Theoretical determination of anisotropic thermal conductivity for
crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)
Matthew P. Kroonblawd and Thomas D. Sewell
Department of Chemistry, University of Missouri–Columbia, Columbia, MO 65211-7600, USA
SUPPLEMENTARY MATERIAL
I. Additional details of weighted least-squares linear regression analysis used in the thermal
conductivity calculations
The temperature gradient within a single block window was computed using weighted leastsquares linear regression of the instantaneous temperatures measured for each slab. The position
assignments xi for each slab were defined in terms of (unsigned) displacement from the cold slab
using the slab separation distances in TABLE SM-I. The linear regression parameters T0 and b,
where b is taken as the temperature gradient from the given time block, were obtained by
minimizing the χ2 merit function
æ T - T - bxi ö
c (T0 , b) = åç i 0
÷ .
si
ø
i=1 è
N
2
2
(SM-1)
The merit function sums over contributions from each slab, excluding the hot and cold slabs,
giving N = 7 terms for the a- and b-stacking supercells and N = 9 terms for the c-stacking
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supercell. The standard deviations σi of the average temperatures of each slab in a particular
block window weight each contribution to the χ2 merit function. Uncertainties were propagated
through the linear regression and all subsequent computations using
ïìæ ¶f ö üï
s f (y1,..., yn ) = åíç ÷ Dyi ý ,
ïè ¶yi ø þï
i=1 î
n
2
2
(SM-2)
where Δyi denotes the uncertainty in quantity yi. Time histories of block-averaged temperatures
for selected slabs in the a- and c-stacking systems are presented in FIG. SM-1. Symbols are
individual block averages and the solid curves are 20-point sliding averages. The onset of a
steady state was taken to occur at time t = 1 ns, denoted by the vertical lines in the figure.
II. Discussion of additional reports of TATB thermal conductivity
During the literature search undertaken to prepare TABLE V of the main article, additional
values for the thermal conductivity of TATB were found that have been omitted from that table
but are presented here for completeness. One particular value,  = 0.544 W m-1 K-1, appeared in
two sources, LASL Explosive Property Data1 and a Los Alamos report by Dobratz.2,‡ In each
instance the value was reported without any discussion regarding the nature of the sample or
experimental method and neither of the reports included a traceable citation. The Dobratz report2
did include a corresponding density of ρ = 1.892 g cm-3, which would likely mean the value
corresponds to a pressed powder experiment. However, because the primary source of this value
could not be identified, the decision was made to omit it from the published table. Another,
‡
Reference numbers correspond to citations given in the supplementary material.
2
higher value of  = 0.8 W m-1 K-1 was also found, with a corresponding temperature of T = 293
K.2 However, because no further details or traceable citation was provided, this value was also
omitted from Table V.
REFERENCES
1
LASL Explosive Property Data (University of California Press, Berkeley and Los Angeles,
California, 1980), p. 156.
2
B. M. Dobratz, "The Insensitive High Explosive Triaminotrinitrobenzene (TATB):
Development and Characterization - 1888 to 1994," Report No. LA-13014-H, 1995.
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TABLE SM-I. Definition of prime basis and supercell parameters.
Supercell
Conduction direction
Slab separation along Transverse surface area
conduction direction (Å) normal to conduction
direction (Å2)
a-stacking
a' = b × c
8.364
1186.0
b' = c × a
7.673
1230.7
c' = a × b
6.405
1128.3
(16a×4b×5c)
b-stacking
(4a×16b×5c)
c-stacking
(4a×4b×20c)
Supercells with minimum transverse dimensions consistent with cutoff distance in the FF
a-stacking
a' = b × c
8.364
711.6
c' = a × b
6.405
634.7
(16a×3b×4c)
c-stacking
(3a×3b×20c)
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FIG. SM-1.
(a)
315
Hot Slab Neighbor
Middle Slab
Cold Slab Neighbor
310
Hot Slab
Temperature
(K)
Temperature (K)
Slab 7 + 7’
305
Slab 4 + 4’
300
295
a
Slab 1 + 1’
Cold Slab
290
b
c
285
1
0
2
3
Time (ns)
4
5
6
Time (ns)
(b)
315
Hot Slab
Temperature
(K)
Temperature (K)
310
Slab 8 + 8’
305
Slab 5 + 5’
300
295
c
290
Slab 2 + 2’
Cold Slab
285
0
1
2
3
Time (ns)
Time (ns)
4
5
6
b
a
FIG. SM-1. (a) Block window average (symbols) and 20-point sliding average (solid curves)
time series of temperatures for three slabs in the a-stacking supercell. Averages are taken over
geometrically equivalent slab pairs and a reduced schematic is provided for reference; for
instance, a single diamond symbol represents the average temperature computed within one
block window (50 ps time interval) and over both slabs 1 and 1', as each is a nearest neighbor to
the cold slab. Results are similar for the b-stacking supercell (not shown). (b) Time series for the
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c-stacking supercell with identical conventions as in (a), but with second-nearest-neighbor (to the
hot and cold slabs) slab temperatures plotted instead of nearest-neighbor ones.
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