Polymorphism, Phase Transition and Lattice Dynamics of Energetic

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C: Energy Conversion and Storage; Energy and Charge Transport

Polymorphism, Phase Transition and Lattice Dynamics of Energetic Oxidizer Ammonium Perchlorate under High Pressure Neelam Yedukondalu, and Ganapathy Vaitheeswaran J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11386 • Publication Date (Web): 04 Jan 2019 Downloaded from http://pubs.acs.org on January 14, 2019

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The Journal of Physical Chemistry

Polymorphism, phase transition and lattice dynamics of energetic oxidizer ammonium perchlorate under high pressure N. Yedukondalu∗,†,‡ and G. Vaitheeswaran∗,¶,§ Advanced Centre of Research in High Energy Materials (ACRHEM), University of Hyderabad, Prof. C. R. Rao Road, Gachibowli, Hyderabad-500046, Telangana, India. , Department of Geosciences, Stony Brook University, Stony Brook, NY, 11794, United States. , School of Physics, University of Hyderabad, Prof. C. R. Rao Road, Gachibowli, Hyderabad-500046, Telangana, India. , and Advanced Centre of Research in High Energy Materials (ACRHEM), University of Hyderabad, Prof. C. R. Rao Road, Gachibowli, Hyderabad-500046, Telangana, India. E-mail: [email protected]; [email protected]

∗ To

whom correspondence should be addressed Advanced Centre of Research in High Energy Materials (ACRHEM), University of Hyderabad, Prof. C. R. Rao Road, Gachibowli, Hyderabad-500046, Telangana, India. †

‡ Department

of Geosciences, Stony Brook University, Stony Brook, NY, 11794, United States.

¶ School of Physics, University of Hyderabad, Prof. C. R. Rao Road, Gachibowli, Hyderabad-500046, Telangana, India. § Advanced

Centre of Research in High Energy Materials (ACRHEM), University of Hyderabad, Prof. C. R. Rao Road, Gachibowli, Hyderabad-500046, Telangana, India.

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Abstract Ammonium Perchlorate (AP) is an efficient energetic oxidizer with high density (1.95 g/cc) and positive oxygen balance (34 %) and it is being served as potential rocket propellant with proper mixture of metal powders/polymeric binders for a long time. In this work, we have systematically investigated the polymorphic phase stability, structural transition and lattice dynamics of AP under high pressure. From our total energy calculations, it is vivid that AP attains global minimum energy structure in Pnma symmetry over Pna21 , however, the difference is very small ∼1 meV per formula unit. Moreover, the calculated phonon dispersion curves reveal that AP is dynamically stable in both Pnma and Pna21 crystal symmetries at ambient pressure which unambiguously shows the existence of polymorphism in AP. The Pnma phase of AP is found to be mechanically unstable above 4 GPa from the computed mechanical stability criteria. The calculated pressure dependent phonon dispersion curves of Pnma phase discloses its dynamical instability at 10 GPa. Mechanical and dynamical instability of Pnma phase clearly demonstrates that AP undergoes a first-order structural phase transition above 4 GPa. The high pressure phase crystallizes in orthorhombic crystal symmetry (P21 21 21 ) at 6.9 GPa which is consistent with the recent experimental results. The anti-cooperative nature of hydrogen bonding and electrostatic interactions is the driving force for this structural phase transition in AP under high pressure.

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Introduction Ammonium Perchlorate (AP, NH4 ClO4 ) is a simple supermolecular system which attracted enormous interest due to its widespread applications in munitions, primarily as oxidizer for solid rocket and missile propellants, in fire-works, air-bag inflater in the automotive industry, and as a component of agricultural fertilizer. 1 Mixing this energetic oxidizer with fuels (metal powder or polymeric binders) generates a self sustained combustion and that makes the mixture as a powerful propellant for rocket launching applications such as NASA shuttle and ESA Arianc-5. Despite of potential applications of AP, its fundamental properties such as crystal structure and thermophysical properties are least understood at ambient as well as at high pressure. In one hand, the crystal symmetry of AP at ambient conditions is still a long debate for researchers whether it crystallizes in Pnma or Pna21 symmetry? Venkatesan 2 reported that AP crystallizes in Pnma symmetry with 4 f .u./cell which is consistent with the previous investigation. 3 However, Peyronel et al 4 re-determined the crystal structure of AP as orthorhombic structure with space group Pna21 . Later series of investigations 5–10 were carried out to determine the crystal structure of AP and they found that AP crystallizes in Pnma symmetry rather than Pna21 . 4 Following, Zhang et al 11 redetermined the crystal symmetry of AP as Pna21 . Davidson et al 12 and Hunter et al 13 revisited the crystal structure of AP using Neutron and X-ray powder diffraction techniques and they observed that AP crystallizes in orthorhombic structure with Pnma symmetry. Very recently, Kang and coworkers 14 reported that AP crystallizes in Pnma symmetry using in − situ angle-dispersive X-ray diffraction (ADXRD) measurements in contrast to Kroonblawd et al 15 who observed that AP crystallizes in Pna21 symmetry based upon synchrotron ADXRD measurements at ambient pressure. In addition, they also proposed that the two structures are practically indistinguishable due to more similarities in their structures but having differences in the positions of hydrogen atoms. On the other hand, energetic materials bind through weak intermolecular interactions and these weak interactions are easily tuned by high pressure. High pressure studies on energetic materials not only provide deep insight on structural phase transitions and polymorphism but also allow us to design novel high energetic density materials. For instance, ammonium and perchlorate ions 3



