CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Hone
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
HOW POINT AND LINE DEFECTS AFFECT DETONATION
PROPERTIES OF ENERGETIC SOLIDS
Maija M. Kuklja
Department of Electrical and Computer Engineering, Michigan Technological University,
1400 Towmend Drive, Houghton, MI, 49931-1295, USA
Abstract. An ab initio study is performed for the initiation of chemistry in high explosive crystals
from a solid-state physics viewpoint. Specifically, we are looking for the relationship between the
defect-induced deformation of the electronic structure of solids, electronic excitations, and chemical
reactions under shock conditions. Band structure calculations by means of the Hartree-Fock method
with correlation corrections were done to model an effect of a strong compression induced by a
shock/impact wave on the crystals with and without lattice defects. Based on the results obtained, an
excitonic mechanism of the earliest stages for initiation of high explosive solids is discussed with
application to cyclotrimethylene trinitramine (also known as RDX) crystal. Experimental verification
of the validity of the proposed model is reported for RDX and heavy metal azides. Thus, the key role
of electronic excitations facilitated by edge dislocations in explosive solids is established and analyzed.
Favorable conditions for RDX explosion as a result of shock compression are discussed.
atomic/electronic rearrangement taking place in
pico- to femto- second range time scales. We believe
that accurate models and simulations connecting the
microscopic properties of atoms and molecules to
the macroscopic behavior of materials will bring
very new perspectives in an initiation of detonation
theory at large.
A wealth of experimental evidence, indicating
that electronic excitations (electrons, holes,
excitons) play a key role in the initiation process,
exist nowadays. A variety of initiation models has
been proposed. Experiment and theory have
suggested that the sensitivity of HE to initiation by
mechanical perturbations or shocks is a strong
function of solid-state properties including crystal
structure and lattice defects. Several studies on the
electronic structure of defects in unstable solids are
available [1,2,3]. Yet, no complete microscopic
theory of early stages for initiation currently exists
in a widely agreed upon form. Specifically, the
problem of how the energy of the shock wave is
INTRODUCTION
Modeling of materials that encompass a range of
length and time scales is crucial to advances in the
understanding such complex phenomena as
explosive decomposition of materials. In this article
we discuss a possibility of a solid state chemical
reaction involving electronic excited states. We
attempt to link computationally obtained results
from simulation of the electronic structure of
different lattice defects in organic high explosive
(HE) solids, a theoretically predicted model for the
excitonic mechanism of initiation in the RDX
([CH2N-NO2]3) crystals
and experimentally
discovered new optical and electronic properties of
HE. We also show how the macro-behavior of solids
such as electrical conductivity, optical absorption
and luminescence, observed for seconds and
minutes, can be explained and consistently
interpreted using theoretically developed quantum
chemical models for lattice defects and an
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transferred into the individual molecules, and how
the energy released can support a chemical reaction,
remains unclear. Also, the relationship between the
defect structure, electronic excitations, and chemical
processes under shock conditions in the detonation
front is not yet established.
In this article, aimed at revealing this
relationship, we analyze the initiation process from a
solid-state physics viewpoint. The theoretical
approach is based on band-structure calculations of a
perfect and defective material under shock
conditions. Specifically, we model an effect of the
strong compression induced by a shock/impact wave
on the crystals with and without lattice defects such
as a molecular vacancy, a vacancy complex, nanocracks, edge dislocations, and a free surface. The
relevant experimental data are also discussed in
great detail.
Energy
dependence
was
investigated
by
proportionally decreasing all lattice constants and
keeping the structure of the RDX molecules in the
crystal unaltered. The pressure was calculated using
the low-temperature formula P=-dU/dV.
To simulate a molecular vacancy in RDX, we
remove one of the eight molecules from the
orthorhombic RDX unit cell. Use of periodic
boundary conditions (supercell model) results in a
model crystal with a concentration of defects as high
as 12.5%. By doubling the size of the supercell and
changing positions of vacancies, we were able to
study the effect of defect distribution, in particular
the formation of vacancy dimers, on the electronic
and optical properties of the solid. In a similar
manner we modeled two-dimensional defects, such
as fine nano-cracks, placed close to each other.
