Relationship between Micrometer to Submicrometer Surface

Feb 27, 2008 - Relationship between Micrometer to Submicrometer Surface Roughness and Topography Variations of Natural Iron Oxides and Trace Element ...
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Relationship between Micrometer to Submicrometer Surface Roughness and Topography Variations of Natural Iron Oxides and Trace Element Concentrations Cornelius Fischer,*,†,§ Volker Karius,§ Peter G. Weidler,| and Andreas Lu¨ttge†,‡ Departments of Earth Science and Chemistry, Rice UniVersity, 6100 Main Street, Houston, Texas, Geowissenschaftliches Zentrum der UniVersita¨t Go¨ttingen, Abteilung fu¨r Sedimentologie & Umweltgeologie, Goldschmidtstrasse 3, D-37077 Go¨ttingen, Germany, and Institut fu¨r Technische Chemie - Abteilung fu¨r Wasser- und Geotechnologie (ITC-WGT), Abteilung Nanomineralogie, Forschungszentrum Karlsruhe GmbH, D-76021 Karlsruhe, Germany ReceiVed October 16, 2007. In Final Form: December 7, 2007 The surface area and roughness of natural iron oxide precipitations were quantified by 3D optical microscopy in order to get information about fluid-rock interface topography in high-permeability zones. Converged surface roughness data of microscale to submicroscale topography show the predominance of macroporous half-pores (>500 nm) and the occurrence of smaller half-pores (4 and 12 µm. Figure 5 shows the results of surface roughness data representing the first convergence length on the convergence graphs. Convergence was found for the fieldof-view length of >4 to 12 µm. Results are shown as a comparison between LSM (x axis) and VSI (y axis) data. One sample (407, goethite) clearly shows different Rt, Rz, and F results when compared with the other samples. For the other samples, the peak-to-valley depth (Rt) ranges from 0.9 to 6.7 µm (VSI) and from 0.9 to 3.7 µm (LSM) (Figure 5a). The 10-point heights (Rz), describing the vertical extension of the surface building blocks, are between 0.6 and 5.7 µm (VSI) and 0.4 and 2.2 µm (LSM) (Figure 5b). The Rt and Rz data are quite similar from VSI and LSM measurements (1:1 line). Root-mean-square roughness (Rq) data are shown in Figure 5c. Large standard deviation bars indicate the broad range of the surface component size distribution. The surface roughness is between 0.1 and 1.5 µm (VSI) and 0.1 and 0.7 µm (LSM). The ratio of the measured surface size to the field-of-view size, F, is between 1 and 2.6 (VSI). Compared to the VSI data, the LSM data show a clearly broader F range between 1.2 and 5.5 (Figure 5d). Surface roughness data regarding higher orders of convergence were not reported and discussed

here because they represent surface features of the iron oxide rock substratum (e.g., clay mineral aggregation due to cleavage planes). 4.5. Surface Roughness and Topography versus the BET Surface. Figure 6 shows LSM and VSI near-convergence surface roughness Rq (Figure 6a,c) and surface factor F (Figure 6b,d) as a function of the BET surface area. (For a BET sample overview, see Table 2.) Rq and F, measured by LSM, correlate linearly with the total BET specific surface area (except for hematite sample no. 310 with a clearly higher relief, see Figure 4). The orientation of the envelopes of the data points (Figure 6a,b) emphasizes this trend. Rq and F, measured by VSI, show no correlation with the BET surface area data. The Rq, F maximum data point envelope, however, is inversely correlated with the total BET specific surface area. 4.6. Relationship between Surface Roughness Parameters. Figure 7 shows F and Rz as a function of Rq for both near convergence (at 4 µm) (Figure 7a,b) and the smallest convergence lengths (at 6-12 µm field length) (Figure 7c,d), calculated using VSI data. The comparison was made to identify the size and importance (i.e., frequency) of surface components that were identified by converged roughness parameters. In other words, are the surface parameter values shown in Figure 7a,b similar to those shown in Figure 7c,d? For near-convergence conditions (Figure 7a,b), F and Rz correlate linearly with Rq. A relatively broad parameter range exists (see envelopes). Comparisons for

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Figure 8. Laser scanning microscopy-based surface roughness data for near-convergence conditions showing (a) F vs Rq and (b) Rz vs Rq.

