Article pubs.acs.org/JPCC
High-Pressure Experimental and DFT‑D Structural Studies of the Energetic Material FOX‑7 Steven Hunter,*,† Paul L. Coster,† Alistair J. Davidson,† David I. A. Millar,† Stewart F. Parker,‡ William G. Marshall,‡ Ronald I. Smith,‡ Carole A. Morrison,*,† and Colin R. Pulham† †
School of Chemistry and Centre for Science at Extreme Conditions, The University of Edinburgh, King’s Buildings, David Brewster Road, Edinburgh EH9 3FJ, U.K. ‡ ISIS Neutron and Muon Facility, STFC Rutherford Appleton Laboratory, Harwell, Oxford, Didcot, Oxfordshire OX11 0QX, U.K. S Supporting Information *
ABSTRACT: This work reports the hydrostatic compression of the perdeuterated αform of FOX-7 using neutron powder diffraction to follow the structural changes up to 4.58 GPa at room temperature. The equation of state for the hydrostatic compression of the α-form over the range 0−4.14 GPa has been determined, and a phase transition was observed over the pressure range 3.63−4.24 GPa. On the basis of dispersion-corrected density functional theory (DFT-D) calculations performed on the γ-form over a range of pressures, the high-pressure form observed in the neutron diffraction experiments can unambiguously be identified as being different from the γ-form and should therefore be denoted as the ε-form. Based on similarities between the simulated and experimental powder diffraction patterns of the γ- and ε-forms, it is suggested that the ε-form adopts a planar, layered structure. The structural responses to pressure of the α-form observed experimentally are reproduced by DFT-D calculations, but in-depth analysis of the bond lengths, angles, dihedrals, and vibrational frequencies calculated in the DFT-D simulations identified a very subtle second-order phase transition at 1.9 GPa. This corroborates results obtained from previous far- and mid-IR vibrational spectroscopic studies. These very small changes in molecular geometry do not manifest themselves in either the measured or calculated lattice parameters or unit-cell volumes and are much smaller than can be detected by diffraction experiments. The results of phonon calculations were compared with experimental inelastic neutron scattering measurements and were used to investigate the effect of pressure on the heat capacities of α-FOX-7. The simulations predict very weak pressure dependencies (approximately −1 J K−1 mol−1 GPa−1), in accordance with the conclusions reached in our previous studies of the energetic material RDX. (orthorhombic, space group P212121),2 which then converts to the γ-form (monoclinic, space group P21/n)4 upon further heating above 446 K. Upon cooling the γ-form to below 348 K, the sample directly, but incompletely, reverts to the α-form.5 Recently, Bishop et al. performed differential scanning calorimetry (DSC) and synchrotron mid-IR measurements which confirmed the α → β → γ transitions in FOX-7 at ambient pressure and room temperature.6 Furthermore, the authors also reported evidence for the γ → δ transition of FOX7 and decomposition above 250 °C, consistent with previous differential thermal analysis (DTA) findings by Chemagina et al.,7 who suggested that heating FOX-7 slightly above 210 °C initially leads to an irreversible phase transition to a δ-form of FOX-7, which was recovered and shown to be stable under ambient conditions. Peiris et al. studied the compression behavior of the α-form under nonhydrostatic conditions using angle-dispersive X-ray powder diffraction at ambient temperature.8,9 This study identified a phase transition above ∼4.5 GPa to a phase that
1. INTRODUCTION Much of the current research into energetic materials (explosives and propellants) is focused on the development of insensitive compositions that improve safety by reducing the risk of accidental initiation. The goal is to design tailored energetic materials that have both specific functionality and a high threshold for accidental detonation. On detonation, these materials experience extreme conditions of both pressure and temperature, and so it is important to discover how their physical properties are affected by these extreme conditions. The insensitive high explosive known as FOX-7 (1,1-diamino2,2-dinitroethylene or DADNE, see Figure 1a) was developed in 1998 and shows much promise as a potential substitute for RDX on account of its reduced sensitivity to initiation. The solid material is bright yellow and has a layered structure that is dominated by dispersion interactions between layers, with relatively strong hydrogen bonds within the layers, as shown in Figure 1b.1−3 There are three structurally characterized phases of FOX-7 (α, β, and γ) at ambient pressure. The α-form (monoclinic, space group P21/n)2 is the most stable under ambient conditions. When heated above 389 K at ambient pressure, a fully reversible transformation into the β-form occurs © XXXX American Chemical Society
