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Transcript of Discovery and design of nuclear fuels
ISSN:1369 7021 © Elsevier Ltd 2009NOVEMBER 2009 | VOLUME 12 | NUMBER 1120
Discovery and design of nuclear fuels
Nuclear fuels are complex, multi-component materials containing
actinides such as Th, U, Np, Pu, Am, Cm and their compounds in
specific fuel forms (oxides, nitrides, carbides, alloys, composites,
etc). Adding to the complexity and creating time-varying
composition, the presence of fission products such as Xe, Cs,
Sr, He, I, and Tc makes understanding the evolving properties of
nuclear fuels a major challenge. For example, sintering of ceramic
fuels requires a strict control of composition, thermal treatment,
pressure, and atmosphere1-3. The large number of control
parameters and the uncertainty associated with them often leads
to intractable problems. Similar issues impact the casting and
stability of metallic fuel rods4,5. Once in the reactor, the fuels
and structural materials (pressure vessels, pipes, ducts, etc.) are
subjected to radiation environments that continuously alter their
To facilitate the discovery and design of innovative nuclear fuels, multi-scale models and simulations are used to predict irradiation effects on properties such as thermal conductivity, oxygen diffusivity, and thermal expansion. The multi-scale approach is illustrated using results on ceramic fuels, with a focus on predictions of point defect concentration, stoichiometry, and phase stability. The high performance computer simulations include coupled heat transport, diffusion, and thermal expansion, and gas bubble formation and evolution in a fuel element consisting of UO2 fuel and metallic cladding. The second part of the paper is dedicated to a discussion of an international strategy for developing advanced, innovative nuclear fuels. Four initiatives are proposed to accelerate the discovery and design of new materials: (a) Create Institutes for Materials Discovery and Design, (b) Create an International Knowledgebase for experimental data, models (mathematical expressions), and simulations (codes), (c) Improve education and (d) Set up international collaborations.
Marius Stan
Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
Email: [email protected]
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thermo-mechanical properties6-10. It is well documented11 that
fuels exhibit radial and angular cracks and the severity of the
structural damage increases with burnup. Root causes of these
phenomena are fission-product migration and accumulation in gas
bubbles12-14 that create porosity and significantly slow down the
transport of heat.
To create improved nuclear fuels for the next generation of reactors,
scientists and engineers are partnering in research and development
work that follows the steps of the scientific method. Modern materials,
including nuclear fuels, are often developed using a combination of
discovery and design (see Box 1), with a certain emphasis on discovery.
To facilitate the discovery and design of innovative nuclear fuels and
structural materials, models and simulations are used to predict
irradiation effects on properties such as formation of point defects and
clusters19-27, chemical species and fission-product migration28-31, gas
bubbles formation32, thermal conductivity33-35, oxygen diffusivity36,37,
dislocations38-41, thermal expansion42, and phase stability/
transformations43,44. One of the most challenging aspects is modeling
the complex electronic structure of materials in general45, and the
actinides (especially Pu) in particular46,47 as well as the stability of their
phases48. Another challenge is modeling high temperature effects such
as entropic contributions to the free energy of liquids49.
Conventional nuclear fuelsRecent applications of a multi-scale methodology (see Box 2) to oxide
nuclear fuels resulted in predictions of irradiation effects on properties
such as thermal conductivity, oxygen diffusivity, and thermal expansion.
The methods cover a large spectrum of time and space scales, from
electronic structure to atomistic, to meso-scale, to continuum55.
For example, atomistic models of point defect have been used
to develop continuum thermo-chemical models of point defect
concentrations and oxygen diffusivity in uranium oxides19 and
plutonium oxides56. Several models include the dependence of the
properties on the oxygen content. Building on thermochemical
studies57-59, the models are further used to predict fuel thermodynamic
properties such as the free energy, and to simulate oxygen diffusion at
various temperatures and oxygen pressures.
Another example, this time at the meso-scale, is related to phase-
field simulations of gas bubbles formation and evolution in the fuel60.
Box 1. Scientific discovery and design of materialsThe definitions below are only intended to clarify the use of various
concepts in this paper. For this purpose, science is defined as a rigorous,
systematic use of observations and logic to support or falsify possible
explanations of natural phenomena. This is not that different from
the Britain’s Science Council definition, discussed in15. The scientific
method of investigating natural phenomena (recently under serious and
loving scrutiny16) consists of a series of steps that involve experimental,
theoretical, and computational methods.