in AP crystal are bonded through weak hydrogen bonding and electrostatic interactions. 9 Extensive studies were devoted to explore the high temperature behavior 16,17 and thermal/shock induced decomposition 18–24 of AP. Peiris et al 10 investigated the pressure effects on structural and spectroscopic properties of AP up to 5.6 GPa using X-ray diffraction, IR and Raman spectroscopic measurements and they reported two first order phase transitions below 3 GPa (at ∼0.9 and ∼2.9 GPa). However, a high pressure neutron diffraction study disclosed that AP undergoes an iso-structural phase transition to a more closely packed structure (phase-II crystallizes in Pnma symmetry, which is 8.6 % denser than phase I) at 3.98 GPa and also phase-II is found to be stable up to 8.1 GPa. 13 High pressure-temperature phase diagram of AP is determined using Raman spectroscopy up to 50 GPa and 450 o C, and they observed a series of phase transition from phase I → II → III → IV at 4.5, 9.9, 27 GPa respectively. 25 The latest combined high pressure in − situ 14 and synchrotron 15 ADXRD and Raman spectroscopic measurements determined that the high pressure phase of AP crystallizes in P21 21 21 and P2 symmetries, respectively and these observations are in contrast to the previously observed iso-structural transition in AP under high pressure. 13,25 On the theoretical perspective, Zhu et al 26 reported thermo-physical properties such as electronic, vibrational and thermodynamics of AP and ammonium dinitramide (ADN) at ambient pressure. Further, they have extended their study to investigate the effect of hydrostatic pressure on structure, electronic and vibrational properties of AP in Pna21 crystal symmetry. 27 Also a theoretical high pressure study on AP disclose that it undergoes a series of structural phase transitions at 1, 4, and 9 GPa 28 and the authors used Pna21 crystal symmetry in their calculations. 27,28 High pressure studies 29,30 of AP with Pnma crystal symmetry including van der Waals interactions explores the structure, electronic, vibrational and absorption properties. Wu et al 29 reported that AP undergoes a structural phase transition at 60 GPa. Therefore, there is an inconsistency between experimental and theoretical studies, within the experimental measurements either using X-ray diffraction and/or spectroscopic measurements on the phase stability of AP. In order to resolve the crystal symmetry at ambient pressure as well as to explore the phase stability of AP under high pressure. In this work, we have investigated polymorphism, pressure induced structural transition, mechanical

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and lattice dynamical properties of AP using additive pair-wise 31–33 dispersion corrected (DC) methods within the frame work of density functional theory.

Methodology and computational details Crystal structure, phase stability and mechanical properties were calculated using projector augmented wave (PAW) method as implemented in VASP package. 34 To treat electron-electron interactions, Perdew-Burke-Ernzerhof parametrization within the generalized gradient approximation (GGA) was considered as the exchange-correlation functional. 35 To obtain the ground state structures at different hydrostatic pressures, geometry optimizations were performed by enabling the convergence criteria less than 1.0 × 10−8 eV for total energies, maximum forces on each atom should be less than 1.0 ×10−4 eV/Åand stresses are less than 0.02 GPa. In order to capture the weak dispersion interactions in the studied ionic-molecular solid AP, we have used additive pairwise DC methods namely D2, 31 TS 32 and TS-SCS 33 as implemented in VASP package. 34 Lattice dynamical calculations were carried out using plane wave pseudo potential (PW-PP) approach within density functional perturbation theory (DFPT) as it was incorporated through CASTEP package. 36 Geometry optimization is performed at ultra-fine quality settings (Energy < 5.0×10−6 eV/atom, maximum force < 0.01 eV/Åand stress < 0.02 GPa) prior to the lattice dynamical calculations using TS method. 32 Normconserving 37 PW-PPs were employed to compute the lattice dynamical properties. The calculations were performed by adopting 950 eV of plane wave cutoff energy and the Brillouin zone is sampling with 2π ×0.04 Å−1 k-spacing according to the Monkhorst-Pack grid scheme. 38 The pressure dependent elastic constants of AP in Pnma symmetry are calculated using VASP as well as with recently developed Finite Pressure Temperature Elasticity (FPTE) 39 package. Both the packages work based on stress-strain relationship but the later one includes pressure correction to the elastic moduli at finite pressure which shows significant contribution especially at high pressures.

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Figure 1: (Color online) Unit cell of AP in Pnma (top) and Pna21 (bottom) symmetries. White, blue, red and light green balls represent hydrogen (H), nitrogen (N), oxygen (O) and chlorine (Cl) atoms, respectively.

