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1

Theory of Corrosion of Glass and Ceramics

William B. White

Materials Research Lalmratory and Department of Geosciences

The Pennsylvania State University University Park, PA 16802

INTRODUCTION

The glasses and ceramics discussed in this chapter are limited to oxide, fluoride, silicate, borate, phosphate, and related compositions that make up common ceramic materials. These materials are electrically insulating and contain few free carriers, so that chemical attack on their surfaces is mainly by acid-base type of reactions rather than electrochemical corrosion involving redox reactions. Crystalline ceramics and non-crystalline glasses of similar composition often have quite different corrosion behavior showing that structure at the atomic scale also plays a role.

The subject is addressed from a generic point of view, with specific examples intended only as illustrations. The object is to set down some of the most important reactions and their controlling parameters.

The literature comes from diverse sources written by rcsearchcrs with very diverse motivations. Interest in glass corrosion comes from the necessity of understanding stability of glass containers, sheet glass, and other glasses in the presence of aqueous solutions (1). In general, the solutions arc highly undersaturated, may be strongly acidic or basic, and the concern is with times in the range of a few years. In contrast, the literature on the dissolution (corrosion) of crystalline ceramics is rclativcly sparse because in the environments in which most of these materials are usc.d, attack by aqueous solutions is not a problem. To geochemists, dissolution of crystalline minerals and rocks is the central process of rock weathering, diagcncsis of scdimcntary rocks, uptake of ions into groundwatcr from aquifer wall rock, and mactions of geothermal waters (2).

2

Theory of Corrosion of Glass and Ceramics 3

Here the fluids are often near saturation and the time spans of interest range from days to tens of thousands of years.

Much of the recent literature on glass corrosion comes from the nuclear waste research community (see Wick’s chapter). Glasses designed for the immobilization of high level nuclear waste are chemically complex but their stability in a variety of fluids, over a temperature range of more than 100 degrees Celsius and, over time scales of thousands of years, is central to hazard assessment models for nuclear waste repositories (3). Finally, art history and archeology may be added to the list of disciplines where rate of weathering of glassy or crystalline objects is important either from the point of view of preservation of historically or aesthetically important artifacts or from the point of view of dating them (4) (see Vandiver’s chapter).

CHEMICAL MECHANISMS OF DISSOLUTION AND CORROSION

Some ceramics are monophasic; that is they are made up of a single crystalline phase. Alumina or periclase refractories, and hot-pressed spine1 or magnesium fluoride optical ceramics are examples. Likewise, most glass can be considered to be a monophasic ceramic. From a point of view of dissolution or corrosion behavior, a monophasic ceramic behaves as a single chemical compound although glass usually doe.s not. Other ceramics are polyphasicr they are made up of more than one crystalline phase. Examples arc the ceramics that have been proposed as nuclear waste immobilization materials, for example the Synroc family of titanium-rich ceramics. Still other ceramics arc made up of crystalline phases plus glass (see McCracken’s chapter).

To a first approximation the dissolution of the individual crystalline phases can be treated independently. This means that one is dealing with the dissolution mechanisms and kinetics of single chemical substances which is a great simplification. The bulk rate, R,,, of dissolution would then be the sum of the dissolution rates of the individual phases, Ri, nomralizcd by the weighted surface areas, SA,.

R,,, = l/SA CSA,R,

If the dissolution of the bulk ceramic is examined in more detail, however, various second order effects appear:

(a) Dominant grains may buffer the reacting solutions and so modify the dissolution behavior of minority grains.

(b) There may be solvent-induced chemical reactions between phases. (c) Some phases in the ceramic or their reaction products may serve to

encapsulate other phases.

Microencapsulant ceramics pose a different sort of problem. These materials

4 Corrosion of Glass, Ceramics and Ceramic Superconductors

utilize a low solubility inc.rt phase to surround and protect other more soluble phases. The bulk dissolution rate of such materials is determined by transport of fluid through the available interconnected pore spaces.

In the most general terms, there arc several chemical mechanisms for the corrosion of crystalline and glassy materials:

(a) Congruent dissolution by simple dissociation. “Congruent” implies that the ratios of constituent elements in solution is the same as that in the dissolving solid. Take as an example the hot-pressed monophasic ceramic MgFz used as an optical window material in the visible and near-infrared regions. Mg F, dissolves in water by a simple dissociation reaction:

MgF, u Mg” + 2F (l-2)

This reaction is independent of pH and at equilibrium reaches a saturation limit which can be calculated from the free energies of formation of the chemical species involved. The surface of the crystalline grains retreats (not necessarily uniformly) as the crystals dissolve. No protcctivc layers are formed and a concentration profile across the crystal surface is a single stair-step (Figure l- 1A).

(b) Congruent dissolution by chemical reaction with the solvent. Dissolution is by acid-base or hydrolysis reaction. No solid reaction products are formed and the surface retrcats without formation of surface layers. An example would be the dissolution of high temperature MgO refractories in acidic solutions:

MgO + ?H+ e Mg” + H,O (I-3)

Here, however, MgO is unstable in the prcscnce of liquid water so there is a competing reaction:

MgO + H,O @ Mg(OH), which in turn dissolves in acidic solutions:

(l-4)

Mg(OH), + 2H’ w Mg2+ + 2H,O (1-S)

At equilibrium, all of these reactions must bc satisfied simultaneously. Direct attack by hydrogen ions is often dominant in low pH regimes while hydrolysis by direct reaction with water is more common in near neutral regimes. Not only reaction rates, but reaction mechanisms may be pH dependent. The dissolving surface, however, retreats uniformly again with a stair-step concentration profile as in Figure I-1A.

