Kinetics of Electron Decay in Hydride Ion-Doped Mayenite - The

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Kinetics of Electron Decay in Hydride Ion-Doped Mayenite Katsuro Hayashi Secure Materials Center, Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Yokohama 226-8503, Japan ABSTRACT: Persistent electrons are generated in hydride (H) ion-doped 12CaO 3 7Al2O3 (C12A7) by UV irradiation at room temperature. The kinetics of thermal electron decay is examined using experimental data collected at 200295 °C. The observed reaction order together with activation energy shifts approximately from one-half to first depending on the electron concentration and temperature. The data is explained by a two-electron transfer reaction (H þ O2 T OH þ 2e) with H0 and Hþ as reaction intermediates and diffusion of these hydrogen species. The observed one-half-order kinetics originates from a zero-order reaction influenced by inhomogeneity of the electron concentration. The electron decay rate is principally determined by the supply of Hþ ions liberated from OH ions. The large activation energy (1.9 ( 0.3 eV) of this process is responsible for the persistence of electrons at room temperature. As the residual electron concentration decreases, the contribution of electron trapping by the intermediate hydrogen species becomes dominant for the rate-determination, shifting the reaction order and activation energy.

1. INTRODUCTION Hydrogen can occupy a number of different lattice sites in host materials to significantly modify their electronic properties. Its amphoteric valence states (Hþ and H ions) often eliminate electrical activity and in some cases act as a source of conductivity.1 12CaO 3 7Al2O3 (C12A7, mayenite) is a material that can incorporate both Hþ and H ions2 and is the best candidate among several kinds of H ion-containing oxides3,4 for investigating how H ions behave in oxide materials. The stoichiometric unit cell of C12A7 is expressed as [Ca24Al28O64]4þ 3 2O2 (Figure 1) and consists of a positively charged cubic lattice framework with a cage structure and 2 extra-framework O2 ions, which occupy 2 of the 12 cages in the unit cell to compensate for the positive charges. These O2 ions can be exchanged for various anions, such as OH,5,6 F,7,8 Cl,7 O, O2,9,10 O22,11 and S2 8 as well as H 1216 using thermochemical processes. The environment inside each cage is particularly suitable for occupation by a monovalent anion with an ionic radius of less than ∼2 nm, which is most likely related to the distance between the two polar Ca2þ ions in each cage and their tolerance for displacement induced by the incorporation of extraframework anions.17 Extraframework anions can also be exchanged for electrons that occupy the space inside the cages in a similar manner to monovalent anions. Electron doping can be achieved either by chemical reduction18,19 or by doping with H ions followed by irradiation with UV light1216 or an electron beam.14 When the concentration of electrons [e] (the square brackets indicate the concentration of the relevant species in cm3) in C12A7 is less than ∼1 1019 cm3, each electron is localized in a cage, similar to Fþ centers in alkaline-earth oxides.3 The Fþ-like electrons in C12A7 induce characteristic optical absorption bands at 2.8 and 0.4 eV.12 The former is ascribed to inter- or intracage transitions of s-like r 2011 American Chemical Society

ground-state electrons to p-like excited states,20 which is analogous to the absorption bands of Fþ centers in alkaline-earth oxides.3 The peak at 0.4 eV is ascribed to adiabatic electron transfer to a neighboring cage.20 Although stoichiometric C12A7 is a good electrical insulator, intercage electron hopping with an activation energy of a few tenths of an electron volt endows C12A7 with electronic conductivity. The intensities of the two absorption bands are proportional to [e] when it is less than ∼5 1020 cm3.18 Irradiation of H ion-doped C12A7 (C12A7:H) with UV light at room temperature generates electrons in cages, which is accompanied by a large change in electron conductivity by the factor of 10 decades. Although the decay of electrons has not been detected at room temperature, conductive C12A7:H reverts to the insulating state within ∼10 min upon heating at ∼300 °C. These properties make it possible to use C12A7:H as a functional transparent conducting oxide material in which a conductive pattern is formed directly by light illumination and can be erased thermally. The mechanism of conversion between the insulating and conducting states appears to be complex and remains unclear. C12A7:H is most sensitive to a wavelength of ∼300 nm (∼4.1 eV), which corresponds to the photoionization energy of an encaged H ion. A quantum chemical calculation using an embedded cluster model estimated this energy to be 4.3 eV.21,22 The photoionization process is described as: H ðcÞ þ nullðcÞ f H0 ðcÞ þ e ðcÞ