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Results and discussion Crystal structure, phase and dynamical stability at ambient pressure As discussed in section I, there is a long debate pertaining to the crystal symmetry of AP whether it crystallizes in centrosymmetric Pnma or non-centrosymmetric Pna21 space group at ambient conditions? In this work, we have investigated relative phase and dynamical stability of AP in these two (Pnma and Pna21 ) crystal symmetries to uncover its thermodynamic ground state. The two crystal symmetries having group-subgroup relationship, 15 and the crystal structure details are summarized in figure 1. In Pnma symmetry, nitrogen, chlorine, two hydrogen and two oxygen atoms occupy 4c Wyckoff cite whereas third oxygen (O3) and hydrogen (H3) atoms occupy 8d Wyckoff cite (see Table 1) and each atom has an inversion center. While in Pna21 symmetry, all the atoms are inequivalent and they occupy 4a Wyckoff cite (see Table 2) as illustrated in figure 1. The four oxygen atoms attached to the chlorine atoms which are involved in the hydrogen bonding through three (Pnma)/four (Pna21 ) inequivalent hydrogen atoms (see figure 1). As depicted in figure 2, Hi(i=1-3)(H3 has equivalent H3′ atom) and Hi(i=1-4) atoms involves in four individual hydrogen bonds to form a periodic wave nature of hydrogen bonding network with neighboring oxygen atoms in Pnma (along xy plane) and Pna21 (along xz plane) crystal symmetries of AP, respectively. By seeding the single crystal X-ray diffraction data as an input, 4,6,9,11,13,15 we simultaneously relaxed both lattice constants and fractional co-ordinates of AP using standard PBE-GGA functional and the dispersion correction (D2, TS and TS-SCS) methods. 31–33 The predicted equilibrium volumes within PBE-GGA functional are overestimated by around ∼ 7.5 % while the obtained equilibrium volumes using various DC methods are found to differ by -3.5 (-3.5) % using D2; +0.2 (+0.2) % using TS; and +0.1 (+1.5) % using TS-SCS methods in Pnma (Pna21 ) symmetry as presented in Table S1(S2) of the supplementary material along with the experimental results and other previous theoretical calculations. Where ’+’ and ’-’ signs represent over- and underestimation of equilibrium volume when compared to the experimental data. 12,13 Under- and overestimation of the lattice constants with similar magnitudes eventually lead to prediction of equilibrium volume

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(a)

(b)

Figure 2: (Color online) The similar periodic wave type hydrogen bonding network of AP in (a) Pnma and (b) Pna21 symmetries. Same color convention is followed for the atoms (H, N, O and Cl) as described in figure 1. 8 ACS Paragon Plus Environment

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closely comparable with the experiments using TS and TS-SCS method as previously reported 13 for AP using TS and D2 methods in Pnma symmetry using CASTEP package. We observe from our present as well as Hunter et al 13 studies, TS and TS-SCS methods reproduce the experimental trends relatively good for AP when compared to D2 method. Therefore, we have used the TS method to identify the correct crystal symmetry of AP in which it crystallizes as a thermodynamic ground state. -189.59 Pnma Total energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Pna2

1

-189.60

-189.61

-189.62

390

395

400 Volume (

405

Å)

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415

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Figure 3: (Color online) Calculated total energy as a function of volume for Pnma and Pna21 crystal symmetries of AP. In Pnma symmetry, AP has lowest energy than Pna21 symmetry which is the thermodynamic ground state of AP at ambient pressure. Low total energy difference (∼ 1 meV/f.u.) between the two crystal symmetries reveals the existence of polymorphism in AP at ambient pressure. As illustrated in figure 3, the calculated total energy curves as a function of volume disclose that AP possesses the lowest energy structure when it crystallizes in the Pnma symmetry rather than Pna21 crystal symmetry which is consistent with the experimental measurements. 13,25 How− ever, there are minor differences in the molecular (NH+ 4 and ClO4 ) arrangements between two

space groups (see figure 1) resulting in very less energy difference (∆E = ∼ 1 meV/f.u.) between these two structures which makes them practically indistinguishable. 15 Therefore, it becomes a

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tedious task for the experimentalists to differentiate whether AP crystallizes in Pnma and Pna21 symmetry? In order to get further insight on phase stability of both crystal symmetries of AP, we also computed phonon dispersion curves along high symmetry directions of the Brillouin zone which explores the dynamical stability of AP in these two crystal symmetries. Interestingly, we found that AP is dynamically stable at ambient pressure in both the crystal symmetries as depicted in figure 4, which implies that AP exists in both the crystal symmetries (Pnma and Pna21). Relatively very low total energy difference (∆E = ∼ 1 meV/f.u.), similar hydrogen bonding networks and dynamical stability of the two structures clearly demonstrates the existence of polymorphism in AP at ambient conditions.

Structural properties and phase transition of AP under high pressure Further, in the present study, we have used Pnma (phase I) crystal symmetry which is the thermodynamic ground state of AP for computation of structural, mechanical and lattice dynamical properties under high pressure. Moreover, crystal structure, elastic constants, vibrational properties and their detailed analysis under hydrostatic pressure in Pna21 crystal symmetry can be found elsewhere. 27,28 The obtained equilibrium structure at 0 GPa has been used to carry out structural relaxations in the pressure range 0-4 GPa with a step size of 0.5 GPa. The pressure dependent lattice constants a and b are strongly over- and under-binded, respectively while the lattice constant c follows the trends of PBE-GGA functional (see figure S1) throughout the studied pressure range. The predicted trends in the present work are consistent with the theoretical calculations by Hunter et al. 13 In addition, Hunter et al 13 observed an iso-structural transition under high pressure using combined X-ray and neutron diffraction measurements around 3.98 GPa with an associated volume collapse of 1.8%. 13 Very recently, high pressure in − situ angle-dispersive X-ray diffraction (ADXRD) measurements by Kang and co-workers 14 reported that AP undergoes to a monoclinic (P2) symmetry at 2.6 GPa and also the ambient phase co-exists with the P2 phase in a wider pressure range from 2.6-11.5 GPa due to slow transition kinetics. Simultaneously, Kroonblawd et al 15 reported that AP undergoes a transition to barite-type structure (which crystallizes in orthorhombic 10