What is immediately apparent in even these simple cxamplcs is that there is a complicated solution che.mistry, often made more complicated by speciation and complexation reactions within the solution. These interactions can be dealt


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AL i&i 0 . . ....: : . _’

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Figure l-l. Sketches showing dissolution mechanisms for ceramics and glasses. A) Congruent dissolution with uniform retreat of dissolving interfacc. R) Incongruent dissolution with reaction product remaining in place. C) Corrosion of surface by chemical reaction between solvent and solid. Dj Leaching of sodium aluminosilicate glass.

with most efficiently by computer programs such as WATEQF, MINEQL, or EQ3 which address the spcciation and saturation of aqueous solutions. For the dissolution process itself, reaction path programs such as PHREEQE or EQ6 are helpful. See Nordstrom et al. (5) for a critical comparison.

(c) Incongruent dissolution with formation of crystalline reaction products. During incongruent dissolution there is a reaction of the original bulk solid with the coexisting liquid to form a new solid phase of different composition. The concentration of dissolved species do not occur in the same ratio as in the parent solid. In all cases there is a less soluble reaction product which may or may not accumulate on the dissolving surface to form a protective (to some cxtcnt) barrier layer. An example of incongruent dissolution is:

SrTiO, + 2H’ w Sr2+ + TiO,


Well crystallized strontium titanate reacts with aqueous solution to release strontium ions into solution but the titanium remains behind as the highly insoluble TiO,. The retreating interface is often sharp. If the reaction products remain behind, the Sr concentration drops abruptly to zero at the reaction interface but the Ti concentration remains high out to the original surface (x, in Figure I-1B). This can be an equilibrium reaction with the strontium concentration at equilibrium being defined by the pH of the solution.

(d) Incongruent dissolution with formation of non-crystalline layers. A different type of reaction occurs when the original bulk phase is a framework structure such as an aluminosilicate. Although the reaction product has a different chemical composition than the original material, structural entities such as partially hydrolysed, polymerized silica and alumina tetrahedra remain. This product is often non-crystalline and has been called the “gel layer.” The chemically modified surface may remain intact, even advance rather than retreat because of the lower bulk density of the gel layer. Sodium aluminosilicate is a prototype example.

NaAlSi,O, + H+ w Na’ + Al,Si,O,(OH), + H$iO, (l-7) (Bull<) (Surface)

Although the reaction product is written with the kaolinite composition, the actual material on the dissolving surface may not be crystalline. There is a pronounced change in chemical composition through the “gel” layer in addition to density and textural changes (Figure I-1C).

(e) Ion Exchange. Ion exchange reactions are those in which the mobile ions are leached from a more resistant matrix while leaving the matrix material more or less intact. Again sodium aluminosilicate can serve as an example.

NaAlSi,O, + H,O+ * (H,O)AlSi,O, + Na’

(Bull<) (Surface) (l-8)

The original interface is preserved (more or less) with the same Si/Al ratio. There is a continuous loss of Na through the leached layer.

There is no sharp distinction between breakup of the dissolving surface with concurrent formation of a gel layer and ion exchange reactions. Likewise there is usually some congruent dissolution as an additional background reaction. For albite this would be:

NaAlSi,O, + 4H,O’ ti Na’ + A13’ + 3bSi0, (l-9)

The net corrosion rate is a sum of rates due to the various chemical reactions and the various reaction mechanisms.

A key consideration is whether or not the solid phase can be in equilibrium with liquid water. If it is, dissolution in closed systems will approach an


equilibrium saturation value and fresh solution must be introduced to keep the dissolution reaction going. If the solid is not stable in the presence of water, the hydrolysis reaction will continue until either the liquid is used up (for small quantities of solution in contact with large pieces of solid) or until the solid phase is entirely broken down (if large volumes of liquid are available). There is a further complication when the material is a glass. Glasses are everywhere metastable with respect to an assemblage of crystals with the same bulk composition. In competition with incongruent dissolution and ion exchange reactions is the recrystallization of the host material.

KINETICS

Rate Equations for Crystalline Ceramics

The uptake of ions in solution as a crystalline material dissolves often follows a reaction curve of the sort shown schematically in Figure l-2A. If the crystalline material can exist in equilibrium with an aqueous solution, there is some concentration of each ionic species for which the solution is saturated. Assuming no material initially in solution, at time zero the crystal dissolves very rapidly. As dissolution proceeds the concentration of dissolved species builds up, the solution rate slows down and gradually approaches zero as the concentration of dissolved species approach their equilibrium concentrations. There is,

therefore, a characteristic reaction time necessary for the system to approach some arbitrarily defined fraction of the saturation concentration.

Models for the. dissolution of crystals and ceramics took as a starting point the traditional theory of reaction kinetics (6). Hetcrogencous reactions occur at the interface between the dissolving crystals and the aqueous solution. The steps involved in any such reaction are:

(a) Transport of reactants to the solid surface. (b) Adsorption of the reactants. (c) Chemical reaction bctwecn an aggressive adsorbed species and

some point of attack on the crystal surface. The detailed atomistic chemistry can be quite complex.

(d) Desorption of the reaction products. (e) Transport of products into the bulk solution.

