Thermodynamic Analysis of Cerium-Based Oxides for Solar

Article pubs.acs.org/EF

Thermodynamic Analysis of Cerium-Based Oxides for Solar Thermochemical Fuel Production Jonathan R. Scheffe*,† and Aldo Steinfeld†,‡ †

Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland Solar Technology Laboratory, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

‡

ABSTRACT: The thermodynamics of ceria-based metal oxides MxCe1−xO2, where M = Gd, Y, Sm, Ca, Sr, have been studied in relation to their applicability as reactive intermediates in solar thermochemical redox cycles for splitting H2O and CO2. Oxygen nonstoichiometry was modeled and extrapolated to high temperatures and reduction extents by applying an ideal solution model in conjunction with a defect interaction model. Subsequently, relevant thermodynamic parameters were computed and equilibrium H2 and CO concentrations determined as a function of reduction conditions (T, PO2) and ensuing oxidation temperature. At 1 atm and above 1673 K, the degree of reduction is negatively correlated to dopant concentration, regardless of the type of dopant considered. Consequently, at a given reduction temperature, more H2 and CO is generated at equilibrium for pure ceria compared to any of the other doped ceria materials considered. Although the reduction enthalpy decreases as the dopant concentration increases, the overall solar-to-fuel energy conversion efficiency is greater for pure ceria (20.2% at δ = 0.1, PO2 = 10 ppm). Only when considering heat recovery of nearly 100% are theoretical efficiencies higher for the dopants.

■

INTRODUCTION Ceria based materials are capable of achieving remarkably high vacancy concentrations at elevated temperatures and low oxygen partial pressures.1,2 As a result, these materials are attractive as reactive intermediates in thermochemical redox cycles for the production of solar fuels.3−5 These H2O/CO2splitting cycles consist of two separate thermochemical reactions, namely, a high-temperature endothermic reduction and a low-temperature exothermic oxidation, as represented by δ CeO2 → CeO2 −δ + O2 (g) (1) 2 CeO2 −δ + δH2O(g) → CeO2 + δH2(g)

(2a)

CeO2 −δ + δCO2 (g) → CeO2 + δCO(g)

(2b)

The thermodynamics of most of the rest of the aforementioned dopants are not well documented to date. The thermodynamics of nonstoichiometric ZrO2−CeO2 have been studied at elevated temperatures using a CALPHAD type modeling approach, but experimental data is limited to much higher ZrO2 mole fractions than are feasible for thermochemical redox cycles.11 Several dopants have been thermodynamically examined based on O2 nonstoichiometry data. Most of these studies were conducted at temperatures much lower than those required for solar thermochemical fuel production. The motivation for much of the work has arisen from the application of ceria as a solid electrolyte in solid oxide fuel cells.1 Dopants are capable of introducing oxygen vacancies at more moderate temperatures than pure ceria, resulting in rapid electron and oxygen transport through the lattice.12 Although dopants such as Y2O3,13 Sm2O3,14−16 Gd2O3,16−18 CaO,16,19,20 and SrO21 have been extensively investigated, there has been very little research devoted to their applications in thermochemical redox cycles for splitting H2O and CO2. Chueh et al.22 experimentally investigated Sm doped ceria for the production of syngas and methane, but the high-temperature thermal reduction was not analyzed. More recently, Meng et al. experimentally investigated several dopants for H2 production including CaO, SrO, and Y2O3, but only under a single oxidizing and reducing condition (500 °C/1500 °C).8 In the present study, the thermodynamics of selected ceria dopants, namely, Y2O3, Sm2O3, Gd2O3, CaO, and SrO, are examined at conditions relevant to thermochemical splitting of H2O and CO2. To do so, we have modeled low-temperature O2 nonstoichiometry data available in the literature, and

Reduction proceeds via the formation of oxygen vacancies and the release of gaseous O2, resulting in the subsequent change in stoichiometry (δ). Oxidation proceeds with H2O and/or CO2, thereby releasing H2 and/or CO and reincorporating oxygen into the lattice. As a result, the number of oxygen vacancies created during reduction is directly related to the yield of fuel production that can be achieved. Because ceria is recycled, the net reaction is simply the splitting of H2O and/or CO2, whose products can be used directly as a fuel or further processed into liquid hydrocarbons via Fischer−Tropsch and other catalytic processes.6 In contrast to the direct thermolysis, fuel and O2 are derived in different steps, thereby eliminating the need for high-temperature separation. A number of dopants have been used successfully in thermochemical redox cycles to promote the reduction of ceria to a nonstoichiometric state at moderate temperatures. Most notably, zirconium oxide3,7,8 and chromium oxide9 doped ceria have exhibited remarkably lower thermal reduction temperatures than undoped ceria. Additionally, Fe, Ni, Mn, and Cu oxide based dopants have been investigated with various degrees of success.10 © 2012 American Chemical Society

Received: November 28, 2011 Revised: January 19, 2012 Published: January 22, 2012 1928

dx.doi.org/10.1021/ef201875v | Energy Fuels 2012, 26, 1928−1936

Energy & Fuels

Article

Accounting for defect interactions has yielded realistic fits to oxygen nonstoichiometry experimental data of undoped and yttria doped ceria for δ as large as 0.1. 13,16 Otake et al.13 found that the predominant defect associations occur according to

extrapolated theoretical O2 nonstoichiometries at higher temperatures. We have computed equilibrium concentrations of H2 and CO production under realistic conditions and considered the effect of the dopant on fuel yields and solarto-fuel energy conversion efficiencies. The motivation for studying these specific dopants arises from their readily available O2 nonstoichiometry data in the literature. Inclusion of other dopants, such as ZrO2, would require an entirely different modeling process, either from a CALPHAD technique11 or more fundamental approach based on thermodynamics of the individual solid phases.23 This analysis provides a framework to straightforwardly determine ceria-based thermodynamic data at high temperatures relevant to thermochemical redox cycles, from lower-temperature data readily available in the literature.

