Current Understanding and Remaining Challenges in Modeling Long-Term Degradation of Borosilicate Nuclear Waste Glasses

Authors


Abstract

Chemical durability is not a single material property that can be uniquely measured. Instead, it is the response to a host of coupled material and environmental processes whose rates are estimated by a combination of theory, experiment and modeling. High-level nuclear waste (HLW) glass is perhaps the most studied of any material yet there remain significant technical gaps regarding their chemical durability. The phenomena affecting the long-term performance of HLW glasses in their disposal environment include surface reactions, transport properties to and from the reacting glass surface, and ion exchange between the solid glass and the surrounding solution and alteration products. The rates of these processes are strongly influenced and are coupled through the solution chemistry, which is in turn influenced by the reacting glass and also by reaction with the near-field materials and precipitation of alteration products. Therefore, those processes must be understood sufficiently well to estimate or bound the performance of HLW glass in its disposal environment over geologic time scales. This article summarizes the current state of understanding of surface reactions, transport properties and ion exchange along with the near-field materials and alteration products influences on solution chemistry and glass reaction rates. Also summarized are the remaining technical gaps along with recommended approaches to fill those technical gaps.

Introduction

The processes responsible for glass alteration and release of radionuclides into the environment include (i) ion-exchange (IX) between the glass matrix and the contacting solution, (ii) hydration of the glass network, culminating in the dissolution of the hydrolyzed network species, (iii) condensation of hydrated silica (whether from solution or recondensation of hydrolyzed surface species) and (iv) precipitation of alteration products.[1] Additionally, (v) the relative concentration of the reactants and products is likely influenced by their transport within the system. The rate of each of these reactions/processes depends on the environmental parameters such as temperature, pH, Eh, concentration of dissolved components in solution and the physical form of materials in contact with the reacting glass. The combined impact of all these factors affecting the rates of each individual reaction over the lifetime of the glass in its disposal facility is what is commonly referred to as the chemical durability of glass. The chemical durability of glass cannot be uniquely measured, but it can be estimated through an understanding of the rates of the individual reactions and processes and how environmental variables influence those rates.

Silicate glass dissolution typically shows a trend as depicted in Fig. 1, a schematic of the generalized results of silicate glass dissolution in a closed or very slowly refreshed system, similar to that expected in a repository setting.[2] Initially, glass alters quickly as it comes into contact with fresh solution because the contacting solution contains low concentrations of the rate-limiting species, the reaction layer is insufficient to control the transport of reactants or products, and/or the surface energy is high relative to an altered state. During this early time of contact, there is exchange of materials between the solution (H2O, OH, H3O+, etc.) and the glass (alkali, alkaline earths, etc.). There is also hydrolysis where the interconnected silica network becomes hydrolyzed and eventually is released into solution as H4SiO4. As the reaction proceeds, the concentrations of glass components in solution continue to rise, but at a slower rate. The slowing of the rate is caused by some combination of a reduced driving force for dissolution and a reduced rate of transport to and from the reacting glass surface.[3, 4] The latter process refers to the existence of a transport-limiting layer within the alteration layer.

Figure 1.

Schematic of glass corrosion process.

Some combinations of glasses and conditions result in a marked increase in the rate of glass alteration after a period of time at relatively low rates. This potential increased rate is labeled Stage III corrosion by some authors.[2, 5-7] Although the cause of this increased rate is uncertain, it is usually associated with the rapid precipitation of silica-containing minerals such as analcime.[8-13] The precipitation of an analcime-like zeolite can reduce the local concentration of rate-limiting species in solution and/or the stability of a transport-limiting layer, thus affecting the rate of glass alteration through various mechanisms described later.

It should be noted that transport phenomena can be divided into two categories. The first is related to the transport of glass components into solution, including transport through the alteration layer and surrounding near-field materials. These processes can have impacts from the nanometer to meter scale. In the second category, transport is through the glass phase itself with water (or other hydrogen-containing ions) exchanging with alkali elements and other glass components in an IX mechanism. These processes are important up to the mm scale.

Several conceptual models have been enumerated to estimate glass corrosion over time and under repository relevant conditions, each linked to a portion of the corrosion mechanisms currently understood. The models are, therefore, grouped by the mechanism they assume to control long-term durability. Although each approach successfully models a large set of existing laboratory data, the long-term predictions (i.e., times that are inaccessible to direct experiments) of models based on different mechanisms differ significantly. We present here a summary of three mechanisms with strong potential to control long-term rate (surface reaction, ion exchange and transport limitation), the data that justify their control over the long-term corrosion rate, and the numerical models used to approximate them. Also introduced is what is known about Stage III corrosion.