ð1Þ

where c and null denote the species in a cage and an empty cage, respectively. This reaction has been evidenced by Received: March 15, 2011 Revised: April 30, 2011 Published: May 18, 2011 11003

dx.doi.org/10.1021/jp202428s | J. Phys. Chem. C 2011, 115, 11003–11009

The Journal of Physical Chemistry C

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Figure 1. Lattice framework of mayenite and encaged anion species relevant to the photogeneration and thermal decay of electrons.

low-temperature electron paramagnetic resonance measurements.15 In this experiment, all of the atomic hydrogen in cages, H0(c), and some of the encaged electrons, e(c), generated by UV irradiation at 10 K were annihilated when the sample was warmed to 100 K. This behavior suggests that H0(c) is so unstable that H0(c) recombined with some of e(c), and the other electrons survived with diamagnetic hydrogen species other than H(c). In our first report concerning C12A7:H,12 we suggested that atomic hydrogen is stabilized by coalescence to form H2 molecules according to an analogy of photogenerated H0 in SiO2.23 However, in the subsequent study, we proposed an alternative reaction:13 H ðcÞ þ O2 ðcÞ þ nullðcÞ T 2e ðcÞ þ OH ðcÞ

ð2Þ

The transient H0(c) releases an additional electron, and the remaining Hþ ion combines with O2(c) to form OH(c). Thus, a pair of H(c) and O2(c) acts as a source of two electrons. This prediction is supported by the reasonable agreement between the enthalpy change of reaction 2 evaluated from the equilibrium [e] at 300700 °C (1.4 eV) and that obtained from a theoretical calculation (1.0 eV).13 The purpose of this study is to obtain further evidence for reaction 2 by employing the kinetics of the thermal decay of photogenerated electrons as a probe. It is demonstrated that the kinetics can be described well by multistep reactions based on reaction 2 mediated by H0 and Hþ species.

2. EXPERIMENTAL METHODS Transparent C12A7 crystals refined by the floating-zone method were cut into slices with dimensions of ∼0.5 5 5 mm. The samples were annealed at 1300 °C under an atmosphere containing 0.2 atm of H2 (balanced with N2) for 6 h using an electronic furnace with an alumina tube and then cooled to room temperature. Both sides of the annealed samples were ground to a thickness of ∼0.3 mm and polished to a mirror finish. UVvis-IR absorption spectra were measured with a Hitachi U-4000 spectrophotometer. The concentration of OH ions, [OH], in the as-prepared sample were evaluated to be 9 1020 cm3 from the intensity of the OH stretching band at 3560 cm1.5 The concentration of H ions, [H], was determined to be 5 1019 cm3 from the absorption coefficient at 4.0 eV, which is in the tail of the absorption band of H ions. The relationship between [H] and the intensity at 4.0 eV has been calibrated by nuclear magnetic resonance spectroscopy of heavily H ion-doped C12A7 samples.16

Figure 2. Change in the concentration of electrons, [e], at temperatures of (a) 200 °C and (b) 295 °C. Blue and red lines are the calculated change in [e] with n = 1/2 and 1, respectively. Estimated time constants are 16.8 h for (a) and 87 s for (b).