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symmetry P21 21 21 (phase II) space group with Z = 4) at ∼ 4 GPa with an associated volume collapse of ∼ 3.3 % based on synchrotron ADXRD and Raman spectroscopic measurements. They also performed first principles calculations and predicted the transition pressure from phase I → II at 8.8 GPa using D3 method but this work does not provide atomic positions for the hydrogen atoms. In the present work, we have considered the experimental structure as an input (without hydrogen atomic positions) 15 and we have predicted the atomic positions of hydrogen atoms of phase II by taking several plausible combinations and relaxing them by preserving the crystal symmetry. The inequivalent (H, N, O and Cl) atoms of the phase II occupy 4a Wyckoff positions (see Table 3) and the complex hydrogen bonding network of phase II are shown in figure S2. As illustrated in figure 5, the calculated relative enthalpy difference of both phase I and II shows that AP undergoes a structural transition from phase I → II at 6.9 GPa within TS method which is closely comparable with the experimental transition pressure of ∼ 4 GPa when compared to 8.8 GPa which is obtained from D3 method. 15 The transition is associated with a volume collapse of 1.8 % which is in good agrement with experimental volume reduction of 1.8 % 13 and 3.3 % 15 as shown in figure 6a. The calculated lattice constants of phase II are decreasing with pressure (see figure 6b). The computed lattice constants and fractional coordinates of ambient (Pnma, Pna21 ) and high pressure (P21 21 21 ) phases of AP are summarized in Tables 1, 2 and 3, respectively within TS method along with the experimental data. 4,7,13,15 We have also calculated the normalized lattice constants of phase I of AP and the computed normalized lattice constants with pressure are presented in figure S1d. With the applied hydrostatic pressure, the lattice constants a, b and c attenuate with distinct compressibilities 94.8, 95.9 and 96.0 % in the studied pressure range. While the experimentally determined axial compressibilities such as a/a0 , b/b0 and c/c0 ) are 94.4, 96.7 and 95.2 % in the pressure range 0.01-3.49 GPa. The calculated axial compressibilities are in very good accord with the experimental data. 13 Also, from the calculated axial compressibilities, AP lattice is found to be the most compressible along a-axis among three (a, b, c) crystallographic axes, which is due to weak intermolecular hydrogen bonding along the a-axis (see figure S1d). As depicted in figure 6, the calculated volume of Pnma phase is

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3240

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T

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X

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Figure 4: (Color online) Calculated phonon dispersion curves of AP in Pnma (left) and Pna21 (right) crystal symmetry at 0 GPa pressure. The three panels represent (a, b) lattice modes including torsional and bending modes of NH4 and ClO4 ions (c, d) N-H wagging, rocking and scissoring modes and ClO4 asymmetric modes (e, f) N-H symmetric and asymmetric stretching modes of AP. 12


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Table 1: Calculated ground state lattice constants and fractional co-ordinates of AP in Pnma symmetry within TS method along with experimental data 7,13 Method This work (0 GPa)

Expt 7 (0 GPa)

Expt. 13 (0.01 GPa)

Lattice Atom parameters (Wyckoff) a = 8.734 N (4c) b = 6.259 Cl (4c) c = 7.343 O1 (4c) O2 (4c) O3 (8d) H1 (4a) H2 (4a) H3 (8d) N (4c) Cl (4c) O1 (4c) O2 (4c) 03 (8d) a = 9.2186 N (4c) b = 5.8108 Cl (4c) c = 7.4505 O1 (4c) O2 (4c) O3 (8d) D1 (4c) D2 (4c) D3 (8d)

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x

y

z

0.1722 0.4241 0.2824 0.5579 0.4255 0.2674 0.2042 0.1062 0.3191 0.4318 0.3142 0.5680 0.4203 0.1887 0.4287 0.3119 0.5651 0.4187 0.2932 0.191 0.1353

0.75 0.25 0.25 0.25 0.0586 0.75 0.75 0.6161 0.2500 0.2500 0.2500 0.2500 0.0487 0.75 0.25 0.25 0.25 0.0484 0.75 0.75 0.6056

0.1868 0.1884 0.0791 0.0683 0.3054 0.1047 0.3226 0.1602 0.6645 0.1916 0.0664 0.1019 0.3036 0.1537 0.1888 0.0609 0.0954 0.3002 0.105 0.2915 0.1090