An experiment is a procedure undertaken to make a discovery, test
a hypothesis, or demonstrate a known fact. This concept is strongly
anchored in immediate reality although recently the concepts of
“computer experiment” and “virtual experiment” have gained some
popularity. A theory is a formal statement of ideas which are proposed
to explain a class of facts or events. Computation is a procedure used
to determine the solution of a mathematical problem by means of a
computer.
Although the scientific method is observed, to various degrees, by
the entire materials science community, there are notable differences
in the scope and methodology, depending on the goal of the research,
the resources, and the scientific or engineering targets. Materials
discovery (see17 as an example) involves exploring and identifying
existing materials with desirable properties and functionality. The
emphasis is on conducting sound research in areas that are likely to lead
to materials with outstanding properties. As with any other discovery
enterprise, being capable and ready to identify the value of specific
results is the key.
Materials design (see18 as an example) aims at creating new materials
with predefined properties and functionality. After defining the properties
of interest, the focus is on optimizing specific parameters of existing
materials or creating completely new materials that exhibit the sought
after properties. The design methodology (Fig. 1) is quite cumbersome
and involves a series of steps and iterations that may or may not
converge toward a set of optimal parameters.
Fig. 1 The materials design methodology involves a series of steps, iterations, and periodic feedback between theory, experiment, and computation.
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NOVEMBER 2009 | VOLUME 12 | NUMBER 1122
Fig. 3 shows a comparison of experimental61 and simulation62 results.
The simulations capture well the nucleation, growth, and coalescence
of gas bubbles in the fuel grains and at the grain boundaries. The
simulations also predict the thermal conductivity dependence on the
porosity associated with the gas bubbles and the impact on the heat
release.
Similar results have been reported on PuO2 fuels56,63,64. Although
not as extensive, the work on other ceramic fuels such as nitrides65,66
or carbides (with application to coated particle fuels67,68), as well as
studies of surrogate materials based on cerium69 or dysprosium66 are
most encouraging.
Fuel performance (see Box 3) is another area that has benefited
from advanced models and simulations70. Understanding complex
phenomena in fuel elements provides important input to reactor
simulations, currently based on homogenization techniques77. Recent
studies have examined in more detail the thermochemistry of the
Box 2. Multi-scale models and simulationsThis section builds upon a recent discussion of modern epistemic
concepts42. A model is a logical description of how a system (material,
in our case) performs. Models can be empirical or theory-based.
Empirical models are collections of experimental observations fitted to
mathematical expressions, such as (but not only) polynomial functions.
When accurate, empirical models are highly valuable for technological
applications. Theory-based models are built upon fundamental principles
developed within or across scientific disciplines (physics, chemistry, etc).
The multi-science models avoid trial-and-error exercises and aim at
providing a deeper understanding of material’s (fuel’s) behavior. Theory-
based models are expected to have better predictive character.
A simulation is the process of conducting experiments or running
computer programs to reproduce, in a simplified way, the behavior of a
system (nuclear fuel, in our case). Simulations describe the evolution of
the system along a certain coordinate, most often the time (correlated
with the burnup level for the case of nuclear fuels).
Both the models and the simulations must be subject to verification
and validation50. Verification is the process by which the fidelity of a
numerical algorithm with respect to underlying mathematical
representation of a model or simulation is established and the errors
in its solution are quantified. Validation is the process through which
the scientific community comes to accept that a particular model
or simulation reliably describes real world behavior. Most validation
processes involve comparison with experimental data. A critical
component, uncertainty quantification is the process of characterizing
and reducing uncertainties of measurements, model predictions, and
simulation results.
To account for all the important materials properties and reactor
phenomena, the multi-scale models and simulations must address a wide
range of space and time scales, starting with the nucleus and the atomic
electronic structure (nm) all the way to the reactor components (meters),
and from defect formation (pico-seconds) to the operating characteristic
times (months, years). Fig. 2 illustrates some of the theoretical and
computational methods used in the multi-scale approach42,51-53. The
information is transferred between scales via characteristic parameters
such as density, energy, temperature, or grain size distribution54. Meso-
scale and continuum methods are often “atomistically informed”, in the
sense that some of the parameters in the methods are optimized against
the output of atomistic calculations.