UV light generated by a Xenon lamp and passed through a visibleinfrared filter (∼100 mW cm2, < 320 nm) was used to generate electrons in C12A7 samples. Both sides of the samples were irradiated at room temperature for totally ∼20 min until the absorbance at 2.8 eV (Fþ band) reached around 23. This absorbance was chosen as the optimum balance between dynamic range and accuracy for the measured data. As inferred from the results of a previous study (e.g., Figure 2 in ref 16), these irradiation conditions do not saturate the sample with electrons, but [e] may have an inhomogeneous distribution. This inhomogeneity effect will be discussed in section 4. Isothermal optical absorption measurements were carried out over the temperature range from 200295 °C using a small electric furnace attached to the spectrophotometer. It took about 5 min to heat the sample from room temperature until it was stabilized at a target temperature. The absorbance at 2.8 eV was converted to [e] using the relationship described in ref 18.

3. RESULTS Figure 2 shows the electron decay characteristics measured at temperatures, T, of 200 and 295 °C. Time zero was defined as the moment at which the temperature of the furnace was judged to be stabilized and thus was not uniquely determined. However, the result of the following kinetic analysis based on the reaction order is independent of the time zero. The general rate equation with respect to [e] is expressed by an exponential law: d½e ¼ k½e n dt

ð3Þ

where t is time, k is the rate constant, and the n is the reaction order. The decay characteristics at 200 and 295 °C were best 11004

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shown in Figure 4. A change in the activation energy was observed for the rate constant data at both concentrations. The activation energy at a lower temperature range of ∼200240 °C (blue lines) was calculated to be 1.9 ( 0.3 eV. This temperature range corresponds to region A in Figure 3, where n was ∼1/2. The activation energy decreased to 0.9 ( 0.3 eV in the higher temperature range (red lines). This temperature range corresponds to region B with n = ∼1. This change in the activation energy supports the presence of a shift in reaction order and the rate-determining process. The half-life of the photogenerated electrons at room temperature was estimated by extrapolation of the data in the lower T region of Figure 4. The estimated value of about 107 years demonstrates that the photogenerated electrons are indeed stable at room temperature. Figure 3. Logarithmic plot of the rate of electron decay against electron concentration, [e], at temperatures from 200 to 295 °C. The dashed line roughly divides the two regions with a reaction order, n, of 1/2 (region A) and 1 (region B). Two gray lines indicate [e] of 3 1016 and 3 1017 cm3.

Figure 4. Arrhenius plots of the rate constants of electron decay at [e] of 3 1016 and 3 1017 cm3.

fitted by one-half-order (n = 1/2) and first-order (n = 1) reactions, respectively. The change in the reaction order suggests that the rate-determining process depends on temperature. A logarithmic plot of d[e]/dt versus [e] for all of the measured data is shown in Figure 3. Data obtained at 250, 265, 280, and 295 °C fluctuated during the initial measurement period. This behavior is caused by small variations in temperature occurring before temperature stabilization and thus is not an inherent characteristic. The slope of the plot corresponds to the reaction order, n. In general, n was approximately 1/2 in the region with higher [e] and lower T (indicated by A in Figure 3), and approached 1 in the region with lower [e] and higher T (indicated by B in Figure 3). The value of n slightly exceeded 1 when [e] < ∼1 1016 cm3 and T > 265 °C. Data for [e] less than ∼1 1016 cm3 was not plotted in Figure 3 because of limitations in data accuracy and resolution. Arrhenius plots of the rate constants at [e] = 3 1016 and 3 1017 cm3, which are indicated by gray lines in Figure 3, are