2Ce′Ce + V ″O → (Ce′CeV ″OCe′Ce)x

where electrons interact with doubly ionized oxygen vacancies to form an electron-vacancy association, (CeCe ′ Vo″ CeCe ′ )x. The associated equilibrium constant, K2, for this reaction can be expressed as K2 =

■

CERIA NONSTOICHIOMETRY The reduction of ceria and doped-ceria, according to Kröger− Vink notation,24 and an ideal solution model (no defect interactions), can be expressed as x x OO + 2CeCe →

1 O2 (g) + V ″O + 2Ce′Ce 2

(3)

and its relation to the standard Gibbs free energy (ΔG°), (5)

Charge and site balances yield the following relations that enable one to solve explicitly for δ as a function of PO2, T, and the dopant concentration X: x ] = 1 − X − 2δ [CeCe

0.5X + δ [V ″O] = 2

X+δ 2

[Ce′Ce] = 2δ

2−X−δ 2

[Ce′Ce] + X 2

V ″O =

[Ce′Ce] + 2X 2

material

2 − X /2 − δ x] [OO = 2

x] = [OO

V ″O =

for+3 dopants and undoped ceria

for+2 dopants

(9)

Table 1. Materials Evaluated, the Temperature Range in which They Were Experimentally Investigated, and Reference temp. range

CeO2 Ce0.99Ca0.01O1.99 Ce0.945Ca0.045O1.955 Ce0.86Ca0.14O1.86 Ce0.99Sr0.01O1.99 Ce0.9Sm0.1O1.95 Ce0.8Sm0.2O1.9 Ce0.9Gd0.1O1.95 Ce0.8Gd0.2O1.9 Ce0.9Y0.1O1.95 Ce0.8Y0.2O1.9

for+3 dopants and undoped ceria [V ″O] =

(8)

The preceding equations, along with knowledge of PO2 and δ from experimental data, enable one to numerically solve for K1 and K2 at a constant temperature. Assuming the natural logarithm of K1 and K2 have reciprocal temperature dependence (see eq 5), it is possible to extrapolate these constants to temperatures relevant to thermochemical fuel production. Experimental O2 nonstoichiometry, as a function of PO2 and temperature, for several dopants has been well documented in the literature. The dopants considered in this analysis are summarized in Table 1, along with the temperature range in which they were experimentally investigated and the accompanying reference.

(4)

ΔG° = − RT ln K1

[Ce′Ce]2 [V ″O]

2δ = [Ce′Ce] + 2(Ce′CeV ″OCe′Ce)x

[Ce′Ce]2 [V ″O]PO21/2 x 2 x [CeCe ] [OO]

(Ce′CeV ″OCe′Ce)x

Charge and site balances yield

where oxygen atoms on oxygen lattice sites (OOx ) and cerium x on cerium lattice sites (CeCe ) result in the formation of oxygen vacancies (VO″ ), electrons localized on cerium lattice sites (CeCe ′ ), and the evolution of gaseous oxygen. The oxygen partial pressure (PO 2) dependence on the equilibrium concentrations of the above species can be derived from the equilibrium constant (K1) of the above reaction, K1 =

(7)

for+2 dopants (6)

For large deviations from stoichiometry, an ideal solution cannot necessarily be assumed. In fact, the equilibrium nonstoichiometry of pure ceria for δ > 0.01 cannot be approximated by an ideal solution model.2 As dopants are introduced into the lattice, deviations up to 0.05 are achievable without discernible defect interactions.15,17 For applications such as thermochemical fuel production, however, δ > 0.05 are often desirable to maximize molar fuel yields.3,4,10 Therefore, a more realistic model of the nonstoichiometry dependence on the PO2 and T relationship is necessary for an accurate prediction of δ, relevant to thermochemical cycles.

