Pressure-induced phase transition in 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) Free

Energy release in detonation and insensitivity to hazards are the two most important parameters that determine the effectiveness and safety of an energetic material (EM). Taking into account that these two characteristics are usually incompatible, 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), the industry standard for an insensitive high explosive, stands out as the optimum choice when insensitivity/safety is of utmost importance. Indeed, among similar materials with comparable explosive energy release, TATB is remarkably difficult to shock-initiate, has a low friction sensitivity, and is thermally stable at ambient pressure to approximately 615 K.¹ 

At ambient conditions, TATB crystallizes in a layered triclinic structure [SG: P-1 (2), Fig. S1] with two molecules per unit cell.² Due to its practical importance, TATB has attracted extensive research effort aiming to elucidate its high-pressure structural behavior. High-pressure experimental unreacted equations of state (UEOS) of EMs up to detonation pressure are important components of high explosive reactive burn models used to predict shock initiation safety and detonation.³ According to a plethora of previous theoretical studies,^4–12 TATB remains in the ambient pressure crystal structure up to at least 100 GPa. In agreement with theoretical predictions, isothermal high-pressure powder and polycrystalline X-ray diffraction studies^13,14 do not report any structural phase transition up to 70 GPa. On the other hand, a Raman spectroscopy study reports that TATB exhibits pressure-induced Raman changes associated with two subtle structural phase transitions at 28 and 56 GPa.¹⁵ These subtle transitions were attributed to changes in the NO₂ configuration and puckering of the six-membered rings, while TATB remains in the ambient pressure crystal structure.

In this letter on the isothermal high-pressure behavior of TATB, we report our concomitant experimental and computational results, using single-crystal X-ray diffraction (SXD) and the evolutionary structural search algorithm USPEX.^16–18 Assessing the unit cell volume of triclinic phases like TATB requires not only determining the lengths of cell axes but also the angles between these axes. Powder diffraction only measures distances between lattice planes, but not angles. Hence, we use SXD as a method to measure both angles and distances between lattice planes. In addition, the strong local scattering intensity of a Bragg peak obtained from SC diffraction is more signal-efficient than powder diffraction. Thus, SXD methods help in studying weak X-ray scatterers like TATB.^13,19 An additional motivation was to help resolve longstanding uncertainty regarding polymorphism in TATB that has persisted since Kolb and Rizzo first reported on a possible, but heretofore unsubstantiated, monoclinic and additional triclinic phase in 1979.²⁰ Their report, combined with observations of second harmonic generation (SHG) inconsistent with the centrosymmetric P-1 structure at ambient²¹ and high-temperature conditions,²² has fueled conjecture on the presence of additional crystalline phases, defects, or structural transitions that might manifest due to the low barrier for sliding of TATB layers.^23–27 

Our SXD results reveal a structural phase transition to a monoclinic structure above 4 GPa. This result agrees with USPEX calculations. The phase transition involves a pressure-induced alteration of the stacking of the layers of the TATB molecules, which results in a higher crystal symmetry transformation (i.e., from triclinic to monoclinic) without an abrupt change of the volume per formula unit (taking H₆C₆N₆O₆ as the formula unit in all analysis).

Diffraction data were obtained at undulator beamline 16-IDB (HPCAT), at the Advanced Photon Source (APS). The primary beam energy was set to 38 keV, and X-rays were focused onto the sample to 3 × 4 μm using Kirkpatrick-Baez mirrors. Selected TATB crystals were mounted in the gasketed diamond anvil cells without applied pressure. Prior to compression, SXD data were collected at ambient pressure in order to check crystal quality, orientation, and absence of polytypism in the crystals. Suitable samples were compressed with neon as the pressure transmitting medium (PTM), to pressures between 0.4 and 1 GPa.²⁸ After increasing pressure, data collection was started with a delay of at least 20 min to minimize the effect of gasket creep during data acquisition. Data were collected with a MAR165 CCD area detector. Calibration of the sample-detector distance, tilt, and geometric distortions was obtained from the NIST CeO₂ diffraction standard using the GSE-ADA software.²⁹ Peak fitting and coordinates were obtained with GSE-ADA.²⁹ A representative example of the indexing is shown in Fig. S2. Indexation was acquired through the Reciprocal Space Viewer (RSV)²⁹ and Cell now³⁰ programs. Typically, 80–150 reflections were indexed. Additional details on the experimental methods are given in the supplementary material.