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Table 2: Calculated ground state lattice constants and fractional co-ordinates of AP in Pna21 symmetry within TS method along with experimental data 4,15 Method

lattice parameters This work a = 8.738 (0 GPa) b = 7.343 c = 6.627

Expt. 4 (0 GPa)

a = 9.227 b = 7.454 c = 5.819

Expt. 15 (0 GPa)

a = 9.240 b = 7.463 c = 5.807

Atom (Wyckoff) N (4a) Cl (4a) O1 (4a) O2 (4a) O3 (4a) O4 (4a) H1 (4a) H2 (4a) H3 (4a) H4 (4a) N (4a) Cl (4a) O1 (4a) O2 (4a) O3 (4a) O4 (4a) H1 (4a) H2 (4a) H3 (4a) H4 (4a) N (4a) Cl (4a) O1 (4a) O2 (4a) O3 (4a) O4 (4a)

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x 0.1724 0.4243 0.4257 0.4257 0.5580 0.2827 0.2041 0.2678 0.1066 0.1066 0.18094 0.43199 0.42064 0.42004 0.56815 0.31487 0.150 0.273 0.150 0.146 0.832 0.063 0.080 0.210 0.092 -0.049


y

z

0.3132 -0.2496 0.3115 0.2504 0.1944 0.4418 0.1945 0.0589 0.4315 0.2504 0.4209 0.2504 0.1773 -0.2496 0.3950 -0.2496 0.3382 -0.1156 0.3382 -0.3840 0.33411 -0.24876 0.30821 0.25082 0.19487 0.45055 0.19770 0.04628 0.39857 0.25745 0.43483 0.24550 0.220 -0.245 0.350 -0.250 0.375 -0.125 0.375 -0.378 0.325 0.780 0.194 0.240 0.295 0.402 0.056 0.248 0.306 0.021 0.093 0.219

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monotonically decreasing with pressure (see figure S1e). We have also obtained equilibrium bulk modulus (B0 ) and pressure derivative of bulk modulus (B′0 ) for phase I and II of AP by fitting the pressure-volume (P-V) data to 3rd order Birch-Murnaghan equation of state (B-M EOS). 40 The obtained B0 and B′0 values using PBE-GGA functional are severely underestimated as expected since the volume of AP with this functional is overestimated by ∼ 7.5% while the computed ones with DC methods are in reasonably good agrement with the experimental results 10,12,13 and recent other theoretical calculations 13,28 as presented in Table S3 for phase I. Therefore, we have computed the B0 and B′0 values for phase II of AP by fitting the P-V data to 3rd B-M EOS obtained from TS method in the pressure range 6.9-20 GPa. The calculated B0 (B′0 ) value 53.3 GPa (4.3) for phase II is overestimated (underestimated) when compared to the experimental value of 34.3 GPa (9.9) 15 which is due to overestimation of transition pressure that is reflected in underestimation of equilibrium volume of phase II resulting in the overestimation of bulk modulus compared to the experimental value. In order to reproduce the experimental B0 value, we have fitted the P-V data to 2nd order B-M EOS in the pressure range 4-20 GPa and the obtained B0 (B′0 ) is 30.3 GPa (4.0) which is closely comparable with the experimental value of 32.13 GPa (4.0). 15 Understanding the inter- and intramolecular interactions in molecular solids is very essential to get a deep insight on structural phase transitions. The intramolecular N-H (N-H1, N-H2 and N-H3) bonds and intermolecular hydrogen bonds with oxygen of perchlorate i.e. H...O (H1...O2, H2...O1 and H3...O3) & their N-H...O distances are found to decrease with pressure as illustrated in figure S3. The high compressible behavior of AP lattice along a-direction is mainly due to the large compressible nature of H1...O2 and H3...O3 (O3′ ) intermolecular hydrogen bonds as illustrated in figure S3b. The intermolecular hydrogen bond angles N-H1(2)...O1(2) increase as a function of pressure to form a linear hydrogen bonding network. Overall, as pressure increases, the inter- and intramolecular interactions decrease to bring the ammonium cation and perchlorate anion to form a close packed structure with high density by forming strong hydrogen bonding networks within the studied pressure range.

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Table 3: Calculated ground state lattice constants and fractional co-ordinates of AP in P21 21 21 crystal symmetry within TS method along with experimental data 15 Method

Lattice parameters This work a = 7.478 (4.5 GPa) b = 6.328 c = 7.175

Expt 15 (4.5 GPa)

a = 7.394 b = 6.309 c = 7.077

Atom (Wyckoff) N (4a) Cl (4a) O1 (4a) O2 (4a) O3 (4a) O4 (4a) H1 (4a) H2 (4a) H3 (4a) H4 (4a) N (4a) Cl (4a) O1 (4a) O2 (4a) O3 (4a) O4 (4a)

x 0.627 0.625 0.469 0.781 0.407 0.663 0.311 0.283 0.478 0.419 0.626 0.627 0.467 0.833 0.441 0.692

y

z

0.279 0.589 0.241 0.090 0.192 0.203 0.278 0.208 0.930 0.526 0.063 0.962 0.748 0.786 0.850 0.0003 0.881 0.891 0.640 0.968 0.291 0.571 0.206 0.091 0.144 0.203 0.278 0.196 0.930 0.520 0.057 0.929

0.2

Pnma P212121

0 H - HPnma (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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6.9 GPa -0.2

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0

4

8 12 Pressure (GPa)

16

20

Figure 5: (Color online) Calculated relative enthalpy difference of high pressure phase (P21 21 21 ) w.r.t to ambient phase (Pnma) of AP. The ambient phase undergoes to a high pressure phase at around 6.9 GPa using TS method which is closely comparable with the experimental transition transition pressure of ∼ 4 GPa compared to the calculated transition pressure of 8.8 GPa with DFT-D3 method 16


Page 17 of 34

400

Pnma 3

Volume (Å )

360

∆V/V = 1.8 % 320 P212121

280

5

0

10 Pressure (GPa)

15

20

(a)

a b c

8 Lattice constant (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


P212121

Pnma

7

6

0

5

10 Pressure (GPa)

15

20

(b)

Figure 6: (Color online) Calculated (a) volume and (b) lattice constants of low (Pnma) and high pressure (P21 21 21 ) phases of AP as a function of pressure using TS method.

