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Ab Initio Molecular Dynamics Study of Temperature Effects on the Structure and Stability of Energetic Solid Silver Azide Weihua Zhu*,†,‡ and Heming Xiao*,† †
Institute for Computation in Molecular and Materials Science and Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, China ‡ State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China ABSTRACT: Ab initio molecular dynamics simulations have been performed to study the effects of different temperatures on the structure and stability of energetic solid silver azide. The results indicate that the NN bond fission takes place at 523 K. The azide sublattice structure broke down prior to the silver sublattice. The initiation decomposition of silver azide is triggered by the NN bond breaking. This will initiate many decomposition reactions and produce many nitrogen radicals, N2, and silver clusters. Silver azide has metallic properties at 573 K. As the temperature increases, its sensitivity becomes more and more sensitive. The calculated power spectra of the velocity autocorrelation function show that the low-frequency vibrational modes become more prominent than the high-frequency ones with increasing temperature. This would allow low-frequency vibrations and rotations to occur more freely than in the solid.
1. INTRODUCTION Metal azides have attracted considerable attention because of their industrial applications as initial explosives, as gas generators, and even as photographic materials at low temperature.13 Also, they are potentially model systems for theories of fast reactions in solids because they are chemically and structurally simple among solids that deflagrate or detonate.4 Silver azide is a sensitive and powerful solid explosive that is used extensively as a detonating agent for explosives.57 Although much research has been done on its structure and properties,817 certain aspects of its behavior are still far from being clearly understood. One such aspect is the structure and stability at high temperature. The investigation of the microscopic properties of energetic materials at high temperature remains to be a challenging task because they possess a complex chemical behavior and risk. Theoretical calculations provide an efficient method to model the physical and chemical properties of complex solids at high temperature as a complement to experimental work. Over the past few years, ab initio molecular dynamics (MD) has become a popular tool for the investigation of materials.1822 In ab initio simulation, the electronic structure is evaluated using density functional theory (DFT), and the corresponding forces are used to move the ions according to classical molecular dynamics. This approach can calculate both the atomic and electronic structure consistently and explore how changes in one are correlated with changes in the other. So far ab initio MD has been used to study the dynamic properties of a variety of liquids and crystals.2326 In this work, we performed ab initio MD simulations to study the effects of different temperatures on the structure and stability of crystalline silver azide. Our main purpose here is to examine r 2011 American Chemical Society
the differences in the microscopic properties of the solid at different temperatures and to understand the effect of the temperature on its thermal decomposition. The remainder of this paper is organized as follows. A brief description of our computational method is given in section 2. The results and discussion are presented in section 3 followed by a summary of our conclusions in section 4.
2. COMPUTATIONAL METHOD Our MD simulations within the framework of DFT were performed using the Vienna ab initio simulation package (VASP).2730 The interaction between the ions and electrons is described by the projector augmented-wave (PAW) method.31 The residual minimization technique29,30 is used to calculate the electronic ground state. The generalized gradient approximation (GGA) proposed by Perdew and Wang,32,33 named PW91, was employed. Ab initio MD simulations were carried out at 298, 473, 498, 523 (melting point), 548, and 573 K, respectively. We controlled the ionic temperature using a Nose thermostat.34 The equations of motion in the extended phase space of Nose dynamics were integrated by using a Verlet algorithm with a time-step of Δt = 2 fs.26 Each ensemble was equilibrated for 3 ps, following which simulations were performed for an additional 6 ps to collect data for statistical analysis. We used energy- and temperature-equilibrium criteria to identify the equilibration times. We used a cutoff of 300 eV (4.132 nm) for the energies Received: July 4, 2011 Revised: September 16, 2011 Published: September 21, 2011 20782
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Figure 1. A 2 2 2 supercell of silver azide crystal. Dark cyan and blue spheres stand for Ag and N atoms, respectively.
of the plane waves included in the wave function expansion. Brillouin-zone integrations were performed using a grid of MonkhorstPack special points. In the ab initio MD simulations, only the Γ point was used. We performed the MD simulation on a 2 2 2 supercell (128 atoms), as shown in Figure 1. The initial positions of the simulation supercell were taken from the experimentally determined X-ray crystal structure.35 We used bond-length criteria to identify the changes in geometry in the simulation. The final electronic density of states was recalculated on an energy cutoff of 500 eV and a k-point mesh of 3 3 3 for a series of representative configurations.
