Crystal Structures and Dynamical Properties of Dense CO2

Crystal structures and dynamical properties of dense CO2

Xue Yonga,1, Hanyu Liua,1,2, Min Wub, Yansun Yaoa, John S. Tsea,2, Ranga Diasc,3, and Choong-Shik Yooc,2

aDepartment of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Canada S7N 5E2; bCollege of Materials Science and Engineering, Zhejiang University of Technology, Hangzhou, 310014, People’s Republic of China; and cDepartment of Chemistry, Washington State University, Pullman, WA 99164-2816

Edited by Ho-kwang Mao, Carnegie Institution for Science, Washington, DC, and approved August 8, 2016 (received for review January 25, 2016)

Structural polymorphism in dense carbon dioxide (CO2) has attracted There are still many outstanding questions regarding the significant attention in high-pressure physics and chemistry for structures and structural transformation of solid CO2 at high the past two decades. Here, we have performed high-pressure temperature and high pressure (3). Among these, the following three experiments and first-principles theoretical calculations to investi- issues are deemed to be immediately significant. The first question is gate the stability, structure, and dynamical properties of dense whether phase IV at 18 GPa and 473 K indeed adopts a bent CO2 CO2. We found evidence that CO2-V with the 4-coordinated ex- molecular structure. It is not unreasonable to speculate that at high tended structure can be quenched to ambient pressure below pressure and high temperature when intermolecular interactions and 200 K—the melting temperature of CO -I. CO -V is a fully coordi- 2 2 thermal vibrations become stronger it may result in a bent CO2 as an nated structure formed from a molecular solid at high pressure intermediary to a fully 4-coordinated structure found in the higher- and recovered at ambient pressure. Apart from confirming the pressure phase V. Second, two three-dimensional extended struc- metastability of CO2-V (I-42d) at ambient pressure at low temper- tures (VTD and VCR) with different space groups synthesized fol- ature, results of ab initio molecular dynamics and metadynamics lowing two thermodynamic pathways were found to coexist in a (MD) simulations provided insights into the transformation pro- similar P-T region (14). Obviously, kinetic barriers associated with cesses and structural relationship from the molecular to the ex- the two transformations are critical in determining the final structure tended phases. In addition, the simulation also predicted a phase obtained at a given thermo-mechanical energy. Thus, characteriza- V′(Pna2 ) in the stability region of CO -V with a diffraction pattern 1 2 tion of the relative stability between these two structures is impor- similar to that previously assigned to the CO -V (P212121) structure. 2 tant to the understanding of the phase diagram. Finally, phase VI Both CO2-V and -V′ are predicted to be recoverable and hard with a Vicker hardness of ∼20 GPa. Significantly, MD simulations found (17) that was found at 70 GPa and 600 K was explained to be an isostructure to CO2-II and Stishovite (P42/mnm)withcarbonatoms that the CO2 in phase IV exhibits large-amplitude bending motions at finite temperatures and high pressures. This finding helps to surrounded by six oxygen atoms forming a highly distorted octahe- explain the discrepancy between earlier predicted static structures dral structure. Although the detailed structure of CO2-VI is still and experiments. MD simulations clearly indicate temperature ef- under debate, it is prudent to examine whether the temporal dy- fects are critical to understanding the high-pressure behaviors of namic structure can give rise to a dynamically disordered carbon dense CO structures—highlighting the significance of chemical atom that can situate in a sixfold coordination while maintaining its 2 3 kinetics associated with the transformations. favorite sp hybridization at high pressure and high temperature. The questions raised above underscore the importance of ki- carbon dioxide | molecular dynamics | high pressure | material science netic barriers and finite temperature dynamics of dense CO2 phases. A previous theoretical study using metadynamics (MD)

