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Melting Kinetics of Confined Systems at the
Nanoscale: Superheating and Supercooling
Cite as: AIP Conference Proceedings 893, 191 (2007); https://doi.org/10.1063/1.2729834
Published Online: 04 May 2007
I. D. Sharp, Q. Xu, C. W. Yuan, D. O. Yi, C. Y. Liao, A. M. Glaeser, A. M. Minor, J. W. Beeman, M. C. Ridgway,
P. Kluth, J. W. Ager, D. C. Chrzan, and E. E. Haller
AIP Conference Proceedings 893, 191 (2007); https://doi.org/10.1063/1.2729834
© 2007 American Institute of Physics.
893, 191
Melting Kinetics of Confined Systems at the Nanoscale:
Superheating and Supercooling
I.D. Sharp,1,2 Q. Xu,1,2 C.W. Yuan,1,2 D.O. Yi,3 C.Y. Liao,1,2 A.M. Glaeser,1,2 A.M.
Minor,4 J.W. Beeman,1 M.C. Ridgway,5 P. Kluth,5 J.W. Ager III,1 D.C. Chrzan,1,2
and E.E. Haller1,2
1.
Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720
Department of Materials Science & Engineering, University of California, Berkeley, California 94720
3.
Lawrence Livermore National Laboratory, Livermore, California 94550
4.
National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, California 94720
5.
Department of Electronic and Materials Engineering, Research School of Physical Sciences and Engineering,
Australian National University, Canberra ACT 0200, Australia
2.
Abstract. In situ electron diffraction measurements of silica-embedded Ge nanocrystals reveal a melting/solidification
hysteresis of 470 K which is approximately symmetric about the bulk melting point. This surprising behavior, which is
thought to be impossible in bulk systems, is well described by a simple, classical thermodynamic model. Surface premelting, which occurs for materials with free surfaces, is suppressed by the presence of the host matrix, thereby allowing
both kinetic supercooling and kinetic superheating of the embedded nanocrystals.
Keywords: nanocrystals, melting, interface energy, superheating, supercooling
PACS: 64.60.-i, 64.70.Dv, 61.46.Hk
substrate by multi-energy ion implantation of 74Ge at
120 keV to 2×1016 cm-2, 80 keV to 1.2×1016 cm-2, and
50 keV to 1×1016 cm-2 followed by thermal annealing
at 1173 K for 1 h under Ar. In situ electron diffraction
was performed between room temperature and 1473 K
± 15 K in a JEOL 3010 microscope using a Gatan
628Ta single tilt heating holder. Several heating and
cooling cycles were performed in 15 K increments and
melting and solidification were characterized by the
intensity change of selected area diffraction patterns
collected after temperature stabilization for ~5 min.
Temperature calibration was achieved by observing
the melting behavior of ion beam synthesized Au
nanocrystals in 500 nm thick silica films. Melting
occurred at the expected temperature, thus confirming
the validity of this experimental technique.
INTRODUCTION
The melting behavior of materials at the
nanoscale is strongly affected by the increasing
importance of the surface. As a result, free-standing
nanocrystals exhibit substantial melting point
reductions relative to their bulk melting point that vary
inversely with the radius of the particle [1,2].
However, for the case of nanocrystals embedded in a
host matrix, the thermodynamic equilibrium melting
point may be either suppressed or enhanced relative to
that of bulk, depending on the relative values of the
solid/matrix and liquid/matrix interface energies.
Here, we show that the kinetic pathways to melting
and solidification also play a critical role in the solidliquid and liquid-solid phase transitions of embedded
nanoscale materials. Thus, both superheating and
supercooling can be observed in a single nanoscale
system with no free surfaces [3].
RESULTS AND DISCUSSION
The integrated diffraction intensity from Ge
nanocrystals
during an in situ heating and cooling
EXPERIMENTAL PROCEDURE
ATTACHMENT
II
is shown
in Fig.
