1594
J. Phys. Chem. C 2008, 112, 1594-1603
Dissolution of Oxide Glasses: A Process Driven by Surface Generation Lorette Sicard,*,† Olivier Spalla,‡ Fre´ de´ ric Ne´ ,§ Olivier Tache´ ,‡ and Philippe Barboux| LIONS (Laboratoire Interdisciplinaire sur l’Organisation Nanome´ trique et Supramole´ culaire), CEA/DRECAM/ SCM, 91191 Gif sur YVette Cedex, France, UniVersite´ Paris Diderot (Paris 7), ITODYS (Interfaces, Traitements, Organisation et Dynamique des Syste` mes), CNRS UMR 7086, Case 7090, 2 Place Jussieu, 75251 Paris cedex 05, France, CEA/DRFMC, 17 rue des Martyrs 38054 Grenoble cedex 9, France, and Ecole Nationale Supe´ rieure de Chimie de Paris, Chimie de la Matie` re Condense´ e de Paris, CNRS UMR 7574, 11 rue Pierre et Marie Curie, 75005 Paris, France ReceiVed: July 6, 2007; In Final Form: NoVember 5, 2007
Grazing incident X-ray scattering (GISAXS) has been used to study in situ the alteration of sodium borosilicate glass monoliths in water. The treatment used to extract the pore volume and the specific surface from the disordered porous media is first introduced and validated by comparing results in other geometries (powders). In the same time, the plane geometry of the GISAXS experiments allows an accurate measurement of the alteration depth. It is shown that the alteration results in the formation of a porous layer, the thickness and porosity of which can be quantitatively assigned to the difference of dissolution between silicon on the one side and boron and sodium on the other. The in situ experiments reveal that a large specific surface develops very rapidly in the layer. No gradient of structure throughout the depth of the altered layer could be observed. Introduction of zirconium promotes a strong increase of the glass durability but increases the specific surface area of the altered layer.
I. Introduction Oxide glasses are widely used for many applications such as transparent windows, insulation fibers, containers, or nuclear waste packaging. In all these applications, the durability of glass in the presence of water is a major issue. First, the time scale is important. For instance, the insulation fibers have to be dissolved rapidly in the physiological liquid in order to protect from diseases the persons exposed to an accidental inhalation.1 On the other limit, one wants the longest durability as possible for nuclear waste storage,2,3 fibers for mechanical reinforcement of concrete, or containers for pharmaceutics. The concept of durability is also important since, depending of the domain of applications, it may be related to the complete loss of the mechanical cohesion due to the total dissolution of a fiber or to the partial release of elements into the solution (radioactive waste, pharmaceutics containers). Also, the change of morphology is to be taken into account. The incongruent loss of soluble species explains the formation of micropores and silica clusters.4 The formation of a porous corroded surface is invisible for a windscreen or a transparent window but strongly affects its mechanical strength and its adhesion properties.5-7 A glass window stored for too long of a time in moisture may no longer be suitable for further surface treatments. After some use, a pharmaceutical vial with porous surface layer may adsorb drugs, trap toxic species,8,9 or release elements detrimental to the pH or the use of the solution.10 The detection of glass surface corrosion is also an important issue in the domain of archeology and fine arts conservation.11-13 Accordingly, a comprehensive * To whom correspondence should be addressed. E-mail: sicard@ itodys.jussieu.fr. Phone: (33) 144279541. Fax: (33) 144276137. † Universite ´ Paris Diderot. ‡ LIONS. § CEA/DRFMC. | Ecole Nationale Supe ´ rieure de Chimie de Paris.
understanding of the microscopic mechanisms involved in the alteration of an oxide glass matrix by water is still the objective of a large amount of works.14-17 In the same time, dissolution of glass is still an interesting problem of physics. Indeed, oxide glasses are not at the thermodynamic equilibrium, and the routes followed by a glasswater system to relax toward a full equilibrium is intrinsically very long and beyond any laboratory experiment time scale. In a closed vessel, the glass alteration reaches a saturation state, the nature of which is still under argument (diffusion limitation, dynamic passivation, or thermodynamic equilibrium of the passivating layer).18 Therefore, the need for a basic understanding is crucial to support any long-term extrapolation.17 In this general framework, our group has developed along the past decade a new approach based on the basic observation that the degraded product from a glass is a porous media with a very high specific surface. This large specific surface multiplies the surface of exchange by a factor up to a few hundred.19 As the dissolution is intrinsically a surface phenomenon, it is guessed that the way the internal surface develops with time depends not only on the rate at which the glass dissolves but also whether the dissolution is congruent or not.20 Indeed, the constitutive elements of the glass do not play the same role: for instance, silicon and boron act as glass formers, whereas sodium and calcium act as modifiers. Then, the initial dissolution of a glass depends on the ratio glass formers/glass modifiers such as the silica content or the B2O3/ Na2O ratio in a borosilicate glass.21 Although the initial dissolution of the pristine glass probably involves ion exchange,12 the hydrolysis, formation of silanols, and recondensation of the silica network is largely involved in the following steps.22,23 Experiments combined with Monte Carlo simulations have shown that a better criterion for durability is based on the partition of the glass components into three classes such as soluble (B or Na, for instance), partially
10.1021/jp075268s CCC: $40.75 © 2008 American Chemical Society Published on Web 01/15/2008
