Diffusion Mechanisms of Radiolytic Species in Irradiated Al (Oxy

Subscriber access provided by YORK UNIV

C: Physical Processes in Nanomaterials and Nanostructures

Diffusion Mechanisms of Radiolytic Species in Irradiated Al (Oxy-)Hydroxides Zhizhang Shen, Eugene S. Ilton, Micah P Prange, Christopher J. Mundy, and Sebastien N. Kerisit J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07809 • Publication Date (Web): 28 Nov 2018 Downloaded from http://pubs.acs.org on December 2, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Diffusion Mechanisms of Radiolytic Species in Irradiated Al (Oxy-)Hydroxides Zhizhang Shen, Eugene S. Ilton, Micah P. Prange, Christopher J. Mundy, and Sebastien N. Kerisit* Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 23

ABSTRACT Rare-event simulations (climbing image nudged elastic band and metadynamics) were performed using density functional theory (DFT) and a hybrid exchange-correlation functional to elucidate and quantify the diffusion mechanisms of radiation-induced species (O−, H0, and H2) in boehmite (γ-AlOOH) and gibbsite (γ-Al(OH)3). The two Al (oxy-)hydroxide phases are known to have much different radiolytic activities, particularly in terms of H2 production, which involves the formation and recombination of hydrogen radicals, but the underlying mechanisms remain unknown. The DFT calculations revealed that O− diffusion occurred via proton-coupled hole transfer with high energy barriers in both phases. In contrast, energy barriers for H0 transfers were generally lower in boehmite than in gibbsite, suggesting a more facile diffusion in boehmite of H radicals to the surface, where H2 formation can take place. Another key difference was the ability of H0 and H2 to diffuse across the structural layers in gibbsite but not in boehmite. Therefore, while the formation of O− and H0 radicals was energetically favored in gibbsite compared to boehmite, the DFT calculations indicated that the mechanisms of diffusion are responsible for the higher H2 yields measured for boehmite compared to gibbsite. The finding that structural differences affect diffusion mechanisms and, in turn, control H2 evolution is likely to apply to metal oxyhydroxides in general.


Page 3 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


INTRODUCTION The inadvertent production of hydrogen during storage of nuclear waste from water hydrolysis, thermal decomposition of organic molecules,1 corrosion of metal containers,2 and irradiation of water- (hydroxyl) bearing solid phases is an important issue.3-10 In particular, the mechanisms that lead to the production of hydrogen gas from irradiated aluminum oxyhydroxides and hydroxides, including common phases present in nuclear waste, are not understood.6,7 For example, boehmite (𝛾-AlOOH) and gibbsite (𝛾-Al(OH)3), ubiquitous in the high-level radioactive waste (HLW) at the Hanford site, WA, U.S.A,11 manifest much different H2 yields under identical radiation conditions7 despite chemical and electronic similarities.12,13 Evidence that the morphology or size of boehmite particles strongly influences H2 yields and that H2 can be trapped in the structure of gibbsite and boehmite6 suggests that bulk transport of radiolytic species is important and that H2 could be a latent threat, if released through dissolution during waste treatment, for example. Related work has shown that nanosheets of boehmite exfoliate and dissolve rapidly, while gibbsite is stable, during exposure to the electron beam in liquid-cell transmission electron microscopy experiments.10 This contrasts strongly with their behavior during caustic dissolution where gibbsite dissolves much more rapidly than boehmite.11 Irradiation of other oxide phases5,14,15 also produce H2 gas and, as in the case of boehmite and gibbsite, the rate controlling pathway(s) leading to H2 formation and eventual release from the solid are not known. In this contribution, we apply high-level theoretical methods to constrain the thermodynamics of radical formation and the diffusion of radiolytic species in boehmite and gibbsite. H2 gas can be generated at the surface and in the bulk by combination of H radicals; in the latter case, we also calculated the diffusivities of H2 through the bulk. The results point to



Page 4 of 23

the importance of mineral structure and morphology as key factors controlling the release of H2 gas from irradiated materials. Based on the detection of O− centers (a hole trapped in 2p orbital of hydroxyl oxygen) and H radicals in the bulk of aluminum (oxy)hydroxides, and the production of H2 gas during irradiation, the following reactions have been proposed by Kaddissy et al.6: > OH ― → > O ― + H0

(1)

