-of-use for functionality such as predicting the stress-corrosion behavior of a new alloy is rather different. Furthermore, “ease of use” for materials scientists and engineers who are not modeling experts means being able to perform specific but complex simulations in an easy and straightforward way, e.g., use of property modules and libraries of flowcharts. A full-time expert modeler has other requirements, namely ergonomic design, intuitive menus, and access to maximal functionality in the quickest ways, avoiding multiple repeats of a certain action, e.g., by defining loops in flowcharts and custom stages. Thus, ease of use remains a significant challenge for developers of e/a/m modeling platforms and there is room for design diversity and products depending on the specific needs of target users.
Scientists and engineers spend many hours on their computers and this time may increase in the future. Hence, ergonomics should not be forgotten and input from the medical science should be taken into account in the design of user interfaces.
Standards are the foundation of efficient communication and interoperability. It is probably fair to say that today’s components for e/a/m materials modeling, for example different DFT programs or forcefield codes, each have their own sets of conventions and data representations, which makes their integration in a common platform a tedious task. In software platforms developed since the 1980s, integration and unification of different programs was achieved by creating data representations and file formats which provides sufficient information to generate program-specific input files. Post-processing then converts the various output formats into a common representation. However, each software platform has had and still has its own set of formats and limited practical standardization has been achieved. However, several common file formats have emerged to exchange structural data of atomistic models between different software platforms. In this respect, significant efforts have been made by crystallographers, which have stimulated the developers of integrated software e/a/m platforms.
An important milestone in the standardization of molecular ab initio calculations was the introduction of the so-called Pople Gaussian basis sets. Thus, Hartree-Fock calculations on a specific molecule with such a standardized basis set yield the same total energies close to machine precision independent of the specific program. This is significant, as complex thermodynamic cycles can be constructed from values taken from calculations performed by different authors with different programs.
In the case of solid-state calculations using DFT, such a standardization has not yet occurred at the same level as in quantum chemistry. Even if two programs use the same approximation for electron exchange and correlation, the resulting total energies still depend on many other computational choices such as specific pseudopotentials or numerical grids used for the radial functions in all-electron methods, number of plane waves, and Fourier grids. This lack of standardization hampers the exploitation of collections of DFT results and represents a major challenge for efforts such as the NoMaD DFT data storage and indexing project . However, the issue of reproducibility in DFT calculations is being addressed .
The situation in forcefield calculations is better than in the realm of DFT calculations. With a given forcefield, computed properties obtained from different programs should result in identical results if the same statistical ensembles and simulation parameters are employed. In practice, results from different simulations carry a statistical uncertainty, but they can be used in a common analysis.
Forcefield methods are used to simulate the behavior of systems such as molecular fluids and polymers. Computing properties reliably for this class of materials hinges on correct statistical sampling and, of course, on the quality of the underlying forcefield. For example, the result for elastic coefficients of a single computation on a single amorphous polymer model has limited meaning, whereas performing the same calculation on 100 different models yields well-defined upper and lower bounds for such properties. Leading modeling platforms provide this type of statistical analysis.
The requirement for performing a set of connected simulations points to another requirement, namely that of reproducible workflows. This is discussed in the next section.
The complexity of scientific software requires documentation detailing the physical equations being solved, explaining the algorithms and parameters, which influence the quality of the solutions, and describing the practical use of the software. Scientific publications related to these programs are valuable as additional source, but they are different from software documentation in purpose and scope. In fact, a complete users’ guide of e/a/m platforms is comparable in volume to a textbook. Documentation is part of the software package and should be updated with each new version of a platform.
Well-designed software systems offer context-sensitive help whenever the user needs specific instructions to accomplish a certain task or needs to understand the available options and implications of their choices. This form of documentation is extremely helpful in intuitive, direct-manipulation interfaces as it relieves the user from switching to different sources during a work session.