Glass/Water Reaction

In the early days of waste glass corrosion studies, it was observed that alkali metals were released into solution at rates that decreased with the square root-time in static experiments,[14-16] whereas silica was released with a linear time dependence in solution-exchange experiments.[17] The surfaces of corroded silicate glasses were found to be highly porous with relatively high molecular water content.[18] It was shown that, within a certain range of reaction progress, the rate of alteration was strongly influenced by the concentration of H4SiO4 in solution.[19, 20] This behavior defines the rate drop or transition regime. Beyond this transition the rate becomes more or less constant, whereas the concentration of H4SiO4 continues to rise slowly.[21]

Åagaard and Helgeson used transition state theory (TST) to model the surface reaction controlled dissolution of aluminosilicate minerals[22]:

display math(1)
  • where r = dissolution rate, g/(m2·day)
  • = rate constant, g/(m2·day)
  • = overall reaction chemical affinity, kJ/mol
  • σ = rate of decomposition of the activated complex relative to the overall reaction, unitless
  • = gas constant, kJ/(mol K)
  • = absolute temperature, K
  • Πai = product of the activities in solution of those components taking part in the reaction
  • ni = stoichiometric reaction coefficient for reactant i, unitless

The reaction chemical affinity, A, can be written as RTln(Q/K) where Q is the ion activity product of the reaction and K is equilibrium constant of the reaction. Using this relationship, and assuming that H+ is the only aqueous species that directly influences the dissolution rate via the activity product term,[23] the rate equation can be rewritten[24]:

display math(2)
  • where inline image = activity of H+
  • η = stoichiometric reaction coefficient for H+, unitless
  • Ea=the apparent activation energy, kJ/mol
  • = ion activity product of the rate-limiting reaction, unitless
  • = equilibrium constant of the rate-limiting reaction (e.g., solubility constant), unitless
  • σ = overall reaction order or “Temkin coefficient,” unitless

The TST approach was first applied to waste glasses by Grambow and colleagues.[20, 25, 26] Because the dissolution rate was found to depend primarily on the solution concentration of silica, it was concluded that the hydration of the last bridging Si-O-Si bond was the rate-limiting step. Therefore, the affinity of glass was modeled as the ratio of the concentration of H4SiO4 in solution to the saturation of H4SiO4 with respect to a silica-containing phase in the given system:

display math(3)

The K term in Eq. (1) is the solubility constant for the equilibrium between the solid under dissolution and the concentration of H4SiO4 in solution. It has been hypothesized that in first approximation, the glass acts like a silica-only solid with respect to the rate-limiting reaction. As glass cannot be in equilibrium with solution, that is, it is unstable with respect to its alteration (reaction) products, K becomes a pseudo-equilibrium constant. The Q/K can therefore never equal one and the reaction will progress, albeit at a low rate, even as [H4SiO4] reaches “saturation,” with respect to solid products. Sinks for H4SiO4 always exist and the glass alters to solid and dissolved products.

A number of modifications were made to this so-called TST-based rate law. Bourcier and colleagues have suggested that the use of a TST-based model is appropriate, but only for reactions that possess a legitimate back-reaction.[27-29] Bourcier argues that a precipitation rate is implicit in the use of TST-based rate equations in order for dissolution rate decreases to occur as the system approaches “saturation.” For that reason, they propose that the reaction of the solution with a reconstructed glass/solution interface is the controlling process. This interface has roughly the same composition as the gel and therefore can and does readily form via precipitation reactions. The dissolution of the glass comes about through the dissolution of this interface and exposure of the glass structure underneath. Others have suggested that more species than H4SiO4 are responsible for controlling the rate of corrosion.[24, 30-33] However, most surface reaction control rate law models use [H4SiO4] for Q. Although there have been attempts to include solution species from other elements in the glass in a rate law, for example, Al,[24, 33] there are open questions yet to be resolved.

Another area of some modification involves the Temkin coefficient: the ratio of the rate of destruction of the activated complex involved in the rate-limiting reaction step with the rate of overall dissolution. Lasaga argues that the use of a value other than one is not valid based on Boudart's[34] original derivation of the equation,[35] and this is typically adhered to. However, a later derivation found that Boudart's work was valid and nonunity Temkin coefficients are theoretically justified.[36] Many researchers have used nonunity Temkin coefficients in the modeling of mineral dissolution kinetics.[37-39] However, to date, few have applied them to waste glass corrosion. An exception is Bourcier who found experimental data of a soda-lime boroaluminosilicate glass was best fit with σ=0.1.[28]

