Electronic structural and electrochemical properties of

Electronic structural and electrochemical properties of lithium zirconates and their capabilities of CO2 capture: A first-principles density-functional theory and phonon dynamics approach Yuhua Duan Citation: J. Renewable Sustainable Energy 3, 013102 (2011); doi: 10.1063/1.3529427 View online: http://dx.doi.org/10.1063/1.3529427 View Table of Contents: http://jrse.aip.org/resource/1/JRSEBH/v3/i1 Published by the AIP Publishing LLC.

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JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 3, 013102 共2011兲

Electronic structural and electrochemical properties of lithium zirconates and their capabilities of CO2 capture: A first-principles density-functional theory and phonon dynamics approach Yuhua Duana兲 National Energy Technology Laboratory, United States Department of Energy, Pittsburgh, Pennsylvania 15236, USA and URS Corp., South Park, Pennsylvania 15129, USA 共Received 1 July 2010; accepted 12 November 2010; published online 6 January 2011兲

Lithium zirconates have attracted researchers’ interests because they can also be used as solid sorbents for CO2 capture. The structural, electronic, and phonon properties of Li2ZrO3, Li6Zr2O7, and monoclinic phase ZrO2 are investigated by the density-functional theory and phonon dynamics. Their electrochemical properties and their thermodynamics of CO2 absorption/desorption are analyzed. The calculated results show that their optimized structures and calculated bulk moduli as well as cohesive energies are in good agreement with experimental measurements. The calculated band gaps are 3.90 eV 共indirect兲, 3.98 eV 共direct兲, and 3.76 eV 共direct兲 for Li2ZrO3, Li6Zr2O7, and ZrO2, respectively. The calculated Li intercalation voltage and energy densities of Li2ZrO3 are higher than that of Li6Zr2O7, which indicates that as a cathode material Li2ZrO3 is better than Li6Zr2O7. The calculated phonon dispersions and density of states show that there is one soft mode in Li2ZrO3 and two soft modes in Li6Zr2O7. From the calculated thermodynamic properties of these two lithium zirconates reacting with CO2, we found that the performance of Li2ZrO3 as a CO2 sorbent is better than that of Li6Zr2O7. In the first half cycle, sorbents absorbing CO2 to form lithium carbonate, Li6Zr2O7 performs better than Li2ZrO3 because the former releases more heat of reaction and has a lower Gibbs free energy and a higher CO2 capture capacity. However, during the second half cycle, regenerating sorbent from carbonate and zirconia to release CO2, the main product is the thermodynamically favorable Li2ZrO3 rather than forming Li6Zr2O7. © 2011 American Institute of Physics. 关doi:10.1063/1.3529427兴

I. INTRODUCTION

As solid electrolytes, lithium salts 共Li4SiO4, Li2ZrO3, etc.兲 are widely used in high-energy lithium secondary batteries since they are both ionic conductors and of the ternary oxides that are thermodynamically stable against Li.1–4 Lithium meta-zirconate 共Li2ZrO3兲 is also one of the best candidate blanket materials for tritium breeding components in the deuterium-tritium fusion reactor.5–8 Moreover, lithium zirconates are good piezoelectric ceramics.9 Nowadays, the burning of fossil fuels is the main energy source for the world economy. One consequence of the use of these carbon based fuels is the emission of huge quantities of CO2 into the atmosphere creating environmental problems such as global climate warming.10–12 One approach to solving such environmental problems is to capture and sequester the CO2.4,13 Experimental investigations conducted in the past few decades found a new application that lithium zirconates are good candidates of solid sorbents for CO2 capture in terms of large CO2 sorption capacity, infinite CO2 / N2 or CO2 / H2 selectivity, good reversibility, and high operating a兲

Author to whom correspondence should be addressed. Tel.: 412-386-5771. FAX: 412-386-4542. Electronic mail: [email protected].

1941-7012/2011/3共1兲/013102/17/$30.00

3, 013102-1

© 2011 American Institute of Physics


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Yuhua Duan

J. Renewable Sustainable Energy 3, 013102 共2011兲

temperature.4,14–29 Nakagawa and Ohashi15,16 first reported that lithium zirconate powder reacts immediately with ambient CO2 in the temperature range of 450– 550 ° C and the products decompose reversibly to lithium zirconate and CO2 at temperatures above 650 ° C. Ida et al.22,23 pointed out that the rate of the CO2 sorption on pure zirconate is controlled by the diffusion of CO2 in the solid lithium carbonate shell, whereas Xiong et al.30 revealed that it is the size of the aggregate of Li2ZrO3 that controls the CO2 sorption rate. A lithium zirconate based membrane has a high separation factor of 4.9 between CO2 and CH4 gas molecules at 600 ° C.31 Recent experimental results also indicated that doping or mixing lithium zirconates with other alkali salts could improve the CO2 sorption.25,26,32 Pfeiffer et al.4 reported that hexa-lithium zirconate 共Li6Zr2O7兲 absorbed four times more CO2 than Li2ZrO3, and its CO2 sorption rate is faster than Li2ZrO3 at short times, but they became similar after long times. Ochoa-Fernandez et al.24,33 showed that the nanocrystalline tetragonal Li2ZrO3 has superior CO2 capture and regeneration properties when compared to monoclinic Li2ZrO3 prepared by solid-state synthesis. Their results demonstrated that both the capture rate and capacity of lithium zirconate depend considerably on the ratio of Li2O to ZrO2, and the enhanced capture rates were observed when a deficiency of Li2O is introduced, where excess ZrO2 as a dispersant introduces more reactive boundaries.34 Recently, they also investigated the effects of steam addition to the stability of Li2ZrO3 in the CO2 capture process and showed that while the presence of steam enhances the capture and regeneration rates, there is a large decay in the absorption capacity when compared with dry capture condition.35 By means of thermodynamics calculation and experimental measurements, Nakagawa and Ohashi16 pointed out that the change from Li2ZrO3 to ZrO2 depends not only on temperature and CO2 partial pressure but also on the presence of molten carbonates 共e.g., alkali carbonates with a molar ratio of Li: K = 62: 38兲. Very recently, Iwan et al.36 explored the equilibrium and kinetics of CO2 reacting with Li2ZrO3 and found that at high temperatures its reaction rate is considerably fast. They also observed relatively slow reaction rates at PCO2 ⬍ 0.4 bar, possibly due to mass transfer limitations. The mechanisms of these reversible reactions are not clear. Essaki et al.18 proposed a reaction model for lithium zirconate absorption of CO2 at room temperature. The CO2 reacts with Li2O in the Li2ZrO3 to form Li2CO3. If H2O is present, the CO2 and Li2O first will hydrolyze before forming Li2CO3. However, they did not explain how the Li2O migrated out of Li2ZrO3 bulk structure, nor did they describe the ensuing changes to the Li2ZrO3 bulk structure. Ida et al.22,23 also proposed a similar double shell model to describe the CO2 sorption mechanism on Li2ZrO3 from a qualitative point of view. They found that in order to continue to form Li2CO3, the lithium has to migrate and cross the Li2CO3 shell. The rate of the CO2 absorption is controlled by the diffusion of CO2 into the solid lithium carbonate shell22,23 and the aggregate size with the Li2ZrO3 bulk.30 Even with these shells on the CO2 absorption process, it was not clearly known as to how the Li2ZrO3 structure changes to ZrO2 and how the Li2O comes out of Li2ZrO3 structure to react with the CO2. In comparison to the previously cited extensive experimental studies on lithium zirconates and related materials, in the literature, there are few theoretical studies, particularly on the electronic structure and lattice dynamics of these lithium zirconates. Using pseudohomogeneous and heterogeneous models, Rusten et al.27 simulated a fixed-bed reactor for the production of hydrogen via sorption-enhanced steam methane reforming using Li2ZrO3 as a CO2-acceptor. Pfeiffer and Bosch4 used molecular dynamics to investigate the thermal stability and CO2 absorption of Li6Zr2O7. Their results indicated that the best temperature for CO2 absorption on Li6Zr2O7 is 550 ° C and that the Li6Zr2O7 does not regenerate after the CO2 desorption, but instead decomposes into Li2ZrO3. In contrast to lithium zirconates, in the literature, the electronic structural properties of zirconia have been extensively investigated.37–39 Our previous results of Li2O capturing CO2 showed that Li2O is good at absorbing CO2, but the reverse reaction to release CO2 can occur only at very low pressure and very high temperature.40 In this study, we first employ first-principles density-functional method to investigate the electronic structural and the lattice dynamical phonon properties of Li2ZrO3 and Li6Zr2O7 extensively, then analyze in detail the properties of CO2 absorption/desorption based on the energetic and thermal dynamical results. The remainder of this report is organized as follows. In Sec. II, we briefly describe the


