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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Role of Electrochemical Surface Potential and Irradiation on Garnet-type Almandine’s Dissolution Kinetics Yi-Hsuan Hsiao, Erika Callagon La Plante, N. M. Anoop Krishnan, Howard A Dobbs, Yann Le Pape, Narayanan Neithalath, Mathieu Bauchy, Jacob N. Israelachvili, and Gaurav N. Sant J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b04459 • Publication Date (Web): 04 Jul 2018 Downloaded from http://pubs.acs.org on July 7, 2018

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The Journal of Physical Chemistry

Prepared for Submission to the Journal of Physical Chemistry C (July 2018)

Role of Electrochemical Surface Potential and Irradiation on Garnet-type Almandine’s Dissolution Kinetics 1 2 3 4 5

Yi-Hsuan Hsiao (*,a), Erika Callagon La Plante (*,a), N. M. Anoop Krishnan (*,†,‡), Howard A. Dobbs (§), Yann Le Pape (**), Narayanan Neithalath (††), Mathieu Bauchy (†), Jacob Israelachvili (§,‡‡), Gaurav Sant* (*,§§,***)

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Abstract

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Nanoscale resolved quantifications of almandine’s (Fe3Al2(SiO4)3) dissolution rates across a

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range of pH’s (1 ≤ pH ≤ 13) – established using vertical scanning interferometry (VSI) – reveal

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that its dissolution rate achieves a minimum around pH 5. This minimum coincides with

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almandine’s point of zero charge (PZC). These trends in almandine’s dissolution can be

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estimated using the Butler-Volmer (BV) equation that reveals linkages between surface

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potentials and dissolution rates, demonstrating proton- and hydroxyl-promoted breakage of Si–

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O bonds. In contrast with well-polymerized silicates, the dissolution of almandine can also occur

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through the rupture of its cationic bonds. This behavior is reflected in the observed influences

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of irradiation on its dissolution kinetics. Molecular dynamics simulations highlight that

Laboratory for the Chemistry of Construction Materials (LC2), Department of Civil and Environmental Engineering, University of California, Los Angeles, CA, USA † Laboratory for the Physics of Amorphous and Inorganic Solids (PARISlab), Department of Civil and Environmental Engineering, University of California, Los Angeles, CA, USA ‡ Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India § Department of Chemical Engineering, University of California, Santa Barbara, CA, USA ** Oak Ridge National Laboratory, Oak Ridge, TN, USA †† School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ, USA ‡‡ California Nanosystems Institute, University of California, Santa Barbara, CA, USA §§ Department of Materials Science and Engineering, University of California, Los Angeles, CA, USA *** California Nanosystems Institute, University of California, Los Angeles, CA, USA * Corresponding author: G. Sant, Phone: (310) 206-3084, Email: [email protected]

*

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Both authors contributed equally to this work.

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Prepared for Submission to the Journal of Physical Chemistry C (July 2018) 16

irradiation induces alterations in the atomic structure of almandine by reducing the

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coordination state of the cations (Fe2+ and Al3+); thereby enhancing its reactivity by a factor of

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two. This is consistent with the minor change induced in the structure of almandine’s silicate

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backbone, whose surface charge densities produce the observed pH dependence (and rate

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control) of dissolution rates. These findings reveal the influential roles of surface potential

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arising from solution pH, and atomic scale alterations on affecting the reactivity of garnet-type

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silicates.

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1.

Introduction and background

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Almandine (Fe3Al2(SiO4)3) – a nesosilicate mineral and an end-member of the garnet family

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(X3Y2(SiO4)3), consists of isolated silicate tetrahedra connected by cations of mixed valence (X =

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Fe2+, Y = Al3+). It is found in abundance in metamorphic1,2 and igneous rocks.3 For this reason,

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garnet-containing sands find extensive use in engineering applications,4–8 e.g., in the form of

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siliceous mineral aggregates (sand and stone) in concrete – a mixture composed of cement,

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aggregates and water,4 in water filtration5 and as abrasives in waterjet cutting.6,8 Since the

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durability of composites such as concrete depends on the durability of its constituents, there is

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a need to understand how the chemical environment (e.g., solution pH), and external stimuli

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(e.g., radiation), which may induce changes in its structure, may affect its properties. This is of

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special relevance in facilities such as nuclear power plants (NPPs) wherein environmental

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variables – e.g., exposure to irradiation and the alkaline environment – could compromise

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concrete’s chemical durability.9–12

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Almandine is composed of mixed-valence cations (Fe2+ and Al3+) and isolated silicate tetrahedra

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and aluminate octahedra, wherein no O atoms are shared between two Si atoms or two Al

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atoms (see Figure 1). Due to the isolated (non-percolating) nature of the silicate tetrahedra,

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almandine is substantially less polymerized than framework silicates such as quartz and albite.14

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As a result, during dissolution, isolated silicate tetrahedra and aluminate octahedra in

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nesosilicates are released intact from reacting surfaces following protonation (or hydrolysis) of

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bonds between Fe2+ and structural oxygens.15 This is unlike the case of tectosilicates (i.e., which

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feature percolated silicate tetrahedra in which all O atoms are shared between Si atoms) such


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as quartz and feldspar wherein bond hydrolysis needs to occur in the silicate tetrahedra to

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release aqueous silicon species. In addition, almandine’s dissolution is also induced by ion-

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exchange or hydrolysis in acidic or caustic media, respectively, processes which control its

