Variability of Radionuclide Sorption Efficiency on Muscovite Cleavage Planes

In deep geological repositories for nuclear waste, the surrounding rock formation serves as an important barrier against radionuclide migration. Multiple potential host rocks contain phyllosilicates, which have shown high efficiency in radionuclide sorption. Recent experimental studies report a heterogeneous distribution of adsorbed radionuclides on nanotopographic mineral surfaces. In this study, the energetic differences of surface sorption sites available at nanotopographic structures such as steps, pits, and terraces are investigated. Eleven important surface sites are selected and the energies of ad‐ and desorption reactions are obtained from density functional theory calculations. The adsorption energies are then used for the parameterization of a kinetic Monte Carlo model simulating the distribution of adsorbed europium on a typical nanotopographic muscovite surface. On muscovite, silicon step sites are favorable for europium sorption and lead to an increased adsorption in regions with high step concentrations. Under identical chemical conditions, sorption on typical nanotopographic surfaces is increased by a factor of three compared to atomically flat surfaces. Desorption occurs preferentially at terrace sites, leading to an overall 2.5 times increased retention at nanotopographic structures. This study provides a mechanistic explanation for heterogeneous sorption on nanotopographic mineral surfaces due to the availability of energetically favorable sorption sites.


Introduction
The storage of high-level nuclear waste is a key global challenge that is still undecided in multiple countries.[3] Such DOI: 10.1002/adts.202300406repositories incorporate a multi-barrier system to ensure that the radiotoxic material will not be released into the biosphere.The multi-barrier system can be separated into the engineered barrier and the host rock.The engineered barrier typically consists of a metal canister containing the nuclear waste, cement or clay buffers, and backfill material. [4]As a key component in this concept, the host rock surrounding the repository serves as an additional, geological barrier.Here, the potential of the host rock for retardation or retention of migrating radionuclides via adsorption reactions is of great interest. [3]7] They can be present as a mineral phase in multiple potential host rocks (clay rock, crystalline rock), as fracture filling materials, and in the nuclear waste container backfill.Among the micas, muscovite is a widely studied phyllosilicate since it is a commonly occurring mineral in multiple natural rocks (e.g., granite, gneiss, and pegmatite) and has a crystal structure similar to that of clay minerals like illite.Thus, muscovite offers an ideal starting point due to its crystal structure with the possibility of future development in both directions, i.e., for applications in crystalline host rocks as well as argillaceous rocks.
Regarding nuclear waste, trivalent actinides are among the most concerning due to their long-term radiotoxicity and strong solubility in water. [8]To simplify the safety issues in the laboratory, many experimental studies used the trivalent lanthanide europium (Eu 3+ ) as a chemical homolog for actinides.][11][12] The sorption properties of radionuclides are an important aspect of quantitative migration prediction.Several experimental studies have investigated europium sorption on muscovite and structurally similar clay minerals, which show potential mechanistic influences on the sorption reactions.Europium sorption on muscovite and similar phyllosilicates is strongly pH-dependent. [5,11,13]At low pH (3-4), only a small amount adsorbs on the surface as outer-sphere complexes keeping a complete hydration shell. [5,10,11,14]With increasing pH, the adsorbed amount increases until all available Eu 3+ is removed from solution at pH 8. [11] Surface complexation modeling confirms these findings. [15]At high pH, innersphere complexes form with a loss of hydration water.Different sorption preferences regarding specific surface sites or structures of sheet silicates have been suggested.Europium is reported to adsorb preferentially on the octahedral layer of kaolinite, [14] while no preference is reported for montmorillonite. [16]Preferential sorption at tetrahedral aluminum substitution sites due to a local negative charge and resulting electrostatic attraction has been suggested in a modeling study. [17]The inner-sphere surface complexes are reported to be monodentate [5,11,15] or multidentate. [11,17]The interlayer cations in the muscovite structure are more stably bound than in other phyllosilicates, thus preventing interlayer exchange with radionuclides. [13,18]or long-term retention, the desorption process is also of key interest.Here, there are a number of experimental studies for various systems.Trivalent actinides readily desorb from phyllosilicate surfaces when complexing agents are added, while pure distilled water does not lead to desorption. [19]Similar results are reported for thorium and ruthenium. [20]On montmorillonite, the adsorption of europium is fully reversible by lowering the pH after sorption. [16]Rubidium can be desorbed from muscovite via cation exchange reactions where the inner-sphere complex is transformed into an outer-sphere complex. [21]In this case, adsorption is twice as fast as desorption.For neptunium, slower desorption than adsorption on goethite has been observed. [22]ere, the desorption is kinetically controlled.The formation of inner-sphere complexes has been suggested to hinder the reversibility of adsorption. [6]ecently, several experimental studies have shown that surface nanotopography leads to spatially heterogeneous adsorption on mineral surfaces.Nanotopography, with its variety of surface building blocks (kinks, steps, terraces), causes variability in surface reactivity.The highest sorption efficiency of europium on calcite was observed on polished surfaces and the lowest on cleaved surfaces. [23]They suggested that the density of reactive kink sites or step sites might cause the heterogeneous adsorption.Consequently, specific portions of the surface topography that exhibit high densities of kink sites or have high nanoroughness are prone to increased adsorption.Additionally, the authors provide a number of previous experimental adsorption studies that show similar sorption efficiency of surfaces with stronger topography or more area. [24,25]For dissolution reactions, it was shown that the density of kink sites is the controlling parameter for surface reactivity. [26]Similar behavior has been shown for curium sorption efficiency on polymineralic (granite) surfaces. [27]Here, surface roughness has been identified as one of the most important parameters affecting the sorption efficiency of quartz and feldspar.Sorption differences on mica surfaces could only be investigated analytically to a very limited extent so far since the Fe content hinders the spectroscopic investigations due to quenching of the luminescence.In addition, stronger bonding complexes with possibly higher denticity have been identified on rougher surface sections.Comparable results have been reported for curium sorption on potassium feldspar surfaces. [28] full explanation of these experimentally obtained quantitative results requires a theoretical and mechanism-based approach for further systematic analysis.Do energetic differences exist in the sorption of specific complexes on nanorough substrate surfaces?Would these differences explain the quantitative contrasts mentioned above?Are similar results to be expected for mica minerals (e.g., muscovite)?Several modeling techniques are available to study adsorption on different scales, e.g., DFT (density functional theory), [29] SCM (surface complexation modeling), [15] KMC (kinetic Monte Carlo), [30,31] and MD (molecular dynamics). [32][35] Europium and trivalent actinides are reported to form tridentate complexes on hematite (001) surfaces, [29] while americium on bentonite is predicted to form bidentate complexes with covalent bonds to surface hydroxyl groups. [36]KMC is a modeling tool to study surface reactions on larger scales with system sizes in the hundreds of nanometers.[39] Adsorption processes in different fields have also been modeled using KMC. [40,41]Recent studies used KMC to investigate the adsorption of contaminants on mineral surfaces.Kurganskaya et al. studied the adsorption of arsenic to hematite nanocrystals. [30]They investigated which nanocrystal morphology is most efficient for the removal of arsenic, demonstrating the potential of KMC to study adsorption on an intermediate scale and providing a link to larger scales.Schabernack et al. developed a KMC model for the adsorption of a generic radionuclide representing trivalent actinides to the muscovite (001) surface to study the influence of the surface nanotopography. [31] critical requirement in KMC models is the parameterization of the site-specific reactions.Ideally, the activation energies of sitespecific reactions would be used in KMC for establishing the relative reactivity of each site.However, since site-specific activation energies are often unavailable experimentally, an effective alternative is to obtain equivalent parameters from DFT calculations using suitable models for the reaction sites.
This study aims to investigate the influence of specific surface sites on the efficiency and spatial heterogeneity of adsorption reactions on mica surfaces using a KMC model.The applied KMC algorithm is based on a previously developed model, [31] that is reparametrized with new energy barriers obtained by DFT calculations for the adsorption reactions of kink, step, and terrace site models.With the new KMC model, we are able to simulate realistic mineral surfaces that exhibit inherent nanotopographies, comparable to those occurring at fracture and fault surfaces of host rocks.Dissolution and precipitation reactions, which preferentially occur at screw dislocations, are responsible for these nanometer-scale surface building blocks. [37,42]Here, crystal surface building blocks such as kink and step sites occur, while atomically flat terrace sites are present on perfectly cleaved surfaces (Figure 1).Notably, the presence of nanotopography also allows the accessibility of fluids to octahedral layer atoms.The KMC surface model is used to study the spatial and site-specific distribution of adsorption efficiency on a crystal surface exhibiting nanotopography.The resulting data are expected to provide generalizable conclusions about actinide retention in potential host rocks.