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CO2 capture by lithium zirconates

theoretical method we employed. In Sec. III, we present the electronic and phonon results for lithium zirconates and compare them with other available data. We then analyze their electrochemical properties by calculating the open circuit voltage and energy densities. Subsequently, we analyze their capabilities for CO2 capture by calculating the chemical potential change for the capture reactions under different external pressures and temperatures. In Sec. IV, we summarize our conclusions. II. THEORETICAL METHODS

The calculations performed in this work are based on first-principles density-functional theory 共DFT兲 with plane-wave basis sets and the pseudopotential to describe the electron-ion interactions. The Vienna ab initio simulation package41,42 was employed in this study to calculate the electronic structures of the lithium zirconates and zirconia materials. In this study, all calculations have been done using the projector augmented wave pseudopotentials and the PW91 exchange-correlation functional. This computational level was shown to provide an accurate description of oxide systems.43 Plane wave basis sets were used with a cutoff energy of 500 eV and a kinetic energy cutoff for augmentation charges of 605.4 eV. The k-point sampling grids of n1 ⫻ n2 ⫻ n3, obtained using the Monkhorst–Pack method,44 were used for these bulk calculations, where n1, n2, and n3 were determined consistent to a spacing of about 0.028 Å−1 along the axes of the reciprocal unit cells. The corresponding k-point sets that we used in our calculations were 7 ⫻ 4 ⫻ 7 for Li2ZrO3, 4 ⫻ 6 ⫻ 4 for Li6Zr2O7, and 8 ⫻ 8 ⫻ 8 for ZrO2, respectively. The valence electrons contain the s and p orbitals of Li and O atoms, and the s, p, and d orbitals of Zr. During the calculations, all atoms in the cell as well as the lattice dimensions and angles were relaxed to the equilibrium configurations. For band structure and phonon dispersion calculations, the symbols and coordinates of the high symmetrical points in the first Brillouin zone of the crystals are taken from Bradley and Cracknell’s definitions.45 When applying these two lithium zirconates as solid CO2 absorbents, we have the following reactions: T,P

Li2ZrO3 + CO2↔ Li2CO3 + ZrO2

共a兲,

T,P

Li6Zr2O7 + 3CO2↔ 3Li2CO3 + 2ZrO2

共b兲,

T,P

Li6Zr2O7 + 2CO2↔ 2Li2CO3 + 2ZrO2 + Li2ZrO3

共c兲,

T,P

Li6Zr2O7 + CO2↔ Li2CO3 + 2Li2ZrO3

共d兲.

Obviously, the product Li2ZrO3 from reactions 共c兲 and 共d兲 can further absorb CO2 by reaction 共a兲 and finally become reaction 共b兲. Assuming the difference between the chemical potential of solid phases 共Li2ZrO3, Li6Zr2O7, ZrO2, and Li2CO3兲 can be approximated by the differences in their electronic energies 共⌬EDFT兲 and their entropies 共⌬Sharm兲 and harmonic free energies 共⌬Fharm兲, we can obtain the temperature and pressure dependent chemical potential 共⌬␮兲 for these reactions,40,46–49 ⌬␮共T,P兲 = ⌬␮0共T兲 − nRT ln共PCO2/P0兲,

共1兲

⌬␮0共T兲 = ⌬EDFT + ⌬EZP + ⌬Fharm共T兲 − T⌬Sharm共T兲 − GCO2共T兲,

共2兲

with

where ⌬EZP is the zero-point energy difference between the reactants and products and can be obtained directly from phonon calculations. n in Eq. 共1兲 is the number of moles of absorbed CO2


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Yuhua Duan

in reactions 共a兲–共d兲. P0 is the standard state reference pressure of 1 bar. The free energy of CO2 共GCO2兲 can be obtained by standard statistical mechanics,50 4

7 N ah ␯ i GCO2共T兲 ⬇ RT + 兺 h␯ /kT − TSCO2共T兲, i 2 −1 i=1 e

共3兲

where Na is the Avogadro constant. The vibrational frequencies 共␯i兲 of CO2 molecule are 673 cm−1共␲u兲, 1354 cm−1共␴g+兲, and 2397 cm−1共␴u+兲,51 from which the zero-point energy of CO2 molecule is obtained with the value of 0.316 eV.40 The entropy of CO2 关SCO2共T兲 in J/mol兴 can be accurately evaluated using the Shomate equation,52 SCO2共T兲 = Aⴱ ln共t兲 + Bⴱt + Cⴱ

E t2 t3 + Dⴱ + ⴱ 2 + G, 2 3 2t

共4兲

where t = T / 1000, and A, B, C, D, E, and G are parameters. For CO2, in the temperature 共T兲 range of 298–1200 K, their values are 24.997 35, 55.186 96, ⫺33.691 37, 7.948 387, ⫺0.136 638, and 228.2431, respectively.52 The enthalpy change for the reactions 共a兲–共d兲, ⌬Hcal共T兲, can be derived from above equations as ⌬Hcal共T兲 = ⌬␮0共T兲 + T关nSCO2共T兲 + ⌬Sharm共T兲兴.

