Nanoscale electrochemical visualization of grain-dependent anodic iron dissolution from low carbon steel

The properties of steels and other alloys are often tailored to suit specific applications through the manipulation of microstructure (e.g., grain structure). Such microscopic heterogeneities are also known to modulate corrosion susceptibility/resistance, but the exact dependency remains unclear, largely due to the challenge of probing and correlating local electrochemistry and structure at complex (alloy) surfaces. Herein, high-resolution scanning electrochemical cell microscopy (SECCM) is employed to perform spatially-resolved potentiodynamic polarisation measurements, which, when correlated to co-located structural information from electron backscatter diffraction (EBSD), analytical scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM), reveal the relationship between anodic metal (iron) dissolution and the crystallographic orientation of low carbon steel in aqueous sulfuric acid (pH 2.3). Considering hundreds of individual measurements made on each of the low-index planes of body-centred cubic (bcc) low carbon steel, the rate of iron dissolution, and thus overall corrosion susceptibility, increases in the order (101) < (111) < (100). These results are rationalized by complementary density functional theory (DFT) calculations, where the experimental rate of iron dissolution correlates with the energy required to remove (and ionise) one iron atom at the surface of a lattice, calculated for each low-index orientation. Overall, this study further demonstrates how nanometre-resolved electrochemical techniques such as SECCM can be effectively utilised to vastly improve the understanding of structureefunction in corrosion science, particularly when combined with complementary, co-located structural characterisation (EBSD, STEM etc.) and computational analysis


Introduction
The microstructural features of steel and other alloys, such as grains of different crystal orientation, grain boundaries and (sub) microscale inclusions, play an important role in the formation of the local anodic and cathodic cells that drive corrosion processes [1]. Indeed, many studies have attempted to resolve the relationship between surface structure and electrochemical activity with metals such as iron [2e5], 316 L stainless steel [6] and aluminium [7]. Although such studies report that the crystal orientation does influence corrosion behaviour, a consistent trend or explanation for this behaviour has not been forthcoming. This is largely attributed to the difficulty in probing local electrochemistry and structure in the same area at complex surfaces, meaning that in practice measurements are often limited to a few measurements on single grains [8]. For this reason, there is a need for techniques that can probe corrosion-related phenomena with high spatial-resolution, an application where scanning electrochemical probe microscopy (SEPM) techniques are most powerful [9].
Presently, the most widely-used SEPM method in corrosion science is scanning electrochemical microscopy (SECM) [10,11]. Although microscale measurements can be made readily with SECM, it is important to note that SECM interrogates electrochemical processes indirectly by measuring fluxes and concentrations at an ultramicroelectrode probe. The application of SECM in corrosion-related measurements is non-trivial, particularly at the nanoscale, for several reasons including topographical changes in the surface and complex intermediate/product speciation (e.g., metal ions in anodic dissolution), which need to be easily detected at the tip. Applying an alternating current in an SECM configuration (AC-SECM) partially resolves these issues, since no redox mediator is required [12,13]. Nevertheless, the quantitative interpretation of data is complicated due to the convolution in the AC-SECM signal of both topography (tip-substrate distance) and electrode kinetics of corroding interfaces. In contrast, the electrochemical droplet cell (EDC) technique [14,15] probes electrochemistry locally and directly by contacting a small (micrometric) area of the surface of interest under a droplet formed at the end of a fluidic probe. Data analysis in the EDC format is straightforward, as well-known electrochemical techniques (e.g., potentiodynamic polarisation) are applied. Two major downsides of the conventional EDC technique are its limited spatial-resolution and low throughput [16]. The EDC has been used to study the degradation of a number of materials, including 304 stainless steel [15,17] and aluminium [7,18,19]. A few works have reported the application of the EDC technique to the dissolution of polycrystalline Fe in NaNO 3 [3] and acetate buffer [2]. The measurements were limited to a few points of ca. 100 mm size on single (100), (101) and (111) crystallographic planes. In these studies, the dissolution rate increased in the sequence (100) < (101) < (111).
Scanning electrochemical cell microscopy (SECCM) is the next generation of the EDC technique, making considerable improvements in terms of spatial-resolution, speed and usability [20,21]. In essence, through the use of much finer pipets (typically 30 nm to 1 mm in diameter [22]) and piezoelectric positioners, SECCM automates the EDC technique, making possible the rapid translation of a nanoscale droplet cell across an electrode surface to perform highresolution electrochemical mapping. SECCM has been shown to be extremely powerful for nanoscale structureefunction studies, being used to probe the electrochemical activity of, for example, molybdenum disulfide [23], sp 2 carbon materials [24], polycrystalline metals [25e27], iron nickel sulfide catalysts [28], metallic nanoparticles [29,30], semiconductors [31] and battery materials [32]. SECCM is also a potentially powerful tool for corrosion-related research, as demonstrated by our recent proofof-concept studies investigating the role of microstructure on the passivating behaviour of low carbon steel in pH neutral solutions of KNO 3 [33].