1023−1773 1073−1773 1073−1773 1073−1773 1073−1773 973−1273 973−1273 973−1373 973−1273 973−1373 973−1373

K K K K K K K K K K K

ref 2 19 19 19 21 15 15 18 17 13 13

Computed values for K1 and K2 are shown in Figure 1 for several dopants and dopant concentrations at temperatures ranging from 1073 to 1373 K. The natural logarithm of both K1 and K2 are shown to have a reciprocal temperature dependence for all materials considered. As expected, K1 increases as the temperature is increased. Alternatively, K2 is inversely correlated to temperature, indicating that defect interactions 1929


Energy & Fuels

Article

of K2, are greater for undoped ceria and decrease as the dopant concentration increases. Predicted O2 nonstoichiometry of 4.5% CaO doped CeO2 from 1073 and 1773 K is shown alongside experimental data in Figure 2a. The fits were derived from extrapolation of K1 and K2 from 1073 to 1373 K, and they are in good agreement with experimental data up to 1773 K and δ = 0.1, although K1 and K2 were only fit up to 1373 K. Additionally, the advantage of accounting for defect interactions is clear when compared to only an ideal solution model, shown in Figure 2b. For δ < 0.01, agreement between the model and data is satisfactory, but for high oxygen nonstoichiometries the model underestimates the data. The agreement between model and data at high temperatures, when accounting for defect interactions, gives assurance that extrapolating to higher temperatures should be applicable when high temperature data is not readily available. Predicted O2 nonstoichiometry up to 1773 K of 10% Sm2O3 doped CeO2, which has been studied extensively below 1473 K, is shown alongside experimental data in Figure 2c and d. Again, the fits are substantially better for δ > 0.01 when accounting for defect interactions. At elevated temperatures, dopant concentration and O2 nonstoichiometry are negatively correlated for all dopants considered. As seen in Figure 3 for T = 1800 K and PO2 = 10−5 atm, pure ceria has a larger predicted δ than all other doped ceria materials considered. The trend does not appear to be dependent on the specific type of dopant. This is contrary to

Figure 1. Best fits of (a) K1 and (b) K2 as a function of temperature (1073 to 1373 K).

become less predominant as the temperature is increased. These results are in good agreement with those of Otake et al.13 and Schneider et al.13,16 Not surprisingly, at a given temperature, K1 increases as the dopant concentration is increased. Additionally, defect interactions, as indicated by the magnitude

Figure 2. Experimental O2 nonstoichiometry data compared to thermodynamic models for (a) 4.5% CaO doped CeO2 accounting for defect interactions, (b) 4.5% CaO doped CeO2 assuming an ideal solution model, (c) 10% Sm2O3 doped CeO2 accounting for defect interactions, and (d) 10% Sm2O3 doped CeO2 assuming an ideal solution model. 1930


Energy & Fuels

Article

Figure 4. Reduction enthalpy at δ = 0.1 as a function of dopant concentration. For Sm2O3 doped CeO2, values were calculated at δ = 0.08.

Figure 3. Predicted deviation from stoichiometry as a function of dopant concentration at T = 1800 K and PO2 = 10−5 atm.

behavior observed at lower temperatures and pressures, where O2 nonstoichiometry increases as dopant concentration increases.2,13,15,17,19,21 However, Meng et al. have shown that, at 1773 K, 10% Y2O3, CaO, and SrO all reduce to a lesser extent than pure ceria, agreeing well with these results.8 These results are contrary to dopants such as Fe2O3, CuO, Mn2O3, NiO, ZrO2, and Cr2O3, which are well documented to increase O2 nonstoichiometry at elevated temperatures compared to pure ceria.3,7−10 In addition to δ achieved at a given temperature, another useful parameter to consider when evaluating various dopants is the reduction enthalpy (ΔHred) required to achieve a given δ. This thermal energy is directly related to the solar input required to drive the redox reaction. Normalized to the degree of reduction, it can be expressed as ΔHred =

δ ∫δ f ΔHO2 i

δf − δi

these materials, values are only integrated to δ = 0.08. As seen, ΔHred tends to decrease as the dopant concentration is increased. For pure ceria and 1% SrO and CaO doped ceria, ΔHred ∼ 860 kJ/mol. For 20% Sm2O3 and Y2O3 doped ceria, ΔHred decreases by more than 10% to 750 kJ mol−1 and 770 kJ mol−1, respectively. Interestingly, ΔHred of Sm2O3 doped ceria is considerably less than that of the other dopants considered. These observations present compelling evidence that although doped ceria is expected to reduce to a lesser extent than pure ceria at a given reduction temperature, there may be advantages in terms of the amount of ΔHred required to achieve that reduction.

■

EQUILIBRIUM THERMODYNAMICS The oxidation of reduced ceria with H2O is simply the sum of ceria oxidation with O2 and water dissociation reactions, as shown:

dδ (10)

where ΔHO2 is defined as the oxygen molar enthalpy and varies as a function of δ. δi is the initial δ before reduction, and δf is the stoichiometry obtained after reduction. Knowledge of ΔHO2 as a function of δ can be derived from O2 nonstoichiometry data as a function of PO2 and T, according to ΔGO2 = RT ln PO2

(11)

ΔGO2 = ΔHO2 − T ΔSO2

(12)

CeO2 −δ +

δH2O → δH2 +

ln PO2 =

RT

−

δ= constant

° ) (ΔG H 2O

(14) ° (ΔGrxn,H ) 2O

where ΔGoxd ° is the standard free energy of ceria oxidation with O2, ΔG°H2O is the standard free energy of water dissociation, and ΔG°rxn,H2O is the standard free energy of ceria oxidation with H2O. According to Sørenson et al., ΔGoxd ° can be determined by numerical integration of the oxygen molar free energy:25 ° ΔGoxd =

ΔSO2 R

δ O2 2

° (ΔGoxd )