3. RESULTS AND DISCUSSION 3.1. Radial Distribution Functions. The radial distribution function g(r) is the probability of finding another atom at a distance r from a specific atom. Figure 2 presents the radial distribution functions of like atoms AgAg and NN at 298, 473, 498, 523, 548, and 573 K. These are calculated by averaging the positions of atoms for the last 6 ps of our simulations. It is seen from Figure 2a that the radial distribution functions for AgAg atom pairs present indications of significant structural changes between 498 and 523 K. The radial distribution function at 498 K has definite peaks similar to those in the 298 K solidstate case. The evolution patterns of curves for the AgAg atom pairs at 298, 473, and 498 K show striking similarity. This shows that the AgAg atom pairs display similar structural ordering in the temperature range. The position of the peaks in the g(r) curves at 298, 473, and 498 K correspond roughly to the separation distances of the Ag+ ions in the 0 K relaxed crystalline structure. At 523 K, the second and third peaks nearly disappear, except for the first peak at about 2.76 Å, corresponding to the nearest-neighbor distance in the 523 K initial lattice structure. The evolution patterns of curves for the AgAg atom pairs at 523, 548, and 573 K show striking similarity. It is also noted that there lack deep valleys in the g(r) curves at 523 K, showing that the Ag+ ions have greater motion. As the temperature increases, the nearest-neighbor peak at 523 K does not disappear, and other peaks disappear. This indicates that the Ag+ ions approach a uniform distribution beyond the nearest-neighbor distance but are still in significant short-distance order. Overall, it is found that the radial distribution functions have weak long-range correlation at 523 K.
Figure 2. Calculated radial distribution functions g(r) for like atoms (a) AgAg and (b) NN at 473, 498, 523, 548, and 573 K.
Similarly, the NN radial distribution functions in Figure 2b show significant structural changes between 498 and 523 K. The radial distribution function at 498 K has definite peaks similar to those in the 298 K solid-state case. The evolution patterns of curves for the NN atom pairs at 298, 473, and 498 K are very alike. This shows that the NN atom pairs display similar structural ordering in the temperature range. The position of the peaks in the g(r) curves at 298, 473, and 498 K correspond roughly to the separation distances of the NN pairs in the 0 K relaxed crystalline structure. At 523 K, the three main peaks at about 1.22, 1.76, and 2.84 Å remain, and other peaks nearly disappear. This indicates that the N atoms are in a broader distribution in the ensemble at 523 K. In addition, the height of the nearest-neighbor peak at 523 K is very lower than that at 498 K. It means that the NN bonds began to break at 523 K. Note that the behavior of the NN pair correlations also indicates weak pairwise structure well beyond the nearestneighbor distance. As the temperature increases, the second and 20783
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Figure 3. Projection of Ag and N atoms onto (001) for the postequilibration period. Dark cyan and blue spheres stand for Ag and N atoms, respectively.