The computation of materials properties can be numerically very demanding and thus computational efficiency is very important. Throughout the evolution of computational materials science platforms, developers have had to face the dilemma of finding the right balance between creating code which can be easily ported between different hardware platforms, and implementations, which seek the highest performance on specific hardware architectures. In the 1980s and 1990s, vector supercomputers offered unprecedented performance gains if special hardware features could be fully utilized. Cray Research produced the most successful of this class of computers. One of the reasons for this success was the excellent balance between vector and scalar performance and the availability of powerful compilers, which did not require deep changes in the computer programs to receive the benefit of the vector architecture. At present, similar arguments hold for parallel architectures. Given the steady progress in computational approaches and in view of the fact that the optimization of a large computer code for a specific hardware architecture can be a daunting and time-consuming task, developers are often reluctant to devote their time to the optimization of a specific hardware architecture such as GPUs. By the time such an optimization is completed, the field may have moved on and the users may have a highly optimized code with obsolete functionality. Efficient compilers and software tools are thus essential for taking advantage of high-performance hardware. One has to keep in mind that various computational approaches such as ab initio quantum mechanics, forcefield-based molecular dynamics, Monte Carlo simulations, and machine learning have quite different requirements for high-performance computing. Care must be taken that each method benefits from advances in high-performance hardware.
Support of a sophisticated scientific software system such as an e/a/m modeling platform is needed on several levels, namely during installation and configuration of the software, in the practical handling of the software, and in the correct and efficient scientific use. The first level is the domain of information technology. Software running on a single machine typically can be installed fully automatically with minimum user intervention. Complex software, which is installed on different machines on a network with different levels of security and access privileges, may require support and customization. The second level, the correct manipulation of the software can either be covered by demonstrations, tutorials, user forums, online support, and training sessions.
In an industrial environment, the time of scientists and engineers is highly valuable. Thus, learning the effective use of a new software tool such as an e/a/m modeling platform and its integration in the engineering process represents a significant investment. To protect this investment, it is critical that the software environment is supported for many years in the form of updates, addition of new functionality, and migration to new hardware systems.
Computational materials science continues to evolve, existing methods are extended, new theoretical methods and algorithms are being developed, and new software systems are being created. Thus, the ability to extend and grow is an essential requirement for the long-term success of an e/a/m platform. This implies a clear modular structure of the software based on a thoughtfully designed data model. Extensions can consist, for example, of the addition of a new approach in solving Schrödinger’s equation, they can mean a new forcefield for molecular dynamics or Monte Carlo simulations, or the addition of a new coarse-graining for large-scale simulations. However, extensions can also mean the addition of new paradigms such as high-throughput calculations.
Scientific software has a life span of many decades, as seen, for example, by computational chemistry programs such as Gaussian , which has its origin in the 1960s when computers had core memories measured in kBytes and were programmed with punch cards. Today’s computing environments for scientific and engineering applications are characterized by a mix of laptops, desktops, local compute clusters, and massively parallel supercomputers using Windows, Mac OS X, and Linux operating systems. Cloud computing and hand-held devices are likely to play an increasing role in the future. Porting a complex software system to a new operating system can be greatly facilitated if software is written in a machine-independent language and if any operating system-dependent parts are well isolated from the bulk of the code. On the other hand, if a software system is tied to a single operating system with a graphical user interface relying on a legacy programming language, then the port to other environments can become a daunting task. A costly re-write of the entire system may be the only way forward.
The properties of materials depend on phenomena reaching over 10 to 20 orders of magnitude in lengths and time scales and span essentially all branches of physics and chemistry. A great number of different approaches and software systems have been developed to deal with this diversity on both the discrete (e/a/m) and the continuum levels. Integration of hitherto separate programs into unified platforms has been pursued since the 1980s, for example Insight II of Biosym Technologies provided access to forcefield-based molecular dynamic programs (Discover) and a quantum chemical program (DMol) in a single platform. Another example is UniChem of Cray Research which provided interoperability between a semi-empirical quantum chemistry program (MNDO91), an ab initio Hartree-Fock program (CADPAC), and a molecular density functional code (DGauss). From a single interface, a user could create an atomistic model, perform a geometry optimization with a semi-empirical method, and use the output of this calculation seamlessly as input for Hartree-Fock or DFT calculations.
More recently, the AiiDA open source project  aims at the development of a platform for automation of calculations, input and output data storage, interoperability within work flows, and for sharing these contents within research communities. Plug-ins for the solid state ab initio plane wave code Quantum Espresso , the molecular quantum chemistry code NWChem , Wannier90 ,  for obtaining maximally localized Wannier functions, and access to structural databases such as the COD [26, 27] are being implemented. Furthermore, related activities can be observed in larger research group and institutions, aiming at such platforms mainly for internal use.