H0 + H0 →H2

(2)

where > OH ― denotes the hydroxyl groups in the crystal, and O− and H0 are the oxygen and hydrogen radicals, respectively. There is also evidence for Reaction 1 in wet silica,16 dry talc,8 and kaolinite17,18 under γ-irradiation. Reaction 1 is divided into the following two half reactions to identify the origin of any energetic difference between boehmite and gibbsite and to compare the energetics of the different sites for both O and H radicals: > OH ― → > O ― + H0(g) > OH ― + H0(g)→ > OH ― ⋯H0

∆𝐸1

(3)

∆𝐸2

(4)

where > OH ― ⋯H0 indicates the trapped H radical in the bulk, H0(g) a hydrogen atom in an otherwise empty periodic simulation cell, and ∆𝐸1 and ∆𝐸2 are formation energies. Two signals in the electron paramagnetic resonance measurements of Kaddissy et al.6 were assigned to polyatomic oxygen radicals, namely O2− and O3−. These species were not considered in this work as their atomic and electronic structures are not known and Kaddissy et al.6 reported the monoatomic oxygen radical species to be the dominant species. Similarly, for Reaction 2, the relative stability of H2 in different sites in the two phases was evaluated using the following reaction: 2 > OH ― ⋯H0→2 > OH ― + H2

∆𝐸3

(5) 4

ACS Paragon Plus Environment

Page 5 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Reaction 2 is assumed to be the rate-limiting step as it involves H0 species diffusing through the lattice and combining to form H2 whereas Reaction 1 is the homolytic cleavage of the O−H bond upon irradiation. COMPUTATIONAL DETAILS Density functional theory (DFT) calculations We used DFT with periodic boundary conditions and, unless otherwise noted, a hybrid exchange-correlation functional (revPBE0, i.e., revPBE19 with 25% exact exchange) to examine the formation energies of O and H radicals and of H2 and their diffusion kinetics in boehmite and gibbsite. All DFT calculations were performed using QUICKSTEP/CP2K,20,21 employing a hybrid Gaussian basis set and an auxiliary plane-wave basis set. We used a plane-wave cutoff energy of 400 Ry for the electron density. All the calculations were performed at the gamma point. Hybrid calculations were carried out with the truncated revPBE0 functional19 with a cutoff radius of 5.6 Å and 4.8 Å for the exchange interactions for boehmite and gibbsite (approximately half of the shortest dimension of the periodic cell), respectively. The Gaussian basis set was of DVZP quality for all three atoms (DZVP-MOLPOT-SR-GTH-q3 for Al, DZVPMOLPOT-SR-GTH-q6 for O, and DZVP-MOLPOT-SR-GTH-q1 for H). The auxiliary density matrix method (ADMM) was employed to speed up the Hartree-Fock exchange calculation.22,23 The auxiliary Gaussian basis sets for the Hartree-Fock exchange were cFIT6, cFIT3, and cFIT3 for Al, O, and H, respectively. All geometry optimizations were performed using BFGS optimizer with a force convergence criterion of 0.0002 Hartree Bohr−1 (~ 0.01 eV Å−1). The H2 molecule was simulated as a singlet state (para hydrogen molecule).



Page 6 of 23

Metadynamics simulations Metadynamics simulations24-27 were performed with CP2K28 to determine the energy barriers for the proton-coupled hole transfers (PCHT), i.e., O− diffusion. Two collective variables (CV) were used in these simulations, namely, 𝑑Ox - Oy, the distance between the two oxygen atoms involved in the proton transfer (CV1), and 𝑑OxH - OyH, the difference in distances between H and each of the two oxygen atoms (CV2, Figure 1A and Figure S1). Gaussian hills with a height of 0.002 Hartree (~0.054 eV) and a width of 0.1 Bohr (0.0529177 Å) were used for each collective variable and laid every 25 fs. The simulations were run in the canonical ensemble (NVT) using a Nosé-Hoover thermostat with a target temperature of 300 K. All metadynamics simulations were performed using revPBE.19 For the transfer across the interlayer in boehmite, an intermittent secondary PCHT between Oy and the nearest-neighbor hydroxyl along the [100] direction was observed during the simulation (4.9 ps). To ensure the PCHT between Ox and HOy was isolated, a second simulation (4.2 ps) was performed with the O−H bond distance of the hydroxyl involved in the secondary transfer constrained to 0.99 Å, which yielded a similar free energy contour map (Figure S3). For gibbsite, the simulation times were 5.4 ps for the transfer across the interlayer and 13 ps for the intralayer transfer. Climbing image nudged elastic band (CI-NEB) method Energy barriers for H0 and H2 transfer were calculated using the CI-NEB method.29,30 Most intermediate images were guessed from constrained energy minimizations of potential transition states and from the atomic displacements in energy minimizations of those potential transition states. Linear interpolation was used when the distance between two adjacent images determined by the previous method was much greater than 1 Å. Each of the images was


