Use of iron oxide nanoparticles for immobilizing phosphorus in-situ: Increase in soil reactive surface area and effect on soluble phosphorus

a r t i c l e i n f o

a b s t r a c t Phosphorus (P) immobilization has potential for reducing diffuse P losses from legacy P soils to surface waters and for regenerating low-nutrient ecosystems with a high plant species richness. Here, P immobilization with iron oxide sludge application was investigated in a field trial on a noncalcareous sandy soil. The sludge applied is a water treatment residual produced from raw groundwater by Fe(II) oxidation. Siliceous ferrihydrite (Fh) is the major Fe oxide type in the sludge. The reactive surface area assessed with an adapted probe ion method is 211-304 m 2 g À1 for the Fe oxides in the sludge, equivalent to a spherical particle diameter of~6-8 nm. This size is much larger than the primary Fh particle size (~2 nm) observed with transmission electron microscopy. This can be attributed to aggregation initiated by silicate adsorption. The surface area of the indigenous metal oxide particles in the field trial soils is much higher (~1100 m 2 g À1 ), pointing to the presence of ultra-small oxide particles (2.3 ± 0.4 nm). The initial soil surface area was 5.4 m 2 g À1 and increased linearly with sludge application up to a maximum of 12.9 m 2 g À1 when 27 g Fe oxides per kg soil was added. In case of a lower addition (~10-15 g Fe oxides per kg soil), a 10-fold reduction in the phosphate (P-PO 4 ) concentration in 0.01 M CaCl 2 soil extracts to 0.3 mM was possible. The adapted probe ion method is a valuable tool for quantifying changes in the soil surface area when amending soil with Fe oxide-containing materials. This information is important for mechanistically predicting the reduction in the P-PO 4 solubility when such materials are used for immobilizing P in legacy P soils with a low P-PO 4 adsorption capacity but with a high surface loading.

Introduction
Agricultural soils with a legacy of elevated soil phosphorus (P) contents from historic P applications represent a chronic source of dissolved P losses to surface waters, contributing to eutrophication (Kleinman et al., 2011;Schoumans and Chardon, 2015). Although halting P applications to these so-called ''legacy P soils" can prevent a further increase in dissolved P losses (Kleinman et al., 2011;Koopmans et al., 2004;Van der Salm et al., 2009), current P emissions to surface waters can be significant and longlasting, requiring additional measures to solve this environmental problem (Buda et al., 2012;Groenenberg et al., 2013;Schoumans et al., 2014).
One strategy for reducing environmental P losses is to immobilize P in-situ in legacy P soils with a low P adsorption capacity by mixing P-adsorbing materials through the P-rich topsoil. To achieve this goal, numerous studies have proposed the use of Fe oxide-containing materials (Agyin-Birikorang et al., 2007;Callery et al., 2015;Elliott et al., 2002;Fenton et al., 2011;Schärer et al., 2007;Stoner et al., 2012). Such materials have been used as well for reducing the level of bioavailable P in lake sediments (Fuchs et al., 2018) as for immobilizing trace metals in contaminated soils (Lin et al., 2019;Nielsen et al., 2014;Rajapaksha et al., 2015).
RIn various studies (Agyin-Birikorang et al., 2007;Callery et al., 2015;Elliott et al., 2002), water treatment residuals (WTRs) have been used for increasing P adsorption to the solid phase, causing a corresponding decrease in the equilibrium P concentration in the soil solution. These WTRs were obtained from drinking water production facilities using Fe or Al salts as coagulant to remove suspended solids and natural organic matter (OM) from raw surface water (Ippolito et al., 2011). The metal oxides in these WTRs have a high phosphate (P-PO 4 ) adsorption capacity, related to a high specific surface area (SSA) and a high site density (Celi et al., 2003;Hiemstra, 2013;Hiemstra et al., 2010a;Wang et al., 2013). For this reason, Fe-and Al-based WTRs have received considerable attention as cost-effective P-adsorbing materials to reduce dissolved P losses from legacy P soils (Ippolito et al., 2011).
A similar strategy to immobilize P can be used for regenerating low-nutrient ecosystems with a high plant species richness on former agricultural land having a legacy of elevated soil P contens (Geurts et al., 2011;Gilbert et al., 2003). A reduction in the level of readily available P in these soils is then required because P enrichment of terrestrial herbaceous ecosystems has been associated with an increase in biomass production and a loss of plant species diversity (Wassen et al., 2005). For example, Ceulemans et al. (2014) found a negative correlation between plant species richness of European grasslands and the level of soil available P as measured with the Olsen P extraction method. In ecological engineering projects, removal of the P-rich topsoil is often used to create P-poor conditions (Verhagen et al., 2001). However, this measure is generally expensive and it can have various undesired effects including a deterioration of soil quality, disturbance of local soil hydrology, removal of soil biota and plant seed stocks, and destruction of archeological remains (Timmermans and Van Eekeren, 2016). Hence, the application of WTRs to the P-rich topsoil of former agricultural land can offer a suitable alternative for reducing the readily available P level. The type and amount of Fe oxides in these materials as well as their specific surface area (SSA) are the major factors in determining the capacity of WTRs to bind P-PO 4 (Celi et al., 2003;Hiemstra, 2013;Hiemstra et al., 2010a;Wang et al., 2013). This type of information is indispensible for surface complexation modelling to predict the bioavailability and mobility of ions in soil (Groenenberg and Lofts, 2014;Hiemstra and Van Riemsdijk, 1996).
In the present study, we investigated the effectiveness of iron oxide sludge application for immobilizing P in-situ in a field trial executed on a former agricultural grassland on a noncalcareous sandy soil. The iron oxide sludge applied is a WTR rich in Fe oxides, derived from the oxidative removal of Fe(II) present in anaerobic groundwater to produce drinking water . In our field trial, soil samples were taken shortly before and 3 and 14 months after sludge application. The field trial soils were used for measuring their SSA and the equilibrium P-PO 4 concentration in 0.01 M CaCl 2 soil extracts to mimic soil solution conditions (McDowell and Sharpley, 2001). Our main goal was to quantify how the change in the solubility of P-PO 4 could be mechanistically interpreted from the increase in the SSA of the field trial soils after sludge application. Since the reactivity of the field trial soils amended with sludge results from the SSA of the indigenous natural metal oxides initially present and the SSA of the Fe oxides added with the sludge, the challenge was to disentangle the contribution of both sources to the overall SSA. Although the SSA of WTRs has been assessed before Makris et al., 2005), the change in the soil surface area after application of WTRs has received no attention yet in P immobilization trials.
To realize the above goal, we identified and characterized the Fe oxides in the initial iron oxide sludge used in the field trial. For this purpose, a suite of physico-chemical methods was used, comprising transmission electron microscopy (TEM), X-ray absorption spectroscopy (XAS), X-ray diffraction (XRD), and BET-N 2 gas adsorption. For assessing the contributions of the indigenous oxides initially present and the Fe oxides added with the sludge to the overall SSA of the field trial soils, we used the so-called ''probe ion" method from Hiemstra et al. (2010a). Since the experimental approach corresponding to this method is rather laborious, we adapted it to make it more convenient for a large series of soil samples.
With our work, we want to demonstrate how the contribution of the Fe oxides added with the iron oxide sludge to the overall SSA of the field trial soils can be resolved by measuring the soil surface area with the adapted probe ion method. The surface areas of the indigenous oxides initially present and the added Fe oxides were compared for disclosing any differences in SSA and corresponding particle diameter. For this comparison, we included the information collected during our physico-chemical characterization of the Fe oxides in the sludge.
In the last part of our work, we want to demonstrate how the P-PO 4 concentration in the 0.01 M CaCl 2 soil extracts is related to the SSA of the field trial soils for providing a mechanistic understanding of the reduction in P-PO 4 solubility after iron oxide sludge application. To put our results in a more practical context, we determined the effect of sludge application on the P saturation index (PSI) of the field trial soils, defined as the molar ratio a between the amount of reversibly adsorbed P-PO 4 and the summed amounts of amorphous Fe and Al oxides (Van der Zee and Van Riemsdijk, 1988). Based on the PSI (Elliott et al., 2002) and how it relates to the P-PO 4 concentration in soil solution, the application rate of Fe oxide-containing materials required to reduce the P-PO 4 solubility to the desired level can be determined when considering a P immobilization scenario for legacy P soils.