Received: November 5, 2014 Revised: January 3, 2015
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DOI: 10.1021/jp5110888 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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significant distortion to the monoclinic α-phase or a possible structural transformation to what was termed the α′-phase. By 6.1 GPa, further spectroscopic changes suggested another phase transition to “an α″-phase”, previously referred to by Peiris et al. as a quasi-amorphous phase. At 200 °C, similar transitions were observed at 2.0 and 5.5 GPa, respectively. Over the P−T range investigated (up to ∼10 GPa and 200 °C) no evidence of sample decomposition was observed.14 Subsequent highpressure Raman spectroscopy studies by Dreger et al. on single crystals of FOX-7 examined its vibrational and polymorphic behavior to elucidate its structural and chemical stability.15,16 Contrary to previous suggestion,14 the authors demonstrated that the high-pressure phases observed above 2 and 4.5 GPa are different to the ambient pressure high-temperature β- and γpolymorphs of FOX-7. The authors noted that the phase transition at 2 GPa from the α-form to a phase denoted as phase I (previously termed the α′ phase in ref 14) involved changes to only a few Raman-active modes and suggested that the changes probably involved alteration of the molecular conformation. In contrast, due to significant changes in both the lattice and intramolecular vibrational modes, the phase transition at 4.5 GPa (denoted phase II and previously termed the α″ phase in ref 14) was suggested to be a reconstructive transition involving both molecular and crystal transformations. Further compression of phase II to 40 GPa and subsequent release of pressure did not cause any irreversible changes, implying that FOX-7 has remarkable chemical stability under high pressures.15,16 The apparent discrepancies in the high-pressure behavior of FOX-7 may arise in part from the different experimental techniques and conditions used to study the compound, e.g., degree of hydrostaticity, and the possibility of X-ray damage. In particular, there is a striking discrepancy between the results of spectroscopic studies that consistently indicate a phase transition near 2 GPa but which is not observed in the X-ray diffraction studies. It is for these reasons that we undertook a hydrostatic compression study of FOX-7 up to 4.6 GPa using neutron powder diffraction. A complementary approach to experiment is atomistic simulation, which provides an effective way to model the properties and structure of crystalline materials. The suitability of density functional theory (DFT) for studying energetic molecular materials has been reported in depth.17−20 There have been several DFT studies on crystalline FOX-7,21,22 but it is well-known that DFT methods are unable to describe accurately the intermolecular interactions of molecular organic crystals without the implementation of some sort of dispersion correction.18,23 Several different approaches for the implementation of dispersion corrections have been adopted. Sorescu and Rice performed theoretical DFT-D predictions at ambient and elevated pressures of the crystallographic properties of ten energetic molecular solids. 23 They concluded that the dispersion-corrected density functional theory method (DFTD) as parametrized by Grimme24 provides significant improvements for the description of intermolecular interactions in molecular crystals at both ambient and high pressures relative to conventional DFT. Appalakondaiah et al. investigated the effects of pressure on the structural and vibrational properties of FOX-7 using first-principles calculations.25 The authors investigated various functionals to calculate the ground state ambient pressure geometry including LDA, GGA-PW91, GGAPBE and the OBS, TS, and G06 dispersion corrections as implemented in the CASTEP software package and concluded
Figure 1. (a) Molecular structure of FOX-7. (b) Solid-state structure of FOX-7. (c) Numerically annotated molecular structure of FOX-7.