This level of interoperability relies on a common platform that uses a data model allowing the creation of program-specific input and the interpretation of the output of one program such that it can be used as input to other programs. The unifying platform thus becomes a hub, which enables to plug in various programs. This model is relatively straightforward to implement for quantum chemical calculations where a system is defined by atomic positions, element type, and possibly magnetic moments.
On the other hand, the interoperability between programs using classical forcefields is more complicated. For example, a Monte Carlo method for the calculation of adsorption isotherms of a liquid in a nano-porous structure may use a united atom (UA) description of interatomic interactions, which cannot be uniquely mapped onto an all-atom (AA) description using a valence forcefield. Nevertheless, algorithms can be found to bridge this gap between different representations as long as the UA and the AA forcefields can describe the entire system. This is no longer the case if a model includes, for example, a metal surface covered with an organic polymer. The popular embedded atom method (EAM) would work well for the metal, but is difficult to reconcile with a valence forcefield, which is available only for the organic part of the system. The interoperability of programs and methods applicable only to a subset of a model is thus problematic.
Such incompatibilities become more complicated if one tries to build bridges between a quantum mechanical description of part of the system coupled to a forcefield description for the surrounding of a chemically reactive area. Such so-called quantum mechanical/molecular mechanical (QM/MM) methods have been pursued since the 1980s especially in biomolecular systems. While conceptually appealing, the practical treatment of the transition between the QM and MM domains remains rather difficult. As mentioned earlier, the merits of multi-scale approaches for complex chemical systems were recognized by the 2013 Nobel prize in chemistry.
Interoperability and coarse-graining open a host of issues, which have yet to be fully resolved. For example, while lumping and clustering techniques seem logical in working from the atomic scale to macroscopic phenomena, de-lumping techniques are required to allow interoperability in both directions. Coarsening of an atomistic model is generally straightforward, for example progressing from an all-atom description to united atoms, anisotropic united atoms, and techniques of dissipative particle dynamics. However, creating chemically correct atomistic models from a coarse grain model, for example in describing a grain boundary, is all but trivial. Significant work lies still ahead to achieve interoperability on these levels.
In the foreseeable future, no supplier is likely to provide a software system covering the entire range of all possible applications on all length and time scales in a single software system. Thus, enhanced interoperability between different software systems is essential for the overall success and impact of materials modeling.
Integration with Experimental Databases
“Numerical simulations without connection to experimental data is like clapping with one hand”, as Arthur J. Freeman used to say. Thus, the integration of experimental databases adds great value to materials modeling platforms. This has been implemented, for example, in the MedeA® software platform, which includes leading crystallographic databases (ICSD, Pearson, Pauling, COD). These databases can be searched with a common interface, although the integrity and uniqueness of each database is preserved. The modeler can search, for example, for all compounds which contain Li and a transition metal, retrieve all such the structures with a few mouse clicks, and initiate calculations such as the computation of the chemical potential of Li ions in all these compounds in a few minutes.
Tracking of Metadata
As in experiments, the results of computations are meaningful if additional information is associated with the computed physical properties. This information includes the type of equations underlying the models, the algorithms and computational parameters being used, the program version, the time, and the scientist/engineer who performed the computations. Present computational platforms provide mechanisms to associate and store these metadata automatically with the results of a computation. This aspect is particularly useful for work done in teams over a long period, where traceability and re-usability are of high value. Reproducibility might indeed be the most valuable aspect, because often one wants to build on previous experience starting with an existing case for verification.
As computed material property data become integrated in an overall engineering process, it is important for legal reasons and for the protection of intellectual property to pay attention to the careful curation of metadata associated with computations. On the other hand, an engineer may just be interested in a value and an error bar and might consider too many meta-data as distraction. This brings us back to the design of user interfaces, where the perception of “best” differs between different users.
Knowledge Management and Best Practices
As staff moves to different positions or retires, it is highly valuable for any organization that the knowledge and accomplishments of these employees is retained and transmitted to their successors. To this end, a good modeling platform should have mechanisms to capture and retain the results of computational investigations in a form that allows new employees to retrieve and to capitalize on previous work. Concepts such as the JobServer of the MedeA®  software platform automatically keep records of all simulations including input and output data together with flowcharts of simulation protocols as well as time stamps and user information, thus helping in the implementation of best practices for research and development.