For a chain of individual reaction steps, the slowest step limits the overall rate. In general, control has been ascribed to either transport (steps a and e) or to surface reaction kinetics (step c).

In a transport-controlled reaction, the surface chemical kinetics arc fast so that migration of ions through the fluid boundary layer becomes rate-limiting. In classical Nernst theory, the change in concentration is simply the flux, j, of


A Time 6 Time

% ______--__ __

C Time D Time

Figure 1-2. Rate curves for uptake of ions in solution according to various dissolution mechanisms. A) Dissolution when solid can come into equilibrium with liquid at saturation concentration, C,. B j Linear kinetics truncated by saturation with respect to a precipitate phase with rapid precipitation kinetics. C) Diffusion-controlled kinetics with a parabolic rate law. D) Dissolution with precipitation of a product phase with sluggish precipitation kinetics,

material across the boundary layer which in turn is controlled by the layer thickness, 6, and the diffusivity, D, of such ions in the liquid. The driving force is supplied by the concentration gradient:

dC/dt = (SA/V)j = (D*SA/GV)(C, - C) = k,(C, - C) (l-10)

where k, is a mass transfer cocfficicnt. The integrated form of the equation is:

C(t) =Cs(l-eKTt) (I-11)

Empirically, it is found that dissolution of substances with solubilities greater than 10m4 moles/liter is usually mass transport limited while dissolution is surface reaction controlled for substances with solubilitics less than 10e5 mole/liter. Most crystalline ceramics and glasses of practical utility are quite insoluble so that dissolution is rarely limited by transport through the fluid boundary layer. Single crystal and polycrystal alkali halide optical materials and some water soluble detector (e.g. triglycinc sulfate) and transducer (e.g. potassium dihydrogen phosphate) materials are obvious exceptions.


Providing that the dissolving solid will eventually come into equilibrium (saturation) with the solution whether by congruent or incongruent dissolution, the bulk rate equation is written:

dC/dt = (SA/V)k,(C, - C) (1-12)

The exponent, n, is the order of the reaction and k, is a reaction rate constant. An alternate expression used for ionic solids is:

Rate = (V/SA)(dC/dt) = k(l - Sz) (1-13)

where SZ is the saturation ratio defined as:

12 = (ion activity product)/(solubility product constant)

If n = 1, first order kinetics, equation I-12 integrates to:

C(t) = (SA/V)C,(l - eeL? (I-14)

the same form as obtained from transport theory but with a much different definition of k. The rate constants in this formulation have units of l/time and can be replaced by a characteristic reaction time (5 = l/k,) which is a measure of the response time of the system. First order reactions are found for those systems where one of the concentration variables is dominant and where there is a one to one atomic reaction at the surface, for example the exchange of an alkali ion by a hydrogen ion. Higher order reactions are often observed. The competing rates of both forward and back reactions are incorporated in equations 1-12 and 1-13. An initial rapid rate, expressing mainly the forward reaction, decreases so that the concentration-time function curves over to become asymptotic to the horizontal line marking the saturation concentration.

Many ceramics, glasses, and minerals cannot exist in equilibrium with aqueous solution under ambient temperatures and pressures. For these substances, the back reaction is not usually observed. The trend toward metastable equilibrium is cut off by the precipitation of new, lower solubility, product phases. The product phases are sometimes hydrated and these can be regarded as the reaction products of the original phase with water. The system is then described by two reactions and two rate equations. The forward reaction is the dissolution of the primary phase. Instead of a back reaction, there is a precipitation reaction which, because it removes ions from solution, is often treated as a back reaction.

When dissolution of the metastablc phases takes place far from equilibrium, the forward reaction rate is little influenced by the build up of reaction species in solution and obeys zero-order kinetics. That is:


dC/dt = (SA/V)k+ (1-15)

This equation leads to a linear concentration - time curve as shown in Figure I- 2B. Obviously, this equation describes only part of the process because the concentration increases without limit at large times, a physical impossibility. The precipitation reactions can be taken separately so that the net concentration of ions in solution is given by:

dC/dt = (SA/V)k+ - (SA’/V)k_(C - C,) o-19

where SA’ is the effective surface area of the precipitates, k, is the forward reaction rate constant and, k. is the precipitation rate constant. (C - Cs) is the supersaturation with respect to the precipitate phases. If the precipitation kinetics are fast relative to dissolution kinetics, the concentration curve is cut off abruptly as shown in Figure l-2B.

The dissolution rates of many materials varies with pH. Hydrogen ion activity can be factored specifically into the rate equations:

dC/dt = (SA/V)k+‘a,+” - (SA’/V)k.(C - C,) (l-17)

The exponent, n, is unity for most crystalline materials in the acid regime. In alkaline solutions, n varies from -0.2 to -0.6.

There is a very large literature on the dissolution kinetics of insoluble ionic salts such as carbonates, sulfates, and phosphates. Most of these materials can exist in equilibrium with aqueous solutions and approach saturation following a rate equation that is some variant of equation 1- 12 as the reaction proceeds under closed system conditions.

The dissolution of oxides often follows equation 1-17. In the example of Fe,NiO, spine1 (Figure l-3), dissolution is congruent and the rate is linear in strongly acidic solutions. As the pH increases, the rate decreases as given by equation I- 17 and in addition a precipitation reaction of iron hydroxides appears. What appears in the solution chemistry is that the Ni2+ concentration continues to increase linearly but at a slow-er rate while the concentration of iron in solution increases even more slowly because of the precipitation reaction, giving the impression of non-stoichiometric dissolution.