was described as “quasi-amorphous”; the phase transition was apparently irreversible and was suggested to be a consequence of molecular decomposition. The authors noted that this phase transition may be dependent upon the degree of shear stress within the sample.8,9 FOX-7 has also been investigated at both high temperatures and high pressures under nonhydrostatic conditions using energy-dispersive X-ray diffraction.10 This work identified a transition to an amorphous phase beyond 280 °C near 2 GPa. Further pressure and temperature cycling suggested that the sample transformed reversibly into and out of the amorphous phase near the phase line, contrary to earlier reports of molecular decomposition, and the authors suggested that X-ray damage may have been the cause of the apparent irreversibility observed in the study by Peiris et al.10 FOX-7 has been studied using IR spectroscopy at ambient pressure11 and by Raman spectroscopy up to 8.2 GPa.8,9 Welch performed high-pressure, ambient-temperature Raman microspectroscopy experiments on FOX-7 that showed evidence of the onset of two phase transitions near 2.65 and 5.5 GPa, with the loss and/or development of new vibrational modes at the proposed phase boundaries.12 Pravica et al. recently performed a high-pressure far- and mid-IR study of FOX-7 up to 28 GPa.13 The authors presented evidence for at least two, possibly three, phase transitions. Spectral changes near 2 GPa suggested a phase transition, similar to earlier work, but which had been discounted by Peiris et al.8 This study also confirmed the phase transition observed by Peiris et al. near 5 GPa. The authors noted that this transition may be sluggish, as it is complete only when the applied pressure approaches 10 GPa, after which FOX-7 undergoes a further phase transition. Contrary to the earlier reports of pressure-induced molecular decomposition, both Welch and Pravica et al. observed no pressure-induced amorphization or decomposition up to 21.5 and 28 GPa, respectively.12,13 Subsequently, Bishop et al. investigated the structural phase stability of FOX-7 as a function of both temperature and pressure using synchrotron mid- and farinfrared spectroscopy.14 During isothermal compression at 100 °C, changes were observed at 2.2 GPa that may be indicative of B
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ambient pressure structure and vibrational properties of αFOX-7. The calculated compression behavior is then analyzed with a particular focus on the high-pressure behavior of the calculated internal molecular geometries and the prediction of the effect of pressure on the heat capacity. The high-pressure phase of FOX-7 is then discussed. The main conclusions of this work are summarized in section 4.
that the PBE+G06 functional best reproduces the α-FOX-7 unit-cell volume at ambient pressure. The authors then proceeded to implement the PBE+G06 (DFT-D) functional to calculate the high-pressure behavior between 0 and 10 GPa in 1 GPa increments, in addition to vibrational properties in 2 GPa increments. The authors also noted that based on enthalpy calculations of the α- and β-forms of FOX-7 they see no sign of the possible α → α′ phase transition and postulated that temperature must play a major role in the transition and/or the level of theory that was used (DFT-D) was not sufficient to recognize the phase transition.25 Similarly, Averkiev et al. examined the pressure effects on the Raman vibrations of αFOX-7.26 The authors applied the DFT-D method as used by Appalakondaiah et al., but rather than the ultrasoft pseudopotential used in ref 25, norm-conserving pseudopotentials were utilized for calculation of accurate Raman intensities. Assignments of intramolecular Raman-active vibrations were provided. The calculated pressure dependence of Raman shifts for the intramolecular and lattice modes were found to be in good agreement with the experimental data; in particular, the calculations predicted correctly a decrease of frequencies for the NH2 stretching modes with pressure. The authors also commented on the experimental evidence for the α → α′ transition (occurrence/disappearance of Raman peaks in addition to change in Raman shift slope at the transition16) and noted that none of these features were reproduced in the calculated spectra and suggested that this was most likely due to the subtle nature of the transition.26 Balu et al. investigated the performance of dispersioncorrected atom-centered pseudopotentials (DCACPs) at describing the ambient-pressure crystal structures of several energetic materials and demonstrated excellent agreement with experiment, which rivaled the results of DFT-D studies.27 In addition, there