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dissolution behavior as a function of the pH, as typical of complex silicates.16

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Figure 1: The crystal structure of pristine almandine (Fe3Al2(SiO4)3) showing isolated Si tetrahedra (dark blue), Al octahedra (light blue), Fe atoms (yellow) and O atoms (red) as visualized using VESTA.13 66 67

The rate of release of aqueous Si is typically regarded as reflecting a mineral’s dissolution rate.17

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Several studies have shown similarities between the mechanisms of nesosilicate’s dissolution,

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wherein hydrated cations leave a dissolving mineral surface, and ligand exchange reactions, in

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which a hydrated cation complex exchanges with protons or hydroxyls in water.15 In almandine,

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Fe2+ cations detach earliest producing an appropriate charge on almandine’s surface due to the

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remaining Si and Al sites. As such, the observed rates of dissolution reflect the combined effects

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of cation release and pH-dependent hydrolysis. This is significant as surface charge variations as

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a function of pH may offer guidance regarding almandine’s pH-dependent dissolution rates.

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Usually, the disordering of a silicate’s atomic structure, when induced at constant composition

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(e.g., due to pressure, temperature or ballistic shocks), is expected to result in elevations of

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chemical reactivity, as indicated by aqueous dissolution rates—although there are exceptions

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depending on the solution’s composition or the silicate’s atomic structure.18 The vast majority

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of such disordering-induced reactivity amplifications have been studied in framework (i.e.,

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percolated) silicates wherein silicate tetrahedra are intimately connected to each other. It is

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unknown whether silicates consisting of isolated (non-percolating) silicate tetrahedra may show

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similar sensitivity to atomic disordering. In order to better understand these aspects, the

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dissolution behavior of disordered (irradiated) almandine was examined using vertical scanning

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interferometry (VSI) from observations of surface retreat. Molecular dynamics (MD) simulations

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and topological constraint theory (TCT) were used to explain the dissolution trends in the

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context of changes in atomic structure, e.g., in terms of the coordination number, bond length,

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and bond angle distributions. It is shown that nesosilicates feature relatively small changes in

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chemical reactivity following irradiation – since their isolated silicate tetrahedra show little if

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any change in structural connectivity. This behavior is consistent with the dissolution

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mechanism revealed from pH-dependent measurements of dissolution rates. Taken together,

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these new insights offer guidance regarding the role of the electrochemical and ballistic

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environment on affecting the durability of garnet-type silicates in aggressive environments.

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2.

Materials and methods

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2.1. Sample preparation and ion-irradiation


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Naturally occurring almandine was sourced from Ward’s Natural Science Company.19 The

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samples were sliced using a low speed diamond saw (IsoMetTM 1000, Buehler Inc.) into a size of

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1 cm × 1 cm × 1 mm. The pristine (non-irradiated) samples were embedded in a cold-cured inert

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acrylic resin (EpoxiCure Resin, PN 203430128: Buehler Inc.). After 24 hours, the resin-mounted

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samples were successively mechanically polished using 400, 600, 800 and 1200 grit SiC

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abrasives, and then using diamond paste (starting from 6, 3, 1 down to 0.25 µm). The polished

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almandine samples had a surface roughness (Sa) of 100 nm over a field of view (FoV) of 1.3 µm

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× 1.3 µm as assessed using vertical scanning interferometry (VSI).

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In addition, polished samples prepared for Ar+ ion implantation were sent to the Michigan Ion

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Beam Laboratory (MIBL). Ion implantation was conducted using 400 keV Ar+ ions at room

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temperature to a total fluence (dose) of 1.0 × 1014 ions/cm2. Ar+ ion irradiation was selected to

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simulate neutron irradiation in nuclear power plants because it offers precise control of the

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temperature and dose, and is known to result in similar alterations to the crystal structure at

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terminal disordering.20,21 The Ar+ implantation depth was calculated using “Stopping and Range

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of Ions in Matter” (SRIM) to be on the order of 420 nm, assuming the samples are defect-free

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single crystals. The calculation assumes that the density of almandine is 4.30 g/cm3, and that it

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features a composition of Fe3Al2(SiO4)3.22 It should be noted however that the natural

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almandine used herein contains minor impurities such as biotite and amphibole as detected

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using polarized light microscopy (Figure 2), which is expected to result in a penetration depth

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greater than 420 nm. The irradiated almandine samples were then adhered to a cylindrical resin

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mount to facilitate handling.


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(a) (b) Figure 2: Representative polarized light microscopy images of a thin section of the almandine sample shown in: (a) plane-polarized light, and, (b) cross-polarized light showing impurities of biotite and amphibole. The sample is dominantly composed of almandine, as evidenced from petrographic analysis. However, the images shown here represent a magnified region selected to demonstrate the presence of impurities. 120 121

2.2. Material characterization

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2.2.1. X-ray Diffraction (XRD)

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Finely powdered almandine was mounted on a rotating sample holder, and analyzed using

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powder x-ray diffraction (XRD). The diffraction patterns were collected using a Bruker D8-

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Advance powder x-ray diffractometer in θ-θ Bragg-Brentano geometry, using Cu-Kα radiation (λ

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= 1.5406 Å) at an accelerating voltage of 40 kV, and a beam intensity of 40 mA. Each pattern

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was recorded for a total duration of 16 minutes at a step size of 0.02° in the range of scattering

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angles, θ, between 10° to 70°. The XRD pattern of the almandine sample is similar to that of

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pure almandine reported in the literature,23 albeit showing the presence of biotite and

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amphibole impurities (see Figures 2-3).

