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Phase Transition in Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) under Static Compression: An Application of the FirstPrinciples Method Specialized for CHNO Solid Explosives Lei Zhang,†,‡ Sheng-Li Jiang,† Yi Yu,† Yao Long,‡ Han-Yue Zhao,† Li-Juan Peng,§ and Jun Chen*,†,‡,∥ †

Software Center for High Performance Numerical Simulation and ‡Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China § Department of Computer Science and Technology, Southwest University of Science and Technology, Mianyang 621010, China ∥ Center for Applied Physics and Technology, Peking University, Beijing 100871, China S Supporting Information *

ABSTRACT: The first-principles method is challenged by accurate prediction of van der Waals interactions, which are ubiquitous in nature and crucial for determining the structure of molecules and condensed matter. We have contributed to this by constructing a set of pseudopotentials and pseudoatomic orbital basis specialized for molecular systems consisting of C/H/N/O elements. The reliability of the present method is verified from the interaction energies of 45 kinds of complexes (comparing with CCSD(T)) and the crystalline structures of 23 kinds of typical explosive solids (comparing with experiments). Using this method, we have studied the phase transition of octahydro1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) under static compression up to 50 GPa. Kinetically, intramolecular deformation has priority in the competition with intermolecular packing deformation by ∼87%. A possible γ → β phase transition is found at around 2.10 GPa, and the migration of H2O has an effect of kinetically pushing this process. We make it clear that no β → δ/ε → δ phase transition occurs at 27 GPa, which has long been a hot debate in experiments. In addition, the P−V relation, bulk modulus, and acoustic velocity are also predicted for α-, δ-, and γ-HMX, which are experimentally unavailable. induced by changing temperature include β → α and α → δ at 102−104 and 160−164 °C, respectively.7 Conversion between the β and δ phases can be triggered by various thermal or mechanical treatments.8−12 β-HMX is the most stable phase and has the highest density under ambient conditions.5 It may undergo a conformational transition and convert to the ε phase under hydrostatic compression at 12 GPa.13,14 At a mechanical compression below 0.05 GPa, δ-HMX may convert to a mixture of α- and β-HMX at room temperature.15 γ-HMX may rapidly transform into its β form when left in contact with dry pyridine16 or under compression of 0.55 GPa15 at room temperature. However, the stability of HMX at ∼27 GPa has been known to be a very challenging issue, and it has been explored by experiments for many years. From 1999 to 2014, various techniques were used to explore the existence of HMX phase transition at ∼27 GPa; however, these results are techniquedependent.11,13,14,17−19 In 1999, Yoo et al. found that HMX converts to the φ phase at 27 GPa from a change in the Raman

1. INTRODUCTION Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) is a widely used explosive in the military, in aerospace, and in modern industry. Research concerning this material is quite popular.1−4 By controlling the rate of crystallization in solution, four different kinds of crystal structures can be obtained, which are known as α, β, γ, and δ phases.5 Understanding the properties of HMX in different phases and its transitions under pressure are useful from the viewpoint of the safety and performance of HMX and its formulations. For example, βHMX has a greater stability against shock or impact and a higher rate of detonation. During its transition to another phase, volume expansion produces large perturbations in the mechanical and combustion characteristics of HMX.6 According to Zelovich−von Neumann−Doering theory, HMX would undergo chemical alteration and consumption during the propagation of the detonation wave. When the shock loading condition offers sufficient time for the formation of a new phase before the chemical reaction starts, the peak pressure of the detonation wave will change. Having been extensively studied by scientists, most of the transitions induced by changing temperatures or loading small compressions are clear. For example, the main phase transitions © XXXX American Chemical Society

Received: August 10, 2016 Revised: October 11, 2016 Published: October 13, 2016 A

DOI: 10.1021/acs.jpcb.6b08092 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

Figure 1. (a) Atomic configurations and (b) interaction energies of the 45 kinds of complexes, and (c) calculated volumes and lattice constants of 23 kinds of explosive solids.

