Ion-Exchange Interdiffusion Model with Potential Application to Long

Article pubs.acs.org/JPCC

Ion-Exchange Interdiffusion Model with Potential Application to Long-Term Nuclear Waste Glass Performance James Joseph Neeway,*,† Sebastien N. Kerisit,‡ Jia Liu,§ Jiandong Zhang,§ Zihua Zhu,§ Brian Joseph Riley,† and Joseph Vincent Ryan† †

Energy and Environment Directorate, ‡Physical and Computational Sciences Directorate, and §Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States ABSTRACT: Ion exchange and interdiffusion are critical processes in glass applications. In the field of aqueous glass corrosion, it is difficult to conclusively deconvolute the process of ion exchange from other processes, principally dissolution of the glass matrix, due to the formation of alteration layers, Therefore, we have developed a method to isolate alkali diffusion that involves contacting glass coupons with a solution of 6LiCl dissolved in functionally inert dimethyl sulfoxide. We employ the method at temperatures ranging from 25 to 150 °C with various glass compositions. Glass compositions include simulant nuclear waste glasses, such as SON68 and the ISG, glasses in which the nature of the alkali element was varied, and glasses that contained more than one alkali element. An interdiffusion model based on Fick’s second law was developed and applied to all experiments to extract diffusion coefficients. The model expands established models of interdiffusion to the case where multiple types of alkali sites are present in the glass. Activation energies for alkali ion diffusion were calculated. The interdiffusion model derived from laboratory experiments is expected to be useful for modeling glass corrosion in a geological repository when silicon concentrations are high.

1. INTRODUCTION In the context of this work, ion exchange is referred to as the overall net reaction in which cations in the pristine glass are exchange with cations dissolved in a contacting fluid. This overall reaction consists of three steps: diffusion of dissolved cations to and from the glass−fluid interface, exchange at the glass−fluid interface, and solid-state diffusion within the glass. The solid-state diffusion is referred to as interdiffusion and leads to the formation of anticorrelated concentration profiles of the inward- and outward-diffusing ions that are dependent on the relative charges of the diffusing species, redox conditions of the glass, and changes in the structure of the glass upon exchange.1−4 Major industrial fields where understanding the ion-exchange process is important are glass strengthening,5−9 bioactive glasses,10 and the glass−water reaction, principally the longterm durability of glasses used to immobilize radioactive waste.11−14 Ion exchange is exploited in glass strengthening, as it has long been recognized that the replacement of alkali cations with different ionic radii between a molten salt bath and an alkali-containing glass will result in stresses (strengthening) at the glass surface.15 For this application, glasses are immerged in molten alkali salts below the glass transition temperature and larger ions from the salt replace smaller ions in the glass.5,6,16 Ion exchange is also recognized as a key process related to the long-term durability of glasses used to immobilize radioactive waste, especially in the presence of aqueous solutions © 2016 American Chemical Society

containing high concentrations of H4SiO4. The fundamental difference between glass-strengthening and glass-durability experiments is that the former relies on alkali−alkali exchange while the latter involves hydrogen−alkali exchange. The present study is a continuation of work published previously17 and exploits the relatively fast alkali−alkali interdiffusion process to develop an alkali interdiffusion model. Assuming that the processes of alkali−alkali interdiffusion and hydrogen−alkali interdiffusion show sufficient similarities, this model could be incorporated into models used to predict the corrosion rate of nuclear waste glasses in a geological repository. This is of particular importance because current glass corrosion models lack experimental data to support the treatment of the diffusion term. Therefore, a more robust understanding of the ion exchange−interdiffusion process is needed to support and develop future glass corrosion models. 1.1. Ion-Exchange Models. In terms of aqueous glass alteration, either H+ or H3O+ from the fluid exchanges with cations, principally monovalent alkali, in the glass. Hydrogen− alkali ion exchange is most predominant in high-alkali glasses, at low temperature, acidic to near-neutral pH, and in solutions near saturation with respect to amorphous silica [SiO2(am)], where the hydrolysis reaction is suppressed.11,12,18,19 For nearReceived: April 11, 2016 Published: April 12, 2016 9374

DOI: 10.1021/acs.jpcc.6b03681 J. Phys. Chem. C 2016, 120, 9374−9384

Article

The Journal of Physical Chemistry C

and is unique to each glass composition. The second model, introduced by Grambow and Müller,11 known as the GM model, assumes the creation of a water diffusion layer between the gel and pristine glass through which Si transport is restricted. The third model, known as glass reactivity with allowance for the alteration layer (GRAAL), introduced by Frugier et al.,37 with updates by Frugier et al.38 and Minet et al.,39 assumes the formation of a passivating reactive interphase (PRI) as Si solution concentrations increase. According to Frugier et al.,37 the PRI “...is assumed to form by water diffusion at the interface with the pristine glass, which hydrolyzes the most soluble glass elements, especially boron.” Again, we emphasize that all three models use some representation of a diffusion term to control the long-term glass alteration rate once the solution has reached saturation with respect to a glassdependent silica phase. However, the treatment of the diffusion term lacks a technical basis in these models and, therefore, a more robust understanding of the ion exchange-interdiffusion process is needed to support and develop future glass corrosion models. 1.2. Justification of Experiments. Because of the difficulty in deconvoluting the hydrolysis and ion-exchange processes, various experimental techniques have been employed to isolate and differentiate between the two. One strategy employed by McGrail et al.18 monitored the release of Mo and Na from simplified Na2O−Al2O3−SiO2 glasses doped with MoO3 glasses and noted that Mo and Na were not released congruently at higher degrees of silica saturation in solution. The authors suggested that the difference in release was due to the rate of Na−H ion exchange, which was higher than the rate of matrix dissolution, indexed by the release of the intermediate element Mo. The difference in moles of Na and Mo released from the glass was used as the ion-exchange and was assumed constant with time. Rébiscoul et al.40 also attempted to isolate the ion-exchange process by exposing glass coupons of various glass compositions to a solution at pH 3 at various temperatures for less than 2 h and measuring H ingress through the use of nondestructive Fourier transform infrared (FTIR) and X-ray reflectivity (XRR) techniques. An additional experiment by Rébiscoul et al.41 using quasielectric neutron scattering (QENS) also isolated proton movement in the glass alteration layer and showed that the mobility was dependent on both the presence of ion in the leachate in the alteration layer and the composition of the alteration layer. Although McGrail et al. and Rebiscoul et al. were able to calculate rates and diffusion coefficients for the ion exchange process into the pristine glass, the experiments did not isolate hydrolysis from ion exchange. Therefore, it is unclear if the rates or diffusion coefficients that were measured were actually those for the pristine glass or those for a surface alteration layer. In this set of experiments, the alkali−alkali ion exchange and interdiffusion processes are studied through the use of Li isotopes in five glasses relevant to high-level waste immobilization: the Na-containing International Simple Glass (ISG),42 ISG-Li (Li substitution for Na), ISG-K (K substitution for Na), SON68,27 and CJ-6.43,44 The Li solution source was a nonaqueous solvent, dimethyl sulfoxide (DMSO). The solvent DMSO was chosen because it does not chemically react with the glass material, can dissolve alkali salts, and has a boiling point of 189 °C, which is higher than the temperatures commonly used to study glass corrosion in aqueous environments. Thus, the ions dissolved in DMSO can exchange and diffuse through the glass without the process being convoluted