Field trial and sampling
The field trial was conducted in the nature reserve area ''Groote Heide" on a noncalcareous sandy soil near Heeze in the south of The Netherlands. In the past, the field trial site was used as an agri-cultural grassland. After abandonment, a semi-natural grassland vegetation developed due to repeated mowing as a management practice for removing nutrients (Timmermans and Van Eekeren, 2016). Two blocks with 8 plots each were established. The plots had a size of 6 by 6 m and were separated by an intermediate distance of 1.5 m. For one block, the upper 5 cm-soil layer of each plot was removed whereas the topsoil remained present in the other block. For both blocks, 3 plots were amended with iron oxide sludge (25 June 2013).
The iron oxide sludge used is an industrial by-product from the production of drinking water in a water treatment facility of Brabant Water Ltd. A description of the process of iron oxide sludge production at this facility  can be found in Section S1 of the Supplementary data. The raw groundwater has a pH of 6.1 ± 0.1 and contains 23.5 ± 2.2 mg Ca L -1 , 10.7 ± 1.3 mg Fe L -1 , 8.9 mg Si L -1 , and 0.07 mg P L -1 . The values for pH, Ca, and Fe represent the average and standard deviation of 13 samples analyzed by Brabant Water Ltd between 2009 and 2012. The values for Si and P are from a single sample collected in 2012 and analyzed at Eawag. Liquid iron oxide sludge was collected from a sedimentation basin at the water treatment facility (Fig. S1) and transported to the field trial site with a tank truck.
The iron oxide sludge was injected from a slurry tank into the soil using a trailing-foot system by cutting a shallow slit in the soil into which the sludge was injected (Fig. S1). Next, the sludge was mixed with the soil by mechanical mixing of the upper 20 cmsoil layer with a cultivator. In the field, a grab sample of the iron oxide sludge was taken from the slurry tank. From each plot receiving sludge, composite soil samples were taken shortly before sludge application. The soil sampling depth was 25 cm for the block where the topsoil remained present whereas it was 20 cm for the block where the upper 5 cm soil layer was removed. For each composite soil sample, 20 subsamples were combined. Soil sampling was repeated 3 months (25 September 2013) and 14 months (8 September 2014) after sludge application.
The sludge and soil samples were dried at 40°C and sieved (2 mm). Before sieving, the sludge sample was crushed.

General chemical properties
The pH was measured in a settling suspension of the sludge in 0.01 M CaCl 2 , prepared at a solution-to-solid ratio (SSR) of 10 L kg À1 and shaken for 2 h on a linear shaker at 180 strokes (S) min À1 . The sludge was digested with Aqua Regia (AR) (Houba et al., 1997) for total element analysis in combination with inductively coupled plasma -optical emission spectroscopy (ICP-OES; Varian Vista Pro, Varian Australia, Mulgrave, Australia) for measuring Cu, Fe, Mn, P, and Zn and high-resolution -inductively coupled plasma -mass spectroscopy (HR-ICP-MS; Thermo Scientific Element 2; Thermo Electron, Bremen, Germany) for As, Cd, Ni, and Pb. Total Al, Ca, and Si contents were analyzed using a desktop energy-dispersive X-ray fluorescence spectrometer (XEPOS+, SPECTRO Analytical Instruments GmbH, Kleve, Germany). The BET-SSA was determined with the BET-N 2 gas adsorption method (Quantachrome Nova; duplicate 6-point analysis). Data for the organic and inorganic carbon (C) contents were taken from  who determined these properties for another batch of sludge from the same water treatment facility.

Acid ammonium oxalate extraction
Since the standard 0.2 M acid ammonium oxalate extraction (AAO) method used for extracting amorphous Fe oxides from soil (Schoumans, 2000;Schwertmann, 1964) may be inadequate for Fe-rich WTRs, we adapted this method for iron oxide sludge searching for the optimal SSR and extraction time. The dried sludge was extracted with 0.2 M AAO (pH 3.0 ± 0.1) at an SSR of 20, 100, 200, 300, and 400 L kg À1 . Duplicate samples of 1.5 g dried sludge were suspended in Â mL 0.2 M AAO solution in polyethylene bottles with Â = 30 mL (20 L kg À1 ), 150 mL (100 L kg À1 ), 300 mL (200 L kg À1 ), 450 mL (300 L kg À1 ), and 600 mL (400 L kg À1 ) and shaken at 180 S min À1 on a linear shaker in the dark. For the SSRs of 20, 100, and 200 L kg À1 , a subsample (5 mL) was taken from the suspensions after 2, 4, and 24 h of shaking. The subsamples were centrifuged for 10 min at 3000 revolutions min À1 (~2100 Â g) and filtered over a 0.45 mm-filter membrane (Aqua 30/0.45 CA Whatman) with removal of the first~2 mL of the filtrate. Subsequently, Fe (Fe ox ), Al (Al ox ), and P (P ox ) were measured by ICP-OES. The pellets precipitated at the bottom of the centrifuge tubes from the subsamples taken after 2 and 4 h were re-suspended in 5 mL 0.2 M AAO and back-donated to the suspensions to maintain a constant SSR during shaking in the remaining extraction period. The amounts of Fe, Al, and P removed from the suspensions with the 5 mL subsamples taken after 2 and 4 h were added up to the amounts of these elements extracted at 4 and 24 h, respectively. For the SSRs of 300 and 400 L kg À1 , subsamples were taken after 4 h of shaking and analyzed as described above. In a parallel experiment with the same setup, the pH was measured in the settling suspensions.

Bicarbonate extraction
The iron oxide sludge was equilibrated with 0.5 M NaHCO 3 according to Hiemstra et al. (2010a) to measure the P-PO 4 concentration in solution. For this extraction, an SSR of 50 L kg À1 was used, prepared by suspending a sample of 1 g dried iron oxide sludge in 50 mL 0.5 M NaHCO 3 . To facilitate removal of OM, 0.4 g powdered activated carbon was added. The activated carbon was pre-cleaned by extraction with 0.2 M AAO in the dark using an SSR of 50 L kg À1 and 180 S min À1 for 12 h, followed by rinsing the material with demineralized water and drying at 70°C. The suspension was shaken on a linear shaker for~255 h at 30 S min À1 to achieve equilibrium. After pH measurement in a settling suspension, it was centrifuged for 10 min at 3000 revolutions min À1 (~2100 Â g) and filtered over a 0.45 mm-filter membrane. The filtrate was acidified with 5 M HCl to pH 2 before measuring P-PO 4 as dissolved reactive P (DRP) using the molybdenum-blue method (Murphy and Riley, 1962) and a fully automated segmented flow analyzer (SFA; San ++ , Skalar, Breda, The Netherlands).