4. DISCUSSION The observed shifts in the reaction order and activation energy suggest that electrons decay through complex processes during isothermal annealing. In this section, first, all possible chemical states for hydrogen in C12A7:H are considered to deduce rate equations for [e], providing a plausible explanation for the observed shifts. However, the observed one-half-order kinetics cannot be completely explained using simple kinetic theory. We next include the effect of inhomogeneity of [e] in a sample, which allows the one-half-order kinetics to be reproduced. Finally, the (photoassisted) thermal reactions occurring in C12A7:H are summarized using a potential barrier model constructed with the activation energies determined from the kinetic analyses. 4.1. General Rate Equation. The overall reaction kinetics was analyzed by employing three consecutive reactions with H0 and Hþ as reaction intermediates. All elemental reactions and relevant rate constants and activation energies are listed in Table 1. The potential barrier for each elemental reaction is presented schematically in Figure 5. The intermediate Hþ should be clearly distinguished from the hydrogen in OH(c). Here the intermediate Hþ ion, described as Hþ(f), is defined as being bound to a framework O2 ion and not sharing a cage with any anions or electrons. The elemental reaction (a) includes dissociation of an OH(c) and migration of the liberated Hþ(f) to the surface of another empty cage, and thereby this process is termed a liberation of Hþ(f) from OH(c). The inverse reaction, (a0 ), is a migration of Hþ(f) on the surface of an empty cage to O2(c) in another cage. In contrast to elemental reactions (a) and (a0 ), the other elemental reactions are most likely mediated by an electron hopping from one cage to another, rather than migration of hydrogen species. According to the chemical equilibrium shown in eq 2, as discussed in ref 5, the equilibrium value of [e] over the temperature range examined in the present study is estimated to be below 1 1012 cm3, which is several orders of magnitude lower than the measured range of [e] plotted in Figure 3. This concentration range was far from the equilibrium concentration and only reflected the transient annihilation of the UV-generated excess electrons. Consequently, the reaction involving the thermal generation of electrons from H ion (c0 ) is ignored in our analysis. Indeed the rate of this reaction may be negligible because the relevant activation energy was theoretically calculated to be as high as 3.5 eV.22 11005



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Table 1. Elemental Reactions Involved in the Thermal Decay of Electrons in C12A7:H Activation Energy notation

a

elemental reaction

þ

rate constant

notation

determined value (eV)

a

OH (c) f H (f) þ O (c)

ka

Ea

1.9 ( 0.3

a0

Hþ(f) þ O2(c) f OH(c)

k0 a

E0 a

1.2 ( 0.8a

0

(0.2 ( 0.1)a

þ

2

b

H (f) þ e (c) f H (c)

kb

Eb

0

b

þ

H (c) f H (f) þ e (c)

0

kb

0

Eb

c

H0(c) þ e(c) f H(c)

kc

Ec

c0

H(c) f H0(c) þ e(c)

0

E0 a Eb = 1.0 ( 0.7 eV

Thus, the following steady-state approximation was applied,24 d½Hþ d½H0 ¼ ¼0 dt dt

ð8Þ

Eq 2 indicates that [OH] and [e] vary simultaneously with: d½OH 1 d½e ¼ dt 2 dt

ð9Þ

By eliminating [Hþ] and [H0] from eqs 49, one obtains: d½e 2ka kb kc ½OH ½e 2 ¼ 0 2 0 dt ka ½O ðkb þ kc ½e Þ þ kb kc ½e 2

ð10Þ

This general rate equation can be divided into three extreme conditions. Case 1: Pseudo-Zero-Order Reaction. When k0 a[O2](k0 b þ kc[e]) , kbkc[e]2, eq 10 can be approximated as a pseudozero-order reaction with respect to [e]: Figure 5. Potential energy diagram of the reaction: H(c) þ O2(c) þ null(c) T 2e(c) þ OH(c). The chemical state of the hydrogen species is taken as the reaction coordinate. Indicated values are those reported in the literature; *1 and *2 are from ref 22, and *3 is an experimental value in ref 13.

The rate equations for OH(c), Hþ(f), H0(c), and e(c) can be expressed as: d½OH 0 ¼ ka ½OH þ ka ½Hþ ½O2 dt

ð4Þ

d½Hþ 0 0 ¼ ka ½OH ka ½Hþ ½O2 kb ½Hþ ½e þ kb ½H0 dt ð5Þ d½H0 0 ¼ kb ½Hþ ½e kb ½H0 kc ½H0 ½e dt

