J Mol Model (2014) 20:2072 DOI 10.1007/s00894-014-2072-4
ORIGINAL PAPER
First-principles study of electric field effects on the structure, decomposition mechanism, and stability of crystalline lead styphnate Zhimin Li & Huisheng Huang & Tonglai Zhang & Shengtao Zhang & Jianguo Zhang & Li Yang
Received: 31 May 2013 / Accepted: 7 November 2013 / Published online: 28 January 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract The electric field effects on the structure, decomposition mechanism, and stability of crystalline lead styphnate have been studied using density functional theory. The results indicate that the influence of external electric field on the crystal structure is anisotropic. The electric field effects on the distance of the Pb–O ionic interactions are stronger than those on the covalent interactions. However, the changes of most structural parameters are not monotonically dependent on the increased electric field. This reveals that lead styphnate can undergo a phase transition upon the external electric field. When the applied field is increased to 0.003 a.u., the effective band gap and total density of states vary evidently. And the Franz-Keldysh effect yields larger influence on the band gap than the structural change induced by external electric field. Furthermore, lead styphnate has different initial decomposition reactions in the presence and absence of the electric field. Finally, we find that its sensitivity becomes more and more sensitive with the increasing electric field. Keywords Decomposition mechanism . Density functional theory . Electric field effect . Electronic structure . Lead styphnate . Stability
Z. Li : T. Zhang (*) : J. Zhang : L. Yang State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China e-mail: [email protected] H. Huang : S. Zhang College of Materials Science and Engineering, Chongqing University, Chongqing 400030, China H. Huang (*) The Key Laboratory of Inorganic Special Functional Materials, College of Chemistry and Chemical Engineering, Yangtze Normal University, Chongqing 408100, China e-mail: [email protected]
Introduction The decomposition reaction of energetic materials can be triggered by various external stimuli, such as impact, friction, heat, static compression, and electric spark. The influences of temperature and pressure on the structure and properties of explosives have been fully studied theoretically and experimentally [1–10]. However, theoretical investigations on energetic solids under external electric field have not been made, although the hazards of energetic materials owing to static charge have been extensively studied experimentally [11–15]. The electrostatic discharge hazard is normally associated with manufacturing and filling operations. And the discharge of static electricity accumulated on a person can supply energy up to 20 mJ, which is possibly bigger than the minimum spark energy required for initiating the energetic materials such as lead styphnate (2,4,6-trinitroresorcinate) and basic lead azide [13]. Hence, the accident resulted from static charge can easily occur in the explosive production plant. Moreover, the electric spark sensitivity of various explosives has been the subject of very many articles in the literature [16–28]. The correlations between the spark sensitivity of explosives and their molecular electronic properties have been well established. While the external electric field influences on the structure and properties of energetic materials are still not well understood. It is known that lead styphnate is a typical primary explosive and has been extensively used for several decades. Therefore, its structure, decomposition mechanism and properties, especially the spark sensitivity, are fully investigated and compared [13–15, 29]. Unfortunately, the geometric and electronic structures and detonation mechanism under external electric field are often difficult to obtain from experiment for practical reasons. Compared with experiment, simulation can provide more detailed information about variations in crystal and molecular structures, initiation mechanism, and stability of energetic materials under applied electric field. In
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fact, there are sufficient computational investigations on the structures and properties of materials including single-walled nanotubes [30–32], graphene nanoribbons [33], guanine aggregates [34], and carbon dioxide [35] under external electric field. To the best of our knowledge, there are no such reports on the primary explosives. Thus, in the present work, firstprinciples periodic calculations have been performed using density functional theory to study the effect of electric field on the geometric and electronic structures, decomposition mechanism, and stability of crystalline lead styphnate.