Structural characterization
For the identification of crystalline compounds, the dried and sieved iron oxide sludge was analyzed by X-ray diffraction (X'Pert Powder diffractometer, Malvern Panalytical; Co Ka X-ray source with Kb (Fe) filter, 40 mV, 45 kV; fixed divergence slits; continuous scan from 15°to 95°2h with 0.017°step size and 2 h total counting time; X'Celerator detector). For characterizing the atomic structure of the Fe(III)-precipitates, the sludge was analyzed with XAS at the SUL beamline at ANKA at the Karlsruhe Institute of Technology (KIT), Germany. About 15 mg of the sludge were mixed with about 150 mg of cellulose and pressed into a 13-mm diameter pellet for analysis in transmission mode at room temperature. Data extraction and analysis was performed in analogy to previous work  using the software code Athena (Ravel and Newville, 2005). The spectra were evaluated by comparison to reference spectra from previous work concerned with the atomic structure of Fe(III)-precipitates formed by Fe(II) oxidation Voegelin et al., 2010).
For the analysis of the iron oxide sludge by TEM, 35 mg of the material were suspended in 100 mL doubly deionized (DDI) water and ultra-sonicated for 10 min (bath sonication) to disperse particle aggregates. The iron oxide sludge suspension was diluted 100fold in DDI water and ultra-sonicated for 10 s with a VialTweeter (Hielscher Ultrasonics GmbH, Germany). One mL of this suspension was centrifuged for 1 h at 14,000 revolutions min À1 (~26000 Â g) onto poly-L-lysine-functionalized TEM grids (Ccoated Cu grids; EM Resolutions; UK). Scanning transmission electron microscope (STEM) analyses were performed on a STEM (HD2700Cs, Hitachi, Japan) operated at 200 kV. Electron microscopy images were collected using a secondary electron (SE) detector and a high-angle annular dark field (HAADF) detector. Signal processing was done using DigitalMicrograph (Gatan Inc., Pleasanton, US).

Chemical analysis of the field trial soils
Soil organic matter (SOM) content was determined by loss-onignition in a muffle furnace (550°C). The soil samples were extracted with 0.01 M CaCl 2 at an SSR of 10 L kg À1 for 2 h on a linear shaker at 180 S min À1 . A subsample was taken for measuring the pH. The remaining suspension was centrifuged for 10 min at 3000 revolutions min À1 (~2100 Â g). After 0.45 mm-filtration, P-PO 4 was measured as DRP using a novel system in which our SFA instrument was equipped with a 50-cm liquid waveguide capillary cell (LWCC; World Precision Instruments) and a LED lamp operating at 880 nm. This instrumental setup leads to an increase in the sensitivity and a 10-fold lower detection limit (~0.06 mM P-PO 4 ) compared to a conventional cell with 5-cm path length (Gimbert et al., 2007). Dissolved organic carbon (DOC) was calculated as the difference between total carbon and inorganic carbon, both measured by using an SFA. Total dissolved P (TDP) was measured using HR-ICP-MS. Dissolved unreactive P (DUP) was calculated as the difference between TDP and DRP. Total dissolved As, Cd, Cu, Ni, and Pb in the 0.01 M CaCl 2 extracts from the soil samples taken at the first and third sampling time were measured using HR-ICP-MS.
To determine Fe ox , Al ox , and P ox , the soil samples were extracted with 0.2 M AAO according to the standard method including an SSR of 20 L kg À1 and a shaking time of 2 h (Schoumans, 2000;Schwertmann, 1964). Other analytical details can be found in Section 2.2.2. Based on the amounts of Fe ox , Al ox , and P ox , the molar PSI (a) was calculated according to: where P ox and [Fe + Al] ox are expressed in mmol kg À1 (Van der Zee and Van Riemsdijk, 1988). The Olsen P extraction method with 0.5 M NaHCO 3 at an SSR of 50 L kg À1 (see Section 2.2.3.) was applied to measure the P-PO 4 concentration in solution after equilibration for~255 h.
For the soil samples taken at the first and third sampling time, the size of the reactive As, Cd, Cu, Pb, Ni, and Zn pools was determined by extracting soil with 0.43 M HNO 3 . The soil samples were extracted at an SSR of 10 L kg À1 on an end-over-end shaker for 4 h with 30 rotations min À1 . Next, the soil extracts were centrifuged for 10 min at 3000 revolutions min À1 (~2100 Â g). After 0.45 mm-filtration, As, Cd, Cu, and Ni were measured by using HR-ICP-MS whereas Zn was measured with ICP-OES.

Surface complexation modelling
The charge distribution (CD) model (Hiemstra and Van Riemsdijk, 1996) was used to calculate the P-PO 4 loading of the iron oxide sludge and field trial soils from the experimental P-PO 4 concentration and pH in the 0.5 M NaHCO 3 extracts (see Section 2.2.3.). A detailed CD modelling description can be found in Hiemstra et al. (2010a). We used a consistent set of binding parameters (log K and CD values) available for goethite. In the CD model calculations for the data of the 0.5 M NaHCO 3 extracts, only competition between P-PO 4 and bicarbonate for binding to sites at the Fe oxide surface was considered. Any additional competition with OM was not included, because excess activated carbon was added to remove OM to supress this interaction.

Statistical analysis
A two-way analysis of variance (ANOVA) was used to test the significance of the effects imposed by the treatments topsoil removal and iron oxide sludge reaction time on the different response variables of the field trial (P < 0.05). For the treatment topsoil removal, the upper 5 cm-soil layer was either removed or remained present whereas the treatment iron oxide sludge reaction time encompassed three soil sampling times, i.e., shortly before and 3 and 14 months after sludge application (see Section 2.1.). The data was transformed prior to analysis to agree with the assumption of data normality when necessary. For the DRP and DUP concentrations in the 0.01 M CaCl 2 soil extracts, Fe ox , and the effective reactive surface area of the field trial soils, a log transformation of the data was used, whereas a double log transformation was used for the reactive Pb pool. The Bonferroni post-hoc test was used to test the significance of the differences between the means of the two treatments. All statistical analyses were performed using GenStat 19th edition (VSN International, 2017).

Composition
Selected chemical properties of the iron oxide sludge used in this study are presented in Table 1. The sludge contains some OM which may originate from the presence of dissolved organic matter (DOM) in the raw groundwater (Postma et al., 1991). Deposition of organic residues in the sedimentation basin may have contributed to the presence of OM in the sludge as well . Iron is the dominant macro-element in the iron oxide sludge, with 33% of its total weight. This is larger than in various other industrial by-products including WTRs used for removing P from solution (Cucarella and Renman, 2009;Ippolito et al., 2011). Calcium (6.3%) is the second most important macro-element and is accompanied by a high inorganic C content of 2.4% (determined for another batch of iron oxide sludge), pointing to the presence of~16% CaCO 3 if all Ca would be present as CaCO 3 . Calcite was indeed identified as a dominant crystalline component of the sludge by XRD (Fig. S2). For Fe(II) removal, the raw groundwater mixed with ample fresh air is led over a filter bed filled with marble grains , which explains the presence of calcite in the sludge as well as its slightly alkaline pH.
Silicon (2.9%) is the third most important macro-element in our iron oxide sludge. This can be explained by co-precipitation of silicate with the Fe oxide particles formed during groundwater treatment , leading to a molar Si/Fe ratio of 0.17 (Table 1). This ratio is intermediate to the range encountered for natural siliceous Fe oxides of 0.06 to 0.37 (Childs, 1992;Cismasu et al., 2011;Jambor and Dutrizac, 1998;Parfitt et al., 1992). The molar Si water /Fe water ratio in the raw groundwater is 1.7 whereas the Si sludge /Fe sludge ratio in the sludge is 0.17. Hence, the Si water / Fe water ratio is 10-fold higher than the Si sludge /Fe sludge ratio. This points to an excess of 1.5 mol Si per mol Fe in the raw groundwater (Si excess /Fe water ), which follows from Si excess /Fe water = Si water /Fe water -Si sludge /Fe sludge if all Fe would precipitate in the sludge (Fe water =-Fe sludge ). The result of this calculation illustrates the abundance of dissolved Si in the raw groundwater (see Section 2.1.).

