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First-principles study of structural, elastic, and electronic properties of triclinic TATB under different pressures
Accepted Manuscript First-principles study of structural, elastic, and electronic properties of triclinic TATB under different pressures Han Qin, Bao-Luo Yan, Mi Zhong, Cheng-Lu Jiang, Fu-Sheng Liu, Bin Tang, Qi-Jun Liu PII:
S0921-4526(18)30621-5
DOI:
10.1016/j.physb.2018.10.003
Reference:
PHYSB 311088
To appear in:
Physica B: Physics of Condensed Matter
Received Date: 22 August 2018 Revised Date:
29 September 2018
Accepted Date: 1 October 2018
Please cite this article as: H. Qin, B.-L. Yan, M. Zhong, C.-L. Jiang, F.-S. Liu, B. Tang, Q.-J. Liu, Firstprinciples study of structural, elastic, and electronic properties of triclinic TATB under different pressures, Physica B: Physics of Condensed Matter (2018), doi: https://doi.org/10.1016/j.physb.2018.10.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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First-principles study of structural, elastic, and electronic properties of triclinic TATB under different pressures
Bin Tang c, Qi-Jun Liu* a,b a
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Han Qin a,b, ∗∗, Bao-Luo Yan a,b, Mi Zhong a,b, Cheng-Lu Jiang a,b, Fu-Sheng Liu a,b,
School of Physical Science and Technology, Southwest Jiaotong University, Key
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Laboratory of Advanced Technologies of Materials, Ministry of Education of China, Chengdu 610031, People’s Republic of China
Bond and Band Engineering Group, Sichuan Provincial Key Laboratory (for
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b
Universities) of High Pressure Science and Technology, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China c
State Key Laboratory of Solidification Processing, Northwestern Polytechnical
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University, Xi’an 710072, People’s Republic of China
Han Qin
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Correspondence about the paper at the following address and e-mail address:
School of Physical Science and Technology, Southwest Jiaotong University, Chengdu,
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Sichuan 610031, People’s Republic of China E-mail: [email protected] Qi-Jun Liu
School of Physical Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan 610031, People’s Republic of China E-mail: [email protected]
∗∗ *
Corresponding author. E-mail: [email protected] Corresponding author. E-mail: [email protected] 1
ACCEPTED MANUSCRIPT Abstract: First-principles calculations were performed to investigate the structural, elastic, electronic and sensitive properties of triclinic TATB crystal. The obtained ground state properties using GGA-PBE method were in agreement with the previous
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theoretical and experimental data. The elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, anisotropy under the hydrostatic pressure from 0 GPa to 30 GPa were calculated and analyzed. Moreover, we found that TATB became
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more and more hardness with the increasing pressure. Furthermore, comparing the
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density of states in different pressures, we can find that the electrons of TATB become more active under ambient pressure.
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Keywords: TATB; Elastic properties; Sensitivity; First-principles calculations
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ACCEPTED MANUSCRIPT 1. Introduction The compound 1,3,5-triamino-2,4,6-trinitrobenzene (TATB, C6H6N6O6) is one of the most outstanding representative of high explosives, whose triclinic crystal
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structure was characterized by Cady and Larson [1]. It is known that this compound exhibits considerably low sensitivity [2,3,4,5] to high temperature, shock as well as impact [6], and is hardly detonated by accidental initiation [7,8]. Because of the
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excellent safety performance and comprehensive performance, TATB is widely
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applied on the field of modern nuclear warheads, reagents in manufacture of liquid crystal displays and deep oil well explorations [8]. As we know, the energetic materials explode at high temperature and high pressure conditions, so it is necessary to investigate the physical and chemical properties of TATB under extreme conditions
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to understand its sensitive characteristics.
Since its first synthesis in 1887 [9], researchers have extensively studied TATB in both experimental and theoretical aspects. At ambient conditions, TATB crystallizes in —
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a triclinic crystal with space group P1. In 1976, Olinger and Cady [10] compressed
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TATB up to 7.02 GPa. They observed ten diffraction peaks at low pressure (P<3.0 GPa), while there are four peaks at higher pressure. At ambient pressure, TATB is decidedly photosensitive [11], and Satijia et al. [12] found that the photosensitive property decreased clearly at pressures exceeding 1.5 GPa. With the increase of pressure, Giefers et al. [13] found that the reaction/decomposition rate decreased significantly because of a positive volume of activation. Pravica et al. [5Error! Bookmark not defined.] performed infrared spectroscopic measurements to 3
ACCEPTED MANUSCRIPT investigate TATB at high pressures up to 10 GPa, and they found that there was no phase transition. Stevens et al. [14] recorded the P-V relationship and static compression of TATB via X-ray diffraction measurements from 0 to 13 GPa.
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Davidson et al. [15] found that there were two subtle structural phase transitions at about 28 and 56 GPa by Raman spectra measurements. Depending on Raman spectra of TATB, Landerville et al. [16] evidenced that no first-order polymorphic phase
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transition appeared up to 27 GPa.
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Due to the fact that some important properties cannot be studied experimentally, the computational modeling and simulations have been used widely in order to better understand the effects of pressure on TATB. Byrd et al. [17] employed several functionals to investigate the TATB crystal and energetic molecular crystals (HMX,
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RDX, CL-20 and PETN) up to 7 GPa. They found that the predicted lattice parameters were lack of agreement with experiments due to the inadequate treatment of vdW interactions within DFT. Using the molecular simulation package
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LUCRETIUS, with the increase of temperature and pressure, Bedrov et al. [18]
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indicated that the considerable anisotropy of TATB with modest softening and significant stiffening appeared, respectively. Budzevich et al. [19] studied TATB under hydrostatic and uniaxial compressions, showing that highly anisotropic behavior occurred under uniaxial compression. Kohno et al. [20] used the molecular dynamics calculations to evaluate the effect of high pressure on TATB. In the pressure range of 1.0 atm to 20.0 GPa, the intermolecular and intramolecular hydrogen bonds were maintained. The interlayer distances decreased from 3.50 to 2.90 Å with the 4
ACCEPTED MANUSCRIPT increasing pressure up to 20 GPa. Fan et al. [21] analyzed the elastic anisotropy of TATB using molecular dynamics simulation. They found that the anisotropy of Young’s modulus exhibited a decreasing trend, but that of shear modulus showed an
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opposite trend, with the increasing pressure from 0 to 50 GPa. In our present study, the effect of pressure on TATB in the crystalline state is evaluated using the density functional theory with generalized gradient approximation
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plus dispersion correction (DFT-D). In our calculation, we focus on the crystal
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structure, elasticity, and electronic structure of TATB in the pressure range of 0 to 30 GPa. The remainder of this paper is organized as follows: in section 2, we describe the general details for calculations using the generalized gradient approximation with Perdew-Burke-Ernzerhof functional (GGA-PBE), the results and discussion are
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presented in section 3, and the conclusion is given in section 4.