Fig. 2 Multi-scale theoretical and computational methods used for materials model development and computer simulations.
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fuel-clad interactions78,79 and the influence of temperature and fuel
stoichiometry changes on the coupling of heat and species transport in
a UO2 fuel element with stainless steel clad80. The results show that
the counterbalancing of the Soret and Fickian fluxes is responsible for
the variation of oxygen concentration in the fuel pellet. Furthermore,
the simulations demonstrate that including the dependence of thermal
conductivity and density on non-stoichiometry can lead to changes
in the calculated centerline temperature that exceed 100 K (Fig. 4).
Additional simulations involved transient regimes and the examination of
the time lag in the response of the temperature and non-stoichiometry
distributions with respect to sudden changes in heat generation rate and
oxygen removal rate. Current work at Los Alamos includes studies of the
effects of porosity on thermal conductivity and thermal expansion81, and
simulations of clad deformation.
Advances in theoretical, experimental and computational capabilitiesAddressing the materials challenges requires a closely coupled
experimental, theoretical, and computational effort directed at
both the scientific and the engineering issues. In this partnership,
new experimental investigation methods such as synchrotron light
sources and proton radiography increase the potential of “in-situ”
characterization of radiation effects on nuclear fuels and provide new
validation opportunities. In addition, theory and high performance
computing expand the investigation space to identify and resolve new
scientific problems.
All top 500 fastest supercomputers in the world can now reach
over a teraflops (1012 operations per second) and the number of
petaflop (1015 operations per second) supercomputers is increasing
BOX 3. Fuel performance capabilitiesA fuel performance capability (FPC) consists of a computer code or
a set of codes that contain models of fuel properties and are able to
simulate phenomena in the nuclear fuel during operation71,72. In a
more general version of this concept, the fuel performance is evaluated
in the entire fuel element (fuel plus clad) and validated “in-pile”73. In
addition to experimental Post Irradiation Examination (PIE), the fuel
performance capabilities are increasingly complex tools in support of
fuel characterization and optimization.
A preliminary design of a new generation Advanced Fuel
Performance Capability (AFPC) was recently proposed42. To
address the nuclear fuels material properties and phenomena, the
capability includes specific computational modules and interacts
with an external database that is continuously updated with the
most advanced models of fuel and materials properties and the
necessary nuclear data. To achieve a consistent predictive character,
many such capabilities are moving away from empirical models and
include theory based models65,70. Other requirements are related to
numerical algorithm design, uncertainty quantification, and software
engineering, including
the use of nested (linear + non-linear) solvers74,75, multi-level
preconditioning, running parallel on large-scale supercomputers, and
easy adaptation to heterogeneous computational platforms.
Fig. 5 shows various paths for fuel performance code development,
using as starting point the USA empirical codes FRAPCON and LIFE.
The blue line represents the path of using “of the shelf” Advanced
Scientific Computing Initiative (ASCI) codes that have been developed
at national laboratories for national security applications, followed by
the addition of physics-based models specific to nuclear fuels. The red
line represents the path chosen by scientists who are interested in first
testing the science-based models in commercial codes such as Comsol
and Abaqus, and only later migrating the codes to high-performance
computers. The best solution might be a balanced approach to
designing a new fuel performance code (green line), based on the
experience accumulated by the European scientists in developing
Transuranus and Pleiades.
As the predictive capabilities continue to improve, fuel performance
codes are expected to become an integral component of nuclear fuels
design and licensing, and of nuclear waste certification processes76.
Fig. 3 Top: Fission gas bubbles in UO2 irradiated in a Pressurized Water Reactor at burnup level 25GWd/t. The sample was annealed at 1275 ºC for 5 hours. Bottom: Phase Field simulations of gas bubble evolution.
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at a fast pace82. Already, neutron diffusion calculations, as well as
some reactor hydrodynamics simulations83,84 are being performed on
such resources. As exaflop computers (1018 operations per second)
are being designed, there is a tremendous opportunity for involving
high-performance computing in nuclear fuels design. However,
high-performance computing requires far more than high-speed
computing. It requires science-based models, innovative numerical
methods, and the ability to generate new ideas85. Here are a few
predictions of exascale computing results and how they can spark
transformational science in support of nuclear fuels discovery and
design:
• Quantum Mechanical calculations of electronic structure properties
of systems consisting of trillions of atoms, compared to the current
hundreds of atoms. Such simulations will predict properties such as
free energy of formation of multi-component metallic and ceramic
fuels.