CeO2 −δ + δH2O → CeO2 + δH2

where ΔGO2 is the oxygen molar free energy and SO2 is the oxygen molar entropy. By equating the preceding equations it is clear that both ΔHO2 and ΔSO2, as a function of δ, can be solved by determining the slope and intercept of ln PO2 verses 1/T for a given δ, as seen below. ΔHO2

δ O2 → CeO2 2

∫δ

δf

i

ΔGO2 dδ

(15)

The oxygen molar free energy is determined from knowledge of the oxygen molar enthalpy and entropy, as discussed in eqs 10−12. ΔGH2O° is derived from known thermodynamic parameters of H2(g), O2(g), and H2O(g). Values were obtained from the NIST-JANAF thermochemical tables. According to eq 13, ΔGrxn,H ° 2O = ΔG°oxd + ΔGH° 2O . Analogously, ΔG°rxn,CO2 = ° 2 . Thus, the oxidation of reduced ceria with H2O ΔG°oxd + ΔGCO

(13)

ΔHred as a function of δ (δi = 0) for all dopants considered is shown in Figure 4. All parameters were calculated directly from experimental data in the literature, and all values are integrated to δ = 0.1, with the exception of 10% and 20% Sm2O3 doped ceria because of insufficient data at high stoichiometries. For 1931


Energy & Fuels

Article

(or CO2) can therefore be considered a competition between the driving force of ceria oxidation with O2 and that of water reduction. Knowledge of the oxygen molar free enthalpy (ΔGO2) as a function of δ can also be used to predict equilibrium yields of H2 and CO during H2O or CO2 oxidation of ceria.5 The equilibrium constant of water reduction (Kw) can be related to PO2, H2, and H2O concentrations at 1 atm: Kw =

[H2]PO21/2 [H2O]

(16)

Combining this with eq 10, the following expression can be derived, which relates the oxygen molar free enthalpy to equilibrium hydrogen and water concentrations:5 ⎡ K [H O] ⎤ ΔGO2(δf = δ − [H2]) = RT ln⎢ w 2 ⎥ ⎣ [H2] ⎦

(17)

Analogous expressions can be derived for the dissociation CO2 or for the simultaneous dissociation of CO2 and H2O. Assuming that the primary mode of CO2 reduction is via the formation of CO rather than C,14 the following equilibrium constant for CO2 reduction, Kc, can be derived Kc =

[CO]PO21/2 [CO2 ]

(18)

Therefore, for simultaneous H2O and CO2 dissociation, ⎡ K [H O] ⎤ ΔGO2(δf = δ − [H2] − [CO]) = RT ln⎢ w 2 ⎥ ⎣ [H2] ⎦ ⎡ K [CO2 ] ⎤ = RT ln⎢ c ⎥ ⎣ [CO] ⎦

Figure 5. (a) ΔGrxn,H ° 2O calculated at δ = 0.1 and (b) subsequent H2 equilibrium concentrations ([H2O]i = 0.1) as a function of temperature for Y2O3 doped CeO2.

(19)

ΔGrxn,H ° 2O at δ = 0.1 for pure CeO2, 10% Y2O3 and 20% Y2O3 doped ceria are shown in Figure 5a. For all materials, the reaction is thermodynamically favorable below about 1200 K. As the dopant concentration increases, ΔGrxn,H2O° becomes less sensitive to temperature. Below 1200 K, the oxidation of ceria has a smaller free energy than either 10% or 20% Y2O3, but the opposite is true at higher temperatures. The implications of this on equilibrium H2 concentrations can be seen in Figure 5b, again for δ = 0.1 and 1 mol oxide. The initial water concentration used in the computation equals that of the δ achieved during thermal reduction ([H2O]i = 0.1). Until 1200 K, pure CeO2 generates more H2 at equilibrium, as expected from the lower free energy change (Figure 5a). However, at higher temperatures, the H2 yield increases with increasing Y2O3 concentration, as a result of the weaker temperature dependence of ΔG°rxn,H2O compared to pure CeO2. This trend is similar for all other dopants and concentrations considered in this study, but for stylistic purposes, the results are omitted from the figure. Interestingly, there are no temperatures where ΔGrxn,H ° 2O for the oxidation of 19% ZrO2 doped ceria is below zero.26 This is evidence that oxidation of reduced ZrO2 doped ceria with H2O may be limited by thermodynamic barriers and require excessive amounts of H2O to proceed. The reaction of reduced ceria in the presence of both H2O and CO2 is dictated not only by the oxygen molar free energy and one equilibrium constant (Kw or Kc), but by both Kw and Kc in relation to one another (see eq 18). The ratio of H2/CO

produced is therefore directly related to the ratio Kw/Kc. For larger H2O equilibrium constants, the production of H2 via H 2 O dissociation is more favorable than CO via CO 2 dissociation. Likewise, for larger CO2 equilibrium constants, the production of CO is more favorable than H2. At temperatures below 1100 K, Kw > Kc, and H2O dissociation is more favorable than CO2 dissociation. The effect of this can be seen from the H2/CO equilibrium plot shown in Figure 6. The reaction considered is reduced 1% SrO doped ceria (δf = 0.081 at 1800 K, PO2 = 10−5 atm) in the presence of H2O and CO2 and in a 2:1 ratio ([H2O]i = 2[CO2]i = 0.162). All ratios of H2/CO are greater than the input ratio of 2:1 until 1100 K, because of the larger H2O equilibrium constant. However, a 2:1 CO/H 2 ratio is predicted when Kw = Kc . At higher temperatures, an unproportionate amount of CO is expected due to a larger equilibrium constant compared to H2O dissociation. Beyond 1000 K, the total yield decreases due to an increasing ΔG°rxn resulting from larger H2O and CO2 dissociation free energies. With larger H 2 O and CO 2 concentrations compared to δf, the equilibrium can be shifted, yet this does not come without an energy penalty because of the sensible heat required to heat excess reactant gases. 1932