have been two independent studies that have implemented the quasi-harmonic approximation in combination with a DFT-D dispersion correction, in order to predict equilibrium volumes and properties at nonzero temperatures, termed DFT-D+T.28,29 Landerville et al.28 used the dispersion correction proposed by Neumann and Perrin30 (which is similar to that of Grimme) to show that the DFT-D+T method improved the prediction of the unit-cell volumes of nitramine crystals over conventional DFT and DFT-D. Using a similar method, Wu et al.29 used the Grimme dispersion correction24 to predict the structure and properties of β-HMX. In this case, the authors determined that the best agreement with experiment for the prediction of the unit-cell lattice parameters and volume was obtained by the DFT-D method rather than DFT-D+T; at ambient pressure the DFT-D method predicted all lattice parameters and unit cell volumes within 1% of experiment. We have previously used the dispersion correction proposed by Grimme24 to simulate accurately not only the high-pressure structures of selected RDX (cyclotrimethylenetrinitramine) polymorphs but also their vibrational and thermochemical properties.31 In this article, we now apply the same computational method to study FOX-7 in order to simulate the effects of pressure on its crystal structures, its vibrational spectra, and ultimately the effect of pressure on its heat capacity. The organization of the paper is as follows. Section 2 describes the specific details of the experimental and computational methods used in this study. Section 3 presents the results of the high-pressure neutron powder diffraction experiments, experimental inelastic neutron scattering (INS) spectra, and the computationally calculated
2. EXPERIMENTAL AND COMPUTATIONAL METHODS 2.1. Sample Preparation. On account of the large incoherent neutron scattering cross section from hydrogen atoms, it was necessary to use a perdeuterated sample of FOX7. This was prepared from a sample of FOX-7 (supplied by Dstl, Fort Halstead, UK) by treatment with NaOD [prepared by the addition of metallic sodium to D2O (99.9 at. %, SigmaAldrich)], followed by neutralization with D2SO4 (99.5 at. %, Sigma-Aldrich). 2.2. Neutron Powder Diffraction. A lightly ground sample (ca. 100 mg) of perdeuterated α-FOX-7 was loaded into a null scattering Ti−Zr alloy capsule gasket,32 together with a small quantity of 4:1 perdeuterated methanol/ethanol as a pressure-transmitting medium (selected on the basis that it remains hydrostatic up to pressures of ca. 9.8 GPa)33 and a small lead pellet as pressure calibrant. The resulting capsule assembly was then compressed within a type V3b ParisEdinburgh (P−E) press34 equipped with standard single toroid anvils with cemented WC cores (Ni binder). The P−E press ram pressure was monitored and varied by means of a computer-controlled hydraulic system. High-pressure neutron powder diffraction data were collected using the PEARL and POLARIS diffractometers at the UK spallation neutron source, ISIS Neutron and Muon Facility.35 Time-of-flight (TOF) neutron powder diffraction data suitable for structure refinement were obtained by electronically focusing the individual detector element spectra from the 2θ ≈ 90° detector banks. The resulting summed pattern was then normalized using the incident beam monitor and the scattering from a standard vanadium calibration sample to account for differing data collection times and the variation of both the incident neutron beam intensity and the detector efficiency as a function of neutron energy, respectively. Lastly, the normalized intensities were corrected for the wavelength and scattering-angle dependence of the neutron attenuation by the anvil (WC) and gasket (TiZr) materials. From these fully corrected TOF powder diffraction patterns, the crystal structure of FOX-7 as a function of pressure was refined by full-profile Rietveld refinement using the GSAS package.36 Sample pressures were calculated from the refined lead lattice parameters and the room-temperature equation of state (EoS) for lead as derived by Fortes37 with an uncertainty of ±0.05 GPa. Data collection times per pressure point ranged between 1 and 6 h at an average proton beam current to the ISIS target of ∼165 μA. 2.3. Inelastic Neutron Scattering (INS). INS spectra (24−4000 cm−1) were recorded using the TOSCA38 instrument at the ISIS Neutron and Muon Facility, which has an energy resolution of ∼1.25%. Approximately 1.8 g of hydrogenous polycrystalline α-FOX-7 was loaded into an aluminum sample can and cooled to T < 20 K in a conventional closed cycle refrigerator, and spectra were recorded for 3−6 h (at an equivalent of 165 μA ISIS proton current). The INS data were visualized and compared to the simulated spectra of the DFT-D calculations using the aCLIMAX program.39 C