Page 7 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


connected by a spring constant of 2.57 eV Å2 (0.05 Hartree Bohr−1). Vibrational frequencies of the diffusing species (H0 or H2) at the transition state and energy-minimum configurations with other atoms being frozen were calculated by finite differences method (Table S2). As expected, a single imaginary frequency (Table S2) was obtained for each transition state configuration except for H2 migration in the [001] direction of boehmite (see caption of Figure S6), confirming that the CI-NEB calculations yielded true transition state configurations. The vibrational frequencies were also used to calculate attempt frequencies according to Vineyard theory,31 that 3𝑁

∏𝑖 = 1𝑣𝑖

∗

is, 𝑣 =

3𝑁 ― 1

∏𝑖 = 1 𝑣TS i

, where N is number of atoms involved in the diffusion process (1 for H0 and 2

for H2), and 𝑣𝑖 and 𝑣𝑇𝑆 𝑖 are the vibrational frequencies of these atoms in the energy-minimum and transition state configurations, respectively. For substitutional impurity diffusion in metals,32 this approach was shown to give errors of at most a factor of 4. Table 1. Energy of Reactions 3 (O radical formation, ∆𝐸1), 4 (H radical formation, ∆𝐸2), and 5 (H2 formation, ∆𝐸3) in boehmite and gibbsite. All energies are in eV. O−

Species

H0

H2

Mineral

Site

∆𝐸1

Site

∆𝐸2

Site

∆𝐸3

Boehmite

O1

6.31

H1

0.03

H21

−4.71

O1

6.24

H1

−0.26

H21

−4.83

O2

6.32

H2

0.28

H22

−3.82

O3

6.01

H3

0.09

H23

−4.13

O4

6.05

H2cav.

−4.06

O5

6.00

O6

6.09

Gibbsite



Page 8 of 23

RESULTS AND DISCUSSION The boehmite structure consists of layers of edge-sharing AlO4(OH)2 octahedra stacked along the [010] direction and linked via hydrogen bonds between hydroxide ions that lie parallel to the [100] direction (Figure 1). The gibbsite structure is similar to that of boehmite in that layers of edge-sharing octahedra, stacked along the [001] direction, are also linked via hydrogen bonds between hydroxide ions, but, unlike in boehmite, the hexagonal-like arrangement of the octahedra results in the formation of cavities within the layers. All hydroxyl oxygen sites in boehmite are identical (Figure 1A) and a single value is therefore reported for the O radical formation, ∆𝐸1. In contrast, ∆𝐸1 for the six unique oxygen (all hydroxyl) sites in gibbsite (Figures 1B and S2) vary where site O5 is the most stable and site O2 the least (Table 1). Further, the most stable site for H0 in gibbsite, H1, is lower in energy with respect to H0(g) than the unique site in boehmite (Table 1). Consequently, the formation of O and H radicals (Reaction 1) is predicted to be energetically favored in gibbsite compared to boehmite.


Page 9 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. (A) Single unique O− site in boehmite (O1) labeled as Ox. The three atoms involved in the collective variables used in the metadynamics simulations are labeled Ox, Oy, and H. (B) Six unique hydroxyl oxygen sites in gibbsite. The corresponding O− sites are created by removing H0 from the hydroxyl. H0 (shown in green) trapping sites in boehmite (C, H1) and gibbsite (D, H1 to H3) H0 can be trapped in one boehmite interlayer site (Figure 1C and Figure S2), whereas H0 can trap in three different gibbsite interlayer sites (Figure 1D and Figure S2). At each interlayer site in gibbsite, H0 is located close to the geometric center of a triangular prism composed of three O atoms from the top layer and three from the bottom. Projected down the [001] direction, sites H2 and H3 are overlapped with Al atoms while site H1 is overlapped with the di-octahedral layer cavity. The average O−H0 distance (2.46, 2.16, 2.22 Å for sites H1 to H3, respectively) 9 ACS Paragon Plus Environment


