Thermal expansion, heat capacity, and compressibility of solid CO<sub>2</sub>

Manzheliı̆, V. G.; Tolkachev, A. M.; Bagatskii, M. I.; Voitovich, E. I.

doi:10.1002/pssb.2220440104

Cited by 52 publications

(53 citation statements)

References 17 publications

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“…This is unlike water ice (ice Ih), in which weak hydrogen-bond vibrations serve as a heat reservoir at low temperatures and cause a deviation from the T 3 behavior. 26 The Debye temperature of the MP2 result at 5 K is 154 K, which is in good agreement with the observed value of 152 ± 1.5 K. 4 3.2. Bulk Modulus.…”

Section: Methodssupporting

confidence: 89%

“…Figure 6 compares the MP2-calculated linear thermal expansion coefficient (α L ) with experiments. 4,41 The MP2/aug-cc-pVDZ curve is twice as small as the experimental results, and given the reasonably accurate predicted values of C V , γ, and V 0 , this is nearly entirely ascribed to the error in B 0 . When the cp-MP2/aug-cc-pVTZ values of B 0 = 12.1 GPa and V 0 = 24.5 cm 3 mol −1 are used instead (with all the other factors unchanged), the calculated results are improved somewhat.…”

Section: Methodsmentioning

confidence: 93%

“…4 Nevertheless, the MP2-predicted value of α is significantly underestimated, while reproducing its temperature dependence well up to 100 K. This is traced, nearly entirely, to large errors (50−100%) in the calculated values of B 0 ; C V , γ, the molar volume at zero pressure (V 0 ), and the individual values of γ ik are all reproduced reasonably accurately by MP2. The thermal pressure coefficient (β), 17,18 whose evaluation does not involve B 0 and which should be directly measurable, agrees well between theory and experiments.…”

Section: Introductionmentioning

confidence: 87%

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Second-Order Many-Body Perturbation Study on Thermal Expansion of Solid Carbon Dioxide

Sode

Hirata

2014

J. Chem. Theory Comput.

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An embedded-fragment ab initio second-order many-body perturbation (MP2) method is applied to an infinite three-dimensional crystal of carbon dioxide phase I (CO2-I), using the aug-cc-pVDZ and aug-cc-pVTZ basis sets, the latter in conjunction with a counterpoise correction for the basis-set superposition error. The equation of state, phonon frequencies, bulk modulus, heat capacity, Grüneisen parameter (including mode Grüneisen parameters for acoustic modes), thermal expansion coefficient (α), and thermal pressure coefficient (β) are computed. Of the factors that enter the expression of α, MP2 reproduces the experimental values of the heat capacity, Grüneisen parameter, and molar volume accurately. However, it proves to be exceedingly difficult to determine the remaining factor, the bulk modulus (B0), the computed value of which deviates from the observed value by 50-100%. As a result, α calculated by MP2 is systematically too low, while having the correct temperature dependence. The thermal pressure coefficient, β = αB0, which is independent of B0, is more accurately reproduced by theory up to 100 K.

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Section: Methodssupporting

confidence: 89%

Section: Methodsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 87%

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Second-Order Many-Body Perturbation Study on Thermal Expansion of Solid Carbon Dioxide

Sode

Hirata

2014

J. Chem. Theory Comput.

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“…The region in which T is less than Tm In this region a molecule is assumed to have three degrees of freedom that act like Debye oscillators and three degrees of freedom that are adequately represented by Einstein oscillators. The rotational partition function can then be written as frot = fD3fE .[2]Here, fE = 1/(1 -e-OE/T) [3] and fD = f(OD/T), [4] in which 0D and 0D represent the Einstein and Debye characteristic temperatures, respectively. The thermodynamic functions calculated from fD as functions of OD/T are available in tables (31), while those forfE can be derived easily from Eq.…”

mentioning

confidence: 99%

“…The rotational partition function can then be written as frot = fD3fE . [2] Here, fE = 1/(1 -e-OE/T) [3] and fD = f(OD/T), [4] in which 0D and 0D represent the Einstein and Debye characteristic temperatures, respectively. The thermodynamic functions calculated from fD as functions of OD/T are available in tables (31), while those forfE can be derived easily from Eq.…”

mentioning

confidence: 99%

Thermodynamic properties of solid C ² H ₄

Eyring²

1979

Proc. Natl. Acad. Sci. U.S.A.