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The Journal of Physical Chemistry C 2.4. Computational Methods. Structure optimizations (at ambient pressure and under hydrostatic externally applied pressure conditions) and vibrational frequency calculations were performed on models corresponding to one unit cell representations of FOX-7 using density functional theory plus dispersion (DFT-D, utilizing the correction scheme of Grimme24) and the plane-wave pseudopotential method as implemented in CASTEP version 5.5.40,41 Treatment of electronic exchange and correlation was handled by the generalized gradient approximation (GGA) formalized by Perdew, Burke, and Ernzerhof (PBE).42 On-the-fly (OTF)43 pseudopotentials generated using the CASTEP software package were used, along with a plane-wave cutoff energy of 650 eV, which ensured convergence of both lattice parameters and total energies (to less than 5 meV per unit cell). Brillouin zone sampling was obtained using constant Monkhorst−Pack44 grids across the pressure series of 2 × 3 × 1 for α-FOX-7, and 2 × 3 × 2 for γ-FOX-7 (giving 2 and 4 k-points in the irreducible Brillouin zone, with spacings of no more than 0.06 and 0.05 Å−1, respectively). The structures were relaxed (using the Broyden, Fletcher, Goldfarb, and Shannon BFGS45 method) to allow both atomic coordinates and unit cell vectors to optimize simultaneously while constraining space group symmetry (convergence criteria: maximum change in system energy = 2 × 10−5 eV, maximum root-mean-square (RMS) force = 0.025 eV Å−1, maximum RMS stress = 0.01 GPa, and maximum RMS displacement = 0.002 Å). Following successful geometry optimization of the experimental starting structures, external hydrostatic pressures were applied at pressures corresponding to those used for collection of experimental data. Zonecentered phonon frequencies were then calculated by finite displacement methods and visualized using the aCLIMAX program.39,46
asymmetric unit were based on the single crystal X-ray structure of Bemm et al.;3 constraints were imposed such that each symmetry/size-related group (all D atoms, all O atoms, all C atoms, and all of the N atoms) had a collective refineable thermal vibration parameter. Subsequently, the lattice parameters, atomic coordinates, isotropic thermal vibration parameters, and peak width parameters were refined at each pressure point. All of the patterns up to a pressure of 3.30 GPa could be indexed to the α-form of FOX-7, and each of these refinements were stable; they converged and produced a physically sensible structure (i.e., no unrealistic bond distances or angles). At a pressure of 3.63 GPa, the diffraction pattern was observed to become more complex, with the appearance of new peaks in addition to those associated with α-FOX-7, suggesting the presence of a new phase. This mixed-phase pattern was also observed at a pressure of 4.14 GPa. However, upon increasing the pressure to 4.24 GPa, the Bragg peaks associated with αFOX-7 disappeared completely to give a pattern that was dominated by a single, intense peak at a d-spacing of 2.73 Å. Closer inspection of the pattern shows at least eight distinct peaks associated with this new phase, indicated by the arrows in Figure 3.
3. RESULTS AND DISCUSSION 3.1. Crystallographic Data. Figure 2 shows the sequence of neutron powder diffraction patterns obtained for perdeuterated α-FOX-7 as a function of increasing pressure, collected from multiple experiments using both the PEARL and POLARIS diffractometers. During Rietveld refinements using the GSAS36 program the following constraints and restraints were imposed: initial bond distance/angle restraints for the
Figure 3. Neutron powder diffraction pattern obtained for FOX-7 at 4.58 GPa (black) and expanded region (red) showing weaker features. Blue vertical markers indicate the positions of peaks associated with the Pb pressure marker; peaks associated with the WC anvils and Ni binder are denoted by orange and green vertical markers, respectively. The black arrows indicate the peaks associated with the new phase.
Figure 4 shows that this new high-pressure phase reverted back to the α-form on decompression, confirming the conclusions obtained using vibrational spectroscopy10,13,15,16 and contrary to earlier reports of molecular decomposition.8,9
Figure 2. Sequence of neutron powder diffraction patterns obtained for perdeuterated FOX-7. Black: α-FOX-7; blue: mixed phase; red: high-pressure phase. Pol indicates POLARIS instrument data sets, and Pea indicates PEARL instrument data sets.