spectra.13 In 2010, Pravica et al. reported a transition to the δ phase near 25 GPa on the basis of alteration of the IR spectra.14 However, in 2004, Hare et al. pointed out that using a NaCl

window could obscure the accuracy of the observation on phase transition at ∼27 GPa because NaCl is known to have a phase transition at 26 GPa.17 In their following experiment, B


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correlation functional in the Perdew−Burke−Ernzerhof (PBE) form. 2.1. Construction of the Pseudopotential and Basis Set. We have constructed the norm-conserving pseudopotential specialized for molecular crystals with C/H/N/O elements by considering the balance between transferability and softness. For each element, first, various electronic configurations of excited states are constructed; second, we adjust the cutoff radii of each channel until the total energies and eigenvalues of all excited states are the same as those from the all-electron calculations ( γ > β > δ, and the values of bulk modulus are ranked as α > β > γ > δ, as shown in Table 2. 3.2. Structure Evolution and Kinetics Process. 3.2.1. Structure Evolutions under Compression: Inter- and Intramolecular. The structure of the material endures squeezing and deformation under compression. Structural deformation of the molecular crystals is contributed by interand intramolecular deformations. The former involves deformation of the intermolecular spatial packing structure and leads to a change in the crystalline symmetry, whereas the latter involves alteration of the covalent bonds of the molecules and a changes in the structures of the constituent units. From Table 3, β-, δ-, and γ-HMX all hold the initial crystalline symmetry under static compression up to ∼50 GPa.

decrease with increasing compression, except for the length of the N−O bond in γ-HMX (Figure 6c). Observing its structural evolution in Figure 5b, it is clear that the H2O molecules gradually approach the adjacent HMX molecules with increasing pressure. The intermolecular contact distance between the H atom (in the H2O molecule) and O atom (in the HMX molecule) decreases from 2.78 Å at 0 GPa to 1.39 Å at 53 GPa. The Mulliken bond order increases from 0.00 to 0.16 e, indicating the interaction between H2O and the −NO2 group. Simultaneously, the N−NO2 groups on the heterocyclic ring alter their positions by bending or twisting, as shown in Figure 5b. Phonons are pivotal to the understanding of shock-induced detonation at the molecular level. According to the multiphonon up-pumping theory advanced by Dlott,46,47 the intramolecular vibrational energy redistribution acts as an intermediate between the shock energy abortion and the bond breaking prior to ignition of the explosive. The unit cell of γHMX is repeated twice along the y direction when calculating the phonon free energies. In Figure 7, we compare the phonon dispersion spectra of γ-HMX at 0 and 53 GPa. Compared to the spectrum at 0 GPa, the spectrum at 53 GPa shows a collective shift toward a higher frequency. Besides, we see a significant change in pattern near 1600 cm−1. At 0 GPa, the vibrational modes at 1609−1626 cm−1 are assigned to the bend of the H−O−H angle (bHOH) in the H2O molecule. Whereas at 53 GPa, due to the close interaction between the H2O molecule and the neighboring HMX molecule, the bHOH mode couples with −NO2 nonsymmetric stretching and the H−C−H angle bending. The corresponding band is also expanded to range from 1645 to 1673 cm−1. Such a reassignment of vibrational modes would probably increase the impact sensitivity of γHMX at high pressure. 3.2.2. Kinetics of Structure Deformation. The response of the crystalline structure at external loading depends on the power that the stimulation offers and the barrier that the deformation has to overcome. As we have mentioned in the previous section, the structure deformation of an explosive is contributed by inter- and intramolecular deformations. Once the external stimulation is able to launch the deformation, the structure evolution is determined by the competition between the two modes. Suppose the possibility to adopt an intermolecular deformation is ϕ and the possibility of an intramolecular deformation is φ, then ϕ + φ = 1. According to the Arrhenius law ⎛ ΔEϕ − ΔEφ ⎞ ϕ = exp⎜ − ⎟ φ k bT ⎝ ⎠

Table 3. Variation of the Crystalline Symmetries of α-, β-, δ-, and γ-HMX ambient pressure high pressure