Energy & Fuels

Article

Figure 6. H2 and CO equilibrium yields for the reaction of 1% SrO doped CeO2 reduced at T = 1800 K and PO2 = 10−5 atm. [H2O]i = 2[CO2]i = 2δ = 0.162.

■

EFFICIENCY ANALYSIS The solar-to-fuel energy conversion efficiency for the production of H2 from 1 mol ceria, according to eqs 1 and 2a is defined as nsolar‐to‐fuel =

HHV H2[H2] Q solar

(20)

where HHV H2 is the higher heating value of hydrogen, 285.5 kJ/mol, [H2] is the amount of H2 produced (in moles) during the water-splitting step per mole CeO2, and Qsolar is the amount of incident concentrated solar energy required to produce that amount of H2. Qsolar is defined as Q solar = {[ΔHH2O|298K → TL [H2O]i +

T

∫T H Cp,CeO2 dT ] L

× (1 − HR ) + ΔHred δ}/nabsorption

(21)

where ΔHH2O|298 K→TL is the enthalpy required to heat water from room temperature to the oxidation temperature (TL), [H2O]i is the initial molar concentration of water, Cp,CeO2 is the heat capacity of CeO2, HR is the fraction of heat recuperated, ΔHred is the reduction enthalpy, δ is the deviation from stoichiometry achieved during thermal reduction, and nabsorption is the solar energy absorption efficiency. ⎛ σT 4 ⎞ ⎟⎟ nabsorption = 1 − ⎜⎜ ⎝ IC ⎠

(22)

where σ is the Stefan−Boltzmann constant, I is the normal beam insolation, and C is the solar flux concentration ratio of the incident concentrated solar radiation.27 The heat capacity of all materials was assumed to be the same as pure ceria because of lack of data available in the literature. Values were extrapolated from Riess et al.28 nsolar‑to‑fuel for Y2O3, G2O3, and CaO doped ceria, as a function of the oxidation temperature in the range 700−1300 K, is shown in Figure 7. In general, nsolar‑to‑fuel decreases as the dopant concentration increases, and it is not highly dependent on the particular type of dopant considered. As a base case, no heat recovery was considered, the δ achieved during reduction was held constant at δ = 0.1, and PO2 = 10−5 atm. The temperature

Figure 7. Solar-to-fuel energy conversion efficiency as a function of the oxidation temperature (δ = 0.1, PO2 = 10−5 atm) for (a) Y2O3 doped CeO2, (b) Gd2O3 doped CeO2, and (c) CaO doped CeO2. No heat recovery is assumed.

required to achieve this δ was interpolated from the thermodynamic models of δ vs PO2. As seen in Figure 7a, pure ceria is expected to achieve a maximum nsolar‑to‑fuel of 20.2% at 1000 K oxidation temperature. This is greater than both 10% and 20% Y2O3 doped ceria, whose maximum efficiencies are 16.5% and 15.7%, respectively. The same trend is observed for 10% and 20% G2O3 doped ceria whose maximum efficiencies are slightly 1933


Energy & Fuels

Article

Table 2. Reduction Temperatures Required to Achieve δ = 0.1 at PO2 = 10−5 atm, Oxidation Temperature at Maximum nsolar‑to‑fuel, and Enthalpic Losses at These Conditions material

Tred (K)

Toxd (K)

H2 (mmol)

heating ceria (kJ)

heating H2O (kJ)

absorption losses (kJ)

dHred (kJ)

CeO2 Ce0.99Ca0.01O1.99 Ce0.945Ca0.045O1.955 Ce0.86Ca0.14O1.86 Ce0.99Sr0.01O1.99 Ce0.9Sm0.1O1.95 Ce0.8Sm0.2O1.9 Ce0.9Gd0.1O1.95 Ce0.8Gd0.2O1.9 Ce0.9Y0.1O1.95 Ce0.8Y0.2O1.9