near-convergence data measured by LSM are highlighted by gray fields in Figure 7a,b. For the first convergence condition (Figure 7c,d), the parameter range is broader when compared to those in Figure 7a,b. Most of the Rq and F data points, however, are in the same range as shown for the near-convergence condition (gray field, compared to Figure 7a). The Rz data are clearly higher when compared to Figure 7b and are nearly constant at 2.5 µm, indicating similar heights of surface building blocks detected at the first convergence condition. To evaluate the near-convergence correlations of VSI measurements in terms of spatial resolution, Figure 8a,b shows F and Rz as a function of Rq, calculated from LSM data at nearconvergence conditions (at 2 to 3 µm sample length). In Figure 8a, F correlates linearly with Rq. Compared to VSI data (Figure 7a), a smaller surface roughness Rq controls the larger F variation of the LSM data. This relationship is underscored by the linear correlation of Rz and Rq (Figure 8b). 4.7. Comparison of Surface Roughness Data and Trace Element Concentrations. Two encrustations were examined to analyze the range of surface roughness data on the scale of hand specimens. Sample 225 is an encrustation of goethite, and sample 406 is an encrustation of X-ray amorphous iron oxides (Table 2). Roughness parameters of eight subsamples of sample 225 (goethite) were analyzed (Figure 9). We calculated roughness parameters for near-convergence conditions (a ) 4 µm) to quantify micrometer to submicrometer surface building blocks. The sizes of root-mean-square roughness (Rq), surface factor (F), and roughness depth (Rt) are relatively small compared to the overall range of these parameters found for iron oxides (Figure 4). Roughness parameters F, Rq, and Rt of the sample matrix (Figure 9) show a linear correlation (Figure 10). The spatial dispersion of the roughness parameter variation of this encrustation is shown in Figure 10b,d. Error bars indicate the standard deviation of the mean value as calculated from three measurements of different points of the same sample region (within the rectangle surrounding sample points, see Figure 9a). Surfer software was used to calculate the roughness parameter interpolations for the entire encrustation area between the sample points using the Kriging method (Figure 9c,e). A similar shape for the modeled Rq and F surfaces was found. The concentrations of P, V, Cu, Zn, Pb, and U were determined from prepared encrustation sections (Figure 9a, squares). The iron-normalized element concentrations are shown against the surface roughness Rq in

Figure 9. Surface roughness data of eight subsamples of a goethite encrustation calculated from VSI measurements (near-convergence condition): (a) encrustation sample 225 and subsample points; (b) F over the encrustation area of eight subsamples; (c) Kriging interpolation of F data over encrustation area; (d) Rq over the encrustation area of eight subsamples; and (e) Kriging interpolation of Rq data over the encrustation area.

Figure 11. For the subsamples of sample 225, no correlation was found between normalized trace element concentrations and surface roughness data. The small range of roughness Rq of the subsamples investigated here is remarkable. We found very similar roughness for all subsamples within the 2σ range of the mean values of Rq for each subsample. Surface roughness parameters of the 15 subsamples of sample 406 (X-ray amorphous iron oxide) are shown in Figure 12. The converged root-mean-square roughness (Rq), surface factor (F), and roughness depth (Rt) are relatively small compared to the overall range of these parameters found in iron oxides (Figure 13a,b; see dashed lines). The parameter range, however, is broader

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Figure 10. Surface roughness data of eight subsamples of a goethite encrustation (sample 225) calculated from VSI measurements (nearconvergence condition): (a) F vs Rq compared to Figure 7a; (b) detail of part a; (c) Rt vs Rq compared to Figure 7b; and (d) detail of part c.

than that found for the goethite sample (225) (Figure 10). Again, the roughness parameters show a linear correlation (Figure 13b,d). Concentrations of P, V, Cu, Zn, Pb, and U were measured for the encrustation parts around the sample points that were analyzed for roughness parameters (Appendix 2). The iron-normalized element concentrations are shown against the roughness Rq (Figure 13). A correlation was found between element concentrations and surface roughness data for uranium only. The correlation between the Fe-normalized trace element concentration and both Rq and F is indicated by R2 ) 0.7 (Figure 15a,b). The Rq and F error bars denote the standard deviation of the mean value as calculated from three measurements of roughness parameters taken near each point of the sample matrix. The spatial dispersion of the roughness parameter variation is shown in Figure 12b,d. On the basis of the measured parameter

data, we calculated roughness parameter interpolations as described previously (Figure 12c,e). A similar shape of the modeled Rq and F surfaces was found for both measured and interpolated Fe-normalized uranium concentrations. The normalized uranium concentration plotted against the spatial sample point distribution shows a surface with an inverted shape when compared to the roughness parameter surfaces (Figure 12b-g). This is made particular visible by the spatial distribution of local maxima and minima in Figure 12c,e,g.