Figure 4. Neutron powder diffraction patterns obtained for FOX-7. Black: 0.38 GPa obtained upon compression; red: 0.36 GPa obtained during decompression after cycling through the high-pressure phase transition. D
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Table 1. Variation in the Unit-Cell Parameters of α-FOX-7 with Pressure (Values in Parentheses Are Estimated Standard Deviations) press. (GPa) a
0.00 0.09a 0.38a 0.47b 0.68a 1.33b 1.34a 1.73b 1.89a 2.20b 2.36b 2.47b 2.58b 2.64a 2.79b 3.30b 3.63a 4.14b a
a (Å)
b (Å)
c (Å)
β (deg)
V (Å3)
χ2
wRp
6.9400(2) 6.9255(10) 6.9014(9) 6.8956(6) 6.8735(10) 6.8371(6) 6.8335(9) 6.8146(6) 6.8046(8) 6.7905(6) 6.7835(6) 6.7810(13) 6.7783(9) 6.7670(8) 6.7622(10) 6.7482(16) 6.7321(11) 6.7291(29)
6.6280(1) 6.5759(6) 6.5052(5) 6.5014(3) 6.4349(6) 6.3428(3) 6.3271(5) 6.2842(3) 6.2531(5) 6.2243(3) 6.2058(3) 6.1955(6) 6.1865(4) 6.1641(5) 6.1562(5) 6.1170(7) 6.0788(6) 6.0629(12)
11.3287(4) 11.3050(22) 11.2701(19) 11.2660(14) 11.2264(21) 11.1698(13) 11.1630(19) 11.1294(12) 11.1121(17) 11.0877(12) 11.0722(12) 11.0697(24) 11.0614(16) 11.0516(15) 11.0438(18) 11.0092(27) 10.9849(22) 10.9555(47)
90.595(3) 90.547(14) 90.471(13) 90.483(9) 90.395(15) 90.318(10) 90.321(14) 90.267(9) 90.263(13) 90.224(9) 90.198(9) 90.202(19) 90.188(13) 90.184(12) 90.147(15) 90.102(21) 90.113(18) 90.142(38)
521.07(2) 514.82(10) 505.96(9) 505.05(6) 496.54(10) 484.39(6) 482.64(9) 476.60(6) 472.81(8) 468.63(6) 466.10(5) 465.06(11) 463.84(7) 460.99(7) 459.75(8) 454.44(12) 449.54(10) 446.96(21)
3.29 0.70 0.70 1.29 0.76 1.30 0.72 1.32 0.70 1.26 1.29 1.07 1.17 0.72 1.17 1.40 0.89 3.13
9.30 10.06 10.83 3.34 11.37 3.61 10.52 3.50 9.74 3.47 3.49 8.83 5.60 10.04 7.43 7.60 14.49 17.00
Signifies data collection using the POLARIS instrument. bSignifies data collection using the PEARL instrument.
conclusions drawn from spectroscopic studies.12−16 This discrepancy is discussed in more detail later, in light of the results obtained from the computational studies. Figure 6 shows the hydrogen-bonding network within the layers. This experimental neutron study also provides rich
Table 1 lists the lattice parameters obtained from Rietveld refinements for the compression of perdeuterated α-FOX-7. Fitting statistics, wRp, and χ2 are listed for each pressure; plots of the experimental lattice parameters can be found in the Supporting Information (Figure S1). In agreement with previous experimental results, the b-axis (which lies in the direction perpendicular to the zig-zagging layers of hydrogenbonded molecules in the structure) is significantly more compressible than the a- and c-axes (over the range 0−4.14 GPa, a/a0 = 0.970, b/b0 = 0.915, and c/c0 = 0.967). The change in unit-cell volume as a function of pressure for α-FOX-7 can be fitted to a third-order Birch−Murnaghan equation of state (eq 1, where the equation of state pressure, P, at a given volume, V, is calculated by least-squares fitting of the parameters V0, B0, and B′: the zero-pressure volume, bulk modulus, and first pressure derivative of the bulk modulus, respectively),47 with parameters V0 = 521.07(0.04) Å3, B0 = 11.81(0.47) GPa, and B′ = 11.41 (0.95) as shown in Figure 5. p=
⎡⎛ V ⎞2/3 ⎤⎫ ⎪ ⎪ 3B0 ⎡⎛ V0 ⎞7/2 ⎛ V0 ⎞5/2 ⎤⎧ 3 ⎢⎜ ⎟ − ⎜ ⎟ ⎥⎨1 + (B′ − 4)⎢⎜ 0 ⎟ − 1⎥⎬ ⎪ ⎪ ⎝ V ⎠ ⎥⎦⎩ ⎢⎣⎝ V ⎠ 2 ⎢⎣⎝ V ⎠ 4 ⎦⎥⎭
(1)
Figure 6. (a) Numerically annotated structure of α-FOX-7 highlighting the hydrogen bonding within the layers. (b) Unit cell of αFOX-7 viewed along the a-axis, which highlights the zigzag nature of the layers of hydrogen-bonded molecules, and it shows how these layers are separated by a distance of b/2, which approximates the interlayer distance.