third nearest-neighbor peaks at 573 K do not disappear and other peaks disappear. This indicates that the NN pair correlation presents a decrease in order at 573 K. In addition, it is interesting to note that as the temperature rises from 498 to 573 K the nearest-neighbor peak shifts from 1.22 to 1.76 Å. It means that the NN distance becomes long with the increment of temperature. Therefore, it may be inferred that the NN bonds completely break at 573 K. This is supported by previous experimental observations that silver azide explodes at 573 K with high brisance when heated rapidly.1,36 3.2. Structural Changes and Decompositions. To obtain a more intuitive picture of the changes in structure with the increment of temperature, we presented the cumulative trajectory plot in Figure 3. The trajectory of each Ag and N atom through the postequilibration period was represented as a series of spheres, projected onto the (001) plane. In this way, we are easily able to visualize how the atoms distribute through the simulation time. In comparison with the 0 K image, the spheres for each atom are strongly localized on a lattice at 473 K. This shows that the atoms are vibrating but still in the crystalline state. The 498 K case clearly displays how the initial disorder allows for greater motions of the N atoms, whereas the Ag atoms remain relatively more localized. The 523 K image presents that the N sublattices are further diffuse while the other lattices remain localized. This indicates that the N sublattices begin to melt at a temperature of 523 K. However, all of the sublattices are less localized than the 473 K case. In the 548 K case, the Ag and N sublattices are further diffuse and melt. In addition, the 573 K image displays that the trajectories cross one another with no discernible structure, indicative of a liquid. The foregoing analyses of the radial distribution functions indicate that the NN bond begins to rupture above 523 K.
This means that the initiation decomposition of silver azide is triggered by the NN cleavage. To validate this we carefully examined the atomic trajectories through the simulation at 573 K. Figure 4 presents snapshots of NN rupture, N2 formation, N radical formation, and Ag cluster formation at 573 K during the thermal equilibration phase. During initial stage, the vibrations of Ag+ and N3 resulted in their collision, and a charge is transferred from N3 to Ag+. Then the azide began to break and formed nitrogen radical, as shown in 1 Agþ þ N 3 f Ag N N N f Ag N N þ N
ð1Þ
This is confirmed by the observation displayed in Figure 4a. Previous report37 also supports the charges transfer from the azide. Therefore, the initial step in the thermal decomposition of silver azide is the NN cleavage, consistent with our structural analysis. As the simulation continues, Ag+ interacted with the azide and caused the azide decomposed in another way to produce N2, as displayed in 2 Agþ þ N 3 f Ag N N N f Ag N þ N2
ð2Þ
Our simulations also observe the decomposition mechanism (see Figure 4b). In fact, it was reported that there is nitrogen gas formed in the thermal decomposition of silver azide.1 Afterward, many azides interacted with Ag+ and broke to form many N radicals, as displayed in Figure 4c. At the same time, certain silver cation captured the electrons from its neighboring azide and formed one silver atom. Then the silver atom interacted with other silver cations under the influence of the azides to form silver clusters, as shown in Figure 4d. Mitchell38 has suggested 20784
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Figure 4. Snapshots of (a) NN rupture, (b) N2 formation, (c) N radical formation, and (d) Ag cluster formation at 573 K during the thermal equilibration phase. The total simulated time passing in this process is 6 ps. Dark cyan and blue lines or spheres stand for Ag and N atoms, respectively.
that silver cluster will be formed during the thermal decomposition of silver azide according to the following mechanism. Agn þ Agþ þ e f Agnþ1 ðn > 2Þ
ð3Þ
This supports our observations in the simulations here. Therefore, the fine spatial and temporal resolution of ab initio MD simulations is very useful for finding chemical reactions and understanding decomposition mechanisms. 3.3. Electronic Structure. The calculated total density of states (DOS) and partial DOS for silver azide at different temperatures are displayed in Figure 5. The DOS at different temperatures are finite at the Fermi energy level. This is most likely because the DOS contain some form of broadening effect. As the temperature increases from 473 to 548 K, the total DOS displays very similar shape. The top of the DOS valence band shows two main peaks that are predominately from the d states. After that, two main peaks are dominated by the p states. In the bottom valence band, the DOS are superimposed by the s and p states. This shows that the electronic structure of silver azide does not have any significant changes. Therefore, in the temperature range below 548 K, there are mainly physical variations in silver azide. However, when the temperature is increased to 573 K, the case is quite different. The DOS peaks in the top valence bands become more dispersive, and furthermore, these have a tendency shifting to the lower energy. This shows that the electronic
Figure 5. Electronic DOS of silver azide at 473, 498, 523, 548, and 573 K. Each curve is averaged over one hundred configurations. The Fermi energy is shown as a vertical line.