Mineralogy
The XRD pattern of the iron oxide sludge revealed the presence of two Fe oxide phases: 2-line ferrihydrite (Fh) and poorly crystalline goethite (Fig. S2). Based on Fe K-edge extended X-ray absorption fine structure spectroscopy,~94% of the Fe was present as Fh, with a small fraction of~6% occurring as goethite (Fig. 1). The Fe(III) in our Fh was less polymerized than synthetic 2-line Fh formed by neutralization of Fe(III) according to standard protocols. This may indicate the formation of smaller Fh particles with a relatively high surface contribution leading to more octahedral edge sharing and less polyhedral corner sharing , which is in line with a smaller coherent scattering domain as observed for co-precipitated siliceous Fh (Cismasu et al., 2014). These findings are in agreement with the well-documented formation of poorly-polymerized siliceous Fh during Fe(II) oxidation in aqueous solutions with silicate (Schwertmann et al., 1984; and water treatment systems (Nielsen et al., 2014;Van Genuchten et al., 2014;Voegelin et al., 2014).
The presence of some goethite in our sludge may be due to Fe (II)-catalyzed Fh transformation in the filter bed with marble grains used for Fe(II) removal from the raw groundwater (Boland et al., 2014;Carlson and Schwertmann, 1990). When all Fe in the sludge would be present as Fh, the total Fe content of 33% corresponds to 48 to 63% of Fh, depending on the molar mass (M) of Fh used. This may range from~82 g mol À1 for FeO 1.4 (OH) 0.2 (Hiemstra, 2013) to~107 g mol À1 in the case of Fe(OH) 3 as the chemical composition (Jambor and Dutrizac, 1998).

Particle size and surface area
In Fig. 2, TEM images of our iron oxide sludge are presented. The primary Fe oxide particles remained highly aggregated despite intensive physical dispersion. This may be due to the presence of adsorbed Si polymers  or OM (Hiemstra et al., 2010a;Kaiser et al., 2012). Structures visible in the Z-contrast and SE images point to a primary particle size of~2 nm. This is in accordance with the results of Cismasu et al. (2011) and Parfitt et al. (1992) who found a primary particle size of~1.5 to 4 nm for natural siliceous Fh. Ultra-fast formation of Fe oxides (~minutes) may lead to particles with a size of about 1.7 nm (Hiemstra et al., 2019;Hiemstra and Zhao, 2016;Mao et al., 2012). Silicate adsorption may inhibit the growth of Fh crystallites (Childs, 1992;Cismasu et al., 2011;Parfitt et al., 1992) and preserve the initial small size of the Fh particles. As long as these particles remain small (<~8 nm), Fh is thermodynamically the most stable nano-sized Fe(III) oxide phase . Hence, co-precipitation of Si and Fe leads to a relatively small particle size and inhibits growth, explaining why crystalline Fe oxides are nearly absent in our iron oxide sludge (Fig. S2).
The SSA of the Fe oxide particles can be calculated from the surface area of a spherical particle and its volume and mass density according to: where SSA is the specific surface area (m 2 kg À1 ), q nano the mass density (kg m À3 ), and d the average diameter of a non-porous spherical particle (m). For primary Fe oxide nanoparticles with a size of 2 nm and a mass density of~3500 kg m À3 (Hiemstra and Van Riemsdijk, 2009), the SSA equals~850 m 2 g À1 . The result of this calculation can be compared with the BET-SSA. Scaling the BET-SSA of 136 m 2 g À1 for our iron oxide sludge (Table 1) to the total Fe content leads to 217 m 2 g À1 when M = 107 g mol À1 for Fe(OH) 3 or 284 m 2 g À1 when M = 82 g mol À1 for FeO 1.4 (OH) 0.2 . Hence, the BET-SSA of the Fe oxide particles in our sludge is about 3-to 4-fold lower than calculated above for the primary Fe oxide particle diameter. This difference can be explained by the observed dense particle aggregation (Fig. 2) under the influence of adsorbed Si polymers , the presence of Ca , or blocking of micro- . The reconstructed LCF represented a combination of 71% Si-Fh*, 23% 2L-Fh, and 6% Goe (effective sum of fitted fractions 102%; r-factor 1.2 Â 10 -3 ). A more extensive discussion of the EXAFS spectrum can be found in Section S2 of the Supplementary data. pores by OM preventing N 2 gas molecules to occupy the internal surface of the aggregates (Eusterhues et al., 2008;Kaiser and Guggenberger, 2003).

Molar P/Fe ratio
The molar P sludge /Fe sludge ratio of 0.016 of our iron oxide sludge is markedly close to the P water /Fe water ratio of 0.012 of the raw groundwater. This illustrates the high affinity of P for Fe (Geelhoed et al., 1997), the latter effectively scavenging P from solution via adsorption to the Fe oxide particles formed by Fe(II) oxidation during groundwater treatment. Combining the SSA of~850 m 2 g À1 for the 2 nm-sized Fe oxide particles (see Section 3.1.3.) with an Fe concentration of 10.7 mg L -1 in the raw groundwater (see Section 2.1.) yields a reactive surface area of 17 m 2 L -1 when a size-dependent molar mass of 101 g mol À1 is used for Fh . Implementing these numbers as input for the CD model in combination with recent binding parameters of P-PO 4 and Si for Fh , more than 95% of all P in the raw groundwater is removed from solution by adsorption to Fh at neutral pH whereas this is only~10% for Si (Fig. S3). The difference in P and Si removal can be explained by the abundance of dissolved Si in the raw groundwater, making it impossible to bind it all. In contrast, nearly all P-PO 4 is bound due to its very high affinity for Fh (Geelhoed et al., 1997) and its 140-fold lower concentration in the raw groundwater.
The apparently high total P content of our iron oxide sludge (0.28%) needs some discussion in light of its potential use for P immobilization to regenerate low-nutrient ecosystems with a high plant species richness on former agricultural land. The total P content of 2.8 g kg À1 is quite similar to the average value of 2.2 g P kg À1 reported for Al-based WTRs (Ippolito et al., 2011). Such total P contents are typical for agricultural soils having received excessive P applications over a prolonged period of time (Koopmans et al., 2007;Lehmann et al., 2005). However, WTRs have a much higher metal oxide content than agricultural soils (Ippolito et al., 2011;Koopmans et al., 2006). Consequently, the molar P/Fe ratio of WTRs will be much lower than for excessively fertilized agricultural soils (Koopmans et al., 2007). Therefore, our iron oxide sludge will be very capable to bind large quantities of P and to reduce the solubility of P when it is applied to legacy P soils. Since the molar P sludge /Fe sludge ratio of 0.016 in our sludge is very low (Table 1), the P will be hardly available for release to solution (Baken et al., 2016).

