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2009, 113, 17–20 Published on Web 12/05/2008
Interplay of Decomposition Mechanisms at Shear-Strain Interface Maija M. Kuklja*,†,‡ and Sergey N. Rashkeev§ Department of Materials Science and Engineering, UniVersity of Maryland, College Park, Maryland 20742, Office of the Director, National Science Foundation, Arlington, Virginia 22230, Center for AdVanced Modeling and Simulation, Idaho National Laboratory, Idaho Falls, Idaho 83415 ReceiVed: September 20, 2008; ReVised Manuscript ReceiVed: NoVember 12, 2008
Understanding the structure and properties of buried interfaces in materials and devices is a great challenge in physics, chemistry, and materials science. Here we present density functional theory (DFT) based simulations of interfaces in a diamino-dinitroethylene (DADNE, C2H4N4O4) molecular crystal. It is shown that interfaces formed in this material by shear-strain deformations affect the energies and activation barriers of DADNE decomposition and that they may be responsible for triggering explosive decomposition in the crystal. Individual molecules located at the interfaces exhibit lowered activation barriers for structural transformations and decomposition processes, which prompts them to serve as nucleation sites for the overall decomposition of the material possibly leading to a chain reaction and explosion. These results shed light on the molecular nature of the localized hot spots in energetic materials and may provide recommendations for rational design of new materials with tailored properties. The determination of the structure and physical and chemical properties of buried interfaces formed inside the material by a deformation is one of great challenges in materials research. The key problem is the difficulty to detect and isolate the weak interface signature from that of the dominant bulk. Most extensive efforts of researchers are focused on exploring optical, electronic, and magnetic properties and sometimes crystallographic structures of the interfaces. Very little is known about their stability. A variety of buried interfaces in energetic molecular materials are of a special interest because of their potential association with hot spots,1 or localized regions that control the dissipation and localization of the mechanical energy and its transfer into the chemical energy.2 The hot spots are assumed to originate instability in the material, which leads to the chemical decomposition and ultimately to an explosive chain reaction that releases large amounts of energy stored in these materials. It is often suggested that sites of the nucleation of chemical decomposition are formed by dislocations, staking faults, grain boundaries, or other similar structural defects and relevant deformations.3,4 However, atomic scale mechanisms of these instabilities and the initiation of chemical processes are far from being understood. This work was motivated by observations of the anisotropic response of Pentaerythritol tetranitrate (PETN) to shock loading.5 Single PETN crystals shocked normal to the (100) and (101) planes were found to be insensitive while those shocked normal to the (110) and (001) planes were found to be relatively sensitive. Numerical analysis using molecular mechanics indicated that steric hindrance, or the interaction between molecules, was more severe for the (110) and (001) directions leading to * To whom correspondence should be addressed. † University of Maryland. ‡ National Science Foundation. § Idaho National Laboratory.
10.1021/jp808367r CCC: $40.75
an enhanced energy transfer and greater reactivity, as a result. This was verified by additional experiments6 and semiempirical calculations implicating shear stress as contributing to the sensitivity when shocked normal to the (110) planes and thermal initiation when shocked normal to (100). For this study, we selected diamino-dinitroethylene, C2H4N4O4 (DADNE), an organic molecular crystal, which is convenient for the modeling of a wide range of properties of energetic materials due to its relatively small molecule and unit cell.7,8 Our ab initio simulations of DADNE supercells suggest that the interfacial regions formed by shear-strain deformations may indeed be responsible for triggering their explosive decomposition and, therefore, may play a crucial role in sensitivity mechanisms of DADNE crystals to external stimuli. A characteristic reduction of the transition energy barriers, which is observed for molecules located at the interface, prompts them to undergo the dissociation while other molecules in the crystal are still intact. We show that the decomposition of DADNE is defined by the interplay between the two major molecular decomposition mechanisms: the nitro-nitrite isomerization with a subsequent NO release and the C-NO2 fission with a NO2 release. Previously, it has been determined that a local stress9 and a shear-strain10-12 in the DADNE lattice lower the activation barrier for the C-NO2 dissociation. In this letter, we show that at a low and moderate interfacial shear-strain, the CONO isomerization has an even lower activation barrier than the C-NO2 decomposition and triggers the deliberation of NO groups, which are highly mobile and chemically active. The direct C-NO2 bond scission, however, is very sensitive to the induced shear-strain and dominates over the CONO isomerization process at the higher interfacial shear-strain. The structure and chemical stability of a buried interface in DADNE were investigated by means of density functional 2009 American Chemical Society
18 J. Phys. Chem. C, Vol. 113, No. 1, 2009
Letters
Figure 2. Shear stress as a function of the shift, characterized by the parameter γc, along the c- lattice vector. The black curve is calculated by using total energies for fully relaxed configurations for each value of γc, the red curve is calculated for instantaneous shifts before the relaxation.