• Quantum Mechanical calculations at finite (room, high)
temperature, in contrast to the current (mostly) 0 K results. This
will enable predictions of properties such as phonon spectra, heat
capacity, bulk moduli, and stress-strain curves in temperature
regimes relevant to manufacturing, operation, and storage of
nuclear materials.
Fig. 5 Classification of some of the codes currently used for fuel performance and paths towards designing a new generation fuel performance capability.
Fig 4. Simulation of heat transport in a UO2+x fuel element with metallic clad. The temperature profile demonstrates that including the stoichiometry x in the thermal conductivity model changes the predicted centerline temperature by more than 100 K.
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• Atomistic (e.g. Molecular Dynamics) simulations of a much larger
number of atoms (1020), compared to the current state of the art
(108). Such capability will allow for simulations of radiation effects
and damage in heterogeneous regions of the fuel, such as grains and
interfaces.
• Atomistic simulations (e.g. coupled Molecular Dynamics and
Monte Carlo) of coupled neutron transport and radiation
cascades in systems consisting of trillions of atoms, for hours or
even days. This will open up an unprecedented investigative space
to include: simulations of fission-products diffusion in the grain and
at the grain boundary, gas bubbles nucleation, and swelling. It will
also enable access to critical phenomena such as stress corrosion
cracking86.
• Meso-scale diffuse-interface (phase-field) or sharp-interface (level-
set) simulations of microstructure evolution under irradiation. These
simulations will most likely be “atomistically informed” and will
include defect formation and recombination processes occurring in
radiation cascades. These simulations will assist the optimization of
advanced, innovative nuclear fuel forms and the design of radiation
resistant structural materials.
• Multi-scale, embedded simulations, covering large time and
space domains. Such simulations will improve on the “first
principles” character of the multi-scale methodology. However,
including all atoms in the simulation of a specific reactor
component is not only impossible but is also undesirable.
Developing comprehensive models and running simulations “at
scale” in sync with a smart transfer of information between scales
remains the best approach.
Innovative nuclear fuelsDiscovery and design will play a crucial role in developing innovative
nuclear fuels and structural materials for the new generations of
fission and fusion reactors87-91. Besides the optimization of the current
fabrication methods, high performance computing will open many
doors to investigating new phenomena in materials. Advances in
theory, experimental techniques, and computational science will lead
to completely new ways of doing science. What will be next? How
about building materials “atom by atom” to create structures capable
of accommodating the local radiation environment? How about “self-
healing” nuclear reactors that recover after accidents? The range of
innovative science is only limited by our imagination.
An integral component of the innovative fuel development is the
understanding of thermal, mechanical, and chemical properties of the
fissile materials, the source of energy in a nuclear reactor. The multi-
scale approach described in the previous section for U-Pu fuels can
be extended to multi-component systems containing Th (ThO2 based
fuels are already here92), Am (already in some mixed oxide fuels93),
Np, Cm and their mixtures, in fuel forms such as ceramics, alloys, and
composites. That requires several essential steps:
• Developing theory-based models of the free energy of the
subsystems, such as the binary and ternary phases.
• Developing theory-based models of the mobility of species
(actinides, fission products, oxygen, nitrogen, etc).
• Performing simulations of coupled thermal and neutron transport,
species diffusion, and deformation in the multi-component
materials that are major candidates for innovative fuels.
Such a study is extraordinarily complex, requires a tremendous
amount of work, and should start now. It takes years to develop a
good understanding of the properties and phenomena in new, multi-
component materials.
One of the goals that bring together the scientific and engineering
communities is to control the properties and phenomena in irradiated
nuclear fuels and materials. As shown in the previous sections,
to achieve this goal the international community must engage in
developing theory-based models that enhance the understanding
of irradiation effects on materials properties and developing the
computational science required to perform high-performance
simulations.
Another important goal is to discover or design new, innovative
fuels and materials for nuclear energy applications. That involves
creating an integrated theoretical, experimental, and computational
validation process and engaging the national and international
communities in solving problems of high complexity.Fig. 6 Schematic representation of the main components of an Institute for Materials Discovery and Design (IMDD).