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2.2.2. Thin section analysis using polarized light microscopy


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The almandine sample was sectioned and trimmed to a thickness of 30 µm (Wagner

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Petrographic) and examined using a polarized light microscope (Leica DM750P).24 This analysis

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revealed impurities in the almandine matrix in the form of biotite and amphibole (Figure 2), in

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agreement with the x-ray diffraction patterns shown in Figure 3.

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Figure 3: The x-ray diffraction patterns of the natural (non-irradiated) almandine powder showing the presence of biotite and amphibole impurities. 138 139

2.3. Zeta potential measurement

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The zeta potential of finely powdered almandine particulates (d50 ≈ 20 µm) was measured by

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suspending 1 g of particulates in 100 mL Milli-Q deionized water (>18 MΩ·cm) that was

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conditioned to an appropriate pH (1, 2, 4, 6, 10, 12 and 13) using NaOH (basic regime) or HCl

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(acidic regime). The suspensions were sonicated for 1 minute after which 1.5 mL of the

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suspension containing the particulates was placed into a cuvette for zeta potential

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measurements. Zeta potentials were measured using a ZetaPALS analyzer from Brookhaven

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Instruments Corporation25 that used an acoustic electrophoresis (i.e., streaming potential)


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method. At each pH, ten discrete measurements of the zeta potential were obtained which

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were then averaged to obtain statistically representative data.

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2.4. Measuring almandine’s dissolution rates using vertical scanning interferometry (VSI)

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Almandine was dissolved under flowing conditions using a flow-through cell (in-line diffusion

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cell, PermeGear) at 25 ± 3 °C at each solution pH. The solutions were prepared by adding NaOH

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or HCl to Milli-Q water (>18 MΩ·cm), and the pH of each solution was measured using a

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ThermoFisher Scientific Orion Versa Star Pro pH Benchtop Multiparameter Meter calibrated

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over the range 1 ≤ pH ≤ 13 at 25 ± 3 °C. The solutions were pumped into the flow-through cell

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using a peristaltic pump (Bio-Rad)26 at flow rates ranging between 0-to-18 mL/minute.

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To correlate atomic (structural) alterations following irradiation to dissolution rates, the

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dissolution rates of pristine and irradiated almandine were measured using vertical scanning

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interferometry (VSI) by quantifying the surface retreat due to dissolution following contact with

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flowing solutions. It should be noted that a portion of the sample surface was covered with an

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inert silicone mask (Silicone Solutions SS-38) to offer a “reference/inert area” from which the

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extent of surface retreat of the dissolving (unmasked) area was measured. Following contact of

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the almandine samples with the flowing solution for a selected contact time, the samples were

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removed from the flow cell, and their surfaces were evacuated of any residual solution by

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exposing them to a stream of compressed air. Thereafter, the silicone mask was peeled off to

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expose the unreacted surface. In the last step, the sample’s surface topography was measured

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using VSI (in air).


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Prepared for Submission to the Journal of Physical Chemistry C (July 2018) 169 170

The nanoscale vertical resolution (1-2 nm) of VSI offers the ability to directly track the change in

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height of the reacting surface with respect to a masked reference, as a function of the solution

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exposure interval. This allows us to assess dissolution rates of reacting (dissolving, precipitating,

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or corroding) materials at unparalleled resolution. VSI images were acquired using a 50× Mirau

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objective (numerical aperture, N.A. = 0.55) which offers a lateral resolution of around 163 nm.

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A single image field acquired using this objective features lateral dimensions of 170 µm × 170

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µm. However, by stitching partially overlapping adjacent images, the field of view (FoV) can be

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virtually expanded such that, herein, a stitched image field with dimensions of 1236 μm × 441

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μm was acquired (N.B.: the image grid consisted of 10 × 3 images). All images were acquired

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while accounting for the effects of tilt, i.e., by nulling the surfaces. The fringes on the sample

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surface correspond to the light and dark bands that are produced by the – constructive

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(amplitude enhances) or destructive (amplitude diminishes) – interference of the light source.

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The operation of nulling the surfaces minimizes and distinguishes the number of fringes that

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are visible inside the field of view (FoV) by adjusting the pitch (P) and roll (R) of the stage, thus

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ensuring that the sample surface is level and is oriented perpendicular to the light source. The

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analyses of acquired VSI images were carried out using Gwyddion (version 2.48)27 which

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quantified the change in height of the un-masked surface area with respect to the “reference

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area”. The change in height (Δh, nm) was divided by the solution contact time (Δt, h) to reveal

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the dissolution rate (DR = Δh/Δt, nm/h). The uncertainty in dissolution rates acquired in this

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manner is estimated to be on the order of 10% due to inherent uncertainties in VSI


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measurements, e.g., low-frequency vibrations that may not be fully damped, or the effects of

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temperature variations in the surrounding environment.

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3.

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MD simulations of irradiation-induced structural alterations in almandine were carried out

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using LAMMPS28 following a previously developed approach.11,29–32 The pristine mineral was

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simulated using the crystal structure of Armbruster et al.23 This unit cell was symmetrically

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expanded in 3D to obtain a supercell consisting of 5760 atoms. Periodic boundary conditions

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were imposed. First, this structure was equilibrated at 300 K using a Nosé-Hoover

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thermostat33,34 for 20 ps. This ensured complete relaxation of the supercell. A constant

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timestep of 1 fs was used during the initial relaxation of the structure.