Dissolution of Oxide Glasses soluble (Si in particular), and weakly soluble atoms (Zr or Al in the pH range 6-9).24,25 The morphology of the altered layer is linked to the content of soluble atoms and to the hierarchical dissolution of the partially soluble atoms with different network bonds.19 A drastic change of alteration regime and morphology can be observed when the amount of soluble elements is such that water can find a percolation pathway through the sample by exchanging these atoms. Also, our discussion is limited to the intermediate steps of dissolution where the alteration is limited to surfaces in the presence of an aqueous solution. This does not involve the deep alteration within long times (geological) or interaction with surrounding media. In such cases, the elements dissolved from the glass will be retained in the secondary phases formed by reprecipitation of the dissolved species,26 and the increasing thickness of the altered layer causes the diffusion in the altered layer to become the limiting parameter.18,27 Although earlier works mentioned the change of morphology during glass alteration with water,28 small-angle X-ray scattering (SAXS) has been quantitatively used only recently to probe the nanostructure of altered layers developed at the surface of micrometric grains.28 For these micrometer-size powders studied in transmission geometry, average values of the morphological characteristic of the altered layer, like the pore volume fraction and the specific surface, can be obtained. However, it is necessary to check whether a proper geometry with flat samples would yield similar results. The initial step of the glass alteration that is related to ion exchange has been studied by X-ray reflectometry in a simultaneous work.29 The present work concerns the formation of the porous layer associated with the incongruent dissolution of all elements. A first aim of this study is thus the detailed measure of the surface generation kinetics during the very first hours of alteration. It has been known for a long time that the kinetics of glass alteration are scaled to the S/V ratio, that is, the external macroscopic glass surface S exposed to the volume V of solution. However, the exact value of the surface area at each time of the alteration is necessary to measure the kinetics of silicon hydrolysis at the microscopic scale and to compare them to models. The glass compositions have been chosen with a content of soluble elements below the percolation threshold. The effects of some important elements on the durability, the pH, and the addition of zirconium and calcium have been the focus of this work from the chemical point of view. A second aim of the present work is to propose a way to access these values using the geometry of a flat macroscopic monolith. Indeed, this simple geometry is more realistic for lots of applications. Moreover, it could offer a chance to obtain a better spatial resolution and, particularly, to measure structure gradients perpendicular to the surface. GISAXS is a technique perfectly suited to the study of thin layers on flat surfaces.30,31 Nevertheless, it is used in general for dry surfaces under vacuum. In the case of glass alteration, the water has to be present during the analysis since the capillary forces can corrupt the structure of the altered layer during drying. Furthermore, altered layers of glass are disordered nanoporous materials and the scattering signature will not present any clear correlation peak characteristic of a well-defined structure. Thus, GISAXS has to be used at a quantitative level dealing with the treatments of images showing only diffuse bumps. A methodology for the analysis of such signals is introduced, and the equations giving the specific area, the porous fraction, and the thickness of the porous layer are given. The possibility to detect chemical and morphological gradients is discussed. Finally, the results obtained
J. Phys. Chem. C, Vol. 112, No. 5, 2008 1595 TABLE 1: Molar Composition and Density of the Glasses Studied ref 1-Zr 2-Zr 3-Zr 1-Ca 2-Ca 3-Ca 1-CaZr 2-CaZr 3-CaZr
SiO2
B2O3
Na2O
CaO
ZrO2
density
70 69.3 68 66.7 70 70 70 69.3 68.6 66.7
15 14.9 14.6 14.3 15 15 15 14.9 14.7 14.3
15 14.9 14.6 14.3 14 13 10 13.9 12.7 9.5
0 0 0 0 1 2 5 1 2 4.8
0 1 2.9 4.8 0 0 0 1 2 4.8
2.56 2.58 2.63 2.67 2.47 2.44 2.38 2.51 2.51 2.51
on glass monoliths using this methodology are compared to those previously obtained by SAXS on powders in order to validate the model and to evaluate the influence of the sample geometry. All this methodology was developed with in situ measurements. The text is organized as follows: In Materials and Methods, the glass compositions are presented together with the alteration modes. Then, the way the GISAXS data have been recorded and treated is presented together with the equations used to extract the important physical parameters (specific surface area, porous fraction, thickness of the porous layer, presence of a gradient through depth). In Results and Discussion, the two types of experiments (batch and in situ) are detailed with quantitative results for both chemical and morphological aspects of alteration. The study aims at understanding the influence of (i) the morphology of the sample (monolith compared to powder), (ii) the mechanism of formation of the layer (in situ experiments), and (iii) the effect of the pH and of Ca and Zr on the characteristics of the altered layer. Finally, in Conclusion, the morphology dependence on both the composition and the time is discussed in the framework of a recent model. II. Materials and Methods Composition of the Glasses. The glasses studied were all derived from the molar composition SiO2/Na2O/B2O3, 70:15: 15. In a first series (1 to 3-Zr), zirconium was added to the reference composition. In a second series (1 to 3-Ca), one part of the Na atoms was replaced by Ca atoms, and in the last series (1 to 3-CaZr), in addition to the substitution described previously, one part of Si atoms was replaced by Zr atoms. Table 1 collects the composition of these different glasses together with their density. The glasses were fused from initial mixtures of oxide or carbonate powders (SiO2, ZrO2, H3BO3, Na2CO3, and CaCO3; all Prolabo chemicals) at 1550 °C for 4 h and poured into a graphite crucible. Afterward, one part of the glasses was crushed and sieved through a multiple stage column in order to get powders. For Ca and CaZr series, the fraction between sieves of mesh size 40 and 100 µm was collected and yielded powders with a specific surface area of 0.075 m2/g (obtained by krypton BET). For the Zr series, the chosen mesh size of the sieves were 32 to 50 µm, yielding powders with a specific surface area of 0.30 m2/g. Using the remaining parts of the fused glass cylinders, we cut monoliths of radius 1.5 cm and thickness 0.25 cm. These monoliths were polished at the optical level. Every monolith develops a polished surface area of 16 cm2. Alteration Modes. Two types of experiments were performed. First, prior to the venue at the European Synchrotron Radiation Facility (ESRF) in Grenoble, some monoliths have been altered in batch experiments for 1 month. Second, in situ alterations were performed on monoliths directly under the X-ray