5. Discussion The iron oxides investigated in this study are encrustations that precipitated during oxidative weathering on bounding surfaces in alum slate or copper shale (Kupferschiefer). On alum slates, we found encrustations of goethite, jarosite, schwertmannite,

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Figure 11. Fe-normalized element concentrations of (a) P, (b) V, (c) Cu, (d) Zn, (e) Pb, and (f) U against surface roughness Rq data of sample 225.

and X-ray amorphous amorphous iron oxides. On weathered copper shale, we found encrustations of X-ray amorphous amorphous iron oxide, magnetite, and hematite. There are two possible explanations for the occurrence of several secondary minerals found on similar substrata. First, the pH of the microenvironments present with the same zone of oxidative weathering could be responsible for the formation of various iron oxides. This variation in microenvironments could be caused by variations in meteoric flow through the oxidizing rock volume. Second, the analyzed minerals that were formed during weathering periods can differ in age and may therefore show different maturation/transformation stages. Aging of iron oxides could be

the reason for the occurrence of different iron oxide minerals (X-ray amorphous iron oxides, schwertmannite, and jarosite vs goethite or hematite) on similar substrata as a result of similar formation conditions.35-37 Discriminating between these two explanations is not possible because of the large uncertainties in weathering age and aging processes. (35) Kennedy, C. B.; Scott, S. D.; Ferris, F. G. Chem. Geol. 2004, 212, 269277. (36) Singer, A.; Schwertmann, U.; Friedl, J. Eur. J. Soil Sci. 1998, 49, 385395. (37) Gagliano, W. B.; Brill, M. R.; Bigham, J. M.; Jones, F. S.; Traina, S. J. Geochim. Cosmochim. Acta 2004, 68, 2119-2128.

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Figure 12. Surface roughness data compared to U concentrations of 13 subsamples of an X-ray-amorphous iron oxide encrustation: (a) encrustation sample and subsample points (missing chemical analysis data are indicated by squares without a white center); (b) F data over an encrustation area of 15 subsamples; (c) Kriging interpolation of F data over the encrustation area; (d) Rq data over the encrustation area of 15 subsamples; (e) Kriging interpolation of Rq data over the encrustation area; (f) Fe-normalized U concentration of 13 subsamples over encrustation area; and (g) Kriging interpolation of Fe-normalized U concentration data over the encrustation area. Red lines show the negative correlation among Rq, F, and U/Fe. (See Figure 15.)

5.1. BET Surface Area. BET surface area data of the iron oxide encrustations investigated here show broad ranges for several types of iron oxides (Figure 3). Magnetite and hematite samples have the lowest microporous and total BET surface areas. Goethite microporous and total BET surface areas are in between the hematite and jarosite surface areas. HCl-extractable (X-ray amorphous) iron oxide samples have the largest microporous and meso- to macroporous BET surface size data. The BET surface area ranges are similar to those reported for synthetic iron oxides.9 We note the strong correlation between the microporous and the total BET surface area (R2 ) 0.8) for the majority of the high HCl-Fe-bearing samples and most of the goethite encrustation samples. This correlation reflects constant ratios between microporous and meso- to macroporous surface portions. We predict that a similar pattern exists for microporous, mesoporous, and macroporous mineral aggregates for most of the iron oxides, particularly for the X-ray amorphous iron oxides. 5.2. Surface Building Block Size Interpreted from NearConvergence-Condition Data. A comparison between VSI- and LSM-based roughness parameter calculations was performed to quantify the differences in surface topography. VSI is able to