Computational methods The initial structure adopted the experimental crystalline structure [36] in which lead styphnate contains two HC6N3O8Pb·H2O molecules per unit cell in a monoclinic lattice with space group P2/c as shown in Fig. 1. The geometry optimization was performed to allow the ionic configuration, cell shape, and volume to change. The total energy of the system was converged less than 1.0×10-5 Ha, the residual force less than 0.002 Ha/Å, the displacement of atoms less than 0.005 Å. Additionally, both the local density approximation (LDA) named PWC [37] and the generalized gradient approximation (GGA) named PW91 [38] were employed. Here we find that the PWC functional better reproduces the crystal structure. Therefore, the geometry relaxation and electronic structure calculation were subsequently performed using the PWC functional. In the geometry optimization and electronic structure calculation, the effective core potentials, DNP basis set, global orbital cutoff scheme, and DIIS technique were used. The SCF tolerance was 1.0×10-6 Ha. Moreover, Brillouin zone sampling was performed by using the Monkhorst-Pack scheme with a k-point grid of 2×2×2. To study the electric field effects Fig. 1 Experimental unit cell of lead styphnate (left) and atomic numbering of the given molecular geometry (right). Gray, blue, red, white, and dark gray spheres stand for C, N, O, H, and Pb atoms, respectively
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on the structural and electronic properties of crystalline lead styphnate. The static external electric fields are separately applied in the a-, b-, and c-directions. In this study, the applied electric field strengths are 0.001, 0.003, 0.005, 0.007, and 0.009 a.u. (1 a.u. = 5.14224×1011 V/m), respectively. All DFT calculations reported in this work were carried out with the DMol3 code [39, 40].
Results and discussion To benchmark the performances of LDA and GGA for reproducing structures of the title compound, the LDA-PWC and GGA-PW91 functionals were selected to fully relax crystalline lead styphnate without any constraint in the absence of an electric field. The computed lattice parameters are given in Table 1 together with the experimental values [36]. It can be seen the errors in the PWC results are slightly smaller than that in the PW91 results in comparison with the experimental values. This indicates that the accuracy of LDA is better than that of the GGA functional, which is consistent with the previous theoretical study [29]. These observations confirm that our computational parameters are reasonably satisfactory. Thus, the PWC functional was used in all subsequent calculations. Crystal structure To show the effect of external electric field on the crystal structure, Fig. 2 displays the relaxed lattice constants (a, b, c, α, β, and γ), unit cell volume (V), and density (ρ) of lead styphnate at applied electric fields varying from 0 to 0.009 a.u. Obviously, there exist different variation trends along three crystallographic directions, revealing that the influence of external electric field on the structure of
J Mol Model (2014) 20:2072 Table 1 Experimental and calculated lattice constants of lead styphnate in the absence of an electric field
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Lattice constants
PWC
PW91
Expt
a/Å b/Å c/Å α/° β/° γ/°
7.446 7.797 8.415 89.84 106.10 90.00
7.736 8.209 8.939 89.78 109.64 89.75
7.519 8.004 8.413 90.00 107.22 90.00
crystalline lead styphnate is anisotropic. As can also be seen, the lattice parameters change slightly in the region of low electric fields below 0.005 a.u. Above this field, increasing the electric filed makes the lattice constants change markedly, especially the a, b, and γ parameters. Moreover, with the increase of electric field, the unit cell volume decreases firstly and then increases. And there is a reverse tendency for the crystalline density. In a word, the changes of most structural parameters are not monotonically dependent on the increased electric field. This indicates that the structure can undergo a phase transition upon the external electric field that could start at an electric field of ~0.007 a.u.