In all cases, the models suffer from the fact that whereas silicate minerals reach equilibrium when K and the apparent dissolution rate drops to zero, glass continues to react. An ad hoc residual rate term (r) was added to the basic rate equation to allow for the use of a simple, constant, K value[40]:

display math(4)

Although the residual rate term is a convenient way to represent the residual glass corrosion rate, it can only be loosely justified by a difference in the thermodynamic energy of the unstable amorphous glass and the mineral used to represent it in geochemical codes. Petit et al.[41] tested this theory of the residual affinity and found that it was not justified by the data. A better understanding of the residual rate is needed to justify the application of such a term in a mechanistic model. In an attempt to develop that explanation, many researchers have turned to a transport barrier or a hybrid approach, in which both transport and reaction affinity are used to describe the dissolution of silicate glasses.

Reactant and Product Transport

Many studies have challenged the ability of the reaction affinity model to represent long-term performance of glass and the use of ad hoc terms such as r. The development of a transport barrier or passivating layer at high solution concentrations provides a mechanistic solution to the residual rate question.[41-45] This is distinct from the ion-exchange process described below in that by this process, alteration products are theorized to form a barrier to the transport of water to the reacting glass surface and/or the transport of reaction products away from the reacting glass surface. The barrier is formed as hydrated glass species (Si-OH, Al-OH, Zr-OH…) react together and with other species (coming from the glass or from the environment) to form a new amorphous material.[45-47]

One of the most compelling arguments for this mechanism is that after a residual rate is obtained for a glass in a near saturated solution, the rate remains significantly lower than the initial rate after exchange with unsaturated deionized water.[48] This demonstrates that the glass dissolution rate cannot be determined solely by solution concentration of H4SiO4. Previous tests (by Chick for example[49]) demonstrating that the “gel” layer on corroded glass is not protective were performed in relatively dilute solutions. The transport-limiting layer is thought to form only under relatively concentrated conditions and its stability requires relatively concentrated solutions to maintain its effectiveness in the long term. Grambow and Strachan suggested that transport control was important but that the gradient was between a solution with high concentrations of H4SiO4 near the glass/gel interface and the lower concentrations in solution or near a precipitating phase.[50]

These considerations have led to progressive models for long-term glass corrosion[48, 51-53] that have culminated in both GM2001[54] and GRAAL model.[43, 55] The GRAAL model relies on the reactivity (i.e., formation and dissolution) of a transport-limiting layer, called the PRI (passivating reactive interphase).[43] The two main equations used to calculate the glass dissolution rate are:

display math(5)
display math(6)
  • where E = dissolved PRI thickness at time t
  • e = PRI thickness at time t
  • rdisso = initial dissolution rate of the PRI
  • rhydr = rate of pristine glass hydration forming the PRI
  • KPRI = thermodynamic constant of the PRI
  • DPRI = Diffusion coefficient of mobile species through PRI

The PRI is a conceptual layer within the glass alteration products that controls the transport rate, consisting mainly of Si and Al.[56-58] The porous gel is simulated by 6 end-members whose characteristics (i.e., rate law parameters) are determined empirically. The actual location and structure of the PRI is incompletely known; it may be a dense area within the gel formed by hydrolysis and condensation reactions,[44, 59-61] or it may be the hydrated residual glass that is partially depleted of alkali metals and boron.[42, 47, 62] A concerted effort of closely coupled theory, experiment, and simulation is being made to identify the location, stability, and characteristics of the PRI.[43, 46, 47, 55, 59-61, 63-66] The GRAAL model has analytical solutions in its simplest version.[62] The more complete version is implemented in a reactive transport code to interpret experimental results.[56, 57, 67] Unlike the GRAAL model, GM2001 (i) takes into account two diffusion processes: water through glass[62] and silica through the alteration layer, (ii) considers only Si in the rate-limiting step, (iii) includes empirical equations to manage the fate of Si and B.[3] To date, no detailed comparison of the two models has been attempted.

It should be mentioned that corrosion rates in D2[18]O were found to be a factor of √2 lower than equivalent rates in H2O and the[18]O was found to penetrate to an even greater depth and extent than the D in Na/Ca/Mg silicate glasses.[68] These differences suggest extensive penetration of the D2[18]O into the glass and are inconsistent with transport control, at least for this composition. It is not yet clear if these results will be applicable to complex multicomponent waste glasses.