共5兲

When considering the phase stability and transitions and the thermodynamics of crystalline materials, their fundamental properties are the phonon frequencies. The approaches of ab initio calculations fall into two classes: the linear response method,53,54 in which the dynamical matrix is expressed in terms of the inverse dielectric matrix describing the response of the valence electron density to a periodic lattice perturbation, and the direct method,55–57 in which the forces are calculated via the Hellmann–Feynman theorem. Here, in this paper, we employ the PHONON software package58 in which the direct method is applied following the formula derived by Parlinski et al.57 to combine ab initio DFT with phonon calculations. Similar to our previous approach,40,59 the phonon dispersion and the thermodynamic properties 共zero-point energy, free energy change, entropy change, etc.兲 can be carried out for each crystal. In turn, the zero-point energy change 共⌬EZP兲 and the phonon free energy change 关⌬Fharm共T兲 in Eq. 共2兲兴 are obtained for the CO2 capture reactions 共a兲–共d兲. In the phonon calculations, a 2 ⫻ 2 ⫻ 2 supercell is created for ZrO2 and Li2ZrO3 from their optimized unit cells that are calculated through DFT. In order to make the shape of the supercell close to cubic and to take into account the proper size of the cell, for Li6Zr2O7, a 1 ⫻ 2 ⫻ 1 supercell, which contains eight formula units of Li6Zr2O7, is used for its phonon property calculations. The displacement of 0.03 Å of nonequivalent atoms is generated. Then for the supercell, the DFT calculations were performed again to obtain the force on each atom due to the displacements. These forces are carried back to the PHONON package58 to calculate the phonon dispersions and density of states. The partition function can be carried out with the phonon dispersions and densities of states. With them, their thermodynamic properties, such as internal energy, free energy, entropy, heat capacity, etc., can be evaluated under different temperature and pressure, which are used in Eq. 共1兲 to calculate the chemical potentials for the reactions 共a兲–共d兲. III. RESULTS AND DISCUSSIONS A. Structural optimization and bulk properties

Lithium zirconates can be synthesized from Li2CO3 and ZrO2 with different ratios.1,2,60–62 Recently, Yin et al.61 reported that substituting Li2CO3 with LiOH can obtain Li2ZrO3 and Li6Zr2O7, and furthermore substituting ZrO2 with Zr共NO3兲4 · 5H2O can obtain Li6Zr2O7 with decreased synthesis time. Although its tetragonal metastable phase could exist,62 lithium metazirconate 共Li2ZrO3兲 usually is in a monoclinic structure with space group C2/c 共No. 15兲.2 At low


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(a)Li2ZrO3

(b) Li6ZrO7 (c) ZrO2 FIG. 1. The crystal structures of lithium zirconates. Biggest ball stands for Zr, smallest for O. c axis is vertical. 共a兲 Li2ZrO3, 共b兲 Li6ZrO7, 共c兲 monoclinic phase of ZrO2.

temperature 共T = 82 K兲, its crystal constants are a = 5.4089 Å, b = 9.0309 Å, c = 5.4144 Å, and ␤ = 112.498°, in which Zr is located at site 共0 , 0.0919, 41 兲, Li occupies sites 共0 , 0.4195, 41 兲 and 共0 , 0.7330, 41 兲, and O atoms are located at sites 共 41 , 41 , 21 兲 and 共0.2578, 0.4779, 0.4195兲.2 As shown by Heiba and El-Sayed,2 there were large anisotropic changes in its lattice parameters as a function of temperature, slight changes in the fractional coordinates of different atoms, and anisotropic changes in the interatomic distances between the different cations. Hexa-lithium zirconate 共Li6Zr2O7兲 also has monoclinic structure with space group C2/c 共No. 15兲.1,60 By comparing the structure of Li2ZrO3 with that of Li6Zr2O7, it can be seen that both of them are of the NaCl type. However, the distributions of the cations are different in these two phases and therefore they can not be considered isostructural.1 As shown in Fig. 1, in Li2ZrO3 all cations have octahedral coordination and its structure has to be considered as close packed, whereas the structure of Li6Zr2O7 is more open, and both Li+ and O2− ions in Li6Zr2O7 may have higher mobility that leads to higher ionic conductivity than Li2ZrO3 does. Although zirconia 共ZrO2兲 can be presented in several different crystal structures under different temperatures and pressures,63 at ambient condition it presents a monoclinic structure with space group P21 / c 共No. 14兲.37,63,64 Here, for the purpose of investigating the thermodynamic properties of the CO2 capture reactions, we only deal with its ambient phase. The crystal structures of these two zirconates and most stable monoclinic ZrO2 phase are shown in Fig. 1. Their experimental crystal structural constants as well as our optimized structural constants are summarized in Table I. From Fig. 1, it can be seen that there are 4 f.u. in each unit cell. In Li6Zr2O7, each Zr atom ¯兲 coordinated with six O and Li atoms is located close to O. The Zr layered is located along 共111 direction 共not exactly parallel to兲. On each layer, Zr is planar coordinated with four O, whereas between each layer, Zr is bonded with O. Similar layered structures can also be seen in the structure of Li2ZrO3, but on each Zr layer, half of the Zr is distorted above the plane and half of the Zr is below the plane. From Table I, one can see that the deviations of our optimized structures of Li2ZrO3 and Li6Zr2O7 from the corresponding experimental measurements are less than 1%. In order to explore the bulk properties of lithium zirconates, we calculate their total energies


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Yuhua Duan

TABLE I. The experimental and optimized crystal structural constants of lithium zirconates and monoclinic zirconia. All of them have 4 f.u. in their unit cells 共Z = 4兲. Lattice constants Crystal and space group Li2ZrO3 C2/c 共No. 15兲a

Fractional coordinates Deviation 共%兲

Expt.

Optimized

a = 5.4089 Å

5.4449 Å

0.66

b = 9.0309 Å c = 5.4144 Å ␤ = 112.498°

9.1212 Å 5.4561 Å 112.288° 250.727

1.00 0.77 ⫺0.18 2.61

v = 244.350 Å3 Li6Zr2O7 C2/c 共No. 15兲b

ZrO2 P21 / c 共No. 14兲c

Expt.

Optimized

Zr: 共0.0000, 0.0919, 0.2500兲

Zr: 共0.0000, 0.0904,0.2500兲

Li: 共0.0000, 共0.0000, O: 共0.2500, 共0.2578,

Li: 共0.0000, 共0.0000, O:.共0.2500, 共0.2689,

0.4195, 0.7330, 0.2500, 0.5816,

0.2500兲 0.2500兲 0.5000兲 0.4779兲

0.4240, 0.7410, 0.2500, 0.5758,

0.2500兲 0.2500兲 0.5000兲 0.4863兲

Zr: 共0.1833, 0.1223, 0.3642兲 Zr: 共0.1835, 0.1226, 0.3649兲 a = 10.4428 Å

10.5312 Å

0.85

b = 5.9877 Å

6.0391 Å

0.86

c = 10.2014 Å 10.3002 Å ␤ = 100.266° 100.223° 644.680 v = 627.665 Å3

0.97 ⫺0.04 2.71

a = 5.1451 Å b = 5.2023 Å

5.2044 Å 5.2706 Å

1.15 1.31

c = 5.3219 Å ␤ = 99.15°

5.3648 Å 99.468°

0.81 0.32

Li: 共0.2927, 0.1286, 0.1075兲共0.4341, 0.4030, 0.3980兲共0.0622, 0.3539, 0.0833兲 O: 共0.0000, 共0.1243, 共0.3784, 共0.2505,

0.1467, 0.3639, 0.3775, 0.3867,

0.2500兲 0.5023兲 0.0216兲 0.2550兲

Li: 共0.2930, 0.1292, 0.1046兲共0.4330, 0.4013, 0.3979兲共0.0605, 0.3559, 0.0852兲 O: 共0.0000, 共0.1324, 共0.3788, 共0.2505,