The modeling of dislocations is more
challenging. The crystal is assumed to be composed
of stacked parallel layers of one-unit-cell thick. To
produce a dislocation with the Burgers vector of
[001] one can slide one crystalline plane with
respect to another part of the solid, along the z
direction. This slip produces a plastic deformation in
the material, and the boundary between the slipped
and unslipped regions is the edge dislocation. Its
position is marked by the termination of an extra
vertical half-plane of the RDX molecules crowded
into the upper half of the crystal. In our calculations
we modeled the dislocation core by a onedimensional (polymer) model. The periodic
translation was applied along the dislocation line d
[010] and no dislocation-dislocation interactions
were included.
The free surface of RDX was simulated by
means of two different solid state models such as a
periodic slab model and a molecular cluster model
[6]. The lattice relaxation induced by defects was
neglected in this study to reduce computational
costs. One can find more details regarding the
calculation techniques and approximations used in
our studies elsewhere [1-2].
The results obtained allowed us to make two
important observations. First, the most studied
defects induce a reduction of the band-gap, even at
zero pressure. The band-gap is most sensitive to the
presence of dislocations due to a strong internal
stress. Second, volumetric contraction usually leads
to the additional narrowing of the gap. This effect
strongly depends on the nature and spatial
SUMMARY OF THE RESULTS
Our calculations of the electronic structure of
explosive solids containing various defects are
performed by means of the standard Hartree-Fock
(HF) method for a periodic system by the code
CRYSTAL95/98 [4]. In this study, we used the 621g split valence set with the modified scaling factor
of 1.10 for the outer (most diffuse) Gaussian
function. In all calculations, internal geometry
parameters of the RDX molecule such as bond
lengths, angles, and torsion angles were taken from
experimental data [5] and fixed, while the lattice
constants were varied to minimize the total energy.
Electron correlation corrections based on the
second-order many-body perturbation theory
(MBPT) are included in the calculations to correct
the value of the optical band gap of the system,
which is overestimated in the HF limit.
Our main objective was to study the effect of
defects on the RDX optical band gap under shock
compression. Our calculations have been performed
for the crystal structures both in equilibrium and
under external hydrostatic compression. The band
gap as a function of the crystal compression V/Vo
was carefully analyzed. A response of the ideal and
defective RDX crystals to the shock/impact wave
excitation was modeled quantum-mechanically with
the rigid molecule approximation. Thus, isotropic
compressibility of the crystal in terms of Volume455
orientation of defects in the solid. For instance, in
crystals containing nano-cracks the gap weakly
depends on the pressure, while in crystals with edge
dislocations the gap drops to 1.5 eV at relatively
small compression, about 92% of a normal crystal
volume Vo.
The correlation correction, which is largely due
to polarization effects, reduces the computed pure,
perfect RDX gap by 8.42 eV to a value of 5.25 eV.
Optical absorption experiments [7] yield 3.4 eV. In
particular, it was found that strong intramolecular
light absorption at wavelengths below 340 nm (3.4
eV) leads to the formation of NO2 radicals. It was
also revealed that this weak absorption band in the
near ultraviolet is not observed in spectra of the
solvated or gas-phase RDX compounds [7]. This fact
coupled with a value difference of nearly 2 eV
between calculation and experiment, leads us to
assume that this absorption is associated with the
essentially solid-state of the matter, with lattice
defects. In our calculations, we model the perfect
crystals while the real solids with some
imperfections were investigated in experiments.
Following our recent study, the dislocation-related
deformation of the electronic structure narrows the
band gap of RDX to 3.3 eV, much closer to the
experimental value (3.4 eV). This creates a new
absorption band, which was not observed for either
the perfect RDX crystal or the isolated RDX
molecule [1]. The obtained results conclude that the
band-gap is most sensitive to the presence of
dislocations, which, unlike other defects, produce
local energy levels in the forbidden gap [8].