Ion Exchange

Most early assessments of glass corrosion mechanisms conclude that IX processes control the reaction kinetics.[14-16, 69-74] Here, IX entails the diffusive replacement of alkali, alkaline earth, and in some circumstances other ions from the glass with hydrogen-containing species (H+ or H3O+) from solution.[74] Ion exchange is thought to occur simultaneously with matrix glass corrosion. Some believe that portions of the glass that have experienced IX will be more susceptible to corrosion due to a change in connectivity, the availability of water in the matrix and the increased pH of solution. Because of the involvement of alkali in IX processes, high alkali glasses are expected to be more susceptible to IX both in rate and extent. The activation energy for IX is significantly lower than that for matrix dissolution. So, at low disposal temperatures anticipated from disposal of glass after high-heat fission product decay, the rates of IX will not drop as steeply as those of matrix dissolution.

The primary evidence presented was an apparent inline image dependence of ion release into solution and sigmoidal profiles of alkali into the leached glass surface. The mid-1980s saw a significant move away from the IX process as a dominant mechanism for glass corrosion after the pioneering work of Grambow.[20] However, it should be noted that several researchers continued to argue for IX control of long-term corrosion rate through the 1980s and 1990s.[75-78] A resurgence of IX control came to the forefront of science again in the late 1990s when McGrail et al. reported a persistent off-set in the normalized releases of Na and B from Hanford high soda glasses.[79-81] This has been followed by the results of others[82-84] until recent work on SON68 glass proposing a solution to bridge the gap between IX and passivation effects.[47]

Impacts of Alteration Product Precipitation

Precipitation of alteration products may change the solution concentrations of key components (e.g., H4SiO4) and may form or consume existing transport barriers, both of which significantly impact the glass corrosion rate. For example, the precipitation of zeolites was found to coincide with a three orders of magnitude higher rate than the residual rate of glass corrosion (r).[2, 5-7] Various theories have been proposed to explain the impacts of alteration products on glass alteration rate including those for surface reaction-controlled corrosion[85-87] and for transport-control models.[12, 58, 88] The ‘time’ at which the precipitation of rate-affecting phases occurs cannot currently be predicted nor can the magnitude of the increase in the glass dissolution rate. Ribet et al.[12, 89] propose that it occurs only under high-pH conditions. Another example is precipitation of Mg-silicate minerals. Precipitation of some Mg-silicate minerals was also found to maintain the glass dissolution at an initial high rate by consuming H4SiO4 from solution,[56, 57, 90-92] while precipitation of some other Mg-silicate minerals was found to depress the glass dissolution by protecting the glass from dissolution.[50, 67, 93] Understanding both the timing and the extent to which alteration products affect the dissolution rate of the glass has benefits to the licensing of a repository and to assuring the public and the regulator that the glass is safely disposed.

The current hypothesis is that the precipitation of zeolites (such as analcime NaAlSi2O6·H2O) affects dissolution by affecting one or more of the previously described mechanisms. The precipitation creates a sink for silicon, reducing the concentrations of Si from solution,[94] which in turn either increases the driving force for glass corrosion (reduce Q/K) or destabilizes the PRI. The result is an increase in the dissolution rate in either case. The hypothesis has generally held valid. However, there are some conflicting data such as evidence for an increase in dissolved Si at the same time as rate acceleration in a simulated waste glass under product consistency test procedures.[5, 12, 13, 95]

Key Factors Affecting Glass Dissolution Rate

Glass Composition

While one or more of the mechanisms mentioned previously are anticipated to be the controlling factor(s) for waste glass dissolution, other effects play a critical role in the development of a robust performance model. The composition and structure of glass is very important to the long-term glass corrosion rate.[96, 103] Although governed generally by the same dissolution and transport mechanisms described above, glasses of significantly different compositions require very different parameterization that may change the dominant mechanism at long times.[21, 97-101] Some glass compositions, for instance, have been shown to form dense regions within the gel layers that slow further dissolution due to water transport restrictions.[101, 102] Additionally, heterogeneous glasses (such as phase separated materials or glasses with crystallization) may require a multiterm equation with terms for each phase in the material. For example, the dissolution of a connected high alkali phase might be dominated by ion exchange and completely dominate the system response over a high-silica phase.[103] Despite these differences, it is a goal of the international community[104, 105] to provide versatile mechanistic models that can accommodate a wide variety of glass compositions and structures through proper model parameterization.

Near-Field Materials

All theories of glass reactivity or passivation layer formation depend strongly on the solution contacted by the glass.[57, 106-108] The composition of the solution is in turn dependent not only on the corroding glass, but also on water flux rate and the near-field materials. The composition, dissolution rate, diffusivity and absorptivity of the near-field materials (such as buffers, overpacks, etc.) have profound impacts on solution chemistry and thereby glass alteration process.[109-119, 121] The presence of certain materials can change the solution such that corrosion is accelerated[57, 122-124] or passivated.[62, 125] In general, the water renewal rate is positively correlated with glass dissolution rate, as a more renewed solution is more dilute in the elements that either controls the dissolution of the glass, the development of passivating layers, or both.