From Academic to Commercial Software
A major part of e/a/m modeling software has been developed in academic research groups. The major driving force for these developments is scientific innovation and advanced functionality. While typically very strong with respect to advanced functionality, present academic software often falls short in many of the requirements discussed in the previous section, for example with respect to ongoing support and interoperability.
Open source software is common in a variety of application areas including electronic structure calculations. The success of Linux is often cited as an argument for this approach. It is remarkable that the most successful solid-state electronic structure program, namely VASP [29, 30], does not fall under this category. While the source code of this program is accessible via a license, maintenance and new developments are handled by a single university research group with clearly defined responsibilities and ownership. Another program, namely CASTEP, is integrated in a commercial modeling platform while other electronic structure codes such as Quantum Espresso, Abinit, CP2K, and Wien2k are distributed either in the form of the GNU General Public License or special licenses. In fact, there is a range of licensing models, e.g., the Apache License, BSD license, GNU General Public License, GNU Lesser General Public License, MIT License, Eclipse Public License, and Mozilla Public License. Each of these schemes has different implications for the transfer from academic research to industrial applications.
There is debate in the community as to which of these licensing schemes is best. It is probably fair to say that there is no simple answer to this question, because it depends on many factors such as scientific and technological maturity, the organizational structure supporting the development, the industrial relevance, and the objectives of the key authors.
Publicly funded academic software is not always “open source,” nor free. Moreover, there are additional aspects/differences between academic and commercial software, such as generality, coverage, and robustness. Academic software is usually application oriented, e.g., proteins, ionic liquids, sorption in specific solids, or the motion of dislocations in a metal. Additionally, academic software typically relies on developments made by non-computer scientists, and optimization is usually not the leading objective. Commercial codes tend to be more robust, more general in terms of methods and operating systems, and better optimized.
Long-term support is often a key issue for academic software. In fact, experience in the domain of finite element methods, computational fluid dynamics, and TCAD for electronic devices has shown that in the long run, the successful industrial deployment of modeling software is best served by commercial providers. In the field of e/a/m modeling, we are witnessing the transition from academic research to industrial application. In this context, efforts are being made to accelerate this transition. For example, the European Commission is funding projects such as the EMMC-CSA  to enhance the industrial uptake of material modeling by industry in the spirit of the ICME.
Zr alloys are primary structural materials in the core of nuclear power reactors. Zr is a key element in the material due to its low neutron absorption cross-section. Alloying elements including Fe, Ni, Cr, Sn, and Nb are added to improve mechanical properties such as yield strength and corrosion resistance. Fe, Ni, and Cr exhibit extremely low solubility and tend to precipitate into secondary phase particles (SPPs). During irradiation, the alloying elements are released from the SPPs and are free to diffuse and interact with defects in the material.
Zr alloys for nuclear applications have been subject to numerous, predominantly experimental, investigations. However, the number of computational studies is steadily growing. Ab initio DFT methods and EAM-based forcefields are valuable approaches that have been employed to study irradiation-induced structural changes in Zr alloys [32, 33]. With the development of experimental techniques such as atom probe tomography (APT), the material can be characterized at the Ångström regime, allowing for direct comparisons between experimental observations and data obtained from an e/a/m modeling platform. For example, APT studies have shown that Fe segregates to metal grain boundaries and ring-shaped features of Fe have been observed in addition to small clusters of not fully developed Fe precipitates . The ring-shaped features can be interpreted as being due to segregation of Fe to dislocation loops.
This example shows that the contact area between experiments and simulations is extending to the behavior of individual atoms. The empirical and theoretical methods complement each other and a state-of-the-art, comprehensive e/a/m modeling platform is a vital part of the synergistic approach.
Computed and experimental elastic coefficients of epoxy thermosets with different resins
Calculated bounds (GPa)
4.396 ± 0.027b
5.103 ± 0.033b
Design of Zero-Strain Cathode Materials for Li-Ion Batteries
These most promising materials were synthesized and characterized by X-ray diffraction as well as electrochemical techniques. The results were consistent with the ab initio predictions .
This behavior is in close analogy to observation for the zero-strain mechanism for Li4Ti5O12, where local distortions in the crystal structure likewise allow this material to keep the volume nearly unchanged upon lithium insertion.