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Achieving these goals requires a new paradigm that favors a much
stronger coupling of the various components of the multi-scale model
and simulation methodology as well as a new level of collaboration
and integration among experimentalist, theorists, and computational
scientists. The sub-sections below outline a few components of a
strategy intended to increase the chances of both controlling properties
and discovering and/or designing better nuclear fuels and structural
materials for the new generations of nuclear reactors.
Institutes for materials discovery and designCreating national and international institutes (centers, hubs, etc)
dedicated to accelerating the discovery and design of improved
materials is an immediate and potentially most rewarding initiative.
The mission of such centers is to provide the scientific environment
and resources (people, supercomputers, and funding) for the
development of theory-based models, simulations, and computational
tools able to assist the discovery and design of nuclear fuels and
structural materials.
The institutes will bring together scientists that are trained in
all three areas: experiment, theory, and simulation, and experts in
one. The model development work will cover a wide range of space
and time scales requiring a well balanced portfolio of expertise. The
participants will collaborate in developing and performing atomistic,
meso-scale, and continuum simulations of irradiation effects and
transport phenomena in reactor materials, to predict and control point
defect formation, microstructure evolution, and materials performance
in reactor environments.
The centers will include state of the art laboratories for small-
scale experiments, computational materials science hubs for model
development and remote simulations on high-performance computers,
meeting rooms equipped with advanced visualization capabilities, and
offices for staff, guest scientists and students (Fig. 6). It is critical for
IMDDs to bring together both mature and early career scientists, in a
work environment that allows for uninterrupted time for science.
Knowledgebase for data, models, and simulationsEvery day, a tremendous amount of data is created as a result of
performing experiments and running simulations. Besides numerical
data storage, analysis, and retrieval much progress was made on
the management of information regarding models (mathematical
expressions), simulations (codes), and the visual representations of their
results (pictures, animations).
As a consequence, creating, updating, and maintaining an
international “knowledgebase” that includes experimental data, models
(mathematical expressions), and simulation results (tables, graphs,
diagrams), all linked to publications and web sites, is now possible. The
knowledgebase will have a user-friendly interface and will use advance
query techniques capable of retrieving numbers, text, and images. The
knowledge-base will be updated with information from the IMDDs
and will serve as a resource for national laboratories, universities, and
companies.
No doubt that such an effort will face numerous challenges,
especially in the area of proprietary information, licensing of fuel
performance codes, and non-proliferation. There is however a
significant amount of fundamental scientific information, such
as thermal, mechanical and chemical properties of generic multi-
component fuels and structural materials, phase stability (phase
diagrams), and transport (diffusion) of elements, that can be shared
without infringing upon restricted data.
EducationThe most important resources for creating innovative nuclear fuels
are the nuclear engineers, materials scientists, physicists, chemists,
computers scientists, etc. Their contribution is essential in advancing
the integrated experimental, theoretical, and computational work
and they are the supreme validation authorities. In recent years, the
nuclear engineering community has taken steps toward engaging
prestigious scientists in nuclear fuels research via conferences and
workshops. Scientists are often tempted to direct their studies toward
the most interesting and challenging scientific areas rather than the
most technologically relevant ones; their attraction to nuclear energy
research is rooted in curiosity. To increase the scientific interest, well-
funded national programs must be created to support fundamental
science in the area of nuclear energy and increase the likelihood of
breakthrough discoveries and creative design.
Computational scientists and software engineers are major
participants in designing and writing fuel performance codes. However,
strong teaming among engineers, scientist, and software developers
is key to creating science-based, high-performance codes capable of
running on the present petaflop and the future exaflop computational
platforms. To expand and improve the quality of the models and
simulations, the international nuclear fuels community must develop a
large pool of experts to cover the necessary theoretical, experimental,
and computational tasks. That can be achieved by including “Models
and Simulation of Nuclear Fuels and Structural Materials” in the
materials science and nuclear engineering programs at universities
across the world.
The involvement of the national and international decision factors
(politicians and managers) in the scientific meetings is an encouraging
recent development. More and more decision factors are becoming
aware of the scientific and computational challenges faced by the
nuclear fuels community and can better provide guidance and financial
support for the future research and development programs.