1596 J. Phys. Chem. C, Vol. 112, No. 5, 2008 beam on the goniometric head of the BM32 line allowing the geometrical orientations required for GISAXS experiments. Batch Experiments. The alterations of the glass monoliths were carried out under static conditions at 90 °C (in order to decrease the alteration time to reasonable values), either in MilliQ water (nonbuffered solutions) or in buffered solutions (pH ) 9.0 and 9.65). The buffered solutions were prepared with TRIS (tris hydroxymethyl-aminomethane) as follows: solution at pH ) 9, 8.07 g of TRIS and 7.6 g of a solution 1 M of HCl were introduced in a flask of 1 L, completed with MilliQ water; solution at pH ) 9.65, 8.07 g of TRIS, 500 mL of a solution 5 × 10-2 M of K2CO3, and 20 mL of a 1 M solution of HCl were introduced in a flask of 1 L, completed with MilliQ water. As classically known,32,33 a key parameter controlling the kinetics of alteration is the ratio between the total surface of glass and the volume of liquid S/V. For these batch experiments, it was fixed at 20 cm-1 since it was shown that the dissolution of silica saturates after 0.5 months for that type of glass in these conditions. As monoliths have a very weak surface, this high ratio imposes to add micrometric glass grains of same composition in the alteration Teflon container. In a typical experiment with Ca and CaZr glasses, a glass monolith plus 780 mg of the corresponding powder and 30 mL of solution were introduced in a Teflon container. The whole system was then left for 1 month at 90 °C before the analysis. First, the concentrations of dissolved ions were measured by chemical analysis. Then, the nanostructure of the altered layer supported on the monolith was characterized by GISAXS without drying the sample. In order to do so, a special cell was designed. It was able to handle the sample under water (at ambient temperature at which the alteration is kinetically extremely slow) and could be put in the beamline of the GISAXS experiments. In Situ Experiments. One main objective of the work was to follow with GISAXS the in situ alteration of monoliths up to the apparent saturation of silicon in solution. Two monoliths (1-Zr and 2-CaZr) were chosen because they were typical for the compositions effects. In order to limit the time of each experiment (since it required a continuous use of the synchrotron line) to 20 h the S/V ratio was increased up to 50 cm-1. Again, powder of the same composition had to be present in the cell in addition to the monolith to control this S/V ratio. Furthermore, these experiments required a second cell especially designed to support a liquid temperature of 90 °C. The cell was equipped with Kapton windows to allow the beam to pass through. To increase its chemical resistance, the cell was made of copper, and the interior of the cell was plated with gold. A self-adhesive heater fixed on the main outer wall of the cell provided the external source of heat. The water temperature inside the cell was controlled by a Pt-100 probe going through the top of the cell. Chemical Analysis. Silicon, boron, and calcium were titrated in solution with colorimetry kits using a WTW (Wissenschaftlich-Technische Werkstatten Gmbh) Photolab S12 spectrophotometer. For silicon, the solutions were first heated for one night at 90 °C in order to dissolve potential colloidal particles. Sodium was titrated by flame absorption spectroscopy. The accuracy of the measurements was estimated at 10% for every element. GISAXS Setup. The experiments were performed on the BM32 beamline at ESRF. The two experimental cells could be positioned onto the goniometric head allowing the precise orientation of the sample through classical procedures. Indeed, in a GISAXS experiment, the X-rays penetrate with a grazing incidence of the order of 1 mrad, and only the surface of the
Sicard et al.
Figure 1. Morphological definitions of the altered layer.
sample is therefore illuminated. In the present case, the beam print on the sample was 30 mm in the longitudinal axis and 70 µm in the transverse direction. The angle of incidence was varied from 0.06° to 0.12°. This always secured a complete illumination in the longitudinal axis. The scattered beam was recorded on a two-dimensional charge coupled device (2D-CCD) camera cooled by a double Peltier system, located at a distance of 100 cm from the sample. A primary vacuum chamber was placed between the sample and the detector, and the direct beamstopper in T shape was fixed inside this chamber, close to the outer Mylar window to avoid the scattering of this window. All of the experiments were carried out with an energy of 27 keV. III. GISAXS Analysis The analysis, at the absolute scale, of the scattering by a porous layer on the top of pristine glass is not very classical and deserves a full and detailed presentation before the results can be presented and discussed. This is the aim of this section to explain how the raw data, that is, counts on the detector, can be linked to geometrical characteristics of the porous layer such as the volume fraction and the specific surface. Morphological Definitions. The different physical properties of the sample are defined in Figure 1. The external medium is water with a refractive index nw ) 1 - δw - iβw. For the pristine glass, n3 ) 1 -δ3 -iβ3. The altered layer is a porous material made of water (w) of volume fraction φ and of a residual solid (sk) of volume fraction (1 - φ) with a composition supposed to be different from the pristine glass. Using the absorption coefficient µi ) (4πβi)/(λ) and the electron density of the material Fi linked to ni by δi ) (λ2)/(2π)reFi where re is the classical electron radius, one can obtain the average electron density of the material F2 and its average absorption coefficient from those of the layer components:
F2 ) φFw + (1 - φ)Fsk
(1a)
µ2 ) φµw + (1 - φ)µsk
(1b)
Surface Scattering versus Bulk Scattering. The scattering of the pristine surface is very weak as compared with the scattering from the altered layer. Nevertheless, when an altered layer is present on the top of the pristine glass, the scattering signal may also come from the two interfaces (water/layer and layer/glass) which become rough during the alteration. Moreover, the surface roughness is coupled with the layer density fluctuation, and they are contributing to the scattered signal in the same range of q. Therefore, this situation is complex and not easily handled from the theoretical point of view. However, the layers that are considered are thick (500-1000 nm), allowing one to assume that the volume contribution dominates the total scattering. The calculations will be done within the distorted wave Born approximation (DWBA).34,35 In the DWBA model, the refractions at the interfaces are taken into account together with transmission at the interfaces and absorption in the altered
Dissolution of Oxide Glasses
J. Phys. Chem. C, Vol. 112, No. 5, 2008 1597 Nevertheless, one can only measure the apparent scattering vector:
b q ) [k Bsc - B k i]
Figure 2. Angles and wave vectors definitions in the GISAXS configuration.