ð6Þ

d½e 0 ¼ kb ½Hþ ½e þ kb ½H0 kc ½H0 ½e dt

ð7Þ

þ

d½e = 2ka ½OH dt

This condition is favored for higher [e] at a given temperature, that is, with the same rate constants. In our experiment, the initial value of [OH] before UV irradiation was 9 1020 cm3 and it varies by a few percent at most after UV irradiation and during isothermal decay. Thus, [OH] can be regarded as a constant. In practice, [OH] decreases with decreasing [e] as found in eq 9, which contributes slightly to increasing apparent reaction order. Case 2: Pseudo-First-Order Reaction. When k0 a[O2](k0 b þ kc[e]) . kbkc[e]2 and k0 b , kc[e], eq 10 can be approximated as a pseudo-first-order reaction with respect to [e]: d½e ka kb ½OH ½e = 2 0 dt ½O2 ka

ð12Þ

This condition is favored when [e] is lower than that in the zero-order case at a given temperature. Case 3: Pseudo-Second-Order Reaction. When k0 a[O2] (k0 b þ kc[e]) . kbkc[e]2 and k0 b . kc[e], eq 10 can be approximated as a pseudo-second-order reaction with respect to [e]: d½e ka kb kc ½OH ½e 2 = 2 0 0 dt ½O2 ka kb

0

Because H (f) and H (c) are unstable intermediates, their absolute concentrations are relatively low compared with those of OH(c) and H(c). Furthermore, their concentration change rates seem to be relatively small after an initial induction period.

ð11Þ

ð13Þ

Similar to [OH], [O2] increases slightly with decreasing [e], thus the variation of [O2] as well as [OH] in eq 13 cause the reaction order to vary a little from its ideal value. 11006



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Figure 6. Effect of initial concentration distribution on the apparent reaction order. (a) Seven initial concentration distributions. (b) Decay characteristics based on zero-order kinetics with the concentration distributions given in (a). Ctot becomes zero at t = 1 for all of the lines. Upper to lower lines correspond to initial concentration distributions 1 to 7. No. 3 is indicated as a bold line. (c) Plot of the data in (b) on a logarithmic scale. (d) Decay characteristics based on first-order kinetics with the concentration distributions given in (a). Ctot becomes 1/2 at t = 1 (half-life) for all of the lines. (e) Plot of the data in (d) on a logarithmic scale.

4.2. Effect of Inhomogeneity on Apparent Reaction Order. Practically, there is often inhomogeneity in the concentration of a chemical species in a solid. In this subsection, the effect of a distribution in the initial concentration of a chemical species on the reaction order is considered. It is demonstrated that such a distribution significantly affects zero-order kinetics, leading to apparent one-half-order kinetics. To mimic various initial distributions of concentration in a simple way, the distribution is represented by a linear function:

fc ðC0 Þ ¼ aC0 þ b

ð14Þ

where C0 is the initial concentration at a certain region, fc is the volume fraction in a bulk sample with an initial concentration of C0, and a and b are constants. The total electron concentration, Ctot, is described by Z 1 Ctot ðtÞ ¼ fc ðC0 ÞCðC0 , tÞdC0 ð15Þ 0

where C indicates the concentration at a certain region with an initial concentration of C0 at time, t. The maximum value of C0 and initial value of Ctot are normalized to be unity. It is assumed that C varies with the rate equation given by eq 3 with reaction orders of 0, 1, 2, ... Part a of Figure 6 shows the distribution functions (eq 14) examined here. An ideal homogeneous distribution corresponds

to a delta function at C0 = 1. The number 1 indicates a slightly inhomogeneous distribution, in which the minimum C0 is half of the maximum C0. As the number of the distribution function increases, the minimum C0 is extended to zero and the volume fraction of the lower C0 region increases. First, C is assumed to have zero-order dependence. The results of calculations are displayed in parts b and c of Figure 6. As found in the slopes for 1 and 2 in the logarithmic plot shown in part c of Figure 6, zero-order regions remain in the initial period, and then the apparent reaction order approaches one-half as time passes (or the total concentration decreases). As the number of the distribution function increases from 3 to 5, the initial concentration distribution becomes more inhomogeneous, and the region exhibiting an apparent reaction order of one-half expands. It is noted that, in the case of a constant distribution function of 5, the decay characteristics exactly follow one-half-order kinetics, as highlighted by bold lines in part c of Figure 6. The analytical description of eq 15 for one-half-order kinetics is given by: Ctot ðtÞ ¼ ½Ctot ð0Þ1=2 kt=22 , 0 e t e 2Ctot ð0Þ1=2 =k ð16Þ For 6 and 7, the apparent reaction order slightly exceeds one-half, which may be, nevertheless, a better approximation than a firstorder reaction. Next, C is assumed to have first-order dependence. As found in the calculated results plotted in parts d and e of Figure 6, 11007