0.1575, 0.3685, 0.3766, 0.3867,

0.2500兲 0.5028兲 0.0222兲 0.2550兲

Zr: 共0.2760, 0.0401, 0.2091兲 Zr: 共0.2776, 0.0432, 0.2085兲 O: 共0.0720, 0.3330, 0.3470兲 O: 共0.0696, 0.3353, 0.3430兲共0.4490, 0.7580, 0.4760兲

共0.4495, 0.7576, 0.4808兲

a

From Ref. 2. From Ref. 60. c From Ref. 64. b

versus the changes of cell volume. From them, we can obtain the relationship between energy and volume or pressure by fitting the equation of state. The most popular and well widely used equation of state is the Birch–Murnaghan equation of state 共E-V兲,65,66 E共V兲 = E 0+

9 ⫻ B 0V 0 16

再冋冉冊册 V0 V

2/3

−1

3

⫻ B0⬘ +

冋冉冊册冋 V0 V

2/3

2

−1

⫻ 6−4⫻

冉冊册冎 V0 V

2/3

. 共6兲

By fitting the calculated data of E-V into Eq. 共6兲, the bulk properties of solids can be obtained. The fitted results of these lithium zirconates and zirconia are listed in Table II. The bulk modulus B is defined as B = B0 + B⬘0 ⫻ P in this scheme, where P is the pressure and here is set to 1 atm. The cohesive energy 共EC兲 is calculated by subtracting the total bulk energy 共E0 in Table II兲 from the sum of total energies of the related atoms 共such as Li, Zr, O兲 using the same level calculations 共in our case, we get ELi = −0.044 03 eV, EZr = −1.298 28 eV, and EO = −1.491 35 eV兲. The calculated EC as well as other values from references are listed in Table II. From Table II, one can see that the calculated bulk modulus of ZrO2 共181.4 GPa兲 is close to those fitted and experimental measured values made by Bouvier et al.63 and Dewhurst et al.37 The calculated cohesive energy of monoclinic ZrO2 共⫺24.447 eV兲 is between the experimental value of ⫺22.85 eV and the local density approximation calculated result of ⫺26.24 eV.39 We also made the DFT calculations for other five phases of ZrO2 共space group numbers: 29, 61, 62, 137, and 225兲. Our results show that the monoclinic phase has the lowest energy, which is consistent with the experimental results that the monoclinic phase is most stable under ambient conditions and


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TABLE II. The calculated bulk modulus, cohesive energy, and the fitted parameters of Birch–Murnaghan equation of state for lithium zirconates and monoclinic zirconia.

Crystal

E0 共eV/cell兲

B0 共eV/ Å3兲

B 0⬘

Li2ZrO3

⫺175.074

0.744

⫺409.144

Li6Zr2O7

⫺114.910

ZrO2

0.698 1.132

V0 共Å3兲

Bulk modulus 共GPa兲

Cohesive energy Ec 共eV兲

4.069

251.155

119.3

37.908

2.728

244.35a 646.708

111.8

88.986

627.67b 145.255 148.12d

181.4 157c

24.447 22.85d

101–212e

23.45e

3.302 2.38c

140.6e a

From Ref. 2. From Ref. 60. c From Ref. 38. d From Ref. 39. e From Ref. 63. b

also consistent with Öztürk and Durandurdu’s recent calculated results.67 However, in the report of Lowther et al.,38 the relative energy of monoclinic ZrO2 is lower than two cubic phases 共Nos. 137 and 225兲 but about 0.02–0.033 eV/atom higher than other three phases 共Nos. 29, 61, and 62兲. Therefore, in our following phonon and CO2 capture calculations, only the monoclinic phase of ZrO2 is considered. Comparing Li2ZrO3 with Li6Zr2O7, one can see from Table II that their bulk moduli are close to each other, but Li6Zr2O7 has much higher cohesive energy than Li2ZrO3. B. Electronic structural properties

The calculated band structures of lithium zirconates 共Li2ZrO3, Li6Zr2O7兲 and monoclinic ZrO2 are shown in Fig. 2. It can be seen that the band structures of these three materials have some similarities. They have two valence bands 共VBs兲 and their shapes look similar to each other. Their second VBs are located below ⫺15 eV while their first VBs are just below the Fermi energy. The calculated band gap of Li2ZrO3 is an indirect one, located between ⌫ and Z high-symmetric points with the value of 3.90 eV, while the calculated band gaps of Li6Zr2O7 and ZrO2 are direct with the values of 3.98 and 3.76 eV, as shown in Figs. 2共b兲 and 2共c兲, respectively. Obviously, the calculated values of their band gaps are close to each other. However, as described in our previous work,40,43 the DFT calculation underestimated the excited-state energy. The calculated band gaps are usually smaller than the experimental measurements, although currently there is no experimental value available for comparison. As summarized in Table III, the band widths of the first and second VBs for Li6Zr2O7 and Li2ZrO3 have only about 0.15 eV difference, while ZrO2 has a larger first valence band width.

(a)

(b)

(c)

FIG. 2. The calculated band structures. 共a兲 Li2ZrO3, 共b兲 Li6Zr2O7, 共c兲 monoclinic ZrO2.


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Yuhua Duan

TABLE III. The calculated band gaps and valance band widths of lithium zirconates and ZrO2, and their corresponding zero-point energies 共Ezp兲, and the entropies 共S兲 at T = 298 K from phonon calculations.

Crystal

First VB width 共eV兲

Second VB width 共eV兲

Band gap 共eV兲

Ezp 共kJ/mol兲

Entropy 共J/mol K兲

Li2ZrO3

3.73

1.01

3.90 共indirect兲

36.108

101.88

96.285

91.63a 233.04

20.102

220.8b 51.30

Li6Zr2O7 ZrO2

3.59

1.14

4.94

1.51

3.98 共direct兲 3.76 共direct兲

50.39a Taken from HSC-Chemistry package 共Ref. 72兲. Taken from Ref. 74.

a

b

Figure 3 shows the calculated total density of states and their corresponding atom partial density of states for Li2ZrO3, Li6Zr2O7, and monoclinic ZrO2. As demonstrated in Fig. 3, the s orbital of O contributes to the lower second VBs of Li2ZrO3, Li6Zr2O7, and ZrO2, while its p orbitals are mainly contributed to their first VBs. In all three cases, all the s, p, and d orbitals of Zr contribute to both VBs, but its d orbitals have higher contributions than its s and p orbitals. From Figs. 3共a兲 and 3共b兲, it can be seen that when compared with its s orbital, the p orbital of Li has a larger contribution to the upper portion of the first VB in both Li2ZrO3 and Li6Zr2O7. From Figs. 1共a兲 and 1共b兲, one can see that in both Li2ZrO3 and Li6Zr2O7, each Zr atom is coordinated with six O atoms and around each O atom is bonded to two Zr atoms. The distances between Zr and O in Li2ZrO3 are 2.07–2.21 Å and in Li6Zr2O7 are 2.05–2.15 Å. The differences between these two structures are mainly caused by the distributions of Li atoms. Their structure similarities give similar band structures. C. Electrochemical properties of lithium zirconates

Lithium zirconates could be used as cathode materials. Their electrochemical properties can be derived directly from the difference in total energies before and after lithium intercalation. This procedure can improve the accuracy through the cancellation of errors.68 Typically, the cathode discharge assumes the half-cell reaction versus Li/ Li+,68–70 LinZrmOk + xLi+ + xe− → Lin+xZrmOk

共e兲.