Acid ammonium oxalate extraction
For the iron oxide sludge, the effectiveness of Fe extraction by 0.2 M AAO was tested. The recovery of Fe extraction depends on the SSR employed in the extraction (Fig. 3A and Table S1). At the lowest SSR of 20 L kg À1 , only 14% of the total Fe content was recovered as Fe ox within an extraction time of 2 h. Prolonging the extraction time to 4 and 24 h had only a small effect on Fe extraction, as the recovery increased to 17 and 21% of the total Fe content, respectively. However, when the SSR was increased to 100 L kg À1 , Fe extraction became nearly complete within 2 h. All Fe was extracted for the SSRs of 200 L kg À1 and higher.
The effectiveness of P extraction at the lowest SSR (20 L kg À1 ) was even lower than for Fe as <2% of the total P content was recovered as P ox (Fig. 3B). At an SSR of 100 L kg À1 , the recovery increased to 71 to 79% (Fig. 3B). At these SSRs, P remains at least partly effectively bound, probably by re-adsorption of released P to yet undissolved Fe oxide particles. For the SSRs of 200 L kg À1 and higher, P extraction was virtually complete, with a P recovery of 94 to 100%. For Al ox , however, the extraction effectiveness was far from complete (Fig. 3C). Hence, only a small fraction of the Al in the sludge is present as nano-sized Al (hydr)oxides. Part of the Al may be present in crystalline forms such as Al silicates (e.g., clay minerals). The pH measured in the AAO extracts decreased with an increase in SSR, from 7.0 at an SSR of 20 L kg À1 to 3.1 at an SSR of 400 L kg À1 (Table S1). However, this is not the main reason for the low Fe recovery for the lowest SSR, as found by our chemical speciation calculations.
Chemical speciation modelling was done to gain insight in the performance of AAO extraction of the iron oxide sludge. The solubility product used in the modelling was calculated for 2 nm-sized Fh particles by applying the Ostwald equation using a surface Gibbs free energy of c = 0.186 J m À2 for Fh , an SSA of~850 m 2 g À1 oxide (see Section 3.1.3.), and a sizedependent molar mass of 101 g mol À1 . This calculation leads to a solubility product of Q so = (Fe 3+ ) . (OH -) 3 = 10 -37.8 . According to our speciation calculations, the solubility of Fh in the iron oxide sludge during AAO extraction at an SSR of 20 L kg À1 is almost pH-independent (Fig. S4) in the range covering our experimental pH values (Table S1). Furthermore, a substantial part of of the oxalate is present as solid Ca-oxalate when using an SSR of 20 L kg À1 (Fig. S5). Crucial for a high effectiveness of Fe extraction by AAO is the SSR employed, as follows from our speciation calculations given in Fig. S6. At the lowest SSR (20 L kg À1 ), the capacity of the 0.2 M AAO solution clearly limits Fe extraction, but increasing the SSR to 200 L kg À1 is sufficient to extract all Fe from the sludge, which is in agreement with our experimental results (Fig. 3A). Furthermore, the use of this high SSR leads to an accurate measurement of the amount of P ox , which is needed for assessing the effective reactive surface area of the sludge, as discussed next.

Reactive surface area of the iron oxide sludge
The effective reactive surface area of the Fe oxides in the iron oxide sludge was assessed with ion surface probing. Since the original probe ion method of Hiemstra et al. (2010a) is rather laborious, a more simple and rapid method is desired. Here, we will introduce a modification to the experimental approach used in the probe ion method through which it can be applied more conveniently to a large series of soil samples. The adapted method will be used first to assess the surface area of the grab sample of the sludge and later it will be applied to the field trial soils. Before describing this modification, first the principle of the probe ion method will be discussed.
For ion surface probing, P-PO 4 is used because this ion is omnipresent in soils and adsorbs predominantly to metal oxides. In the original method of Hiemstra et al. (2010a), soil samples were equilibrated in 0.5 M NaHCO 3 at a series of different SSRs for~10 days before measurement of the P-PO 4 concentration in solution. This chemical matrix fixes the pH, ionic strength, and carbonate concentration, supresses the influence of Ca and Mg ions on P-PO 4 adsorption to metal oxides via their precipitation as carbonates, and desorbed and dissolved OM is largely removed due to the excess activated carbon addition (see Section 2.2.3.). In combination, this leads to the dominance of the interaction of P-PO 4 and bicarbonate with Fe and Al oxides allowing an interpretation of the measured equilibrium P-PO 4 concentration in the 0.5 M NaHCO 3 solution with the CD model, yielding the effective reactive surface area (A) of the soil sample as well as the amount of reversibly adsorbed P-PO 4 (R ev ).
During soil equilibration in 0.5 M NaHCO 3 , the total amount of reversibly adsorbed P-PO 4 will be redistributed over the solution and solid phase according to the following mass balance: where R ev represents the total amount of reversibly adsorbed P-PO 4 (mol kg À1 ) initially present in the soil sample when collected in the field, A the effective reactive surface area of the soil sample (m 2 kg À1 ), C the P-PO 4 surface loading (mol m À2 ), SSR the solution-tosolid ratio employed (L kg À1 ), and c the equilibrium P-PO 4 concentration in the solution phase (mol L -1 ).
As mentioned, in the original probe ion method of Hiemstra et al. (2010a) a series of different SSRs was used for equilibrating soil in 0.5 M NaHCO 3 to calculate R ev and A. A less laborious approach is the use of P ox as a proxy for the reversibly adsorbed P-PO 4 pool (R ev ) in combination with a single 0.5 M NaHCO 3 extraction to yield the equilbrium P-PO 4 concentration (c). The latter can then be directly translated to the corresponding P-PO 4 surface loading (C) using the CD model. Details on the single NaHCO 3 extraction and the surface complexation modelling with the CD model can be found in Sections 2.2.3. and 2.4.1., respectively. Combining C in Eq. (3) with the experimental value of P ox for the reversibly adsorbed P-PO 4 pool (R ev ), the effective reactive surface area (A) can be derived. The use of P ox as a proxy for R ev seems justified, because R ev agreed reasonably well with P ox for a series of Dutch agricultural topsoils used to develop the probe ion method (Hiemstra et al., 2010a). Furthermore, the use of P ox is in line with findings from a long-term P desorption experiment with a P sink where all P ox could be desorbed (Lookman et al., 1995).
Our modified approach was applied to all field trial soils as well as the grab sample of the iron oxide sludge taken from the slurry tank during sludge application in the field. For the sludge, P ox measured at an SSR of 200 L kg À1 and an extraction time of 4 h (see Section 2.2.2.) was taken as R ev in Eq. (3). For the value of c, we used the DRP concentration measured in the 0.5 M NaHCO 3 extract of the sludge at an SSR of 50 L kg À1 (Table 1). This SSR is intermediate to the series of different SSRs employed by Hiemstra et al. (2010a) for the 0.5 M NaHCO 3 extraction method.
With the approach used, a value of 113 m 2 g À1 was calculated for the effective reactive surface area of the iron oxide sludge. When scaled to the amount of Fe ox extracted at an SSR of 200 L kg À1 for 4 h (Fig. 3A), the surface area of the Fe oxide particles in the sludge is 211 m 2 g À1 when M = 89 g mol À1 (FeOOH). The corresponding equivalent spherical particle diameter is~8 nm accord- Fig. 3. Acid ammonium oxalate-extractable Fe ox (A), P ox (B), and Al ox (C) at a different solution-to-solid ratio (SSR) for an extraction time of 2, 4, and 24 h. The Fe ox , P ox , and Al ox contents are expressed as a percentage of their total contents present in the iron oxide sludge (Table 1). For the SSRs of 300 and 400 L kg À1 , an extraction time of 4 h was used.
ing to Eq. (2), which is much larger than the TEM-based primary particle size of~2 nm (Fig. 2). This difference in size can be explained by the aggregation of the primary particles, as discussed in Section 3.1.3. The aggregation of these particles is rather irreversible when assessing the surface area with the probe ion method. This will be further discussed in relation to the surface area of the metal oxide particles in the field trial soils.