The Journal of Physical Chemistry C the initial distribution function has little influence on the decay characteristics. Similar to first-order kinetics, second-order kinetics are almost independent of the initial distribution function. It is concluded, therefore, that only zero-order kinetics is influenced largely by the initial concentration distribution. The apparent reaction order approaches one-half because of the inhomogeneity in the initial concentration of the sample. In particular, the constant concentration distribution produces apparent one-half-order kinetics. First- or higher-order kinetics are hardly affected by such inhomogeneity. These findings are applicable to any kinetic study as well as aiding to understand the reaction order with respect to [e] in C12A7:H. 4.3. Interpretation of the Observed Electron Decay Kinetics. Region A. One-half-order decay of [e] was observed for the data obtained at 250 °C (part a of Figure 2) and for region A in Figure 3. It is interpreted that the zero-order reaction with respect to [e] exhibits one-half-order kinetics because of the inhomogeneity of [e] in the samples. This inhomogeneity is most likely caused by incomplete irradiation of the samples with UV light before performing optical experiments. Because the penetration depth of UV light is limited due to the photoabsorption of H ions, photogeneration of electrons is saturated only at the surface of the samples after UV irradiation for ∼20 min. When the slopes in region A in Figure 3 are compared with the calculated values in part c of Figure 6, the initial concentration distribution function 4 seems to describe the initial electron concentration distribution in our samples the best. This suggests that the photogeneration of electrons in the inner region of the sample either did not proceed at all or occurred at about an order of magnitude less than the saturated concentration. This argument for inhomogeneous generation of electrons in the sample is convincing because the opposite side of a sample irradiated with UV light on only one side for about 10 min remains insulating. This kind of inhomogeneity in [e] is relaxed rapidly in gas or liquid phases, so one-half-order kinetics may be characteristic of solid or heterogeneous systems in which stirring is not available. For example, one-half-order kinetics has been observed in the reduction of TiO2.25 Again, region A is essentially interpreted by the zero-order kinetics given by eq 11. The rate-determining step is the liberation of Hþ(f) from OH(c), and the observed activation energy (blue lines in Figure 4) corresponds to Ea. The value of the activation energy (Ea = 1.9 ( 0.3 eV) agrees closely with that observed for OH ion diffusion in this material (1.7 ( 0.2 eV), which is governed by the same rate determining step.5 This agreement provides further evidence that OH(c) is involved in the electron decay process, as described by the inverse reaction of eq 2. Region B. As demonstrated in the previous subsection, the first-order kinetics is not influenced by inhomogeneity in the initial [e]. Thus, the observed first-order kinetics in the data obtained at 295 °C (part b of Figure 2) and Region B (Figure 3) can be analyzed as it is. Because of similar factors regarding the weak dependence of [OH] on [e], a reaction order of one or slightly higher should be observed under the conditions described by eq 12. In practice, a reaction order of ∼1 was observed at lower [e] (region B in Figure 3). The overall reaction rate is governed by the liberation of Hþ(f) from OH(c) and subsequent electron trapping by Hþ(f) to form H0(c). The observed activation energy (red lines in Figure 4) corresponds

