COMMENTARY
Synergistic science
SIDNEY YIP is at the Department of Nuclear Engineering and Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge,
Massachusetts 02139, USA.
Should computational materials science be recognized
as a field with a role in the community comparable to
computational physics or chemistry? With the emergence
of multiscale modelling, the answer is a resounding ‘yes’.
a
1,600
Figure 1 Melting curve of
crystal argon. a, The solid
curve shows predictions from
free-energy calculations
based on molecular dynamics
simulation combined with a
dynamic Clausius–Clapeyron
integration method10. The
various experimental
measurements are indicated
by the symbols. b, The
crossing of the Gibbs free
energies (G) at a pressure of
50 MPa for the crystal and
liquid phases defines the
melting point (arrow). c,
Corresponding differences in
entropy (S) and enthalpy (H )
between the liquid and crystal
reveal the role of entropy in the
two phases.
Melting curve of argon
1,400
1,200
Pressure (MPa)
1,000
800
600
Simulation
400
Experiment
200
0
50
100
150
200
250
300
Temperature (K)
c
b
1.5
–5.9
Liquid
–6.0
Energy (10–2 eV)
–6.2
T(Sliquid–Scrystal)
1.4
Melting point
–6.1
G (10–2 eV)
T
he way we think about simulations and
materials research is changing dramatically.
One reason is the advent of large-scale
computations, once a rare resource, which
make powerful simulation methods readily
accessible to the average researcher. Less obvious but
equally significant are conceptual and technical
advances being made in materials modelling —
by which I mean theory and simulation with due
consideration for experiments. Together, these
developments point to the emergence of a quantitative
approach for dealing with a very wide range of physical
structures and phenomena, one that uniquely
complements the traditional methods of theory
and experiments.
There are certain problems concerning the
fundamental description of materials properties and
behaviour, previously regarded as intractable, that are
now becoming amenable to simulation and predictive
analysis (two examples are described in the text below).
One might say that these new results arise because
materials modelling embraces practically all of the
disciplines within science and engineering; in turn it is
enriched by the contributions of a multidisciplinary
community with diverse expertise and perspectives. It
is also tempting to regard computational materials as a
new framework in which to organize research
initiatives and bring out the synergistic potentials of
cooperation among the different parts of the broad
church of materials research. In the Brave New World
of science-based simulations, there are opportunities
for innovations in universities, corporate and
government research organizations — from the
introduction of broad-based curricula to the creation
of centres and laboratories for collaborations across
traditional boundaries.
Multiscale materials modelling has come to
symbolize this emerging field. It does this by linking
simulation models and techniques across the micro-to-
Crystal
–6.3
–6.4
–6.5
1.3
Hliquid–Hcrystal
1.2
1.1
Melting point
1.0
–6.6
0.9
–6.7
80
85
90
95
100
Temperature (K)
nature materials | VOL 2 | JANUARY 2003 | www.nature.com/naturematerials
105
80
85
90
95
100
105
Temperature (K)
3
© 2002 Nature Publishing Group
COMMENTARY
macro length and timescales. The ultimate goal is to be
able to analyse and eventually control the outcome of
critical materials processes, which tend to be highly
nonlinear, inhomogeneous, or non-equilibrium in
nature. In this paradigm, electronic structure would be
treated by quantum-mechanical calculations, atomistic
processes by molecular dynamics or Monte Carlo
simulations, mesoscale microstructure evolution by
methods such as finite-element, dislocation dynamics,
or kinetic Monte Carlo,
continuum behaviour
THE TIME IS RIPE FOR CURRICULUM and
by field equations well
known in fluid and solid
INITIATIVES THAT ENCOURAGE
mechanics. The vision
STUDENTS, ALONG WITH THE
driving multiscale
modelling is simply that,
FACULTY, TO LEARN AND WORK
by combining these
WITHOUT DISCIPLINARY BOUNDARIES different methods of
modelling, one can attack
new classes of problems in a much more comprehensive
manner than when the methods are used individually.