delocalization in the system greatly increases at 573 K. Also, the DOS peaks in the conduction bands become wider. This leads to a band gap closure between conduction and valence bands in the 20785
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Figure 6. Band gaps of silver azide as a function of temperature.
system. It means that silver azide has metallic properties at 573 K. The aforementioned observations indicate that silver azide starts to explode at 573 K. Thus, it may be inferred that temperature effects seems to produce a significant thermal population of electronic excitations in the system and result in its decomposition and explosion. Such metallization has been also found to occur under hydrostatic compression in the covalently bonded energetic materials nitromethane,39 cyclotrimethylenetrinitramine,40 and 1,3,5,7-tetranitro-1,3,5,7-tetrazocine.41 The band gap lowering or closure greatly increases the probability of the electronic excitation of the crystal that may cause chemical decomposition of molecules constituting the explosive. This further supports our conclusion here. Finally, we try to correlate the stabilities (or explosive characters) of silver azide at different temperatures with the electronic structure. Our previous theoretical studies16,4349 on energetic crystals within the framework of periodic DFT have shown that a first-principles band gap criterion17 is founded to measure sensitivity for a series of energetic crystals. In other words, for energetic crystals with similar structure or with similar thermal decomposition mechanism, the smaller the band gap is the easier the electron transfers from the valence band to the conduction band and the more they becomes decomposed and exploded. A possible explanation may be that the increased sensitivity is caused by the increased number of excited states due to optical band gap reduction.50 As can be seen in Figure 6, the band gap of silver azide gradually decreases with the increment of temperature. At 573 K, there is a band gap closure in the system. According the first-principles band gap criterion,17 it may be inferred that the sensitivity for silver azide becomes more and more sensitive with the temperature increasing. This is supported by numerous experimental observations that an external thermal action increases the sensitivity of explosives to detonation initiation.1,51 3.4. Velocity Autocorrelation Function Power Spectrum. In this section, we turn to investigate the vibrational behavior of silver azide. The power spectrum of the velocity autocorrelation function (VAF) provides a measure of vibrational frequencies, that is, analogous to the phonon spectra in the solid.52,53 The VAF is defined as follows 1 N ½vi ðt0 Þvi ðtÞ VAFðtÞ ¼ N i¼1
∑
ð4Þ
Figure 7. Power spectra of the VAF for silver azide at 473, 498, 523, 548, and 573 K.
where vi(t) is the velocity of atom i at time t. N is the total number of atoms in the system. We choose t0 to correspond to the beginning of the time-averaging frame. The power spectrum of VAF is then defined as the absolute square of the Fourier transform of the VAF. Figure 7 displays the power spectra of the VAF for silver azide at different temperatures. It is observed in Figure 7 that the frequencies of the major peaks remain roughly the same at 473 and 498 K. This shows little change in the vibrations. Therefore, the ionic units are present in the system. In the 473 and 498 K cases, the peaks in the low-frequency region of 30300 cm1 can be attributed to lattice translational and rotational vibrations. The ∼500-cm1 peak is N3 bending vibrations. The mode of the frequency at ∼1420 cm1 involves the N3 stretching and translational vibrations. At 473 K, the ∼500- and ∼1420-cm1 peaks are significantly stronger than the 30300-cm1 peaks. The same is true of the 498 K case except for the ∼1420-cm1 peak. It means that higher frequency internal vibrations (vibrations within azide units) dominate at low temperature. This corresponds to a crystalline solid for the system. However, when the temperature is increased to 523 K (melting point), the situation is quite different. At 523 and 548 K, the frequencies of the major peaks present nearly the same. In comparison with the 473 and 498 K cases, the high-frequency ∼500- and ∼1420-cm1 peaks become less important than in the 523 and 548 K cases. In addition, the high-frequency modes are less prominent than the low-frequency modes with increasing temperature. Thus, the decrease in the prominence of the high-frequency modes would allow low-frequency vibrations and rotations to occur more freely than in the solid. This may be due to the breakdown in the crystal structure. These observations are in agreement with the beginning of liquidlike behavior at 523 K. In the 573 K case, the frequencies of the major peaks are slightly different from those in the 523 and 548 K cases; moreover, the former have smaller peaks than the latter. This appears to be since silver azide has decomposed.