1805.4 1823.4 1837.1 1912.4 1819.8 1887.6 1935.8 1858.9 2002.7 1993.9 2020.3

1000 900 900 800 900 900 900 800 800 900 800

91.9 96.8 95.7 96.1 96.4 92.2 89.5 96.8 96.3 95.0 96.2

64.0 73.3 74.4 88.1 73.0 78.4 82.2 83.8 95.3 86.8 96.7

7.0 6.6 6.6 6.2 6.6 6.6 6.6 6.2 6.2 6.6 6.2

15.6 17.6 18.2 24.0 17.4 20.8 22.9 24.5 37.2 29.3 32.9

43.1 43.3 41.9 39.8 42.7 38.7 31.8 41.6 40.4 40.7 38.3

lower at 15.2% and 13.5%. As the dopant concentration decreases below 10%, in the case of 1% and 4.5% CaO doped ceria, the behavior approaches that of pure ceria but never exceeds its maximum efficiencies (Figure 7c). In the case of pure ceria and low dopant concentrations, nsolar‑to‑fuel peaks between 900 and 1000 K. This is in contrast to higher dopant concentrations, whose efficiencies peak at lower temperatures, mainly because of lower predicted H2 equilibrium yields at higher temperatures. These results indicate that although reduction enthalpies (ΔHred) decrease as the dopant concentration increases, the total energy required to reduce ceria still increases as the dopant concentration increases. Individual enthalpy requirements at maximum efficiencies (δ = 0.1, PO2 = 10−5) are summarized in Table 2 for all materials considered, and it is clear that the largest energy losses come from heating ceria (∫ TTLHCp,CeO dT). The required reduction temperature increases as the dopant concentration increases, resulting in larger sensible heat requirements and lower efficiencies. For example, pure ceria is expected to reduce to δ = 0.1 at 1805.4 K, and heating from 1000 K to this temperature requires 64 kJ mol−1. In contrast, 20% Y2O3 is not expected to reduce to δ = 0.1 until 2020.3 K, resulting in 96.7 kJ mol−1 required. Additionally, adsorption losses are proportionally greater for doped materials because of their T4 dependence. The energy required to heat water is much smaller than all the other aforementioned losses. Thus, recovery of the sensible heat of ceria during the redox cycles has a substantial impact on the efficiency. The theoretical maximum efficiencies of pure ceria and 4.5% and 14% CaO doped ceria, assuming HR = 0, 50, and 100% is shown in Figure 8. While 100% efficiency is, of course, not practical, it is conceptually interesting to decouple reaction enthalpies from recyclable heat to understand what the ultimate thermodynamic limits of the process are. Increasing HR from 0% to 50% results in efficiency increases of 46% for pure ceria, 49% for 4.5% CaO, and 54% for 14% CaO. The increase in efficiencies scales with the dopant concentration because of the larger contribution of reduction enthalpies compared to heating ceria and water. However, pure ceria is still expected to be more efficient compared to the doped materials. Only at 100% heat recovery do the reduction enthalpies dominate compared to heating losses and absorption losses. Even so, 14% CaO doped ceria is only 2% more efficient than pure ceria (60.1% verses 58.1%), though its reduction enthalpy is 8.3% smaller (39.8 to 43.1). The discrepancy between these numbers is the result of larger absorption losses due to higher reduction temperatures (1912.4 K versus 1805.4 K). 2

Figure 8. Solar-to-fuel energy conversion efficiency as a function of heat recovery for CaO doped CeO2.

For a given material, nsolar‑to‑fuel for CO2 splitting is slightly higher than that for H2O splitting because of the higher HHV of CO, more favorable oxidation conditions at higher temperatures (larger Kc), and less sensible heat required to heat the CO2. For example, the reaction of pure ceria reduced to δ = 0.1 at PO2 = 10−5 atm with 0.1 mol CO2 results in a maximum nsolar‑to‑fuel = 21.6%, compared to 20.2% for H2O splitting.

■

CONCLUSIONS

Oxygen nonstoichiometry of several doped cerium oxide-based materials was modeled as a function of temperature and oxygen partial pressure. When allowing for defect interactions to occur, δ up to 0.1 can be modeled accurately. This is in contrast to an ideal solution model, which is only capable of modeling experimental data up to δ = 0.01 for pure ceria and 0.05 for large dopant concentrations. With an accurate model in hand, experimental data, which is readily available at low temperatures, can be extrapolated and applied to higher temperature relevant to thermochemical redox cycles. Although an increase in dopant concentration results in a higher concentration of oxygen vacancies at low temperatures and oxygen partial pressures, the reverse trend is observed at higher temperatures and pressures for all dopants considered. Under conditions applicable to thermochemical redox cycles (T > 1700 K, PO2 = 10−5 atm), pure ceria is expected to achieve 1934


Energy & Fuels

Article

a larger deviation from stoichiometry than all of the dopants and concentrations considered. The free energy of oxidation (ΔGrxn°) of reduced ceria with either H2O or CO2 becomes less sensitive to temperature as the dopant concentration is increased. As a result, below 1200 K, ΔG rxn ° is greater for pure ceria compared to doped ceria, resulting in higher H2 and CO yields. However, above 1200 K, ceria reacts more efficiently with H2O and CO2 as the dopant concentration is increased, and yields are higher compared to pure ceria. The molar ratio of H2 to CO, when reduced ceria is exposed to H2O and CO2 simultaneously, is governed only by the relative ratio of H2O dissociation and CO2 dissociation equilibrium constants, Kw and Kc. Therefore, for a given H2O/ CO2 ratio, the resulting H2/CO ratio is expected to be the same at the point where Kw = Kc (1100 K). Finally, the solar-to-fuel efficiency is negatively correlated to dopant concentration for all materials considered. Although the reaction enthalpy to achieve a given δ decreases as the dopant concentration increases, the efficiency was largely dictated by the energy required to heat ceria. Because the required reduction temperature to achieve a given δ increased as the dopant concentration increased, this energy loss was greater than the reduction in reaction enthalpy. Only under conditions in which heat recovery approached 100% do the solar-to-fuel efficiencies of doped species surpass pure ceria. The maximum theoretical efficiency of pure ceria at 0% and 50% heat recovery, at δ = 0.1, was 20.2% and 29.5%, respectively. Although pure ceria appears to have a greater potential for efficiently for splitting H2O and CO2 compared to the dopants considered in this study, there are several other dopants that are potentially more promising. Dopants such as ZrO2, CrO2, Fe2O3, NiO, Mn2O3, and CuO have all be shown to be reduced at lower temperatures than pure ceria,3,7,9,10 but there is limited thermodynamic information available in the literature to allow a comparison in terms of nonstoichiometry (δ) and solar-to-fuel efficiency (nsolar‑to‑fuel). Other aspects to be considered when comparing dopants are the impact on kinetics, volatization, sintering, and cylclability.