Characterization of the field trial soils
Selected chemical properties of the field trial soils are presented in Table 2. Removal of the upper 5 cm soil layer before iron oxide sludge application caused a significant decrease in SOM. The difference in SOM between the plots without and with topsoil remained intact after application of iron oxide sludge, although it was not statistically significant at the third sampling time. Sludge application did not lead to a significant change in the DOC concentration in the 0.01 M CaCl 2 soil extracts. Instead, the DOC concentrations were linearly related to the amount of SOM (Fig. S7). This identifies SOM as the principal source of DOM, released via processes such as desorption, dissolution, and decomposition of OM (Kalbitz et al., 2000).
Iron oxide sludge application caused a significant increase in pH, which can be attributed to proton consumption due to dissolution of calcite present in the sludge (see Section 3.1.1.). Plotting the pH against the amount of oxides added with the sludge as determined with the AAO extraction revealed a nonlinear increase in the pH from 4.5 to 7.3 with the amount of added oxides (Fig. S8).
The size of the reactive pools of As, Cd, Cu, Ni, Pb, and Zn did not change upon iron oxide sludge application (Table S2). This can be attributed to the small amounts of trace metals in the sludge (Table 1). A decrease was found in the total dissolved concentrations of As, Cd, Cu, Ni, Pb, and Zn in the 0.01 M CaCl 2 soil extracts (Table S2). However, this decrease was only statistically significant for total dissolved Ni and Pb when the sludge was applied to the plots without topsoil.
The Fe ox content of the soil samples collected 3 and 14 months after iron sludge application showed a statistically significant increase (Fig. 4A) whereas no significant changes were found in the Al ox and P ox contents (Fig. 4B and C). This illustrates the difference in the origin of these elements. The coefficient of variation for the Fe ox content increased from~20% to~40% after sludge application. This high variation is probably caused by an inhomogenous distribution of the sludge among and within the individual plots of the field trial. One of the reasons for the high spatial heterogeneity in the Fe ox content may be demixing of the liquid sludge in the slurry tank before the application (Fig. S1). Clearly, it is not a trivial task to apply suspended materials homogeneously to soil in a large-scale field trial. However, the unintended variation in the Fe ox content of the field trial soils turned out to be advantageous for our study. The variation in the Fe ox content is expected to lead to variation in the reactive surface area of the field trial soils, which can help to explain the variation encountered in the DRP concentration in the 0.01 M CaCl 2 soil extracts (see Section 3.6.).

Effects of iron oxide sludge on P solubility in the field trial soils
Before iron oxide sludge application, DUP contributed on average 62 ± 1% and 79 ± 5% to the TDP concentration in the 0.01 M CaCl 2 soil extracts of the plots without and with topsoil, respectively (Fig. 4D). Hence, the TDP concentration is dominated by DUP, which is typical for extensively managed soils such as our field trial soils (Lehmann et al., 2005). This DUP can consist of organic P compounds and P-PO 4 associated with mineral colloids including clay, metal oxides, and metal ion clusters bound by humic substances (Hens and Merckx, 2002;Jiang et al., 2017;Regelink et al., 2013). The application of sludge caused a statistically significant decrease in the DUP concentration in the 0.01 M CaCl 2 soil extracts of the plots without topsoil. For the plots with topsoil, DUP decreased only significantly 14 months after sludge application. The reduction in the DUP concentration can be explained by binding of specific soluble organic compounds to oxides added with the sludge (Celi et al., 2003;Lü et al., 2017).
Iron oxide sludge application caused a statistically significant decrease in the DRP concentration in the 0.01 M CaCl 2 soil extracts of the plots with topsoil (Fig. 4E). For the plots without topsoil, this effect was only significant three months after sludge application. Since the spatial heterogeneity in the Fe ox content is high (see Section 3.3.), it is better to assess the effect of sludge application on P-PO 4 solubility from the relationship between the DRP concentration in the 0.01 M CaCl 2 soil extracts and the increase in the oxide content for the individual field trial plots (Fig. 4F). The reduction in the DRP concentration becomes high at an intermediate and high oxide addition. At our field trial site, a reduction in the DRP concentration to 0.3 mM was possible with an addition of~10 to 15 g Fe oxides per kg soil. A further increase in the amount of added oxides is much less effective for further reducing the DRP concentration.