Molecular structure The electric field causes the changes in not only the unit cell but also the molecular geometry. Some important geometrical parameters including bond lengths and bond angles at various electric fields are presented in Figs. 3 and 4, respectively. From Fig. 3, we can observe the following features. (i) On the whole, the variations of the bond lengths with external electric field are quite different. With the applied field increasing from 0 to 0.009 a.u., some bonds elongate continuously, others shorten gradually, still others vary arbitrarily. In particular, all the Pb–O bonds that denote the position of Pb ion with respect to organic moiety and water molecule do not monotonically change with the increasing electric field. These observations demonstrate again that crystalline lead styphnate can undergo a phase transition upon the external electric field. (ii) The changes of the bond lengths in the lower electric field range are much smaller than those at higher electric fields. (iii) The variations of interatomic distances of the ionic Pb–O bonds are larger than those of the covalent bonds. And the maximum change of the Pb–O bond lengths is 0.165 Å, which occurs at the electric field of 0.007 a.u. It is worth while to note that, for the Pb–O ionic interactions, the larger geometry changes do not lead to large changes in the electronic structure as presented in the next section. (iv) The maximum changes of
Fig. 2 Calcuted lattice constants (a, b, c, α, β, and γ), unit cell volume (V), and density (ρ) of lead styphnate at different electric fields
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Fig. 3 Variation of the bond lengths with electric field. Δmax denotes the maximum variation
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Fig. 4 Variation of the selected bond angles with electric field. Δmax denotes the maximum variation
the C–C, C–H, C–N, C–O, N–O, and O–H bond lengths are 0.021, 0.030, 0.016, 0.013, 0.050, and 0.050 Å, respectively. And all of them arise at the electric field of 0.009 a.u. Clearly, the maximum variations of the N–O and O–H bond lengths are much bigger than those of the other covalent bond lengths. Therefore, the initial decomposition of lead styphnate may be closely related to the N–O and O–H chemical bonds in the presence of the electric field. And it will be further discussed infra. Similarly, from Fig. 4 several features can also be summarized as follows. First, most bond angles change regularly with
Fig. 5 Total DOS of lead styphnate at various electric fields
the increase in electric field. Second, the variations of the bond angles, especially the C–C–C bond angles, in the lower field range are much smaller than those at higher electric fields. Finally, the O–N–O and C–C–C bond angles have different maximum change values. The maximum change of the former is 2.4°, and that of the latter is 4.3°. Density of states and decomposition mechanism An analysis of density of states (DOS) is very helpful to understand the changes in electronic structure caused by ex-
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Fig. 6 Partial DOS of lead styphnate at the electric fields of 0 and 0.009 a.u.
ternal electric field. Figure 5 presents the calculated total DOS for crystalline lead styphnate at different electric fields. As can be easily seen, the DOS curve scarcely changes at the electric field of 0.001 a.u., indicating that the electronic structure of lead styphnate does not have any significant changes. However, in the field range from 0.003 to 0.009 a.u., the shape of the DOS curve changes remarkably, and the conduction band has a tendency of shifting to the lower energy, consequently leading to a reduction in band gap and showing that the presence of external electric field maybe increases the probability of electronic excitations.
Fig. 7 Band gaps of lead styphnate as a function of electric field
A previous theoretical study [29] without external electric field reveals that the C–O bond fission may be favorable in the decomposition of crystalline lead styphnate. Additionally, the above-mentioned observations show that the bond length variations of the ionic Pb–O bonds and the covalent N–O and O–H bonds are much bigger than those of the other bonds. Therefore, the partial DOS of Pb ions, water molecules (H2O), C–O bonds (CO), and nitro groups (NO2) at the electric fields of 0 and 0.009 a.u. are comparatively analyzed and displayed in Fig. 6. Apparently, in the absence of external electric field, the top of the valence band is dominated by the states of the C–O bonds. So, the C–O moiety is the active center for the decomposition of lead styphnate, and the C–O bond rupture may be preferential, which is in accord with the previous report [29]. When the applied field turns into 0.009 a.u., the DOS of the Pb ions hardly vary in the valence band, indicating that there are almost no electric field influences on the occupied states of the Pb ions. However, the external electric field makes the DOS peak in the valence band of the water molecules, C–O bonds, and nitro groups split. Obviously, this leads to the DOS peak becomes lower, and the electron distribution is more delocalized. More interestingly, the electric field results in a strong shoulder at the Fermi level for the DOS of nitro groups. It is inferred that the electron transfers from the top valence band to the conduction band may lead to the breaking of the N–O bonds. Combining with the bond length variations mentioned above, we can conclude that the N–O bond fission may be preferential in the decomposition of crystalline lead styphnate under external electric field.