2. Computational methods
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First-principles calculations were carried out within the density functional theory
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with the norm-conserving pseudopotential method. In this paper, we have employed the Cambridge Sequential Total Energy Package (CASTEP) code [22]. For the exchange-correlation interaction, the generalized gradient approximation with the Perdew-Burke-Ernzerhof
functional
[23]
was
adopted.
The
pseudo-atomic
calculations [24] were performed and the H 1s1, C 2s22p2, N 2s22p3 and O 2s22p4 were treated as the valence shells. We used a k-point grid of 2×2×2 for the Brillouin zone sampling, which was based on the Monkhorst-Pack scheme [25]. The convergence 5
ACCEPTED MANUSCRIPT test calculations energy and the final energy in different kinds of k-points have been considered shown in Fig. S1, indicating that the k-point of 2×2×2 used of TATB crystal is adoptable. The cut-off energy of 830 eV was adopted. We used the DFT-D
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method to solve the van der Waals interactions [26], where the TS (Tkatchenko and Scheffler) [27] and the G (Grimme) [28] corrections to GGA-PBE have been adopted. As the convergence criterion, the total energy of the system converged to less than
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5.0×10-6 eV/atom, the maximum force was lower than 0.01 eV/Å, the maximum stress
3. Results and discussion 3.1. Structural parameters
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was less than 0.02 GPa, and the maximum displacement was less than 5×10-4 Å.
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The molecular structure and crystal structure including 48 atoms of TATB are shown in Fig. 1. Our calculated lattice parameters for TATB (a=9.12 Å, b=9.13 Å, c=6.63 Å, α=109.51°, β=91.40°, γ=119.97° and V=438.36 Å3 [29] and a=9.13 Å,
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b=9.15 Å, c=6.77 Å, α=109.15°, β=91.66°, γ=119.98° and V=449.86 Å3 with the G
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and TS corrections, respectively) are in good agreement with the previous theoretical [18,21,30] and experimental values [1,14]. The corresponding bond lengths and bond angles are consistent with the theoretical [31] and experimental results [1]. Comparing with the experimental volume [Error! Bookmark not defined.], the overestimation with the GGA-PBE+TS calculations is about 1.67%, while the underestimation with the GGA-PBE+G calculations is about 0.93%. As we can see, the calculated results with the GGA-PBE+G method are closer to the experimental results. Therefore, the 6
ACCEPTED MANUSCRIPT calculations under different pressures at this work are based on the GGA-PBE+G method. The first-principles calculations of the TATB crystal are conducted using the
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GGA-PBE+G for pressure up to 30 GPa. In Fig. 2, we show the lattice parameters of TATB as the functions of pressure. Results obtained from the simulations using GGA-PBE+G method are compared to the calculated data and the experimental data.
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Our calculated results show that the lattice constants a, b, and c decrease
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monotonically with increasing pressure and perfectly reproduce the calculational data of Rykounov [30] and basically in agreement with the tendency of the experimental data of Stevens [14]. In Fig. 3, the normalized volume is shown as a function of pressure along with previous theoretical [18,21,30,32] and experimental [10,14]
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results. Comparing with the theoretical and experimental results, our results are in agreement with the experimental results, especially satisfying the recent results by Stevens [14] in the range of 0-13 GPa. In addition, our results are basically consistent
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with the theoretical results of Bedrov [18] and Rykounov [30].
3.2. Elastic and mechanical properties The elastic and mechanical properties are important to know the effects of
external conditions on TATB. Hence, we investigate the corresponding properties. As we know, the elastic constants are associated with the mechanical properties which can be used to judge the mechanical stability of materials. So far, the experimental works of elastic constants of TATB have not been reported because of the difficult 7
ACCEPTED MANUSCRIPT tests for the molecular crystal. However, there are a few theoretical investigations [18,21,30,33]. The TATB as a triclinic crystal has 21 independent elastic constants. The elastic constants of TATB are determined by the generalized Hooke’s law [34],
= [ ]
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where the resultant proportional elastic stiffness matrix [Cij] is shown: (1)
where is the stress vector and is the strain vector. With the triclinic C
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C C C
C C C C
C C C C C
C C C C C C
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C =
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structure, the [ ] of TATB is obtained as follows [35]:
(2)
The calculated independent elastic constants of TATB crystal using the GGA-PBE
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method at 0 GPa are shown in Table 1. Comparing with the theoretical values, the calculated results with the GGA-PBE show the same anisotropy in the elastic response of TATB. According to the Hooke’s law, when the force is the same, the
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larger value of elastic constant is, the smaller the strain is. Moreover, the C44, C55 and
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C66 roughly correspond to the deformations of the lattice angles α, β and γ. We conclude that the γ is the most stable angle due to that the elastic constant C66 is clearly larger than C44/C55, which is consistent with the changed trends of lattice angles in Fig. 2.
Using the elastic constants, the anisotropy characteristic of TATB is obtained. It can be given by the equivalent Zener anisotropy measure Aeq [36]:
A = 1 + A" # + $ 1 + A" # − 1
(3) 8
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'(
)'(
A* = A=
#
(4)
+'),-
(5)
+'),- .' *//
(6)
*00 )*0-
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If A = 1, the material is fully isotropic. Otherwise, it is anisotropic. The value of the equivalent Zener anisotropy factor of TATB at 0 GPa is 1.78, indicating that TATB crystal is an anisotropic material. Using the above formulas, we obtain the
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relationship between the anisotropy factor and the pressure, which is shown in Fig. 4.