The dissolution of anhydrous silicate minerals such as olivines, pyroxenes, quartz, and feldspars, particularly, have been examined in detail by the geochemical community because of their importance in the weathering of igneous and metamorphic rocks. There is a large amount of literature on the dissolution of feldspars, for example.

Rimstidt and Barnes (8) showed that the dissolution kinetics of quarlz follow a variant of equation l- 17.

(1-18)


20 40 60 80

Time (days)

Figure 1-3. Dissolution of nickel ferrite in strongly acidic solution. Data from Nachlas

(7).

M is the mass of solvent, Si is an abbreviation for H,SiO,, y is the activity coefficient for H4Si04 (near unity because H4Si04 is neutral and dilute), aslo is the activity of silica (= 1 for pure quartz), and asi is the activity of dissolved silica. The rate constants are functions of tcmpcrature but the system is independent of pH. Later investigators have shown that dislocations emerging from the crystal surface accelerate the dissolution rate (9). It was also found that the reaction is pH independent only below pH = 6; above this value, the rate increases as an+-o.5 (10).

Lasaga (6) has reviewed the older data. In general, silicates dissolve by a surface reaction mechanism and often show linear dissolution with strong pH dependence of the sort described by equation 1-17. Lasaga has made an intercomparison both by the rates themselves and by considering the length of time required for a one millimeter cube of the crystal to completely dissolve (Table l-l).

When the dissolution kinetics of silicate minerals were first examined, the concentration-time curves appeared to be paraboloid and it was assumed that the rate-controlling feature was a barrier layer on the surface, analogous to the layers that had been observed on glasses. However, when later w{orkers looked for the surface layers with increasingly sophisticated characterization methods, the layers were not found. The initial rapid rate appears to be due to dissolution of small


Table l-l. Rate of Release of Silica at 25°C and pH = 5

Mineral Composition Rate (moles cmm2day-‘)

Lifetime* (years)

Quartz Muscovite Forsterite K-Feldspar Albite Enstatite Diopside Nepheline Anorthite

Si02 KAl$i,O,,,(OH), Mg,SiO, KAlSi,O, NaAlSi,O, MgSiO, CaMgSi,O, NaAlSiO, CaAl,Si,O,

8.64 x lo-l3 2.56 x IO-l3 1.2 x 1o-‘2 1.67 x lo-l2 1.19 x l&l’ 1.0 x 1O“O 1.4 x lo-lo 2.8 x 1O-9 5.6 x 1O-9

34 x lo6 2.7 x 106 0.6 x lob 0.52 x 106 80,000 8,800 6,800 211 112

* Mean time required for the complete dissolution of a l-mm crystal. All data from Lasaga (11).

particles attached to the surface of mineral grains and solution attack on high energy sites on the crystal surface such as the emergence points of dislocations, grain boundaries, and cleavage cracks (12). When these are consumed, the rate slows down to that of the bulk material but the overall rate curve gives a misleading impression of parabolic kinetics. When the effect of changing surface activity is taken into account, most silicate minerals so far examined dissolve by a linear kinetics mechanism.

It has been gcncrally agreed that most of the mineral dissolution reactions are acid-base reactions and that at the heart of the matter is the reaction of a proton, hydronium ion, or water molecule with the cations on the surface of the crystal. Dissolution rates are highly sensitive to the presence of active sites for such attack. Stumm (13) and his colleagues have proposed an atomistic model in which the rate of dissolution is given by:

Rate (molts m-2sec-‘) = kX,PjS (l-19)

where k is a rate constant in units of see-‘. X, rcprcsents the mole Caction of dissolution active sites. Pj is the probability of finding a specific site in the coordination arrangement of the precursor complex, and S is the surface concentration of sites in units of moles me2. The surface complexes - chelates or metal-proton complexes - are taken as the intermediate steps in the rate-limiting detachment of cations from the surface into solution. Application of the model leads to macroscopic rate equations of the form given above. Computation of the parameters of the theory from first principles or determination of surface concentrations by direct mcasuremcnt are not possible at present.


Rate Equations for Glasses

The analysis of the corrosion and dissolution behavior of glasses had its roots in the container industry. Container glasses must be optimized for low rates of extraction of the component elements by whatever liquid is placed in the container. Early theory was cast almost entirely in terms of leach rate. There is a preferential dissolution of more soluble ions from multicomponent glasses by a process of ion exchange controlled by the diffusion of H’ (or H,O’) into the glass coupled with the diffusion of leachable ions out of the glass.

Glass leaching is usually described in terms of Fick’s laws in one dimension:

dC/dt = d/dx(D dC/dx) (l-20)

where D is the diffusivity of the leachable ion. For a planar interface with a constant diffusivity, the solution of equation l-20 leads to the observed parabolic rate law, with rate constant, $, which is often given in a simple empirical form:

Rate (moles cm-2) = k, + k$” (1-21)

The constant term, k, is usually not zero and has been attributed to rapid initial surface exchange between hydrogen (or hydronium) ions and cxchangcablc ions on or near the fresh glass surface. Like the corresponding models for crystalline silicate dissolution, the above equation describes only the forward reaction rate. The reaction continues without limit and if the supply of liquid is sufficient, the reaction ends only when the entire glass specimen has been leached (Figure l- 2C).