saturation conditions, predominance of the ion-exchange process is due to the fact that ion exchange is not affected by solution saturation with respect to amorphous silica. This final point is of particular importance in regard to repository conditions where near-saturation conditions are expected to persist for long time periods.11,13 Additionally, this ionexchange reaction serves to raise the pH of the aqueous solution which, in turn, promotes the dissolution reaction due to the rate of network hydrolysis increasing as pH increases. Though obvious, it deserves stating that, in comparison to alkali−alkali ion exchange, where similar alkali can be exchanged between the fluid and the solid (e.g., Na+ for Na+), hydrogen-alkali ion exchange inherently occurs between two dissimilar species. Diffusion of a hydrogen-containing species into a pristine mineral or glass surface has long been recognized as one of the processes through which glasses and minerals are altered. Rana and Douglas20,21 were among the first to recognize this. They reasoned that because the release of sodium ions from the glass into solution exhibited a square root time dependence, the initial dissolution behavior of the glass occurred through a diffusion process. The basis for this reasoning is Fick’s second law, which will be explained further below. On the other hand, Rana and Douglas noted that the square root time dependence persisted only at short time periods. As the reaction progressed, linear time dependence was observed. Boksay et al.22,23 refined the results of Rana and Douglas by incorporating derived alkali profiles in the solid and implementing a diffusion model that eventually took into account a retreating surface. This latter step was assumed to account for the linear time dependence at sufficiently long reaction times. Doremus24 eventually expanded on the model of Boksay et 22,23 to allow for inward- and outward-diffusing ions to have al. different diffusion coefficients. The model was then corroborated with improved technology that allowed for more accurate probing of the elemental profiles in the solid.25,26 More advanced studies that treat experimental observations exhibiting diffusion behavior generally rely on the models proposed by Boksay and Doremus.27 It should be noted that diffusion of water has also been attributed as the rate-controlling mechanism for glass and mineral corrosion.11,28 Presently, there exist three main empirical models of longterm nuclear waste glass corrosion, which will be explained in more detail in the following paragraph. A fourth conceptual model of glass dissolution based on a dissolution/precipitation mechanism is also available, but diffusive mechanisms are inherently not considered in such a system.29−31 Additionally, Monte Carlo simulations and molecular dynamics methods are being developed to describe molecular-scale reactions involved in glass dissolution.32−36 Each of the three empirical models contains two terms: (1) an affinity term, which accounts for the slowing of the glass dissolution rate with increased Si in solution, and (2) a diffusion-based term, which accounts for continued glass dissolution at high Si-solution concentration. However, the three main principle empirical models of longterm glass corrosion differ on how glass continues to corrode once the solution is saturated with respect to a silica polymorph. The first model, constructed for low-activity waste (LAW) glasses and introduced by McGrail et al.,13 assumes a constant release of Na from the glass into solution where Na+ in the glass is substituted by H+ in solution. The temperature-dependent Na−H exchange constant is obtained from experimental data 9375


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The Journal of Physical Chemistry C Table 1. List of Glass Compositions (mol %)a composition (mol %)

a

glass

SiO2

B2O3

Al2O3

CaO

ZrO2

Ce2O3

Li2O

Na2O

CJ-6 SON68 ISG ISG-Li ISG-K

56.6 52.7 60.1 60.0 60.2

15.1 14.0 16.0 15.9 16.0

3.6 3.4 3.8 3.8 3.8

5.0 5.4 5.7 5.7 5.7

1.5 1.6 1.7 1.7 1.7

1.4 0.2

5 4.6

11.8 11.4 12.6

K2O

others 6.7

12.9 12.6

37

The list of other elements in SON68 is given elsewhere. .

by any of the other aqueous corrosion mechanisms. In the present study, we have added different glass compositions to study the effect of various alkalis and we extend tests to different temperatures to calculate activation energies of the alkali−alkali ion exchange process. The previous model17 has been refined to allow for diffusion on different alkali sites on the glass instead of treating alkali ion profiles independently in the case where the glass contains more than one alkali. The application of these results is discussed in terms of the role of these processes in the long term behavior of radioactive waste glasses in a geologic repository.

during the annealing process. This was evidenced by a subtle blue color that appeared upon annealing. Coloration was not observed with the quenched samples. Therefore, glass coupons were cut from larger pieces obtained from quenching on the steel plate. The large faces of the coupons were the inner portion of the large pieces. The annealed glass bars and quenched pieces were then cut with a wire saw to a size slightly thicker than the final desired target thickness. The coupons were hand ground with 320− 1200 grit sandpaper (US) on a lapping wheel and then cleaned. They were then hand polished on 6-μm diamond/white felt on a lapping wheel until the slices were reasonably polished. After this, the samples were cleaned and mounted on 0.9 kg (2-lb) pucks and polished in 1-μm diamond/oil/nylon on a vibratory polisher overnight. The mounts were cleaned and polished with colloidal silica in H2O and a final B felt cloth for 2−8 h to a final polish. The polishing procedure was redone with the other face of the glass coupon. When the polishing was complete, samples were cleaned in acetone and then ethanol. 2.2. Diffusion Experiments. The 6LiCl was obtained from 6 Li2CO3 by dissolving 6Li2CO3 in water (0.1 M) and titrating the solution to pH 4 with 1 M HCl. Excess water was removed by placing the solution in a vacuum furnace at 45 °C overnight then raising the temperature in the furnace to 150 °C for 2 h. The presence of LiCl was confirmed with XRD. The enriched 6 LiCl (95.62%) was dissolved in dimethyl sulfoxide (DMSO, Sigma) to obtain a final concentration of 4.5 g LiCl/kg DMSO. Water was removed from the DMSO by contacting the solvent with molecular sieves (Type 3A, Sigma-Aldrich) for 24 h. The diffusion experiment system design involved inserting a fused silica crucible in a stainless steel container (inner volume ∼20 mL). A schematic representation of the system is given elsewhere.17 The polished glass coupons were hung with the use of a platinum wire from a horizontal fused silica rod and completely submerged in the 6Li/DMSO solution. The interior liner was capped with a quartz lid and sealed with Teflon tape to minimize evaporation of DMSO from the container. After the system was prepared, the containers were placed in the oven at the desired temperature and for the desired duration. When each glass coupon was removed from the vessel at the end of an experiment, it was rinsed with clean DMSO, water, and ethanol and then dried in an oven at 90 °C for 10 min. All of the experimental durations, temperatures, and glass compositions are presented in Table 2. We note that ToFSIMS profiles were also obtained from “as prepared” coupons and coupons that were placed in DMSO (no alkali) at 120 °C for approximately 18 days. The ToF-SIMS data show both the 6 Li and 7Li isotopes having a slight depletion over the first few hundreds of nanometers after 18 days at 120 °C. However, the extent of this depletion is small when compared to the extent of ion exchange measured for this glass at this temperature when