Molecular dynamics (MD) simulations

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To simulate ballistic impacts resulting from irradiation, an atom was chosen randomly from the

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supercell. Note that weighted collision probabilities based on the neutron cross sections of the

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elements were used while choosing the atom. Then, this chosen atom was accelerated with a

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kinetic energy equivalent to that gained from an elastic collision with an incident neutron —

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taken to be 600 eV in this case. The accelerated atom, also known as the primary knock-on

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atom (PKA), then collided with other atoms in the supercell, called secondary knock-on atoms

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(SKAs). The collisions of these atoms (PKA and SKAs) with other atoms in the supercell resulted

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in a ballistic cascade. Ballistic cascades could result in high temperatures locally, which reduce

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to ambient temperatures following relaxation. Therefore, to avoid any spurious effects of the

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thermostat on the dynamics of the damage cascade, a spherical region with a radius of 10 Å


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was created around the PKA. All atoms outside this spherical region were kept at a constant

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temperature of 300 K by a Nosé-Hoover thermostat. Furthermore, the atoms inside the sphere

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are treated within the NVE ensemble.35,36 This ensures that the dynamics of the damage

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cascade, occurring within the spherical region, remain unaffected by the velocity scaling used

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by the thermostat. It should be noted that the objective of defining a 10 Å cutoff is not to

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distinguish the region of the system that can experience some local heating from the one that

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cannot. In fact, the entire system is free to experience temporary heating (that is, if potential

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energy is converted into kinetic energy). The Nosé-Hoover thermostat is used to simulate the

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gradual energy dissipation that will occur due to heat exchange with the thermostat (i.e., due to

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heat exchange of the excited zone with the bulk material in real situations). Rather, the

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objective of defining a 10 Å-radius around the PKA wherein the NVE ensemble is enforced is to

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ensure that the fast dynamics of the atoms colliding during the ballistic cascade is not affected

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by any spurious effect of the thermostat. The size of this radius was determined by computing

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the maximum spatial extent of the ballistic cascade occurring around the PKA for a given

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incident energy. Further details regarding this methodology can be found in Wang et al. 2015.32

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Here, a Buckingham potential parameterized by Teter and splined with the Ziegler-Biersack-

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Littmark (ZBL) potential was used to capture realistic short-range repulsive interactions during

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the ballistic cascades37. The choice of this potential was made since Teter’s force-field offers

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excellent predictions of the structure of aluminosilicate glasses,38–40 while suitably describing

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the crystal structure of pristine almandine.

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Due to the high velocities and excessive collisions of atoms, a variable timestep was used during

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the ballistic cascade to avoid numerical errors. Otherwise, a timestep of 1 fs was used. The

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dynamics of the cascade was simulated for 15 ps. This was found to be long enough to ensure

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the convergence of both the temperature and energy of the system. After each collision, the

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system was further relaxed in the NPT ensemble at 300 K and zero pressure for another 5 ps.

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This allowed complete relaxation of the structure. This process was repeated in an iterative

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fashion, with different knock-on atoms, until the system exhibited saturation in terms of both

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its enthalpy and density29. Any further irradiation was found to have no effect on the density or

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enthalpy of the irradiated almandine structure.

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4.

Results and discussion

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4.1.

The dissolution behavior of pristine almandine in acidic and basic environments

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The steady-state dissolution rates of pristine and irradiated almandine were measured using

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VSI at a flow rate of 13.5 mL/min after a total solution contact time of 6 hours. This flow rate

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was selected following measurements of dissolution rates over a wide range of flow rates since

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it is known that both the flow rate and period of solution contact affect attainment of the

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steady-state dissolution condition (see Figure 4a). The flow rate dependent dissolution analysis

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indicated that: (a) for flow rates greater than 8 mL/min, the dissolution rate of almandine

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became invariant with flow rate (e.g., see Figure 4a) indicating that steady-state dissolution has

252

been achieved; wherein the rate of release of constituent species from almandine is constant,

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and, (b) flow rates greater than 8 mL/min were sufficient to prevent the formation and

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accumulation of aluminum hydroxide (Al(OH)3) and ferrous hydroxide (Fe(OH)2) precipitates41


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on almandine’s surface which could compromise measurements of surface topography, and

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surface retreat using VSI. This is because, when causticity is abundant, following the equation

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M2+ + nOH- → M(OH)n(s), where, M is a metal ion, almandine’s dissolution results in the

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precipitation of Al(OH)3 and Fe(OH)2 on account of their low solubilities.

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While dissolution is noted to be incongruent at short solvent contact times, at steady-state,

261

dissolution is congruent, i.e., stoichiometric, as evidenced by separate measurements of

262

elemental compositions of reacted solutions at acidic pH by inductively coupled plasma-optical

263

emission spectrometry (ICP-OES), consistent with Walther et al. (1996).42 The observed

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incongruency during initial stages of dissolution is typical to aluminosilicates, and the

265

preferential release of either Al42–44 or Si45 initially has been previously observed at acidic pH.

266

The enhanced rate of Si release relative to Al in the almandine sample may be on account of the

267

size differences of silicate tetrahedra and aluminate octahedra, and the prevalence of isolated

268

silicate tetrahedra in almandine’s structure.