Theoretical calculations were performed using density functional theory^31,32 (DFT) implemented in the Vienna Ab-initio Simulation Package³³ (VASP). The Perdew-Burke-Ernzerhof³⁴ (PBE) generalized gradient approximation functional was used with projector-augmented wave (PAW) pseudopotentials.^35,36 The Grimme D2 dispersion correction³⁷ was used to account for long range intermolecular interactions present in molecular crystals such as TATB. A molecular crystal structure search for high-pressure polymorphs of TATB was performed at 0 GPa and 10 GPa using the first principles evolutionary crystal structure prediction method USPEX.^16–18 The lattice parameters, lattice angles, and atomic positions were optimized at fixed hydrostatic pressure. For the structure search, the enthalpies were calculated with a plane wave basis set with a plane wave energy cutoff of 450 eV and a k-point spacing of 0.07 Å⁻¹. The self-consistent field accuracy threshold was set to 1 × 10⁻⁶eV, and optimizations of the ionic degrees of freedom were performed with a force-based accuracy threshold of 3 × 10⁻² eV Å⁻¹. The search was performed with 4 formula units in the unit cell (i.e., four TATB molecules). The ambient pressure P-1 phase contains two formula units in the unit cell, so it is also found during the search with four formula units. The computational expense precluded using a larger system size and thus those unit cells with more than four formula units in the primitive cell were not covered by the search. Two different searches were performed. The first search used an initial guess of the volume to generate structures based on the calculated volume of the P-1 phase. In the second search, the lattice parameters obtained from experiment were used as the initial guess for the lattice parameters to generate structures.

The lowest enthalpy structures from the search were used to perform more accurate calculations of the pressure and energy as a function of volume using the same settings as above with the following exceptions: a plane wave energy cutoff of 700 eV and a k-point spacing of 0.05 Å⁻¹. Convergence tests on the energy cutoff and k-point density showed that with these settings, the energy was converged to less than 0.1 meV atom⁻¹. The lattice parameters, atomic configurations, and hydrostatic pressure were optimized as a function of volumetric compression ratio V/V₀ at T = 0 K.

TATB was indexed in the known triclinic metric from ambient pressure up to 3.5 GPa based on the SXD results obtained from crystals mounted within the diamond anvil cell. Between 3.50 and 3.68 GPa and beyond, indexation clearly favored a nonprimitive monoclinic cell (either C- or I-centered, depending on chosen metric setting) with double the cell volume of the triclinic structure. This implies a crystal structure with four formula units per unit cell without an abrupt change of the volume per formula (TATB molecule) unit. The results of the SC indexing are shown in Fig. 1 and Table S1. Pressure-induced phase transitions may be mimicked by insufficient sampling of reciprocal space in a diamond anvil cell, through deviatoric stresses, or through twinning upon a symmetry-reducing transition. The present case is arguably a phase transition because symmetry increases rather than decreases and because all reflections comply with the extinction rules of a nonprimitive lattice. Deviatoric stress mimics a reduction rather than an increase in symmetry. Twinning may mimic higher symmetry but occurs upon symmetry-reducing transitions and the low-pressure phase of TATB is already in the lowest crystal symmetry. Finally, insufficient sampling of reciprocal space may result in arbitrary metrics but is not expected to comply with the general extinction of a nonprimitive lattice.

We consider the observation that all observed reflections comply with the extinction rules of an I-center monoclinic cell as a very strong indication that TATB transforms to a monoclinic structure between 3.50 and 3.68 GPa. Such a transition might be induced by minute deviatoric stresses or initial crystal imperfections. However, neon is fairly hydrostatic up to 15 GPa³⁸ and solidifies above 4.8 GPa, which is above the phase transition pressure. Thus, it is likely that the neon PTM has no effect on the observed phase transition. The pressure dependent lattice parameters and volumes for the compression cycle are shown in Figs. 1(a) and 1(b), respectively. We conducted fits to the experimental P–V data using a second-order Birch-Murnaghan EOS.³⁹ The determined B₀ values strongly indicate that the high-pressure phase of TATB is much less compressible [B₀ = 45(5) GPa] than the P-1 phase [B₀ = 19(3) GPa].

The experimental set of reflections is more than sufficient for indexation, but the low number of unique reflections is insufficient for modeling the structure of a complex molecular crystal like TATB. To gain deeper insight into the high-pressure monoclinic structure, we performed a first principles molecular crystal structure search using USPEX.^16–18 Interestingly, in addition to P-1, two stable monoclinic structures were found, namely, I2/a and C2/c. Both predicted phases belong to SG C2/c (15), albeit in different settings, and both have four formula units per unit cell in agreement with the SC diffraction results [see supplementary material crystallographic information files (cif) for the predicted structures]. These structures are approximately degenerate in enthalpy with P-1, but I2/a is slightly lower in enthalpy than P-1 from about 1–20 GPa (Fig. 2). The trend with pressure shows that I2/a becomes lower in enthalpy than P-1 from 0 to 12 GPa, while C2/c becomes lower in enthalpy than either phase at much higher pressures (Fig. 2). The enthalpy differences are too small to definitively determine which is lower in enthalpy (and thus to predict the phase transition pressure), but it is clear that the monoclinic structures are at least nearly degenerate in enthalpy with P-1.