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As we can see, with the pressure increasing, the anisotropy of TATB roughly tends to decrease, showing that the high pressure can reduce the anisotropy of TATB. To further describe the anisotropy, the universal anisotropy index Au [36] is used as follows: 53
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A" = 5 24 + 54 − 6
(7)
B8 = 9 [+C + C + C , + 2+C + C + C ,]
(8)
1⁄B; = +S + S + S , + 2+S + S + S ,
(9)
[+C + C + C , − +C + C + C , + 3+C + C + C ,]
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G8 =
(11)
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15⁄G; = 4+S + S + S , − 4+S + S + S , + 3+S + S + S ,
(10)
where BV (GV) and BR (GR) are the upper and lower bounds of the bulk (shear) modulus [37]. Fig. 5 shows the universal anisotropy index of TATB in the pressure range of 0 to 30 GPa. At the early stage (0～4 GPa), the universal anisotropy index decreases rapidly, while it tends to slow down at the stage of 5～30 GPa. It indicates that the elastic anisotropy of TATB becomes weaker and weaker with the increasing pressure, which is a similar changing pattern in the previous calculated result [21]. To 9
ACCEPTED MANUSCRIPT directly see the change, we draw the three-dimensional (3D) diagrams [38] of the Young’s modulus at 0 GPa, 10 GPa, 20 GPa and 30 GPa in Fig. 6. Our results agree with the recent anisotropy study of Fan et al. [21].
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The bulk modulus (B), shear modulus (G), Young’s modulus (E) and Poisson’s ratio (ν) under pressure are analyzed using the Voigt-Reuss-Hill approximation [39,40], which can be obtained as follows:
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B =(B; + B8 )/2 G =(G8 + G; )/2 952
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E = 5.2
5)2
ν = 5.2
(12)
(13) (14) (15)
Fig. 7 illustrates the effects of pressure on these mechanical properties. These
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values of mechanical properties increase with the increasing pressure. From 0 GPa to 30 GPa, the increases of the B, G, E and ν of TATB are about 883.64%, 751.12%, 750.88% and 8.22%, respectively. From the range of 0 to 10 GPa, the bulk modulus
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and the shear modulus agree well with the Rykounov’s data [30]. The Pugh theorem
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[41] can evaluate the ductile/brittle property of TATB using the ratio of the bulk modulus and the shear modulus (B/G). If the B/G ratio is larger than 1.75, the crystal is ductile; otherwise, it is brittle. The value of 1.470 for B/G indicates the brittleness of the TATB crystal. In addition, the hardness of TATB is explored through calculation of the Vickers hardness (HV), which is a measure of the resistance of the solid matter against ambient pressure, CD = 2+E F,G.I − 3, where k=G/B. Fig. 8 shows the pressure dependent of B/G ratio and hardness for TATB. Although there are slight 10
ACCEPTED MANUSCRIPT perturbations that are probably caused by rotation or proton transfer in TATB, it is notable that the B/G and hardness of TATB increase with the increasing pressure. As
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we can see, starting from 2 GPa, TATB has changed from brittleness to ductility.
3.3. Electronic properties
The electronic band structure of TATB under 0 GPa based on the GGA-PBE+G is
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calculated and presented in Fig. 9. As we know, the band structure greatly depends on
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the interactions between electronic orbits. Moreover, at zero pressure, the valence-band maximum is 0 eV appearing on the direction of F → Q and the conduction-band minimum is 2.366 eV appearing on the Q point, which is similar with the calculated results 2.37 eV [42]. However, these calculated values are smaller
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than the experimental data 6.6 eV [43]. The PBE functionals will underestimate the band gap by 30 to 100% [44,45]. In our previous work [29], we also calculated the band gap is 3.484 and 3.250 eV using the B3LYP and HSE06 functional. However,
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they are also smaller than the experimental data. Fig. 10 presents the band structures
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under hydrostatic pressure of 0 GPa, 15 GPa and 30 GPa. It’s clear to see that the band dispersion increases while the band gap decreases with the increasing pressure. The calculated band gaps at 15GPa and 30GPa equal 1.859eV and 1.613eV, respectively. Meanwhile, the pressure of TATB as a function of band gap is shown in Fig. 11. It is also clear to see that the pressure decreases the band gap of TATB crystal. The calculated total density of states (TDOS) of TATB is plotted in Fig. 12 and the partial density of states (PDOS) of TATB is presented in Fig. 13, respectively. 11
ACCEPTED MANUSCRIPT Comparing the TDOS of TATB at 0GPa, 10GPa, 20GPa and 30GPa, we can see that the peaks of TDOS of TATB decrease with hydrostatic pressure while the TDOS dispersion increases. In other words, the electrons of TATB become more active under
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ambient pressure. From the calculations of the PDOS of TATB, the peak in the valence band near Feimi level is mainly contributed by the p orbital of C, O and N atoms in NO2. The peak in conduction band near Feimi level is mainly offered by the
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p orbital of C, O and N atoms. It can be inferred that the C-N-O2 acts an active center.
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It is also expected that the increasing pressure from 0 GPa to 30 GPa gives wider but smaller peaks.
4. Conclusion
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The structural, elastic, electronic and sensitive properties of TATB crystal under different pressures are systematically analyzed by using the first-principles method based on the density functional theory. The structural parameters are calculated with
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the increasing pressure. We find that the obtained parameters at 0 GPa using
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GGA-PBE+G method are more consistent with the former theoretical and experimental data. With the increasing pressure, the volume of TATB decreases. The elastic anisotropy and the elastic modulus, including bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio are calculated. Moreover, using the Vickers hardness equation, we find that TATB becomes more and more hardness with the pressure increasing. Finally, comparing the density of states in different pressures, the electrons of TATB become more active under ambient pressure. 12
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Acknowledgments This work was supported by the National Natural Science Foundation of China
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(Grant No. 11574254), the Fundamental Research Funds for the Central Universities (Grant No. 2018GF08), the fund of the State Key Laboratory of Solidification Processing in NWPU (Grant No. SKLSP201843), the Doctoral Innovation Fund
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Program of Southwest Jiaotong University (Grant No. D-CX201735) and the Doctoral
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Students Top-notch Innovative Talent Cultivation of Southwest Jiaotong University.