TABLE 2: Electronic Density (G) Real (δ) and Imaginary (β) Contribution to the Refractive Index at 27 KeV for Water and 1-CaZr Pristine Glass water pristine glass
δ (27 keV)
β (27 keV)
0.33 0.7
3.64 × 10-7 7.73 × 10-7
1.8 × 10-10 5.13 × 10-9
layer. The refraction induces (i) an interfacial transmission coefficient t12 and (ii) a shift in the q value for an elementary scattering process when counted in the material and when observed from the outside medium. When the interface is too rough, these corrections can be neglected. Nevertheless, the two corrections due to refraction are linked since they come from the same phenomenon. The first step in DBWA is to define a reference state from which perturbations will be calculated. A natural solution for the reference state is to take a smooth interface between water and a “homogeneous” altered layer. In that case, the refraction will be calculated using the average density and absorbing properties of the altered layer. The perturbation to the reference states consists in the presence of porosity inside the alteration layer. The values of the different parameters used in the analysis are presented in Table 2 for water and for the typical glass 1-CaZr. They yield an initial critical angle of 0.052° for the water-glass interface. Assuming a residual solid equal to the pristine glass and a porosity of φ ) 0.5, the critical angle θc,1,2would go down to 0.037°. Scattering Cross Section of the Altered Layer. In the framework of DWBA, the intensity of the GISAXS signal can be expressed as the scattering cross section (dσ)/(dΩ) (q bt) of the full layer of volume V ) z0*A which can be written as:
dσ (q b) ) dΩ t r2e
Indeed, this scattered intensity is recorded on a 2D CCD detector located at a distance D from the sample along the y axis. A pixel on the camera corresponds to a scattering axis Ψ,θsc. The line defined by z ) 0 is attributed to the horizon of the sample, and the line of pixel defined by x ) 0 is attributed to the intercept of the camera with the incident plane. Within the small angle approximation, one gets:
qx )
F (e/Å3)
|tin| |tsc|
2
r δF(b′) r e ∫∫ dbr db′r δF(b)
i(q bt .b r -b q *t .b′) r
(2)
V
where |tin|2 and |tsc|2 are the transmission coefficients when going from water to the material layer under the incident and scattered angles θin and θsc. Because of refraction, four wave vectors have to be defined: B ki incident wave vector outside the material layer; B kt incident wave vector inside the material layer; B kt,sc scattered wave vector inside the material layer; andk Bsc scattered wave vector outside the material layer. Angles and wave vector are defined in Figure 2. The elementary scattering process appears in the material layer with a scattering vector
Bt,sc - B k t] b q t ) [k
(3a)
2π x 2π cos(Ψ) ) λ λ D
[ ]
(4a)
2 2 π zi - z π ) [θ2i - θ2sc] qy ) 2 λ λ D
qz )
[ ] [
2π z - zi 2π z + θi ) λ D λ D
]
(4b)
(4c)
where zi is the altitude of the direct nonrefracted beam. Along the camera axis x, qx is the unique component to vary; meanwhile, qy or qz are both evolving along the line z. This means that two axis of fluctuations of the density in the material are probed with a unique axis on the camera. This might be a problem for the analysis. Fortunately, the fluctuations ranges that are observed are not the same for qy and qz as revealed by eq 4: for a given z, qy , qz. With the geometry (extension of the camera equals 65 mm) involved in the present system, there are no experimental volume fluctuations in the qy range which is probed (0-0.02 nm-1). The next step is to introduce the correction of refraction in the scattering vector coordinates to go from (dσ/dΩ)(q b) which is measured to (dσ/dΩ)(q bt) which is the only intrinsic characteristic of the layer. The observation, that the difference between q and qt does not depend on Ψ, means that the refraction implies only a z correction on the CCD image. Nevertheless, this correction has to be done directly on the image before any radial averaging. From the pixel coordinates (x,z), b q is first calculated using eqs 4. Then the coordinates of scattering vector b qt inside the altered layer are deduced for each pixel using:
qt,x,y ) qx,y qt,z )
2
(3b)
2πn2 [sin(θt) - sin(θt,sc)] λ
(5a) (5b)
with θt and θt,sc being deduced from θi and θsc through refraction laws. Initial Data Treatment. Before going further in the analysis of the link between (dσ/dΩ)(q bt) and the structure of the altered layer, some preliminary treatments of the raw image have to be done. Indeed, additive terms are present in the total intensity received by the detector, and they have to be subtracted. First, the total contribution on the detector coming from the sample ∆N/∆Ω in counts/s per solid angle is
dσ ∆N ) KNΦ0 T ∆Ω dΩ w
(6)
where Φ0 represents the flux of photons (in counts/s per surface unit perpendicular to the direction of propagation) and Tw being the transmission coefficient through a path L of upper liquid medium. KN is the normalization constant (equal to the ratio of
1598 J. Phys. Chem. C, Vol. 112, No. 5, 2008
Sicard et al.
the efficiency of the detector by the efficiency of the monitor counting Φ0). It is obtained using a standard such as Lupolen in classical transmission mode on the same setup:
∆NLupo 1 ) KN TLupoΦ0 eLupoILupo ∆Ω
Im(kt,sc,z) ) (7)
with eLupo ) 0.3 cm being the thickness of the reference and ILupo ) 6 cm-1 for q ) 0.3 nm-1 the reference value. Once Φ0 and ∆NLupo are measured, the constant can be deduced. Indeed, the liquid medium where the X-rays propagate absorb both the incident and the scattered lights. In the approximation of small angles, the total path in the upper medium is always L (length of the cell 30 mm). Thus, Tw ) e-µwL with µw the absorption coefficient of water. The altered layer is not the only source of scattered intensity received on the camera detector; the medium above the sample also scatters. The total contribution on the detector from the solvent is simply:
∆Ns dΣ ) Φ0 VsTw ∆Ω dΩ
(9)
Finally, there is also a fluorescence contribution, for some glasses, mainly due to the presence of Zr in the altered layer (the Zr K-edge is at 18 keV). ∆Nexp 1 dΣw 1s ∆NFluo dσ 1 ∆NFD - Vs (q b) ) dΩ t ∆Ω TwΦ0 dΩ Φ0 ∆Ω Φ0Tw ∆Ω
(10)
The last contribution slightly depends on q for a given incident angle. As it contributes only when the scattering signal is weak, that is, at large angles, its q dependence can be neglected, and it is considered as a constant to be substracted after the radial average (this constant depends on the incident angle). In practice, every data matrix is first subtracted from the electronic background then corrected from distortion. Then, the water contribution and direct contribution are subtracted. The fluorescence background contribution is subtracted after the azimuthal average which is performed as explained in the next section. DWBA Analysis. Coming back to eq 2, the complex nature of the scattering vector (due to the absorption part of the refraction index) can be introduced: dσ (q b) ) dΩ t r2e |tin|2 |tsc|2