Page 10 of 23

correlates with the H0 formation energy, whereby short distances translate to less exothermic formation energies. Perhaps surprisingly, the cavity site in the structural unit of gibbsite does not exhibit any stability towards trapping H0 (i.e. it is not an energy minimum). In contrast, electron paramagnetic resonance experiments have indicated that H0 can be trapped in a similar Al-O octahedral layer cavity in kaolinite.18 The fact that complementary calculations found the structural unit cavity in kaolinite to be an energy minimum for H0 (data not shown) indicates that our theoretical approach is robust and that the result for gibbsite is correct. In sum, site H1 should accommodate H0 more favorably than the two other sites in gibbsite as well as the one site in boehmite, whereas H0 prefers the site in boehmite over sites H2 and H3 in gibbsite (Table 1). Energy minima for H2 were found at the same three sites H0 traps in, albeit with the geometric center of the H2 molecule slightly offset with respect to the position of H0 in the same site, as well as in the structural cavity in gibbsite, but only at one site in the interlayer of boehmite (Figure S2). ∆𝐸3 values are all highly exothermic (Table 1) but site H21 in gibbsite is the most stable (approximately 0.7 to 1.0 eV lower in energy than other sites in gibbsite and 0.12 eV lower than the site in boehmite). O− diffusion in boehmite and gibbsite is coupled to proton transfer; the overall process will therefore be referred to as proton-coupled hole transfer. PCHT pathways were explored with metadynamics simulations24 using two collective variables: 𝑑Ox - Oy, the distance between the two oxygen atoms involved in the proton transfer, and 𝑑OxH - OyH, the difference in distances between H and each of the two oxygen atoms (Figure 1A). To avoid computationally prohibitive calculations, the metadynamics simulations were performed with revPBE and the energy barriers at the revPBE0 level were then estimated using a series of energy minimizations with the two 10 ACS Paragon Plus Environment

Page 11 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CVs constrained to specific values in the vicinity of the transition state, as determined from the revPBE free energy contour maps (Figure S3). Table 2. Energy barriers, ∆𝐸 ∗ , for O−, H0, and H2 transfers in boehmite and gibbsite. All energies are in eV. Boehmite Species O−

H0

H2 †From

Gibbsite

Direction

∆𝐸 ∗

Direction

∆𝐸 ∗

[100] interlayer

1.16†

across interlayer

1.00†

intralayer

1.41†

[100] interlayer

0.27‡

interlayer H1−H2

0.60−0.65§

[001] interlayer

0.50‡

interlayer H1−H3

0.44−0.54§

across structural layers

0.41‡

[100] interlayer

0.42‡

interlayer H21−H22

>1.01*

[001] interlayer

0.86‡

interlayer H21−H23

>0.70*

across structural layers

>0.77*

constrained revPBE0 energy minimizations at fixed CV values determined from the

revPBE metadynamics simulations. ‡From

revPBE0 CI-NEB calculations.

§From

constrained revPBE0 energy minimizations at fixed H0 position determined from the

revPBE0 CI-NEB calculation of interlayer H1-H3 transfer through TS2. *Based

on ∆𝐸 ∗ > (∆𝐸𝑖3 ― ∆𝐸𝑗3) where i and j are final and initial H2 sites involved in the

transfer, respectively. Given proton orientations, PCHT can only occur across the interlayer region of boehmite; in contrast, both interlayer and intralayer (parallel to the basal surface) PCHT in gibbsite is allowed. Electronic structures for configurations in the transition region (Figure S4) demonstrate that PCHT is a sequential process where PT occurs before HT and is the rate-limiting step. The 11 ACS Paragon Plus Environment


Page 12 of 23

overall and PT (𝑑OxH - OyH ≈ 0 Å) energy barriers in boehmite are 1.16 eV and 0.84 eV, respectively, and those for interlayer and intralayer PCHTs in gibbsite are 1.00 eV and 0.94 eV, and 1.41 eV and 1.07 eV, respectively (information on the approach used to calculate these values from the free energy contour maps is provided in Table S1). The energy barrier for PT correlates with the initial O−O distance. The energy barriers for the overall PCHT are presented in Table 2.