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Band gap and stability The band gaps of bulk lead styphnate at different electric fields are shown in Fig. 7. In addition to the band gap reduction due to structural change resulted from external electric field (the black line in Fig. 7), the effective band gap is also reduced by the Franz-Keldysh effect (FKE). Here we should note that the red line in Fig. 7 denotes the band gap reduction induced by structural change and FKE. It can be seen that the band gap decreases gradually with the applied field increasing. And the effect of FKE on the band gap is greater than that of the structural change. Moreover, the aforementioned observations indicate that the electric field influences on the distance of the ionic interactions are stronger than those on the covalent interactions, and the larger variations of the ionic Pb–O bond lengths occur at the electric field of 0.007 a.u. While the band gap lowers dramatically at 0.009 a.u. in the case of structural change. This may be because the lead ions almost do not have contributions to both the top of the valence band and the bottom of the conduction band in the absence and presence of external electric field as displayed in Fig. 6. As is well-known, band gap is an important parameter to characterize the electronic structure of solids and retains close connection to some bulk properties. Here we discuss the correlation of stabilities (or sensitivity properties) of lead styphnate at different electric fields with the band gap. A previous investigation [29] has shown that there is a relationship between the band gap and impact sensitivity for crystalline styphnic acid and its metal salts. That is, the smaller band gap corresponds to the higher impact sensitivity. As depicted in Fig. 7, the band gap of lead styphnate gradually reduces with the increment of applied electric field. According to the first-principles band gap criterion [41], we can conclude that the sensitivity for lead styphnate becomes more and more sensitive with the external electric field increasing. Note that, for energetic materials, the initiating reaction of detonation is taken to be an electronic excitation process [42–45]. Thus, a possible explanation may be that the increased sensitivity is caused by the increased number of excited states due to optical band gap reduction.
Conclusions We have performed a detailed theoretical study of electric field effects on the structure, decomposition mechanism, and stability of crystalline lead styphnate. The obtained results show that the influence of external electric field on the crystal structure is anisotropic. The molecular geometry variations in the lower field range are much smaller. Moreover, the electric field effects on the distance of the ionic interactions
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are stronger than those on the covalent interactions. While the changes of most structural parameters are not monotonically dependent on the increased electric field, indicating that lead styphnate can undergo a phase transition upon the external electric field. Additionally, the band gap and total density of states change markedly when the electric field is increased to 0.003 a.u. Furthermore, the Franz-Keldysh effect can yield larger influence on the band gap than the structural change. In the presence of external electric field, the N–O bond cleavage may be preferential in the decomposition of lead styphnate. As the electric field increases, its sensitivity becomes more and more sensitive. Acknowledgments This work was supported by the National “973”project, the Natural Science Foundation of Chongqing (Grant No. cstc2011jjA50013), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ111310), and the State Key Laboratory of Explosion Science and Technology (Grant No. ZDKT08-01, Grant No. YBKT10-03).
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ORIGINAL PAPER
First-principles study of electric field effects on the structure, decomposition mechanism, and stability of crystalline lead styphnate Zhimin Li & Huisheng Huang & Tonglai Zhang & Shengtao Zhang & Jianguo Zhang & Li Yang
Received: 31 May 2013 / Accepted: 7 November 2013 / Published online: 28 January 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract The electric field effects on the structure, decomposition mechanism, and stability of crystalline lead styphnate have been studied using density functional theory. The results indicate that the influence of external electric field on the crystal structure is anisotropic. The electric field effects on the distance of the Pb–O ionic interactions are stronger than those on the covalent interactions. However, the changes of most structural parameters are not monotonically dependent on the increased electric field. This reveals that lead styphnate can undergo a phase transition upon the external electric field. When the applied field is increased to 0.003 a.u., the effective band gap and total density of states vary evidently. And the Franz-Keldysh effect yields larger influence on the band gap than the structural change induced by external electric field. Furthermore, lead styphnate has different initial decomposition reactions in the presence and absence of the electric field. Finally, we find that its sensitivity becomes more and more sensitive with the increasing electric field. Keywords Decomposition mechanism . Density functional theory . Electric field effect . Electronic structure . Lead styphnate . Stability
Z. Li : T. Zhang (*) : J. Zhang : L. Yang State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China e-mail: [email protected] H. Huang : S. Zhang College of Materials Science and Engineering, Chongqing University, Chongqing 400030, China H. Huang (*) The Key Laboratory of Inorganic Special Functional Materials, College of Chemistry and Chemical Engineering, Yangtze Normal University, Chongqing 408100, China e-mail: [email protected]