International collaborationsIn addition to improved experiments, models, simulations, and
computational capabilities, a coherent nuclear energy program requires
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national and international collaborations. To cover the necessary
areas of expertise, organizing workshops and sessions on models and
simulations of nuclear materials at international conferences is a
natural strategy component. Only two of the many important scientific
meetings in this area are discussed below.
The Materials Models and Simulations for Nuclear Fuels (MMSNF)
workshop series aims at stimulating discussions and research to
advance theory-based model development, high-performance
computer simulations, and experimental validation for nuclear fuels
applications. The workshops series started in June 9-10, 2003 in
Santa Fe, NM, USA with support from the Advanced Fuel Cycle
Initiative program, funded by the USA Department of Energy,
and the Los Alamos National Laboratory. The workshops usually
bring together around fifty experts in experiments, theory, and
models and simulations from twelve countries or more. The most
recent edition of the workshop (Albuquerque, USA) resulted in an
evaluation of atomistic, meso-scale, and continuum simulation
methods and their impact on nuclear fuel design. The next edition
(MMSNF-9) will be part of the Nuclear Materials Conference, NuMat
2010, in Germany.
The Working Party on Multi-scale Modelling of Fuels and Structural
Materials for Nuclear Systems (WPMM) was created in January
2008, with guidance and support from the Nuclear Energy Agency
(NEA), to address scientific and engineering aspects of fuels and
structural materials. The main goal of WPMM is to establish multi-
scale models and simulations as validated predictive tools for the
design of nuclear systems, fuel fabrication, and fuel performance.
The main tasks include: identification of fundamental problems,
development of atomistically-informed models and simulations of
nuclear fuels and structural materials properties, promoting high
performance computer simulations, and maintaining synergy with
experimental work. Validation of simulation and model predictions is
also a priority as well as the development of new applied mathematics
and software tools.
More initiatives of this type are needed to increase the quality
and intensity of the debate over scientific and engineering problems
relevant to nuclear fuels (including spent fuels94) and nuclear energy
in general95. In many areas, such as the thermo-mechanical and
chemical properties of the fuels, the number of components of the
system subject to investigation is so large (thousands) that no country
alone can study all of them in a reasonable timeframe. Partition of
work and good international collaboration form the best strategy for
increasing the understanding and controlling the properties of such
materials.
Summary and outlookNew generation, innovative nuclear fuels will be complex, multi-
component systems that must perform well in the radioactive
and corrosive reactor environment. The development of such fuels
involves scientific methods focused on both discovery and design.
In this context, multi-scale models and simulations are capable of
investigating a wide range of space and time scales and interact with
fuel performance capabilities to create complex tools in support of
fuel characterization and optimization. In particular, high performance
computing can contribute to increasing the predictive character of
models and simulations and can inspire new ways of doing science.
This approach is expected to become an integral component of nuclear
fuels design, licensing, and waste certification processes.
A new strategy for nuclear fuel development, that involves
discovery and design as equal partners and drivers, is discussed in this
paper. The strategy promotes a much stronger coupling of the various
components of the multi-scale model and simulation methodology and
a much stronger collaboration and integration among experimentalist,
theoreticians, and computational scientists. To this end, it is important
to create research institutes for materials discovery and design and to
create and maintain an international knowledgebase for data, models,
and simulation results. The strategy advocates for direct interactions
among scientists, engineers, and decision factors (politicians and
managers) via international workshops and conferences.
Such initiatives, complemented by other ideas from the international
community, will provide the framework for a stronger integration of
theory, experiments and simulations, leading to an improved control of
the properties and phenomena in reactor materials, and the discovery
and design of new, innovative nuclear fuels and structural materials.
AknowledgementsThis work was occasionally supported by the U. S. A. Department of
Energy via the Advanced Fuel Cycle Initiative (AFCI), the Global Nuclear
Energy Partnership (GNEP), and the Nuclear Energy Advanced Models
and Simulations (NEAMS) Programs.
Further informationInteresting web pages:MMSNF-7: http://itu.jrc.ec.europa.eu/index.php?id=36&type=&iEntryU
ID=164&iEntryPID=68
NEA: www.nea.fr
Roadrunner supercomputer: www.lanl.gov/roadrunner/
High Performance Computing workshop: www.cels.anl.gov/events/
workshops/extremecomputing/nuclearenergy/agenda.php.
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