α-HMX

β-HMX

δ-HMX

γ-HMX

(43) Fdd2 (1) P1

(14) P21/c (14) P21/c

(169) P61 (169) P61

(7) Pc (7) Pc

(12)

the mode with a lower energy barrier has a higher possibility of occurrence. Here ΔEϕ and ΔEφ are the energy barriers of interand intramolecular deformations, respectively. We first study the kinetics of intermolecular structure deformation, characterized mainly by a change in the molecular spatial packing. Here, we establish a simplified model with two boat-HMX molecules. One of the molecules is placed at the center of an ellipsoid, and the other molecule migrates along the high-symmetry path of the ellipsoid from the top of the y axis (denoted by 0), to the top of the x axis (denoted by 1), to the top of the z axis (denoted by 2), and finally back to 0. The NEB method40,41 is used to calculate the energy barriers along the 0 → 1 → 2 → 0 path, as shown in Figure 8a and Table 4. To accomplish the molecular packing transition, the lowest

Only α-HMX shows an alteration in the molecular packing structure, with the symmetry degenerating from space group Fdd2 to P1. In Figure 5a, we represent the boat-HMX molecule by its centroid, and variation of the molecular packing structure is clearly seen. Next, we explore the intramolecular deformation by monitoring the covalent bond lengths of HMX molecules. In both boat- and chair-HMX molecules, there are four types of bonds, that is, N−N, N−C, N−O, and C−H. From Figure 6, the lengths of all these bonds were found to monotonously G


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Figure 5. Structure evolution of (a) α- and (b) γ-HMX under static compression. The black spheres in (a) represent the centroid of the boat-HMX molecule.

Figure 6. Covalent bond lengths of N−N, N−C, N−O, and C−H (Å) as a function of pressure.

According to eq 12, the possibility of intramolecular structure deformation is generally higher than the possibility of intermolecular packing variation by ∼87%. 3.2.3. Decisive Factor of the Stable State: Molecular Configuration. When the system reaches thermodynamic equilibrium, the most stable state is the one with the lowest total energy. In this section, we estimate the contributions of the molecular configurations and crystalline symmetries to the total energy. To estimate the contributions of various molecular packing structures to the total energy, we use boat-HMX molecules to build crystals with four kinds of space groups, that is, (7) Pc, (14) P21/c, (43) Fdd2, and (169) P61, as shown in Table 4. The crystals with No. 43 and No. 169 space groups are α-HMX and δ-HMX, respectively, whereas those with No. 7 and No. 14 space groups are newly built crystals, as shown in Figure 9a,b.

barrier to overcome is 0.52 eV and the highest barrier is 0.92 eV. For the intramolecular configuration evolution, that is, the boat ↔ chair transition, the most possible deformation path is rotating the −NO2 group by ∼180°. For the other atoms, the supposed images are simply linear interpolations between the boat- and chair-form configurations. As shown in Figure 8b and Table 4, the boat → chair transition barrier is 0.45 eV and the chair → boat barrier is 0.64 eV. As summarized in Table 4, intermolecular deformation has a higher energy barrier than intramolecular deformation. If the external stimulation yields a power between 0.45 and 0.52 eV, only the boat → chair intramolecular deformation is launched; if the external power is higher than 0.92 eV, then all of these mentioned deformations are possible, whereas the deformation with a lower barrier has a higher probability of occurrence. H


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Table 4. Energy Barriers during Structure Deformation and Energy Difference with Different Molecular Configurations and Crystalline Symmetries Energy Barrier (eV) intermolecular intramolecular intramolecular (H2O migration) intramolecular (H2O around) Energy Difference

Figure 7. Calculated phonon spectra of γ-HMX at 0 and 53 GPa. Experimental Raman48 and IR15 spectra are also shown for comparison.