Positions of these dislocation-induced electronic
states in the band gap are strongly dependent on
shear stress and/or molecular motion in the solid [8].
The dramatic narrowing of the optical band gap,
related to the high shear strain, leads to the splitting
off of local levels from both the top of the valence
band and the bottom of the conduction band. These
local states, having bonding and antibonding
character, respectively, are attributed to the weakest
N-NO2 bond in any RDX molecule located near the
dislocation core. From this observation one may
conclude that the lowest energy electronic
excitation, i.e. promotion of an electron from the
highest occupied molecular orbital (HOMO) to the
lowest unoccupied molecular orbital (LUMO) may
lead to the breaking of the N-NO2 bond. The nature
of the HOMO to LUMO excitation and its relation
to the molecular decomposition has been also
established in earlier theoretical [9] and
experimental [7] studies.
Interesting conclusions follow from our recent
study on the thermal decomposition of solid RDX
[6]. The molecule in the crystal has different
energetic barriers for cleavage of the N-NO2 bonds,
and a molecule located near the surface can more
easily dissociate than a molecule buried in the bulk
crystal. Hot spots are known to be associated with
lattice defects such as vacancies, voids, pores,
cracks, dislocations, and others. It is well established
that defective solids, in particular, RDX typically
has a high concentration of imperfections even at
low temperatures, are much more sensitive to
initiation than high quality (perfect) crystals. Our
results lead us to the suggestion that one of the
reasons for initiation on hot spots is the reduced
energetic barrier for the decomposition of molecules
placed on defects. Obviously, the surface induced
effect must be taken into account studying the
initiation mechanisms. Further, we investigated a
time-dependent lattice response to the mechanical
perturbation, specifically how the vacancy diffusion
dynamics is affected by the impact wave progressing
across the solid [10]. The developed method based
on thermodynamics illustrates that the impact wave
interacts with the lattice defects (vacancies) creating
the vacancy super-saturation zone, which is moving
further with the impact wave. Once the exothermic
chemical reaction in the chemically active zone is
triggered, this will result in an appearance of the
self-sustained regime, and therefore, an impact wave
may be transferred to detonation. A good illustrating
example is the well examined pore collapse
mechanism. The analysis performed may help in a
consistent interpretation of the existing experimental
data, and in providing useful insights for the
understanding of mechanisms for detonation
initiation in explosive molecular solids.
A MODEL OF INITIATION OF CHEMISTRY
In this section we examine the role of electronic
excitation in the initiation of chemical reactions for
the example of solid RDX. We attempt to
understand how such a fast process as electronic
excitation, promoted by lattice defect (especially,
456
edge dislocations) and pressure, affects macroproperties of HE and finally leads to an explosion.
Let us now consider a way by which the
reaction goes through the excited state potential
energy surface. We propose the following scenario
as illustrated in Figs. 1 and 2. The system is in the
ground state (point A) until the impact wave arrives.
Volumetric contraction, induced by a shock/impact
wave progressing through a solid, leads to an
additional narrowing of the optical gap [1-2]. In
other words, an impact wave drives the system to the
point F. From this point the molecule has a chance
to be excited to the triplet state (or an excited singlet
state) [7]. The probability for this excitation at point
F is higher than at the equilibrium (point A) due to
the locally reduced gap and an increased
temperature. Our ab initio calculations of the
compressibility of the defect-free RDX crystal show
that a pressure of 30 GPa causes a gap reduction of
about 2 eV. The pressure of -15-20 GPa locally
reduces the gap to about 1 eV for RDX containing
an edge dislocation. Usually RDX has a rather high
concentration of these defects, typically 5*1012
dislocations per cm2 [1]. This corresponds to about
8.5*1016 molecules located near to dislocation cores
in a 1mm3 sample. Then, a simple estimate shows
that about 3.1*107 such molecules will be excited by
the impact front. We would like to note that we use
here the energy gap corresponding to the optical (or
vertical) electronic transition illustrated by the
vertical arrow at point F in Fig. 1. In fact, the
thermal excitation of electrons requires even less
energy due to nuclear relaxation in the excited state.