The open circuit voltage 共OCV兲 for an intercalation reaction involving x Li+ ions can be evaluated from the energy difference if volume and entropy effects are neglected,68

(a)

(b)

(c)

FIG. 3. The calculated total and partial density of states. 共a兲 Li2ZrO3, 共b兲 Li6Zr2O7, 共c兲 monoclinic ZrO2.


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OCV ⬇

E共LinZrmOk兲 + xE共Li _ metal兲 − E共Lin+xZrmOk兲 , xF

共7兲

where F is the Faraday constant. The energy density 共E⍀ in Wh/l兲 and the specific energy 共Em in Wh/kg兲 for battery reaction are given by E⍀ = −

⌬E , ⍀

共8兲

Em = −

⌬E , m

共9兲

where ⌬E is the energy difference between the reactant 共LinZrmOk兲 and product 共Lin+xZrmOk兲, ⍀ is the mean volume of 1 f.u. of reactant and 1 f.u. of product in the discharge reaction 共e兲, and m is the mean mass of 1 f.u. of reactant and 1 f.u. of product. Using the same calculating procedure, for Li metal, the calculated E共Li_ metal兲 = −1.8860 eV/ atom. From Table I, it can be seen that when removing one Li from Li2ZrO3 there are two possibilities corresponding to upper and lower layers of Li, as shown in Fig. 1共a兲. For the case of Li6Zr2O7, as shown in Table I and Fig. 1共b兲, it contains three different groups of Li and each group has two Li. In order to keep the crystal symmetry as high as possible, instead of removing one Li, we remove two Li atoms from Li6Zr2O7 creating three possible configurations of Li4Zr2O7. Therefore, in this work, the OCVs are calculated for Li6Zr2O7 with x = 2 and for Li2ZrO3 with x = 1 in Eq. 共7兲, respectively. The optimized lattice parameters for the reduced lithium zirconates are listed in Table IV. Cases A–C correspond to removing different types of Li atoms 共shown in Table I兲 one by one. Comparing Table IV with Table I, one can see that removing different sets of Li results in different structures and electrochemical properties due to the different environments of these Li sets in the crystal structures, as shown in Figs. 1共a兲 and 1共b兲. Interestingly, except for case B of LiZrO3, after removing one set of Li, the crystal structures are expanded because of more repulsions caused by less Li and almost all atoms in the crystal rearranged to a new equilibrium. The calculated OCV, energy density 共E⍀兲, and the specific energy 共Em兲 of their lithium intercalation reactions for Li2ZrO3 and Li6Zr2O7 are also summarized in Table IV. Obviously, from Eqs. 共7兲 and 共9兲, if the cell energy of the reduced crystal is lower, its OCV and Em should be higher. However, their energy density 共E⍀兲 could be lower because it also depends on the cell volume, as shown in Eq. 共8兲. The difference of the calculated OCV between two cases of Li2ZrO3 / LiZrO3 is 0.01 V, while in the case of Li6Zr2O7 / Li4Zr2O7 the difference is about 0.3 V. Comparing Li2ZrO3 with Li6Zr2O7, one can see that the Li2ZrO3 has higher OCV, energy density, and specific energy, which means that as a cathode material Li2ZrO3 is better than Li6Zr2O7. D. Dynamical phonon properties

As shown in Table I for each solid, there are 4 f.u. 共Z = 4兲 in each unit cell. However, the primitive cells of Li2ZrO3 and Li6Zr2O7 only contain 2 f.u. while the primitive cell of monoclinic ZrO2 still contains 4 f.u. Therefore, there are 90 phonon modes in Li6Zr2O7 and 36 phonon modes in Li2ZrO3 and ZrO2. The calculated phonon dispersions of lithium zirconates 共Li2ZrO3, Li6Zr2O7兲 and monoclinic phase of ZrO2 are shown in Figs. 4共a兲–4共c兲, respectively. In Table V, we summarize our calculated phonon frequencies of these three solids together with the corresponding irreducible representations. Unfortunately, in the literature we did not find any experimental or theoretical data to compare with. Obviously, all of the vibrational modes are nondegenerate 共Au, Ag, Bu, and Bg兲 because their crystal point groups are quite low with C2h, and half of them are Raman active and the other half infrared active, as shown in Table V. It can be seen from Figs. 4共a兲 and 4共b兲 that along the wave-vector there are some soft modes in these two lithium zirconates. In the case of Li2ZrO3 关Fig. 4共a兲兴, one soft mode belonging to acoustical branch is around the high-symmetric points Z and L. In the dispersion curve of Li6Zr2O7, as shown in Fig. 4共b兲, there


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TABLE IV. The optimized lattice constants, cell volume, total energies of LiZrO3 and Li4Zr2O7, and the calculated OCV, energy density 共E⍀兲, and the specific energy 共Em兲 of their lithium intercalation reactions for lithium zirconates. Lattice constants

Structure LiZrO3: Case A

Case B

Li4Zr2O7: Case A

a = 6.1872 Å

Zr: 共0.0000, 0.0806, 0.2500兲

b = 8.8161 Å c = 5.9307 Å ␤ = 123.401°

Li: 共0.0000, 0.7235, 0.2500兲 O: 共0.2500, 0.2500, 0.5000兲共0.3137, 0.5964, 0.4636兲

V = 270.071 Å3 a = 4.5394 Å

Zr: 共0.0000, 0.1140, 0.2500兲

b = 10.3432 Å c = 5.3850 Å ␤ = 104.10°

Li: 共0.0000, 0.4016, 0.2500兲 O: 共0.2500, 0.2500, 0.5000兲共0.2506, 0.5316, 0.4903兲

V = 245.218 Å3 a = 10.3946 Å b = 6.0193 Å

Zr: 共0.1918, 0.1191, 0.3560兲 Li: 共0.3320, 0.0834, 0.1406兲

c = 10.5972 Å ␤ = 108.302° V = 629.506 Å3

Case B

a = 10.3601 Å b = 6.1031 Å c = 11.0272 Å ␤ = 91.815° V = 696.891 Å3

Case C

Fractional coordinates

a = 10.3557 Å b = 6.1452 Å c = 10.0011 Å ␤ = 93.943° V = 634.946 Å3

共0.0641, O: 共0.0000, 共0.1261, 共0.3158,

0.3215, 0.0287, 0.3473, 0.3154,

Cell energy 共eV/cell兲

OCV 共V兲

E⍀ 共Wh/l兲

Em 共Wh/kg兲

⫺149.232 88

4.57

447.14

1157.16

⫺149.034 31

4.62

473.36

1165.83

⫺364.8457

3.65

313.65

1119.46

⫺362.3738

3.96

314.70

1183.34

⫺364.6780

3.67

313.48

1123.70

0.0661兲 0.2500兲 0.4760兲 0.0203兲

共0.2068, 0.3856, 0.2349兲 Zr: 共0.1764, 0.1045, 0.3341兲 Li: 共0.2995, 0.1003, 0.0660兲共0.4377, 0.4210, 0.4119兲 O: 共0.0000, 0.0795, 0.2500兲共0.1848, 0.3025, 0.5139兲共0.3763, 0.3793, 0.0413兲共0.2201, 0.4345, 0.2815兲 Zr: 共0.1809, 0.1675, 0.3568兲 Li: 共0.4227, 共0.0823, O: 共0.0000, 共0.1429, 共0.4382, 共0.2763,

0.3570, 0.3468, 0.2202, 0.3729, 0.4430, 0.3728,

0.3655兲 0.0788兲 0.2500兲 0.5202兲 0.0181兲 0.2351兲

are two soft modes along the wave-vectors V-⌫ and Z-⌫. In the case of monoclinic ZrO2, as shown in Fig. 4共c兲, no obvious soft mode was found. However, using a similar approach, Sternik and Parlinski71 found a soft model branch in the cubic phase of ZrO2 and considered it as an ensemble of independent anharmonic oscillators of the parabola-Gaussian or of the 2-4 polynomial forms.