Compared with solid materials, fluids offer a tremendous advantage in connecting the macroscopic scale with atomistic simulations. In many cases, macroscopic properties such as the density, viscosity, and the vapor pressure can be obtained directly from atomistic simulations involving only of the order of a thousand molecules given proper statistical averaging over configurational space to obtain reliable results.
The computations are based on statistical thermodynamics using isochoric Gibbs Ensemble Monte Carlo simulations to determine the equilibrium between the vapor and liquid phases as a function of temperature [44, 45]. The interactions between atoms are described by a classical forcefield which expresses the total energy of a system as a summation of different terms which are described by mathematical functions containing adjustable parameters. These forcefield parameters describe interatomic interactions such as the bond strength between a carbon and oxygen atom as a function of the local chemical environment. They are obtained by fitting to data from first-principles quantum mechanical calculations on representative molecules as well as by calibration using a training set of experimental data. Once these forcefield parameters are defined, they are used in systematic and transferable way to perform calculations for a large number of molecules. The development of forcefield parameters for organic systems has a history of many decades and today excellent forcefields for such computations are available [46, 47].
The boiling points computed for 100 different organic compounds agree very well with the experimental data, as illustrated in Fig. 9, with an absolute average deviation of 1.4%. Note the wide range of different organic compounds and the fact that all data points are bound within a relatively tight tolerance. This means that the approach has good predictive power and thus can be used in design cycles.
For all non-aromatic compounds, the anisotropic united atom (AUA) forcefield [48, 49, 50, 51, 52, 53, 54, 55, 56, 46] has been used. For the aromatic compounds, the TraPPE forcefield has been used . The two forcefields used have been chosen for their high quality, allowing fast and high accuracy vapor-liquid-equilibrium calculations of the families of compounds included in this work.
Such computations of the pure compounds can be extended to different temperatures, leading to a complete description of the vapor-liquid equilibrium or to different temperatures and pressures, leading to a complete description of the gas or the liquid phase, even at supercritical conditions.
Importantly, this approach can be also used for any mixtures of the above compounds, thus providing vapor-liquid phase diagrams for a rather large design space, which can now be explored computationally in an optimization process.
Many design and engineering problems involve not just single phases (solid, liquid, gas) but most often different phases in contact. Forcefield simulations can be applied in such systems, to study, for example, the sorption and diffusion of a molecular fluid into a micro-porous solid .
Properties of Molten Metals
Perspectives and Conclusions
Present software platforms for materials modeling on the level of electrons and atoms have emerged from two major sources, namely molecular modeling systems used earlier in chemical research and computer programs developed by researchers in the field of solid-state physics and statistical mechanics. The resulting software platforms are used in academic research and their industrial deployment is growing. However, this field is presently characterized by groups of ab initio programs with similar functionality while there are still major gaps, which need to be filled.
Present computer codes originate predominantly from academic research groups and thus are driven by the quest for leading research. Although some of these codes are integrated in e/a/m software platforms and are commercially supported, it is fair to say that fundamentally, these codes retain a mostly academic character. This reflects the actual state of the theory underlying ab initio solid-state computations. The present theoretical underpinning such as density functional theory is very useful, but this level of theory is not yet fully satisfactory; new and better approximations to describe interacting many-electron systems are still evolving, which makes this field naturally somewhat dynamic. Consequently, in academia, functionality is the major driving force rather than stability, robustness, error handling, standardization, and interoperability. Thus, programs that combine state-of-the-art scientific functionality with a good measure of the other attributes discussed above have emerged as clear leaders in their league.
On the level of forcefield-based codes for molecular dynamics and Monte Carlo simulations, the picture is somewhat different. Algorithmically, this level is quite mature, but the Achilles heel of this type of simulations is the quality and coverage of the underlying forcefields or interatomic potentials. Forcefield developments have been pursued with great vigor since the 1980 especially for biological systems such as DNA and proteins, which led subsequently to the extension of this methodology to the simulation of synthetic polymers and, more generally, to the simulation of organic molecular systems including liquids. Hence, simulations of such systems have reached a remarkable accuracy, as demonstrated in this review for the case of the calculation of boiling points of organic liquids. In contrast, the same cannot be said for the simulation of inorganic systems such as metals, alloys, semiconductors, and insulators. For these types of systems, the neglect of a quantum mechanical description of the electronic degrees of freedom often encounters severe limitations, creating a serious challenge for the simulation of complex systems that require models consisting of millions of atoms and many millions of configurations.