Furthermore, a dynamic response of the lattice to
excitation by a shock/impact wave in terms of
probability and population of the electronic excited
states, is expected to be much more pronounced.
As mentioned above, when the system is excited,
an electron is removed from HOMO to LUMO, and
the energy is localized on a single N-NO2 stretching
mode. If the electronic excitation is long-lived
(triplet excited states are known to live much longer
than the period of nuclear vibrations), then this
excess energy can be released in a form of nuclear
motion [11] and, with a high probability, result in
the breaking of the N-NO2 bond. In Figs. 1 and 2,
this situation is visualized as the system's movement
along the path from B to C accompanied by the
release of products (R and NO2 radicals) having
high kinetic energy. The chemical reaction can go
further with an additional energy release as indicated
by the arrow in Fig. 2. This increases the local
pressure and temperature around the defect and
drives the point F for neighboring molecules even
higher in energy (F1). It is also seen from Fig. 1 that
pressure approaching the metallization pressure
(point D) is too high compared to the experimentally
observed values. Therefore, metallization of the
sample (insulator to metal phase transition), as was
suggested earlier, is not the necessary pre-condition
for the initiation of chemistry leading to the chain
reaction and explosion. Even a moderate reduction
of the band gap can trigger initiation.
E(eV)
5.25
2.0 --
0,0 --
•"1M.NO2
R
FIGURE 2. Sketch of the RDX molecular energy as a function of
the N-NO2 distance R.
FIGURE 1. Schematic plot of the crystal energy per unit cell as a
function of crystal compression, V/Vo. The energy terms for the
the ground state (S) and excited state (T) of the system are shown.
457
Our proposed model of initiation triggering by
electronic excitations associated with the dislocation
presence in the crystal was illustrated on RDX high
explosive molecular crystal. Consistent results were
recently obtained for PETN [C(CH2ONO2)4] crystal
[8], which represents an intermediate case between
primary and secondary high explosives with respect
to sensitivity to detonation. A number of
experimental and theoretical data described in the
literature lead us to believe that the suggested model
of initiation may be general for all solid molecular
explosives. In the next section we show some
evidence in favor of this proposal for some HE.
content will ignite at a shock pressure of 2 GPa or
less [16].
A dislocation-induced effect on early stages of
slow decomposition in the electric field has been
experimentally studied for AgN3 whiskers [18]. It
was observed that gas (a product of chemical
reaction) evolved mostly from dislocation etch pits.
Next, mobility of dislocations, caused by their
magnetic moment, was used for a significant
reduction of the dislocation density in the crystal,
which is, in fact, electrical cleaning of the sample.
Further, electric current was applied to the cleaned
samples for 20 hours, and neither etch pits nor gas
emission were observed during all that time. Then,
the initial properties of the sample were restored and
gas emission regions near etch pits were observed
again. The obtained results suggest the association
of the regions of the increased chemical reactivity,
responsible for the initial stages of decomposition,
with dislocations. Furthermore, a series of
experiments were performed to study kinetics of the
pre-explosion conductivity of AgN3 crystals using
YAG:Nd3+ laser pulse initiation (1064 nm, lOmJ, 30
ps) the methodology of which is described
elsewhere [17]. Two groups of samples were
probed: one set of crystals with the dislocation
density -2-103 cm"2, and another set of "pure"
crystals with the dislocation density less than 102
cm"2. A comparison of kinetics of pre-explosion
conductivity for these two groups of crystals show
that chemical decomposition in crystals with a low
density of dislocations develops noticeably slower
than in the highly defective samples.
Experimental studies revealed the chainreaction nature of explosive decomposition of heavy
metal azides such as AgN3, T1N3, PbN6 [17-18]. Preexplosion conductivity, optical absorption, and
luminescence observed lead us to believe that not
only triggering of initiation is related to electronic
excitations but also the development of the process.