269 270

The dissolution of nesosilicates such as Ca2SiO4, Mg2SiO4, Be2SiO4, Ni2SiO4 and Co2SiO4 occurs

271

through mechanisms including the rupture of cationic bonds and release of silicate tetrahedra,

272

and hydrolysis of Si-O bonds within the silicate structural units.39,15 In general, the dissolution

273

rates in acidic media of silicates consisting of a single framework cation have been found to

274

scale in ascending order with the size of the framework cation (Figure 4b).15 Westrich et al.

275

explained this scaling in acidic solutions as being indicative of the relative ease of exchanging

276

the framework cation with protons during ion-exchange controlled dissolution.15 In proton-


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promoted dissolution, bridging oxygens at the mineral surface are replaced by water molecules

278

or hydroxyl ions; the replaced hydrated ions are ultimately released from the mineral to the

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aqueous solution. The rate of solvent exchange correlates with size of hydrated ions,

280

particularly since, larger cations have a larger surface area to accommodate more protons in

281

associative exchange, which make them easier to detach. A comparison of almandine’s

282

dissolution rate, a mixed-cation nesosilicate, with single-cation nesosilicates shows a trend that

283

is consistent with this concept (Figure 4b). This is indeed suggested by the work of Westrich et

284

al. which estimated dissolution rates for mixed-cation nesosilicates by a linear rule of mixtures

285

for solid-solution compositions (e.g., analogous to Vegard’s law)46 as shown in Equation (1):39

286

(a) (b) Figure 4: (a) The dissolution rate of almandine as a function of flow rate quantified using vertical scanning interferometry (VSI). Beyond a flow rate of 8 mL/min the dissolution rate plateaus demonstrating a flow rate independence. (b) The dissolution rates of nesosilicates as a function of their cationic radii. Taking into account the average cationic radius (Fe2+, Al3+) of almandine, the dissolution rate of almandine (i.e., a mixed cation nesosilicate) estimated using Equation (1) (red) closely matches its measured dissolution rates (green) in agreement with the broader trend that relates dissolution rates and ionic radii for nesosilicates (blue). 287


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𝑟"𝐴$ 𝐵& (𝑆𝑖𝑂+ )- . = 𝐴01.% [𝑟(𝐴0 (𝑆𝑖𝑂+ )5 )] + 𝐵01.% [𝑟(𝐵8 (𝑆𝑖𝑂+ )9 )]

Eq. (1a)

289

𝐷; "𝐴$ 𝐵& (𝑆𝑖𝑂+ )- . = 𝐴01.% [𝐷; (𝐴0 (𝑆𝑖𝑂+ )5 )] + 𝐵01.% [𝐷; (𝐵8 (𝑆𝑖𝑂+ )9 )]

Eq. (1b)

290

where, r is the cation radius, Dr is the dissolution rate, A and B are metal cations, and at.%

291

represents the atomic fraction of a given cation in the mixed-cation composition. Of course, the

292

implicit condition that needs to be satisfied in the case of mixed-cation nesosilicates is that the

293

cations feature similar sizes. A similar relationship can be expected at high pH, such that cations

294

with a larger field strength (i.e., ratio of charge to radius) induce faster dissolution because of

295

their tendency to concentrate OH-, which causes bond polarization. The cation influence

296

detailed above describes the variation in rates for a given pH. Steady-state dissolution rates of

297

almandine also vary with pH, as shown in Figure 5(a). In general, it is seen that dissolution rate

298

achieves a minimum at around pH 5 – featuring increases on either side of this dissolution

299

minimum. Such dependencies of (alumino)silicate dissolution rates on solution pH have been

300

observed extensively wherein the dissolution rate scales as a function of {𝑎}? 47–49 where ‘{a}’

301

denotes the activity of an ion a, typically H+ or OH- species depending on the solution pH, and n

302

is an empirical fitting coefficient. When the logarithm of the dissolution rates is plotted as a

303

function of the solution pH – n is often noted to vary between 0.3 ≤ n ≤ 0.5 for silicates.42,50

304 305

Furthermore, it is noted that almandine’s zeta potential decreases systematically from acidic to

306

basic regimes with the point of zero charge (PZC) – sited around pH 5 – corresponding to the

307

point at which the surface charges of Al and Si surface sites are minimized.42 Due to the

308

presence of H2O, an oxide mineral’s surface is generally covered in varying degrees with

309

“surface hydroxyl groups”, e.g., Si–OH.51 For the case of pure silica, the minimum total surface


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charge is affected only by H+ and OH- in the solution, without any specific adsorption on the

311

surface, and hence the PZC and isoelectric point (IEP) are equivalent. In acidic solutions, the

312

reaction between a silicate surface and the solution interface can be written as:

313

Si − OH + H + → Si − OH 2+

314

Therefore, positive charges are present on the mineral surface. When the surface contacts

315

alkaline solutions, the reaction can be written as:

316

Si − OH + OH − → H 2O + Si − O −

317

This explains the origin of the negative surface charge of silicates in basic solutions.51 Based on

318

studies on quartz and aluminum oxide, Walther et al.42,44 observed that the minimum in the

319

dissolution rate occurs at the pH where the sum of absolute charge from Si in quartz or Al in

320

aluminum oxide is minimized—i.e., pH 2.5 and 8.4 for quartz and corundum, respectively.42

Eq. (2a)

Eq. (2b)

321

(a) (b) (c) Figure 5: (a) The dissolution rates of pristine almandine measured at a flow rate of 13.5 mL/min showing the dissolution minimum in the mid-pH region (pH 5). (b) The zeta potential of pristine almandine measured as a function of solution pH. (c) The dissolution rate of pristine almandine as a function of its zeta potential showing that the dissolution minimum occurs at the pH where the sum of the absolute value of surface charge (Al and Si) is minimized; i.e., the point of zero charge (PZC, pH 5) is achieved. Also shown is a comparison of measured (blue circles) and estimated dissolution rate for pristine almandine (dashed red line) using Equation (3).