Theoretical Methods
In this study, two numerical methods, DFT and KMC, are combined to investigate heterogeneous inner sphere sorption reactions at adsorption sites on crystal surfaces.The KMC model is able to simulate large surfaces, with thousands of atoms, comparable to the field-of-view of atomic force microscopy measurements.As parameters, the KMC model requires activation energy barriers for each individual adsorption site to compare the reactivity of the adsorption sites.The different adsorption sites are defined by their local coordination environment at the crystal surface.Thus, we can represent selected adsorption sites with cluster models and use DFT to calculate site-specific sorption energy barriers suitable for the KMC parameterization.

Adsorption Sites
Phyllosilicates consist of layers with tetrahedral (T) and octahedral (O) coordinated cations.Muscovite exhibits a TOT structure, where an octahedral layer is encompassed by two tetrahedral layers (see Figure 2).The tetrahedral layer consists of silicon (Si) and aluminum (Al(T)) cations.The upper tetrahedral layer always covers the (001) surface, otherwise, the stability of the structure would be low.The octahedral layer on the (001) face is only accessible via steps on the surface and consists of aluminum (Al(O)) cations.Crystal surface atoms can be generally sorted into kink, step (sometimes called ledge), and terrace sites. [43]The more complex muscovite crystal structure requires the definition of two different kink sites resulting in four surface sites: kink 1, kink 2, step, and terrace. [38]This results in a total of eleven different sites (four Si(T), four Al(T), and three Al(O)).Tetrahedral step and kink sites are available in the upper and lower tetrahedral layers, which influences their coordination.However, this influence usually occurs in the second coordination sphere and is assumed to have only a minor influence on the resulting energy values.In some cases, lower-layer sites have the same coordination as different upper-layer sites (e.g., lower kink 1 and upper kink 2).Here, the energy values can be used for both sites.Additionally, the step orientation influences the coordination of all step and kink sites.Similar to the layer effect, for some sites the coordination is identical to that of another orientation (e.g., upper kink 1 on the (110) face and lower kink 2 on the (100) face).We focused on the creation of a consistent dataset for the eleven different sites of the (110) face to be able to study differences between the local sites.Some site coordinations of this dataset are also applicable to other step orientations.All sites and their corresponding abbreviations and coordination are listed in Table 1.