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ACCEPTED MANUSCRIPT [45] R. V. Tsyshevsky, O. Sharia, M. M. Kuklja, The Journal of Physical Chemistry C,
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ACCEPTED MANUSCRIPT Fig. 1. (a) Molecular structure of TATB, (b) Crystal structure of TATB (hydrogen: white; carbon: gray; oxygen: red; nitrogen: blue). Fig. 2. The lattice parameters of TATB as the functions of increasing pressure. Fig. 3. The effect of pressure on normalized volume.
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Fig. 4. The equivalent Zener anisotropy factor as a function of pressure. Fig. 5. The universal anisotropy index as a function of pressure.
Fig. 6. The three-dimensional (3D) diagrams of the Young’s modulus at (a) 0 GPa, (b)
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10 GPa, (c) 20 GPa and (d) 30 GPa.
Fig. 7. The pressure dependence of bulk modulus (B), shear modulus (G), Young’s
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modulus (E) and Poisson’s ratio (ν) for TATB.
Fig. 8. Pressure dependent of B/G ratio and Hardness for TATB. Fig. 9. The band structure of TATB at 0GPa.
Fig. 10. Band structures of TATB at the hydrostatic pressure of (a) 0GPa, (b) 15GPa
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and (c) 30GPa.
Fig. 11. Band gap of TATB as a function of pressure.
zero).
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Fig. 12. Total density of states of TATB at different pressures (The Feimi level is set to
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Fig. 13. Partial density of states of TATB at (a) 0GPa and (b) 30GPa (The Feimi level is set to zero).
Table 1. Elastic constants (GPa) of TATB crystal at 0 GPa.
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Table 1. Elastic constants (GPa) of TATB crystal at 0 GPa.
32.02 20.13 7.53 0.48 0.89 12.43 8.23 5.8 5.18 0.04 0.49 -0.03 1.78 -0.27 1.67 -0.6 -0.44 -1.03 0.03 0.44 0.04
83.2 78.3 18.9 1.7 1.5 30.0 21.9 -2.4 -0.3 -0.8 -0.6 2.9 0.1 -0.4 2.5 -0.6 -0.5 0.1 0.0 -0.3 0.6
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82.04 79.75 19.43 19.91 14.64 34.18 11.05 5.17 11.87 1.27 -21.02 -4.90 -30.86 1.42 -5.58 -3.44 -1.97 9.42 4.18 -9.13 -12.87
Polarizable FF
Nonpolarizable FF
65.7±0.5 62.0±1.0 18.3±0.5 1.4±0.3 0.68±0.06 21.6±0.7 18.5±0.5 4.0±2.0 5.0±1.0 -0.2±0.3 -1.0±0.1 1.0±1.0 0.6±0.2 -0.5±0.2 1.0±1.0 0.2±0.3 -0.4±0.1 -0.4±0.7 0.1±0.2 0.3±0.2 0.4±0.1
57.7±0.5 58.0±1.0 17.0±0.5 1.0±0.3 0.6±0.2 20.3±0.8 16.2±0.7 3.2±0.5 5.7±0.6 0.1±0.1 -0.9±0.2 0.0±1.0 0.6±0.2 -0.5±0.3 2.0±0.8 -1.0±0.4 -0.3±0.2 -1.0±0.5 0.01±0.04 -0.5±0.1 0.1±0.1
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66.96 61.26 30.77 14.30 12.32 26.49 5.25 10.84 18.05 0.51 -16.05 -3.55 -19.78 1.30 -4.49 -2.92 -2.02 11.80 4.19 -5.68 -8.97
Classical MD[18]
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GGA-PBE+G
DFT-D2[30]
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GGA-PBE+TS
Lammps/MD[21]
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C11 C22 C33 C44 C55 C66 C12 C13 C23 C14 C15 C16 C24 C25 C26 C34 C35 C36 C45 C46 C56
This work
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Cij
Ab initio values [33] 78.4 — 19.7 0.9 — 29.7 16.8 0.8 — — — — — — — — — — — — —
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Fig. 1. (a) Molecular structure of TATB, (b) Crystal structure of TATB (hydrogen:
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white; carbon: gray; oxygen: red; nitrogen: blue).
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Fig. 10. Band structures of TATB at the hydrostatic pressure of (a) 0GPa, (b) 15GPa and (c) 30GPa.
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Fig. 11. Band gap of TATB as a function of pressure.
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Fig. 12. Total density of states of TATB at different pressures (The Feimi level is set to zero).
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(b) Fig. 13. Partial density of states of TATB at (a) 0 GPa and (b) 30 GPa (The Feimi level is set to zero).
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Fig. 2. The lattice parameters of TATB as the functions of increasing pressure.
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Fig. 3. The effect of pressure on normalized volume.
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Fig. 4. The equivalent Zener anisotropy factor as a function of pressure.
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Fig. 5. The universal anisotropy index as a function of pressure
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Fig. 6. The three-dimensional (3D) diagrams of the Young’s modulus at (a) 0 GPa, (b) 10 GPa, (c) 20 GPa and (d) 30 GPa.
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Fig. 7. The pressure dependence of bulk modulus (B), shear modulus (G), Young’s modulus (E) and Poisson’s ratio (ν) for TATB.
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Fig. 8. Pressure dependent of B/G ratio and Hardness for TATB.
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Fig. 9. The band structure of TATB at 0 GPa.