2. EXPERIMENTAL PROCEDURES 2.1. Glass Fabrication and Preparation. Five different glasses were fabricated and used in this study: SON68, CJ-6, ISG, ISG-Li, and ISG-K. SON68, ISG-Li, and ISG-K were fabricated at PNNL, the CJ-6 coupons were supplied by the Commissariat à l’énergie atomique et aux énergies alternatives (CEA),44 and the ISG glass was supplied by MoSci (Rolla, MO). The ISG glass is part of a large batch that was fabricated to be used in an international effort to reach a consensus on the mechanisms controlling the long-term glass dissolution rate.42 The first glass, SON68, was chosen because of its nearly identical composition to the R7T7 radioactive waste glass currently being produced at the Areva reprocessing site in La Hague, France. The SON68 glass has been the focus of a majority of glass alteration experiments conducted by the international waste glass corrosion community during the past decade. The CJ-6 glass composition is a simplified version of SON68 and was initially designed to investigate the role of the major elements in SON68 during corrosion. The molar ratios of the 8-oxide CJ-6 glass are equivalent to those found in SON68 with Si/B, Si/Na, and Si/Al equal to 1.88, 2.40, and 7.87, respectively, in both glasses.44 ISG is also a simplified version of SON68, with the same oxide components as CJ-6 except for Li2O and Ce2O3. ISG was first introduced as “CJ4”.43,44 Two other glasses, ISG-Li and ISG-K, were fabricated by replacing Na in ISG on a molar basis with either Li (ISG-Li) or K (ISG-K). The molar ratios of all the components are identical. The compositions of the major oxides in the five glasses are presented in Table 1. Glasses fabricated in house were made by batching carbonates and oxides of the various metals, melting the mixtures within a platinum crucible for 1 h within a furnace, and quenching on a stainless steel plate. The quenched glass was then crushed and remelted to ensure a homogeneous solid. The melt temperature was 1250 °C for SON68, 1325 °C for ISG-Li, and 1400 °C for ISG-K. For SON68 and ISG-K, the second melt was poured into rectangular molds and annealed at 560 °C for 1 h and then allowed to cool to room temperature in the annealing furnace. For ISG-Li, phase separation occurred 9376


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The Journal of Physical Chemistry C ∂C ∂ ⎛⎜ ∂C ⎞⎟ = D ∂t ∂x ⎝ ∂x ⎠

Table 2. List of Experimental Temperatures and Experimental Duration for the Various Ion-Exchange Experiments with 6Li as the Inward-Diffusing Cation glass CJ-6

SON68

temp (°C)

duration (days)

25 60 90 120 150 25 90 150

30, 90, 270 21, 50, 93 10, 30, 90 2, 7, 21 3, 10 90, 190, 262 10, 30, 90 3, 10

glass ISG

ISG-Li

ISG-K

temp (°C)

duration (days)

60 90 120 60 90 120 90 120

14, 35 4, 9 2, 7 10, 22, 30 1, 9 0.3, 2 3, 9, 30 7, 20

(1)

where C is the concentration, x is the depth, t is the time, and D is the diffusion coefficient. If the diffusion of a given alkali species is independent from any other species, D is a constant with time and depth. We refer to this case as isolated diffusion. In this case, a simple analytical solution47 can be written to relate the concentration of the alkali species at depth x, C(x), to its concentration at depth x = 0, C0: x C(x) = C0 erfc 2 (Dt ) (2) However, the experiments performed in this work also involved the interdependent diffusion of two different alkali species. We refer to this case as interdiffusion. In this case, diffusion coefficients are not constant with time and depth. In addition, glasses may contain more than one type of alkali ion, such as in CJ-6 and SON68, which contain both Li and Na. Therefore, the model must consider diffusion on more than one type of exchange site. As a result, the overall diffusion coefficient of species A, DA, is defined as the sum of the diffusion coefficients, Di, on all the sites, i, available to this species, weighted by the fraction of each site, wi

Li is present in the solution. Therefore, we conclude that any polishing effects or possible effects of DMSO on the measured alkali profiles are negligible. 2.3. ToF-SIMS Technique. The coupon surfaces were analyzed with time-of-flight secondary ion mass spectrometry (ToF-SIMS) depth profiling. A ToF-SIMS spectrometer (TOF.SIMS5, IONTOF GmbH, Münster, Germany) was used to perform depth profiling experiments. A dual beam depth profiling strategy was used. A 20 keV Arn+ beam was used as a sputter beam, due to its high depth profiling rate and mild charging at the sputtering interface, which was scanned on a 200 × 200 μm2 (for Arn+ beam) area.45 However, the depth resolution of the 20 keV Arn+ beam was not as good as that of a low energy (e.g., 1.0 keV) O2+ beam.45 Therefore, if Arn+ beam depth profiling showed the diffusion depth was shallower than 100 nm, a new depth profiling measurement was performed with a 1.0 keV O2+ beam as the sputter beam, which was scanned on a 300 × 300 μm2 area. In most cases, after normalization, the depth profiles obtained from the 20 keV Arn+ sputtering were consistent with the depth profiles obtained from the 1.0 keV O2+ sputtering, and the data from the O2+ sputtering provided more data points for modeling. A 25.0 keV Bi+ beam was used as an analysis beam for all cases, which was scanned on a 100 × 100 μm2 area at the center of the sputter crater. More ToF-SIMS experimental details can be found in previous publications.45,46 It should be noted that the relatively high Li+, Na+, and K+ signal noise was due to a Poisson correction needed as a result of the dead time during signal counting. After the SIMS measurement, a stylus profilometer was used to measure the crater depth, and a constant sputter rate was assumed for depth calibration. We note that the data obtained near the surface have some inherent uncertainties due to surface contamination, surface roughness, and the time to obtain a stable sputtering surface. 2.4. Interdiffusion Model. In this section, the mathematical framework used to interpret the depth profiles obtained experimentally is described in detail. The 6Li in the nonaqueous DMSO solution is found to exchange only with other alkali ions (i.e., 6Li, 7Li, Na, and K) from the pristine glass; therefore, only mass conservation equations are considered in the model. In addition, the model assumes that the alkali species dissolved in the solution are in excess throughout the duration of the experiments. Finally, any difference in the diffusion coefficients of different isotopes of the same element is negligible as demonstrated below. The model describes the diffusion of the alkali ions using Fick’s second law

n

DA =

∑ Diwi (3)

i=1

where n is the total number of sites available to species A and n

∑ wi = 1 (4)

i=1

We note that the superscript indicates the site on which the species are diffusing and the subscript indicates the diffusing species or the extent of exchange if two different species are exchanging. The diffusion coefficient on each site is then described by the equation for interdiffusion in ionic materials48 D̃ i =