17



Table 4: Calculated and experimental elastic constants (Ci j in GPa) of AP in Pnma symmetry. Parameter This worka This workb Expt.c Expt.d Otherse C11 27.0 27.7 25.1 22.97 24.62 C22 30.4 30.9 24.6 23.56 25.51 C33 41.1 42.3 31.5 30.12 32.30 C44 7.7 7.8 6.6 4.69 5.89 C55 9.5 9.7 4.7 5.84 5.99 C66 9.5 9.3 10.3 9.64 8.37 C12 17.1 17.4 16.3 16.60 16.04 C13 12.7 12.6 11.5 7.35 10.32 C23 10.8 10.6 7.6 10.33 9.24 a Calculated elastic constants using VASP in Pnma symmetry b Calculated elastic constants using FPTE method interfacing with VASP in Pnma symmetry c Measured elastic constants using Brillouin scattering: Ref. 41 d Measured elastic constants using ultrasonic resonance frequencies: Ref. 42 e Calculated elastic constants using CASTEP in Pna2 symmetry: Ref. 28 1

Elastic constants and mechanical stability under high pressure Elastic constants not only provide the fundamental knowledge on mechanical stability but also give good insight on the strength of intermolecular interactions. Exploring strength of intermolecular interactions under high pressure provides an insight on understanding the compressibility and pressure induced structural phase transformations especially for molecular crystalline solids. AP is an ionic-molecular solid, therefore, the computation of elastic constants and lattice dynamical properties are essential to disclose the stability of AP at ambient as well as at high pressure. AP has nine independent elastic constants since it crystallizes in the orthorhombic structure at ambient conditions in Pnma symmetry. 13,25 The calculated second order elastic constants using VASP as well as with FPTE method are given in Table 4 along with the experimental data and there is a close agreement between our calculated ones and observed elastic constants using Ultrasonic and Brillouin scattering measurements. 41,42 This clearly shows the reliability of FPTE method in computing the second order elastic constants. Liu et al 28 calculated the pressure dependence of elastic constants of AP in Pna21 symmetry using CASTEP package. The calculated second order elastic constants obey well known Born’s stability criteria which indicates that AP is mechanically stable at ambient pressure. The three diagonal elements (C11 , C22 , C33 ) of elastic tensor can be used to 18


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Page 19 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


correlate the strength of intermolecular interactions in a molecular crystal along three (a, b, and c) crystallographic directions and also this correlation could be consistent with compressibilities of lattice along the crystallographic axes. The calculated elastic constants follow the trends as C11 < C22 < C33 which is consistent with axial compressibility results (as discussed in section IIIB). The trends determined by experimental measurements 42 C11 < C22 < C33 which is in contrast to the trends C22 < C11 < C33 followed by Brillouin scattering measurements of Vazquez et al. 41 However, the difference in the magnitude between the two elastic constants C11 & C22 is relatively very small which is approximately ∼ 0.5 GPa. The inclusion of pressure correction in FPTE method (see figure 7a) reflects in the magnitude of elastic constants under high pressure when compared to the computed pressure dependent elastic constants using VASP (see figure S4a). The evolution of shear (C55 & C66 ) and dilation (C13 & C23 ) elastic constants with pressure shows the importance of pressure correction in calculating pressure dependent elastic constants and the details are found elsewhere. 39 When non-zero hydrostatic pressure is applied to a crystal, the derived mechanical stability criteria from Sinko and Smirnov modified elastic constants 43,44 in general and for an orthorhombic AP crystal in particular are simultaneously satisfied. With the modified elastic constants, the derived mechanical stability criteria M2 and M3 (the derived equations for M2 and M3 are given in our previous study 45 for an orthorhombic symmetry) are violated above 4 GPa for the investigated compound as presented in figure 7a & b. This clearly demonstrates that the mechanical instability of AP above 4 GPa which is closely comparable with the experimentally determined phase transition pressure of 3.98 GPa using X-ray and neutron diffraction measurements. 13,15

Lattice dynamics and IR spectra under high pressure Lattice dynamical properties (phonon dispersion & density of states and IR/Ramam spectra) provide good insight on structural stability, phase transitions and bonding properties of materials. To understand the dynamical stability and hydrogen bonding at ambient well as at high pressure, we have calculated phonon frequencies of AP at centre of Brillouin zone. Since AP consists of 40 atoms per cell, which results in 120 vibrational modes and symmetry decomposition of vibrational 19



80

Elastic constants (GPa)

60

C11

C66

C22

C12

C33

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C44

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C55

40

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(a) M3

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0 4

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0 2

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2

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5

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(b)