■

■

ΔGoxd ° = standard free energy change of ceria oxidation (with O2), kJ mol−1. ΔGrxn,CO ° 2 = standard free energy change of ceria oxidation (with CO2), kJ mol−1. ° 2O = standard free energy change of ceria oxidation ΔGrxn,H (with H2O), kJ mol−1. ΔGO2 = oxygen molar free energy, kJ mol−1. ΔG° = standard free energy change, kJ mol−1. ΔHO2 = oxygen molar enthalpy, kJ mol−1. ΔHred = enthalpy of reduction, kJ mol−1. HHVH2 = higher heating value of hydrogen, kJ mol−1. HR = fraction of heat recovered. I = normal beam insolation, W m−2. Kc = CO2 dissociation equilibrium constant. Kw = H2O dissociation equilibrium constant. K1 = ideal solution model equilibrium constant. K2 = defect interaction model equilibrium constant. OOx = oxygen atom on oxygen lattice site. PO2 = oxygen partial pressure, atm. Qsolar = solar energy input per mol CeO2, kJ. R = ideal gas constant, kJ mol−1 K−1. ΔSO2 = oxygen molar enthalpy, kJ mol−1. T = temperature, K. TH = reduction temperature, K. TL = oxidation temperature, K. VO″ = oxygen vacancy. X = dopant concentration. δ = degree of nonstoichiometry. δi = degree of nonstoichiometry before reduction. δf = degree of nonstoichiometry after oxidation. nabsorption = solar energy adsorption efficiency. nsolar‑to‑fuel = solar-to fuel energy conversion efficiency. σ = Stefan−Boltzmann constant, 5.6705 × 10−8 W m−2 K−4.

REFERENCES

(1) Mogensen, M.; Sammes, N. M.; Tompsett, G. A. Physical, chemical, and electrochemical properties of pure and doped ceria. Solid State Ionics 2000, 129 (1−4), 63−94. (2) Panlener, R. J.; Blumenthal, R. N.; Garnier, J. E. A thermodynamic study of nonstoichiometric cerium dioxide. J. Phys. Chem. Solids 1975, 36 (11), 1213−1222. (3) Abanades, S.; Legal, A.; Cordier, A.; Peraudeau, G.; Flamant, G.; Julbe, A. Investigation of reactive cerium-based oxides for H2 production by thermochemical two-step water-splitting. J. Mater. Sci. 2010, 45 (15), 4163−4173. (4) Chueh, W. C.; Falter, C.; Abbott, M.; Scipio, D.; Furler, P.; Haile, S. M.; Steinfeld, A. High-flux solar-driven thermochemical dissociation of CO2 and H2O using nonstoichiometric ceria. Science 2010, 330 (6012), 1797−1801. (5) Chueh, W. C.; Haile, S. M. A thermochemical study of ceria: Exploiting an old material for new modes of energy conversion and CO2 mitigation. Philos. Trans. R. Soc., A 2010, 368 (1923), 3269− 3294. (6) Graves, C.; Ebbesen, S. D.; Mogensen, M.; Lackner, K. S. Sustainable hydrocarbon fuels by recycling CO2 and H2O with renewable or nuclear energy. Renewable Sustainable Energy Rev. 2011, 15 (1), 1−23. (7) Le Gal, A.; Abanades, S.; Flamant, G. CO2 and H2O splitting for thermochemical production of solar fuels using nonstoichiometric ceria and ceria/zirconia solid solutions. Energy Fuels 2011, 25 (10), 4836−4845. (8) Meng, Q.-L.; Lee, C.-I.; Ishihara, T.; Kaneko, H.; Tamaura, Y. Reactivity of CeO2-based ceramics for solar hydrogen production via a

AUTHOR INFORMATION

Corresponding Author

*Telephone: +41-44-633-9380. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work has been financially supported by the European Commission under Contract No.285098 (Project SOLARJET).