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detect flat macropores or building blocks (d > 500 nm, h > 2 nm), whereas LSM can detect isometric macropores or building blocks (d, z > 100 nm). These differences allow us to make interpretations about the occurrence, frequency, variation in size of pores and building blocks. Information about the smallest surface building blocks can be derived from the calculated roughness parameter results of the near-convergence condition. Remarkable differences were detected for parameter F only (Figure 4). Using the Rt and Rz calculations, we conclude that the iron oxide surfaces are composed of a relief with an amplitude range of approximately 1 µm. Most of the samples show surface roughnesses (Rq) of hundreds of nanometers. Rq results are slightly smaller than Rz height data. Because Rt data are also similar to Rz data, most of the building blocks or half pores on the surface must have a Vertical dimension similar to Rz. The surface building blocks occur frequently on the surface; otherwise, the Rq values, which represent the surface topography standard deviation, would be much smaller. The higher Rz/Rq ratio found for the first convergence condition {Figure 5 vs Figure 4; first convergence (mean Rz ≈ 3 µm/mean Rq ≈ 0.6 µm ) 5) vs near convergence (mean Rz ≈ 1 µm/mean Rq ≈ 0.3 µm ) 3.3)} indicates that most of the surface building blocks are smaller than the converged Rz size reported in Figure 5b. In other words, the surface building blocks derived from near-convergence data occur more frequently on the encrustation surface than those resulting from first-convergence data. Because both VSI and LSM data show similar Rt, Rz, and Rq results, the lateral extension of surface building blocks responsible for the roughness data must be larger than 500 nm (as a result of the lateral resolution of the VSI method). This is also evident in the 3D image reconstructions from the x, y, and z data (Figure A1). From the clearly higher F values found using LSM measurements (Figure 4d), we also conclude that some building blocks must exist with a lateral extension of 100-500 nm. This interpretation is possible from the lateral resolution of LSM and VSI. Compared to LSM-based F calculation results, the differences and the range of all of the F data calculated from VSI measurements are small. In contrast to LSM data, the small differences measured by VSI are able to show the occurrence of flat macropores (or flat building blocks with height differences that are smaller than 100 nm). If such halfpores occured more frequently, then the F results calculated from VSI data would be higher than those calculated from LSM data. 5.3. Surface Building Block Size Interpreted from Converged Roughness Parameters. Convergence was found for a field-of-view length of several micrometers (Figure 5). Surface building blocks have heights (Rz) of approximately 3 µm. As mentioned above, these larger components do not dominate the overall surface area size (Figure 4d vs Figure 5d). Moreover, surface roughness Rq is smaller than 1 µm for most of the measurements. The small Rq value indicates that the smaller surface building blocks (see roughness results of the nearconvergence condition) occur frequently and dominate the surface relief. In contrast, the larger components characterized by data derived from the first-convergence condition occur infrequently. This causes the low Rq values reported for the first convergence condition. The F values calculated from the first convergence data are not significantly higher than those of the near-convergence calculations. Thus, we conclude that the smaller components, interpreted from the near-convergence roughness data, are responsible for the main part of the encrustation surface area size.

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Figure 13. Surface roughness data of 15 subsamples of a X-ray amorphous iron oxide encrustation (sample 406) calculated from VSI measurements (near-convergence condition): (a) F vs Rq compared to Figure 7a; (b) detail of part a; (c) Rt vs Rq compared to Figure 7b; (d) detail of part c.

5.4. Surface Building Block Size Interpreted from VSI, LSM, and BET Data Comparison. The comparison between surface parameters (Rq, F; near-convergence condition) and the total BET surface area data shows a linear correlation for LSM data (Figure 6a, b). This indicates that the BET surface area correlates with the surface roughness caused by surface building blocks that were detected by LSM. Figure 2 illustrates the occurrence of isometric macropores that resulted in the LSM F surface data. Surface building blocks of this dimension were not detected by VSI measurements. No correlation between VSI surface parameters (Rq, F; near-convergence condition) and BET surface area was found (Figure 6c,d). We conclude that the surface components detected by LSM are the largest pores that contribute to the BET surface area results presented here. 5.5. Surface Parameter Variation versus Geochemical Variation. We also suggest a possible correlation between the

micrometer-to-submicrometer surface topography and the trace element concentration. This correlation does not simply reflect the common chemical sorption of dissolved trace element species from aqueous solution onto iron oxide surfaces. We suggest the putative adsorption of fine particles (colloids) onto mineral surfaces10 (Figure 2). To distinguish trace element variations arising from this process alone, the Variation of trace element concentration from molecule adsorption, proportional to the iron oxide concentration, was removed from the data by Fe normalization of trace element concentration. Subsamples of two hand specimens were analyzed. For the goethite sample (Figure 10), no correlation was found. No surface roughness dispersion range exists to explain geochemical variations. For the X-ray amorphous encrustation (sample 406, Figures 13-15), a broader surface roughness range was found. The larger variation of surface roughness of sample 406 compared