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Prepared for Submission to the Journal of Physical Chemistry C (July 2018) 322 323

As such, for aluminosilicates, the dissolution minima are expected to be determined by

324

composition, i.e., the Al/Si ratio, which dictates the pH at which the surface features minimum

325

(zero) surface charge. Since alkalis and alkaline earth cations tend to leach rapidly from

326

aluminosilicates and be replaced by protons, it is the residual Al and Si left on the surface that

327

determine the value of this pH.42,52 For example, for Al/Si < 1 (e.g., almandine; Al/Si = 0.67) the

328

surface charge and dissolution rate minimum is observed at a pH between 4 and 6, as noted in

329

Figure 5(a-b). This pH-dependence of dissolution rate is controlled by the electrosorption of H+

330

and OH− ions on terminal surface Al or Si sites. Since pure SiO2 and Al2O3 exhibit a dissolution

331

minimum at pH 2.5 and 8.4, respectively, it is expected that, in acidic regimes (pH < 7), the

332

surface charge for SiO2 is close to 0, and is relatively low in magnitude compared to its value in

333

high pH conditions. The opposite is true for Al2O3, which exhibits high surface charge at low pH

334

compared to SiO2, and while it becomes increasingly negative in alkaline conditions, it remains

335

smaller than of SiO2.42,53,54 This analysis affords the use of surface charge, as indicated by zeta

336

potentials, to estimate the dissolution kinetics of silicates. It should be noted however that zeta

337

potential does not discriminate the identity of surface sites, and is only sensitive to the total

338

charge arising from both Si or Al sites on the mineral surface.

339 340

Recently, Kristiansen et al. showed that the dissolution kinetics of silica enhanced with applied

341

potential.55,56 Such a dissolution rate-applied potential scaling can be described using the

342

Butler-Volmer equation as shown in Equation (3) below:

343

𝐷; = −𝐶𝑒

CD

E ∆J FG H

Eq. (3a)


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Prepared for Submission to the Journal of Physical Chemistry C (July 2018) KL -M

R S FG O,U

Eq. (3b)

𝐶=

345

where, Dr is the mineral dissolution rate (mol/cm2/s), α is a transfer factor, and the product α

346

·∆U (mV) reveals the surface potential (note that in the fitting below, ∆U is the zeta potential,

347

mV),57 e/kBT is the “thermal voltage” which equals to 1/25.8 (mV-1) at room temperature (K),

348

where e is the charge on an electron, kB is Boltzmann’s constant (eV/K), T is the temperature

349

(K), and C (mol/cm2/s) is a material specific constant based on its molar mass (Mm, 497.75

350

g/mol) and density (ρ, 4.30 g/cm3), and where Ea is the activation energy of the dissolution

351

reaction (kJ/mol), z is the collision frequency (z, s-1), p is a steric factor (1/6), and A denotes the

352

surface area that is available for dissolution (m2). It should be noted that the negative sign

353

preceding the transfer factor is eliminated if the surface potential is positive.

NO

𝑒 PQ

C

344

354 355

By regression, Equation (3a) can be fitted to the dissolution rates of pristine almandine in acidic

356

and basic regimes, separately, to recover C (2.5) and α (3.8 and 1.6), respectively, as shown in

357

Figure 5(c). The fitting applies a transfer factor to describe the difference between the surface

358

potential and zeta potential (i.e., if the surface potential and zeta potential were equal, α = 1).57

359

The difference in numerical values of α reflects a change in dissolution mechanism (e.g., ion

360

exchange in acidic solution or hydrolysis in basic solution) with pH. The reasonableness of the

361

fitted values of the transfer factor can be assessed from knowledge of the electrical potential as

362

a function of distance from the particle surface as shown in Equation (4):58,59

363

ϕ = ϕ 0 e −κ x

364

⎛ 1 M 2 2 ∞⎞ κ =⎜ ∑ zi e ni ⎟ ⎝ εrε 0 kT 1 ⎠

Eq. (4a) 1/2

Eq. (4b)


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where, 𝜑W (mV) is the surface potential at x = 0 (i.e., at the mineral surface, nm), 𝜅 is the inverse

366

of the Debye length60 (nm-1) which depends on the solution’s ionic strength, εrε0 is electrical

367

permittivity, zi is the valence of the ionic species, ni∞ is the number density in the bulk solution,

368

and M is the number of species (Na+, OH-, H+, Cl-). As such, 1/𝑒 C[$ = α, i.e., the transfer factor

369

in Equation (3a). At pH 13, for a 0.1 mol/L NaOH solution, setting x ≈ 0.3 nm to describe the

370

position of the slip results in a transfer factor: 1/𝑒 C[$ = 1.47 which is similar to the value

371

suggested by fitting Equation (3a) to the data in Figure 5(c) under alkaline conditions (α = 1.6).