These hydrostatic neutron powder diffraction data provide no evidence of a phase transition at ∼2 GPa, in agreement with previous XRD diffraction studies,8−10 but in contrast to the
structural information, in particular the hydrogen (deuterium) positions within the crystal structure, which in turn reveal information regarding hydrogen bonding. For example, the O2···H4 hydrogen bond decreases most with pressure, from 2.244 Å at ambient pressure to 2.026 Å at 4.14 GPa. Furthermore, the interlayer separation decreases from 3.318 to 3.031 Å over this pressure range. Full tables of the hydrogenbond lengths and the interplanar distances as a function of pressure can be found in Tables S1 and S2 of the Supporting Information.
Figure 5. Unit-cell volume of α-FOX-7 as a function of hydrostatic pressure for the experimental data reported in Table 1, fitted with third-order Birch−Murnaghan equation of state. Circle: POLARIS instrument data; square: PEARL instrument data. E
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Table 2. Comparison of the Unit Cell Parameters Calculated at Ambient Pressure Using the DFT-D Method with Results Obtained from Experiment and Previous DFT-D Studies α-FOX-7 parameter
expa (ref 3) (SEDTUQ)
DFT-D (ref 23)
DFT-D (ref 25)
DFT-D (ref 26)
DFT-D (this work)
a (Å) b (Å) c (Å) β (deg) V (Å3)
6.941 [1] 6.569 [1] 11.315 [2] 90.55 [2] 515.889
6.8973 (−0.6) 6.4488 (−1.8) 11.2919 (−0.2) 90.98 (0.5) 508.74 (−1.4)
6.99 (0.7) 6.52 (−0.8) 11.31 (−0.0) 91.23 (0.8) 515.45 (−0.1)
7.03 (1.3) 6.52 (−0.8) 11.33 (0.1) 91.02 (0.5) 519.03 (0.6)
7.0049 (0.9) 6.4738 (−1.4) 11.3091 (−0.1) 90.946 (0.4) 512.78 (−0.6)
a
The numbers in square brackets are the estimated standard deviations of experimental values. The values in parentheses are the percentage error deviations from experimental values.
