Kinetics and thermodynamic behavior of carbon clusters under high pressure and high temperature Page: 4 of 4
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between these endpoints. The resulting barrier
height is in agreement with the LDA results of
bulk activation energies4 Considering the differ-
ences in the methods being compared, the agree-
ment in the shape and location of the transforma-
tion barrier is excellent.
The second part of this paper deals with dif-
fusion kinetics and thermodynamic aspects of car-
bon clusters. On the thermodynamic side, we
explored the phase diagram of carbon at high
temperature and pressure via molecular dynam-
ics using the bond order potential developed by
BrennerP This potential allows for realistic break-
ing and formation of bonds and reproduces cor-
rect bond strengths for many bonding possibilities
found in hydrocarbon systems, including correct
structures for all the common hybridization states
(sp, sp2 and sp3) of carbon under ambient condi-
tion and allowance for the breaking and formation
of covalent bonds. The particular features exam-
ined are the diamond melting line and the local
structure of the liquid phase.
The resulting melting line agrees remarkably
well with experiment near the graphite- diamond-
liquid triple point. The slope of the melting line
is positive, in agreement with high pressure sound
speed experiment. The original Brenner poten-
tial represents only the covalent-bonding with a
short-range cutoff. We need to include the non-
bonded term to simulate sheet-sheet interactions
which hold two-dimensional graphite structures
together. This effort is in progress.
Liquid carbon has never been "seen" under
a controlled laboratory environment. A recent
flash-heating experiment by Togay& sugests an in-
triguing possibility6'7 that the liquid carbon may
have two phases separated by a first-order phase
change. In light of this we have been exploring the
structure of the liquid phase by computer simula-
tions with the Brenner potential. The local struc-
tural change with density appears to occur over a
relatively small density interval. Though it alone
is not an evidence for a phase transformation, it
is suggestive of one.
In addition to the diamond-graphite transition
kinetics, we need to consider the coagulation ki-
netics of carbon clusters by diffusion. The present
model uses Smoluchowski equations to describe a
change in concentration ck of k atom clusters withtimes
dck/dt = : kjcicj
2c Ikjkcj,
:1(1)
where kii = 47r(DZ + Dj)Rij (D1 = diffusion con-
stant of a clusters with i atoms; Rij = collision
diameter between clusters of sizes i and j). Using
an approximate but reliable solution ck, the time-
dependent surface energy correction < AE > to
the bulk carbon energy can be obtained by aver-
aging AEk - E(k = co) -- E(k) over ck.
We have implemented < AE > in a multi-
phase multi-component chemical equilibrium code
to account for the surface correction to the Gibbs
free energy of diamond and graphite clusters at a
given time. An application of the code has shown
that a difference between theory and experiment
in the detonation velocity of TNT at some initial
density is attributable to metastable processes in-
volving nanometer size clusters of carbon formed
during detonation.
Acknowledgments
This work was done under the auspices of the US
DOE at the Lawrence Livermore National Labo-
ratory under contract No. W-7405-ENG-48.
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Glosli, J N; Ree, F H & Winter, N W. Kinetics and thermodynamic behavior of carbon clusters under high pressure and high temperature, article, May 4, 1998; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc671759/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.