0.92, 0.64, 1.36, 2.12,

0.62, 0.52 0.45 1.19 1.97

configuration

energy (eV)

crystalline symmetry

energy (eV)

boat chair

0.19 0.00

(7) Pc, newly built (14) P21/c, newly built (43) Fdd2, α-HMX (169) P61, δ-HMX

0.00 0.23 0.20 0.14

eV, implying that most crystalline symmetry variations alter the total energy only slightly, whereas the molecular structure transition leads to a significant change in the total energy. For example, both β-HMX and the newly built crystal have the same symmetry [with (14) P21/c space group], whereas they are packed with different kinds of molecules (former with chair and latter with boat). The energy difference between the two crystals is up to 0.33 eV. Thus, the type of constituent unit, that

From Table 4, the energy difference between the boat- and chair-HMX molecules is 0.19 eV. Of the four kinds of crystals packed with boat-HMX molecules, the energy difference between any two of them is 0.03, 0.06, 0.09, 0.14, 0.20, and 0.23 eV, respectively. Most of these values are lower than 0.19

Figure 8. Energy barriers along the paths of (a) intermolecular packing evolution and (b) intramolecular configuration deformation. I


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Figure 9. New crystals built using boat-HMX molecules with (a) Pc and (b) P21/c space groups.

tions are different from those of the other three polymorphs. In the present work, we have considered the chemical potential of H2O. From Figure 10, γ-HMX is more stable than a system with separated β-HMX and H2O. This is consistent with the experiment, in which γ-HMX can be formed by mixing an acetone solution of HMX with a large amount of water.15,16 With an increase in pressure, the Gibbs free energy difference between the two polymorphs becomes smaller. When the pressure increases to 2.10 GPa, both the β and γ phases of HMX coexist. On further increasing the pressure, γ-HMX loses its H2O molecule and changes its crystalline structure to that of β-HMX. According to Rao et al., the application of a few kbar of pressure at 300 K has roughly the same effect on a crystal lattice as cooling it to 77 K.15,49 Thus, the pressure at which the phase transition occurs at room temperature should be ∼1 GPa lower than 2.1 GPa. This satisfactorily agrees with the experimental observation of the γ-HMX → β-HMX transition under compression at 0.55 GPa at room temperature.15 Taking into consideration the experimental observation that β-HMX converts to a new ε phase at 12 GPa13,14 and that there is no volume phase transition under 50 GPa,18 we have plotted the phase diagram of HMX at 0 K, as shown in Figure 10. Note that we have also performed vibrational free energy calculations for the β and α polymorphs to estimate the contribution of this term to the Gibbs free energy change. At 300 K, the vibrational free energy difference between the α and K ) is slightly lower than that at 0 K β polymorphs (ΔFvib,300 β→α vib,0 K K vib,300 K (ΔFβ→α ). The value of ΔFvib,0 is roughly one β→α − ΔFβ→α 0K order of magnitude smaller than ΔGβ→α. Therefore, vibration free energy will slightly shift the positions of the curves in Figure 10, but it does not significantly change the phase transition pathways. However, we declare that neglecting the effect of temperature will probably lead to the omission of some details of the phase conversion process. For example, from Figure 10, we cannot predict that δ-HMX may convert to a mixture of α- and β-HMX at 0.05 GPa at room temperature.15 3.3.2. Effect of H2O during Phase Transition. Besides mechanical compression, solvents also have the function of accelerating the γ → β transition.16 The γ-HMX crystal may be kept for long periods without solvent, whereas it transforms into the β-form rapidly when left in contact with dry pyridine at room temperature. H2O in γ-HMX migrates to and is absorbed by pyridine on coming in contact with it. In this section, we study the effect of H2O migration during the γ → β phase transition.

is, the molecular configuration, plays a decisive role in the total energy. Of the three known phases of HMX crystals, only β-HMX is constituted of chair-form molecules, whereas α-HMX and δHMX are composed of boat-form molecules. Therefore, βHMX has the lowest total energy and is the most stable phase. Note that γ-HMX has not been discussed because it contains not only HMX molecules but also H2O molecules. 3.3. Phase Transition. 3.3.1. Phase Transition among α-, β-, δ-, and γ-HMX. We take the Gibbs free energy of β-HMX along the pressure axis as a standard and set the value to zero. The curves of Gibbs free energy changes during the β → α and β → δ transitions are shown in Figure 10. At 0 GPa, β-HMX is