olid carbon dioxide (CO2) has a phase diagram rich in Spolymorphs, which exhibit great diversity in intermolecular Significance interactions, chemical bonding, and crystal structures (1–7). Colloquially known as dry ice, solid CO2 has a cubic Pa3 structure Using multiple theoretical techniques, the temperature and pres- (phase I) under ambient pressure (8). At around 10 GPa, the cubic sure dependence of the structures and dynamics of dense CO2 structure transforms to another molecular phase (Cmca,phase were investigated. Near the transition to the extended structure, CO2 molecules were found to exhibit large-amplitude bending III) with different stacking pattern of CO2 molecules. At sufficient vibrations. A 4-coordinated Pna21 structure (CO2-V′)withadif- compression, the molecular O = C = O bonds in solid CO2 are fraction pattern similar to CO2-V (P212121) was found. Both CO2-V replaced by an extended network of single C-O bonds, forming ′ 3 and -V are predicted to be metastable at ambient pressure. This CO4 tetrahedral units with sp hybridized carbon atoms. The onset result is in agreement with the experimental recovery of CO2-V of such transformation occurs at 20 GPa, where the phase III below 200 K at ambient pressure. This 4-coordinated structure P mnm Pnnm transforms to a pseudotetragonal phase II ( 42/ or ) formed from main group molecules was recovered from high ∼ P β above 500 K and then to phase IV ( 41212 -cristobalite struc- pressure. Both recovered fully extended CO2 solids possess high- ture) above ∼750 K (9–12). Continuing the compression to energy density and hardness. 40 GPa and then heating the product to 1,800 K, CO2 further transforms to a nonmolecular polymeric strucutre VTD with the Author contributions: H.L., J.S.T., and C.-S.Y. designed research; X.Y., H.L., and R.D. per- tridymite-like P2 2 2 structure (13, 14). Interestingly, following formed research; X.Y., H.L., and M.W., Y.Y., J.S.T., and C.-S.Y. analyzed data; and X.Y., H.L., 1 1 1 Y.Y., J.S.T., and C.-S.Y. wrote the paper. a different synthesis path, that is, heating the phase III first at The authors declare no conflict of interest. 20 GPa and then compressing the product to 39 GPa and heating This article is a PNAS Direct Submission. it again to ∼1,800 K, a different polymeric phase (CO2-VCR)ina 1X.Y. and H.L. contributed equally to this work. β-cristobalite–like I-42d structure was obtained (15, 16). The 2To whom correspondence may be addressed. Email: [email protected], John.Tse@ structural dependence on the thermodynamic synthetic pathway usask.ca, or [email protected]. indicates strong kinetics effects associated with the molecular-to- 3Present address: Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138. nonmolecular transformations, allowing many metastable struc- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. tures to form in dense CO2. 1073/pnas.1601254113/-/DCSupplemental.

11110–11115 | PNAS | October 4, 2016 | vol. 113 | no. 40 www.pnas.org/cgi/doi/10.1073/pnas.1601254113 Downloaded by guest on September 27, 2021 two distinct structures in the same thermodynamic region but prepared from different pathways suggested the importance of kinetic effects and the products may be metastable. The stability of the P212121 structure has been examined by a number of calculations where the theoretically optimized structure was found to deviate significantly from the structure proposed from experiment (3). We now have confirmed the proposed P212121 structure is indeed mechanically unstable, revealed from many imaginary branches of its phonon band structure at 40 GPa (Fig. 1A). The imaginary modes are located throughout the entire Brillouin zone, indicating the structure is also dynamically unstable at 0 K and 40 GPa. To explore the potential energy surface, we “shock” compressed the precursor structure, molecular phase III (Cmca), to 50 GPa at 300 K, using molecular dynamics simulations. A supercell con- sisting of 96 atoms was used in this calculation. Examinations of the time-dependent evolution in the stress tensor components and volume (Fig. 1A) have identified several structural transformations along the compression, following (expected) successive changes in 2 3 chemical bonding from sp hybridized molecular CO2 to mixed sp -sp and eventually to fully sp3 3D-extended structure (Fig. 1B). At step 23, the Cmca structure lost its molecular identity completely and transformed to a planar structure with mixed threefold (sp2) and fourfold (sp3) coordinated C atoms. Such a structural motif is similar to that previously proposed for the ionic CO2 (19). After ∼70 steps, the sp2 bonding in the structure is gradually replaced by sp3 bonding, linking the CO2 planes with their neighboring planes. At step 179, an extended sp3 bonded structure is fully developed. This structure has a Pna21 space group and is composed of 8 formula 3 units (f.u.) of CO2 (named here CO2-V′) in which all C atoms are sp hybridized with bridging O atoms. Note that this structure is different from another previously predicted fourfold coordinated structure (20) coincidentally with the same Pna21 space group but with 4 f.u. The discovery of two fourfold coordinated structures that are A formed from the molecular phase III is significant (Fig. 2 ). The CHEMISTRY calculated equation of states (Fig. 3) shows at 40 GPa, the β-cristobalite I-42d (VCR) structure is still the thermodynamic ground state, but the predicted Pna21 structure is substantially Fig. 1. Vibrational properties and structure changes under compression.