DFT Calculations
To obtain sorption energy barriers for the KMC parameterization, Eu(III) desorption energy curves were calculated with DFT using a finite cluster approach, as detailed below.All calculations were performed with the ADF (Amsterdam density functional) program [44,45] using the PBE (Perdew-Burke-Ernzerhof) exchange-correlation functional, [46] and TZP (triple-zeta polarized) Slater-type basis sets with large frozen core. [47]Scalar relativistic effects were included via the zeroth-order regular approximation (ZORA). [48]Water solvation effects were implicitly simulated with the COSMO model (conductor-like screening model). [49]The calculations were conducted with numerical quality set to "Good" and default convergence criteria.
The bare octahedral and tetrahedral adsorption sites are represented as cluster models (Figure 2) extracted from the crystallographic structure of muscovite obtained by Catti et al. [50] The kink and step sites are characterized by the number of first and second tetrahedral and octahedral Si and Al neighbors, as described above.Oxygen dangling bonds were capped with H atoms, resulting in terminal OH or H 2 O groups attached to the Si and Al atoms.The corresponding Al(T) sites were created by replacing a Si atom with Al.Since the cluster models for the Si adsorption sites were electrically neutral, the models for the Al(T) adsorption sites resulted in a net charge of −1 because of the lower valence of Al.Such charged models are commonly used in DFT calculations of, e.g., zeolites. [51,52]The structures were optimized with the second and further Si and Al nearest neighbors fixed at their experimentally determined crystallographic positions to simulate the constraints imposed by the solid structure.
The next step was the construction of the adsorption complexes.Adsorption complexes were constructed by placing an Eu(OH) 3 molecule at a reasonable distance (based on the Eu-O-Si/Al bond length) from the optimized adsorption site, and reoptimizing the structures under the same constraints applied to the bare adsorption sites.Note that, in these optimizations, no constraints were placed on the positions of atoms in the Eu(OH) 3 fragment in order to increase the chances of finding the adsorption complex with the lowest energy for each adsorption site.Eu(OH) 3 was chosen as adsorbate because it is the predominant Eu 3+ (aq) species at pH 9-10. [53]t last, the desorption energy curves were obtained by modeling the Eu(OH) 3 detachment as a sequence of constrained geom-etry optimizations, starting from the optimized adsorption complex.For each step, the Eu(OH) 3 adsorbate was shifted perpendicularly to the surface plane by ca.0.05 Å and the resulting structure was reoptimized.For each optimization, in addition to the constraints in second and further Al and Si nearest neighbors, the position of the Eu atom was kept fixed to avoid "resorption" during the optimization procedure.
It should be noted that several simplifications were made in this procedure.For example, the cluster models do not reflect the negatively charged surfaces observed experimentally at pH 9-10, which are balanced with positively charged ions in solution.Similarly, the solution environment is only implicitly simulated, neglecting the presence of charged ions and the description of specific solute-solvent interactions, especially the exchange of H 2 O ligands with the Eu coordination shell.Such Table 1.List of all studied muscovite surface sites with the corresponding abbreviation used here.The site coordination is given here in the first and second neighbor coordination based on the description by Kurganskaya and Luttge. [38]The corresponding DFT cluster models are shown in Figure 2. approximations would represent serious flaws, if the goal were to obtain accurate activation energies.However, the goal here is to obtain suitable parameters for the KMC model, meaning that, as long as the approximations affect all adsorption sites similarly, the resulting energy barriers would still be sufficient to establish the relative reactivity of the sites and the KMC simulations would still be representative of the Eu adsorption on nanotopographic surfaces.Additionally, the errors caused by the chosen functional have a low influence on the KMC result, as long as the error is similar for all systems that we compare.The desorption trajectories calculated with DFT are available in the research data.

KMC Simulation of Adsorption Distribution
In this study, we present the KMC simulation of europium adsorption on a muscovite (001) surface.The surface size is 400 × 100 × 8 unit cells in the a, b, and c directions.Periodic boundary conditions are applied to the surface edges leaving access only to the (001) face.In the dissolution simulation, five defects are placed initially and 2 million atoms are dissolved.In the following adsorption part, 15 thousand Eu(OH) 3 molecules are adsorbed to the generated surface.The number of Eu(OH) 3 atoms is chosen to yield a surface coverage of 0.33 Eu(OH) 3 per unit cell area.This value is selected as the limit since it results in charge compensation of the negative muscovite surface charge which drives the adsorption reaction. [54]Therefore, the number of Eu(OH) 3 on the surface can be considered representative.
The KMC model used in this study is based on a previously developed model. [31]For a schematic overview of the model algorithm, see Figure 3.The model is composed of two distinct parts.In the first part, a muscovite surface of a given size is created and defects are placed in the crystal structure.Then, the dissolution of the surface is simulated based on the implemented bondbreaking energies, leading to the formation of a nanotopography.This part closely follows the KMC model developed by Kurganskaya and Luttge, [38] and a more detailed model description can be found therein.The KMC model for muscovite dissolution was parameterized and validated using AFM datasets of dissolving muscovite surfaces. [55]he second part simulates europium adsorption on the muscovite surface.Here, the nanotopography simulated in the first part is used directly.The model can be separated into these two parts because the dissolution [55] is much slower than adsorption [54] and, thus, won't occur during the adsorption step.For each surface site, an adsorption probability is computed based on the adsorption energy barriers obtained from DFT (cf.Table 1 and Figure 2).The probability calculation is based on a Boltzmann distribution: where P is the adsorption probability of site type i, ΔE is the adsorption energy barrier of site type i, k is the Boltzmann constant, and T is the temperature.Room temperature was used in all calculations.
In each iteration of the KMC simulation, an adsorption site is selected following the "Divide-and-Conquer" algorithm by Meakin and Rosso, [56] which is based on the "N-fold" algorithm. [57]Here, an integrated probability is calculated based on the number of atoms per site type N i and the corresponding adsorption probability P i : The integrated probability is recalculated in every iteration due to the changing number of free adsorption sites.Sites with a high number of atoms and a high adsorption probability cover larger intervals.Most surface atoms belong to one of the terrace sites since all other sites are available only along steps.In addition to the site coordinations we have defined (Table 1), a large number of other site coordinations exist on the surface.These sites differ in most cases by their second coordination sphere and contain only a small number of surface atoms.To include these sites in the simulation, they are considered equivalent to the site with the closest coordination.Here, similarities in the first coordination sphere are considered to be of higher importance than in the second coordination sphere.As a result, all the atoms of the muscovite surface are available as potential adsorption sites in the simulation.
In the next simulation step, a random number x falling in an interval is generated to select a site type for the adsorption reaction: Once the site type has been selected, a second random number is generated to select the individual surface atom for the adsorption reaction.This process is repeated until the set number of adsorbed atoms is reached.An internal simulation timer is computed by counting every adsorption reaction attempt.In the model, it is possible that a surface atom which is already occupied by a Eu(OH) 3 is selected again for the adsorption reaction in subsequent iteration steps.In this case, no adsorption occurs but the number of adsorption attempts is increased, leading to slower adsorption as adsorption progresses.This results in a Langmuirtype adsorption behavior.If a site type becomes fully occupied, its integrated probability reaches zero and no more adsorption reactions can occur to that site type.