Figure 10. Change of Gibbs free energy (kJ/mol) along the pressure (GPa) axis during the β → α, β → δ, and β → γ transitions.

evidently the most stable phase, followed by α-HMX, and then δ-HMX. The order of stability is perfectly consistent with the experimental observations.5 Here, we clearly see that no β → δ phase transition occurs from 0 to 50 GPa. In the entire pressure region, the stability order is maintained; thus, no phase transitions among the three polymorphs are observed. Our conclusion is supported by the experimental observations: βand α-HMX are proven to be stable up to ∼50 GPa at room temperature,15 and β → α, β → δ, and α → δ transitions occur at a higher temperature7 or at room temperature with applied compression.15 γ-HMX related phase transition is also seldom related by computational simulations, partially because its specie proporJ


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Figure 11. Energy barriers during the boat → chair transition, with (a) H2O staying around the HMX molecule and (b) H2O migrating from the neighborhood of the HMX molecule to infinity.

(3) A possible γ → β phase transition is found at around 2.10 GPa and the migration of H2O has an effect of kinetically pushing this process, which agrees well with the experimental observation. We make it clear that no β → δ/ε → δ phase transition occurs at 27 GPa, which has long been a hot debate in experiments. (4) The P−V relation, bulk modulus, and acoustic velocity for the four polymorphs of HMX are calculated, which are mostly experimentally unavailable.

To simulate the effect of H2O migration, we have established a model using one HMX molecule and one H2O molecule, with the H2O molecule moving from the neighborhood of the HMX molecule to infinity during the boat → chair transition of the HMX molecule. For the reference state, H2O is kept in the surroundings of the HMX molecule. From Figure 11a,b, the boat → chair transition barrier is 1.36 eV when the H2O migration process is included. If H2O remains in the surroundings of the HMX molecule, the boat → chair transition has to overcome an energy barrier of 1.76 eV. Because the final state of the transition is β-HMX and separated H2O, the additional energy of H2O dissociating from chairHMX should be considered. The dissociation energy is calculated to be 0.36 eV. Therefore, the total barrier to overcome is 2.12 eV, which is much higher than the 1.36 eV barrier for the H2O migration process. This indicates that migration of H2O kinetically pushes the boat → chair transition, which is part of the process of γ → β phase transition. From Table 4, the presence of H2O has drastically enlarged the energy barriers of intramolecular transitions. Without H2O, the energy barriers of the boat ↔ chair transition are 0.45 and 0.64 eV; the intermolecular packing structure evolution costs an energy less than 0.92 eV. However, with a H2O molecule present, the barriers of the boat ↔ chair transition are significantly enlarged, by ∼1 eV. Because α-, β-, and δ-HMX do not contain H2O, the β ↔ α/δ phase transitions are kinetically much easier than the γ ↔ β transition.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b08092. Coordinates of noncovalent interacting complexes (ZIP)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86 10 61935175. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grant No. 11572053 and 11604017), the Development Foundation of China Academy of Engineering Physics (Grant No. 2014A0101004), and Science Challenge Project (No. JCKY2016212A502). We thank Dr. Qun Zeng for sharing the structures and interaction energies of the E19 complexes. Dr. Erin Hayward is acknowledged for a critical reading of the manuscript.

4. CONCLUSIONS We have constructed a set of pseudopotentials and a basis set specialized for molecular crystals consisting C/H/N/O elements. The reliability of the method is verified from the interaction energies of 45 kinds of complexes (comparing with CCSD(T)) and the crystalline structures of 23 kinds of typical explosive solids (comparing with experiments). Using this method, we have explored the phase transitions among α-, β-, γ-, and δ-HMX. The main conclusions are as follows: (1) Under compression, the symmetry of α-HMX degenerates from the Fdd2 space group to the P1 space group, whereas the molecular configuration of γ-HMX is altered, with the H2O molecule approaching the HMX molecule nearby. (2) Under external stimulation, the boat ↔ chair configuration deformation has a priority of ∼87% in the competition with intermolecular packing deformation.

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REFERENCES

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