in the c- direction because for the a- shift the humps and grooves of the zigzag-shaped layers move parallel to each other and their wave functions barely overlap), calculated as
σc ) Figure 1. Relaxed six-layer (3 + 3) slab of the crystalline DADNE: (a) for an ideal crystal (γa ) 0, γc ) 0; no shear-strain applied) and (b) for a crystal exposed to a c- directed shear-strain (γa ) 0, γc ) 0.3). a, b, and c are the translational lattice vectors; arrows show the directions of the applied shear-strain deformation in which the three upper layers are shifted relative to the three lower layers. The molecular structures of an equilibrium DADNE molecule (c) and a CONO isomer (d) are also shown. The C atoms are shown in gray, O in red, N in blue, H in white.
theory (DFT) calculations within the generalized-gradient approximation (GGA) for the exchange-correlation (the GGA of Perdew, Burke, and Ernzerhof (PBE)13 was employed), plane waves, periodic supercells, and ultrasoft pseudopotentials for C, N, O, and H, using the VASP codes.14 The relaxed structures for the defect-free DADNE crystal agree with the experiment15,16 as well as with previous calculations based on the force field,17 DFT,18,19 and Hartree-Fock16 methods. In order to simulate shear-strain deformations, we constructed supercells formed by six molecular-layer slabs (or (3 + 3) slabs) separated by a 10 Å layer of vacuum.11,12 The shear-strain was introduced by shifting the three upper layers of the slab relative to the three lower layers in the directions parallel to the layer’s plane (i.e., the ac- plane) on vectors ∆ ) γaa + γcc (Figures 1a,b). The two γ- parameters were varied in the range from 0 to 1 (the unity corresponds to the in-plane shift on the whole translational vector). The decomposition and structural rearrangement barriers for molecules placed at the two interfacial layers (where the shear-strain is maximal) were calculated using the nudged elastic band approach20 for each vector ∆. In order to eliminate the drift of the supercell as a whole in the relaxation process, we fixed the position of one carbon atom attached to the NH2 group for each molecule in the lower layer of the slab. This constraint is physically justified because the main contribution to the relaxation is related to NO2 groups. The interfacial shear stress σ was estimated from the dependence of the total energy Etot of the supercell on the shift parameters γa and γc. Figure 2 shows the shear stress as a function of the shift along the c- lattice vector (the shift along the a- vector (γc ) 0) is energetically less costly than the shift
1 ∂Etot(γc) · Sac ∂xc
(1)
where Sac is the size of the interfacial area within one supercell, and xc is the coordinate along the c- vector. The total energies may be taken (i) for fully relaxed configurations for each value of γc, or (ii) for instantaneous shift configurations before any relaxation of the system. Hence, the curve (i) corresponds to a fast deformation of the system by a shock wave (and should be considered as the upper bound for the shear stress),21 while the curve (ii) represents a reasonable model for an adiabatic compression (and gives the theoretical limit for the shear stress in DADNE ideal crystal). The calculated curves σc(γc) exhibit a regular, nearly symmetric behavior with the center of inversion at γc ) 0.45, σc ) 0 (Figure 2). The zero stress at the points γc ) 0 and 1 corresponds to the equilibrium state (no shift) and to the shift on the whole period of the lattice, respectively. The zero stress value at γc ) 0.45 relates to the maximum of the total energy and reflects the maximal distortion of the NO2 groups. This inversion point corresponds to an unstable equilibrium where the system may move in either direction, toward increasing or decreasing γc parameter. The almost linear parts of the σc(γc) curve near γc ) 0 and 1 obey Hook’s law for small shifts, with a deviation starting above γc ) 0.25 (and below γc ) 0.75). The absolute value of the shear stress does not exceed 2 GPa (consistent with static compression experiments16,22) for fully relaxed total energies and reaches 16 GPa (consistent with pressures in shock waves) for the instantaneous shifts. The