(A) Phonon band structure of experimental P212121 structure and temporal variation of the volume in the shock compression. (B) Distinctive intermediate structures found in the compression run. The arrows indicate significant changes in the chemical bonding.

(18) explored the minimum energy structures only in a limited P-T range of the potential energy surface. The dynamical behavior of the stable and metastable structures and the consequences to the observed structures were not investigated. Here, we performed extensive ab initio simulations of solid CO2 at finite temperatures and high pressures with the objective to resolve the discrepancies and controversies about the structural and dynamical properties of dense CO2. The results led to the prediction of the possible quench recovery of the extended phase. For this purpose, we have performed spectroscopic experiments to investigate the metastability of CO2-V at ambient pressure.

Structural Alchemy of Phase V (CO2-V) Despite extensive experimental and theoretical efforts, controversies still surround the origin and stability of two experimentally observed structures for phase V (3). The first reported phase V of CO2 was synthesized by compressing a sample to 44 GPa followed by laser heating to 1,600 K. The final structure was found to have the tridymite P212121 structure (CO2-VTD)(13).Atthesamepres- sure, another structure with a distorted β-cristobalite (CO2-VCR, I d in the -42 space group) was obtained (13) from a different Fig. 2. Candidate structures and phonon structure. (A) Candidate structures

thermodynamic path by first laser heating CO2 at 21 GPa and of dense CO2 obtained from shock compression. (B and C) Phonon band then compressing the sample to 41 GPa. Clearly, the existence of structure for Pna21-8fu structure at (B) 0 GPa and (C) 40 GPa.

Yong et al. PNAS | October 4, 2016 | vol. 113 | no. 40 | 11111 Downloaded by guest on September 27, 2021 structures, which is often overlooked but not uncommon in theoretical structural prediction studies at high pressure. The calculated X-ray diffraction (XRD) patterns of several low-energy structures are compared with the experimental result in Fig. 4. It is clear that the XRD pattern of the P212121 structure, after a geometry optimization, is in poor agreement with the experiment. Surprisingly, the calculated XRD data of the P-1 structure obtained from a MD relaxation with a 2 × 2 × 2 supercell of the P212121 structure are in better agreement with the experiment. Significantly, the calculated XRD pattern of Pna21-8fu is also in reasonable agreement with the experiment; in particular, the low-angle Bragg peak profiles are reproduced. The exceptions are two weak reflections predicted at 9.6° and 10.2° but apparently missing in the experiment. It is apparent that the kinetic (thermal barrier) effect is a critical factor in the formation of the fourfold coordinated nonmolecular CO2 solid. Depending on the thermodynamic path, a number of metastable structures can be formed. The I-42d distorted cristobalite structure (CO2-VCR) is the global minimum (11). The possible existence of the predicted Pna21-8fu (CO2-V′) structure that has a diffraction pattern similar to experiment also deserves detailed investigation. To fully evaluate the phase diagram, we have also searched for other stable solid CO2 phases between 0 GPa and 50 GPa, using the particle swarm optimization (PSO) structure prediction method (21). The structural search identified the experimentally observed I-42d structure along with several low-energy structures (Fig. 3) although not all of the structures revealed from molecular dynamics calculations. This observation is important as all structure search methods were designed to locate the global energy minimum structures and therefore not expected to yield metastable structure formed from low-energy transition pathways accessible at room temperature. The calculated transition pressures obtained from differences of the enthalpy (at 0 K) and Gibbs free energy (at 300 K) for the transformation of molecular CO2-III Cmca to CO2-VCR I-42d of 18 GPa and 20 GPa, respectively, are much lower than the experimentally observed Fig. 3. Stability of candidate structure. (A) Calculated enthalpies of candi- transition pressure of ∼40 GPa. A possible reason for such a date structures of solid CO2 as a function of pressure. A, Inset shows the delayed transition is the presence of a large kinetic barrier in Gibbs free energy difference of Cmca and I-42d structure at 300 K. the experiments. To overcome this barrier, the I-42d structure (B) Equations of states of dense CO2.(B, Inset) Expanded low-enthalpy region. was synthesized by first heating CO2-III at ∼20 GPa, likely to CO2-IV (P41212, α-cristobalite-like), followed by further compression and heating to produce phase VCR at 40 GPa. Such a more stable than P212121 (VTD). As well, the phonon band structures of the Pna21-8fu structure computed at 0 GPa (Fig. 2B) and 40 GPa (Fig. 2C) show no imaginary frequency, indicating that this structure is metastable and may be quench recoverable. It is also noteworthy that, from the calculated pressure-volume data, the Pna21-8fu structure is “denser” than the I-42d structure even though the latter is energetically more stable. Experimentally, the CO2-VCR (I-42d) structure was found to coexist with CO2-VTD (P212121)(14)TheI-42d, Pna21-8fu structures, as well as the P43212andPna21-4fu structures (Table S1) obtained from structure prediction (see below), are all composed of CO4 tetrahedral units with sp3 hybridized carbon atoms. The very small energy difference between these candidate structures may explain the diversity of observed structures of extended CO2 phase V in the pressure regime above 40 GPa. Slight changes in the experimental conditions (reaction path) may result in different products. The metastability of different structures with a similar sp3 carbon–oxygen network arises from the high kinetic barriers that hinder both forward and back- ward transformations. To examine possible reversible reactions, MD simulations were performed on the I-42d structure at 300 K and at reduced pressures. No structural transformations were observed after a long simulation, indicating the existence of a significant reverse transformation barrier. The existence of a Fig. 4. Calculated XRD data of several candidate structures compared with large kinetic barrier facilitates the formation of metastable experiment data.