Desorption Energy Curves
For each surface site, the energy is computed with increasing Eu(OH) 3 -site distance (Figure 4).All energy curves show the absolute energy minimum values in the adsorbed position at the surface (minimum desorption).In the adsorbed state, Eu(OH) 3 is generally coordinated to two surface oxygen atoms.Only in the Al(T)-T site the Eu atom is located directly above the Al atom  [38] Here, a realistic surface nanotopography is generated.This surface is used subsequently in the second part (green) to simulate the corresponding adsorption distribution.
and coordinated to all three surrounding bridging oxygen atoms, whereas in the Si─T it is only coordinated to two bridging oxygens.For all tetrahedral steps and kinks the Eu atom is positioned between the tetrahedral and octahedral layer and is coordinated to a dangling oxygen atom from the site and a bridging oxygen atom to the octahedral layer.For octahedral sites, the Eu atom is either coordinated to two dangling oxygen atoms from the site (Al(O)-S, Al(O)-K2) or to one dangling and one bridging oxygen atom (Al(O)-K1).For a detailed view of the site coordination, the desorption files are available in the associated research data.At high Eu(OH) 3 -site distances, the energy curves in all calculations converge to a constant value (maximum desorption).Here, the Eu(OH) 3 is completely dissolved and does not interact with the muscovite surface.Most sites exhibit a single maximum value between the adsorbed and dissolved states.The difference between this maximum and the dissolved state energy constitutes the adsorption energy barrier, while the difference between the maximum and the adsorbed state provides the desorption energy barrier.Energy barrier values differ for all defined sites for both adsorption and desorption.A few sites have adsorption energy barriers close to zero, with the maximum close to the dissolved state energy (Si─S, Al(O)─S, Al(O)─K2).For all surface sites, the desorption energy barrier is larger than the adsorption energy barrier.A set of secondary minima and maxima can be observed for the Si-K2, Al(T)-S, Al(O)-S, and Al(O)-K2 sites.In these cases, the largest available energy barrier is selected for the KMC model.

Adsorption and Desorption Energy Barriers
The energy barrier values for adsorption and desorption computed based on DFT curves are presented in Figure 5.For the adsorption reaction pathway, the overall energy barrier values are small with a maximum energy barrier of 23.9 kJ mol −1 .The adsorption energy barrier for the tetrahedral sites follows a sequence: The step sites exhibit the lowest energy barrier, followed by the kink 2 and terrace sites.The kink 1 sites show the highest barrier energy of all the tetrahedral surface sites.In the tetrahedral layer, the Al(T) sites always exhibit higher energy barriers than their Si(T) counterparts with differences between 5.3 and 7.5 kJ mol −1 .The octahedral surface sites follow a different order of energy barriers.In contrast to the tetrahedral sites, the kink 1 site here provides the lowest energy barrier, followed by the step and kink 2 sites.Al(O)-K1 has the lowest overall energy barrier of 0.3 kJ mol −1 , thus being the most favored adsorption site on the surface.The second most favorable site is the Si-S.Both of these sites are found only on surface steps.The Al(O)-K2 sites have the highest overall energy barrier at 23.9 kJ mol −1 .
For desorption reactions, the energy barriers are generally higher (Figure 5b).In the tetrahedral layer, the lowest energy barrier is found at the terrace sites, followed by the step site.For Si(T), the kink 1 and 2 sites have a very similar energy barrier value.Al(T) shows a lower barrier for kink 2 compared to the kink 1 sites, which have the highest barrier energy of all sites.In the octahedral layer, the kink 1 site has the lowest barrier, which is still at the same level as the Si-S site.The Al(O)-S site has a slightly higher barrier energy, followed by the Al(O)-K2 site.