Figure 2. Images included in the CI-NEB calculations of H0 transfer along (A) the [100] direction and (B) the [001] direction in boehmite. (C) Energies of the five images shown in (A) relative to that of the first image. (D) Energies of the five images shown in (B) relative to that of the first image. Since H0 traps in relatively symmetric sites in both phases, a climbing image nudged elastic band method29,30 was employed to calculate the energy barriers for H0 transfers. H0 12 ACS Paragon Plus Environment

Page 13 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


transfer in boehmite (Figure 2) is much easier along the [100] direction compared to the [001] direction (Table 2). Figure 3A illustrates one pathway for H0 transfer from site H1 to site H3 in the interlayer of gibbsite. At the transition state (inset of Figure 3C), H0 is roughly at the geometric center of a near square formed by four hydroxyl oxygen atoms. Based on gibbsite symmetry, the transition state has 6 inequivalent sites. In other words, there are 6 pathways for H0 transfer from site H1 to site H2 or site H3 (Figure S5). The energy barriers for the other 5 pathways were therefore estimated from energy minimization by constraining the H0 to the center of the respective near square of hydroxyl oxygens. The energy barriers for transfers to site H3 are lower than those to site H2 (Table 2 and Figure S5), as expected based on the relative stability of sites H3 and H2 (Table 1). H0 can also transfer across the di-octahedral layer (from site H1 to site H1 in another interlayer) via the cavity in the structural unit (Figure 3B, D). The energy barrier for this pathway is lower than those for interlayer transfer in gibbsite (Table 2).



Page 14 of 23

Figure 3. Images included in the CI-NEB calculations of H0 transfers (A) from site H1 to site H3 in gibbsite (image 5 is directly underneath an Al site) and (B) across the structural layer in gibbsite. (C) Energies of the five images shown in (A) relative to that of the first image. The configuration of the transition state (the fourth image) is shown in the inset. (D) Energies of the seven images shown in (B) relative to that of the first image. The calculated energy barriers for H2 diffusion along the [100] direction (fastest direction) and [001] direction in boehmite are 0.42 eV and 0.86 eV, respectively (Figures 4 and S6 and Table 2). The energy barrier for diffusion along any direction in gibbsite should be at least greater than 0.70 eV (Table 2). Importantly, ∆𝐸 ∗ is systematically higher for H2 than for H0 for a given diffusion direction.

Figure 4. (A)-(E) Five images included in the CI-NEB calculations of H2 transfer along [100] direction in boehmite. One hydrogen of the H2 is colored in white and the other in green. (F) Energies of the five images relative to that of the first image.


Page 15 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


That the homolytic cleavage of the O−H bond is more favorable in gibbsite than boehmite suggests, all else equal, that gibbsite should yield higher H2 than boehmite; experiments, however, have demonstrated that the opposite occurs. In order to resolve this apparent discrepancy, we quantified radical and H2 diffusion in boehmite and gibbsite by calculating first their site-to-site transfer rates, R: 𝑅 = 𝑣 ∗ 𝑒∆𝐸

∗

/𝑘𝑇

(6)

where 𝑣 ∗ is the attempt frequency, ∆𝐸 ∗ is the energy barrier (Table 2), k the Boltzmann constant, and T the temperature. The attempt frequencies were obtained from vibrational frequency calculations (Table S2) and are listed in Table S3 together with the resulting transfer rates at room temperature. Diffusion coefficients were then calculated using the 1D EinsteinSmoluchowski equation: 𝐷 = 𝜆2𝑅/2

(7)

where 𝜆 is the transfer distance. Ratios of diffusion coefficients for a select set of transfer pairs at room temperature are given in Table S4. Following from the discussion in Kaddissy et al.,6 two simultaneous pathways for H2 formation and release are envisaged: (1) Diffusion of H0 species to the particle surface, where Reaction 2 can take place, and (2) H2 formation through Reaction 2 within a particle and subsequent solid-state diffusion of H2 to the surface for release. Considering pathway (1) first, the fact that H0 can diffuse across structural layers in gibbsite but not in boehmite implies that H0 diffusion is three dimensional in gibbsite but only two dimensional in boehmite. H0 radicals created within a particle are thus able to reach the basal surfaces in gibbsite but are concentrated to side surfaces in boehmite. Because the basal surfaces dominate the particle morphologies of both phases,33-35 the three-dimensional diffusion in gibbsite should lead to a dilution of the H0 15 ACS Paragon Plus Environment