In this study, the local rate of iron dissolution has been correlated to the crystal orientation in order to unveil how different grains may support anodic processes in the formation of galvanic corrosion cells. With SECCM, thousands of spatially-resolved electrochemical (potentiodynamic polarisation) measurements are made using a 150 nm diameter nanopipet probe filled with aqueous sulfuric acid (pH 2.3), over a polycrystalline body centred cubic (bcc) low carbon steel surface. Used widely as a construction material, low carbon steel is both relatively cheap and easily manufactured into particular shapes without splitting or wrinkling [34]. Acidic solutions, such as the sulfuric acid investigated herein, are commonly used to remove scales and corrosion products from carbon steels, however without the extensive use of inhibitors, these cleaning processes can also have a detrimental impact (i.e., corrosion) on the condition of the steel surface [35]. By combining the spatially-resolved electrochemical data from SECCM with structural information from electron backscatter diffraction (EBSD) and scanning transmission electron microscopy (STEM) in the same areas as the electrochemical measurements, microscopic structure (e.g., crystal orientation) is shown to play an important role in modulating the corrosion susceptibility of low carbon steel. We attempt to rationalise these observations by complementary density functional theory (DFT) calculations.

Experimental
Electrode material and chemical reagents. The substrate used in this study was a low carbon steel, the chemical composition of which is presented in Table 1. The samples, of size 5 Â 21 mm, were mounted in a conductive mounting compound (KonductoMet. Buehler, U.S.A) using a mounting press (SimpliMet. Buehler, U.S.A). Samples were then polished on a polishing cloth (TriDent. Buehler, U.S.A) with a polishing machine (AutoMet 3000 Pro. Buehler, U.S.A) using 9 mm, 3 mm and 1 mm polishing suspensions followed by a final polish using 0.05 mm alumina suspension (MasterPrep Alumina. Buehler, U.S.A) on a different cloth (MicroCloth. Buehler, U.S.A). To remove contamination from polishing suspensions, samples were cleaned with acetone, soapy water and then deionised water before being blown dry. Sulfuric acid (H 2 SO 4 , Merck, 96%) was used as supplied. All solutions were prepared with ultrapure deionised water (Integra HP, Purite, U.K.), which has a resistivity of 18.2 MU cm at 25 C.
Surface characterisation. SEM and EBSD characterisation was carried out with a Zeiss SUPRA FE-SEM (Zeiss, Germany), using a Nordlys EBSD detector (Oxford Instrument, U.K.). SEM images and EDS data were collected at 10 keV, whereas EBSD images were collected at 20 keV, with the sample tilted at 70 to the detector. Following EBSD characterisation, grains that were chosen for study were either on or close to the low index orientations, (100), (101) and (111). Criteria set in this study was 10 deviation from the desired orientation.
Before TEM analysis, the sample was first extracted from the surface with focussed ion beam (FIB) milling using a ThermoFisher Scientific Scios DualBeam (ThermoFisher, U.S.A). In brief, an area of the surface chosen for examination was coated by a Pt layer to protect the area from damage. The regions surrounding this area were then subjected to a beam of Ga ions which effectively milled through the surface. Before removal, the examination area was attached to a tungsten rod with the use of deposited Pt, and once attached, the area was then cut free from the surface. The extract was then attached to carbon coated copper TEM grid, again with the use of deposited Pt. The extract was then 'thinned' with the Ga ion beam until a cross section of the SECCM scanning site was clearly visible. STEM was subsequently carried out on the thinned sample with a ThermoFisher Talos F200X FEG (ThermoFisher, U.S.A).
SECCM probe fabrication. Borosilicate capillaries (GC120F-10. Harvard Apparatus, U.S.A) were mounted on a laser puller (P-2000. Sutter Instruments, U.S.A) and pulled to give an opening diameter of approximately 150 nm at the end of the pipet (as confirmed by FE-SEM). Pulling parameters: Line 1: HEAT 350, FIL 3, VEL 30, DEL 220, PUL -; Line 2: HEAT 350, FIL 3, VEL 40, DEL 180, PUL 120. The pulled pipet was then filled with 5 mM H 2 SO 4 , producing a droplet at the tapered end. Silicone oil (Fluka Analytical) was used to Table 1 Chemical composition of the low carbon steel determined using energy dispersive X-ray spectroscopy.  Fig. 1a, which has been discussed in greater detail previously [30,33]. The nanopipet was mounted on a z-piezoelectric positioner (P-753.2 LISA. PhysikInstrumente, Germany) which was then positioned near to the surface manually with a micropositioner. The sample stage was placed on top of a xy-piezoelectric positioner (P-621.2 PIHera, PhysikInstrumente) for fine horizontal movement. As the nanopipet was approached to the surface automatically (at 3 mm/s), a voltage (0.563 V vs Ag/AgCl) was applied to the QRCE so that a surface current (i surf ) was detected once the droplet had made contact with the substrate. This surface current response was used as the feedback parameter to halt the approach. The threshold used during approach was set at ca. 2 pA for this study. Note that the nanopipet itself did not make contact with the surface.