4. CONCLUSIONS In this study, we have performed ab initio MD simulations to study the effects of different temperatures on the structure and 20786
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The Journal of Physical Chemistry C stability of energetic solid silver azide. The calculated radial distribution functions indicate that the NN distance becomes long with the increase of temperature from 498 to 523 K and the NN bond fission happens at 523 K. An examination of the atomic trajectories through the simulation time suggests that the azide sublattice structure broke down prior to the silver sublattice. The initiation decomposition of silver azide is triggered by the NN bond breaking. This will initiate many decomposition reactions and produce many nitrogen radicals, N2, and silver clusters. From the electronic structure at different temperatures, it is found that silver azide has metallic properties at 573 K. As the temperature increases, its sensitivity becomes more and more sensitive, consistent with the experimental reports. The calculated power spectra of the VAF show that the lowfrequency vibrational modes become more prominent than the high-frequency ones with increasing temperature. This would allow low-frequency vibrations and rotations to occur more freely than in the solid.
’ AUTHOR INFORMATION Corresponding Author
*Fax: +86-25-84303919. E-mail:
[email protected] (W.Z.);
[email protected] (H.X.).
’ ACKNOWLEDGMENT This work was supported by the NSAF Foundation of National Natural Science Foundation of China and China Academy of Engineering Physics (Grant No. 10876013), the Specialized Research Fund for the Doctoral Program of Higher Education (200802881043), the Opening Project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (KFJJ10-13M), and the NUST Research Funding (No. 2011YBXM08). ’ REFERENCES (1) Fair, H. D.; Walker, R. F. Physics and Chemistry of the Inorganic Azides, Energetic Materials; Plenum Press: New York, 1977; Vol. 1. (2) Garner, W. E. Chemistry of the Solid State; Butterworths Scientific Publications: London, 1955. (3) Yoffe, A. D. Developments of Inorganic Nitrogen Chemistry; Colburn, C. B., Ed., Elsevier: New York, 1996; p92. (4) Bowden, F. P.; Yoffe, A. D. Fast Reactions in Solids; Butterworths Scientific Publications: London, 1958. (5) Chandhri, M. M. Nature Phys. Sci. 1973, 242, 110. (6) Tang, T. B.; Chandhri, M. M. Proc. R. Soc. A 1979, 369, 83. (7) Tang, T. B.; Chandhri, M. M. J. Thermoanal. 1980, 17, 359. (8) Tang, T. B.; Chandhri, M. M. Phys. Rev. B 1984, 30, 6154. (9) Xiao, H.-M.; Li, Y.-F. Sci. China B 1995, 38, 538. (10) Xiao, H.-M.; Li, Y.-F. Banding and Electronic Structures of Metal azides; Science Press: Beijing, 1996; p 88 (in Chinese). (11) Aluker, E. D.; Zhuravlev, Yu. N.; Zakharov, V. Yu.; Kravchenko, N. G.; Krasheninin, V. I.; Poplavnoi, A. S. Russ. Phys. J. 2003, 46, 855. (12) Gordienko, A. B.; Poplavnoi, A. S. Russ. Phys. J. 2004, 47, 1056. (13) Oleshko, V. I.; Korepanov, V. I.; Lisitsyn, V. M.; Tsypilev, V. P. Tech. Phys. Lett. 2004, 30, 937. . D.; Aduev, B. P.; Krechetov, A. G.; Nurmukhametov, (14) Aluker, E D. R.; Pashpekin, A. S.; Tupitsyn, E. V.; Shvaiko, V. N. Combust., Explos., Shock Waves 2005, 41, 467. (15) Zhu, W. H.; Xiao, H. M. J. Solid State Chem. 2007, 180, 3521. (16) Zhu, W. H.; Xiao, H. M. J. Comput. Chem. 2008, 29, 176. (17) Zhu, W. H.; Xiao, H. M. Struct. Chem. 2010, 21, 657.
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