⎡ ∂ ln γA ⎤ DsiD bi 1 + ⎥ ⎢ ∂ ln CA ⎦ P , T CADsi + (1 − CA )D bi ⎣

(5)

where γA is the activity coefficient of species A, A is taken to be the alkali species initially in the pristine glass and the “∼” indicates an interdiffusion coefficient. This equation describes the flux of each species as a function of both the chemical potential gradient and the electrical potential gradient while imposing electrical neutrality. eq 5 is usually written as a function of the diffusion coefficients of the two interdiffusing species in the pure end-member phases. However, because some of the pristine glasses contain more than one alkali species and, as will be described below, a fraction of the alkali ions was found not to participate in the diffusion process (nonexchangeable fraction), eq 5 is written as a function of the bulk diffusion coefficient (0% of available sites exchanged), Db, and surface diffusion coefficient (100% of available sites exchanged), Ds. The term in brackets in eq 5 is referred to as the thermodynamic factor and accounts for nonideal mixing. In the case of ideal mixing, the activity coefficients are equal to 1 and independent of concentration, and therefore, the thermodynamic factor simplifies to 1. 2.5. Computational Mathematics. The diffusion model was solved on a one-dimensional grid using the Crank− Nicolson method, a finite difference method that uses second9377


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The Journal of Physical Chemistry C order central difference in space and trapezoidal rule in time. The grid point spacing was set to 1−10 nm and the integration time step to 1−10 s. Initial conditions (t = 0) were as follows: Coutward = 0 and Cinward = 1 at x = 0, and Coutward = 1 and Cinward = 0 at x > 0, where the outward and inward subscripts stand for the alkali species initially in the pristine glass and in the DMSO solution, respectively. Neumann boundary conditions were applied at both surface and pristine glass boundaries.

3. RESULTS AND DISCUSSION 3.1. Data Normalization. The raw intensities were normalized to 27Al before fitting the data with the interdiffusion model. 27Al was selected because of its relatively high abundance in all the pristine glasses studied here and the relatively high sensitivity of the ToF-SIMS technique for this isotope. This normalization step acts as a smoothing function to compensate for analytical artifacts such as changes in intensities as a function of depth. For example, the 27Alnormalized intensity of 7Li at depth x, (7Li/27Al)x is defined as (7Li/27Al)x =

I

Figure 1. Diffusion profiles of 6Li (left) and 7Li (right) in ISG-Li contacted with the 6LiCl/DMSO solution for 1.0 and 9.2 days at 90 °C. Solids lines are experimental data. Dashed lines are model profiles. Correlation coefficients for each individual fit are provided in the figure. See Table 3 for diffusion coefficients.

behavior. The diffusion coefficients derived from these experiments are presented Table 3. As predicted by the model, good fits were obtained with a single diffusion coefficient. These results also suggest that the assumption that the difference in mass between the two isotopes is negligible is valid. 6 Li interdiffusion with ISG provides an example where, unlike in the case of ISG-Li, the exchanging cations are chemically different. ISG contains only Na as an alkali; therefore, eq 3 becomes

7

Li

27

(6) I Al where I is the raw intensity of the specified isotope. Next, a correction is made to account for the natural abundance (NA) of 6Li in the pristine glass x (7Li/27Al)NA = (7Li/27Al)x +

(7Li/27Al)x ⟨ Li/6 Li⟩pristine 7

(7)

where ⟨ Li/ Li⟩pristine is the average Li/ Li ratio in the pristine glass. A similar equation is written for 6Li in which the second term on the right-hand side is subtracted from the first term instead of being added to it. For some profiles, it was observed that the normalized intensities for the outward-diffusing species did not go to zero at the solution/glass interface. This observation indicates that not all of the alkali ions initially in the glass are equally available for exchange, which is expected based on variations in their structural role. Therefore, a portion of the alkali ions was considered nonexchangeable, and the nonexchangeable fraction was taken as the alkali intensity at the solution/glass interface, x0. The intensities were then normalized to subtract this nonexchangeable fraction. For 7Li, for example, the normalization relationship is as follows 7

[7Li]x =

6

7

DLi = D Na = D̃ Na

6

(8)

where ⟨ Li/ is the average value of the NA-corrected, 27 Al-normalized intensity of 7Li. 3.2. Depth Profiles and Modeling. 3.2.1. ISG-Li, ISG, and ISG-K. ISG-Li contains only one alkali species, lithium. Therefore, diffusion is modeled as taking place on one site type and eq 3 becomes simply: 7

27

Al⟩pristine NA

DLi = DLi

6

eq 5 was used to obtain D . Examples of Li diffusion profiles obtained in ISG are presented in Figure 2. An initial fit assuming ideal mixing (i.e., with a thermodynamic factor of 1) inaccurately reproduced the experimental results, suggesting that the mixing between Li and Na in the glass was nonideal. This result was unsurprising given the size mismatch between Li and Na. Figure 2 shows that a significant improvement with respect to the agreement with the ToF-SIMS depth profiles was achieved when the thermodynamic factor was allowed to differ from unity. Model fits are presented in Table 3. A ratio of 50 Na for DNa s /Db was found to give good results and was thus kept constant for all temperatures to limit the number of free parameters. ISG-K coupons were contacted with the 6LiCl/DMSO solution at 90 and 120 °C. ISG-K has the same composition as ISG, except for full substitution of Na by K on a molar basis; therefore, the glass only has one site for alkali−alkali exchange. Additionally, the substitution for K by Li involves the replacement of the relatively large K ion by the much smaller Li ion. Consequently, these experiments allowed for investigating the effects of increasing the size mismatch between the exchanging ions. Figure 3 shows the 6Li and K diffusion profiles obtained at 90 and 120 °C together with model fits. 6Li diffusion into ISG-K is much slower than in any of the other glasses considered in this work. At longer time periods and the higher temperature, 6Li and K show anticorrelated profiles close to the surface; but K exhibits a slight continuous depletion beyond this region. This could be an artifact of the analysis technique whereby the drift of the K intensity may be slightly higher than that of Al, and this effect is then exaggerated in the normalized profile due to the normalization to the nonexchangeable fraction. At 10 days and 90 °C, although the 6Li

x 0 (7Li/27Al)NA − (7Li/27Al)xNA pristine x0 ⟨7Li/27Al⟩NA − (7Li/27Al)NA

(10)