372

This is a significant finding that supports the use of electrical surface potentials (or alternatively,

373

zeta potential) as a proxy of mineral dissolution rates. As such, it is evident that the dissolution

374

rate of a mineral correlates with the surface potential as described by a modified Butler–

375

Volmer equation. This suggests that mineral dissolution is fundamentally linked to the

376

electrochemistry of surfaces. Not only does this finding provide new insights into dissolution

377

dynamics in general, but it offers a means to potentially estimate dissolution rates from

378

measured zeta potentials, and vice versa. The universality of the observed relationship between

379

zeta potentials and dissolution rate is an important aspect that needs to be further clarified.

380

Nonetheless, taking the examples of the oxide surfaces of Al2O3 and SiO2,42 and of mica, silica

381

and zircon,55 it can be argued that the observed relationship is indeed – general, and broadly

382

applicable – i.e., to both simple, and complex oxide surfaces.

383 384 385

4.2.

Using MD simulations and topological constraint theory to assess dissolution rate alterations following structural changes induced by irradiation


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To elucidate the effects of irradiation on chemical durability, the dissolution rate of irradiated

387

almandine was measured in acidic and basic media. In general, irradiation resulted in an

388

increase (up to 2x, where x is the dissolution rate of pristine almandine at a given pH) in

389

dissolution rate across all pH levels (Figure 6a). Importantly, the slope of the dissolution rate-pH

390

trendline is unaffected, whether almandine may be irradiated or not, indicating that

391

electrochemical controls on dissolution remained unaffected by radiation (see Section 4.1). This

392

also highlights that while irradiation can alter absolute dissolution rates, it does not alter the

393

rate controlling step(s) in dissolution (i.e., the dissolution mechanism/pathway). Previously,

394

Pignatelli et al. and Hsiao et al. have shown that silicate dissolution rates substantially elevate

395

following a mineral’s exposure (e.g., quartz, albite) to irradiation.11,12 This is on account of the

396

structural disordering/amorphization that is induced. However, both quartz and albite feature

397

highly polymerized structures wherein their silicate tetrahedra are intimately connected to

398

each other – forming a periodic framework. Consequently, irradiation induces substantial

399

depolymerization as a result of which quartz’s dissolution rate can elevate by up to 3 orders of

400

magnitude and albite’s dissolution rate can increase by up to 20 times at a fixed pH.12

401

Contrastingly, almandine shows a comparatively marginal increase (doubling) of its aqueous

402

dissolution rate following irradiation.

403 404

Since MD simulations provide direct access to the trajectory of atoms, they offer direct insight

405

into the nature of atomic alterations induced in almandine’s structure following irradiation.

406

Analysis of the pair distribution functions (PDF, g(r)), before and following irradiation, as shown

407

in Figure 6(b) indicates that almandine’s short-range order (SRO, 3 Å), a substantial smoothening/dissipation

410

of the PDF is observed, indicative of vitrification.62–64

411

(a) (b) Figure 6: (a) The dissolution rates of pristine and irradiated almandine as a function of the solution pH. The similar slopes in acidic and basic regimes clarify that irradiation does not induce a change in the dissolution mechanism, and the elevation in dissolution rates simply arises from a reduction in cation coordination. (b) The pair distribution functions (g(r)) of pristine and irradiated almandine. 412 413

The effects of vitrification on structural connectivity/rigidity can be quantified within the

414

framework of topological constraint theory (TCT).65,66 TCT reduces complex atomic networks to

415

a simple network consisting of nodes (atoms) and rigid-members (atomic bonds).67 This allows

416

computation of the rigidity of an atomic network as described by the average number of

417

topological constraints placed on a given atom in the network (nc, unitless). The constraints

418

herein include: (a) the radial bond-stretching (BS), and, (b) the angular bond-bending (BB)

419

variants which maintain bond lengths and bond angles fixed around their average values,

420

respectively. Following Maxwell’s stability criterion,68 atomic networks can be categorized as:


Page 22

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(1) flexible (𝑛] < 3), showing floppy internal modes of deformation,69 (2) stressed-rigid (𝑛] >

422

3), featuring eigenstress due to mutually incompatible constraints,70,71 or (3) isostatic (𝑛] = 3),

423

being rigid but free of eigenstress. This nature of analysis reveals that the number of constraint

424

per atom (nc) for almandine decreased from 2.85 to 2.18, from the pristine to the irradiated

425

state, respectively. This reduction in the number of constraints, or network rigidity, as also

426

reflected by the smoothening of the MRO is on account of: (1) a change in the coordination of

427

87.8% of Al atoms from octahedral to tetrahedral coordination, (b) a change in the coordination

428

of 74.4% of Fe-species from being 8-coordinated Fe to becoming 5-or-6 coordinated, and, (3)

429

the formation of non-bridging oxygen (NBO) atoms, by an amount equivalent to 33% of all O

430

atoms, which do not exist in pristine almandine.