S0921-4526(18)30621-5
DOI:
10.1016/j.physb.2018.10.003
Reference:
PHYSB 311088
To appear in:
Physica B: Physics of Condensed Matter
Received Date: 22 August 2018 Revised Date:
29 September 2018
Accepted Date: 1 October 2018
Please cite this article as: H. Qin, B.-L. Yan, M. Zhong, C.-L. Jiang, F.-S. Liu, B. Tang, Q.-J. Liu, Firstprinciples study of structural, elastic, and electronic properties of triclinic TATB under different pressures, Physica B: Physics of Condensed Matter (2018), doi: https://doi.org/10.1016/j.physb.2018.10.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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First-principles study of structural, elastic, and electronic properties of triclinic TATB under different pressures
Bin Tang c, Qi-Jun Liu* a,b a
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Han Qin a,b, ∗∗, Bao-Luo Yan a,b, Mi Zhong a,b, Cheng-Lu Jiang a,b, Fu-Sheng Liu a,b,
School of Physical Science and Technology, Southwest Jiaotong University, Key
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Laboratory of Advanced Technologies of Materials, Ministry of Education of China, Chengdu 610031, People’s Republic of China
Bond and Band Engineering Group, Sichuan Provincial Key Laboratory (for
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b
Universities) of High Pressure Science and Technology, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China c
State Key Laboratory of Solidification Processing, Northwestern Polytechnical
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University, Xi’an 710072, People’s Republic of China
Han Qin
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Correspondence about the paper at the following address and e-mail address:
School of Physical Science and Technology, Southwest Jiaotong University, Chengdu,
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Sichuan 610031, People’s Republic of China E-mail: [email protected] Qi-Jun Liu
School of Physical Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan 610031, People’s Republic of China E-mail: [email protected]
∗∗ *
Corresponding author. E-mail: [email protected] Corresponding author. E-mail: [email protected] 1
ACCEPTED MANUSCRIPT Abstract: First-principles calculations were performed to investigate the structural, elastic, electronic and sensitive properties of triclinic TATB crystal. The obtained ground state properties using GGA-PBE method were in agreement with the previous
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theoretical and experimental data. The elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, anisotropy under the hydrostatic pressure from 0 GPa to 30 GPa were calculated and analyzed. Moreover, we found that TATB became
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more and more hardness with the increasing pressure. Furthermore, comparing the
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density of states in different pressures, we can find that the electrons of TATB become more active under ambient pressure.
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Keywords: TATB; Elastic properties; Sensitivity; First-principles calculations
2
ACCEPTED MANUSCRIPT 1. Introduction The compound 1,3,5-triamino-2,4,6-trinitrobenzene (TATB, C6H6N6O6) is one of the most outstanding representative of high explosives, whose triclinic crystal
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structure was characterized by Cady and Larson [1]. It is known that this compound exhibits considerably low sensitivity [2,3,4,5] to high temperature, shock as well as impact [6], and is hardly detonated by accidental initiation [7,8]. Because of the
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excellent safety performance and comprehensive performance, TATB is widely
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applied on the field of modern nuclear warheads, reagents in manufacture of liquid crystal displays and deep oil well explorations [8]. As we know, the energetic materials explode at high temperature and high pressure conditions, so it is necessary to investigate the physical and chemical properties of TATB under extreme conditions
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to understand its sensitive characteristics.
Since its first synthesis in 1887 [9], researchers have extensively studied TATB in both experimental and theoretical aspects. At ambient conditions, TATB crystallizes in —
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a triclinic crystal with space group P1. In 1976, Olinger and Cady [10] compressed
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TATB up to 7.02 GPa. They observed ten diffraction peaks at low pressure (P<3.0 GPa), while there are four peaks at higher pressure. At ambient pressure, TATB is decidedly photosensitive [11], and Satijia et al. [12] found that the photosensitive property decreased clearly at pressures exceeding 1.5 GPa. With the increase of pressure, Giefers et al. [13] found that the reaction/decomposition rate decreased significantly because of a positive volume of activation. Pravica et al. [5Error! Bookmark not defined.] performed infrared spectroscopic measurements to 3
ACCEPTED MANUSCRIPT investigate TATB at high pressures up to 10 GPa, and they found that there was no phase transition. Stevens et al. [14] recorded the P-V relationship and static compression of TATB via X-ray diffraction measurements from 0 to 13 GPa.
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Davidson et al. [15] found that there were two subtle structural phase transitions at about 28 and 56 GPa by Raman spectra measurements. Depending on Raman spectra of TATB, Landerville et al. [16] evidenced that no first-order polymorphic phase
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transition appeared up to 27 GPa.
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Due to the fact that some important properties cannot be studied experimentally, the computational modeling and simulations have been used widely in order to better understand the effects of pressure on TATB. Byrd et al. [17] employed several functionals to investigate the TATB crystal and energetic molecular crystals (HMX,
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RDX, CL-20 and PETN) up to 7 GPa. They found that the predicted lattice parameters were lack of agreement with experiments due to the inadequate treatment of vdW interactions within DFT. Using the molecular simulation package
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LUCRETIUS, with the increase of temperature and pressure, Bedrov et al. [18]
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indicated that the considerable anisotropy of TATB with modest softening and significant stiffening appeared, respectively. Budzevich et al. [19] studied TATB under hydrostatic and uniaxial compressions, showing that highly anisotropic behavior occurred under uniaxial compression. Kohno et al. [20] used the molecular dynamics calculations to evaluate the effect of high pressure on TATB. In the pressure range of 1.0 atm to 20.0 GPa, the intermolecular and intramolecular hydrogen bonds were maintained. The interlayer distances decreased from 3.50 to 2.90 Å with the 4
ACCEPTED MANUSCRIPT increasing pressure up to 20 GPa. Fan et al. [21] analyzed the elastic anisotropy of TATB using molecular dynamics simulation. They found that the anisotropy of Young’s modulus exhibited a decreasing trend, but that of shear modulus showed an
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opposite trend, with the increasing pressure from 0 to 50 GPa. In our present study, the effect of pressure on TATB in the crystalline state is evaluated using the density functional theory with generalized gradient approximation
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plus dispersion correction (DFT-D). In our calculation, we focus on the crystal
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structure, elasticity, and electronic structure of TATB in the pressure range of 0 to 30 GPa. The remainder of this paper is organized as follows: in section 2, we describe the general details for calculations using the generalized gradient approximation with Perdew-Burke-Ernzerhof functional (GGA-PBE), the results and discussion are
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presented in section 3, and the conclusion is given in section 4.