∫∫dbr db′r e
-Im(q bt)(b+ r b′) r
r b′) r δF(b) r δF(b′)e r iRe(qbt).(b(11)
V
with Im(q bt)(r b + b′) r ) [Im(kt,sc,z) - Im(kt,z)]*(z + z′). The full expression for the Im(kzt ) is given in reference books.36 When the incident angle θi is large enough and satisfies the condition |θ2i - θ2c | . β2 - βw, θc being the critical angle of the interface and β being the difference of absorption between the
∆µ 2θt,sc
and
Im(kt,z) )
∆µ 2θt
(12)
with ∆µ ) (1 - φ)(µsk - µw). The above conditions are fully satisfied in the present experiment using θi ) 0.08°, λ ) 0.46 Å, θc ) 0.04°, the β values reported in Table 2, and the collecting data with an exit angle above the critical angle. The layer is thick, the correlation relevant only on a length scale δ, so there is a large amount of volume where δ < z; in the attenuation factor, z′ can be replaced by z. In that case, one gets
dσ (q b ) ) |tin|2|tsc|2 dΩ t
∫Vdbr e∆µ z[(θ
t,sc-θt)/(θtθt,sc)]
Iabs(q bt,b) r
(13)
with
bt,b) r ) Iabs(q
(8)
Vs being the total volume illuminated by the direct and reflected beams and dΣ/dΩ is the intensity scattered by a unit volume of water. At low angle, the small divergence of the incident beam also contributes by some direct wings which have to be corrected. This can be measured when the cell is empty:
∆NFD T ∆Ω w
two media (water and altered layer), the expression can be simplified to
r b′) r r b)δF( r b′) r eiRe(qb )(b∫Vdb′δF( t
(14)
being the scattering cross section per unit volume at the position r in the altered layer. When Iabs(q bt,r b) depends on b, r the integration in eq 8 has to be performed. When Iabs(q bt,r b) does not depend on b r (meaning in particular that there is no gradient perpendicular to the surface), the above integral can be simplified:
dσ (q b ) ) |tin|2|tsc|2Iabs(q bt)A dΩ t
∫-Z0 dz e∆µ z[(θ
t,sc-θt)/(θtθt,sc)]
(15)
0
The last integral corresponds to an effective thickness zeff of the sample, which slightly depends on the geometry of the experiment
dσ bt)Azeff(qz,t,θt) (q b ) ) |tin|2|tsc|2Iabs(q dΩ t
(16)
It has to be noticed that the first term |tin|2 depends on θin, and the second term |tsc|2 depends on θsc. Finally, for an infinitely thick layer, the effective thickness is
zeff )
[
]
1 2π θt θt 1 ∆µ λ qz,t
(17)
and for a finite thickness, there is a trivial additional term:
zeff )
[
]
1 2π θt θt 1 (1 - e-∆µ z0[1/θt(1-(2π/λ)(θt/qz,t))]) ∆µ λ qz,t
(18)
It is clear that zeff ≈ z when the thickness is very small. It appears that zeff is not constant along a circle around the center of the direct beam. Nevertheless, it depends only on the z altitude. To be calculated, zeff(qz,t,θt) requires the knowledge of the incident angle, the thickness z, and the absorption coefficient of the layer (which also depends on the density of the skeleton, its composition, and the volume fraction of water pores). The matrix (dσ/dΩ)(q bt) is therefore divided by the matrix |tin|2|tsc|2Azeff(qz,t,θt) before the radial averaging which is finally performed in order to get Iabs(q bt). When there is no gradient in the structure of the altered layer, the treatment proposed by eq 16 should deliver a centrosymmetric image independent of the incident angle. This will be shown to be the case in the results section. The influence of the different levels of treatment has been tested and is provided in annex. The results show that (1) omitting the contributions from refraction or absorption yields
Dissolution of Oxide Glasses
J. Phys. Chem. C, Vol. 112, No. 5, 2008 1599 The total mass of the skeleton is obtained from the titration of extracted elements:
msk S Figure 3. Relationship between leaching of elements and thickness of the altered layer.
corrupted P(q) data and (2) the theoretical calculation of the scattering by a layer composed of two sublayers with a same pore volume and different pore size does not depend on the incident angle. It is very difficult to measure that sort of gradient in the present system and beam energy. But in the results section, the absence of influence of incident angle will be tested in order to check that the whole procedure of scaling is correct. Link with the Geometrical Definitions. The alteration is done in a solution volume V with an initial geometric surface of the glass S. For every element i of the glass, one can define an equivalent thickness of glass from which it is totally extracted: sol
ei )
V ci S cg
and cgi are the mass concentration (expressed in where csol i 3 g/cm ) of the element i in the solution and in the glass. The mass concentration of the element i in the glass is obtained from its mass percentage mgi and the glass density (Fg in grams per cubic centimeter)
cgi ) mgi Fg Because of the noncongruent loss of elements, the equivalent thickness of glass removed is not the same for all elements. The largest equivalent thickness is always the one associated with B or Na. In the present case, the two values are always very close. Usually, boron is considered as an alteration tracer as it is totally soluble.37 A recent model is to consider that the silicon in solution comes only from a totally dissolved layer (Figure 3). Thus, silicon is considered to be present in the porous layer with the same spatial concentration as in the pristine glass. Consequently, an altered layer thickness zc can be calculated from the difference between the equivalent thickness of leached boron and the equivalent thickness of leached silicon by formula:
S V
(
csol B cB0
-
)
csol Si c0Si
(19)
After the alteration, the alteration layer has an experimental thickness of z (which will have to be compared to zc). The total mass of the skeleton per unit surface is msk/S and its density is dsk. Therefore, the volume fraction of pores can be written as:
msk Sdskz
( ) csol B c0B
-
csol i
(21)
c0i
with c0i being the concentration of the element of type i in the pristine glass, Mw,i is its molar mass, and csol i is the concentration of extracted element i in solution. One must specify that the summation (eq 21) contains the contribution of oxygen. The total amount of oxygen released by the glass cannot be measured, but it is calculated assuming that all elements are removed as oxides (Na2O, B2O3, SiO2, ...). From the SAXS analysis, one gets:
Q)
∫ IAbs q2 dq ) 2π2Φ(1 - Φ)(Fesk - FHe O)2 2
(22)
where Fesk and FHe 2O are the scattering length density of the skeleton and the water, respectively. As already mentioned, Iabs depends directly on z, Φ, and Fsk (through ∆µ). In addition, there is a last subtle point which is that the contrast in scattering length density between the skeleton and the liquid depends on Fsk.