Introduction The decomposition reaction of energetic materials can be triggered by various external stimuli, such as impact, friction, heat, static compression, and electric spark. The influences of temperature and pressure on the structure and properties of explosives have been fully studied theoretically and experimentally [1–10]. However, theoretical investigations on energetic solids under external electric field have not been made, although the hazards of energetic materials owing to static charge have been extensively studied experimentally [11–15]. The electrostatic discharge hazard is normally associated with manufacturing and filling operations. And the discharge of static electricity accumulated on a person can supply energy up to 20 mJ, which is possibly bigger than the minimum spark energy required for initiating the energetic materials such as lead styphnate (2,4,6-trinitroresorcinate) and basic lead azide [13]. Hence, the accident resulted from static charge can easily occur in the explosive production plant. Moreover, the electric spark sensitivity of various explosives has been the subject of very many articles in the literature [16–28]. The correlations between the spark sensitivity of explosives and their molecular electronic properties have been well established. While the external electric field influences on the structure and properties of energetic materials are still not well understood. It is known that lead styphnate is a typical primary explosive and has been extensively used for several decades. Therefore, its structure, decomposition mechanism and properties, especially the spark sensitivity, are fully investigated and compared [13–15, 29]. Unfortunately, the geometric and electronic structures and detonation mechanism under external electric field are often difficult to obtain from experiment for practical reasons. Compared with experiment, simulation can provide more detailed information about variations in crystal and molecular structures, initiation mechanism, and stability of energetic materials under applied electric field. In
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fact, there are sufficient computational investigations on the structures and properties of materials including single-walled nanotubes [30–32], graphene nanoribbons [33], guanine aggregates [34], and carbon dioxide [35] under external electric field. To the best of our knowledge, there are no such reports on the primary explosives. Thus, in the present work, firstprinciples periodic calculations have been performed using density functional theory to study the effect of electric field on the geometric and electronic structures, decomposition mechanism, and stability of crystalline lead styphnate.
Computational methods The initial structure adopted the experimental crystalline structure [36] in which lead styphnate contains two HC6N3O8Pb·H2O molecules per unit cell in a monoclinic lattice with space group P2/c as shown in Fig. 1. The geometry optimization was performed to allow the ionic configuration, cell shape, and volume to change. The total energy of the system was converged less than 1.0×10-5 Ha, the residual force less than 0.002 Ha/Å, the displacement of atoms less than 0.005 Å. Additionally, both the local density approximation (LDA) named PWC [37] and the generalized gradient approximation (GGA) named PW91 [38] were employed. Here we find that the PWC functional better reproduces the crystal structure. Therefore, the geometry relaxation and electronic structure calculation were subsequently performed using the PWC functional. In the geometry optimization and electronic structure calculation, the effective core potentials, DNP basis set, global orbital cutoff scheme, and DIIS technique were used. The SCF tolerance was 1.0×10-6 Ha. Moreover, Brillouin zone sampling was performed by using the Monkhorst-Pack scheme with a k-point grid of 2×2×2. To study the electric field effects Fig. 1 Experimental unit cell of lead styphnate (left) and atomic numbering of the given molecular geometry (right). Gray, blue, red, white, and dark gray spheres stand for C, N, O, H, and Pb atoms, respectively
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on the structural and electronic properties of crystalline lead styphnate. The static external electric fields are separately applied in the a-, b-, and c-directions. In this study, the applied electric field strengths are 0.001, 0.003, 0.005, 0.007, and 0.009 a.u. (1 a.u. = 5.14224×1011 V/m), respectively. All DFT calculations reported in this work were carried out with the DMol3 code [39, 40].
Results and discussion To benchmark the performances of LDA and GGA for reproducing structures of the title compound, the LDA-PWC and GGA-PW91 functionals were selected to fully relax crystalline lead styphnate without any constraint in the absence of an electric field. The computed lattice parameters are given in Table 1 together with the experimental values [36]. It can be seen the errors in the PWC results are slightly smaller than that in the PW91 results in comparison with the experimental values. This indicates that the accuracy of LDA is better than that of the GGA functional, which is consistent with the previous theoretical study [29]. These observations confirm that our computational parameters are reasonably satisfactory. Thus, the PWC functional was used in all subsequent calculations. Crystal structure To show the effect of external electric field on the crystal structure, Fig. 2 displays the relaxed lattice constants (a, b, c, α, β, and γ), unit cell volume (V), and density (ρ) of lead styphnate at applied electric fields varying from 0 to 0.009 a.u. Obviously, there exist different variation trends along three crystallographic directions, revealing that the influence of external electric field on the structure of
J Mol Model (2014) 20:2072 Table 1 Experimental and calculated lattice constants of lead styphnate in the absence of an electric field
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Lattice constants
PWC
PW91
Expt
a/Å b/Å c/Å α/° β/° γ/°
7.446 7.797 8.415 89.84 106.10 90.00
7.736 8.209 8.939 89.78 109.64 89.75
7.519 8.004 8.413 90.00 107.22 90.00
crystalline lead styphnate is anisotropic. As can also be seen, the lattice parameters change slightly in the region of low electric fields below 0.005 a.u. Above this field, increasing the electric filed makes the lattice constants change markedly, especially the a, b, and γ parameters. Moreover, with the increase of electric field, the unit cell volume decreases firstly and then increases. And there is a reverse tendency for the crystalline density. In a word, the changes of most structural parameters are not monotonically dependent on the increased electric field. This indicates that the structure can undergo a phase transition upon the external electric field that could start at an electric field of ~0.007 a.u.