Discussion of Sorption Energies
Literature data for activation energy barriers of individual adsorption reactions are limited and even more difficult to obtain for specific processes such as the sorption of trivalent actinides on muscovite.Thus, activation energy values are often estimated based on assumptions or arbitrarily selected when they are required for parameterization. [30,31]In a previous study on the sorption of radionuclides on muscovite (001) surfaces, the differences in adsorption energy barriers were based on the different cation coordinations and followed the order Al(O) > Al(T) > Si. [31] The assumptions were based on a general preference for adsorption on the octahedral layer that has been observed for kaolinite [14] and preferred adsorption on Al(T) in the tetrahedral layer due to the negative local charge and increased electrostatic attraction. [17]In the present study, energy barrier values are obtained from firstprinciples calculations and provide more accurate insight based on robust assumptions (Figures 4 and 5).However, it cannot be excluded that the computed energy values do not represent the correct absolute value due to missing influence from, e.g., adsorbed cations blocking surface sites or water molecules in the system.Nonetheless, it can be assumed that the values are correct when they are related to each other.For the KMC model, the correct relative values are sufficient (cf.Equations 1 and 2).From DFT calculations, preferential sorption at the octahedral layer can be confirmed for the Al(O)-K1 site.However, both other octahedral sites have higher energy barriers than the tetrahedral analog.Within the tetrahedral layer, the energy barriers of all sites are lower for silicon compared to Al(T), which disproves the previous assumption based on electrostatic attraction.Additionally, this also shows that a reported preference for aluminum over silicon sites is not generally valid and only applies to the Al(O)-K1 site. [16]An influence of surface site coordination (kink, step, and terrace) on the probability or affinity of adsorption has been suggested previously for calcite. [58]However, the order of adsorption probability proposed there (kink > step > terrace) cannot be generally applied to our system.Another study identified variating adsorption energies for molecules from shale gas on calcite surfaces depending on the site coordination. [59]nterestingly, the Si-T site shows a comparatively low energy barrier, which results in a strong influence on the adsorption distribution.This also increases the importance of the (001) phyllosilicate face, where these sites are located during the adsorption.Phyllosilicate edge sites on the (hk0) faces are highly similar in coordination to the presented step, and kink sites are widely considered more reactive toward adsorption reactions. [14,60,61]he terrace sites on the (001) face do not provide terminal hy-droxyl groups for bond formation.Instead, any inner-sphere sorption must occur via bridging oxygen atoms between surface tetrahedra.However, the DFT calculations show that this does not strongly affect the activation energy barrier and adsorption can occur at these sites comparatively easily.
The existence of a secondary energy minimum for the Si-K2, Al(T)-S, Al(O)-S, and Al(O)-K2 sites potentially represents an intermediate metastable state, such as an outer-sphere complex or a change in the solvation layer (manifested here as changes in the solute cavity in COSMO) at these adsorption sites.Especially in the latter case, a more thorough investigation (possibly including explicit solvent molecules) would be of interest.The minima are located at Eu(OH) 3 -site distances of 6.5, 5.7, 6.3, and 6.3 Å respectively.Three different adsorption heights for divalent metal cations on the muscovite (001) surface have been identified. [62]Inner-sphere complexes are found within 2.5 Å, while outer-sphere complexes are located between 3.5 and 4.5 Å above the surface.An extended outer-sphere complex is defined in the region between 5 and 10 Å, which would correspond to the secondary minima in our DFT calculations.For the Pu 3+ adsorption on the muscovite (001) surface an average adsorption height of 18 Å is reported. [63]However, this unusually high value might be explained by the formation of nanoparticles on the surface. [54]The desorption energy barriers are currently not included in the KMC model.However, they should allow for a prediction of surface site influence on desorption processes and, more generally, on their importance in radionuclide retention.The energy barriers for desorption are 4 to ≈500 times higher than for adsorption.It is expected that a higher desorption energy barrier leads to slower desorption reaction kinetics under identical conditions. [21,22]Desorption energy barriers are lowest for the two terrace sites on the (001) face.This indicates weaker adsorption and could be caused by the previously described bonding to surface oxygen atoms that already form bonds to two surface cations.Both step and kink sites offer terminal hydroxyl groups that could lead to stronger surface bonding and the observed higher desorption energy barriers.This effect is similar to the suggested stronger complexation on rougher surfaces. [27,28]Therefore, the DFT data suggest that desorption reactions occur first and predominantly at the (001) terrace sites of the mineral surface.The stronger bonding at step and kink sites leads to a higher retention potential at surface steps, etch pits, and edge faces.On average, the kink sites appear to form more strongly adsorbed complexes with higher desorption energy barriers.This increases the importance of mineral surface nanotopography for the long-term retention or retardation of radionuclides.

KMC Simulation of Adsorption on a Muscovite (001) Surface
The adsorption energy barriers presented in Section 3.1.2and Figure 5a are used as parameters in the KMC model.In the KMC model, a muscovite (001) surface is created and five surface-exposed defects are placed into the structure.The defects have a depth of 10 nm, which corresponds to 10 TOT layers of the muscovite crystal.In the following dissolution simulation, the defects open up to form etch pits that grow in the preferred (110) direction, leading to oval etch pits (Figure 6a).The density of surface steps increases toward the center of each of the five etch pits.Additionally, supersteps with a height of two TOT layers may form on the surface and can mostly be found close to etch pit centers.Their formation is mainly caused by different growth directions between the top and bottom TOT layers due  6.The top row shows the total number of adsorbed atoms at each surface site for silicon, tetrahedral aluminum, and octahedral aluminum.Silicon terrace sites dominate the overall adsorption, followed by the silicon step sites.In the bottom row, the graphs show the corresponding percentual occupancy of the surface sites.The occupancy directly follows the order of energy barriers shown in Figure 5a, with low energy barriers leading to high site occupancy.
to a crystallographic rotation. [38]The simulated surface provides a representative snapshot of a dissolving muscovite surface as observed in experimental investigations. [55]Further dissolution does not result in a decrease in surface roughness as progressive dissolution leads to the opening of new hollow cores and the deepening of existing etch pits.
Adsorption occurs over the entire surface and adsorbates can be found at terrace as well as at steps and kink sites (Figure 6b,c).Highlighting the adsorption at step and kink sites allows for the visualization of the etch pit shapes.Generally, the adsorption appears to be homogeneously distributed over the entire surface with no clearly visible preference for specific sites or structures.However, a simple comparison between the occupation of the adsorption sites in the left and right halves of the surface shows that the right half has consistently higher occupancy.At low total occupation (0.8%), the right half shows an occupation of 0.9% compared to the left half's value of 0.7%.At higher total occupation, the right half has 8.4% of all sites occupied compared to 7.9% occupation in the left half.
The existence of preferential adsorption sites at nanotopographical structures is analyzed by comparing the number of europium atoms at each type of surface site with proceeding adsorption (Figure 7).Most Eu(OH) 3 is adsorbed at Si-T sites since it is the most abundant surface site on the muscovite surface (69.3%) and has a comparatively low energy barrier (8.1 kJ mol −1 ).About 13% of Si-T sites are occupied during the simulation.The second highest amount of Eu(OH) 3 is adsorbed at Si-S sites.This site type accounts for only 2.3% of all available surface sites but is preferred for adsorption because of its low energy barrier (2.5 kJ mol −1 ).About 50% of Si-S sites are occupied by Eu(OH) 3 which makes it the second most occupied.At all other sites, about an order of magnitude less Eu(OH) 3 is adsorbed.Si-K1 provides a similar amount of sites as Si-S but does not play a major role in the adsorption distribution due to its higher energy barrier (10.1 kJ mol −1 ).Due to the generally higher activation energy barriers of tetrahedral aluminum sites, only a small number of Eu(OH) 3 is adsorbed there.The most preferred adsorption sites are Al(O)-K1.About 70% of the Al(O)-K1 sites are occupied at the end of the simulation.However, the Al(O)-K1 and the other two octahedral sites are rarely present on the muscovite surface.They are easily soluble and therefore not very stable on the surface.The comparison of site occupancy directly reveals the implemented energy barriers.Here, sites with low energy barriers show high occupancy.At sites with high occupancy, the adsorption process slows down due to the increasing probability of sorption attempts to already occupied positions, as can be seen for Si-S and Al(O)-K1.