∑niZi - Fe HO ∑niMw,i 2
(23)
where LT is the electron scattering length (2.82 × 10-15 m) and ni is the molar fraction of element i in the skeleton. Therefore, for an assumed dsk, there is a unique z for which the values of Φ calculated by the two eqs 20 and 22 are identical. Anyway, there is not a unique couple (dsk,z) able to fit the data. Once the absolute intensity is known, the specific surface Σsk (square meters per gram) of the porous layer can be deduced using the Porod relation:38
lim IAbsq4 ) 2π(Fesk - FHe 2O)2(ΣskFsk)
(24)
In summary, the density of the skeleton dsk is first fixed (equal to that of the pristine glass). Then, the important parameters which can be extracted are (1) the equivalent chemical thickness of the corroded layer zc equal to the equivalent thickness of leached boron minus the equivalent thickness of leached silicon, (2) the thickness of the corroded layer z obtained from initial GISAXS treatment at different angles, (3) the porous volume fraction obtained from eq 22, and (4) the specific surface area of the porous fraction obtained from eq 24. IV. Results and Discussion
assuming that zMax ) eB.
Φ)1-
∑i V
c0i Mw,i
∆F ) Fske - FHe 2O ) LTdsk
i
zc ) eB - eSi ) )
)
S
(20)
Comparison between Alteration on Monoliths and on Powders. The new opportunities offered by GISAXS were checked by comparing the characterization of an altered layer at the surface of monolith with the more classical characterization of altered layers at the surface of grains.19 Experiments at two different angles of incidence were performed on the glass 2-Zr altered for 1 month. First, a raw image is shown in Figure 4a where refraction effects are evident close to the horizon of the sample. This delivers a noncentrosymmetric experimental image. Assuming initially that no gradient was present, the procedure proposed in eq 16 was applied. The resulting image, plotted in Figure 4b became centrosymmetric. The treatment was done at two different angles. As the corrected images were
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Figure 5. Comparison between SAXS analysis of altered powders and GISAXS of altered monoliths. The intensities are defined for a unit volume of altered layer in both cases (SAXS data, lines; GISAXS data, symbols).
Figure 4. Illustration of the data treatment of a GISAXS image. The raw CCD image (a) shows a distortion along the z axis. After subtraction of the solvent contribution and the different geometric corrections (absorption, refraction, and fluorescence), the image becomes centrosymmetric (b). Two radial averages after correction at two different angles yield the same absolute scattering (c) for the two different incident angles 0.06° (in gray) and 0.12° (in black; the intensities are not yet normalized by the Lupolen factor).
centrosymmetric, a radial averaging could be performed. The resulting SAXS diagrams are shown in Figure 4c. The very good overlap between the curves obtained at two different angles confirms the idea that no measurable composition gradients are present (within the sensitivity of the experiment). This case was reproduced for all of the samples and alteration times. This indicates that the simple treatment proposed by the use of eq 16 is valid for every sample in this work and allows us to obtain the average structure of the altered layer. The next step was to quantitatively compare the structure obtained at the surface of monoliths to the one obtained at the surface of the grains for the same alteration conditions. A previous work had reported the SAXS measured on powders of the same Zr series altered at 20 cm-1 in MilliQ water.39 Comparisons between monoliths and grains can thus be made quantitatively. The scaled scattering GISAXS diagrams of 1 and 3-Zr altered monoliths are plotted in Figure 5 together with the SAXS diagrams previously obtained on the same systems. The curves overlap well both in form and in intensity. This proves that the same porous structure is found, with a similar pore diameter, specific surface area, and porous volume fraction. This also validates the quantitative GISAXS treatment for the extraction of the values of the specific surface of pore fraction. Table 3 gives the correspondence between the powders and the monoliths features found in the cases of 1-Zr and 3-Zr. Again, we stress that, in every case described in this paper, the curves obtained at different incident angles varying from
Figure 6. GISAXS diagrams obtained during the alteration of 2-CaZr at 50 cm-1. The data are plotted in intrinsic scattering cross section per unit surface of the sample (no dimension thus).
TABLE 3: Comparison between the Alteration Features (Density of the Skeleton, Thickness of the Altered Layer z Compared with the Equivalent Thickness of Boron zmax, Porous Fraction O, and Specific Surface Area Σ of Monoliths and Powders 1-Zr z0 [µm] r ) z/zmax φ Σ (m2/g)
3-Zr
monolith
powder
monolith
powder
1.48 0.79 0.24 150
0.72 0.25 145
0.37 1.00 0.33 450
0.98 0.28 425
0.06 to 0.12° superimpose. This means that the altered layer is homogeneous both in structure and in chemistry. Using SAXS is much easier than GISAXS from many points of view, but the advantage of GISAXS over SAXS is to always probe the same part of the glass during kinetics studies. In addition, the GISAXS measurements allow an accurate determination of the altered thickness in a clean geometry (flat surface). In Situ Experiments. The glass named 2-CaZr was altered in MilliQ water at a S/V of 50 cm-1 directly under the X-ray beam. The evolutions of the treated signal with q and time are reported in Figure 6. Again, treatments at two different incident angles yield the same results showing that it is not possible within the sensitivity of the experiment to detect a structure gradient perpendicular to the surface at any time of this shortterm alteration.
Dissolution of Oxide Glasses
J. Phys. Chem. C, Vol. 112, No. 5, 2008 1601 TABLE 5: Values of Final pH and Equivalent Thicknesses of Na, B, and Si in Solution after Alteration for 1 Month at 90 °C in Water at Various pH (S/V ) 20 cm-1) final pH eNa [µm] eB [µm] eSi [µm] initial pH ) 9.0
Figure 7. Leaching kinetics of silicon, boron, sodium, and corresponding total oxygen as a function of time.