̃ Na

(9) 6

When ISG-Li is placed in contact with a Li-bearing DMSO solution, the two exchanging species are chemically identical and DLi is therefore constant with time and depth. To test this model prediction, 6Li was exchanged with ISG-Li at three temperatures (Table 2). The lithium diffusion profiles obtained at 90 °C are presented in Figure 1 as an example. Experiments carried out at 60 and 120 °C showed a similar 9378


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The Journal of Physical Chemistry C Table 3. Compilation of the Diffusion Coefficients of Various Alkali Ions in Different Glasses Used in This Studyc Li sites glass ISG-Li

CJ-6

SON68

ISG

ISG-K

Db

temp (°C) 60 90 120 25a 60 90 120 150 25a 90 150 60 90 120 90b 120b

4.0 1.3 1.5 1.0 9.0 2.0 6.0 6.0 8.0 2.0 4.0

× × × × × × × × × × ×

Na/K sites Ds

nonexchangeable fraction −21

10 10−19 10−18 10−24 10−23 10−21 10−20 10−19 10−25 10−21 10−19

0.75 0.65 0.58 0.05 0.04 0.06 0.07 0.04 0.08 0.02 0.05

1.5 2.0 3.5 4.0 4.0 1.0 2.0 4.0 2.5 7.0 8.0 2.4 4.0

× × × × × × × × × × × × ×

10−24 10−22 10−20 10−19 10−18 10−24 10−20 10−18 10−21 10−20 10−19 10−22 10−21

Db

1.5 1.0 1.8 2.0 2.0 1.0 1.0 2.0 5.0 1.4 1.6 6.0 5.0

× × × × × × × × × × × × ×

10−24 10−22 10−20 10−19 10−18 10−24 10−20 10−18 10−23 10−21 10−20 10−23 10−22

nonexchangeable fraction

ideal?

0.72 0.58 0.60 0.66 0.61 0.77 0.70 0.68 0.90 0.85 0.89 0.74 0.60

yes yes yes yes yes yes yes yes no no no yes yes

a

c Na b Depth profiles were too shallow to precisely determine DNa s /Db . Depth profiles were too shallow to reliably determine if mixing was nonideal. All diffusion coefficients are in m2 s−1.

Figure 2. Diffusion profiles of 6Li (top) and Na (bottom) in ISG contacted with the 6LiCl/DMSO solution for different durations at 60, 90, and 120 °C. Solids lines are experimental data. Dashed lines are model profiles. Correlation coefficients for each individual fit are provided in the figure. See Table 3 for diffusion coefficients.

profile depths are also sufficient to obtain an order-ofmagnitude estimate of the diffusion coefficients. 3.2.2. CJ-6 and SON68. Results from the three glasses presented in the previous section (ISG-Li, ISG, and ISG-K) monitored the direct exchange of one alkali ion for another. In this section, we discuss the results obtained from 6-oxide CJ-6, a glass with equal molar ratios of major elements to ISG, and 26-oxide SON68, a high-level waste simulant glass on which CJ6, and all other glasses presented in this study, are based. Both CJ-6 and SON68 contain a mixture of Li and Na. These glass compositions allow the extension of this study to ion exchange with multiple species and completing the range of alkali contents of interest [i.e., Li-only (ISG-Li), Na-only (ISG), Konly (ISG-K), and mixed Li and Na (CJ-6 and SON68)]. In a previous study, we presented experiments of Li diffusion in CJ6 and SON68 performed at 90 °C.17 Those results showed that

profile shows some penetration into the glass, the K profile does not show any depletion. Low diffusion coefficients precluded obtaining data at temperatures lower than 90 °C in an appreciable time period. For that reason, the activation energy for Li diffusion in ISG-K is not included in the Results and Discussion. Because of the uncertainties associated with the first tens of nanometers with the ToF-SIMS technique, we cannot determine whether K was indeed not exchanged in this experiment or if this is an artifact of the analysis technique. Therefore, these results should be taken with caution due to the very shallow depth profiles in some of the experiments. Nonetheless, they demonstrate unequivocally that, in aluminoborosilicate glasses, Li−K exchange is much slower than Li− Na exchange and, a fortiori, slower than Li-for-Li exchange. The 9379


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species were involved in the ion exchange reaction. In addition, the results also showed a constant Ca profile across the analyzed surface even though this alkaline earth species is capable of participating in the ion exchange process.1 Since CJ-6 and SON68 contain both Li and Na, interdiffusion is considered to take place on Li sites and Na sites. When contacted with a 6Li-bearing DMSO solution, Li can diffuse on both types of sites whereas Na is assumed to only diffuse on Na sites. Therefore DLi = DLiw Li + D̃ Na w Na

(11)

D Na = D̃ Na

(12)

where w Li and w Na are calculated from the nominal compositions of each glass and DLi = D bLi

D̃ Na = Figure 3. Diffusion profiles of 6Li (top) and K (bottom) in ISG-K contacted with the 6LiCl/DMSO solution for different durations at 90 and 120 °C. Solids lines are experimental data. Dashed lines are model profiles. Correlation coefficients for each individual fit are provided in the figure. See Table 3 for diffusion coefficients.

(13)

DsNa D bNa C NaDsNa

+ (1 − C Na)D bNa

(14) 6

7

Because diffusion on Li sites only involves Li and Li, eq 14 reduces to the isolated diffusion case. For diffusion on Na sites, good agreement with the experimental depth profiles was obtained without considering nonideal mixing. It is possible that a small deviation from ideal mixing exists but could not be Na resolved with this approach. A ratio of 2 for DNa s /Db was found to give good results and was kept constant for both glasses and all temperatures to limit the number of fitting parameters (with the exception of the depth profiles obtained at 25 °C for both

the total alkali intensity remained constant in the glass but that the individual profiles of the three alkali species, 6Li, 7Li, and Na, varied with depth, thereby demonstrating that all three

Figure 4. Diffusion profiles in CJ-6 of 6Li (top), 7Li (middle), and Na (bottom) at (from left to right) 25, 60, 90, 120, and 150 °C and various experimental durations. Data are solids lines and fits are dashed lines. Correlation coefficients for each individual fit are provided in the figure. See Table 3 for diffusion coefficients. 9380