Page 16 of 23

surface density and thus a decrease in the efficiency of Reaction 2. Moreover, regardless of the high dependence of H0 diffusion on pathways in gibbsite, H0 diffusion is at least 68 times greater in boehmite compared to gibbsite at room temperature (Table S4). This suggests a greater chance, within the timescale of experiments such as those performed by Kaddissy et al.,6 for H0 to diffuse to the surface of boehmite relative to gibbsite and then combine with another H0 (Reaction 2) to release H2 gas. Significant differences between boehmite and gibbsite are also evident when considering pathway (2). Whereas the energy barrier of a given H2 transfer increases relative to that for the same H0 transfer in both phases, the resulting decrease in transfer rates and associated diffusion coefficients is more extensive in gibbsite than in boehmite, resulting in diffusion coefficients at least 5 orders of magnitude lower for gibbsite than for the [100] direction in boehmite at room temperature (Table S4). This suggests that any H2 formed in the bulk solid phase has a better chance of escaping boehmite compared to gibbsite. Consequently, our theoretical treatment suggests that faster diffusion of H0 and H2 in boehmite compared to gibbsite, not the efficiency of radiolytic events, better explain the experimental results of Westbrook et al.7 showing that boehmite yields much more H2 than gibbsite under irradiation. The present analysis is also relevant for gaining a better understanding of the relative H2 yield of boehmite and bayerite (a close polymorph of gibbsite) under irradiation, where boehmite releases more H2 at room temperature than bayerite. That H2 yields decreased markedly with decreasing boehmite particle size, as discussed in Kaddissy et al.,6 is further evidence that the primary production of radicals is not a key differential in H2 productivity, consistent with the present analysis. Further, our finding that the energy barriers for H0 and H2 diffusion are high (well above thermal energy) suggests a mechanistic reason for


Page 17 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the presence of appreciable trapped H2 in boehmite and, by analogy with gibbsite, bayerite. In this regard, although the origin of so-called trapped H2 was not precisely determined by experiment,6 theory suggests that the diffusion of H0 in the structures is slow and therefore conducive to Reaction 2. Once formed, calculations indicate that H2 diffusion is even slower, which could lead to long residence times for H2 in the bulk. Consequently, H2 trapped in irradiated Al (oxy)hydroxides could pose a potential latent risk in Al-rich nuclear waste. CONCLUSIONS This work provides the first molecular-level theoretical treatment concerning the formation and diffusion of O−, H0, and H2 in irradiated boehmite and gibbsite. Having established the primary importance of the diffusion of radiolytic species in the bulk as distinguishing the response of two major hydroxylated Al phases to radiation, future work is positioned to focus on quantifying fluxes for comparison with experiment. In this regard, it would be beneficial to draw on the growing literature in radiation detection materials where kinetic Monte Carlo methods are used to upscale atomic/molecular events to model macroscopic or collective transport of radiolytic species.36,37 ACKNOWLEDGMENTS This research was supported by the Laboratory Directed Research and Development (LDRD), Nuclear Process Science Initiative (NPSI) at Pacific Northwest National Laboratory (PNNL). The computational work was performed using PNNL Institutional Computing at PNNL and the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy (DOE) Office of Science User Facility operated under Contract No. DE-AC02-05CH11231. CJM was supported by the U.S. DOE, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division. PNNL is a multiprogram national 17 ACS Paragon Plus Environment


Page 18 of 23

laboratory operated for the U.S. DOE by Battelle Memorial Institute under Contract No. DEAC06-76RLO-1830. AUTHOR INFORMATION Corresponding Author *Phone: (509) 371-6382; e-mail: [email protected] SUPPORTING INFORMATION Energy minimum configurations, configurations from metadynamics simulations, and transition state configurations of O−, H0, and H2 in boehmite and gibbsite; free energy contour maps constructed from the revPBE metadynamics simulations; images used in the CI-NEB calculations of the H2 transfer along the [001] direction in boehmite; relative energies at the revPBE0 level of configurations extracted from the revPBE metadynamics simulations; calculated vibrational frequencies of H0 and H2; attempt frequencies and transfer rates of O−, H0, and H2 in boehmite and gibbsite; ratios of diffusion coefficient for select pairs of transfers. REFERENCES (1) Bryan, S. A.; King, C. M.; Pederson, L. R. Thermal and Radiolytic Gas Generation in Hanford High-Level Waste. Trans. Am. Nucl. Soc. 1999, 81, 97-98. (2) Sharland, S. M.; Agg, P. J.; Naish, C. C.; Wikramaratna, R. S. Gas Generation by Metal Corrosion and the Implications for near-Field Containment in Radioactive Waste Repositories, Power Reactor and Nuclear Fuel Development Corp., Tokyo, Japan, PNC-TN--1100-94-003, 1994. (3) Thomas, J. K. Physical Aspects of Radiation-Induced Processes on Sio2, -Al2o3, Zeolites, and Clays. Chem. Rev. 2005, 105, 1683-1734. 18 ACS Paragon Plus Environment