Figure 7: (Color online) Calculated (a) second order elastic stiffness coefficients and (b) derived mechanical stability criteria of AP in Pnma symmetry as a function of pressure using FPTE packages. M2 and M3 violate the mechanical stability criteria above 4 GPa of pressure. The equations for M2 and M3 can be found elsewhere. 45

20


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modes for AP in orthorhombic Pnma symmetry is as follows: Γacc = B1u ⊕ B2u ⊕ B3u Γopt = 17B1u ⊕ 11B2u ⊕ 17B3u ⊕ 12B1g ⊕ 18B2g ⊕ 12B3g ⊕ 18Ag ⊕ 12Au Earlier Zhu et al 26,27 and recently Wu et al 29 made a detailed vibrational analysis of each vibrational mode at centre of Brillouin zone using Pna21 and Pnma space groups, respectively. As discussed in section IIIA, we have shown that AP has global minimum energy when it crystallizes in Pnma space group and it is referred as thermodynamic ground state (see figure 3). AP is found to be dynamically stable at 0 GPa from the calculated phonon dispersion as shown in figure 4. Further to identify the dynamical stability of AP at high pressure, we have also calculated the phonon dispersions at high pressures 5 and 10 GPa. We could see that all phonon modes are real along high symmetry directions of the Brillouin zone at 5 GPa whereas soft acoustic lattice mode is observed at 10 GPa along Γ-direction (see figure 8b) and the corresponding vibrational eigen vector is depicted in figure 9a. This clearly indicates dynamical stability and instability of AP at 5 and 10 GPa of pressures, respectively as depicted in figure 8. The results suggest that AP undergoes a first order type structural phase transition since in the first order phase transition the structural phase change occurs before the mode frequency is able to goes to zero. 46 Despite of potential applications of AP as an oxidizer in rocket propellent applications, the presence of toxic perchlorate ion causes acid rains and it can show significant affect on the function of thyroid gland. Therefore, there is an extensive research devoted to discover an alternative for AP but it becomes difficult to replace AP because of its high oxygen balance, density, moderate energetic performance (6.50 km/s and 17.64 GPa), 47 structural stability and less hygroscopic nature. For instance, ADN is found to be an alternative for AP. In our previous study, 47 we have compared the calculated IR spectra of AP and ADN at ambient pressure which shows that red-shift of N-H stretching frequencies of ADN when compared to AP which clearly suggests strong hydrogen bonding nature of ADN over AP which is the drawback of ADN in spite of its high energetic performance (8.09 km/s and 25.54 GPa) and eco-friendly nature. Therefore, ADN can form strong hydrogen bonding networks with moisture in the atmosphere which eventually leads to more hygroscopic nature of ADN over AP 48

21



600 -1

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-1

)

)

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3300

3240

3300

3240

3180

3180

Z

T

Y

S

X

U

R

(e)

Z

T

Y (f)

Figure 8: (Color online) Calculated phonon dispersion curves of AP in Pnma symmetry at 5 (left) and 10 GPa (right) of pressures. The imaginary lattice modes show the dynamical instability of AP at 10 GPa. The three panels left (5 GPa) and right (10 GPa) represent the same vibrational analysis as illustrated in FIG. 4. 22


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and our results are consistent with the experimental data. 48 Later, we turn our attention to under-

Figure 9: (Color online) Selected eigen vectors (a) lattice mode (becomes imaginary at 10 GPa) (b) symmetric stretching (c & d) asymmetric stretching modes of AP in Pnma symmetry. stand the high pressure spectroscopic behavior of AP. Pressure dependent IR spectra provides a good insight on exploring the phase stability and possible correlation on how strength of hydrogen bonding varies as a function of pressure. 45,47 As illustrated in figure 10, the lattice vibrational mode frequencies arise from both NH4 and ClO4 molecular ions oscillations, rotation and translation motion of NH4 units which are increasing with pressure. This clearly indicates hardening of lattice up on compression as depicted in figure 10a & b. The bending, symmetric and asymmetric stretching vibrational modes of ClO4 anions show blue-shift under pressure as presented in 23



figure 10c. The internal vibrational modes such as N-H bending, rocking, scissoring, symmetric and asymmetric modes show blue-shift as a function of pressure. However, B2u modes in the frequency ∼ 1416 cm−1 , which lift the degeneracy due to strong coupling between NH4 and ClO4 units leading to blue- and red-shift of these vibrational modes under high pressure as shown in figure 10d & e. This results demonstrate that rotation of NH4 and ClO4 molecular units as a function of pressure. Finally, the N-H symmetric and asymmetric stretching modes (see figure 9) show blue-shift with increasing pressure due to shortening of N-H intramolecular interactions (see figure S3a) as a function of pressure up to 10 GPa as illustrated in figure 10f. 49 The possible mechanism for structural phase transition in AP is similar to the ionic-molecular solids under high pressure. AP is a simple supramolecular system in which NH4 and ClO4 ions are bound together by two dominant noncovalent interactions namely hydrogen bonding and electrostatic interactions at ambient pressure. As pressure increases, the NH4 and ClO4 ionic-molecular units become close to each other due to reduction in the distances between two the adjacent molecules to form a closely packing structure with high crystal density as observed in Hunter et al 13 and Dunuwille et al 25 studies using X-ray and Raman spectroscopic measurements. The electrostatic interactions are enhanced between NH4 and ClO4 ions and hydrogen bonding is also strengthened due to close packing structure at high pressure. With further compression, the Gibbs free energy of the AP crystal increases which eventually leads to anti-cooperative nature between hydrogen bonding and electrostatic interactions above ∼ 4 GPa due to rotation of the NH4 ions which is reflected in the bending vibrational modes of AP as a function of pressure (see figure 10d). In both Hunter et al 13 and Dunuwille et al 25 studies, they observed a iso-structural phase transition at ∼ 4 GPa and Kang et al 14 proposed that high pressure phase of AP crystallizes in P2 symmetry. However, very recent high pressure study 15 on AP reported the crystal structure of high pressure phase and the present study results are consistent with the recently determined crystal structure 15 of high pressure phase of AP.