The build-up of ions in solution, however, may exceed the solubility of secondary reaction products which may then precipitate. Because of sluggish precipitation kinetics for silicate and aluminate reaction products, there can be considerable overshoot so that the concentration curve appears as shown in Figure 1-2D.

A good example of the comparative behavior of glasses and crystals of the same composition is provided by NaAlSi,O,, which occurs naturally as high quality crystals of the mineral albite and which can be made into an aluminosilicate glass. Figure l-4 shows the comparison in corrosion behavior of the three elements that make up the material. The uptake of Si into solution is identical within experime.ntal error regardless of whether the source is crystal or glass. The parabolic shape to the curve results from continued upward drift of pH rather than from diffusion-controlled kinetics. The removal of Na from crystalline albite is such that the Na/Si ratio is about 1:3 as required from the formula, thus confirming a congruent dissolution of the crystal. Sodium uptake from the glass, however, is much larger than that of silicon suggesting that sodium is being leached from a depth in the glass in addition to its dissolution


30

N; 25

2 20 3 2 15

5 10

1 5

0

18

N; 15

: 12 z z 9

1 6

Crystal

I a 888

Crystal _

I ~8108B,11@ I) a l l 0 0 8

1 I 1 I I 3

0 400 800 1200 1600 2000

Time (hours)

Figure 1-4. Comparison of the uptake of ions by dissolution of crystalline albite, NaAlSi,O,, and albite composition glass. Solid and open symbols show reproducibility of duplicate runs. Data extracted from Zellmer and White (14).


at the surface. The removal of Al from the glass occurs to a point where the AI/S ratio is a little less than 1:3, the expected value from the chemical formula. This concentration of aluminum far exceeds the solubility of both aluminum hydroxides and the aluminosilicate layer silicates, so the retention of aluminum in solution must be me&stable. However, Al extracted from the crystalline albite rises to a maximum a short time after the commencement of the experiment and then falls back to a low level. The results suggest much more rapid precipitation kinetics for the crystal compared to the glass of the same composition.

The albite example illustrates the continuing and unresolved problem of how to deal with the reaction layers that form during glass dissolution. Preferential extraction of leachable ions forms a leach layer that acts as a diffusion barrier to further extraction. Precipitation of network-forming ions such as silicon, aluminum, and boron not only forms an additional gel layer which may or may not act as a diffusion barrier, it also acts as a substrate for the adsorption and perhaps chromatographic separation of precipitating metal ions. The gel layer is metastable and ultimately recrystallizes. The near surface environment of a dissolving or corroding glass is thus quite complicated as illustrated in Figure l- 5.

Crystalline precipitate build-up

Figure l-5. Sketch showing a corroded glass surface with ion-depleted leach layer, overlying precipitate or “gel” layer with ultimately recrystallizes into reaction product phases on the surface. From Mend4 (1.5).

Leaving aside the additional complication of the gel layer, the ongoing dissolution process is composed a diffusive part with mobile ions moving outward through the depleted leach layer and the dissolution of the leach layer itself. It has long been recognized (16) that the parabolic kinetics seen at the early stages of glass dissolution shift asymptotically into linear kinetics at long


times as would be expected if there was a steady state balance between diffusion and the surface reaction controlled dissolution of the glass surface. Empirically this is expressed by an equation of the form:

Rate(g*m-2) = At1’2 + Bt (l-22)

Equation l-22 forms the basis for many models of glass dissolution, usually accomplished by deriving an analytical form for the empirical constants A and B (see Eppler’s chapter).

For silicate glasses, the cumulative uptake of silica in solution (in absence of a gel layer) is the best indicator of the degree of dissolution of the glass. One description of the process is the Wallace-Wicks equation for the dissolution behavior of nuclear waste glasses (17) (see Wicks’ chapter).

dC/dt = [kC,( 1 - SA/V C, - C)]/[ 1 + k q/D C] (l-23)

where C is the concentration of silica in solution, C, is the saturation concentration of silica, k is a rate constant, q is an empirical constant, and D is the diffusivity of silica through the leached layer.

The recognition seems to have dawned, long ovcrduc, that the build-up of leached layers and gel layers on dissolving silicate glasses are transient phenomena and that ultimately the dissolution of glass is also a surface reaction controlled process. Current work on glass dissolution is often expressed as variants of the Grambow equation (see Grambow’s chapter):

Rate = k+(l - aJK) (l-24)

where k+ is a forward reaction rate constant, a, is the activity of dissolved silica, and K is the equilibrium constant for the dissolution reaction. The silica activity, a_ is sometimes replaced by the reaction quotient, Q, in which case equation l- 24 is essentially identical to equation 1-13 that describes the surface-reaction controlled dissolution of crystalline ceramics in terms of a saturation ratio.

Phosphate glasses are generally less resistant to corrosion in aqueous solutions than silicate glasses. Studies of the dissolution of a family of alkali-calcium-phosphate glasses (18) shows that no leached layer is formed. These glasses dissolve uniformly by a surface reaction mechanism.

SURFACES

Characterization of Surface Layers

Dissolution mechanisms and rates for crystalline ceramics and glasses


depend quite critically on the initial surface and on the evolution of leached layers, gels layers, and reaction product layers as the dissolution process proceeds. Characterization of these surfaces has brought into play nearly every surface characterization tool known to materials science (19). For those glasses that develop substantial surface layers, characterization by scanning electron microscopy, photoelectron spectroscopy, and diffuse reflectance infrared spectroscopy has proved useful. Depth profiling techniques such as secondary ion mass spectroscopy and sputter-induced optical emission spectroscopy both in conjunction with ion milling allow measurement of diffusion profiles through the glass surface layers (see Lodding’s chapter). Success in measuring hydrogen concentrations in the hydrated layers has also been obtained by resonant nuclear reaction methods and by Rutherford backscattering.