C-NO2 dissociation barrier of interfacial molecules varies between 93.4 kcal/mol (for γc ) 0 and 1) and 43.7 kcal/ mol (for γc ) 0.45; see Figures 3a,c, 4 and Table 1; the dissociation barrier is much less sensitive to an a- shift, and we always take γa ) 0 in this work). For instantaneous shifts in the range 0.3 < γc < 0.55, the wave functions of the NO2 groups at the neighboring interfacial molecules strongly overlap, hence, the lattice relaxation causes a significant deformation of these interfacial layers. The great reduction of the C-NO2 activation barriers reflects the fact that a significant fraction of the shear-strain related elastic energy is accumulated inside the C-NO2 bonds, which facilitates the detachment of the NO2 groups. The split NO2 group relaxes in an interstitial position
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J. Phys. Chem. C, Vol. 113, No. 1, 2009 19
Figure 3. Comparative scheme of reaction energies (indicated by red horizontal bars and red numbers) and corresponding activation barriers (blue horizontal bars and blue numbers) in the course of the two possible decomposition pathways ((a,c) depict the direct C-NO2 decomposition; (b,d) depict the C-NO2-to-CONO isomerization) of interfacial DADNE molecules with a subsequent formation of free NO groups, their migration across the molecular layers (along the b axis), and formation of free interstitial NO2 groups between the layers. Upper panel (a,b) corresponds to an ideal crystal (γa ) 0, γc ) 0). Lower panel (c,d) corresponds to a crystal exposed to a high level of the shear-strain deformation (γa ) 0, γc ) 0.45). All the energies are in kcal/mol.
Figure 4. The activation barriers for NO2 fission and CONO formation as function of shear-strain level in a DADNE crystal.
TABLE 1: Energy Barriers of the Decomposition of a DADNE Molecule in the Crystal (kcal/mol)
ideal crystal (γa ) 0, γc ) 0) shear-strained crystal (γa ) 0, γc ) 0.45)
C-NO2 break
CONO formation
NO split from CONO isomer
93.4
41.4
9.2
43.7
50.6
9.2
between the interfacial layers. However, the reversed energy barrier is relatively low (Figure 3a,c), hence if the NO2 group is not involved in other reactions right after scission, the NO2 group can restore the chemical bond within the molecular radical. These results may help to explain irreversible structural changes above 4.5 GPa observed in X-ray-diffraction experi-
ments and also manifested in darkening of DADNE samples from yellow to dark brown observed in optical polarized microscopy experiments.22 Our calculations suggest that nonhydrostatic compression above 2 GPa causes irreversible decomposition of DADNE in the vicinity of shear-strain interfaces while molecules in ideal bulk stay intact. The barrier reduction is also consistent with differential scanning calorimetry experiments on condensed DADNE phase, estimating thermal decomposition energy as ∼58 kcal/mol8, which is lower than calculated thermal dissociation energy of gas phase DADNE (67-70 kcal/mol)18,19 and by far lower than DFT calculations give for an ideal DADNE crystal (∼90 kcal/mol).10-12 This result is consistent with the observation of the chemical reaction progressing at discrete localized regions and not uniformly over the sample in DADNE23 and somewhat echoes observations in other materials.4,5,24 The calculated reduced decomposition barriers9-12 imply that the interface molecules in DADNE are first candidates to decompose when the external energy is available, and that the chemical reaction is likely to originate at sites of high shear-strain.12 Another important decomposition mechanism that competes with the direct C-NO2 rupture is the C-NO2 to CONO isomerization (Figure 1c,d). The CO-NO bridge in the CONO complex is less stable than C-NO2 bond due to a redistribution of electronic density. The CO-NO bond breaks easily with the barrier of 9.2 kcal/mol. We probed a propagation of the formed NO product in the lattice and found that the NO group is highly mobile and chemically active25 (Figures 3b,d, 4 and Table 1). The reverse restoring of the initial CO-NO bond is unlikely to occur because the freed up NO group quickly moves away from the dissociated molecule; it can migrate laterally (parallel to the layers) with a low barrier (below 11.5 kcal/mol) thus reducing the statistical probability of the restoring event. The NO group can also migrate vertically through the layers; in this case the migration barrier is higher (∼27.6 kcal/mol) due to strong interactions of the NO group with the neighboring DADNE molecules in this layer, which significantly distorts them. While crossing the layer, the NO may capture O atom from one of the molecules, forming a free interstitial NO2 molecule.25 The energy barrier for such a capture, 36.8 kcal/ mol is only 9.2 kcal/mol higher than the transition state energy for crossing the layer without any chemical changes (Figure 3b,d). Therefore, the final product of a single C-NO2 to CONO isomerization process is either a free interstitial NO group or an interstitial NO2 group as in a direct C-NO2 decomposition. We note that the migration activation energies are lower than the barriers for both isomerization and decomposition, which implies that once the decomposition is initiated, the migration of products definitely occurs. Previous gas phase calculations26 showed that the barriers of the C-NO2 to CONO isomerization and the C-NO2 rupture are comparable, that is, both of these processes are likely to take place at the early stage of the decomposition. In this study, we found that the C-NO2 decomposition in DADNE crystal is much more intricate as compared to the gas phase due to collective molecular and electronic behavior in the solid. In particular, we found that although the CONO isomerization process exhibits a lower activation barrier in the ideal material, it is barely affected by the shear strain deformation; this is because the CONO group has a small activation volume, is floppy, and easily relaxes to a low energy configuration. Unlike this, the high energy activation barrier for the NO2 scission process in ideal material significantly reduces in the vicinity of the shear-strain interfaces.
20 J. Phys. Chem. C, Vol. 113, No. 1, 2009 The results described above allow us to conclude that initiation in a perfect DADNE crystal is likely to be triggered by a CONO formation followed by the NO group split off. Formed NO species are mobile and chemically active, and likely to form NO2 molecules; that is, the diffusive propagation of NO through the lattice may contribute to the appearance of both NO and NO2 products observed in experiments on thermal decomposition of this material.8,27 In an imperfect DADNE crystal (for example, in a crystal containing high concentration of interfaces, dislocation pile ups, or grain boundaries), at a moderate shear-strain levels, the CONO formation requires a somewhat similar energy barrier to the C-NO2 break, that is, both the initiation mechanisms compete. At higher shear-strain levels, the direct C-NO2 rupture suppresses the CONO isomerization, and the faster one-step decomposition mechanism dominates. These ab initio simulations clearly demonstrate that shearstrain plays a crucial role in the stability of molecules in DADNE energetic crystals. As energetics (the reaction energy and the activation barrier) of decomposition chemistry of high energy materials largely contributes to the sensitivity of these materials to the initiation of detonation,28 it is tempting to directly associate the shear-induced reduction of the activation barrier, obtained here, with the sensitivity to detonation initiation. However, the correlation between the level of shear-strain and the sensitivity is extremely complex as the chemistry is not limited to the shear-strain-induced decompositions at the interfaces. The most certain conclusions obtained so far are the following: (i) Shear-strain-induced effects control the intricate interplay of chemical reactions in DADNE crystals, the C-NO2 break (producing NO2) and the nitro-nitrite isomerization (producing NO). (ii) Shear-strain reduces the activation barriers for initiation of certain chemical reactions; this reduction is the structure- and reaction- specific. (iii) Dynamic effects and diffusion processes should be taken into account. These results may help to elucidate ignition mechanisms caused by the mechanical impact or shock and relate these