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Figure 5. Diffusion profiles in SON68 of 6Li (top), 7Li (middle), and Na (bottom) at (from left to right) 25, 90, and 150 °C and various experimental durations. Data are solids lines and fits are dashed lines. Correlation coefficients for each individual fit are provided in the figure. See Table 3 for diffusion coefficients.

previously presented,17 however, the fits presented here are obtained using the new formulation of the model. Diffusion coefficients were often slightly lower in SON68 compared to CJ-6. 3.3. Summary of Diffusion Coefficients and Temperature Dependence. Numerous alkali−alkali diffusion experiments were performed at various temperatures with several glasses and the data from these experiments have been compiled and are presented in Table 3. Additionally, Arrhenius plots of the natural logarithm of the diffusion coefficient as a function of the inverse temperature of the experiments are given in Figure 6. Arrhenius behavior is observed for all systems with sufficient temperature-dependence data. The activation

glasses, which were too shallow to adequately differentiate bulk and surface diffusion). Consequently, only two free parameters Li (DNa b and Db ) were varied at each temperature to optimize the agreement between calculated and experimental depth profiles. Results for diffusion experiments performed on CJ-6 at 25, 60, 90, 120, and 150 °C, along with model fits, are presented in Figure 4. By and large, these data showed good fits of the interdiffusion model to the experimental profiles and allowed for the determination of the activation energy for alkali diffusion in CJ-6 (see section 3.3). Diffusion coefficients for 6Li ranged from 1.0 × 10−24 m2/s at 25 °C to 6.0 × 10−19 m2/s at 150 °C. Bulk diffusion coefficients for Na (Db) ranged from 1.5 × 10−24 m2/s at 25 °C to 2.0 × 10−18 m2/s at 150 °C. The largest deviations between experiment and modeling occur at the lowest temperature, i.e., 25 °C. At 25 °C the deviation between experiment and modeling is most likely the result of difficulties in ToF-SIMS measurements at the surface of the solid that are magnified when concentration profiles are shallow. This is evidently the case for the data obtained after 29.8 and 90.6 days. However, at 269.6 days, when the 6Li penetration depth is near 20 nm, the profiles showed good agreement between experiment and modeling. Experiments with SON68 coupons were performed at 25, 90, and 150 °C. These temperatures allow us to bracket the temperature range of interest and to determine the activation energies for alkali diffusion. The data from CJ-6 have demonstrated successful application of the interdiffusion model at various temperatures. In Figure 5, we present data and fits for inward-diffusing 6Li+ and outward-diffusing 7Li+ and Na+. The data from the SON68 experiment at 90 °C were

Figure 6. Arrhenius plots of the natural log of the diffusion coefficients of Li and Na as a function of the reciprocal temperature. When bulk and surface values of the diffusion coefficient are available, the bulk value is displayed to represent intrinsic diffusion coefficient. 9381


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The Journal of Physical Chemistry C Table 4. Activation Energies (kJ/mol) for Lithium and Sodium Diffusion in Aluminoborosilicate Glasses site

CJ-6

SON68

ISG-Li

Li Na

117 ± 4 (R2 = 0.997) 127 ± 13 (R2 = 0.979)

110 ± 1 (R2 = 1.000) 122 ± 4 (R2 = 0.999)

108 ± 6 (R2 = 0.997)

ISG 105 ± 4 (R2 = 0.996)

4. CONCLUSION In summary, we have developed a method to isolate the ionexchange process from matrix dissolution at relatively low temperatures (25−150 °C). By changing the chemical composition of the glass, notably the type of alkali ion, and the source solution, various combinations of diffusing alkali ions were examined. Profile shapes characteristic of isolated diffusion were shown for Li−Li exchange, and sigmoidal diffusion profiles were obtained for glasses containing only Na and K. For glasses containing only Na or K, the diffusion profiles showed very sharp tails in the bulk of the glass, which was attributed to nonideal mixing of Li and Na or K for these glass compositions. The ToF-SIMS measurements also highlighted the presence of a sizable nonexchangeable fraction, indicating that not all alkali ions participated in the ion exchange process. This phenomenon was attributed to the different structural roles alkali ions serve in borosilicate glasses. Future experiments focused on H+−M+ ion exchange will determine whether a portion of the alkali ions are also excluded from the ionexchange process when H+ penetrates the glass. The models developed from the alkali−alkali ion exchange experiments could be implemented into a model of H+−M+ exchange. Once parametrized, these models can then be easily implemented into glass corrosion models using diffusion coefficients and activation energies obtained from this experimental method.

energies of the observed processes were calculated by dividing the slope by the ideal gas constant, R. As could be inferred by the nearly parallel fits to the Arrhenius plots, the systems exhibited similar activation energies (Table 4), between approximately 105 and 127 kJ/mol. There was some evidence that mixed alkali glasses (SON68 and CJ-6) exhibit higher activation energies than single alkali glasses. This effectively illustrates the decrease of the activation energy with increasing Na content in the pristine glass. The trends between Li and Na are more conclusive. Lithium diffusion exhibited a consistently lower activation energy (108−114 kJ/mol) than sodium diffusion (116−126 kJ/mol), regardless of glass composition, original location (glass or solution), or counter-diffusing ion. It bears repeating that only a fraction of the alkali ions in the glass appeared to be available for diffusion and the diffusion coefficients (and thus the activation energies) reflect only these exchangeable species. The fraction of nonexchangeable sites is presented in Table 3. The values of the activation energies derived in this work match well with values reported in the industrial ion-exchange literature. The exact activation energies for ion exchange with between glass and molten salts vary depending on the ions in question and the glass composition but generally range from 100 to 150 kJ/mol.5,49 An experiment using the Japanese P0798 simulant nuclear waste glass and a molten salt Na source also yielded a Na−Na activation energy of 113 kJ/mol;50 however, the absolute diffusion coefficient given in that study was 2 orders of magnitude lower than the diffusion coefficients obtained in the present study. The reason for the difference in activation energies is unknown but may be attributed to the use of Na+ as the source species and not the smaller Li+ species. In general, considering the fact that, below the glass transition temperature, glass behaves as a solid, as well as the fact that the processes examined the studies largely depended on solid-state interdiffusion, it is not surprising that the activation energies for these measurements of interdiffusion fall within the same range. What is more surprising is the range of activation energies for nuclear waste glasses reported in the literature for ion exchange in aqueous conditions. To this point, activation energies measured for ion-exchange processes in nuclear waste glasses were found to be on the order of 30−50 kJ/mol.12,18,51 There are many differences between the aforementioned studies and the present work; primarily that hydrogen (or hydronium) was involved as the inward-diffusing species and that glass dissolution was occurring concurrently. The large difference between alkali−alkali exchange activation energies and hydrogen−alkali exchange activation energies suggests the possibility of two concurrent reaction processes. We hypothesize that a chemical reaction involving the dissociation of O−H bonds that does not occur during alkali−alkali exchange is the most likely secondary process. The chemical reaction may be the dissociation of either a hydronium ion or molecular water to provide a source for the hydrogen that exchanges with alkali in the glass through the interdiffusion mechanism discussed previously.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +1 509-375-5397. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS These studies were supported by the U.S. Department of Energy (DOE) through the Office of Nuclear Energy. We would like to thank Dr. Stéphane Gin of the CEA for useful discussions and for supplying the CJ-6 glass. We also thank Dr. Peter Rieke (PNNL) for his help in improving the manuscript, Jodi Mayer (PNNL) and Carmen Rodriguez (PNNL) for help in glass fabrication, and Clyde Chamberlin (PNNL) for help in sample preparation. Pacific Northwest National Laboratory is operated for the DOE by Battelle Memorial Institute under Contract No. DE-AC06-76RLO 1830. The research described in this paper was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the U.S. Department of Energy’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory in Richland, WA.