Molecular structure The electric field causes the changes in not only the unit cell but also the molecular geometry. Some important geometrical parameters including bond lengths and bond angles at various electric fields are presented in Figs. 3 and 4, respectively. From Fig. 3, we can observe the following features. (i) On the whole, the variations of the bond lengths with external electric field are quite different. With the applied field increasing from 0 to 0.009 a.u., some bonds elongate continuously, others shorten gradually, still others vary arbitrarily. In particular, all the Pb–O bonds that denote the position of Pb ion with respect to organic moiety and water molecule do not monotonically change with the increasing electric field. These observations demonstrate again that crystalline lead styphnate can undergo a phase transition upon the external electric field. (ii) The changes of the bond lengths in the lower electric field range are much smaller than those at higher electric fields. (iii) The variations of interatomic distances of the ionic Pb–O bonds are larger than those of the covalent bonds. And the maximum change of the Pb–O bond lengths is 0.165 Å, which occurs at the electric field of 0.007 a.u. It is worth while to note that, for the Pb–O ionic interactions, the larger geometry changes do not lead to large changes in the electronic structure as presented in the next section. (iv) The maximum changes of
Fig. 2 Calcuted lattice constants (a, b, c, α, β, and γ), unit cell volume (V), and density (ρ) of lead styphnate at different electric fields
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Fig. 3 Variation of the bond lengths with electric field. Δmax denotes the maximum variation
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Fig. 4 Variation of the selected bond angles with electric field. Δmax denotes the maximum variation
the C–C, C–H, C–N, C–O, N–O, and O–H bond lengths are 0.021, 0.030, 0.016, 0.013, 0.050, and 0.050 Å, respectively. And all of them arise at the electric field of 0.009 a.u. Clearly, the maximum variations of the N–O and O–H bond lengths are much bigger than those of the other covalent bond lengths. Therefore, the initial decomposition of lead styphnate may be closely related to the N–O and O–H chemical bonds in the presence of the electric field. And it will be further discussed infra. Similarly, from Fig. 4 several features can also be summarized as follows. First, most bond angles change regularly with
Fig. 5 Total DOS of lead styphnate at various electric fields
the increase in electric field. Second, the variations of the bond angles, especially the C–C–C bond angles, in the lower field range are much smaller than those at higher electric fields. Finally, the O–N–O and C–C–C bond angles have different maximum change values. The maximum change of the former is 2.4°, and that of the latter is 4.3°. Density of states and decomposition mechanism An analysis of density of states (DOS) is very helpful to understand the changes in electronic structure caused by ex-
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Fig. 6 Partial DOS of lead styphnate at the electric fields of 0 and 0.009 a.u.
ternal electric field. Figure 5 presents the calculated total DOS for crystalline lead styphnate at different electric fields. As can be easily seen, the DOS curve scarcely changes at the electric field of 0.001 a.u., indicating that the electronic structure of lead styphnate does not have any significant changes. However, in the field range from 0.003 to 0.009 a.u., the shape of the DOS curve changes remarkably, and the conduction band has a tendency of shifting to the lower energy, consequently leading to a reduction in band gap and showing that the presence of external electric field maybe increases the probability of electronic excitations.