2. Computational methods
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First-principles calculations were carried out within the density functional theory
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with the norm-conserving pseudopotential method. In this paper, we have employed the Cambridge Sequential Total Energy Package (CASTEP) code [22]. For the exchange-correlation interaction, the generalized gradient approximation with the Perdew-Burke-Ernzerhof
functional
[23]
was
adopted.
The
pseudo-atomic
calculations [24] were performed and the H 1s1, C 2s22p2, N 2s22p3 and O 2s22p4 were treated as the valence shells. We used a k-point grid of 2×2×2 for the Brillouin zone sampling, which was based on the Monkhorst-Pack scheme [25]. The convergence 5
ACCEPTED MANUSCRIPT test calculations energy and the final energy in different kinds of k-points have been considered shown in Fig. S1, indicating that the k-point of 2×2×2 used of TATB crystal is adoptable. The cut-off energy of 830 eV was adopted. We used the DFT-D
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method to solve the van der Waals interactions [26], where the TS (Tkatchenko and Scheffler) [27] and the G (Grimme) [28] corrections to GGA-PBE have been adopted. As the convergence criterion, the total energy of the system converged to less than
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5.0×10-6 eV/atom, the maximum force was lower than 0.01 eV/Å, the maximum stress
3. Results and discussion 3.1. Structural parameters
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was less than 0.02 GPa, and the maximum displacement was less than 5×10-4 Å.
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The molecular structure and crystal structure including 48 atoms of TATB are shown in Fig. 1. Our calculated lattice parameters for TATB (a=9.12 Å, b=9.13 Å, c=6.63 Å, α=109.51°, β=91.40°, γ=119.97° and V=438.36 Å3 [29] and a=9.13 Å,
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b=9.15 Å, c=6.77 Å, α=109.15°, β=91.66°, γ=119.98° and V=449.86 Å3 with the G
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and TS corrections, respectively) are in good agreement with the previous theoretical [18,21,30] and experimental values [1,14]. The corresponding bond lengths and bond angles are consistent with the theoretical [31] and experimental results [1]. Comparing with the experimental volume [Error! Bookmark not defined.], the overestimation with the GGA-PBE+TS calculations is about 1.67%, while the underestimation with the GGA-PBE+G calculations is about 0.93%. As we can see, the calculated results with the GGA-PBE+G method are closer to the experimental results. Therefore, the 6
ACCEPTED MANUSCRIPT calculations under different pressures at this work are based on the GGA-PBE+G method. The first-principles calculations of the TATB crystal are conducted using the
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GGA-PBE+G for pressure up to 30 GPa. In Fig. 2, we show the lattice parameters of TATB as the functions of pressure. Results obtained from the simulations using GGA-PBE+G method are compared to the calculated data and the experimental data.
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Our calculated results show that the lattice constants a, b, and c decrease
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monotonically with increasing pressure and perfectly reproduce the calculational data of Rykounov [30] and basically in agreement with the tendency of the experimental data of Stevens [14]. In Fig. 3, the normalized volume is shown as a function of pressure along with previous theoretical [18,21,30,32] and experimental [10,14]
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results. Comparing with the theoretical and experimental results, our results are in agreement with the experimental results, especially satisfying the recent results by Stevens [14] in the range of 0-13 GPa. In addition, our results are basically consistent
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with the theoretical results of Bedrov [18] and Rykounov [30].
3.2. Elastic and mechanical properties The elastic and mechanical properties are important to know the effects of
external conditions on TATB. Hence, we investigate the corresponding properties. As we know, the elastic constants are associated with the mechanical properties which can be used to judge the mechanical stability of materials. So far, the experimental works of elastic constants of TATB have not been reported because of the difficult 7
ACCEPTED MANUSCRIPT tests for the molecular crystal. However, there are a few theoretical investigations [18,21,30,33]. The TATB as a triclinic crystal has 21 independent elastic constants. The elastic constants of TATB are determined by the generalized Hooke’s law [34],
= [ ]
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where the resultant proportional elastic stiffness matrix [Cij] is shown: (1)
where is the stress vector and is the strain vector. With the triclinic C
C C
C C C
C C C C
C C C C C
C C C C C C
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C =
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structure, the [ ] of TATB is obtained as follows [35]:
(2)
The calculated independent elastic constants of TATB crystal using the GGA-PBE
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method at 0 GPa are shown in Table 1. Comparing with the theoretical values, the calculated results with the GGA-PBE show the same anisotropy in the elastic response of TATB. According to the Hooke’s law, when the force is the same, the
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larger value of elastic constant is, the smaller the strain is. Moreover, the C44, C55 and
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C66 roughly correspond to the deformations of the lattice angles α, β and γ. We conclude that the γ is the most stable angle due to that the elastic constant C66 is clearly larger than C44/C55, which is consistent with the changed trends of lattice angles in Fig. 2.
Using the elastic constants, the anisotropy characteristic of TATB is obtained. It can be given by the equivalent Zener anisotropy measure Aeq [36]:
A = 1 + A" # + $ 1 + A" # − 1
(3) 8
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'(
)'(
A* = A=
#
(4)
+'),-
(5)
+'),- .' *//
(6)
*00 )*0-
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If A = 1, the material is fully isotropic. Otherwise, it is anisotropic. The value of the equivalent Zener anisotropy factor of TATB at 0 GPa is 1.78, indicating that TATB crystal is an anisotropic material. Using the above formulas, we obtain the
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relationship between the anisotropy factor and the pressure, which is shown in Fig. 4.