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to Ea E0 a þ Eb (= 0.9 ( 0.4 eV). Therefore, the value of E0 a Eb is calculated to be 1.0 ( 0.7 eV. As for elemental reaction (a0 ), its potential barrier, E0 a, is equivalent to the activation energy for the intercage migration of Hþ(f) because, once Hþ reaches the surface of an O2 ionoccupied cage, they appear to form OH(c) spontaneously. Elemental reaction (b) is accomplished by an electron hopping to an Hþ(f)-occupied cage and subsequent formation of H0(c) because the mobility of e(c) is much higher than that of Hþ(f). The potential barrier of reaction (b), Eb, should be close to the activation energy for intercage electron hopping. Therefore, a rough estimation of E0 a is 1.2 ( 0.8 eV, if the value of Eb is assumed to be 0.2 ( 0.1 eV. The estimated potential barrier for Hþ(f) migration, E0 a, agrees reasonably with theoretically calculated values, 1.01.5 eV.22 The second-order region may appear when the supply of Hþ(f) is sufficient and its consecutive reduction is suppressed because of a limited supply of electrons. Although no clear second-order dependence was observed in our experiments, it may appear if more precise measurement is achieved at lower [e] and higher temperature than was currently accomplished. 4.4. Potential Barrier Model. The forward and reverse reactions described by eq 2 will be reviewed using the potential diagram illustrated in Figure 5. Photoionization generates the first electron and H0. Its photon energy is theoretically calculated to be 4.3 eV. Relaxation of cage geometry then reduces the energy of the system via dissipation into lattice vibration.22 These processes are also shown in Figure 5. Although the barrier for the generation of a second electron is relatively low, a larger barrier ascribed to the migration of Hþ(f) needs to be overcome to stabilize a second electron, otherwise the two electrons will recombine with Hþ(f) to return to H(c). This explains why electrons photogenerated at low temperature have a shorter lifetime.15 Meanwhile, the most important elemental step for controlling the rate of the inverse reaction is the liberation of Hþ(f) from OH(c). The large potential barrier of this step is related to the unprecedented thermodynamic stability of OH(c) in C12A7; the formation enthalpy of OH in C12A7 is larger than those in typical proton conducting oxides by 30120%.5,6 This is also a reason for the persistence of photogenerated electrons at room temperature in C12A7.

5. CONCLUSIONS The thermal decay of electrons in C12A7:H can be interpreted as the inverse reaction of H(c) þ O2(c) f 2e(c) þ OH(c), where intermediate species Hþ(f) and H0(c) play crucial roles in elemental reaction steps. The reaction kinetics in the region with higher [e] and lower T (region A) is essentially a zero-order reaction with respect to [e]. The observed half-order kinetics can be explained by considering the initial inhomogeneity in [e] caused by the limited penetration of UV light into the sample. The overall reaction rate is determined by the liberation of Hþ(f) from OH(c). The activation energy of this step of 1.9 ( 0.3 eV agrees well with that reported for OH ion diffusion, validating the proposed reaction scheme. The large activation energy of this step is responsible for the slow decay rate of electrons. In the region with lower [e] and higher T (region B), the supply of electrons governs the overall reaction rate, leading to first-order kinetics. From these analyses, the activation energy for Hþ(f) migration was estimated to be 1.2 ( 0.8 eV. 11008