Fig. 7 Band gaps of lead styphnate as a function of electric field
A previous theoretical study [29] without external electric field reveals that the C–O bond fission may be favorable in the decomposition of crystalline lead styphnate. Additionally, the above-mentioned observations show that the bond length variations of the ionic Pb–O bonds and the covalent N–O and O–H bonds are much bigger than those of the other bonds. Therefore, the partial DOS of Pb ions, water molecules (H2O), C–O bonds (CO), and nitro groups (NO2) at the electric fields of 0 and 0.009 a.u. are comparatively analyzed and displayed in Fig. 6. Apparently, in the absence of external electric field, the top of the valence band is dominated by the states of the C–O bonds. So, the C–O moiety is the active center for the decomposition of lead styphnate, and the C–O bond rupture may be preferential, which is in accord with the previous report [29]. When the applied field turns into 0.009 a.u., the DOS of the Pb ions hardly vary in the valence band, indicating that there are almost no electric field influences on the occupied states of the Pb ions. However, the external electric field makes the DOS peak in the valence band of the water molecules, C–O bonds, and nitro groups split. Obviously, this leads to the DOS peak becomes lower, and the electron distribution is more delocalized. More interestingly, the electric field results in a strong shoulder at the Fermi level for the DOS of nitro groups. It is inferred that the electron transfers from the top valence band to the conduction band may lead to the breaking of the N–O bonds. Combining with the bond length variations mentioned above, we can conclude that the N–O bond fission may be preferential in the decomposition of crystalline lead styphnate under external electric field.
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Band gap and stability The band gaps of bulk lead styphnate at different electric fields are shown in Fig. 7. In addition to the band gap reduction due to structural change resulted from external electric field (the black line in Fig. 7), the effective band gap is also reduced by the Franz-Keldysh effect (FKE). Here we should note that the red line in Fig. 7 denotes the band gap reduction induced by structural change and FKE. It can be seen that the band gap decreases gradually with the applied field increasing. And the effect of FKE on the band gap is greater than that of the structural change. Moreover, the aforementioned observations indicate that the electric field influences on the distance of the ionic interactions are stronger than those on the covalent interactions, and the larger variations of the ionic Pb–O bond lengths occur at the electric field of 0.007 a.u. While the band gap lowers dramatically at 0.009 a.u. in the case of structural change. This may be because the lead ions almost do not have contributions to both the top of the valence band and the bottom of the conduction band in the absence and presence of external electric field as displayed in Fig. 6. As is well-known, band gap is an important parameter to characterize the electronic structure of solids and retains close connection to some bulk properties. Here we discuss the correlation of stabilities (or sensitivity properties) of lead styphnate at different electric fields with the band gap. A previous investigation [29] has shown that there is a relationship between the band gap and impact sensitivity for crystalline styphnic acid and its metal salts. That is, the smaller band gap corresponds to the higher impact sensitivity. As depicted in Fig. 7, the band gap of lead styphnate gradually reduces with the increment of applied electric field. According to the first-principles band gap criterion [41], we can conclude that the sensitivity for lead styphnate becomes more and more sensitive with the external electric field increasing. Note that, for energetic materials, the initiating reaction of detonation is taken to be an electronic excitation process [42–45]. Thus, a possible explanation may be that the increased sensitivity is caused by the increased number of excited states due to optical band gap reduction.
Conclusions We have performed a detailed theoretical study of electric field effects on the structure, decomposition mechanism, and stability of crystalline lead styphnate. The obtained results show that the influence of external electric field on the crystal structure is anisotropic. The molecular geometry variations in the lower field range are much smaller. Moreover, the electric field effects on the distance of the ionic interactions
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are stronger than those on the covalent interactions. While the changes of most structural parameters are not monotonically dependent on the increased electric field, indicating that lead styphnate can undergo a phase transition upon the external electric field. Additionally, the band gap and total density of states change markedly when the electric field is increased to 0.003 a.u. Furthermore, the Franz-Keldysh effect can yield larger influence on the band gap than the structural change. In the presence of external electric field, the N–O bond cleavage may be preferential in the decomposition of lead styphnate. As the electric field increases, its sensitivity becomes more and more sensitive. Acknowledgments This work was supported by the National “973”project, the Natural Science Foundation of Chongqing (Grant No. cstc2011jjA50013), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ111310), and the State Key Laboratory of Explosion Science and Technology (Grant No. ZDKT08-01, Grant No. YBKT10-03).
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