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Figure 14. Fe-normalized element concentrations of (a) P, (b) V, (c) Cu, (d) Zn, (e) Pb, and (f) U against surface roughness Rq data of sample 406.

to that of sample 225 could explain the contrasting correlation behavior. For sample 406, an inverse, linear correlation was found between the surface roughness Rq and the uranium concentration of the analyzed subsamples (Figures 14f and 15). This means that smoother surface parts (Rq ≈ 250 nm) contain more uranium than those having a higher surface roughness (Rq ≈ 400 nm). The same correlation was found for parameter F. Therefore, the half-pores responsible for the resulting surface variation have diameters of >500 nm. The surface height variation is in the range of 1 to 2 µm (derived from Rt). Although we can measure surface topography variations and determine a correlation between these results and the uranium concentration of the

encrustation, the causality of this correlation remains open to debate. Moreover, the reason for the lack of correlation between the surface roughness data and the concentration of other elements analyzed here is unknown. It is possible that the encrustation’s P concentration shows a correlation to surface roughness if the subsamples with the lowest and the highest concentrations are neglected. We conclude that for both findingssthe limited roughness variation range and the lack of roughness versus the concentration correlation for the V, Cu, Zn, and Pbsa partitioning process could be responsible. Such partitioning behavior related to the micrometer/submicrometer surface topography is a further indication of the potential migration and subsequent adherence

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Figure 15. Fe-normalized U concentration of 13 subsamples of a X-ray amorphous iron oxide encrustation (sample 406) against (a) surface roughness Rq and (b) surface ratio F calculated from VSI measurements. The linear regression was calculated.

of U-bearing colloids38,39 to the surface of sample 406, as reported in several studies.40-42 Experimental investigations are necessary to explain the correlation discussed here. To explain the potential importance of surface roughness, however, such experimental investigations must exclude sorption reactions on the molecular scale. Then, the explanation of micrometer/submicrometer surface topography variations and their potential effects on trace element concentration could improve the understanding of trace metal uptake by iron oxides in nature. Since the review article by Hochella,43 a multitude of studies have been performed to show variations of mineral surface reactivity on atomic- and molecular-scale topography. However, here we ask for the mineral surface reactivity on the scale of small particles or colloids. In other words, a second type of mineral surface reactivity is discussed here, which is superimposed on the reactivity on the molecular scale. Moreover, the role that microorganisms play during the formation of iron oxides and the uptake of trace elements by iron oxides needs to be included in further investigations and interpretations. There could be a relationship between microorganism activity and micrometer/submicrometer surface topography features as well as trace element uptake. Several studies showed that trace element immobilization results from metal oxide formation and microorganism activity (e.g., for As,44 P, Ba, Ma, Pb, Sr, V, and Zn precipitation45-47).

6. Summary (1) Bounding surfaces in rocks are highly permeable zones within the rock volume. Encrustations often occur at bounding surfaces. Therefore, the characterization and quantification of (38) Krawczyk-Barsch, E.; Arnold, T.; Reuther, H.; Brandt, F.; Bosbach, D.; Bernhard, G. Appl. Geochem. 2004, 19, 1403-1412. (39) Artinger, R.; Rabung, T.; Kim, J. I.; Sachs, S.; Schmeide, K.; Heise, K. H.; Bernhard, G.; Nitsche, H. J. Contam. Hydrol. 2002, 58, 1-12. (40) Lieser, K. H.; Ament, A.; Hill, R.; Singh, R. N.; Stingl, U.; Thybusch, B. Radiochim. Acta 1990, 49, 83-100. (41) Baalousha, M.; Kammer, F. V. D.; Motelica-Heino, M.; Baborowski, M.; Hofmeister, C.; Le Coustumer, P. EnViron. Sci. Technol. 2006, 40, 2156-2162. (42) Pourret, O.; Dia, A.; Davranche, M.; Gruau, G.; Henin, O.; Angee, M. Appl. Geochem. 2007, 22, 1568-1582. (43) Hochella, M. F. ReV. Mineral. 1990, 23, 87-132. (44) Ohnuki, T.; Sakamoto, F.; Kozai, N.; Ozaki, T.; Yoshida, T.; Narumi, I.; Wakai, E.; Sakai, T.; Francis, A. J. Chem. Geol. 2004, 212, 279-290. (45) Ferris, F. G.; Hallbeck, L.; Kennedy, C. B.; Pedersen, K. Chem. Geol. 2004, 212, 291-300. (46) Toner, B.; Manceau, A.; Webb, S. M.; Sposito, G. Geochim. Cosmochim. Acta 2006, 70, 27-43. (47) Villalobos, M.; Bargar, J.; Sposito, G. Elements 2005, 1, 223-226.