11112 | www.pnas.org/cgi/doi/10.1073/pnas.1601254113 Yong et al. Downloaded by guest on September 27, 2021 constant-pressure constant-temperature molecular dynamics calculations. Therefore, we conjecture that the metastability of CO2-V is largely a manifestation of kinetics in origin. To provide insights into the observed metastability of CO2-V, we have performed MD (23–25) simulations to examine the structure evolution of CO2-V upon pressure unloading. Theo- retical details of the MD method have been documented in book chapters and reviews (23, 24). In essence, it is a conceptual ex- tension of the idea of constant-pressure MD simulation. By filling the energy minima with a series of history-dependent Gaussian potentials in collective variables (order parameters), the potential energy surface at finite temperature and pressure can be explored. In the case of structural phase transformation, the collective variables are the scaled lattice vectors of the supercell. The calculation was started with the β-cristobalite–like I-42d structure at 40 GPa and 300 K (Fig. S1A). Within the first Fig. 5. Experiential Raman and metastablity CO2-V. Raman spectra of CO2-V obtained during pressure unloading at ambient temperature (A) and low 120 metasteps, the free energy of the system dropped after re-

temperatures (B), showing the metastability of CO2-V at ambient pressure ducing the pressure. Then, the system stabilized at 0 GPa and below 200 K. there is little change in the enthalpy. After release of the pressure from 40 GPa, the simulation cell expanded, with the volume 3 3 per CO2 unit increased from 297.5 Å to 360.21 Å . The te- thermal path clearly helps to overcome the energy barrier, as the tragonal lattice constants a and b increased from 7.1 Å to 7.7 Å α β transition from -cristobalite-like phase IV to -cristobalite-like with only a very small change in the c axis. Very similar results phase V would require only the rotation of the O-C-O bond. were obtained using different Gaussian widths and heights (Fig. S1 B and C). The metadynamic calculations indeed confirm that Metastability of CO2-V at Ambient Pressure the I-42d structure of CO2-V can be preserved at 0 GPa (Fig. The chemical stability of molecular CO2 is traced to the presence S2), consistent with the experiment. of strong π bonding. The formation of single-bonded extended B = π CO2 (Fig. 1 ), however, indicated that the C O bond can be Mechanical Properties of Recovered CO2-V transformedtointermolecularσ bonds by applying pressure, Previously CO2-V was found as a crystalline superhard phase. leading to technically important polymorphs. The CO2-V (10, 13, With the metastability of this phase established, it is of great 14, 22) has been predicted to exhibit intriguing properties such as interest to evaluate the hardness of the recovered CO2-V at optical nonlinearity and superhardness in addition to the high- ambient pressure. For this purpose, we have performed stress– energy density, making it attractive as an energetic