TABLE 4: Kinetics of Evolution of the Thickness (z) of the Altered Layer Measured by GISAXS (z) and That Estimated by the Chemical Method (zc); Porous Volume Fraction, Specific Surface, and Equivalent Pore Radius of the Glass 2-CaZr Altered in MilliQ Water at 50 cm-1 a time (h)
z (nm)
zc (nm)
φ
Σ (m2/g)
3Φ/Σ (nm)
4 6,5 15 20
107 141 301 353
113 139 288 292
0.19 0.24 0.28 0.38
274 347 325 393
0.8 0.8 1 1.2
a Results are obtained assuming a density of 2.6 for the resulting skeleton.
Three main conclusions can be drawn. First, a signal is measurable in the q range of the experiment. This shows that the altered layer is a nanostructured material. The second important point is with regard to the behavior at large q. Indeed, a very well-defined q-4 regime is obtained even after only 3 h. This Porod regime is the signature of an abrupt interface in the medium between at least two phases. This strongly supports the description of the altered layer as a porous material where a true solid phase (the residual dense skeleton) is in direct contact with the interstitial water and ions. The remarkable last point is that the q dependence does not evolve with time. Indeed, after 3 h, the signal rises almost equally at every q with no shape deformation, meaning that the internal structure remains always the same but with a proportion of altered volume which increases. For given durations, the alteration was repeated in the laboratory in order to obtain the concentrations of each ion leached in the solution. The results of these chemical analyses are reported in Figure 7. The concentration of silicon in solution increases during the first 6 h and then saturates. On the contrary, the concentrations of both sodium and boron still increase after 20 h and therefore do not reach a constant value on the time scale of the experiment. Finally, no calcium or zirconium were found in solution: both ions appear to be insoluble at the pH of the experiment. The chemical titrations measurements were used together with the GISAXS results as explained in the treatment section to extract the exact thickness, the specific surfaces, and pore volumes of the altered layer. The results are reported in Table 4. The thickness of the altered layer increases quickly during the first hours of the experiment. After 15 h, the alteration slows down. While in the first part of the alteration the thicknesses calculated by GISAXS and by the chemical model agree very well, in this second part of the kinetics, the equivalent chemical thickness is lower than the one measured experimentally. This indicates that a rearrangement of the structure occurs at this
2-Zr 3-Zr 1-Ca 2-Ca 3-Ca 1-CaZr 2-CaZr 3-CaZr initial pH ) 9.65 2-Zr 3-Zr 1-Ca 2-Ca 3-Ca 1-CaZr 2-CaZr 3-CaZr
9.3 9.2 9.5 9.4 9.3 9.4 9.3 9.1 9,6 9.6 10.1 9.9 10.1 9.9 9.9 9.9
0.139 0.069 1.058 0.881 1.012 0.898 0.546 0.260 0.182 0.120 1.244 1.146 1.459 1.545 1.338 0.667
0.185 0.102 1.145 0.930 1.179 1.088 0.693 0.350 0.234 0.178 1.342 1.352 1.517 1.616 1.446 0.650
0.025 0.019 0.168 0.147 0.066 0.127 0.075 0.067 0.022 0.020 0.330 0.276 0.336 0.189 0.127 0.111
stage resulting in a thicker but more porous layer.40 This is confirmed by the porous fraction value which progressively increases with time together with an increase of the specific surface of the layer. On the contrary, the equivalent pore radius is almost constant (which is a direct expression of the conservation of the shape of the diagrams with time). The insolubility of zirconium probably plays an important role in the difference between the two values of thickness, preventing the shrinkage of the glass.39,41 Finally, the porous fraction tends toward the equivalent volume of oxygen linked to the Na and B atoms in the pristine glass. Influence of the Composition and pH Over the Alteration of Glass. For an S/V ratio equal to 20 cm-1, the alteration slows down after a few days. More precisely, the glasses tend to a quasi-stationary state after 1 month. Consequently, this time of alteration can reasonably be chosen as a reference in order to examine the influences of the pristine composition and of the pH on the alteration kinetics. A first result is that zirconium and calcium are not found in the solution whatever the pH of alteration and the composition of the glass are. Zirconium is probably retained in the altered layer. However, it appears that all experiments with glasses containing calcium give a higher pH. The amount of buffer was not sufficient to fix the pH. Calcium may have dissolved from the glass and reprecipitated as a hydroxide or as a borate. On the contrary, sodium, boron, and silicon atoms are leached from the glass. The concentrations of these three elements have been reported in Table 5 for the various glasses altered at pH ) 9.0 and pH ) 9.65 with the equivalent thickness of glass removed. The equivalent thickness of boron can be considered as the actual thickness of glass leached (zmax). It is an indicator of the glass durability, and it has been plotted as a function of the zirconium content for glasses containing also Ca or not and at different pH (Figure 8). The points corresponding to Zr ) 0% are those obtained on the series with calcium only (Ca series). In this pH range, the solubility of silica strongly depends on the pH value. Zirconium has a strong positive effect on the durability of the glass whatever Ca is present or not. For the CaZr glasses, the equivalent thicknesses are higher than for the Zr series. This is probably more an effect of the higher pH of the leached solution than of Ca in the structure. The role of zirconium has already been discussed in previous works. It is well-known to enhance the durability of glass in alkaline solutions.38 It acts as a hard network former difficult to dissolve. Indeed, Zr inserts in the glass with a sixfold coordination of oxygen shared with other network formers (Si,
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Figure 8. Equivalent thickness layer of glass zmax (maximum of equivalent thickness of boron) as a function of the Zr content.