It is generally agreed that the rate controlling diffusion step in the leaching of glass in the diffusion of hydrogen ions, hydronium ions, or water molecules into the glass surface. Models for dissolution based on this premise give good agreement with data (20). Comparison of the actual diffusivities of hydrogen-bearing species diffusing in compared with alkali ions diffusing out strongly support the diffusion of hydrogen-bearing species as the rate controlling step (21). Quantitative comparison of H/Na ratios within the diffusion profiles by sputter-induced optical emission spectroscopy (22), by resonant nuclear reaction (23), and by Rutherford backscattcring (21) gives values in the range of 1.7 to 3.0, eliminating hydrogen ions but supporting cithcr water molecules or hydronium ions or some combination of the two. Most of these kinds of experiments have been done either in near-neutral or in intermediate pH regimes. There is a cross-over between hydrogen ion as the reactive species at low pH and direct hydration by neutral water molecules in the near-neutral pH regime and it may be that no experiments have yet been done in sufficiently acidic system to observe hydrogen ion diffusion.

For the most part, gel layers, where they form, are not rate controlling. The gel layer is often permeable, patchy, and is sometimes obscrvcd to be peeled free of the glass surface. The chemistry within the gel layer is extremely complex as is the morphology of the layers. As indicated by the sketch in Figure l-5, the gels are often non-planar and may have a complex internal structure with great variation in chemical composition within the layer. These layers occur on glasses with complex bulk composition such as the nuclear waste glasses and geochemical reaction path models seem to be adequate for a description of the reaction products found in the layer (24,25).

Demonstration of the absence of controlling surface layers in the dissolution of crystalline silicates and other ceramic materials is a much more difficult proposition. It has long been assumed that thcrc would be a build up of hydrated layers on feldspars and other silicate crystals analogous to the layers that form on glasses of similar composition. Careful scanning Auger spectroscopic examination of feldspar surfaces reveals a chemical reaction layer only a few nanometers thick (26). Very careful hydrogen depth profiling using resonant


nuclear reactions showed a hydration layer on a scale of less than 50 nm on a diopside, CaMgSi,O,, crystal that was interpreted to be the zone of active surface reaction (27). Such a zone of intermediate hydrated complexes would be consistent with the atomistic model described by equation 1-19.

Role of Surface to Volume Ratios

Dissolution rates are usually expressed in terms of the change in concentration of the solution as a function of time or as the mass of material released from a unit area of the dissolving solid as a function of time. Thus the various rate equations contain a scaling term usually expressed as SA/V, the surface area of the dissolving solid divided by the volume of solution. The relation between the uptake of dissolved ions and the dissolution rate is:

dC/dt = (SAIV) Rate (l-25)

Although the rate at which a dissolution reaction occurs is a property of the system as discussed in previous sections, the time required for the system to reach saturation or any prescribed fraction of saturation is directly proportional to the SA/V ratio. Expressed somewhat differently, the time for a particular experimental result to be achieved is scaled by the SA/V ratio. One must keep this relationship in mind when comparing results of experiments with quite different SAN ratios (28) (see Clark/Zoitos chapter).

Dissolution reactions of fine powders with high surface area appear to take place faster than coarse grained or bulk materials although the rate, which by definition is normalized to surface arca, may be the same. Likewise, reactions between thin liquid films and bulk solids reach equilibrium faster than the dissolution of the same solid into a large volume of liquid. For this reason, circulating pore fluids in permeable cements, ceramics, or rocks arc likely to quickly come to equilibrium.

Several caveats must be observed concerning SA/V ratios. (a) Many laboratory experiments are carried out with modest amounts of solid in large volumes of solution (small SA/V) whereas many applications of the laboratory results are to situations of large surface and modest amounts of liquid (large SAN). (b) Surface area is notoriously difficult to measure. Many porous materials are now known to be fractal, that is the magnitude of the surface area depends on the scale of the “ruler” with which one measures it. (c) Surface areas may change with time as dissolution proceeds. SA/V should bc written SA(t)/V and not merely as a constant in the rate equation.


SYSTEM VARIABLES

Open and Closed Systems: Rates of Transport

In a thermodynamic sense, a closed system is one in which the total mass is fixed; an open system is one in which one or more components may be transported across the system boundaries. Dissolution in closed systems proceeds until the solution reaches saturation or until the source material is completely broken down or dissolved as described by the appropriate rate equation. Open system is used with two meanings in the literature of glass and ceramic dissolution. In one sense, the activities of certain components of the reaction chemistry can be controlled by external reactions. Examples are systems in which pH is buffered or in which the activity of dissolved silica is controlled by the presence of silicate minerals. In the second sense, open systems are those in which there is a continuous movement of liquid through the system. This includes laboratory experiments in which the leach solution is periodically replaced by fresh solution, various flow-through experiments (see Clark/Zoitos chapter), and, in the natural environment, systems with continuously flowing or percolating water.

The characterizing parameter is the transport rate/dissolution rate ratio. If this ratio is large, the dissolving glass or ceramic will be continuously bathed in fresh solution and the dissolution rate will be controlled by the initial slope of the rate curve, (dC/dt),, as indicated in Figure 1-2A. If the ratio becomes very small, the concentration of ions in solution will be given by the saturation values and the removal of mass from the system will be determined by the flow rate of the solution.