material. strain calculations (26) to compute the Vicker hardness of CO2-V However, this structure is thermodynamically stable only at high in both I-42d and Pna2 structures recovered at ambient pres- CHEMISTRY ∼ – 1 pressures (above 20 40 GPa), which poses a significant challenge sure. Fig. 6 shows the calculated shear and tensile strength along sp3 for the practical use. On the other hand, the metastability of the several crystallographic directions. The lowest pressure in which bonding is expected to result in considerable kinetic stability of the the stress collapses determines the hardness of the material. CO2-V that may be sufficient for an ambient-pressure recovery. Thus, the computed bulk and shear moduli of I-42d (Pna21-8fu) Experimentally, the transformation of CO2-V to CO2-I is strongly structures at 0 GPa are 130 GPa and 131 GPa (142 GPa and controlled by kinetics; the remnant of CO2-V can be seen well 124 GPa), respectively. Using the empirical hardness and shear below 10 GPa. This result demonstrates the possibility of kineti- modulus relationship (27), we estimate the hardness of Pna21- cally stabilizing CO2-V at low temperature at ambient pressure. 8fu and I-42d structures to be 22 GPa and 21 GPa, respectively. Fig. 5 shows the spectral evidence that CO2-V is indeed ki- These estimated values are verified from ab initio calculations of netically stabilized at ambient pressure below 200 K—the melt- the ideal strengths of the I-42d and Pna21-8fu structures. The ing temperature of CO2-I (dry ice). The presence of phase V is evident from its characteristic Raman ν(O-C-O) peak at − ∼670 cm 1 at ambient pressure. At ambient temperature (Fig. 5A), the ν(O-C-O) intensity of quenched CO2-V is strong over a large pressure range between 40 GPa and 10 GPa, but substantially reduces below 10 GPa and eventually disappears below 2–4 GPa, as CO2-V disassociates into CO2-I. In contrast, at low temperatures (Fig. 5B), the ν(O-C-O) intensity remains strong even at ambient pressure, as long as the temperature is main- tained below 200 K—the melting temperature of CO2-I at ambient pressure. The recovery of CO2-V at ambient pressure below 200 K re- veals a small thermal barrier (ΔT = 100 K < 0.01eV) to convert extended CO2-V into molecular CO2-I, which is in stark contrast to a large C-O bond energy (∼3–4 eV) required to disassociate the corner-shared tetrahedral network of CO2-V. Thus, it is conceivable that the observed small thermal barrier is due to the surface/interface melting of CO2-V, signifying the catalytic effect of CO2-I that zips off the extended network structure of CO2-V. The melting temperature of CO2-V, on the other hand, would be 2 substantially higher than 200 K and roughly proportional to ∼θD −2/3 −1 ρ or ∼1,100 K for θD = 670 cm for CO2-V at ambient pres- Fig. 6. Ideal strength. The calculated tensile and ideal strength (hardness)

sure in comparison with diamond. This expectation is confirmed by of I-42d (A and B)andPna21-8fu (C and D)CO2-V structures.