431

(a) (b) Figure 7: Representative snapshots of the simulated atomic structure of: (a) pristine and (b) irradiated almandine. For clarity, only SiO44- units are shown (Si: yellow, O: red) to highlight the state of silicate connectivity through the network. 432 433

It is important to note, the decrease in the number of constraints (Δnc = 0.67) in almandine

434

results mostly from a decrease in cationic coordination number(s) rather than a change in the


Page 23


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atomic connectivity of silicate tetrahedra (e.g., a change in Si–O bond length or Si–O–Si bond

436

angle in the case of framework silicates). This is significant as, following Hsiao et al. (2017), Δnc

437

= 0.67 should result in an increase of dissolution rate by around 200 times for typical silicate-

438

based materials.12 However, a much more modest increase in dissolution rates (and hence

439

decrease in chemical durability) is noted. The breakdown of the previously suggested

440

relationship between dissolution rate and number of constraints per atom can be understood

441

from the fact that, in contrast to more polymerized silicates,72 irradiation does not induce

442

changes in the connectivity of almandine’s silicate backbone – but rather only eases the

443

breakage of cationic (Fe2+ and Al3+) bonds in the structure. In silicates, dissolution implies the

444

breakage of high-energy Si–O bonds, which often serves as the rate-limiting step of

445

dissolution.73,74 As shown in Figure 7(a), pristine almandine initially exhibits isolated SiO4 units

446

(i.e., no Si–O–Si bonds are present). Both before and following irradiation, dissolution can

447

proceed without requiring the breakage of Si–O bonds. As such, SiO44- units are directly

448

transferred into solution as rigid blocks.

449 450

Upon the disordering of almandine’s network following irradiation although some Si–O–Si

451

bonds form, they are limited. Hence, many SiO44- units remain isolated or form small clusters

452

(see Figure 7b) so that silicate chains (i.e., –Si–O–Si– bonds) do not percolate throughout the

453

atomic network. This is partially on account of the composition which tends to form Si–O–Al

454

bonds rather than Si–O–Si or Al–O–Al bonds – in partial compliance with Loewenstein’s “Al-

455

avoidance” rule. 75,76 Consequently, dissolution can also occur through another path such as

456

breakage of cationic bonds rather than Si–O bonds. It is the former process that is enhanced by


Page 24

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irradiation, particularly through changes in the cation’s coordination numbers. It should be

458

noted that the small silicate clusters (i.e., with 2 or 3 Si atoms) that form upon irradiation are

459

expected to be released into solution as rigid units (rather than individual SiO44- groups), which

460

explains the slight increase (around 2x) in dissolution rate. Hence, in nesosilicates, dissolution

461

rates are enhanced by facilitated extraction of their cations rather than by affecting the

462

connectivity of the silicate network.

463 464

5.

Summary and conclusions

465

This study presents new insights into almandine’s dissolution behavior in acidic and basic

466

regimes; and following exposure to radiation. First, dissolution kinetics are shown to be

467

correlated with a mineral’s surface charge. In particular, it is shown that the minimum

468

dissolution rate is achieved at pH 5, corresponding to the pH at which almandine, which has a

469

garnet-type structure, achieves a minimum (absolute) value of total Al and Si surface charge.

470

This allows the dissolution rates of almandine to be estimated using a modified Butler-Volmer

471

equation, highlighting the critical role of surface electrochemistry on dissolution processes.

472

Second, it is highlighted that almandine experiences relatively small elevations in dissolution

473

rates following irradiation, as compared to percolated silicates such as quartz and albite with

474

feature higher levels of polymerization. Molecular dynamics simulations show that unlike

475

framework silicates, silicate connectivity in the garnet-type almandine remains broadly

476

unaffected upon irradiation. Instead, the coordination numbers of the cations Fe2+ and Al3+

477

decreases, causing a modest, but constant, enhancement in rates across the entire solution pH

478

range. Thus, the mechanisms of dissolution, which include both breakage of cationic bonds and


Page 25


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subsequent release of intact silicate tetrahedra as well as pH-dependent hydrolysis of Si–O

480

bonds, are reflected in the observed irradiation effect on overall dissolution rate. As such, the

481

outcomes of this work offer new insights into the origin of, and rate controls on the reactivity of

482

non-percolated garnet-type silicates across a wide range of solution pH’s and specifically

483

highlight how surface electrochemistry and surface potential, and network polymerization

484

affect dissolution processes in natural and engineered material systems. This understanding

485

gained, i.e., of electrochemical controls on dissolution processes can be applied not only within

486

an earth science perspective, but also to a diversity of engineered and biological systems

487

including: nuclear waste disposal, glass corrosion, cementation processes, hard tissue systems,

488

and micro- and nanofluidic systems, in which an understanding of the controls on reactivity of

489

oxide surfaces is of considerable importance.

490 491

Acknowledgements

492

The authors acknowledge financial support for this research provisioned by the: Department of

493

Energy’s Nuclear Energy University Program (DOE-NEUP: DE-NE0008398), National Science

494

Foundation (CAREER Award: 1253269), the U.S. Department of Transportation (U.S. DOT)

495

through the Federal Highway Administration (DTFH61-13-H-00011) and University of California,

496

Los Angeles (UCLA). The contents of this paper reflect the views and opinions of the authors

497

who are responsible for the accuracy of data presented. This research was carried out in the

498

Laboratory for the Chemistry of Construction Materials (LC2), Molecular Instrumentation

499

Center, and Laboratory for the Physics of Amorphous and Inorganic Solids (PARISlab) at UCLA.


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As such, the authors gratefully acknowledge the support that has made these laboratories and

501

their operations possible.

502 503

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504

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FeO-(Fe2O3)-Al2O3-SiO2-(H2O) at Elevated Pressures. Contrib. Mineral. Petrol. 1971, 31,

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