FIG. 4. The calculated phonon dispersions. 共a兲 Li2ZrO3, 共b兲 Li6Zr2O7, 共c兲 monoclinic ZrO2.


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TABLE V. The calculated vibrational frequencies for each irreducible representation vibrational mode of Li2ZrO3, Li6Zr2O7, and monoclinic ZrO2 共unit: cm−1兲. R stands for Raman-active modes and I stands for the infrared-active modes. Li2ZrO3

Li6Zr2O7

Monoclinic ZrO2

Modes

Freq.

Modes

Freq.

Modes

Freq.

Modes

Bu共I兲a Au共I兲a Bu共I兲a Bu共I兲 Bg共R兲

⫺0.2 ⫺0.2

Bu共I兲a Au共I兲a

0.1 0.2

Au共I兲 Bg共R兲

283.3 284.8

Ag共R兲 Au共I兲

0.2 73.9 88.5

Bu共I兲a Bg共R兲 Au共I兲

0.2 75.0 84.5

Ag共R兲 Bu共I兲 Au共I兲

288.7 294.3 307.2

Bu共I兲

152.1 181.4 194.4 209.5

Ag共R兲 Ag共R兲 Bu共I兲 Bg共R兲

86.8 97.9 126.3 131.5

Bg共R兲 Ag共R兲 Bg共R兲 Bu共I兲

217.2 225.0

Bu共I兲 Au共I兲

133.4 134.6

231.3 241.1 260.8 267.1

Au共I兲 Ag共R兲 Au共I兲 Bg共R兲

272.2 299.3 314.3 317.9 331.2 358.4 360.8 400.3

Bu共I兲 Bg共R兲 Ag共R兲 Au共I兲 Bg共R兲 Bu共I兲 Bu共I兲 Au共I兲 Bg共R兲 Ag共R兲 Au共I兲 Au共I兲 Bg共R兲 Bu共I兲 Bg共R兲 Ag共R兲 Bu共I兲 Ag共R兲 Au共I兲 Bu共I兲 Bg共R兲 Bg共R兲 Ag共R兲 Bu共I兲 Au共I兲 Au共I兲 Bg共R兲 Ag共R兲 Bu共I兲 Au共I兲

Freq.

Modes

Freq.

425.6 431.3

Bu共I兲a Au共I兲a

0.0 0.1

Ag共R兲 Bg共R兲 Bu共I兲

444.6 446.2 447.0

Bu共I兲a Ag共R兲 Bg共R兲

0.2 119.2 168.0

308.6 310.4 318.5 319.6

Au共I兲 Bg共R兲 Bu共I兲 Ag共R兲

447.6 448.8 448.9 466.6

Ag共R兲 Au共I兲 Ag共R兲 Bg共R兲

174.7 174.7 183.3 221.4

Au共I兲 Au共I兲

322.0 331.4

Bu共I兲 Bg共R兲

479.1 485.3

Bu共I兲 Au共I兲

229.3 241.7

154.0 155.2 187.7 189.5

Au共I兲 Bg共R兲 Ag共R兲 Ag共R兲

337.5 338.7 340.3 346.4

Au共I兲 Bg共R兲 Ag共R兲 Ag共R兲

490.0 490.3 491.8 500.2

Au共I兲 Bu共I兲 Ag共R兲 Bg共R兲

251.2 298.9 312.0 313.1

Bu共I兲 Ag共R兲 Bg共R兲 Au共I兲 Bu共I兲 Au共I兲 Bg共R兲 Ag共R兲

192.1 195.6 205.7 218.8 219.6 220.6 221.0 222.7

Bu共I兲 Bg共R兲 Bg共R兲 Bu共I兲 Ag共R兲 Bg共R兲 Ag共R兲 Au共I兲

352.6 353.4 358.7 359.1 359.4 363.7 366.9 378.7

Au共I兲 Bu共I兲 Ag共R兲 Bg共R兲 Au共I兲 Ag共R兲 Bu共I兲 Au共I兲

515.7 517.3 530.5 534.9 556.0 570.6 576.8 580.3

Bu共I兲 Bg共R兲 Ag共R兲 Au共I兲 Bu共I兲 Ag共R兲 Bg共R兲 Au共I兲

320.9 330.1 344.1 348.1 355.5 385.0 386.6 398.0

400.6 401.1

Bu共I兲 Ag共R兲

228.7 238.6

Bu共I兲 Bg共R兲

383.3 396.8

Bg共R兲 Bu共I兲

585.3 593.3

Bu共I兲 Ag共R兲

406.4 465.9

428.9 450.9

Au共I兲 Bu共I兲

243.8 248.6

Bu共I兲 Au共I兲

397.8 398.6

Ag共R兲 Bg共R兲

628.0 631.9

Au共I兲 Bu共I兲

478.0 480.6

466.3 470.0 471.2 472.4 488.4 556.9 560.9 569.6 727.7

Bg共R兲 Ag共R兲 Bu共I兲

255.2 265.1 273.5

Bg共R兲 Ag共R兲 Bu共I兲

404.4 405.2 415.5

Au共I兲 Bu共I兲 Bg共R兲

702.6 764.6 812.9

Bg共R兲 Bg共R兲 Ag共R兲 Au共I兲 Bg共R兲 Ag共R兲 Au共I兲 Bu共I兲 Bg共R兲

485.1 524.0 534.9 567.7 589.5 624.7 625.8 708.0 742.1

a

Acoustical branches represent the motion of mass center.

From Fig. 4, one can see that in all three solids the lowest three modes 关one longitudinal 共LA兲 Au and two transverse 共TA兲 Bu兴 at ⌫ point 共which frequencies are very close to zero, as shown in Table V兲 represent the motion of mass center and are infrared active. As we know during phonon dispersion calculations, the translational-rotational invariance conditions for these solids are not fulfilled because the PHONON package does not know which independent parameters of the force constants should be renormalized in order to obey the translational-rotational invariance. Consequently, the acoustic phonon modes may not begin at the zero frequency at the center of the Brillouin zone.57,58 Therefore, the calculated frequencies at ⌫ points, as shown in Fig. 4 and


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FIG. 5. The calculated phonon density of states.