Qualitative Analysis of Heterogeneity
The KMC model is set to conditions far from equilibrium, where the available sites far exceed the number of adsorbing europium atoms.Therefore, the model shows the initial response of the system to adsorption.Complete coverage, where any local contrast would be lost, is never achieved.To identify any local sorption increase, an adsorption density is calculated by using the kernel density estimation method (Figure 8).Kernel density estimation is an alternative method to the commonly used histogram.It allows for the calculation of a smooth probability density function and has the advantage over histograms in that no definition of bins is required for 2D applications. [64]Here an exact estimation of the density values is used: Where n is the number of elements in vector vX or vY.vX i is the ith element in vector vX and vY i is the ith element in vector vY. x and  y are the optimal bandwidth values.For more details see the Origin 2021 manual.The resulting probability distribution can be analyzed to find local increases or decreases in adsorption.In the KMC simulation, an increased density of adsorbed atoms can be seen at etch pit centers (Figure 8 ROI 1) and surface steps (Figure 8 ROI 2) in comparison to atomically flat surface areas.Surface steps (Figure 8 ROI 2) lead to a moderate increase in density of ≈1.5 times compared to the atomically flat surface.Multiple steps in close vicinity or two-layer supersteps increase this effect even further.Close to the center of all etch pits, the concentration of surface steps is extremely high.The highest adsorption density is observed here, with a density increase of more than three times compared to the atomically flat surface (Figure 8 ROI 1).The observation of adsorption density directly allows for the identification of topography structures such as etch pits or steps (see Figures 6a and 8).
The increase in local adsorption is caused by two effects.The first effect is based on the favorable adsorption to Si-S sites.These sites only occur at surface steps and show a high occupancy compared to most other sites due to the low energy barrier (cf. Figure 7).A high concentration of steps provides a high concentration of Si-S sites leading to a high local concentration of adsorbed Eu(OH) 3 .The second effect is caused by the 2D representation of the 3D surface.Surface steps offer sites on the vertical step walls that are superimposed by the 2D projection, where the vertical surface area is not considered.However, this effect is also inherent in experimental techniques that map surface adsorption (concentration) and has been observed there. [23,27,28]The KMC simulation shows that the mineral surface nanotopography influences the adsorption distribution of europium and homologous  6d) on the muscovite surface is overlaid with a kernel density estimation of the local adsorbed europium density.An increase in atom density is visible when comparing flat surface sections with surface steps and etch pits.Single steps result in an intermediate increase in density (1.5-fold), while a cluster of multiple steps, often located near an etch pit center, causes a stronger increase in density (>3-fold).Two regions of interest (ROIs) are magnified to highlight the local contrast and compared to the local topography (Figure 6a).ROI 1 shows the center of an etch pit with a high accumulation of steps leading to a strong increase in adsorption density.ROI 2 shows a shallower section with two major steps.Adsorption is increased at the steps compared to the atomically flat areas of ROI 2, but not as much as in the center of the pit of ROI 1.
trivalent actinides.Surface steps originating at crystal defects are identified to be the key structure controlling heterogeneous adsorption.The concept of surface topography influence on adsorption distribution is illustrated in Figure 9. Based on the KMC results, the atom density in each of the three surface domains can be derived by normalizing the number of adsorbed atoms to the surface area (Table 2).The etch pit with multiple steps in a small area (Figure 9c) shows a twofold increase in adsorption compared to the large field of view of the KMC surface (Figure 8) and a threefold increase compared to atomically flat sections (Figure 9a).A single step (Figure 9b) can lead to a 1.5-fold increase in adsorption compared to the large FOV.These results are in agreement with the calculated kernel density discussed above.The surface domain with multiple steps (Figure 9c) is similar to the surface nanotopography of powder materials with a high concentration of reactive sites.Crystal powder samples are often used to determine experimentally the sorption potential of minerals in batch experiments. [5,12]Our data suggest that powder sorption results lead to an overestimation of retention by at least a factor of three, with potential implications for prognostic use.For desorption, a factor is estimated based on the relation between the adsorption factors and the corresponding predominant energy barrier (Table 2).The estimation suggests increased desorption at atomically flat surface areas where terrace sites dominate by a factor of 2.5.
Octahedral surface sites do not play a major role in the adsorption distribution on the (001) muscovite surface.Their concentration on the surface is up to two orders of magnitude lower than the tetrahedral sites (Figure 7).It could be expected that these sites play a more important role on the (hk0) faces of phyllosilicates, where they are more readily accessible for adsorption as surface atoms. [7,65]n larger scales, mineral surface topography can be evaluated by computing the surface nanoroughness. [23,27]An elevated surface nanoroughness indicates strong local changes in topography, where a high concentration of highly reactive sites such as steps and kinks can be found. [26]Experimental results show that a high surface roughness on minerals leads to a higher amount of sorption on the examples of mica, [27] calcite, [23] and feldspar. [28]he formation of more strongly bound complexes is reported on feldspar, quartz, and mica. [27,28]Large calcite sample sections with well-defined topographic features, e.g., increased kink den-sity in fields of view of several hundred micrometers compared to atomically flat sample surfaces have been studied experimentally and analytically. [23]Here, surface portions with increased nanoroughness show an adsorption efficiency enhanced by more than one order of magnitude compared to flat cleaved surfaces.The authors also provide a comparison to multiple previous studies that support the influence of surface topography on adsorption.Ducros, Housley, and Piquard studied the adsorption of oxygen on rhenium single crystals that were prepared with different surface structures. [25]In this experiment, the atomically flat crystal surface adsorbed 6.84•10 14 atoms cm −2 , while the surface with kinks and steps adsorbed nearly twice the amount of oxygen with 11.9•10 14 atoms cm −2 .An influence of the calcite surface nanotopography on the availability of different adsorption sites and a potential impact on the location of adsorption has been suggested. [24]he methods used in the experimental studies to visualize the adsorption distribution cannot achieve the resolution of individual steps on the mineral surface.Therefore, topographic features such as single steps and pits cannot be distinguished with respect to sorption efficiency on complex sample surfaces.However, these larger-scale adsorption distributions can be mechanistically explained by our numerical investigations.Nanorough mineral surfaces have a high concentration of surface steps, which provide a high concentration of preferential adsorption sites with comparatively low adsorption energy barriers.Here, the sorption efficiency is increased compared to smoother surface areas.When a measured pixel in an experiment has a higher Table 2. Generalized comparison of the sorption efficiency of various typical surface domains (A-C, see Figure 9), related to the large field of view of the KMC simulation (Figure 8).The desorption factor is based on the predominant energy barriers on the flat (terrace) and the nanorough (step) surface.The relation between the two energy barrier values is used to estimate a factor for the desorption efficiency.This is achieved by using the relation between the sorption factor and the corresponding predominant energy barriers for adsorption.step concentration on average, a higher radionuclide uptake is measured.From the wide range of different minerals that show this behavior according to literature data, it can be expected that the identified mechanism of surface site coordination on the adsorption is valid for various minerals.