A model based on formation of hot holes
(characteristic time of the process is T~10"9 s) and
reproduction of their quasi-local hole states (the
lifetime of holes in quasi-local state has been found
not to exceed 10"14 s) in the band gap was developed
to explain explosive behavior of solids. The
appearance of such short-lived states creates
conditions for the recurrence of the chain of the
processes needed for the shock propagation through
the solid and finally an explosion.
EXPERIMENTAL EVIDENCE
The theoretically developed model was
buttressed experimentally very recently [12]. The
initiation of RDX by laser excitation under modest
pressure conditions (up to 5.0 GPa) suggests that
sample initiation occurred in a discrete region of the
crystals and not uniformly across the sample. From
this it was concluded that absorption must have
occurred at point or line defects. In that study,
theory favored absorption at a dislocation or a
vacancy associated with a dislocation core. The gap
of the RDX crystal containing this complex defect is
very sensitive to pressure and significantly reduced
(less than 2.25 eV with the pressure in the GPa
range). Thus, it is demonstrated that the energy
associated with this defect is consistent with the
absorption of the green excitation wavelength
observed experimentally, whereas normally RDX is
transparent to green light [12,13]. Initiation on voids
(the pore collapse mechanism) does not provide a
satisfactory explanation here because vacancies,
pores, voids, and free surfaces do not produce local
electronic states in the band gap. Therefore, new
absorption bands are not expected due to these
defects. It has also been reported that eliminating or
severely reducing the number of moving
dislocations during rapid deformation will reduce
the number and intensity of shock induced hot spots
within the crystal. Carefully prepared crystals of the
explosives RDX, TNT, HMX, and PETN, with
limited defect content and few dislocations, are
nearly impossible to ignite at shock pressures often
in excess of 40 GPa [14-15]. Similar crystals of the
same materials but with high defect/dislocation
458
DISCUSSION AND CONCLUSIONS
ACKNOWLEDGEMENTS
We have studied the initiation of chemistry in
high explosive crystals from a solid-state physics
viewpoint. In particular, we were attempting to
reveal the interplay between the defect-induced local
deformation of the electronic structure of solids, fast
electronic excitations, and chemical reactions under
shock conditions. In other words, we analyzed how
the experimentally observed macro-behavior of HE
solids can be consistently interpreted using the
theoretically developed model for a fast electronic
excitation facilitated by a local micro-deformation,
and how this can lead to a macro chain reaction
propagating through the solid and result in an
explosion.
Band structure calculations by means of the
Hartree-Fock method with correlation corrections
were performed to model an effect of the
shock/impact wave on the crystals with and without
lattice defects. Based on the results obtained, an
excitonic mechanism of the earliest stages for
initiation of high explosive solids is discussed with
application to the RDX crystal. Experimental
evidence for feasibility of this mechanism is
analyzed.
We would like to draw attention to some
fundamental aspects of the problem considered here,
which are far beyond the only elucidation of the
mechanism of HE decomposition. We believe that
this article convincingly demonstrates a very
interesting possibility for realization of the chemical
reaction in the solid state. The necessary condition
for the chemical reaction to occur in liquids and
gases is known to be the real migration of reactants
towards each other, their collisions, and interactions
with virgin molecules. The nature of chain reactions
in solids is more complex. A completely different
situation is possible [17-18]. Here, electronic
excitations migrate across the crystal. Localization
of these excitations at definite sites of the crystalline
lattice (structure or impurity defect) leads to the
appearance (birth!) of actual radicals at the
necessary site. Thus, a sufficiently slow process of
migration of real heavy particles (usually, diffusion
process, which is inconsistent with the experimental
data on explosive decomposition of solids) is
replaced by much faster migration of electronic
excitations (quasi-particles).
The author is very grateful to C.M. Tarver and
E.D. Aluker for their encouragement and stimulating
discussions. Research has been supported in part by
the Materials Research Institute at the Lawrence
Livermore National Laboratory under contract with
DOE.
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