■

NONMENCLATURE C = flux concentration ratio of incident radiation, dimensionless. Cp,CeO2 = heat capacity of ceria, kJ mol−1. CeCex = cerium atom on cerium lattice site. CeCe′ = electron localized on cerium lattice site. (Ce′ CeV″OCe′Ce)x = electron-vacancy association. ΔG °CO2 = standard free energy change of CO2 dissociation, kJ mol−1. ΔGH° 2O = standard free energy change of H2O dissociation, kJ mol−1. 1935


Energy & Fuels

Article

two-step water-splitting cycle with concentrated solar energy. Int. J. Hydrogen Energy 2011, 36 (21), 13435−13441. (9) Singh, P.; Hegde, M. S. Ce0.67Cr0.33O2.11: A new low-temperature O2 evolution material and H2 generation catalyst by thermochemical splitting of water. Chem. Mater. 2009, 22 (3), 762−768. (10) Kaneko, H.; Miura, T.; Ishihara, H.; Taku, S.; Yokoyama, T.; Nakajima, H.; Tamaura, Y. Reactive ceramics of CeO2−MOx (M = Mn, Fe, Ni, Cu) for H2 generation by two-step water splitting using concentrated solar thermal energy. Energy 2007, 32 (5), 656− 663. (11) Huang, S.; Li, L.; Vleugels, J.; Wang, P.; Van der Biest, O. Thermodynamic prediction of the nonstoichiometric phase Zr1−zCezO2−x in the ZrO2−CeO1.5−CeO2 system. J. Eur. Ceram. Soc. 2003, 23 (1), 99−106. (12) Inaba, H.; Tagawa, H. Ceria-based solid electrolytes. Solid State Ionics 1996, 83 (1−2), 1−16. (13) Otake, T.; Yugami, H.; Yashiro, K.; Nigara, Y.; Kawada, T.; Mizusaki, J. Nonstoichiometry of Ce1−xYxO2−0.5x−δ (x = 0.1, 0.2). Solid State Ionics 2003, 161 (1−2), 181−186. (14) Chueh, W. C.; Haile, S. M. Electrochemical studies of capacitance in cerium oxide thin films and its relationship to anionic and electronic defect densities. Phys. Chem. Chem. Phys. 2009, 11 (37), 8144−8148. (15) Kobayashi, T.; Wang, S.; Dokiya, M.; Tagawa, H.; Hashimoto, T. Oxygen nonstoichiometry of Ce1−ySmyO2−0.5y−x (y = 0.1, 0.2). Solid State Ionics 1999, 126 (3−4), 349−357. (16) Schneider, D.; Godickemeier, M.; Gauckler, L. J. Nonstoichiometry and defect chemistry of ceria solid solutions. J. Electroceram. 1997, 1 (2), 165−172. (17) Wang, S.; Inaba, H.; Tagawa, H.; Dokiya, M.; Hashimoto, T., Nonstoichiometry of Ce0.8Gd0.2O1.9−x. Electrochemical Society: Pennington, NJ, 1997; Vol. 144. (18) Wang, S.; Inaba, H.; Tagawa, H.; Dokiya, M.; Hashimoto, T. Nonstoichiometry of Ce0.9Gd0.1O1.95−x. Solid State Ionics 1998, 107 (1−2), 73−79. (19) Garnier, J. E.; Blumenthal, R. N.; Panlener, R. J.; Sharma, R. K. A thermodynamic study on CaO-doped nonstoichiometric cerium dioxide. J. Phys. Chem. Solids 1976, 37 (4), 368−378. (20) Park, J. H.; Blumenthal, R. N.; Panhans, M. A. Direct measurement of thermodynamic properties in nonstoichiometric CaO-Doped cerium dioxide by coulometric titration. J. Electrochem. Soc. 1988, 135 (4), 855−859. (21) Blumenthal, R. N.; Garnier, J. E. The electrical conductivity and thermodynamic behavior of SrO-doped nonstoichiometric cerium dioxide. J. Solid State Chem. 1976, 16 (1−2), 21−34. (22) Chueh, W. C.; Haile, S. M. Ceria as a thermochemical reaction medium for selectively generating syngas or methane from H2O and CO2. ChemSusChem 2009, 2 (8), 735−739. (23) Yokokawa, H.; Sakai, N.; Kawada, T.; Dokiy, M. Chemical potential diagrams for rare earth−transition metal−oxygen systems: I. Ln−V−O and Ln−Mn−O System. J. Am. Ceram. Soc. 1990, 73 (3), 649−658. (24) Kröger, F. A.; Vink, H. J., Relations between the concentrations of imperfections in crystalline solids. Solid State Physics, Frederick, S., David, T., Eds.; Academic Press: 1956; Vol. 3, pp 307−435. (25) O.Toft, S. Thermodynamic studies of the phase relationships of nonstoichiometric cerium oxides at higher temperatures. J. Solid State Chem. 1976, 18 (3), 217−233. (26) Shah, P. R.; Kim, T.; Zhou, G.; Fornasiero, P.; Gorte, R. J. Evidence for entropy effects in the reduction of ceria−zirconia solutions. Chem. Mater. 2006, 18 (22), 5363−5369. (27) Steinfeld, A. Solar thermochemical production of hydrogenA review. Solar Energy 2005, 78 (5), 603−615. (28) Riess, I.; Ricken, M.; Nölting, J. On the specific heat of nonstoichiometric ceria. J. Solid State Chem. 1985, 57 (3), 314−322.

1936


Thermodynamic Analysis of Cerium-Based Oxides for Solar

Recommend Documents