KMC Model Simplifications
In the KMC model, several simplifications are employed to provide a reliable model in a first step.At the current stage, only adsorption is simulated.Therefore, any adsorbed species remains on the surface.Obviously, desorption can occur in such systems as well as adsorption.The DFT results show a large difference between the energy barriers for desorption reactions compared to those of the adsorption reaction (see Figure 5 in the results section).These differences result in integrated probability values that are more than nine orders of magnitude lower than for adsorption when assuming a constant number of sites (adsorption: 0.1 to 56%; desorption: 10 −9 -10 −46 %).Therefore, in the system simulated in this study with 15 thousand Eu(OH) 3 adsorbing on a blank surface with a much larger number of surface cations as adsorption sites, direct implementation of desorption would not show any effect.The simulation of desorption requires a more precise modeling of the adsorption sites, which is currently limited by the number of surface cations.In reality, adsorption should be limited by the electrostatic attraction of the crystal surface, which decreases as the surface becomes charge-compensated. [54]Additionally, local repulsion of adsorbing Eu(OH) 3 needs to be considered due to electrostatic or steric repulsion effects.A specific limitation of adsorption sites decreases the effective probability over time which in turn increases the importance of desorption.In its current state, the model is able to predict the initial surface adsorption response, where the number of adsorption sites is far greater than the adsorption species.This maps initial efficiency and competitive behavior, and thus spatial heterogeneity.In addition, surface diffusion is an effect that needs to be considered for a precise system evolution over time.The influence of surface diffusion on the muscovite -Eu(OH) 3 system is difficult to predict, since to our knowledge, there are no data describing the movement of atoms on the surface and the corresponding energy barriers.[68][69] However, in these studies, the crystal surface is in contact with a gas phase and temperatures are elevated compared to our conditions.As a first indication, the available literature suggests that surface diffusion is more important than desorption due to the potentially lower energy barriers.
For future model improvement, the investigation of the influence of surface diffusion on the heterogeneity of surface adsorption is thus suggested as first step.As secondary step, desorption together with limiting factors on the number of adsorption sites can further improve the predictive capabilities of an adsorption KMC model on actinide-sheet silicate interaction.

Implications for General Applications
On the larger scale of host rock formations for potential repositories, the contained minerals and their surface configurations can influence the potential to sorb radionuclides from pore water.It can therefore be speculated that retention efficiency may be higher in host rocks where minerals have previously undergone dissolution processes.Additionally, remobilization of radionuclides to the biosphere may be less likely on such substrates in general due to the higher desorption energy barriers at kink sites.Most rocks consist of multiple mineral phases that can potentially sorb radionuclides.Here the type of mineral appears to be the most important influence driving the distribution of radionuclide adsorption. [27,70]Phyllosilicates show a high affinity for radionuclide sorption, while for example, quartz has a low affinity.The surface nanotopography consequently controls the sorption efficiency for minerals of the same type.The reported variability of the sorption efficiency should be considered in large-scale simulations for the safety assessment of nuclear waste repositories.Our simulations suggest a potential increase in adsorbed species concentration of up to three times due to an increase in nanotopography.The current use of average values such as distribution coefficients derived from batch experiments using powder samples cannot describe the observed variability.In general, the surface nanotopography of minerals should be considered as a parameter for the estimation of sorption uptake variability.Paleoweathering or hydrothermal processes can alter crystal surfaces in the vicinity of fracture zones.Diagenetic processes in sedimentary rocks may have a similar effect.Due to slow reaction kinetics, crystal surfaces are not always available as "healed" equilibrium surfaces after such processes, and nanotopography as a controlling parameter cannot be neglected. [71]his study provides a first approach toward a mechanistic understanding of heterogeneous sorption on mineral surfaces.The current approach is simplified in comparison to what can be expected in natural rock systems, e.g., no large mineral surfaces are available for the calculation of sorption energies, no explicit water molecules are included and no cations are presorbed on the surface.Therefore, the sorption energies might be subject to further effects that are not yet included.However, our approach is able to show first contrasts in sorption energies and the sorption distribution on mineral surfaces, which provides a promising starting point for further investigations.