Page 19 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(4) LaVerne, J. A.; Tandon, L. H2 and Cl2 Production in the Radiolysis of Calcium and Magnesium Chlorides and Hydroxides. J. Phys. Chem. A 2005, 109, 2861-2865. (5) Fourdrin, C.; Aarrachi, H.; Latrille, C.; Esnouf, S.; Bergaya, F.; Le Caër, S. Water Radiolysis in Exchanged-Montmorillonites: The H2 Production Mechanisms. Environ. Sci. Technol. 2013, 47, 9530-9537. (6) Kaddissy, J. A.; Esnouf, S.; Durand, D.; Saffre, D.; Foy, E.; Renault, J.-P. Radiolytic Events in Nanostructured Aluminum Hydroxides. J. Phys. Chem. C 2017, 121, 6365-6373. (7) Westbrook, M. L.; Sindelar, R. L.; Fisher, D. L. Radiolytic Hydrogen Generation from Aluminum Oxyhydroxide Solids: Theory and Experiment. J. Radioanal. Nucl. Chem. 2015, 303, 81-86. (8) Lainé, M.; Allard, T.; Balan, E.; Martin, F.; Von Bardeleben, H. J.; Robert, J.-L.; Le Caër, S. Reaction Mechanisms in Talc under Ionizing Radiation: Evidence of a High Stability of H• Atoms. J. Phys. Chem. C 2016, 120, 2087-2095. (9) Lainé, M.; Balan, E.; Allard, T.; Paineau, E.; Jeunesse, P.; Mostafavi, M.; Robert, J.-L.; Le Caër, S. Reaction Mechanisms in Swelling Clays under Ionizing Radiation: Influence of the Water Amount and of the Nature of the Clay Mineral. RSC Adv. 2017, 7, 526-534. (10) Conroy, M.; Soltis, J. A.; Wittman, R. S.; Smith, F. N.; Chatterjee, S.; Zhang, X.; Ilton, E. S.; Buck, E. C. Importance of Interlayer H Bonding Structure to the Stability of Layered Minerals. Sci. Rep. 2017, 7, 13274. (11) Peterson, R. A.; Buck, E. C.; Chun, J.; Daniel, R. C.; Herting, D. L.; Ilton, E. S.; Lumetta, G. J.; Clark, S. B. Review of the Scientific Understanding of Radioactive Waste at the U.S. Doe Hanford Site. Environ. Sci. Technol. 2018, 52, 381-396.



Page 20 of 23

(12) Huestis, P.; Pearce, C. I.; Zhang, X.; N'Diaye, A. T.; Rosso, K. M.; LaVerne, J. A. Radiolytic Stability of Gibbsite and Boehmite with Adsorbed Water. J. Nucl. Mater. 2018, 501, 224-233. (13) Prange, M. P.; Zhang, X.; Ilton, E. S.; Kovarik, L.; Engelhard, M. H.; Kerisit, S. N. Electronic Response of Aluminum-Bearing Minerals. J. Chem. Phys. 2018, 149, 024502. (14) Reiff, S. C.; LaVerne, J. A. Radiolysis of Water with Aluminum Oxide Surfaces. Rad. Phys. Chem. 2017, 131, 46-50. (15) Petrik, N. G.; Alexandrov, A. B.; Vall, A. I. Interfacial Energy Transfer During Gamma Radiolysis of Water on the Surface of Zro2 and Some Other Oxides. J. Phys. Chem. B 2001, 105, 5935-5944. (16) Cannas, M.; Leone, M. Photoluminescence at 1.9 Ev in Synthetic Wet Silica. J. Non-Cryst. Solids 2001, 280, 183-187. (17) Scholz, G.; Stösser, R. Atomic Hydrogen as Spin Probe in Thermally and Mechanically Activated Materials. Phys. Chem. Chem. Phys. 2002, 4, 5448-5457. (18) Toriyama, K.; Lund, A.; Okazaki, M. Trapped Hydrogen Atoms Radiolytically Formed in Natural and Synthetic Kaolinites: An Electron Paramagnetic Resonance Study. Phys. Chem. Chem. Phys. 2000, 2, 4697-4701. (19) Zhang, Y.; Yang, W. Comment on "Generalized Gradient Approximation Made Simple". Phys. Rev. Lett. 1998, 80, 890-890. (20) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and Accurate Density Funcitonal Calculations Using a Mixed Gaussian and Plane Waves Approach. Comput. Phys. Comm. 2005, 167, 103-128.