the surface roughness and topography of encrustations are prerequisites to the evaluation of potential interaction between the interface topography and fluid suspension load. (2) The surface topography microscopy results presented here demonstrated the potential and the usefulness of employing converged surface roughness parameters when quantifying the dimensions and frequency of half-pores at interfaces. (3) Surface topography variations in the micrometer/submicrometer range could be responsible for interaction processes between iron oxide encrustations and the fluid load. This conclusion is based on a linear correlation found between the half-pore height (as well as the surface area) and the uranium concentration of iron oxide encrustation subsamples of a hand specimen. However, other trace element concentrations did not correlate to surface topography variations. Therefore, for a fundamental understanding of the promising approach introduced here, well-defined natural and experimental systems must be investigated. (4) It is probable that three interacting factors control geochemical processes at iron oxide interfaces: the sorption of molecules, the sorption of micrometer-/submicrometer-sized particles (colloids), and the activity of microorganisms at interfaces. Further studies should try to evaluate the varying importance of these factors to understand geochemical processes at interfaces in nature better. Acknowledgment. We thank three anonymous reviewers for very useful comments that significantly improved this article. Thanks to Rolf S. Arvidson for helpful discussions and for assistance with the English-language presentation.We gratefully acknowledge support for this study from the Deutsche Forschungsgemeinschaft (grant FI1212/1), from ONR grant N0001406-1-0115, from MURI grant FA9550-06-1-0292, and from the Alexander von Humboldt-Foundation (Feodor Lynen Fellowship to C.F.).

Appendix 1: Application of the Concept of Converged Roughness Parameters If a measurement’s field of view is within the size of a structural component (“building block”), then the length and height of this block would dominate the amplitude of the surface roughness parameters. If the field of view is minimized, then the impact of such a building block on roughness parameters is diminished. Smaller building blocks that sit on top of a larger building block, however, will dominate the surface roughness values. Natural surfaces are likely to show such a mixture of differently sized

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Figure A1. Comparison of vertical scanning interferometry (VSI) microscopy data sets and SEM pictures of the same iron oxide encrustation: (a) (x, y, z) data set (range: x ) 163 µm, y ) 123 µm, z ) 14.8 µm) of vertical scanning interferometry microscopy measurements showing surface components in a size range of some tens of micrometers; (b) VSI data set showing surface components of approximately 10 µm length; (c) SEM picture of the same field of view used for data measurement in part b, indicating the similar size of surface components; (d) VSI data; and (e) SEM picture of surface textures in the micrometer and submicrometer range.

building blocks; therefore, we applied the concept of surface roughness convergence in this study. We define a surface parameter as converged if neighboring data points of the convergence graph show a flat slope (df(a)/da near 0, where a is length) in contrast to the adjoining steep-slope sections of the graph (e.g., Figure A3a). If this criterion is satisfied, then the converged parameter value can be used to characterize and quantify the topography of the associated surface section. This concept was applied to rock surfaces by Fischer and Lu¨ttge25 for the first time to demonstrate the variation in reactivity of a rock surface during an ongoing weathering process. An example of differently sized surface building blocks forming a rock surface is presented in Figure A1a-e. This example clearly demonstrates the need for converged surface parameters. Figure A1a shows a typical 3D (x, y, z) data set (size 123 × 163 µm2, z range 14.8 µm). Here, the surface of a goethite encrustation

Figure A2. Three-dimensional view of the surface relief calculated from VSI data presented in Figure A1d.

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Figure A3. Convergence graphs of roughness parameters (a, c) Rt, Rz, and Rq and (b, d) F. (a, b) Two convergence sites. Additionally, the parameter data for a ) 4 µm indicate componenets with a lateral extension smaller than 4 µm (near-convergence condition due to R and F minima). (c, d) One-parameter convergence. The parameter data at a ) 4 µm are far from convergence (F maximum).