There is a crossover when the ratio is near unity as illustrated in Figure l-6 for a nuclear waste glass. At high flow rates (short residence times) the glass surface is simply corroded by the highly undcrsalurated solutions and all elements dissolve at about the same rates. The leach rate becomes maximum and constant. At slower flow rates there is a preferred release of boron and sodium because these elements tend not to accumulate in precipitate phases. Aluminum has the slowest release rates because it tends to reprccipitate in the gel layers. At the lowest flow rates, saturation effects are the main controlling factors. Similar results are found for other nuclear waste glasses and ceramics (29).

The combination of high surface area to volume ratios and slow flow rates in porous media leads to the conclusion that the leaching of concretes and grouts, the evolution of sedimentary rock basins, and perhaps the extraction of radionuclides from high level nuclear waste repositories can be modeled using only saturation limits and models for the fluid flow field. The Pigford model (30) for nuclear waste repositories is based on this premise. Under certain circumstances the rate of extraction of elements from a mass of solid is nearly independent of the detailed chemical kinetics of the dissolution process.


Flow rate (m/year 1

F I 1000 100 10 1 0.1 0.01

0.01 0.1 1 10 100

Residence time (years 1

Figure 1-6. Normalized leach rates for elements extracted from a nuclear waste glass scaled to flow rate and residence time. Catholic University data drawn from Mendel’s report (15).

pH as an Open System Variable

Dissolution experiments can often be broadly classified into “free drift” and “pH stat” types. In a free drift experiment, usually a closed system, the surface reaction of dissolving crystals or glass consumes hydrogen ions leading to a gradual increase in pH. Because the dissolution process is driven by the hydrogen ion activity, the concomitant loss of hydrogen ions causes a continuous decrease in dissolution rate in addition to changes in rate caused by buildup of leach layers or the onset of back reactions due to saturation effects. For certain glasses reacted with water, the pH can drift into a strongly alkaline regime which promotes breakdown of the silica framework and the rate of dissolution again increases. In pH stat experiments, either pH is buffered to maintain a constant value, or an automatic titrating system adds acid to the system to maintain pH at a constant value. pH stat experiments allow more accurate determination of rate constants; free drift experiments arc a better representation of changing mechanisms and competing rate processes.


Eh as an Open System Variable

Most of the literature on dissolution kinetics concerns ceramics and glasses composed of silicates, phosphates, and other compounds of alkali and alkaline earth elements where redox potentials are not relevant. Although Eh (or pe) plays the same role in redox reactions that pH does in acid-base reactions, unlike the H’ ion, there is no free electron in solution. Thus most solutions are poor Eh buffers and Eh is much more treacherous as a system variable (31) (see Jantzen’s chapter). Eh does play a critical role in the dissolution of ceramics or glasses containing variable valence ions. The solubility of the ions depends strongly on their valence state. In principle, rate equations for dissolution reactions of variable valence materials should contain an electron activity term analogous to the hydrogen ion activity term in equation l-17; however, few examples are available in the literature. Iron is a case in point. Compounds of Fe’+ are often relatively soluble whereas Fe3’ forms insoluble hydroxide precipitates. Figure l-7 shows the dissolution of Fe,NiO, in acid solution with the solution exposed to the atmosphere with its high oxygen pressure (labeled “oxidizing”) compared with the same solution in the presence of hydrogen gas with a palladium catalyst used to expedite the reaction of hydrogen with the solution. The reducing conditions maintain the dissolved iron in the ferrous state and prevent build-up of a ferric hydroxide layer. The dissolution reaction, as determined from the metal ratios, remains congruent.

Redox reactions are of greatest importance in the dissolution of metal-containing waste forms. As a rule of thumb (to which iron and manganese are exceptions) the lower valcncc states tend to form insoluble oxides while the higher valence states are more soluble. Uranium dioxide used in reactor fuel pellets is highly insoluble but in oxidizing environments uranium oxidizes to U6’ which in the form of the uranyl, UO, 2+, ion becomes moderately soluble (33). ‘9~ in its tetravalent state forms low solubility oxide compounds but readily oxidizes to the highly soluble Tc7’.

EFFECTS OF TEMPERATURE

The Arrhenius Rate Law

The rate of most dissolution reactions increases exponentially with temperature obeying the Arrhenius equation:

-E,/RT Rate = A,e (1-W


60 I I I I I

Ni Fe2 O4

10 15 20

Time (days 1

25

Figure 1-7. Dissolution of Fe,NiO, spine1 in acid solution (pH = 1, T = 7O”Cj under oxidizing (ambient atmosphere) and reducing (hydrogen gas at one atm.) conditions. From reference (32).

The pre-exponential factor, A,, has a complex theoretical form and is usually taken as an empirical factor. The activation energy E, is taken as a measure of the barrier height that must be surpassed for reaction to occur.

Diffusion processes provide low energy barriers and E, takes on values in the range of a few kJ per mole. Surface reactions have a more substantial barrier, typically on the order of 80 kJ/mole, whereas recrystallization processes have activation energies of several hundred kJ/mole. Experimental values for E, can be obtained by examining the dependence of rate, rate constant, diffusivity, or uptake of ions in solution as a function of temperature (see Clark/Zoitos chapter). These values can be used as evide.nce for the dissolution mechanism.

