Technical Comments

Non-molecular Carbon Dioxide (CO2) Solids

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Science  07 Jan 2000:
Vol. 287, Issue 5450, pp. 11
DOI: 10.1126/science.287.5450.11a

Iota et al. (1) reported a new polymeric (non-molecular) phase of CO2 solid synthesized at high pressure (∼40 GPa in a diamond anvil cell) and at high temperature (∼1800 K by laser heating). Raman scatterings at various pressures were measured in situ, and the observed Raman frequencies differ significantly from those of molecular CO2. Iotaet al. tentatively assigned the spectra to a quartz-like phase of CO2. The new phase is nearly recoverable at ambient conditions (upon release of pressure, it retains the new structure all the way down to only 1 GPa, where it unfortunately reverts back to the molecular phase).

Shortly after this experimental work, Serra et al. (2) reported a total energy calculation of several possible phases of CO2 using plane wave pseudopotential density functional theory (PWP-DFT). They concluded that there should be a transition from a molecular phase to a phase isostructural to SiO2 α-quartz in the range of 35 to 60 GPa. Their results support the work of Iota et al.

We concurrently investigated polymeric phases of CO2theoretically (3) and concluded that the observed structure is not quartz, but cristobalite-like at pressures of at least up to many tens of gigapascals. We find that the β-cristobalite phase (I4̄2d) is lower in energy than α-quartz (P3221) by 0.4 eV/CO2. These results are obtained by using the local density approximation (LDA) and a plane wave cutoff of 29 Ry. A generalized gradient approximation (GGA) (4) was also used to evaluate the energies of the optimized structures, and was found to have little effect on the relative energetics of the polymeric phases. This energy difference is substantial and we expect that the theoretical technique of PWP-DFT that we used (5) can reliably predict the relative energetics of these structures.

To further substantiate this conclusion, we computed the vibration modes and their pressure dependence, and compared them with the Raman spectrum of Iota et al. Compared to that of α-quartz, our calculated Raman spectrum for β-cristobalite is far more consistent with the experimental data. The signature A1 mode at about 790 cm−1 (at 40 GPa) has an average pressure derivative of 3.2 cm−1/GPa, while our calculations give 3.5 cm−1/GPa and 2.0 cm−1/GPa for β-cristobalite and α-quartz, respectively. This mode in cristobalite is a bond stretching mode of oxygen with motionless carbon. The pressure derivatives of the other modes show a more striking contrast. In particular, the E mode near 900 cm−1(at 40 GPa) has little dependence on pressure (10 to 20 cm−1) in the Iota et al. experiments; the same pressure insensitivity of this mode is seen in our calculated spectrum of β-cristobalite, whereas in α-quartz we find a shift of over 150 cm−1. We believe that this and similar analyses of the other Raman modes, along with our total energy calculations, eliminate α-quartz as a possible candidate.

Serra et al. (2) also considered cristobalite, but did not favor it as a possible candidate. They chose a linear C–O–C bond angle in cristobalite (effectively transforming the I4̄2d structure to the “special case” Fd3̄m C9 structure). This would cause a mild energy increase in SiO2. However, unlike SiO2, CO2 has a deep energy minimum at the C–O–C bond angle near 124° (3). The energy difference between the linear system and one with an optimized C–O–C angle is nearly 2 eV/CO2. Thus, Serra et al. incorrectly concluded that cristobalite is a high energy structure. The other extreme of a C–O–C bond angle of 109° (defective chalcopyrite) also yields a high energy structure. These considerations underscore that assumptions about the properties of CO2 based on the behavior of SiO2 will likely be incorrect. The small energy difference between the wide range of SiO2 polymorphs is largely a result of SiO2's tolerance for a wide range of Si-O-Si inter-tetrahedron angles, while the C–O–C bond angle is quite stiff about the 124° minimum.

REFERENCES AND NOTES

Non-molecular Carbon Dioxide (CO2) Solids

Response: Dong et al. discuss the results of structural refinement calculations that they made on some of the non-molecular CO2 phases that we proposed in our work (1). They find that Ī42d β-cristobalite is favored over α-quartz, at unspecified pressure.

Predicting that non-molecular CO2 phases can be produced under high pressure and temperature was the main point of our report. This prediction was simultaneously confirmed by the experiments of Iotaet al. (2). The comment by Dong et al. reinforces this prediction.

Moreover, as recognized by Dong et al., we, too, considered the Ī42d β-cristobalite structure as a possible candidate for the ground state, although only in its extremal cases: a C–O–C bond angle of 180° as in “ideal cristobalite” (referred to simply as “cristobalite” in our report) and a C–O–C bond angle of 109° cristobalite (referred to as “m-chalcopyrite” in our report). We reported that the ideal cristobalite is very high in enthalpy and thus unlikely to be a good candidate for the ground-state structure. We also reported that, at 100 GPa, the 109° cristobalite only has a slightly higher enthalpy than does α-quartz. It is likely that the optimal C–O–C bond angle in Ī42d β-cristobalite will vary with pressure. Some additional preliminary results indicate the possibility of a pressure window of stability for Ī42d β-cristobalite between the molecular crystal and the α-quartz structures, with a C–O–C bond angle somewhat larger than 109°. This seems to agree with recent experimental findings (3), showing that the product of the transformation of CO2observed upon increasing pressure up to about 40 GPa and heating up to 1800 K may indeed be a mixture of the SiO2-like structures trydimite and cristobalite.

REFERENCES

Non-molecular Carbon Dioxide (CO2) Solids

Response: Dong et al. state that the structure of polymeric CO2 discovered in recent high-pressure experiments (1) is cristobalite-like rather than quartz-like (2). Dong et al. used the same theoretical framework as Serra et al. (2) with different results and interpretations, with which I agree. The calculated (vibrational and total energies) properties by Dong et al. seem to better describe Iota et al.'s experimental results (1).

However, there are many other polymorphs of SiO2 with similar energetic stabilities, many of whose structures have not been considered in either this or previous calculations (2). For example, none of the many polymorphs of tridymites have been considered, despite their structural and energetic similarities to β-quartz and crystoballite (4). I believe that, because of the complexity in those crystal structures and the similarity in their energetics (particularly of quartz, crystobalite and many forms of tridymites), it is difficult to entirely rule out any one structure without experimental verification of the structure of polymeric CO2 by x-ray diffraction. Our recent x-ray results (4) show that the diffraction pattern of CO2-V is more closely related to those of tridymite polymorphs. There seems no obvious reason to consider polymeric CO2 to be one of the structures found in SiO2.

Nevertheless, the work underlying this exchange (3) is important and deserves recognition for pointing out other SiO2 structures (cristobalite and tridymite as candidate structures for the extended carbon dioxide).

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