TABLE 6: Results of the GISAXS Analysis after 1 Month of Alteration at S/V ) 20 cm-1 for Samples 1 to 3-CaZr: Maximum Altered Thickness (zmax), Thickness of the Altered Layer Determined by GISAXS (z), Dissolution Ratio: r ) z/zmax, Specific Surface Area (Σ), and Porous Volume (O) of the Altered Layer where the Last Column Summaries, as a Matter of Comparison, the Values of the Altered Layer Thickness zc Calculated from Chemical Considerations pH
reference zmax (µm) z (µm) r ) z/zmax ∑ (m2/g)
9.0
1-CaZr 2-CaZr 3-CaZr 9.65 1-CaZr 2-CaZr 3-CaZr
1.088 0.693 0.350 1.616 1.446 0.667
0.98 0.60 0.32 1.20 1.20 0.60
0.90 0.87 0.91 0.74 0.83 0.90
170 250 270 100 185 260
φ
zc (µm)
0.29 0.22 0.22 0.15 0.18 0.22
0.96 0.62 0.28 1.43 1.32 0.56
B, ...).23,42 The introduction of [ZrO6/2]2- in the silica network first locally increases the connectivity of the glass network since octahedral units replace tetrahedral ones. Second, it immobilizes two sodium ions for compensation of its charge and thus decreases the proportion of network modifiers. Since Zr is dispersed within the glass, it forms local points, where the dissolution cannot occur or slowly occurs. From a morphological point of view, zirconium prevents the dissolution of the glass because of its insolubility and constitutes preferential sites of recondensation for silicon. Thus, the presence of zirconium results in a decrease of the pore size, implying a larger specific surface area as can be seen in Table 6. On the contrary, higher pH lead to larger dissolution rates of silica. Saturation is reached at higher silica concentration. In the same time, a faster ripening of the porosity occurs,40 and lower specific area are observed for the glasses altered at pH ) 9.65 than those altered at pH ) 9.00. Conclusion A GISAXS methodology was developed to study the flat interface between a corroded glass and water. This method gives access to the specific area, the porous fraction of the corroded layer. In this case, the results are exactly similar to those obtained by conventional SAXS on powders. This shows that, despite the irregular morphology of ground glass grains, the SAXS study of powders, faster and simpler, is also valid. However, in addition to the powders studies, the GISAXS geometry allows us to quantitatively probe the thickness of the corroded layer in a correct geometry as well as to access the thinner altered layers giving access to shorter times of alteration. The in situ experiments carried out on a SiO2/Na2O/B2O3/ CaO/ZrO2 glass reveal that the alteration develops very rapidly a porous layer with a high specific area (100-250 m2/g). The morphology of this porous layer is stabilized as soon as it appears and only its thickness increases. The quantitative extraction of the thickness and porosity confirms that the thickness of the altered layer is directly related to the difference of dissolution between the very soluble elements such as boron
and sodium and the weakly soluble elements such as silicon. The altered layer is a porous silica network formed by the incongruent leaching of sodium and boron and the ripening of the residual oxide network through dissolution and recondensation. Because of faster dissolution kinetics occurring at higher pH, the pore size is larger, and the specific surface area of the altered layer is lower. The addition of Ca, through the pH increase that it causes, leads to a thicker corroded layer. Zr plays a strong role in increasing the durability of the glass. Paradoxically, large amounts of zirconium lead to a more durable glass but with an altered layer which has a larger specific area. Finally, no chemical or morphological gradient was detected through the layer depth. From a general point of view, this work opens new perspectives in the use of GISAXS to probe porous disordered media at the quantitative level. Acknowledgment. The authors are indebted to Franc¸ ois Rieutord and Jean-Se´bastien Micha from the BM32 beam line at the European Synchrotron Radiation Facility for their help during the GISAXS experiments. We also want to thank P. Frugier for the CEA-Marcoule for his help in preparing the monoliths. Supporting Information Available: Additional experimental details. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Scholze, H. Glastechnische Berichte 1988, 61, 161-171. (2) Advocat, T.; Jollivet, P.; Crovisier, J. L.; del Nero, M. J. Nucl. Mater. 2001, 298, 55-62. (3) Lutze, W.; Malow, G.; Ewing, R. C.; J., M.; Jercinovic Keil, K. Nature 1985, 314, 252-255. (4) Trens, P.; Denoyel, R.; Guilloteau, E. Langmuir 1996, 12, 12451250. (5) West, J. K.; Hench, L. L. J. Mater. Sci. 1994, 29, 5808-5816. (6) Etienne, P.; Calas, S.; Portal, S. Phys. Chem. Glasses 2001, 42, 320-323. (7) Michalske, T. A.; Bunker, B. C. J. Am. Ceram. Soc. 1993, 76, 2613-2618. (8) Yokota, H.; Kiyonaga, H.; Kaniwa, H.; Shibanuma, T. J. Pharm. Biomed. Anal. 2001, 25, 1001-1007. (9) Shellenberger, K.; Logan, B. E. EnViron. Sci. Technol. 2002, 36, 184-189. (10) Longnecker, M. P.; Zhou, H.; Klebanoff, M. A.; Brock, J. W. Ann. Epidemiol. 2003, 13, 178-181. (11) Charbonneau, C.; Elias, M.; Frigerio, J. M. Opt. Commun. 2007, 270, 280-289. (12) Sterpenich, J.; Libourel, G. J. Non-Cryst. Solids 2006, 352, 54465451. (13) Messiga, B.; Riccardi, M. P. J. Cult. Herit. 2006, 7, 334-338. (14) Bunker, B. C. J. Non-Cryst. Solids 1994, 179, 300-308. (15) Jantzen, C. M.; Plodinec, M. J. J. Non-Cryst. Solids 1984, 67, 207223. (16) Doremus, R. H. Chemical durability: Reaction of water with glass. In Glass Science, 2nd ed.; John Wiley & Sons: New York, 1994; pp 215240. (17) Vernaz, E.; Gin, S.; Je´gou, C.; Ribet, I. J. Nucl. Mater. 2001, 298, 27-36. (18) Inagaki, Y.; Shinkai, A.; Idemistu, K.; Arima, T.; Yoshikawa, H.; Yui, M. J. Nucl. Mater. 2006, 354, 171-184. (19) Spalla, O.; Barboux, P.; Sicard, L.; Lyonnard, S.; Bley, F. J. NonCryst. Solids 2004, 347, 56-68. (20) Hench, L. L.; Clark, D. E. J. Non-Cryst. Solids 1978, 28, 83-105. (21) Adams, P. B.; Evans, D. L. Chemical durability of borate glasses. In Borates glasses: Structure, Properties, Applications; Pye, L. D., Frechette, V. D., Kreidl, N. J., Eds. Plenum: New York, 1978; Vol. 12, pp 525-537. (22) Robinet, L.; Coupry, C.; Eremin, K.; Hall, C. J. Raman Spectrosc. 2006, 37, 1278-1286. (23) Angeli, F.; Gaillard, M.; Jollivet, P.; Charpentier, T. Geochim. Cosmochim. Acta 2006, 70, 2577-2590.
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