The calculated values for the lattice parameters and the cell volume of I2/a are given in Figs. 1(a) and 1(b), respectively. Experiment and theory agree closely for the lattice parameters and the cell volume for the two phases up to 16 GPa. The calculated volume and lattice parameters are consistently lower than those observed experimentally due to the fact that the calculated values are obtained at 0 K. The calculated EOS of TATB using DFT at room temperature investigated previously⁹ shows that thermal effects account for about a 3% increase in volume. The calculated a and b lattice parameters for P-1 show better agreement with experiment than c due to the smaller compressibility along a and b, and thus, the thermal expansion has less of an effect. There is also a larger difference in the c lattice parameter because, as is well known, DFT gives a poor description of van der Waals bonding. Consistent with P-1, the difference between experiment and theory for I2/a is smaller along the b lattice parameter because the b lattice parameter is in the basal plane of the TATB molecules [Figs. 3(a) and S1]. The difference between experiment and theory is slightly larger for the a and c lattice parameters for I2/a because both these lattice parameters are partially normal to the basal plane.

Both the I2/a and C2/c structures have four formula units or four unique molecules of TATB in the unit cell. The I2/a structure adopts an ABA′B′ stacking of the TATB layers, in contrast to the AB stacking in P-1. In order to better understand the structural difference between P-1 and I2/a, an overlay of both was generated using the Generalized Crystal-Cutting Method⁴⁰ (GCCM) and DFT-optimized unit cells at 10 GPa (Fig. 3). The two structures were rotated to align the basal plane (i.e., layer) normal vector of each along the same direction in a shared Cartesian frame. A translation of I2/a was then applied to align the atomic coordinates of a single layer with those of a single layer in P-1, which we denote as layer A. From the overlay, it is apparent that the new structure differs from P-1 by translations of whole layers (arrows in Fig. 3) and that layers A′ and B′ are distinct from layers A and B in the I2/a structure.

The mechanism of the phase transition is a change in layer stacking which must be first order because it involves a sublattice displacement, or straightforwardly, it is a displacive not a distortive transition. The first two Landau criteria for a second-order phase transition appear to be met due to the group-subgroup relationship of the structures and due to the small decrease in the volume (volume decrease is nonzero in DFT calculations) at the phase transition pressure. However, the third Landau criterion for a second-order phase transition is not met because the sublattice displacement mechanism is not based on softmodes, and hence, it cannot be second-order. In addition, geometry optimization within DFT captures pressure-induced distortions that can cause a second-order phase transition⁴² but that is not observed here.

Nearly isochoric transitions in low symmetry materials such as TATB are hard to probe by powder diffraction. Powder diffraction measures distances between lattice planes but not angles. Hence, mathematically neither triclinic structures nor cells like the high-pressure phase of TATB can be refined. Previous powder diffraction¹³ studies avoided this problem by fixing the angles of the triclinic cell to the values at ambient conditions. While this is not far from reality below 3–4 GPa, this bias also prevented the detection of the monoclinic transition. The strong anisotropy of the layered TATB structure induces preferred orientation in powder patterns (Fig. S3) and, in the case of samples that are polycrystalline aggregates rather than powder, also texture (prevalence of multiple orientation axes from anisotropic plastic deformation). These effects render the intensities of TATB powder patterns less informative and hide the actual change in symmetry.

In summary, our concomitant experimental, using SXD, and theoretical, using DFT combined with USPEX, studies of TATB under pressure reveal the existence of a pressure-induced phase transition to a monoclinic structure above 4 GPa. Our study highlights the importance of performing SC XRD when probing structural changes in energetic materials under pressure and the close synergy with structural prediction algorithms to elucidate the structure of the high-pressure phases.

See supplementary material for additional details on the experimental methods, the experimentally determined unit cell dimensions of TATB as a function of pressure (Table SI), Fig. S1 for the schematic representations of the TATB crystal structures, Fig. S2 for a representative example of a TATB SC diffraction image, and Fig. S3 for a comparison between the calculated and the experimental X-ray patterns of TATB at 10 GPa.

This work was performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National Security, LLC, under Contract No. DE-AC52-07NA27344. We thank the high explosives Dynamic Materials Properties research program at LLNL and the LLNL LDRD program (18-SI-004) for funding support of this project. This work was performed at HPCAT (Sector 16), Advanced Photon Source (APS), Argonne National Laboratory. HPCAT operations are supported by DOE-NNSAs Office of Experimental Sciences. The APS is a U. S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The use of the COMPRES-GSECARS gas loading system was supported by COMPRES under NSF Cooperative Agreement No. EAR-1606856 and by GSECARS through NSF Grant No. EAR-1634415 and DOE Grant No. DE-FG02-94ER14466.