The appeal of this point of view is evident from
recent conferences and workshops, special issues of
journals, and calls for proposals by funding agencies,
where multiscale modelling is the central theme1–7.At a
workshop in Bodega Bay (USA) in 2001, the context was
modelling plasticity and failure in metals — technical
issues critical to the science-based stewardship of the US
nuclear stockpile8. Not only was the integration of
simulation methods singled out for discussion, but also
the incorporation of experiments. At another
international conference in London (UK), last year9, the
focus was on how the array of current capabilities for
materials modelling on different length scales can be
applied to industrial problems.
I believe that, despite the current attention, one
should continue to reflect on, and examine why and
how computational materials can remain a vital field.
One should bear in mind those enduring characteristics
that allow us to gain insights not available from
experiment or theory only. The foundations of
multiscale modelling are conceptually and
computationally quantifiable; they can be as physically
realistic as the existing laws of physics and chemistry.
For example, through atomistic simulations, the effects
of intermolecular interactions on the physical
properties of liquids and solids can be scrutinized at any
level of detail. This knowledge can be correlated with the
specific features of the interatomic potential to explain
the bulk behaviour of a material in terms of models of
interatomic forces. Moreover, through quantummechanical calculations, one can understand how
chemical bonds are formed and broken in terms of the
charge distribution of the electrons.
In a simulation one has direct control over the
initial and boundary conditions, and access to
complete information on the electronic structure and
molecular levels. This makes it possible to unravel the
microscopic mechanisms underlying a particular
phenomenon. This is also the most promising route to
achieve systematic structure–property correlations.
To illustrate the power of this concept, let us consider
how atomistic simulations could contribute to our
understanding of crystal melting and plastic
deformation, two basic, natural phenomena that
continue to hold scientific interest.
The prediction of a phase transition through
calculation of the free energies (G) of the coexisting
phases is a long-standing challenge in statistical
mechanics. Figure 1a shows the melting curve of argon
determined by a single non-equilibrium molecular
dynamics simulation10. Because no experimental
information of any kind was used, the quantitative
correspondence with experimental results is direct
evidence of our ability to describe the thermodynamic
behaviour of simple materials. Although both Gliquid and
Gcrystal decrease with increasing temperature (Fig. 1b) it
is enlightening that Gliquid decreases at a faster rate.
One sees from the entropic contributions to the free
energy difference between the liquid and crystal (Fig.
1c) that melting is driven by the more rapid entropy
increase in the liquid relative to that in the crystal.
Results such as these provide hope that we may one day
understand the amorphous state in the same
quantitative manner.
The origin of crystal plasticity lies in the nonlinear
response of the dislocation core to the local strain
environment at the atomic level, a process that is
notoriously difficult to probe. A basic issue, raised in
both Bodega Bay8 and London9, is the homogeneous
nucleation of a dislocation and its subsequent mobility.
Figure 2 shows a molecular dynamics simulation of the
emission of dislocation loops in an initially defect-free
thin film under a nano-indenter at the limit of elastic
stability11. With relatively few defects present, it is
possible to observe the formation and subsequent glide
4
nature materials | VOL 2 | JANUARY 2003 | www.nature.com/naturematerials
Figure 2 Molecular dynamics simulation of dislocation nucleation. Atomistic details of a dislocation
loop punched out in a single-crystal Cu thin-film under an indenter reveal the subsequent emission
and gliding path (composite of three snapshots) of a prismatic loop to the lower surface of the film11.
Each atom is colour-coded with respect to the number of its nearest neighbours. Only defective atoms
are shown; these are distinguished by either their energy or their immediate environment relative to
that for atoms on the perfect lattice, and they comprise only a small fraction of the total number of
atoms used in the simulation.