Radiation and Decay

Additionally, the glass structure and solution composition could both be impacted by radioactivity.[126-131] The impacts of beta-gamma radiation on glass corrosion are primarily through radiolysis changing the composition of solution (Eh, pH, and dissolved species concentrations).[132-138] Recent work has also shown only a minor impact of gamma-dose on the residual rate of SON68 glass in near saturated conditions.[129] Radiation damage effects in glass waste forms are dominated by the ballistic effects of alpha particles and alpha nucleus recoil. These impacts can increase the stored energy of the glass, may cause swelling or contraction of the glass by up to roughly 1%, and can increase the glass fictive temperature[128, 130, 139-143] These effects are composition dependent and saturate at doses of roughly 1018 α-decay/g (somewhat independent of dose rate). The mechanisms governing waste form dissolution will not change due to decay or radiation. The rates of reaction will be most affected by solution chemistry effects of radiolysis.

Glass Surface Area

Because glass alteration rates are typically normalized to the reacting surface area, the reacting surface area is a critical parameter needed to estimate the lifetime of glass in its disposal environment. At the scale of the canister, defining the reactive surface area is more complicated as cracks are formed during the cooling. The resulting network depends on many parameters such as the cooling scenario, the geometry of the canister, the density of defects (bubbles, crystals…) within the glass. Various empirical methods, recently supported by thermomechanical simulations taking into account the viscoelasticity of the glass, mechanical parameters and threshold and critical stresses indicate that the exposed surface area of a R7T7 glass canister filled with 400 kg of glass can range from 10 to 100× the geometric surface of the cylindrical glass waste form (1.7 m2) depending on the vitrification process parameters and the cooling scenario.[144-147] Similar studies performed on the larger U.S. High-level nuclear waste (HLW) glass canisters showed a range of surface area's between 4 and 17 ×  the geometric surface area.[148] The accessibility of surfaces in tight cracks by water and the reactivity relative to the free surface may change the estimates of reactive surface area from the total crack surface areas estimated. A better understanding of these surface areas, their reactivity, and how it evolves during the life of the waste form is both uncertain and impactful to performance estimates and so must be considered.

Evaluation and Testing

Standard practice ASTM C1174[149] provides logical steps that can be followed to develop a performance model for any waste form or engineered material in any geologic environment through integrated testing, modeling, and evaluation activities. It stresses the importance of formulating a clear definition of the problem, characterizing the disposal environment, maintaining interfaces and iterations between testing and modeling activities, using analog materials and analog systems to gain insights into the degradation behavior, and both validating the conformity of the model to the mechanism of interest and confirming the appropriateness of applying the model to the disposal system. A multination collaboration is working together to apply these principles to the glass corrosion problem.[105]

One key portion of that methodology is the use of analog materials. Robustness, reliability, accuracy, and predictability of the models far beyond laboratory testing capability can be evaluated thanks to ancient glasses.[150, 151] Both natural (basaltic glass, obsidian, meteorites) and archeological artifacts (Roman glass, stained glass window, slags from iron making, etc.) have given insight into how silicate glasses behave in various natural environments.[65, 151-158] However, none of the studied cases is similar to any expected nuclear system: glass compositions are different and the environmental conditions often are very dissimilar from those expected in a geological disposal of HLW or ILW glass. That is why a full understanding of the mechanisms controlling the dissolution of analog materials and the development of models to compare the different systems is required.[159] In general, this mechanistic understanding is the key to comparing different glasses, disposal conditions, and near-field environments.[105, 153, 157]

Conclusions

Even after decades of research, glass corrosion continues to bring challenging questions to the scientific community. As a metastable phase, thermodynamics predict that glass will irreversibly transform in contact with water into more stable phases, but the fundamental question is to know at which rate this process will occur with enough confidence to bound the expected behavior in repository conditions. As synthetized in this paper, a deep, multiscale investigation of the basic processes is necessary to understand and bound the performance of waste glass in repository disposal setting. The high chemical durability of glass and the very long time scales that the glass must survive make these studies particularly challenging and require a fundamental understanding of the processes involved in glass corrosion and how environmental conditions will change the rates for each of the concurrent and coupled processes. The increase of fundamental understanding will increase confidence in the calculation of glass performance out to geologic time scales, allowing partial reliance on glass durability for safety margins.

A number of papers are supplied in this special issue of the International Journal of Applied Glass Science that highlight the state of the art in waste glass corrosion research and help to develop a more fundamental understanding of the processes leading to waste glass alteration and how their rates change with changing environmental conditions.

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