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As we can see, with the pressure increasing, the anisotropy of TATB roughly tends to decrease, showing that the high pressure can reduce the anisotropy of TATB. To further describe the anisotropy, the universal anisotropy index Au [36] is used as follows: 53
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A" = 5 24 + 54 − 6
(7)
B8 = 9 [+C + C + C , + 2+C + C + C ,]
(8)
1⁄B; = +S + S + S , + 2+S + S + S ,
(9)
[+C + C + C , − +C + C + C , + 3+C + C + C ,]
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G8 =
(11)
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15⁄G; = 4+S + S + S , − 4+S + S + S , + 3+S + S + S ,
(10)
where BV (GV) and BR (GR) are the upper and lower bounds of the bulk (shear) modulus [37]. Fig. 5 shows the universal anisotropy index of TATB in the pressure range of 0 to 30 GPa. At the early stage (0～4 GPa), the universal anisotropy index decreases rapidly, while it tends to slow down at the stage of 5～30 GPa. It indicates that the elastic anisotropy of TATB becomes weaker and weaker with the increasing pressure, which is a similar changing pattern in the previous calculated result [21]. To 9
ACCEPTED MANUSCRIPT directly see the change, we draw the three-dimensional (3D) diagrams [38] of the Young’s modulus at 0 GPa, 10 GPa, 20 GPa and 30 GPa in Fig. 6. Our results agree with the recent anisotropy study of Fan et al. [21].
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The bulk modulus (B), shear modulus (G), Young’s modulus (E) and Poisson’s ratio (ν) under pressure are analyzed using the Voigt-Reuss-Hill approximation [39,40], which can be obtained as follows:
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B =(B; + B8 )/2 G =(G8 + G; )/2 952
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E = 5.2
5)2
ν = 5.2
(12)
(13) (14) (15)
Fig. 7 illustrates the effects of pressure on these mechanical properties. These
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values of mechanical properties increase with the increasing pressure. From 0 GPa to 30 GPa, the increases of the B, G, E and ν of TATB are about 883.64%, 751.12%, 750.88% and 8.22%, respectively. From the range of 0 to 10 GPa, the bulk modulus
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and the shear modulus agree well with the Rykounov’s data [30]. The Pugh theorem
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[41] can evaluate the ductile/brittle property of TATB using the ratio of the bulk modulus and the shear modulus (B/G). If the B/G ratio is larger than 1.75, the crystal is ductile; otherwise, it is brittle. The value of 1.470 for B/G indicates the brittleness of the TATB crystal. In addition, the hardness of TATB is explored through calculation of the Vickers hardness (HV), which is a measure of the resistance of the solid matter against ambient pressure, CD = 2+E F,G.I − 3, where k=G/B. Fig. 8 shows the pressure dependent of B/G ratio and hardness for TATB. Although there are slight 10
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we can see, starting from 2 GPa, TATB has changed from brittleness to ductility.
3.3. Electronic properties
The electronic band structure of TATB under 0 GPa based on the GGA-PBE+G is
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calculated and presented in Fig. 9. As we know, the band structure greatly depends on
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the interactions between electronic orbits. Moreover, at zero pressure, the valence-band maximum is 0 eV appearing on the direction of F → Q and the conduction-band minimum is 2.366 eV appearing on the Q point, which is similar with the calculated results 2.37 eV [42]. However, these calculated values are smaller
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than the experimental data 6.6 eV [43]. The PBE functionals will underestimate the band gap by 30 to 100% [44,45]. In our previous work [29], we also calculated the band gap is 3.484 and 3.250 eV using the B3LYP and HSE06 functional. However,
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they are also smaller than the experimental data. Fig. 10 presents the band structures
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under hydrostatic pressure of 0 GPa, 15 GPa and 30 GPa. It’s clear to see that the band dispersion increases while the band gap decreases with the increasing pressure. The calculated band gaps at 15GPa and 30GPa equal 1.859eV and 1.613eV, respectively. Meanwhile, the pressure of TATB as a function of band gap is shown in Fig. 11. It is also clear to see that the pressure decreases the band gap of TATB crystal. The calculated total density of states (TDOS) of TATB is plotted in Fig. 12 and the partial density of states (PDOS) of TATB is presented in Fig. 13, respectively. 11
ACCEPTED MANUSCRIPT Comparing the TDOS of TATB at 0GPa, 10GPa, 20GPa and 30GPa, we can see that the peaks of TDOS of TATB decrease with hydrostatic pressure while the TDOS dispersion increases. In other words, the electrons of TATB become more active under
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ambient pressure. From the calculations of the PDOS of TATB, the peak in the valence band near Feimi level is mainly contributed by the p orbital of C, O and N atoms in NO2. The peak in conduction band near Feimi level is mainly offered by the
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p orbital of C, O and N atoms. It can be inferred that the C-N-O2 acts an active center.
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It is also expected that the increasing pressure from 0 GPa to 30 GPa gives wider but smaller peaks.
4. Conclusion
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The structural, elastic, electronic and sensitive properties of TATB crystal under different pressures are systematically analyzed by using the first-principles method based on the density functional theory. The structural parameters are calculated with
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the increasing pressure. We find that the obtained parameters at 0 GPa using
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GGA-PBE+G method are more consistent with the former theoretical and experimental data. With the increasing pressure, the volume of TATB decreases. The elastic anisotropy and the elastic modulus, including bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio are calculated. Moreover, using the Vickers hardness equation, we find that TATB becomes more and more hardness with the pressure increasing. Finally, comparing the density of states in different pressures, the electrons of TATB become more active under ambient pressure. 12
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Acknowledgments This work was supported by the National Natural Science Foundation of China
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(Grant No. 11574254), the Fundamental Research Funds for the Central Universities (Grant No. 2018GF08), the fund of the State Key Laboratory of Solidification Processing in NWPU (Grant No. SKLSP201843), the Doctoral Innovation Fund
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Program of Southwest Jiaotong University (Grant No. D-CX201735) and the Doctoral
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Students Top-notch Innovative Talent Cultivation of Southwest Jiaotong University.
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ACCEPTED MANUSCRIPT [29] B.L. Yan, H. Qin, Z.K. He, Y. Wei, K. Chang, B.L. Guo, B. Tang, D.H. Fan, Q.J. Liu, Physica B 546 (2018) 1. [30] A.A. Rykounov, J. Appl. Phys. 117 (2015) 215901. [31] A.D. Stephen, P. Srinivasan, P. Kumaradhas, Computational and Theoretical
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Chemistry 967 (2011) 250.