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REFERENCES

(1) Hellmann, R. The Albite-Water System 0.4. Diffusion Modeling of Leached and Hydrogen-Enriched Layers. Geochim. Cosmochim. Acta 1997, 61, 1595−1611. (2) Smedskjaer, M. M.; Zheng, Q.; Mauro, J. C.; Potuzak, M.; Mørup, S.; Yue, Y. Sodium Diffusion in Boroaluminosilicate Glasses. J. NonCryst. Solids 2011, 357, 3744−3750.

9382


Article


(26) Lanford, W. A. Hydration of Soda-Lime Glass. J. Non-Cryst. Solids 1979, 33, 249−266. (27) Gin, S.; Ryan, J. V.; Schreiber, D. K.; Neeway, J. J.; Cabié, M. Contribution of Atom-Probe Tomography to a Better Understanding of Glass Alteration Mechanisms: Application to a Nuclear Glass Specimen Altered 25 Years in a Granitic Environment. Chem. Geol. 2013, 349−350, 99−109. (28) Bunker, B. C. Molecular Mechanisms for Corrosion of Silica and Silicate Glasses. J. Non-Cryst. Solids 1994, 179, 300−308. (29) Geisler, T.; Nagel, T.; Kilburn, M. R.; Janssen, A.; Icenhower, J. P.; Fonseca, R. O. C.; Grange, M.; Nemchin, A. A. The Mechanism of Borosilicate Glass Corrosion Revisited. Geochim. Cosmochim. Acta 2015, 158, 112−129. (30) Hellmann, R.; Cotte, S.; Cadel, E.; Malladi, S.; Karlsson, L. S.; Lozano-Perez, S.; Cabié, M.; Seyeux, A. Nanometre-Scale Evidence for Interfacial Dissolution−Reprecipitation Control of Silicate Glass Corrosion. Nat. Mater. 2015, 14, 307−311. (31) Geisler, T.; Janssen, A.; Scheiter, D.; Stephan, T.; Berndt, J.; Putnis, A. Aqueous Corrosion of Borosilicate Glass under Acidic Conditions: A New Corrosion Mechanism. J. Non-Cryst. Solids 2010, 356, 1458−1465. (32) Zapol, P.; He, H.; Kwon, K. D.; Criscenti, L. J. First-Principles Study of Hydrolysis Reaction Barriers in a Sodium Borosilicate Glass. Int. J. Appl. Glass Sci. 2013, 4, 395−407. (33) Pierce, E. M.; Frugier, P.; Criscenti, L. J.; Kwon, K. D.; Kerisit, S. N. Modeling Interfacial Glass-Water Reactions: Recent Advances and Current Limitations. Int. J. Appl. Glass Sci. 2014, 5, 421−435. (34) Kerisit, S.; Pierce, E. M. Monte Carlo Simulations of the Dissolution of Borosilicate and Aluminoborosilicate Glasses in Dilute Aqueous Solutions. Geochim. Cosmochim. Acta 2011, 75, 5296−5309. (35) Kerisit, S.; Pierce, E. M. Monte Carlo Simulations of the Dissolution of Borosilicate Glasses in near-Equilibrium Conditions. J. Non-Cryst. Solids 2012, 358, 1324−1332. (36) Kerisit, S.; Ryan, J. V.; Pierce, E. M. Monte Carlo Simulations of the Corrosion of Aluminoborosilicate Glasses. J. Non-Cryst. Solids 2013, 378, 273−281. (37) Frugier, P.; et al. SON68 Nuclear Glass Dissolution Kinetics: Current State of Knowledge and Basis of the New GRAAL Model. J. Nucl. Mater. 2008, 380, 8−21. (38) Frugier, P.; Chave, T.; Gin, S.; Lartigue, J. E. Application of the GRAAL Model to Leaching Experiments with SON68 Nuclear Glass in Initially Pure Water. J. Nucl. Mater. 2009, 392, 552−567. (39) Minet, Y.; Bonin, B.; Gin, S.; Frugier, P. Analytic Implementation of the GRAAL Model: Application to a R7T7-Type Glass Package in a Geological Disposal Environment. J. Nucl. Mater. 2010, 404, 178−202. (40) Rébiscoul, D.; Bruguier, F.; Magnin, V.; Gin, S. Impact of SodaLime Borosilicate Glass Composition on Water Penetration and Water Structure at the First Time of Alteration. J. Non-Cryst. Solids 2012, 358, 2951−2960. (41) Rébiscoul, D.; Cambedouzou, J.; Matar Briman, I.; Cabié, M.; Brau, H. P.; Diat, O. Water Dynamics in Nanoporous Alteration Layer Coming from Glass Alteration: An Experimental Approach. J. Phys. Chem. C 2015, 119, 15982−15993. (42) Gin, S.; et al. An International Initiative on Long-Term Behavior of High-Level Nuclear Waste Glass. Mater. Today 2013, 16, 243−248. (43) Jégou, C. Mise en Évidence Expérimentale des Mécanismes Limitant L’altération du Verre R7T7 En Milieu Aqueux. Critique et Proposition D’évolution du Formalisme Cinétique. Doctoral Thesis. Université de Montpellier II, 1998. (44) Rajmohan, N.; Frugier, P.; Gin, S. Composition Effects on Synthetic Glass Alteration Mechanisms: Part 1. Experiments. Chem. Geol. 2010, 279, 106−119. (45) Wang, Z.; et al. Argon Cluster Sputtering Source for Tof-SIMS Depth Profiling of Insulating Materials: High Sputter Rate and Accurate Interfacial Information. J. Am. Soc. Mass Spectrom. 2015, 26, 1283−1290.