Because values for the activation energy of reaction limited dissolution tends to bc about the same indcpcndcnt of the chemistry of dissolution, the dependence of dissolution rate on tcmpcrature appears to be very similar for many diverse types of reactions. Figure 1-8 shows some data on the release of ions into solution for a nuclear waste ceramic. The elements extracted include an alkali ion (Cs), an alkaline earth (Sr) and a rare earth (La). These elements are partitioned between several crystalline phases in the ceramic. In spite of these complications, the Arrhenius plots arc linear with roughly the same slope.


1000

2 5 100

E

6 ._

E +J s 10

2

8

1

I I 1 I ,

f Scheelite

+ Apatite)

(Pollucite)

(Monazite + Fluorite 1

100 200 300

Temperature (” C 1

l/T (K-l)

Figure l-8. Dissolution of a r&car waste ceramic as measured by the concentration in solution after 4 weeks at a pressure of 35MPa at the temperatures plotted. The ceramic is polyphasic with the source for each element given in parenthesis on the plot.

Figure I-9 compares the tem~raturc dependence of the dissolution of silica from natural tektite glasses with the tcm~rature dependence of the dissolution rate of silica glass and crystalline quartz based on the rate equations of Rimstidt and Barnes. Again the Arrhenius plots are linear with roughly the same slope. The intercepts, of course, vary widely but the similar slopes reflect the similar values of the activation energies for all sorts of acid-base reactions.


lo-* *-

‘3 N

‘E 2 1o-3

Temperature f “C f

700 75 50 25

Tektite

2.5 3.0 3.5 4.0

1000/T (K-’ )

Figure l-9. Rate of silica loss from crystalfinc quartz, silica glass, and from tektite glasses as a function of temperature. Quartz data and silica glass data calculated from equations of Rimstidt and Barnes (8) based on initial rates (no silica in solution). Tektite data are from Barkatt et al. (34). Crosses refer to indochinites; circles to australites.


Dissolution in Supercritical Fluids

The vapor pressure of water exceeds one atmosphere at 100°C and although the liquid-solid reactions can be followed to temperatures above lOO”C, a pressurized system is required to maintain the liquid. The critical point of water is at 27.5 MPa and 373°C. Above the critical point of water, the distinction between the liquid and the vapor phase disappears.

Dissolution curves of crystalline ceramic materials usually continue through the critical point without a break. However, P-T-X phase diagrams for the system must be taken into consideration. Changing P and T can drive the system into new phase regions and then entirely new dissolution reactions and corresponding new kinetics regimes appear.

For glasses and other metastable phases, however, reactions in hydrothermal regions may be quite different. One major new factor that occurs is the change in mechanism of solid-solid recrystallization reactions. Recrystallization in dry systems or at low temperatures is controlled by solid state diffusion. Rates are low and crystallization often occurs only on geologic time scales making glass indefinitely “stable” on the human time scale. In hot liquids and more so in supercritical fluids, the crystallization mechanism shifts to one of dissolution and recrystallization. There is a great increase in recrystallization rate which typically has an activation energy of 300 to 400 kJ/mole, thus a much steeper slope on the Arrhenius plot. Short exposure to hydrothermal fluids often drives a system to the equilibrium assemblage of solid phases and the dissolution kinetics becomes that of the crystalline reaction products rather than the glass. Thick reaction layers of complex chemistry form rapidly on glasses reacted under hydrothermal conditions (35).

Corrosion by the Vapor Phase

Glasses can be hydrated and recrystallized by direct reaction with water in the vapor phase (36-38). Ionization in the vapor phase is negligible so that there is no question that neutral H,O rather than H’ or H,O’ is the active agent. Chemical profiles through the hydrated layer show a buildup of alkalis and other easily leachable elements on the surface. Unlike dissolution in liquid water where these elements are carried away in solution, vapor phase hydrolysis provides no transport mechanism and thus the hydration profiles for vapor hydrated glasses and water leached glasses are the reverse of each other. Hot water vapor, typically at 26OO”C, also promoted the recrystallization of the glass surface with the development of many small crystals of the phases appropriate to the glass composition.

The substantial corrosion of glasses by water vapor underscores the importance of hydrolysis of the network-forming elements as part of the overall dissolution process. This aspect of the mechanism is rarely included explicitly in discussion of the rate-controlling mechanisms.


SUMMARY AND CONCLUSIONS

Glasses and crystalline ceramics composed of oxides, silicates, borosilicates, and phosphates dissolve in aqueous solutions by a combination of hydrolysis of the framework-building elements near the surface and by acid-base reactions with the cations. Diffusion of mobile ions across depleted leach-layers may be rate controlling for some glasses. Rates usually increase linearly with hydrogen ion activity and exponentially with temperature.

Intense research activity in the decade of the 1980’s, mainly carried out by the nuclear and hazardous waste communities in the case of complex glasses and waste immobilization ceramics and cements and by the geochcmical community in the case of crystalline silicates has lead to some convergence in the description of the kinetics. There is considerable agreement on the forms of rate equations and on the relative importance of the various chemical reactions and chemical mechanisms of dissolution on a macroscopic scale. Understanding of corrosion mechanisms on an atomic scale is rudimentary although substantial current research is focused on this problem.

ACKNOWLEDGEMENTS

Experimental work on low temperature reactions of ceramics and glass on which this review was based is supported by the National Science Foundation under Grant No. DMR-8812824.

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