Table V, are not exactly zero, but very close to ⱕ0.2 cm−1 共as shown in Table V兲. The calculated phonon density of states of lithium zirconates and zirconia is shown in Fig. 5. As one can see that there are some similarities among these three compounds, their frequencies span up to 24 THz, and the number of high frequency modes is small and forming a separate band, as shown in Fig. 4. From the partial density of states of each displaced atom and the polarization vector analysis 共not show in the figure兲, overall, it can be found that the higher frequency region 共⬎17 THz in Fig. 5兲 comes from the O displacements while the lower frequency region 共⬍6 THz in Fig. 5兲 comes from the Zr displacements. Among the middle range 共6–17 THz兲, the vibrational frequencies are from all types of atoms. Among them, Zr vibrations mainly contribute to the low portion of this range 共⬍10 THz兲. As shown in Fig. 1 and Table I, each element may have more than one type with different coordination environments in the crystal. Therefore, their phonon dispersion behaviors are also different. The soft mode in Li2ZrO3 is mainly from Zr displacements with one type of Li displacements, while the soft modes in Li6Zr2O7 are mainly from Zr displacements with a small contribution from O vibration. The calculated phonon free energy of each solid versus temperature is shown in Fig. 6共a兲, from which the zero-point energies can be obtained and are listed in Table III. In order to explore their properties of capturing CO2, the thermodynamic properties of Li2ZrO3 are also shown in the same figure.40 As one can see, the zero-point energies of these solids are significant and must be included into predicting their thermodynamic properties 关Eq. 共2兲兴. From Fig. 6共a兲, one can see that at low-temperature Li6Zr2O7 has higher free energy compared with Li2ZrO3. However, when the temperature is increased, its free energy decreased rapidly. Figure 6共b兲 shows the calculated entropies of these solids versus the temperatures. Obviously, at 0 K, their entropies are zero and increase with increasing temperature. As shown in Table III, similar to other systems of larger number of solids,49 our calculated entropies of these three solids at room temperature are quite close to the experimental measured values, which indicate that our theoretical approach can achieve reasonable results and therefore can be used to evaluate other unknown systems. By


013102-13

(a)



(b)

FIG. 6. The calculated thermodynamical properties of ZrO2, Li2ZrO3, Li6Zr2O7, and Li2CO3. 共a兲 Free energies including zero-point energy vs temperatures. 共b兲 Entropies vs temperatures.

including these free energies and entropies at different temperatures into Eqs. 共1兲 and 共5兲, the thermodynamic properties of the reactions of lithium zirconates capturing CO2 can be evaluated, as described in Sec. III E. E. Capabilities of lithium zirconates capture CO2

From experimental investigations, lithium zirconates are good candidates of solid sorbents for CO2 capture in terms of large CO2 sorption capacity, infinite CO2 / N2 or CO2 / H2 selectivity, good reversibility, and high operating temperature.4,14–29 According to Eq. 共5兲, the calculated heat of reaction 共enthalpy change兲 for reactions 共a兲–共d兲 versus the temperatures is plotted in Fig. 7共a兲 and also summarized in Table VI. For comparison, the available experimental data for the reaction of Li2ZrO3 capturing CO2 from HSC-Chemistry database72 are also shown in Fig. 7共a兲. For the reaction of Li2ZrO3 capture CO2, as seen in Fig. 7共a兲, the data from HSC-Chemistry database have two discontinuities at temperatures of 623 and 683 K, which correspond to the solid-solid phase transitions of the product Li2CO3 at those temperatures.72 However, in the literature, there is no crystal structure available for those high-T solid phases of Li2CO3. Therefore, as an approximation, we used the structure of its low-T phase 共⬍623 K兲 to represent its structure in high-T range. The temperature effects were partially taken into account by phonon dynamics at different temperature without specific phase transition. That is why in Fig. 7共a兲, the simulated enthalpy of the

(a)

(b)

FIG. 7. The calculated thermodynamic properties of the reactions of lithium zirconates capturing CO2. 共a兲 The heat of reaction vs temperature. For the case of Li2ZrO3, the data from HSC are also presented in this figure. The discontinuities of HSC data at 623 and 683 K indicate solid-solid phase transitions of product Li2CO3. 共b兲 The contour plotting of calculated chemical potentials vs CO2 pressures and temperatures of the reactions. Y-axis plotted in logarithm scale. Only ⌬␮ = 0 curve is shown explicitly. For each reaction, above its ⌬␮ = 0 curve, their ⌬␮ ⬍ 0, which means the lithium zirconates absorb CO2 and the reaction goes forward, whereas below the ⌬␮ = 0 curve, their ⌬␮ ⬎ 0, which means the CO2 starts to release and the reaction goes backward to regenerate the sorbents.


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TABLE VI. The weight percentage of CO2 capture, the calculated energy change ⌬EDFT, the zero-point energy changes ⌬EZP, and the thermodynamic properties 共⌬H, ⌬G兲 of the CO2 capture reactions 共unit: kJ/mol兲. The turnover temperatures 共T1 and T2兲 of the reactions of CO2 capture by solids under the conditions of precombustion 共PCO2 = 20 bar兲 and postcombustion 共PCO2 = 0.1 bar兲 are also listed.

Reaction Li2ZrO3 + CO2 ↔ Li2CO3 + ZrO2

Absorbing CO2 共wt %兲

⌬EDFT

⌬EZP

⌬H 共T = 300 K兲

⌬G 共T = 300 K兲

28.75

⫺146.648

11.311

⫺158.562

Turnover T 共K兲 T1

T2

⫺103.845 ⫺113.18a

1000

780

⫺117.564

1140

880

1 3 Li6Zr2O7 + CO2 2 ↔ Li2CO3 + 3 ZrO2

39.28

⫺155.942

8.6243

⫺162.69a ⫺169.500

1 2 Li6Zr2O7 + CO2 1 1 ↔ Li2CO3 + 2 Li2ZrO3 + 2 ZrO2

26.19

⫺160.583

7.2808

⫺174.962

⫺124.417

1220

930

Li6Zr2O7 + CO2 ↔ Li2CO3 + 2Li2ZrO3

13.09

⫺174.525

3.2501

⫺191.369

⫺144.997

1500

1110

From HSC-Chemistry database package 共Ref. 72兲.