mechanisms to definite types of imperfections such as interfacial deformations, dislocations, stacking faults, or grain boundaries. Hopefully, they will also allow for making definite conclusions regarding the mechanisms of sensitivity in energetic molecular crystals and providing recommendations for guided design of new materials with tailored low sensitivity. Acknowledgment. This work is supported in part by ARO MURI (Grant W9011NF-05-1-0266), by the INL LDRD program and by the DoE, Office of Nuclear Energy under DoE Idaho Operations Office Contract DE-AC07-051D14517, and by a grant of computer time from the High Performance Computing program at the INL. Also, this research used resources of the NERSC, which is supported in part by the U.S. DoE under Contract No. DE-AC02-05CH11231. M.M.K. is grateful to the Office of the Director of National Science
Letters Foundation for support under the IRD Program. Any appearance of findings, conclusions, or recommendations, expressed in this material are those of the authors and do not necessarily reflect views of NSF. References and Notes (1) Bowden, F. P.; Yoffe, Y. D. In Initiation and Growth of Explosion in Liquids and Solids; Cambridge University Press: London, 1952, pp 6465. (2) Tokmakov, A.; Dlott, D.; Fayer, M. J. Phys. Chem. 1993, 97, 1901. (3) Coffey, C. S.; Sharma, J. Phys. ReV. B 1999, 60, 13. (4) Kuklja, M. M.; Aduev, B. P.; Aluker, E. D.; Krasheninin, V. I.; Krechetov, A. G.; Mitrofanov, A. Yu. J. Appl. Phys. 2001, 89, 4156. (5) (a) Dick, J. J.; Ritchie, J. P. J. Appl. Phys. 1994, 76, 2726. (b) Dick, J. J. J. Appl. Phys. 1997, 81, 601. (6) (a) Yoo, C. S.; Holmes, N. C.; Souers, P. C.; Wu, C. J.; Ree, F. H.; Dick, J. J. J. Appl. Phys. 2000, 88, 70. (b) Wu, C.; Ree, F. S.; Yoo, C. S. Propellants, Explos., Pyrotech. 2004, 29, 296. (7) Latypov, N. V.; Bergman, J.; Langlet, A.; Wellmar, U.; Bemm, U. Tetrahedron 1998, 54, 11525. ¨ stmark, H.; Langlet, A.; Bergman, H.; Wingborg, N.; Wellmar, (8) O U.; Bemm, U. In Proceedings of the 11th International Detonation Symposium, Snowmass, Colorado, 1998, ONR 33300-5; ONR: Arlington, VA, 2000, p 807. (9) Rashkeev, S. N.; Kuklja, M. M.; Zerilli, F. J. Appl. Phys. Lett. 2003, 82, 1371. (10) Kuklja, M. M.; Rashkeev, S. N.; Zerilli, F. J. Appl. Phys. Lett. 2006, 89, 071904. (11) Kuklja, M. M.; Rashkeev, S. N. Appl. Phys. Lett. 2007, 90, 151913. (12) Kuklja, M. M.; Rashkeev, S. N. Phys. ReV. B 2007, 75, 104111. (13) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (14) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 48, 13115. ¨ stmark, H. Acta Crystallograph., Sect. C 1998, 54, (15) Bemm, U.; O 1997. (16) Kuklja, M. M.; Zerilli, F. J.; Peiris, S. M. J. Chem. Phys. 2003, 118, 11073. (17) Sorescu, D. C.; Boatz, J. A.; Thompson, D. L. J. Phys. Chem. A 2001, 105, 5010. (18) Gindulyte´, A.; Massa, L.; Huang, L.; Karle, J. J. Phys. Chem. A 1999, 103, 11045. (19) Politzer, P.; Concha, M. C.; Grice, M. E.; Murray, J. S.; Lane, P.; Habibollazadeh, D. J. Mol. Struct. (THEOCHEM) 1998, 452, 72. (20) Mills, G.; Jonsson, H.; Schenter, G. K. Surf. Sci. 1995, 324, 305. (21) For a typical shockwave velocity (a few kilometers per second), the shock wave will drive a shift of at least a few angstroms during the relaxation time of NO2 groups (∼100 fs; see ref 12). (22) Peiris, S. M.; Wong, C. P.; Zerilli, F. J. Chem. Phys. 2004, 120, 8060. (23) Plaksin, I.; Ribeiro, J.; Mendes, R.; Campos, J.; Almada, S.; Gois, J. Proceedings of the 39th International Annual Conference of ICT on Energetic Materials, June 26-27, 2008; DWS Werbagentur und Verlag GmbH: Karlsruhe, Germany, 2008. (24) Kunz, A. B.; Kuklja, M. M.; Botcher, T. R.; Russel, T. P. Thermochim. Acta. 2002, 384, 279. (25) Details of chemical activity of NO product in the DADNE lattice and the nature of the diffusion transition states and reaction barriers will be reported in a forthcoming publication. (26) Kimmel, A. V.; Sushko, P. V.; Shluger, A. L.; Kuklja, M. M. J. Chem. Phys. 2007, 126, 234711. (27) Gao, H.-X.; Zhao, F.-Q.; Hu, R.-Z.; Pan, Q.; Wang, B.-Z.; Yang, X.-W.; Gao, Y.; Gao, S.-L. Chin. J. Chem. 2006, 24, 177. (28) Brill, T.; James, K. Chem. ReV. 1993, 93, 2667.
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