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The significant structures procedure of liquids has been used to calculate the thermodynamic properties of solid C2H4. Two degeneracy terms were used to describe the behavior in the vicinities of the two phase transitions. The calculated entropy and specific heat apee well with experimental results from a few kelvins to the melting point. Less 1969). Two transitions at 27.0 and 22.1 K were observed in solid heavy methane (1) indicating that, in this material, there exist three solid structures. X-ray measurements revealed a face-centered cubic structure of the molecules (8, 9), except for the low-temperature phase of C2H4, which is face-centered tetragonal (25). Measurements of the nuclear magnetic susceptibility indicated that partial conversion between the three nuclear spin species occurs at 4.2 K (24). Based on all these measurements, the phase transitions in solid methanes are believed to arise from orientational structure change. The theory of these transitions was first studied with statistical mechanics by James and Keenan (26) and has been developed into a quantum-mechanical theory by Yamamoto et al. (27) (refer to this reference for further references in this series up to 1977). The theory of James and Keenan is a classical molecular field theory assuming that the octupole-octupole interaction is the dominant intermolecular force. The three phases in C2H4 are the tetragonal phase III (ferrorotational), the octahedral phase II (antiferrorotational), and the disordered phase I, with a first-order transition followed by a second-order transition. A coherent neutron scattering study (14) confirmed the phase I and phase II structures but ruled out the phase III model proposed by James and Keenan and left the structure of phase III an unsettled issue. The quantum mechanical approach has been successful in many aspects. However, the mathematics involved in such an approach is quite complicated and there are still many problems yet to be solved. In this study, the attempt has been made to use a simple partition function to describe all phases and from it to calculate the thermodynamic properties of solid C2H4 from a few kelvins up to the melting point. The objective of this study is to expand a procedure that has had considerable success in the past in describing liquids to cover this very interesting problem. THEORY In our model a single partition function is written for all three solid phases. The applications of this model are given elsewhere (28,29). For the solid phase of C2H4 molecules, the following structures are considered to be significant. (i) The notations used in Eq. 1 are: frot, rotational partition function; Es, the energy of sublimation; R, gas constant; T, temperature; k, Boltzmann's constant; N, Avogadro's number; q, cluster size; a', change of energy per molecule; X, fraction of molecules with phase III structure; and b', a constant. We have used unity for the partition function for the internal vibrations because the internal vibrational frequencies of C2H4 are quite high [v1 ...

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Stratigraphy and evolution of the buried CO₂ deposit in the Martian south polar cap

Bierson

Phillips

Smith

et al. 2016

Geophysical Research Letters

122

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Observations by the Shallow Radar instrument on Mars Reconnaissance Orbiter reveal several deposits of buried CO2 ice within the south polar layered deposits. Here we present mapping that demonstrates this unit is 18% larger than previously estimated, containing enough mass to double the atmospheric pressure on Mars if sublimated. We find three distinct subunits of CO2 ice, each capped by a thin (10–60 m) bounding layer (BL). Multiple lines of evidence suggest that each BL is dominated by water ice. We model the history of CO2 accumulation at the poles based on obliquity and insolation variability during the last 1 Myr assuming a total mass budget consisting of the current atmosphere and the sequestered ice. Our model predicts that CO2 ice has accumulated over large areas several times during that period, in agreement with the radar findings of multiple periods of accumulation.

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Thermal expansion, heat capacity, and compressibility of solid CO₂

Cited by 52 publications

References 17 publications

Second-Order Many-Body Perturbation Study on Thermal Expansion of Solid Carbon Dioxide

Second-Order Many-Body Perturbation Study on Thermal Expansion of Solid Carbon Dioxide

Thermodynamic properties of solid C ² H ₄

Stratigraphy and evolution of the buried CO₂ deposit in the Martian south polar cap

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Thermal expansion, heat capacity, and compressibility of solid CO2

Cited by 52 publications

References 17 publications

Second-Order Many-Body Perturbation Study on Thermal Expansion of Solid Carbon Dioxide

Second-Order Many-Body Perturbation Study on Thermal Expansion of Solid Carbon Dioxide

Thermodynamic properties of solid C 2 H 4

Stratigraphy and evolution of the buried CO2 deposit in the Martian south polar cap

Contact Info

Product

Resources

About

Thermal expansion, heat capacity, and compressibility of solid CO₂

Thermodynamic properties of solid C ² H ₄

Stratigraphy and evolution of the buried CO₂ deposit in the Martian south polar cap