a

Li2ZrO3 capture CO2 reaction does not have discontinuity compared to the HSC data. As one can see from Fig. 7共a兲, overall our calculated heat of reaction for Li2ZrO3 is close to the data from HSC-Chemistry database, especially in the temperature range of 600–900 K, which is the temperature range for CO2 capture. Since there are no experimental data available for Li6Zr2O7, in Fig. 7共a兲 only our calculated reaction heats of Li6Zr2O7 capturing CO2 关reaction 共b兲–共d兲兴 are plotted. From them, one can see that Li6Zr2O7 absorbs CO2 to form lithium carbonate and lithium meta-zirconate 共Li2ZrO3兲, and the Li2ZrO3 can further absorb CO2 to dissociate to most stable ZrO2. According to Eq. 共1兲, for the reactions of lithium zirconates capturing CO2, we can explore the relationship among the chemical potential 关⌬␮共T , P兲兴, the temperature, and the CO2 pressure 共PCO2兲. This kind of relationship for reactions 共a兲–共d兲 is shown in Fig. 7共b兲. The line in Fig. 7共b兲 indicates that for each reaction, the ⌬␮共T , P兲 is approaching zero. Around the line is a good region for the absorption and desorption because of the minimum energy costs at the given temperature and pressure. Above the line, the solid 共Li2ZrO3, Li6Zr2O7兲 is favorable to absorb CO2 and to form Li2CO3, while below the line the Li2CO3 is favorable to release CO2 and regenerate lithium zirconate solids back. As described above and shown in Fig. 7, all of these reactions are thermodynamically favorable over a quite wide range of temperatures 共⬍900 K兲 and PCO2, which means that under this temperature range the CO2 is thermodynamically favored by lithium zirconates. But as a CO2 solid sorbent, the sorbent should not only be easy to absorb the CO2 in the first half cycle but also easy to release the CO2 from products 共Li2CO3 and ZrO2, for example兲 in the second half cycle. The operating conditions for absorption/desorption processes are depending on the pre- and postcombustion technologies. Under precombustion conditions, after water-gas shifting, the gas stream mainly contains CO2, H2O, and H2. The partial CO2 pressure is around 20–25 bar and the temperature is around 673–723 K. To minimize the energy consumption, the ideal sorbents should work at these pressure and temperature ranges to separate CO2 from H2. This temperature, denoted T1, is listed in Table VI, and is the temperature above which the lithium zirconates cannot absorb CO2 anymore and will start to release CO2. This indicates that during the first half cycle to capture CO2, the operating temperature should be lower than T1, whereas the operating temperature may be higher than T1 共depending on the desired obtained CO2 pressure兲 during the second half cycle of sorbents regeneration to release CO2. For postcombustion conditions, the gas stream mainly contains CO2 and N2, the partial pressure of CO2 is around 0.1–0.2 bar, and the temperature range is quite different. However, the low-temperature capture is desired. The DOE programmatic goal for postcombustion CO2 capture is to capture at least 90% CO2 with the cost in electricity no more


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than 35%, whereas in the case of precombustion CO2 capture, the goal is to capture at least 90% CO2 with the cost in electricity no more than 10%.73 The turnover temperatures 共denoted as T2兲 for postcombustion capture by these two lithium zirconates are also listed in Table VI. From Table VI and Fig. 7共b兲, one can see that these two lithium zirconates capture CO2 up to higher temperatures 共T1 ⬎ 1000 K兲 compared with desired precombustion condition 共673–723 K兲. Therefore, they are not good sorbents for capturing CO2 in precombustion technology. However, they could be used for high-temperature postcombustion CO2 capture with T2 = 780 and 880 K for Li2ZrO3 and Li6Zr2O7, respectively, as experimental results indicate that Li2ZrO3 reacts immediately with ambient CO2 共PCO2 = 1 bar兲 in the range of 723–823 K and products react and return reversibly to lithium zirconate at temperatures above 873 K.15,16,31 From Fig. 7共b兲, one can see that during the first half cycle of absorbing CO2, the Li6Zr2O7 can be fully converted into ZrO2 and Li2CO3 because the partial reactions 关共c兲 and 共d兲兴 do not gain any energetic advantage. Interestingly, during the second half cycle of capturing, when the Li2CO3 and the ZrO2 react with each other to release CO2 and regenerate the sorbent back, only Li2ZrO3 can be regenerated. As shown in Fig. 7共b兲, the reaction curve of Li2ZrO3 capturing CO2 is always higher than the other three curves of Li6Zr2O7 reacting with CO2. Therefore, the regeneration first forms Li2ZrO3, not Li6Zr2O7. The Li6Zr2O7 can only be formed either at low CO2 pressure 共T fixed兲 or at high temperature 共PCO2 fixed兲 through Li2ZrO3 further reacting with Li2CO3 and ZrO2. In order words, no matter what the initial solid is Li2ZrO3 or Li6Zr2O7, after first sorption/ desorption cycle, the following cycle is only for the reaction Li2ZrO3 + CO2 = Li2CO3 + ZrO2 and there is no Li6Zr2O7 left in the system. This is in good agreement with the experimental findings as Pfeiffer et al.4 reported that the hexa-lithium zirconate 共Li6Zr2O7兲 absorbed four times more CO2 than Li2ZrO3, and its CO2 sorption rate is faster than Li2ZrO3 at short times, but after long times, their capture behaviors became similar. This result indicates that there is no advantage to use Li6Zr2O7 over Li2ZrO3 as CO2 sorbent because they have the same functionality after the first cycle. From Table VI and Fig. 7共b兲, one can see that the reverse reaction is not just to dissociate Li2CO3 but also to regenerate Li2ZrO3 from Li2O by reacting with ZrO2, which involves net energy gain, and lay down the conditions for ⌬␮ ⬎ 0 compared with the case of Li2O. In other words, the presence of ZrO2 can destabilize the stable phase of Li2CO3 and make the reverse reaction to release CO2 less energy required.40 IV. SUMMARY AND CONCLUSIONS

The electronic structural and phonon properties of Li2ZrO3, Li6Zr2O7, and monoclinic phase ZrO2 are investigated by the density-functional theory and phonon dynamics. Their electrochemical properties and the thermodynamic properties of CO2 absorption/desorption are analyzed. The optimized structures and calculated bulk modulus and cohesive energy are in good agreement with experimental measurements. The calculated band gaps are 3.90 eV 共indirect兲, 3.98 eV 共direct兲, and 3.76 eV 共direct兲 for Li2ZrO3, Li6Zr2O7, and ZrO2, respectively. The s orbital of O contributes to the lower second VBs of Li2ZrO3, Li6Zr2O7, and ZrO2, while its p orbitals mainly contribute to their first VBs. In all three cases, all the s, p, and d orbitals of Zr contribute to both VBs, but its d orbitals have higher contributions than its s and p orbitals. In both Li2ZrO3 and Li6Zr2O7, comparing with its s orbital, the p orbital of Li has a larger contribution to the upper portion of their first VBs. By assuming half-cell reaction versus Li/ Li+, the calculated Li intercalation open circuit voltages and energy densities of Li2ZrO3 are higher than that of Li6Zr2O7, which indicate that as a cathode material Li2ZrO3 is better than Li6Zr2O7. The phonon dispersions and phonon density of states for Li2ZrO3 and Li6Zr2O7 were calculated by the direct method. For Li2ZrO3, around the high-symmetric points Z and L, there is one soft mode that originates mainly from displacing Zr atoms and displacing one type of Li atoms. In Li6Zr2O7, among the high-symmetric point intervals V-⌫ and Z-⌫, there are two soft modes which are mainly from Zr displacements with a small contribution from O vibration. Based on the phonon dispersion, the phonon free energy, the


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internal energy, and the entropy of these solids were evaluated within the harmonic approximation and have been used to analyze the chemical potentials of the reactions of CO2 capture by these two lithium zirconates. From the calculated thermodynamical properties of these two lithium zirconates reacting with CO2, we found that overall the performances of Li2ZrO3 capturing CO2 are better than that of Li6Zr2O7. In the first half cycle for the sorbent to absorb CO2 to form lithium carbonate, Li6Zr2O7 is better than Li2ZrO3 because the former reaction releases more heat of reaction and has a lower Gibbs free energy and a higher CO2 capture capacity. However, during the second half cycle to regenerate the sorbent from carbonate and zirconia and to release CO2, instead of forming Li6Zr2O7, the main product is the thermodynamically favorable Li2ZrO3. Therefore, compared with Li2ZrO3, there is no advantage for using Li6Zr2O7 as CO2 sorbent. ACKNOWLEDGMENTS

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