Reactive surface area of the field trial soils
Our modified probe ion method was used to determine the effective reactive surface area of the field trial soils. Similar to the iron oxide sludge, the DRP concentrations measured in 0.5 M NaHCO 3 at an SSR of 50 L kg À1 (Table S3) were used as the values for c in Eq. (3) and C was calculated with the CD model. For R ev , the values of the P ox contents were used (Fig. 4C), as measured by the standard AAO method (Schoumans, 2000;Schwertmann, 1964).
The application of iron oxide sludge caused a statistically significant increase in the effective reactive surface area of the soil samples collected from the plots with topsoil after 3 months whereas no significant effect was found for the soil samples collected after 14 months (Fig. S9). For the plots without topsoil, sludge application did not lead to a significant change in the surface area. One of the main reasons why the application of the sludge did not result in a consistent increase in the soil surface area for the plots without and with topsoil is most likely related to the high spatial heterogeneity in the Fe ox content (see Section 3.3.).
The relation between iron oxide sludge application and the effective reactive surface area of the soil samples from the individual plots becomes more evident when plotting the reactive surface against the increase in the oxide content (Fig. 5). The data points fit well to a linear relationship (R 2 adj = 93% and P < 0.001). The intercept equals the surface area of the initial soil before sludge application. For the initial soil, the surface area is 5.4 ± 0.3 m 2 g À1 , increasing Table 2 Selected chemical properties of the field trial soils. Values represent average ± standard deviation of 3 plots, either with topsoil removed (0-5 cm) or present. Different letters denote a significant difference (P < 0.05). up to a maximum of 12.9 m 2 g À1 after sludge amendment. The slope of the relationship reveals the surface area per unit mass oxides added. The thus calculated surface area of the added Fe oxide particles is 304 ± 24 m 2 g À1 when M = 89 g mol À1 for FeOOH and 78 g mol À1 for Al(OH) 3 . Since the surface area of the Fe oxide particles in the grab sample of the iron oxide sludge taken from the slurry tank in the field is 211 m 2 g À1 (see Section 3.2.), the surface area can be said to range between 211 and 304 m 2 g À1 with an intermediate value of~260 m 2 g À1 . This value can be compared to the BET-SSA of the sludge after scaling it to the oxide content, resulting in a surface area of 217 to 284 m 2 g À1 with an intermediate value of~250 m 2 g À1 (see Section 3.1.3.). Hence, the results of the BET-SSA and our adapted probe ion method are rather similar.
All data points in Fig. 5 align well to the same linear relationship. Consequently, no transformation of the Fe oxides added with the iron oxide sludge into more crystalline oxides with a larger particle size seems to have occurred after a residence time in soil of 3 to 14 months. The relative stability of the added Fe oxide particles may be due to the adsorption of P-PO 4 (Borch et al., 2007;Makris et al., 2005) and OM (Hiemstra et al., 2019) as well as the presence of Si in the sludge, as discussed in Section 3.1.3. However, transformation of Fe oxides into more crystalline oxides in cannot be excluded as Fh may reform in topsoils as part of the biogeochemical recycling of Fe (Jambor and Dutrizac, 1998). One other factor which needs to be taken into account when discussing the relative stability of the added Fe oxide particles is the length of our field trial, because it may not have been long enough to observe a measurable aging effect. The apparent lack of such an aging effect is in line with the results of Nielsen et al. (2014) who found a half-life of circa 4 years for the in-situ transformation of a Si-containing Fh buried in soil into more crystalline Fe phases whereas Schwertmann et al. (2004) determined a half-life of circa 7 years for Fh transformation into goethite and hematite in an invitro experiment at 4°C and pH 6.
It is interesting to compare the surface areas of the Fe oxide particles added with the iron oxide sludge and the indigenous metal oxide particles initially present in the field trial soils. The initial soil surface area at zero oxide addition is 5.4 ± 0.3 m 2 g À1 (Fig. 5). This surface area can be scaled to the Fe ox and Al ox contents of the soil samples taken before sludge application yielding a surface area of 1298 ± 303 m 2 g À1 when M = 89 g mol À1 for FeOOH and 78 g mol À1 for Al(OH) 3 . However, this surface area has been derived using the molar mass of crystalline oxide materials whereas oxide nanoparticles have a higher molar mass resulting from a larger contribution of surface groups . To estimate these molar masses in a consistent manner, we treated the indigenous metal oxides either as nano-Fh or as nano-gibbsite using a set of equations from . This leads to a molar mass of nano-Fh and nano-gibbsite of 105 and 90 g mol À1 , respectively. Values represent average ± standard deviation of 3 plots, either with topsoil removed (0-5 cm) or present. Different letters denote a significant difference (P < 0.05). In Fig. 4F, the DRP concentration in the 0.01 M CaCl 2 soil extracts is plotted against the increase in the oxide content for the individual field trial plots after iron oxide sludge application. The amount of added oxides was calculated from the difference in the Fe ox and Al ox contents before and after sludge amendment and using a molar mass of 89 g mol À1 for FeOOH and 78 g mol À1 for Al(OH) 3 . The white and grey symbols represent the plots without and with topsoil, respectively. To guide the eye, an exponential curve was added.
Combining these masses with the amounts of Fe ox and Al ox , we calculate a corresponding surface area of 1117 ± 216 m 2 g À1 . This can be translated to a particle size using the appropriate mass densities, which are very different for both nano-materials, i.e., 3400 kg m À3 for nano-Fh and~2300 kg m À3 for nano-gibbsite . This results in an equivalent particle size of 2. 3 ± 0.4 nm. This is very close to the TEM-based size of~2 nm for the primary Fe oxide particles in the sludge (Fig. 2). However, the primary particles in the sludge are highly aggregated due to the presence of adsorbed Si (see Section 3.1.3.), leading to a loss in surface area as opposed to the indigenous metal oxide particles initially present in the field trial soils. The indigenous metal oxide particles are likely embedded in a matrix of OM. In this matrix, the OM molecules are soft and penetrable for ions, keeping the internal surface area accessible for P-PO 4 and the particles separated from aggregation (Hiemstra et al., 2010a).
3.6. The relation between P-PO 4 surface loading and P-PO 4 solubility in the field trial soils In Fig. 6A, the adsorption isotherm of P-PO 4 is given using P ox as a measure of the reversibly adsorbed P-PO 4 pool and the DRP concentration in the 0.01 M CaCl 2 soil extracts before and after iron oxide sludge application. When P ox is presented on a soil mass basis (mmol g À1 ), the data points are highly scattered. This is caused by spatial heterogeneity, especially for the Fe ox content (see Section 3.3.). By scaling P ox to the surface area of the soil samples, a large part of the scattering disappears (Fig. 6B), revealing the P-PO 4 adsorption isotherm. Some variation remains because the soil samples differ for example in pH and DOC concentration (Table 2), which may affect P-PO 4 adsorption density (Hiemstra et al., 2010b;Regelink et al., 2015). The L-shape of the isotherm is typical for a high affinity ion adsorption (Hiemstra et al., 2010a). The ion adsorption behavior can be described very well with the Langmuir equation (R 2 adj = 84% and P < 0.001) having a Q max of 2.6 ± 0.1 mmol m À2 . This value can be compared to the maximum P-PO 4 adsorption density of different Fe oxide types. In the case of goethite, the P-PO 4 adsorption density is usually limited to about 2.5 to 3.5 mmol m À2 , depending on its crystallinity (Hiemstra and Van Riemsdijk, 1996). For Fh, a higher maximum P-PO 4 adsorption density can be found. Under acid conditions (pH 4 or 4.5), the value ranges from 3.9 to 4.6 mmol m À2 (Celi et al., 2003;Hiemstra and Zhao, 2016;Wang et al., 2013) whereas it is about 2 mmol m À2 at a pH of 7 (Hiemstra, 2013;Hiemstra and Zhao, 2016). The sludge-amended field trial soils had a pH between 5.7 and 7.3 (Fig. S8).
From a practical perspective, one can scale P ox to the sum of the molar Fe ox and Al ox contents present in the field trial soils. The data collection requires only a single 0.2 M AAO extraction. This concept of scaling is known as the PSI as defined in Eq. (1) by a (Van der Zee  and Van Riemsdijk, 1988). For our field trial soils, this scaling method leads to an excellent description of the data using the Langmuir equation (R 2 adj = 96% and P < 0.001) (Fig. S10). Conceptually, the underlying assumption of the PSI is a constant surface area per mole Fe ox + Al ox present in soil. In our case, this assumption is incorrect because the overall surface area of our field trial soils originates from two distinct sources, i.e., the indigenous metal oxides initially present and the Fe oxides added with the iron oxide sludge. The difference in surface area between both sources (see Section 3.5.) introduces variation into the overall surface area per mole Fe ox + Al ox for the soil samples. Interestingly, however, the PSI scaling appears to compensate for the variation in overall surface area and for variation in chemical properties including pH and adsorbed OM (Table 2), which all affect the P-PO 4 adsorption density. The results of this study thus confirm the usefulness of the PSI approach to straightforwardly determine the application rate of Fe-rich WTRs required for reducing the P-PO 4 concentration in soil solution to a desired level (Elliott et al., 2002).