(3) Guo, X.; Pivovarov, A. L.; Smedskjaer, M. M.; Potuzak, M.; Mauro, J. C. Non-Conservation of the Total Alkali Concentration in Ion-Exchanged Glass. J. Non-Cryst. Solids 2014, 387, 71−75. (4) Wu, X.; Moskowitz, J. D.; Mauro, J. C.; Potuzak, M.; Zheng, Q.; Dieckmann, R. Sodium Tracer Diffusion in Sodium Boroaluminosilicate Glasses. J. Non-Cryst. Solids 2012, 358, 1430−1437. (5) Gy, R. Ion Exchange for Glass Strengthening. Mater. Sci. Eng., B 2008, 149, 159−165. (6) Sglavo, V. M. Chemical Strengthening of Soda Lime Silicate Float Glass: Effect of Small Differences in the KNO3 Bath. Int. J. Appl. Glass Sci. 2015, 6, 72−82. (7) Varshneya, A. K. The Physics of Chemical Strengthening of Glass: Room for a New View. J. Non-Cryst. Solids 2010, 356, 2289− 2294. (8) Calahoo, C.; Zhang, X.; Zwanziger, J. W. Nanoindentation Study of the Surface of Ion-Exchanged Lithium Silicate Glass. J. Phys. Chem. C 2016, 120, 5585. (9) Maurizio, C.; Quaranta, A.; Ghibaudo, E.; D’Acapito, F.; Broquin, J. E. Ag Site in Ag-for-Na Ion-Exchanged Borosilicate and Germanate Glass Waveguides. J. Phys. Chem. C 2009, 113, 8930−8937. (10) Tilocca, A. Realistic Models of Bioactive Glass Radioisotope Vectors in Practical Conditions: Structural Effects of Ion Exchange. J. Phys. Chem. C 2015, 119, 27442−27448. (11) Grambow, B.; Müller, R. First-Order Dissolution Rate Law and the Role of Surface Layers in Glass Performance Assessment. J. Nucl. Mater. 2001, 298, 112−124. (12) Ojovan, M. I.; Pankov, A.; Lee, W. E. The Ion Exchange Phase in Corrosion of Nuclear Waste Glasses. J. Nucl. Mater. 2006, 358, 57− 68. (13) McGrail, B. P.; Bacon, D. H.; Icenhower, J. P.; Mann, F. M.; Puigh, R. J.; Schaef, H. T.; Mattigod, S. V. Near-Field Performance Assessment for a Low-Activity Waste Glass Disposal System: Laboratory Testing to Modeling Results. J. Nucl. Mater. 2001, 298, 95−111. (14) Gin, S.; Guittonneau, C.; Godon, N.; Neff, D.; Rebiscoul, D.; Cabié, M.; Mostefaoui, S. Nuclear Glass Durability: New Insight into Alteration Layer Properties. J. Phys. Chem. C 2011, 115, 18696−18706. (15) Kistler, S. S. Stresses in Glass Produced by Nonuniform Exchange of Monovalent Ions. J. Am. Ceram. Soc. 1962, 45, 59−68. (16) Varshneya, A. K.; Milberg, M. E. Ion Exchange in Sodium Borosilicate Glasses. J. Am. Ceram. Soc. 1974, 57, 165−169. (17) Neeway, J. J.; Kerisit, S.; Gin, S.; Wang, Z.; Zhu, Z.; Ryan, J. V. Low-Temperature Lithium Diffusion in Boroaluminosilicate Glasses. J. Non-Cryst. Solids 2014, 405, 83−90. (18) McGrail, B. P.; Icenhower, J. P.; Shuh, D. K.; Liu, P.; Darab, J. G.; Baer, D. R.; Thevuthasen, S.; Shutthanandan, V.; Engelhard, M. H.; Booth, C. H.; Nachimuthu, P. The Structure of Na2O-Al2O3-SiO2 Glass: Impact on Sodium Ion Exchange in H2O and D2O. J. Non-Cryst. Solids 2001, 296, 10−26. (19) Hamilton, J. P.; Pantano, C. G. Effects of Glass Structure on the Corrosion Behavior of Sodium- Aluminosilicate Glasses. J. Non-Cryst. Solids 1997, 222, 167−174. (20) Rana, M. A.; Douglas, R. W. The Reaction between Glass and Water. Part I. Experimental Methods and Observations. Phys. Chem. Glasses 1961, 2, 179−195. (21) Rana, M. A.; Douglas, R. W. The Reaction between Glass and Water. Part 2. Discussion for the Results. Phys. Chem. Glasses 1961, 2, 196−204. (22) Boksay, Z. G.; Bouquet, G.; Dobos, S. The Kinetics of the Formation of Leached Layers on Glass Surfaces. Phys. Chem. Glasses 1967, 8, 140−144. (23) Boksay, Z. G.; Bouquet, G.; Dobos, S. The Kinetics of the Formation of Leached Layers on Glass Surfaces. Phys. Chem. Glasses 1968, 9 (2), 69−71. (24) Doremus, R. H. Interdiffusion of Hydrogen and Alkali Ions in a Glass Surface. J. Non-Cryst. Solids 1975, 19, 137−144. (25) Lanford, W. A. 15N Hydrogen Profiling: Scientific Applications. Nucl. Instrum. Methods 1978, 149, 1−8. 9383


Article

The Journal of Physical Chemistry C (46) Wang, Z. Y.; Jin, K.; Zhang, Y. W.; Wang, F. Y.; Zhu, Z. H. TofSIMS Depth Profiling of Insulating Samples, Interlaced Mode or NonInterlaced Mode? Surf. Interface Anal. 2014, 46, 257−260. (47) Crank, J. The Mathematics of Diffusion, 2nd ed.; Clarendon Press: Oxford, 1975. (48) Brady, J. B., Diffusion Data for Silicate Minerals, Glasses, and Liquids. In Mineral Physics & Crystallography a Handbook of Physical Constants; Ahrens, T. J., Ed.; Wiley, 1995; AGU Ref. Shelf 2, pp 2269− 590.10.1029/RF002p0269 (49) Varshneya, A. K. Fundamentals of Inorganic Glasses; Academic Press Inc.: San Diego, 1994. (50) Nonaka, K.; Nakajima, H.; Mitsui, S.; Echigoya, J. Self-Diffusion of 22Na and 137Cs in Simulated Nuclear Waste Glass. Mater. Trans. 2002, 43, 654−659. (51) Shutthanandan, V.; Baer, D. R.; Thevuthasan, S.; Adams, E. M.; Maheswaran, S.; Engelhard, M. H.; Icenhower, J. P.; McGrail, B. P. High Energy Ion Beam Studies of Ion Exchange in a Na2O-Al2O3-SiO2 Glass. J. Appl. Phys. 2002, 91, 1910−1920.

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