Page 21 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(21) Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J. Cp2k: Atomistic Simulations of Condensed Matter Systems. Comput. Mol. Sci. 2014, 4, 15-25. (22) Guidon, M.; Hutter, J.; VandeVondele, J. Robust Periodic Hartree-Fock Exchange for Large-Scale Simulations Using Gaussian Basis Sets. J. Chem. Theory Comput. 2009, 5, 30103021. (23) Guidon, M.; Hutter, J.; VandeVondele, J. Auxiliary Density Matrix Methods for HartreeFock Exchange Calculations. J. Chem. Theory Comput. 2010, 6, 2348-2364. (24) Laio, A.; Parrinello, M. Escaping Free-Energy Minima. Proc. Natl. Acad. Sci. 2002, 99, 12552-12556. (25) Iannuzzi, M.; Laio, A.; Parrinello, M. Efficient Exploration of Reactive Potential Energy Surfaces Using Carr-Parrinello Molecular Dynamics. Phys. Rev. Lett. 2003, 90, 238302. (26) Laio, A.; Rodriguez-Fortea, A.; Gervasio, F. L.; Ceccarelli, M.; Parrinello, M. Assessing the Accuracy of Metadynamics. J. Phys. Chem. B 2005, 109, 6714-6721. (27) Laio, A.; Parrinello, M. Computing Free Energies and Accelerating Rare Events with Metadynamics. Lect. Notes Phys. 2006, 703, 315-347. (28) Vanden-Eijnden, E.; Ciccotti, G. Second-Order Integrators for Langevin Equations with Holonomic Constraints. Chem. Phys. Lett. 2006, 429, 310-316. (29) Henkelman, G.; Jónsson, H. Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113, 99789985. (30) Henkelman, G. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 9901.



Page 22 of 23

(31) Vineyard, G. H. Frequency Factors and Isotope Effects in Solid State Rate Processes. J. Phys. Chem. Solids 1957, 3, 121-127. (32) Wu, H.; Mayeshiba, T.; Morgan, D. High-Throughput Ab-Initio Dilute Solute Diffusion Database. Sci. Data 2016, 3, 160054. (33) Zhang, X.; Zhang, X.; Graham, T. R.; Pearce, C. I.; Mehdi, B. L.; N'Diaye, A. T.; Kerisit, S.; Browning, N. D.; Clark, S. B.; Rosso, K. M. Fast Synthesis of Gibbsite Nanoplates and Process Optimization Using Box-Behnken Experimental Design. Cryst. Growth Des. 2017, 17, 6801-6808. (34) Zhang, X.; Cui, W.; Page, K. L.; Pearce, C. I.; Bowden, M. E.; Graham, T. R.; Shen, Z.; Li, P.; Wang, Z.; Kerisit, S.et al. Size and Morphology Controlled Synthesis of Boehmite Nanoplates and Crystal Growth Mechanisms. Cryst. Growth Des. 2018, 18, 3596-3606. (35) Prange, M. P.; Zhang, X.; Bowden, M. E.; Shen, Z.; Ilton, E. S.; Kerisit, S. N. Predicting Surface Energies and Particle Morphologies of Boehmite (-Alooh) from Density Functional Theory. J. Phys. Chem. C 2018, 122, 10400-10412. (36) Wang, Z.; Williams, R. T.; Grim, J. Q.; Gao, F.; Kerisit, S. Kinetic Monte Carlo Simulations of Excitation Density Dependent Scintillation in Csi and Csi(Tl). Phys. Status Solidi B 2013, 250, 1532-1540. (37) Prange, M. P.; Xie, Y.-L.; Campbell, L. W.; Gao, F.; Kerisit, S. Monte Carlo Simulation of Electron Thermalization in Scintillator Materials: Implications for Scintillator Nonproportionality. J. Appl. Phys. 2017, 122, 234504.


Page 23 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC GRAPHICS


Diffusion Mechanisms of Radiolytic Species in Irradiated Al (Oxy

Recommend Documents