Linking and coupling quantum mechanical domains with those requiring forcefield simulations remains as a major challenge for the creation of e/a/m modeling platforms. This goes beyond the integration of various programs in a single software system which is already accomplished by leading modeling platforms. The partitioning of a system into domains that are handled by a forcefield or by a quantum mechanical description is not automated and relies on the user’s decisions. Moreover, the coupling between these domains poses serious challenges, especially between metals and non-metallic solids or fluids.
The creation and optimization of forcefield parameters “on-the-fly” is an intriguing perspective and, in fact, novel tools have emerged that facilitate the generation of forcefield parameters from ab initio training sets. Yet, the choice of the appropriate forcefield type and the optimization of the parameters is far from being a fully automated and robust process.
The next level of linking in a comprehensive e/a/m modeling platform can be summarized as coarse-graining/fine-graining. There is clearly a lack of tools which would facilitate this task. As pointed out earlier, one needs to think not only about coarse-graining, but one should also consider the inverse, namely fine-graining, starting, for example, from a model of a microstructure represented at the continuum level and resolving the structure of dislocations and grain boundaries on the atomistic level.
Linking the microstructure to the processing and the chemistry of the material under consideration is yet another step, which should be part of an ICME implementation. While major efforts are made at this level, the communication with the e/a/m levels leave ample room for improvements. Creating overarching software environments remains a daunting task. Extrapolating from current activities, the connection in multi-scale approaches will be first implemented for specific applications such as additive manufacturing and thus will remain rather narrowly focused.
Integration into comprehensive software platforms and interoperability between platforms are certainly important and highly useful, but the main bottleneck remains on the level of the theoretical and computational approaches.
This brings us to the issue of the economics of the development and support of materials modeling platforms in a still rapidly evolving field. In contrast to molecular modeling in the pharmaceutical industry, materials modeling is subject to quite different boundary conditions. The goal of pharmaceutical research and development is very focused and well defined, namely the discovery of novel molecules with specific therapeutic effects. To support this effort, molecular modeling platforms serving this market have been developed and are commercially supported. In contrast, the materials-related industry is extremely diversified in its goals with each sector being relatively small, but very specialized. For example, the development of a high-performance steel is quite different from the optimization of a Schottky barrier in a semiconductor; the optimization of polymers for use in printed circuit boards requires quite different knowledge and tools than the search for better solid-state electrolytes for Li-ion batteries, novel materials for data storage, or rare-earth free magnetic materials. Each of these materials science problems requires quite different and very sophisticated simulation tools to make a valuable contribution to the engineering process. However, many of these materials, for example high-performance thermoelectric materials, represent only a small fraction of the value of the final product, and yet a new material, such as cobalt-oxide cathodes, can enable extraordinary technologies, such as lithium-ion batteries. The rewards for investment in advanced materials discovery and process optimization can be substantial.
There is also a desire to transfer research from industry to academic groups, which either develop their own software or rely on open source software, which is adapted for the problem at hand by indentured graduate students and post-docs. In some circumstances, this can inhibit investment in building the comprehensive e/a/m software platforms that fulfill the criteria discussed earlier in this review. Hence, in addition to the intrinsic scientific and technological challenges, there are also economic hurdles which are to be overcome.
One perspective is the open-source paradigm combined with a licensing scheme which keeps the software and all its future enhancements in the public. The initial investment is made by public funding until the community of developers and users is large enough to sustain future developments. While such a paradigm has worked well for software such as the Linux operating system, it is questionable if highly specialized and sophisticated scientific software can be developed and sustained in the long run by this approach. The future of the excellent LAMMPS molecular dynamics program  will show how this paradigm will play out in the long run.
Another perspective is the rise of commercial software companies building integrated software platforms, which are professionally engineered and supported. As pointed out earlier, the investment for creating and supporting such integrated software environments is very substantial because of the high degree of sophistication and specialization in materials science.