1. During
heating,
CREDIT LINE (BELOW) TO BE INSERTEDcycle
ON THE
FIRST
PAGE
OF ONLY
THEsignificant
diffraction intensity is observed up to 1400 K, well
Ge nanocrystals,
with
an
average
diameter
of
5.1
PAPERS ON PP. 191 - 192, 213 - 214, 315 - 316, 333 - 334, AND 1177 - 1178
above the bulk Ge melting point of 1211 K. Upon
nm, were formed in a 500 nm thick SiO2 film on a Si
CP893, Physics of Semiconductors, 28th International Conference
edited by W. Jantsch and F. Schäffler
2007 American Institute of Physics 978-0-7354-0397-0/07/$23.00
191
cluster and a critical solid cluster is required during the
heating and cooling cycle, respectively [3]. Together,
these kinetic effects lead to the observed hysteresis in
the melting and solidification of silica-embedded Ge
nanocrystals.
We note that, although melting and solidification
are kinetically limited, the nucleation rate of critical
clusters follows a threshold behavior. Therefore, these
experimental results are not highly sensitive to the
heating and cooling rates during measurement.
The solid lines in Fig. 1 show the results of a
quantitative model for the kinetically limited melting
and solidification. Theory and experiment are in
excellent agreement. In general terms, the width of the
hysteresis is governed primarily by the magnitude of
γGe(S)/Ge(L). The position of the hysteresis loop is
dictated by the size-dependent equilibrium melting
point of nanocrystals, given by Eq. 1, which is
dependent on the relative values of γGe(S)/matrix and
γGe(L)/matrix). In the present case, the melting and
solidification hysteresis loop is nearly symmetric
about the bulk melting point and we find that γGe(S)/matrix
≈ γGe(L)/matrix.
FIGURE 1. Integrated intensity of the Ge diffraction rings
during an in situ heating and cooling cycle. Superheating
and supercooling are both observed, resulting in melting
point hysteresis. The solid line shows the predictions of the
kinetic theory of melting and solidification for silicaembedded Ge nanocrystals.
cooling, Ge diffraction rings do not reappear until
~930K. These results indicate that silica-embedded
Ge nanocrystals exhibit a dramatic melting/
solidification hysteresis of ~470 K which is nearly
symmetric about the bulk melting point.
The equilibrium melting point for embedded
nanocrystals, Tm(r), varies with particle radius as [3,4]:
Tm (r ) − Tmbulk ∝
CONCLUSION
Both superheating, which is not observed in bulk
systems, and supercooling have been observed during
in situ thermal cycling of silica-embedded Ge
nanocrystals. The large (~470 K) hysteresis can be
described using a simple, classical thermodynamic
theory. Given the relevant interface energies and the
geometry of the system, this model could be
straightforwardly applied to other nanoscale systems
to identify and predict the kinetic pathways for melting
and solidification.
Tmbulk
(γ Ge( L) / matrix − γ Ge( S ) / matrix ) (1)
Lr
where L is the latent heat of fusion, r is the particle
radius, and γi is the interfacial energy of interface i.
However, we find that equilibrium deviations of the
melting points of nanocrystals from the bulk value can
not explain the large hysteresis present in Fig. 1.
Supercooling of liquids below the equilibrium
solidification point is a well known phenomenon that
occurs due to the energy barrier associated with
nucleation of a solid cluster of the critical size [5].
However, for all known materials γS/V > γL/V + γS/L and
it is thermodynamically favorable for surface premelting to occur. Therefore, nucleation of the liquid
phase is not required and superheating above the
equilibrium melting point is not observed in bulk
systems.
For the case of embedded nanocrystals, a wider
range of interfacial energies is available based on the
choice of materials. Surface pre-melting is suppressed
if γS/matrix < γL/matrix + γS/L and for systems exhibiting
this interfacial energy balance, superheating is
possible. For the case of Ge nanocrystals embedded in
silica, the interfacial energy balances are such that
heterogeneous nucleation of both a critical liquid
ACKNOWLEDGMENTS
This work was supported in part by the Director,
Office of Science, Office of Basic Energy Sciences,
Division of Materials Science and Engineering, of the
U.S. Department of Energy under contract No. DEAC02-05CH11231 and in part by U.S. NSF Grant No.
DMR-0405472.
REFERENCES
1. P. Buffat and J.-P. Borel, Phys. Rev. A 13, 2287 (1976).
2. A.N. Goldstein, C.M. Echer, and A.P. Alivisatos,
Science 256, 1425 (1992).
3. Q. Xu, et al., submitted for publication (2006).
4. P.R. Couchman and W.A. Jesser, Nature 269, 481
(1977).
5. D. Turnbull and R.E. Cech, J. Appl. Phys. 21, 804
(1950).
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