Conclusion
Our DFT calculations demonstrate that the local environment of surface sites influences the activation energy barrier for Eu(OH) 3 adsorption.Preferential adsorption positions for Eu(OH) 3 on the muscovite (001) surface are identified at the silicon step site and the Al(O) kink 1 site.Desorption reactions have higher energy barriers and show a preference to occur at terrace sites.By applying the DFT results into a KMC model, we are able to simulate the adsorption of Eu(OH) 3 on realistic surface models with large-scale distribution of adsorption sites of different types.We show that heterogeneous adsorption can be explained by sitespecific differences in adsorption probability and the distribution of those sites on the mineral surface.The preferential silicon step site can be found in high concentrations on surface steps originating at crystal defects in the muscovite structure.Here an increase in the concentration of adsorbed atoms can be observed.A high concentration of steps often found at surface etch pits leads to the strongest increase in surface sorption.This provides a mechanistic explanation for the heterogeneous distribution of adsorbed radionuclides that have been observed in experiments.Rough mineral surfaces exhibit large numbers of steps and pits on the nanometer scale.Here adsorption is strongly increased due to the high amount of available reactive sites.Additionally, adsorption to surface kink and step sites increases the desorption energy barrier leading to improved resistance to a radionuclide release from the mineral surface.The presented model is an initial step toward a precise description of the influence of surface reactivity on adsorption.In the future, this effect should be considered in larger-scale reactive transport models that can simulate 3D pore geometries including bigger surfaces and multiple minerals.This allows for the long-term investigation of the influence of site-specific adsorption and surface nanotopography on the safety of nuclear waste repositories.

Figure 1 .
Figure 1.Schematic representation of heterogeneous sorption to mineral surfaces.The mineral surface (grey spheres) offers different adsorption sites for radionuclides (orange spheres).These adsorption sites (red) are defined by their first (green) and second (blue) coordination sphere in the crystal structure.This coordination environment of each site can influence the adsorption energy barrier.Consequently, this influence can lead to preferential adsorption sites, which influence the overall adsorption distribution on crystal surfaces.

Figure 2 .
Figure 2. Representation of the adsorption complex cluster models for the DFT calculation of ad-and desorption energy barriers.First, second, and further neighbors are used to characterize the individual adsorption sites.In total seven sites are shown: four tetrahedral sites T-K1, T-K2, T-S, T-T (with T = Si, Al(T)), and three octahedral sites O-K1, O-K2, O-S (with O = Al(O)).See Table1for more details.Cations belonging to the muscovite surface site are shown as polyhedra.

Figure 3 .
Figure 3. Flowchart for the KMC simulation.The first part (blue) simulates the dissolution of the muscovite surface and is based on the model by Kurganskaya and Luttge.[38]Here, a realistic surface nanotopography is generated.This surface is used subsequently in the second part (green) to simulate the corresponding adsorption distribution.

Figure 4 .
Figure 4. Energy curves of all muscovite sites showing the system energy over increasing Eu(OH) 3 desorption for (Left) silicon, (Center) tetrahedral aluminum, and (Right) octahedral aluminum surface sites.All sites show an energy barrier when following the opposite reaction path for adsorption.Data points at larger distances are not shown since the curve is converged.The energy barrier values are presented and compared in Figure 5.

Figure 5 .
Figure 5. Bar chart of a) adsorption energy barriers and b) desorption energy barriers for all 11 sites (see Table 1 and Figure 2) based on the calculated energy curves (Figure 4).Adsorption energy barriers show a clear trend for tetrahedral sites (Si, Al(T)): Step < Kink 2 < Terrace < Kink 1. Tetrahedral aluminum has higher energy barriers than silicon for all sites with factors between 1.5 and 4. Octahedral aluminum (Al(O)) shows an energy barrier order of Kink 1 < Step < Kink 2. It also provides the sites with the lowest (Kink 1) and highest (Kink 2) energy barriers.

Figure 6 .
Figure 6.KMC simulation of Eu(OH) 3 adsorption on the muscovite (001) plane.a) Muscovite (001) surface after the dissolution simulation.Initially, five defects with a depth of 10 nm were placed in the surface.With proceeding dissolution, the defects open up and form etch pits on the surface.The adsorption distribution for a surface cation occupation of b) 0.8% (1500 Eu(OH) 3 ), c) 4.1% (7500 Eu(OH) 3 ), and d) 8.1% (15 000 Eu(OH) 3 ).

Figure 7 .
Figure 7. Adsorption site statistics for the muscovite surface in Figure6.The top row shows the total number of adsorbed atoms at each surface site for silicon, tetrahedral aluminum, and octahedral aluminum.Silicon terrace sites dominate the overall adsorption, followed by the silicon step sites.In the bottom row, the graphs show the corresponding percentual occupancy of the surface sites.The occupancy directly follows the order of energy barriers shown in Figure5a, with low energy barriers leading to high site occupancy.

Figure 8 .
Figure 8.The adsorption distribution after 15 thousand adsorbed Eu(OH) 3 (Figure6d) on the muscovite surface is overlaid with a kernel density estimation of the local adsorbed europium density.An increase in atom density is visible when comparing flat surface sections with surface steps and etch pits.Single steps result in an intermediate increase in density (1.5-fold), while a cluster of multiple steps, often located near an etch pit center, causes a stronger increase in density (>3-fold).Two regions of interest (ROIs) are magnified to highlight the local contrast and compared to the local topography (Figure6a).ROI 1 shows the center of an etch pit with a high accumulation of steps leading to a strong increase in adsorption density.ROI 2 shows a shallower section with two major steps.Adsorption is increased at the steps compared to the atomically flat areas of ROI 2, but not as much as in the center of the pit of ROI 1.

Figure 9 .
Figure 9. Schematic representation of three different surface nanotopography configurations and the corresponding local adsorption distributions.Adsorbed atoms are sorted to terrace and step/kink sites.Step/kink sites (orange) have slightly lower adsorption and a much higher desorption energy barrier compared to terrace sites (green).a) On an atomically flat surface area, the adsorbed europium is adsorbed mostly homogeneously, preferably to silicon terrace atoms.Desorption is expected to be comparatively quick.b) A single surface step leads to a local increase in adsorption along the step while the surrounding flat surface is similar to (a).Desorption is decreased at the surface step leading to stronger retention.c) An etch pit leads to the formation of multiple steps in high local concentration leading to the highest concentration of adsorbed europium.Here the strongest retention can be expected since most atoms adsorb to step or kink sites with high desorption energy barriers.