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[38] J. Feng, B. Xiao, R. Zhou, W. Pan, Acta Mater. 61 (2013) 7364. [39] R. Hill, Proc. Phys. Soc. A 65 (1952) 349. [40] G.N. Greaves, A.L. Greer, R.S. Lakes, T. Rouxel, Nature Mater. 10 (2011) 823.
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[41] S.F. Pugh, The London, Edinburgh, and Dublin Philosophical Magazine and
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Journal of Science 45 (1954) 823. [42] C. J. Wu, L. H. Yang, L. E. Fried, J, Quenneville, T. J. Martinez, Physical Review B, 67 (2003) 235101.
[43] S. Kakar, A.J. Nelson, R. Treusch, C. Heske, T. van Buuren, I. Jiménez, P. Pagoria, L.J. Terminello, Phys. Rev. B 62 (2000) 15666. [44] R. V. Tsyshevsky, O. Sharia, M.M. Kuklja, The Journal of Physical Chemistry C, 118 (2014) 9324.
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118 (2014), 26530.
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ACCEPTED MANUSCRIPT Fig. 1. (a) Molecular structure of TATB, (b) Crystal structure of TATB (hydrogen: white; carbon: gray; oxygen: red; nitrogen: blue). Fig. 2. The lattice parameters of TATB as the functions of increasing pressure. Fig. 3. The effect of pressure on normalized volume.
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Fig. 4. The equivalent Zener anisotropy factor as a function of pressure. Fig. 5. The universal anisotropy index as a function of pressure.
Fig. 6. The three-dimensional (3D) diagrams of the Young’s modulus at (a) 0 GPa, (b)
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10 GPa, (c) 20 GPa and (d) 30 GPa.
Fig. 7. The pressure dependence of bulk modulus (B), shear modulus (G), Young’s
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modulus (E) and Poisson’s ratio (ν) for TATB.
Fig. 8. Pressure dependent of B/G ratio and Hardness for TATB. Fig. 9. The band structure of TATB at 0GPa.
Fig. 10. Band structures of TATB at the hydrostatic pressure of (a) 0GPa, (b) 15GPa
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and (c) 30GPa.
Fig. 11. Band gap of TATB as a function of pressure.
zero).
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Fig. 12. Total density of states of TATB at different pressures (The Feimi level is set to
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Fig. 13. Partial density of states of TATB at (a) 0GPa and (b) 30GPa (The Feimi level is set to zero).
Table 1. Elastic constants (GPa) of TATB crystal at 0 GPa.
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Table 1. Elastic constants (GPa) of TATB crystal at 0 GPa.
32.02 20.13 7.53 0.48 0.89 12.43 8.23 5.8 5.18 0.04 0.49 -0.03 1.78 -0.27 1.67 -0.6 -0.44 -1.03 0.03 0.44 0.04
83.2 78.3 18.9 1.7 1.5 30.0 21.9 -2.4 -0.3 -0.8 -0.6 2.9 0.1 -0.4 2.5 -0.6 -0.5 0.1 0.0 -0.3 0.6
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82.04 79.75 19.43 19.91 14.64 34.18 11.05 5.17 11.87 1.27 -21.02 -4.90 -30.86 1.42 -5.58 -3.44 -1.97 9.42 4.18 -9.13 -12.87
Polarizable FF
Nonpolarizable FF
65.7±0.5 62.0±1.0 18.3±0.5 1.4±0.3 0.68±0.06 21.6±0.7 18.5±0.5 4.0±2.0 5.0±1.0 -0.2±0.3 -1.0±0.1 1.0±1.0 0.6±0.2 -0.5±0.2 1.0±1.0 0.2±0.3 -0.4±0.1 -0.4±0.7 0.1±0.2 0.3±0.2 0.4±0.1
57.7±0.5 58.0±1.0 17.0±0.5 1.0±0.3 0.6±0.2 20.3±0.8 16.2±0.7 3.2±0.5 5.7±0.6 0.1±0.1 -0.9±0.2 0.0±1.0 0.6±0.2 -0.5±0.3 2.0±0.8 -1.0±0.4 -0.3±0.2 -1.0±0.5 0.01±0.04 -0.5±0.1 0.1±0.1
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66.96 61.26 30.77 14.30 12.32 26.49 5.25 10.84 18.05 0.51 -16.05 -3.55 -19.78 1.30 -4.49 -2.92 -2.02 11.80 4.19 -5.68 -8.97
Classical MD[18]
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GGA-PBE+G
DFT-D2[30]
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GGA-PBE+TS
Lammps/MD[21]
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C11 C22 C33 C44 C55 C66 C12 C13 C23 C14 C15 C16 C24 C25 C26 C34 C35 C36 C45 C46 C56
This work
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Ab initio values [33] 78.4 — 19.7 0.9 — 29.7 16.8 0.8 — — — — — — — — — — — — —
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Fig. 1. (a) Molecular structure of TATB, (b) Crystal structure of TATB (hydrogen:
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white; carbon: gray; oxygen: red; nitrogen: blue).
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Fig. 10. Band structures of TATB at the hydrostatic pressure of (a) 0GPa, (b) 15GPa and (c) 30GPa.
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Fig. 11. Band gap of TATB as a function of pressure.
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Fig. 12. Total density of states of TATB at different pressures (The Feimi level is set to zero).
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(b) Fig. 13. Partial density of states of TATB at (a) 0 GPa and (b) 30 GPa (The Feimi level is set to zero).
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Fig. 2. The lattice parameters of TATB as the functions of increasing pressure.
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Fig. 3. The effect of pressure on normalized volume.
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Fig. 4. The equivalent Zener anisotropy factor as a function of pressure.
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Fig. 5. The universal anisotropy index as a function of pressure
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Fig. 6. The three-dimensional (3D) diagrams of the Young’s modulus at (a) 0 GPa, (b) 10 GPa, (c) 20 GPa and (d) 30 GPa.
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Fig. 7. The pressure dependence of bulk modulus (B), shear modulus (G), Young’s modulus (E) and Poisson’s ratio (ν) for TATB.
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Fig. 8. Pressure dependent of B/G ratio and Hardness for TATB.
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Fig. 9. The band structure of TATB at 0 GPa.