’ AUTHOR INFORMATION Corresponding Author

Phone: þ81-45-925-5337; fax: þ81-45-924-5365; e-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by a Grant-in-Aid for Elements Science and Technology Project (No. 08055013), and a Grant-in-Aid for Young Researchers A (No. 19685019) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. ’ REFERENCES (1) Kilic-, C-.; Zunger, A. Appl. Phys. Lett. 2002, 81, 73–75. Van de Walle, C. G; Neugebauer, J. Nature 2003, 423, 626–628. Peacock, P. W.; Robertson, J. Appl. Phys. Lett. 2003, 83, 2025–2027. Cox, S. F. J.; Gavartin, J. L.; Lord, J. S.; Cottrell, S. P.; Gil, J. M.; Alberto, H. M.; Piroto Duarte, J.; Vil~ao, R. C.; Ayres de Campos, N.; Keeble, D. J.; Davis, E. A.; Charlton, M.; van der Werf, D. P. J. Phys.: Condens. Matter 2006, 18, 1079–1119. (2) Hayashi, K.; Hirano, M.; Hosono., H. Bull. Chem. Soc. Jpn. 2007, 80, 872–884. (3) Chen, Y.; Orera, M.; Gonzalez, R.; Williams, R. T.; Williams, G. P.; Rosenblatt, G. H.; Pogatshnik, G. J. Phys. Rev. B 1990, 42, 1410–1416. Gonzalez, R.; Monge, M. A.; Munoz-Santiuste, J. E.; Pareja, R.; Chen, Y.; Kotomin, E.; Kukla, M. M.; Popov, A. I. Phys. Rev. B 1999, 59, 4786–4790. (4) Poulsen, F. W. Solid State Ionics 2001, 145, 387–397. Hayward, M. A.; Cussen, E. J.; Claridge, J. B.; Bieringer, M.; Rosseinsky, M. J.; Kiely, C. J.; Blundell, S. J.; Marshall, I. M.; Pratt, F. L. Science 2002, 295, 1882–1884. Norby, T.; Widerøe, M.; Gl€ockner, R.; Larring, Y. Dalton Trans. 2004, 3012–3018. Bowman, A.; Claridge, J. B.; Rosseinsky, M. J. Chem. Mater. 2006, 18, 3046–3056. (5) Hayashi, K.; Hirano, M.; Hosono., H. J. Phys. Chem. B 2005, 109, 11900–11906. (6) Lee, D.-K.; Kogel, L.; Ebbinghaus, S. G.; Valov, I.; Wiemhoefer, H.-D.; Lerch, M.; Janek, J. Phys. Chem. Chem. Phys. 2009, 11, 3105–3114. Strandbakke, R.; Kongshaug, C.; Haugsrud, R.; Norby, T. J. Phys. Chem. C 2009, 113, 8938–944. (7) Jeevaratnam, J.; Glasser, F. P.; Glasser, L. S. D. J. Am. Ceram. Soc. 1964, 47, 105–106. (8) Zhmoidin, G. I.; Chatterjee, A. K. Cem. Concr. Res. 1984, 14, 386–396. (9) Hayashi, K.; Hirano, M.; Matsuishi, S.; Hosono, H. J. Am. Chem. Soc. 2002, 124, 738–739. Hayashi, K.; Matsuishi, S.; Ueda, N.; Hirano, M.; Hosono, H. Chem. Mater. 2003, 15, 1851–1854. (10) Ruszak, M.; Witkowski, S.; Sojka, Z. Res. Chem. Intermed. 2007, 33, 689–703. (11) Hayashi, K.; Hirano, M.; Hosono, H. Chem. Lett. 2005, 34, 586–587. Kajihara, K.; Matsuishi, S.; Hayashi, K.; Hirano, M.; Hosono, H. J. Phys. Chem. C 2007, 111, 14855–14861. (12) Hayashi, K.; Matsuishi, S.; Kamiya, T.; Hirano, M.; Hosono, H. Nature 2002, 419, 462–465. (13) Hayashi, K.; Sushko, P. V.; Shulger, A. L.; Hirano, M.; Hosono, H. J. Phys. Chem. B 2005, 109, 23836–23842. (14) Hayashi, K.; Toda, Y.; Kamiya, T.; Hirano, M.; Yamanaka, M.; Tanaka, I.; Yamamoto, T.; Hosono, H. Appl. Phys. Lett. 2005, 86, 022109. (15) Matsuishi, S.; Hayashi, K.; Hirano, M.; Hosono, H. J. Am. Chem. Soc. 2005, 127, 12454–12455. (16) Hayashi, K., J. Solid State Chem. 2011, in press. (17) Nomura, T.; Hayashi, K.; Kubota, Y.; Takata, M.; Kamiya, T.; Hirano, M.; Hosono, H. Chem. Lett. 2007, 36, 902–903. Hayashi, K.; Sushko, P. V.; Munoz Ramo, D.; Shluger, A. L.; Watauchi, S.; Tanaka, I.;

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