© 2002 Nature Publishing Group
COMMENTARY
of a prismatic dislocation loop. Simulations of this type,
once deciphered in detail, can reveal the mechanistic
processes that govern the early stages of plastic
deformation. In contrast, Fig. 3 shows the complexity of
dislocation microstructure generated by two colliding
crack tips in a simulation using about a billion atoms12.
This is much more challenging to analyse; in the
multiscale modelling context, it illustrates the need for
mesoscale methods capable of incorporating the
essential physics from the microscopic scales11,13,14.
It is clear that there will be no shortage of problems
for materials modelling, offering both fundamental
challenges and technological relevance. Although not all
problems require a multiscale approach, materials
research will benefit greatly from the bridging of
different length and timescales. There has been relatively
less progress in linking timescales, but the difficulties are
no less formidable, and if anything the needs (and
opportunities) are even greater.
Everyone who takes part in this growing enterprise
shares the responsibility of maintaining a healthy respect
for the challenges of multiscale modelling and adopting a
realistic view of what constitutes success. The time is ripe
for curriculum initiatives that encourage students, along
with the faculty, to learn and work without disciplinary
boundaries, and to exploit new computational
technologies, in visualization, scientific packages and data
mining.And whenever we get the opportunity to create
centres or groups dedicated to computational materials,
the challenge will be to demonstrate how physics,
chemistry, biology and engineering models can all play
central roles in the study of materials.
References
1.
2.
3.
4.
5.
6.
7.
J. Comput. Aid. Mater. Des. (Special Issue) 3, (1996).
Campbell, G. H. et al. Mater. Sci. Eng. A 251, 1–22 (1998).
Curr. Opin. Solid State Mater. Sci. (Special Issue) 3, (1998).
J. Comput. Aid. Mater. Des. (Special Issue) 6, (1999).
Mater. Res. Soc. Symp. Proc. (Special Issue) 538, (1999).
Mater. Res. Bull. (Special Issue) 26, (2001).
Stoneham, A. M., Howe, A. & Chart, T. Predictive Materials Modelling DTI/OST
Figure 3 Dislocation
microstructure formed by two
crack tips, visible as notches
at the top and the bottom, as
they move toward each
other12. The results were
generated by a large-scale
molecular dynamics
simulation. Only the defective
atoms are shown; these
comprise a small fraction of
the total number of atoms used
in the simulation.
Foresight Report DTI/Pub5344/02/01/NP, URN 01/630 (2001).
8. Workshop on Multiscale Modeling of Materials Strength and Failure Bodega Bay,
California, USA, October 7–10, 2001.
9. International Conference on Multiscale Materials Modelling Queen Mary,
University of London, UK, June 17–20, 2002.
10. de Koning, M., Antonelli, A. & Yip, S. J. Chem. Phys. 115, 11025–11035 (2001).
11. Li, J., Van Vliet, K. J., Zhu, T., Yip, S. & Suresh, S. Nature 418, 307–310 (2002).
12. Abraham, F. F. et al. Proc. Natl. Acad. Sci. USA 99, 5783–5787 (2002).
13. Haslam, A. J., Moldovan, D., Phillpot, S. R., Wolf, D. & Gleiter, H. Comp. Mater.
Sci. 23, 15–32 (2002).
14. Bulatov, V., Abraham, F. F., Kubin, L., Devincre, B. & Yip, S. Nature 591, 669–672
(1998).
Acknowledgements
I thank D. Wolf, F. Abraham, A. S. Argon, V. Bulatov, L. Kubin, J. S. Langer,
T. A. Tombrello and S. Suresh for sharing with me their insights on simulation and
materials research, and many collaborators, especially J. Li, M. de Koning
and K. Van Vliet, for recent work leading to the views expressed here. I also
thank A. M. Stoneham for correspondence on materials modelling perspectives
and assessments.
nature materials | VOL 2 | JANUARY 2003 | www.nature.com/naturematerials
5
© 2002 Nature Publishing Group