Table 3. Assigned Spectrum of the Computationally Calculated Fundamental Modes for α-FOX-7 Compared to the INS Spectrum Reported in This Work DFT-D ν (cm−1)
corresponding exptl modeb
INS (this work) ν (cm−1)
4 5 6 7 8 9 10 11 12 13 14−15 16 17−20 21−22 25 23−24 26−27 28 29 30 31 32 33−34 35−36 37−38 39−40 41−44 45−48 49−52 53−56 57−60 61−64
29.3 48.1 57.9 60.1 67.3 76.3 77.1 81.5 86.5 91.7 93.4 97.3 100.1 109.3 119.6 113.5 122.9 124.4 128.9 130.9 145.4 150.6 148.0 165.7 256.1 263.8 319.5 326.6 384.6 445.4 455.8 476.5
m2 m5 m7 m8 m9 m10 m11 m12 m13 m14 m15 m16 m17 m18 m19 m20 m21 m22 m23 m24 m25 m26 m27 m28 m33 m34 m36 m37 m39 m41 m42 m43
27 46 53 58 64 69 72 79 85 88 95 97 103 112 117 122 138 145 148 150 162 164 173 177 238 241 317 327 388 453 464 474
65−66 67−68 71−72 69, 70, 73, 74
558.8 599.6 611.5 610.9
m46 m47 m48 m49
529 559 584 602
mode
a,b
a,b
DFT-D ν (cm−1)
corresponding exptl modeb
INS (this work) ν (cm−1)
assignment
mode
lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice CN2 wag, NO2 twist CN2 wag, NO2 twist CN2 wag, NO2 twist lattice lattice CN2 wag, NO2 twist NO2 twist NO2 twist NO2 twist CN2 wag, NO2 twist CN2 wag CN2 wag CN2 scissors CN2 wag CN2 wag CN2 scissors CN2 scissors CN2 scissors, NH2 twist NH2 wag NH2 wag NH2 wag CN2 scissors
75−76, 77− 78 79−82, 83− 84 85−88 89−92 93−96
639.6
m50
627
NH2 wag
671.9
m51
679
715.3 740.6 765.1
m52 m53 m54
720 742 769
97−100 101−104
783.9 837.3
m55 m56
784 808
105−108 109−112 113−116
1017.8 1068.7 1148.5
m61 m62 m64
1036 1068 1134
117−120 121−124
1167.6 1251.7
m65 m68
1146 1260
125−128
1368.6
m71
1371
129−132
1413.2
m72
1392
133−136
1480.6
m74
1463
141−142
1517.4
m75
1485
145−148
1573.8
m76
1538
153−160
3421.5
m108
3331
161−168
3556.9
m109
3432
CN2 wag, NH2 twist; NH2 wag CN2 wag CN2 wag NO2 scissors, NH2 twist NH2 twist NO2 scissors, NH2 rock NH2 wag NH2 wag CN2 asymmetric stretch CC stretch, NH2 wag CN2 asymmetric stretch, NH2 wag CN2 symmetric stretch NO2 asymmetric stretch, NH2 scissors NO2 asymmetric stretch, NH2 scissors CC stretch, NO2 asymmetric stretch, NH2 scissors NO2 asymmetric stretch, NH2 scissors NH2 symmetric stretch NH2 asymmetric stretch
assignment
a
Where there are multiple modes, the DFT-D value stated is an average of the contributing modes. bThe respective experimental INS and computationally calculated modes are named in accordance with the annotated spectral comparisons given in Figures S2−S5.
3.2. Computational Study at Ambient Pressure. 3.2.1. Structure of α-FOX-7. α-FOX-7 crystallizes in the monoclinic crystal system with space group P21/n: the unit cell contains 4 FOX-7 molecules, giving a total of 56 atoms. Table 2 compares the results of the geometry optimization with experiment and with previous dispersion-correction studies. Lattice parameters agree with experimental values to within 1.4%, and the overall unit-cell volume differs from experiment
by only 0.6%. These results are consistent with previous DFTD studies and confirm that the computational model used (implementing the Grimme dispersion correction) can accurately describe the intermolecular interactions in crystalline α-FOX-7. 3.2.2. Vibrational Properties. Following the geometry optimizations, comprehensive finite displacement phonon calculations (including symmetry) were performed at the F
DOI: 10.1021/jp5110888 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
undoubtedly because the calculation was performed at only the gamma-point in k-space, and so there are no acoustic modes present and the effects of phonon dispersion have been neglected. For a hydrogen-bonded system like FOX-7 it would be expected that there will be significant dispersion in the modes, which will have the effect of “filling in” the lattice mode region. The excellent agreement between experiment and theory both for the crystallographic lattice parameters and for the vibrational frequencies and intensities confirms the conclusion reached during the previous study of crystalline RDX31that the computational model accurately describes both the intraand intermolecular interactions in these molecular energetic materials. 3.3. Compression Behavior of α-FOX-7. 3.3.1. Effect of Pressure on Lattice Parameters. Figure 8 shows that the
gamma point in k-space to obtain the vibrational properties of α-FOX-7. Table 3 shows a comparison of the calculated fundamental (gamma-point) modes for α-FOX-7 with the experimental INS spectrum determined in this study. The majority of the calculated fundamental vibrational modes are in good agreement (