24


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1700

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-1 ) Frequency (cm

(e)

3150

3200

3250

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3350

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-1 ) Frequency (cm

(f)

Figure 10: (Color online) Calculated Infrared spectra (a) lattice modes (b) torsional and bending modes of NH4 and ClO4 ions (c) ClO4 asymmetric modes (d, e) N-H wagging, rocking, scissoring and bending modes (f) N-H symmetric and asymmetric stretching modes of AP in Pnma symmetry as a function of pressure.

25



Conclusions In conclusion, first principles calculations were carried out to investigate phase stability, structural phase transition and lattice dynamical properties of AP under high pressure. The predicted ground state properties such as lattice constants, equilibrium bulk modulus, pressure derivative of bulk modulus using pair-wise dispersion corrected methods are consistent with the experimental results as well as recent theoretical calculations. The low total energy difference and dynamical stability of AP in both Pnma and Pna21 crystal symmetries at ambient pressure indicating the polymorphism in AP at ambient conditions. AP attains global minimum energy structure when it crystallizes in Pnma symmetry and it is designated as thermodynamic ground state of AP. The calculated axial compressibility along three crystallographic axes follow the order as a > b > c and the corresponding second order elastic constants increases from C11 → C22 → C33 due to weak intermolecular hydrogen bonding along a-axis. All the calculated elastic constants increase with pressure except elastic constant C11 which shows soft nature at around 5 GPa. Mechanical instability of AP in Pnma symmetry around 4 GPa is predicted from the derived mechanical stability criteria under hydrostatic pressure. In addition, the computed phonon dispersion curves under high pressure disclose the dynamical instability of AP at 10 GPa. Both mechanical and dynamical instability clearly demonstrates that AP undergoes a first-order structural phase transition to high pressure phase which crystallizes in orthorhombic (P21 21 21 ) structure at 6.9 GPa and it is in good accord with the recent experimental results. The anti-cooperative nature between the two noncovalent interactions hydrogen bonding and electrostatic interactions might be reason for the structural phase transition in AP under high pressure.

Supporting Information The supporting information contains ground state structural properties (Tables S1 and S2), equilibrium bulk modulus (Table S3) and lattice constants (Fig. S1), bond parameters (Fig. S3), elastic constants (Fig. S4) as a function of pressure and crystal structure of high pressure 26


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phase II (Fig. S2).

Acknowledgments Authors would like to thank DRDO through ACRHEM for financial support under Grant No. DRDO/18/1801/2016/01038:ACREHM-PHASE-III and the CMSD, University of Hyderabad, for providing computational facilities. NYK would like to thank Science and Engineering Research Borad and Indo-US Scientific Technology Forum for providing financial support through SERB Indo-US postdoctoral fellowship. NYK would like to thank Dr. M. Mahdi Davari Esfahani, Stony Brook University, NY, USA for his valuable discussions on FPTE package. Part of computation (pressure induced structural transition and pressure dependent elastic constants using FPTE package) were mainly performed on QSH cluster at Stony Brook University, NY, USA.

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(45) Yedukondalu, N.; Vaitheeswaran, G.; Anees, P.; Valsakumar, M. C. Phase Stability and Lattice Dynamics of Ammonium Azide under Hydrostatic Compression. Phys. Chem. Chem. Phys. 2015, 17 (43), 29210-29225. https://doi.org/10.1039/C5CP04294A. (46) Venkataraman, G. Soft Modes and Structural Phase Transitions. Bull. Mater. Sci. 1979, 1 (3-4), 129-170. https://doi.org/10.1007/BF02743964. (47) Yedukondalu, N.; Ghule, V. D.; Vaitheeswaran, G. High Pressure Structural, Elastic and Vibrational Properties of Green Energetic Oxidizer Ammonium Dinitramide. J. Chem. Phys. 2016, 145 (6), 064706. https://doi.org/10.1063/1.4959900. (48) Cui, J.; Han, J.; Wang, J.; Huang, R. Study on the Crystal Structure and Hygroscopicity of Ammonium Dinitramide. J. Chem. Eng. Data 2010, 55 (9), 3229-3234. https://doi.org/10.1021/je100067n. (49) N. Yedukondalu, Ph.D. dissertation, "Computational study of energetic materials under hydrostatic compression", University of Hyderabad, 2016.

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Polymorphism, Phase Transition and Lattice Dynamics of Energetic

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