Chemical stability of molten 2,4,6-trinitrotoluene at high pressure
Supplementary appendix - equation of state
Table 1. Comparison of ambient state measurements on TNT with those predicted by the
Sesame model. The properties are: initial density (), ambient pressure bulk sound
velocity (c), constant pressure specific heat (Cp), Grüneisen parameter (), and Debye
temperature (D).
a
Ref. 7, for  = 1.64 g/cc.
b
Ref. 2.
c
Ref. 3.
d
Based on vibrational
modes.
Property
 (g/cc)
c (km/s)
Cp (J/gK)
  10-4 (K-1)

D (K)
Measured
1.62-1.64
2.30a
1.071b
2.071c
1.04d
-
Predicted
1.628
2.31
1.069
2.066
1.00
1255
An equation of state (EOS) for inert TNT was constructed using the Sesame model,4 in
which the pressure and specific internal energy are expressed as a three-part
decomposition:
X(r,T) = f (r )+ Xnuc (r,T)+ Xelec (r,T)
(1)
For X = { P, E} . These terms represent the purely elastic (0 K, or “cold curve”), thermal
ionic, and thermal electronic contributions, respectively; coupling between the latter two
is neglected but expected to be small across the domain of interest. A Debye model was
used for Enuc , from which Pnuc follows as
P = rGE
(2)
In the Mie-Grüneisen (quasiharmonic) approximation.5 Thermal electronic contributions
were ignored due to the insulating character of TNT at the relatively low temperatures
surveyed. Cold curve properties such as the isothermal bulk modulus and its pressure
derivative were constrained by a quadratic fit to the shock data,1,6-8 and the Debye
temperature was adjusted in order to recover the ambient specific heat.2 A
thermodynamically complete set of ambient-state property values are compared with
model predictions in Table 1. The computed principal Hugoniot is overlaid with
experimental unreacted Hugoniot data from references 1 and 6-8 in the Figure below.
Supplementary appendix figure. Calculated principal Hugoniot from the
thermodynamically complete equation of state overlaid with experimental unreacted
Hugoniot data from the literature for  = 1.62-1.64 g/cc TNT.
1
R. J. Wasley, and J. F. O’Brien, Proc. 4th Int. Det. Symp., ACR-126, Vol. 99, 239
(1965).
2
C. M. Yin, Z. R. Liu, G. H. Wang, C. Y. Wu, Proc. 17th Int. Pyrotechnics combined with
the 2nd Beijing Int. Symp. on Pyrotechnics and Explosives, Vol. 1, 515-521 (1991).
3
R. M. Vrcelj, J. N. Sherwood, A. R. Kennedy, H. G. Gallagher, T. Gelbrich, Cryst.
Growth Des. 3, 1027-1032 (2003).
4
S. P. Lyon, J. D. Johnson, “Sesame: The los alamos national laboratory equation of state
database,” Tech. Rep. LA-UR-92-3407 (Los Alamos National Laboratory, 1992).
5
M. T. Dove, Introduction to Lattice Dynamics (Cambridge University Press, 1993).
6
S. P. Marsh, LASL Shock Hugoniot Data (University of California Press, 1980).
7
R. J. Wasley, and F. E. Walker, J. Appl. Phys. 40, 2639-2648 (1969).
8
V. S. Ilyukhin, P. F. Pokhil, O. K. Rozanov, N. S. Shvedova, Sov. Phys. Dokl. 5, 337
(1960).
Supplementary video. A multiple frame optical video of TNT melting at 4 GPa is
available as a supplementary data file. The optical video shows the visual progression of
decomposition of TNT at 4 GPa with a heating rate of 3 K/min. Decomposition was
observed at 4.0 ± 0.1 GPa and 515 ± 3 K.
Supplementary Figure 1. Photomicrographs showing the visual progression of
melting/decomposition at 4 GPa. This experiment was performed visually, with brief
monitoring of the pressure by the shift of ruby fluorescence with P, T. (a) 505 K, (b)
511.6 K, (c) 501 K (melt-onset), (d) 515 K (complete decomposition). The total time
elapsed from (a) to (d) is ~15 minutes with a heating rate of 2.6 K/min.
Supplementary Figure 2. Characterization of the decomposition product at high P/T by
(a) Raman and (b) XRD from two separate measurements. Both the Raman spectrum,
and XRD pattern of the carbon product are consistent with sp3-based amorphous carbon
(a:C-H) (see references 23-25) (c-e) Raman spectra corresponding to the micrographs in
Figure 1 (main text) for liquid (c), metastable (glass-like) (d), and recrystallized sample
(E). It is noted that the Raman spectra were collected with 1-5 s exposure (687 nm) and
less than 5 mW of laser power at the sample. (f-h) Far-infrared spectra of TNT in the
solid (f), mixed solid-liquid (g), and recrystallized states, with images of the TNT in the
DAC at this conditions. Note that there are few discernable changes in the far-IR spectra
below the decomposition boundary.