The evolution of this field will likely represent a combination of these two perspectives. There is a place for sharing software in the early stages of conceptual and algorithmic development in the spirit of academic research so that complex software systems can be created without unnecessary and time-consuming duplication of effort. However, as software technology matures and its innovative appeal for academic research diminishes, the industrial value of such software tends to rise as it moves from the stage of leading research to industrial production. Concurrently, the need for robustness and long-term support will increase. In fact, this is analogous to the development and transition of other research and development tools such as X-ray diffractometers, NMR machines, and scanning tunneling microscopes. Leading edge research at one stage becomes a production tool in a later stage and it is quite reasonable to assume that the same trend will take place in the field of software platforms for materials modeling.
In view of the tremendous importance of advanced materials and processes for the future of our civilization, the perspectives for ICME are very bright. However, vision, commitment, investment, skill, and persistence will be necessary to move this field forward and to reap its benefits for society. The challenges are many and the right expectations must be projected. The embedding of e/a/m platforms in ICME frameworks will open unprecedented possibilities for the design of materials and processes, but all participants in this process must continue to support each other, including universities, government laboratories, funding agencies, software companies, and industry. A Golden Age of ICME is ahead of us. Let us proceed with confidence!
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 723867.
- 4.Rozanska X, Stewart JJP, Ungerer P, Leblanc B, Freeman C, Saxe P, Wimmer E (2014) High-throughput calculations of molecular properties in the MedeA® environment: accuracy of PM7 in predicting vibrational frequencies, ideal gas entropies, heat capacities, and Gibbs free energies of organic molecules. J Chem Eng Data 59:3136–3143Google Scholar
- 5.Allen MP, Tildesley DJ (1987) Computer simulations of liquids. Clarendon Press, OxfordGoogle Scholar
- 6.Jorgensen WL (2002) OPLS force fields, Encyclopedia of computational chemistry, John Wiley & SonsGoogle Scholar
- 13.Schmitz GJ, Prahl U (2016) Handbook of software solutions for ICME. John Wiley & SonsGoogle Scholar
- 18.NoMaD (Novel Materials Discovery) http://nomad-repository.eu/cms/. Accessed 14 November 2016
- 19.Lejaeghere K, Bihlmayer G, Bjorkman T et al. (2016) Reproducibility in density functional theory calculations of solids. Science 351:6280Google Scholar
- 20.Gaussian G09 (2016) http://www.gaussian.com/. Accessed 14 November 2016
- 22.Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti G L, Cococcioni M, Dabo I, Dal Corso A, Fabris S, Fratesi G, de Gironcoli S, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen A P, Smogunov A, Umari P, Wentzcovitch R M (2009) J Phys: Condens Matter 21 395502. doi: 10.1088/0953-8984/21/39/395502
- 27.Gražulis S, Daskevic A, Merkys A, Chateigner D, Lutterotti L, Quirós M, Serebryanaya NR, Moeck P, Downs RT, Le Bail A (2012) Crystallography Open Database (COD): an open-access collection of crystal structures and platform for world-wide collaboration. Nucleic Acids Res 40. doi: 10.1093/nar/gkr900
- 28.MedeA® – Materials Exploration and Design Analysis (2016) Materials Design, Inc. www.materialsdesign.com
- 31.EMMC-CSA (2016) European Materials Modelling Council – Coordination and Support Action. European Commission, Directorate-General for Research & Innovation, Industrial Technologies, Advanced Materials and Nanotechnologies Grant number 723867Google Scholar
- 35.Rigby D, Saxe P, Freeman C, Leblanc B (2014) Computational prediction of mechanical properties of glassy polymer blends and thermosets, in Advanced Composites for Aerospace, Marine and Land Applications, Sano T, Srivatsan TS, Paretti MW (eds.) John Wiley; ISBN 8791118888919Google Scholar
- 42.Rosciano F, Christensen M, Eyert V, Mavromaras A, Wimmer E (2014) Reduced strain cathode materials for solid state lithium ion batteries. International Patent Publication Number WO2014191018 A1Google Scholar
- 43.Yiannourakou M, Ungerer P, Leblanc B, Ferrando N, Teuler J-M (2013) Overview of MedeA®-GIBBS capabilities for thermodynamic property calculation and VLE behavior description of pure compounds and mixtures: application to polar compounds generated from lingo-cellulosic biomass. Mol Simul 39:1165–1211Google Scholar
- 62.Taihei M, Hidetoshi F, Takaharu U, Masayoshi K, Kiyoshi K (2005) Surface tension measurement of molten metal using a falling droplet in a short tube. Transactions JWRI 34:29Google Scholar