Conclusions
Siliceous Fh is the dominant Fe oxide type in the iron oxide sludge used in this study. The TEM-based size of the primary Fh particles is~2 nm, equivalent to a theoretical SSA of~850 m 2 g À1 . However, the effective reactive surface area is~260 m 2 g À1 when using the modified probe ion method, corresponding to a size of~6 to 8 nm when expressed in an equivalent spherical particle diameter. This size is much larger than the TEM-based primary Fh particle size. Hence, these particles are strongly aggregated due to linkage by adsorbed Si polymers, causing a loss in surface area. This is in contrast with the indigenous metal oxide particles initially present in the field trial soils, which have a size of 2.3 ± 0.4 nm. This is very similar to the primary Fh particle size in the sludge. However, the surface area of the indigenous metal oxide particles is much higher (~1100 m 2 g À1 ) due to little aggregation. Sludge application increased the surface area of the field trial soils from 5.4 up to a maximum of 12.9 m 2 g À1 and strongly reduced the P-PO 4 concentration in the 0.01 M CaCl 2 soil extracts. A reduction in the P-PO 4 concentration to 0.3 mM was possible at an addition of~10 to 15 g oxides per kg soil. A higher addition is much less effective in further reducing the P-PO 4 concentration. The adapted probe ion method is a useful tool for assessing the surface area of metal oxides in Fe-rich WTRs as well as soils amended with such materials. Information on the surface area of Fe oxides is crucially important to understand how Fe oxide-containing materials can reduce the P-PO 4 solubility when such materials are used for immobilizing P in legacy P soils with a low P-PO 4 adsorption capacity but with a high surface loading.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

S1.
Iron oxide sludge production process 15 The iron oxide sludge used in this study is an industrial by-product from the production of 16 drinking water from groundwater by a water treatment facility (Brabant Water Ltd), located 17 near Vessem in the south of The Netherlands. The process of iron oxide sludge production 18 at this water treatment facility has previously been described by . In 19 short, anaerobic groundwater is pumped up from an aquifer at a depth between 21 and 54 20 m. The Fe(II) is removed from the raw water by mixing it with ample fresh air, leading to 21 the oxidation of Fe(II) and precipitation of Fe oxides with a concomitant release of protons. 22 The acid is neutralized by filtering the water over marble grains. With ample air added and 23 slow filtering, a sludge of Fe oxides forms in the filter. The sludge is regularly removed 24 from the filter by backwashing. The backwash water with the sludge is collected in a 25 sedimentation basin. The sludge particles gradually settle at the bottom of the basin, 26 forming a wet sediment which continues to build up until the basin needs to be cleared. 27 Next, the sediment is transferred into a drying bed for dewatering. Since the sludge from 28 the drying bed gets a structure with large solid clods, it is difficult to mix this material with 29 the soil. Therefore, liquid iron oxide sludge from the sedimentation basin was used in the 30 field trial. The sludge was collected from the basin by pumping the wet sediment into a 31 tank truck (Fig. S1). 32

S2.
Structural characterization of the iron oxide sludge with EXAFS 33 The EXAFS spectrum of the iron oxide sludge sample taken directly from the slurry tank in 34 the field (Fig. S1) presented in Figure 1 in the main text could perfectly be reproduced as 35 a mixture of the spectra of three reference compounds: 71% Si-containing ferrihydrite (Si-36 Fh*), 23% two-line ferrihydrite (2L-Fh) and 6% goethite (Goe) (effective sum of fitted 37 fractions 102%; r-factor 1.2×10 -3 ). Although the first two reference spectra are relatively 38 similar and the fitted fraction of goethite was low, each spectrum significantly improved 39 the quality of the fit compared to the respective two-component fit. In addition, the 40 presence of a small fraction of goethite was supported by the XRD pattern of the iron oxide 41 sludge (Fig. S2).
The reference Si-Fh* corresponds to a siliceous Fh formed by the oxidation of 0.5 mM 43 dissolved Fe(II) in a bicarbonate-buffered solution at pH 7.0 containing 0.5 mM silicate 44 (molar Si/Fe ratio of 1), i.e., under conditions comparable to those under which the iron 45 oxide sludge used in our field trial is formed. The reference material 2L-Fh is formed by 46 forced hydrolysis of a concentrated Fe(III) solution through base addition. The small variations in the two spectra can be attributed to a lower degree of distortion of Fe(III)-48 octahedra and a lower degree of 3-dimensional Fe polymerization in Si-Fh* than 2L-Fh 49 . The seemingly higher degree of polymerization of Fh in the iron oxide 50 sludge than of Si-Fh* formed under similar chemical conditions (oxidation of Fe(II) in the 51 presence of bicarbonate and silicate) may be due to the lower Si concentration in the raw 52 groundwater from the water treatment facility of Brabant Water Ltd (8.9 mg L -1 ) than in 53 the synthetic groundwater (14 mg L -1 ) from which the Si-Fh* was derived. In addition, 54 aging of Fh in the iron oxide sludge over time may have contributed to the difference 55 between Fh in the sludge and the Si-Fh* derived from the synthetic groundwater, although 56 Si is known to significantly inhibit Fh transformation kinetics. The minor fraction of goethite 57 in the iron oxide sludge may have formed during Fe(II) oxidation in the filtration bed with 58 marble grains, promoted by the presence of calcite or it may indicate some moderate aging 59 of the Si-stabilized Fh. 60

S3.
Chemical speciation calculations for acid ammonium oxalate extraction of 61 the iron oxide sludge 62 Chemical speciation calculations were done to calculate the solubility of Fh present in the 63 iron oxide sludge in 0.2 M acid ammonium oxalate (AAO) at different values for the the 64 solution-to-solid ratio (SSR). At a given pH, the solubility of Fh will depend on its particle 65 size. For 2 nm-sized primary Fh particles with a theoretical SSA of ~850 m 2 g -1 oxide (see 66 Section 3.1.3. in the main text) and a size-dependent molar mass of 101 g mol -1 (Hiemstra,67 2018b), one can calculate a solubility product of Qso = (Fe 3+ ) . (OH -) 3 = 10 -37.8 by applying 68 the Ostwald equation in case of a surface Gibbs free energy of  = 0.186 J m -2 (Hiemstra, 69 2015). In this calculation, a solubility product of Qso = 10 -40.6 was used for the related Fh 70 (pH < 3), inorganic Fe-OH complexes contribute to the total dissolved Fe concentration as 99 well. In the iron oxide sludge, a relatively small amount of Al oxides is present (Table S1). 100 All Al is strongly complexed in solution with oxalate and, therefore, it is not present as 101 Al(OH)3 (s). 102 The solubility of Fh present in the iron oxide sludge is rather limited when an SSR of 20 L 103 kg -1 is used in the 0.2 M AAO extraction method, as follows from the above speciation 104 calculations. The use of a higher SSR will lead to more Fh dissolution, as demonstrated in 105 Figure S6. The use of an SSR of 200 L kg -1 suffices to dissolve all Fh from the iron oxide 106 sludge by extraction with 0.2 M AAO. 107 Table S1 138 Acid ammonium oxalate-extractable amounts of Feox, Alox, and Pox and α for the iron oxide sludge at a different solid-to-solution ratio (SSR) and an extraction time of 2, 4, 139 and 24 h. For the SSRs of 300 and 400 L kg -1 , an extraction time of 4 h was used. Furthermore, the pH measured in the acid ammonium oxalate extracts of the iron oxide 140 sludge at the different SSRs and extraction times is given. All values represent average ± standard deviation of duplicate samples.  149 Table S3 150 The DRP concentration measured in 0.5 M NaHCO3 extracts from the field trial soils at an SSR of 50 L kg -1 , based 151 on a modified Olsen P method (Hiemstra et al., 2010). Values represent average ± standard deviation of three 152 plots, either with topsoil (0-5 cm) removed or topsoil present.

197
The white and grey symbols represent the plots without and with topsoil, respectively. To guide the eye, an 198 exponential curve was added (*** significant at the P < 0.001 level).