Figure A4. Box-whisker plots of convergence length a and surface roughness parameters F, Rq, Rz, and Rt.

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is composed of hills and valleys with a size of ca. 50 µm in length and 14 µm in height. A close view of the encrustation {x, y, z data set (Figure A1b) and SEM image (Figure A1c)} shows surface building blocks that are 10 µm in size. These features have a flat shape (Figure A1b, see arrows). Figure A1d,e depicts even smaller surface building blocks (diameter of approximately 1 µm) as compared to the ones shown in Figure 2b,c. A 3D image calculated from the data set of Figure A1d is given in Figure A2. Because Figure A1d is not only an image (such as Figure A1e) but also a 3D set of height data, a statistical approach can be used to evaluate the surface topography quantitatively. Our approach to parameter convergence is demonstrated in Figure A3a-d and applied to the surface topography data shown in Figures A1 and A2. Figure A3a shows the convergence of Rt, Rz, and Rq, and Figure A3b shows the convergence of F. The latter parameter is critically dependent on the size of the field of view, which is expressed by the length of the field axis, a. The convergence steps of roughness parameters are highlighted in Figure A3a-d. Figure A3c,d demonstrates the absence of surface components on the scale of a ) 4 µm. The detected absence of convergence underlines the importance of the direction of convergence within the data set. In contrast to Figure A3a,b, the corresponding data from Figure A3c,d at a ) 4 µm lack convergence and do not provide information about surface building block height and width. Generally, the surface components are not periodically arranged at rock surfaces. As a consequence, the direction of convergence must consider surface inhomogeneities. The importance of the direction of convergence is illustrated in more detail in Figure A4. Box-whisker plots show the dispersion of surface topography parameters from six different, arbitrarily chosen data sets gathered from the same sample. Each data set represents a field of view measuring 123 × 163 µm2. Convergence analyses were performed in two directions for each data set. A recurrent bisection of the measuring field provided smaller and smaller data sets. From the 12 resulting convergence graphs, only 6 near-convergence results were found and 9 convergence results with convergence lengths of a ) 6-12 µm, 9 convergence results with a ) 12-24 µm, and 4 convergence

Fischer et al. Appendix 2: Geochemical Data concentration [mg/kg] sample

position

P

V

Cu

Zn

Pb

U

Fe [wt %]

225-11 225-12 225-13 225-14 225-21 225-22 225-23 225-24 406-12 406-13 406-14 406-21 406-22 406-23 406-24 406-31 406-32 406-33 406-34 406-42 406-43 406-44 406-54

(0, 0) (15, 0) (30, 0) (45, 0) (0, -15) (15, -15) (30, -15) (45, -15) (15, 0) (30, 0) (45, 0) (0, -15) (15, -15) (30, -15) (45, -15) (0, -30) (15, -30) (30, -30) (45, -30) (15, -45) (30, -45) (45, -45) (45, -60)

11 062 8196 9027 8449 8050 7232 7390 8082 8347 4996

1386 418 656 577 898 821 878 928 801 305

749 413 355 241 667 511 497 451 935 631

614 215 370 217 582 183 175 214 513 458

23 22 23 17 24 19 24 17 21 16

10 9 11 12 7 7 9 12 23 16

19.2 11.8 10.0 8.3 13.4 10.3 10.1 10.2 13.7 9.8

12 682 9679 7416 5085 14 981 9042 11 918

931 758 611 251 1157 477 1038

1382 1239 957 608 1506 1070 1463

556 413 439 245 688 479 441

33 26 20 13 37 22 28

30 26 20 13 35 23 28

19.7 16.4 13.2 8.2 22.4 14.8 20.2

9987 8567 10 758 10 806

822 624 674 998

1044 1104 1362 1508

560 608 465 480

30 24 30 39

25 22 27 29

17.0 14.3 18.2 18.0

results with a ) 35-69 µm. The Box-whisker plots of surface topography parameters Rt, Rz, Rq, and F indicate the dispersion of each parameter regarding convergence length a (short axis length of the rectangular field of view). There is good correlation between the order of convergence and height parameters Rt and Rz. The convergence length a represents the wavelength of each building block (i.e., the length of a “hill” or a “valley”), and Rz and Rt represent the respective heights. This example illustrates our ability to detect the size range of building blocks by analyzing converged roughness parameter data. LA703221K