Yong et al. PNAS | October 4, 2016 | vol. 113 | no. 40 | 11113 Downloaded by guest on September 27, 2021 maximum bending amplitude is 6.7° at 300 K and increases to 9.8° at 600 K. The results obtained with the R-3c phase IV at 30 GPa are similar in the amplitudes of O = C = O bending of 7.0° and 9.6° at 300 K and 600 K, respectively. The results show even at a relatively high pressure of 30 GPa, the O-C-O linkage is highly fluxional and the instantaneous angles are severely bent. The large thermal fluctuation indicates the weakening of the 2 C-sp hybridization in O = C = O before the transformation to the sp3 hybridized tetrahedral network structure. In fact, similar thermal fluctuation was previously suggested for a dynamically 3 disordered, sixfold structure of CO2-VI while maintaining the sp hybridization on carbon atoms (17). Conclusions In summary, we have performed a comprehensive survey of the finite temperature structures of several high-pressure polymorphs of CO2 with MD calculations. This theoretical study expands the scope of previous work (e.g., ref. 18) and offers significant insight into the structure and structural transformations of various structures in the phase diagram of CO2.In particular, we find that temperature is an important factor for Fig. 7. The temporal evolution of the O-C-O angle of different CO2-IV phases. understanding the dynamical properties of dense CO2 phases. For example, in CO2-IV the molecules are found to execute large-amplitude bending fluctuation even at high pressures. The weakest stress and, therefore, the hardness for I-42d and Pna21- 8fu structures are 26 GPa and 27 GPa, respectively (Fig. 6), in most significant finding is the prediction and experimental con- favorable agreement with the empirical model. The results sug- firmation that metastable CO2-V can be recovered under am- gest that the recovered CO -V should be a hard material at bient pressure. This study demonstrates that an extended 3D 2 3 ambient pressure. fully sp solid synthesized at high pressure can be recovered below 200 K, the melting temperature of CO2-I. In addition, MD Dynamic Structure and Large-Amplitude Fluctuations in simulations also revealed a structure for CO2-V′ with the Pna21 CO2-IV space group with the calculated diffraction pattern in reasonable Now we turn our attention to the finite temperature dynamic agreement with the experimentally observed pattern of CO2-VTD. Pna properties of the intermediate CO2-IV that was reported to The 21 structure is also predicted to be quenchable and, like the be stable above 15 GPa at temperatures higher than 500 K by β-cristobalite I-42d structure, both recovered samples are relatively laser heating CO2-II and -III (10), in the intermediate pressure– hard with estimated Vicker hardness of 20 GPa. temperature range between the stability fields of molecular and nonmolecular extended 3D phases. The earlier powder XRD Methods performed in situ at 300–750 K and 11–50 GPa suggests that the Multiple computational techniques were used to study the temperature and structure of CO2-IV is in P41212 with bent CO2 molecules (10). pressure dependence of the structures and dynamics of dense CO2. The PSO Subsequent single-crystal X-ray work performed on a quenched structure prediction method was used to find the structure of CO2-V. Ab initio molecular dynamics and MD were performed to study the dynamical CO2 phase, after the initial synthesis at 11.7 GPa and 830 K and annealing at 15 GPa and 830 K (11), suggested a different stability and metastability of the extended CO2. The MD algorithm used in the present study uses scaled components of the edge vectors of the simu- structure in R-3c with linear CO2. Once again, the two different P T lation cell as collective variables (24, 25). The driving force that guides the structures were obtained following very different - paths and evolution of the simulation cell is the derivative of the Gibbs free energy that result has raised questions concerning the true stability re- R c with respect to the six collective variables, which were updated in every gion of the -3 structure (3). metastep toward a low-energy pathway to neighboring minima. The in- Here, we do not discuss the origin of the two structures, but ternal coordinates of the system were equilibrated in an ab initio molecular focus on the temporal variation of the O = C = O angle of dynamics simulation associated with every metastep. Phonons were calcu- molecular CO2. For this purpose NPT (N, number of particles; P, lated with a supercell method. For further details, see SI Methods. pressure; T, temperature) MD simulations were performed on the P41212 and R-3c structures at 30 GPa and two temperatures, ACKNOWLEDGMENTS. We thank Dr. Judah Goldwasser for his enthusiastic 300 K and 600 K. The results of the calculations are shown in encouragement and support. This study was supported by Defense Ad- = = vanced Research Projects Agency Grant W31P4Q-12-1-0009, National Science Fig. 7. It is clear in both structures the average O C O angle Foundation Division of Materials Research Grant 1203834, and the Carnegie- is 180°. However, the calculated fluctuations of the O = C = O US Department of Energy Alliance Center. X.Y. acknowledges financial sup- angle from linearity are substantial. For the P41212 structure, the port from the China Scholarship Council.

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