Upon contacting the substrate surface via the nanopipet meniscus, a potentiodynamic polarisation experiment was performed by sweeping the potential at the QRCE from 0.563 to À1.437 and back to 0.563 V vs Ag/AgCl and the resulting surface current was recorded. Data points were recorded as an average of 128 samples taken every 4 ms (i.e., approximately every 0.5 ms). After the experiment for each scanning point had concluded, the nanopipet was then retracted from the surface (at 10 mm/s) and moved automatically to the next scanning site defined by the hopping distance. The process was repeated over a grid of scanning sites to map the electrochemical response of the surface.
Mass-transport in the nanopipet orifice is similar to the spherical diffusion at ultramicroelectrodes due to contribution of the radial component in the tapered capillary [36]. Steady-state conditions are thus established rapidly during measurements (vide infra) and the solution composition at the tip orifice is re-set to the bulk composition between each successive meniscus landing in a new location, due to rapid diffusional exchange between the end and the bulk of the nanopipet [37]. Note, further, that the anodic dissolution of iron is independent of the Fe 2þ concentration in solution [38]. Although SECCM measurements are made on a much more rapid timescale than classical corrosion measurements, SECCM studies identify electron-transfer kinetics at different active sites, and are thus pertinent to understanding corrosion processes.
The entire SECCM apparatus was mounted on an optical table (RS2000. Newport, U.S.A) supported on vibration isolation supports (S-2000. Newport, U.S.A). The set up was also shielded with a Faraday cage equipped with heat sinks and vacuum panels to minimise noise and variations in temperature. The QRCE potential was controlled with respect to ground and the current flow at the substrate was measured using a home-built electrometer. Data acquisition and fine control of all instrumentation was achieved using an FPGA card (PCIe-7852 R) controlled by a LabVIEW 2016 Software and data processing. The experimental data was processed using the Matlab R2016b (Mathworks, U.S.A) and Ori-ginPro 2016 64bit (OriginLab, U.S.A) software packages. The possible identity of the corrosion products formed during SECCM (and observed with STEM imaging) was calculated using the HY-DRA and MEDUSA software package (KTH, Sweden) [39], which considers the thermodynamically stable species (i.e., at equilibrium) that may exist under a given experimental condition. The following solid (iron oxysulphate) corrosion products were predicted: Fe(OH) 2 , FeSO 4 $7H 2 O, Fe 2 (SO 4 ) 3 , Fe 2 O 3 , FeOOH and H 3 OFe 3 (SO 4 ) 2 (OH) 6 .
Density function theory calculations. The Quantum Espresso [40] software toolbox was used to perform plane wave basis set Kohn-Sham Density Functional Theory (DFT) [41] calculations with ultrasoft pseudopotentials [42]. Pseudopotentials were all taken from the PSLibrary, version 1.0 [43]. A plane-wave kinetic energy cut-off of 800 eV was found to converge binding energies to at least 2 significant figures (in eV units). A Monkhurst-Pack grid of 4 Â 4 Â 1 k-points with no origin shift [44] was found to be adequate to converge energies with respect to Brillouin zone sampling.
Slab models of (100), (101) and (111) Fe planes with a finite thickness of 5 layers were employed to model Fe dissolution energies. A vacuum gap of 7 Å on both sides of the slab in the z-direction was used to simulate open boundary conditions. Additionally, any remaining spurious interactions through the zboundary were corrected using the Martyna-Tuckerman dipole correction scheme [45] as implemented in the Environ model [46,47]. The solvation model was used to account for solvent interaction energy terms between the surface and the solvent and between the dissolved iron and the solvent. To parameterise the continuum solvent model for water, the parameters suggested previously [46,47] were used. This was found to converge the surface energies down to 0.001 eV error.
First, a variable-cell geometry optimisation of the bulk metal cell was performed to find a converged lattice parameter. In the case of hcp crystal structure of Fe, these were a ¼ b ¼ c ¼ 2.71177 Å. Slabs formed from the bulk metal were used in a fixed-cell geometry optimisation constraining the position of the two layers furthest from our simulated surface to calculate the bare surface energy in vacuum ðE bV Þ and in solvent ðE bS Þ.
A single layer of Fe atoms was manually removed from the surface. The following equation was used to compute binding energies of the Fe layer ðE FeÀFe Þ: where E Fe 2þ refers to the energy of a Fe 2þ cation in the centre of a solvent box, with the same parameters used for the slab calculations. Normalisation by the number of atoms (N) in a layer (n) was used to account for packing densities of individual grains. An electronic energy convergence tolerance of 2 Â 10 À6 eV was used throughout these calculations. A Broyden charge density mixing [48] scheme, with local Thomas-Fermi screening [49] and Gaussian electronic smearing, with a smearing width of 0.1 eV were used to account for the metallic nature of our systems. We used the BFGS geometry optimisation scheme [50] with tolerances of 2 Â 10 À5 eV per atom in energy, 0.05 eV per in maximum force, 0.002 Å in maximum atomic displacement and in the case of the variable-cell, bulk geometry optimisation, 0.1 GPa maximum stress.

Results and discussion
SECCM: Operational Principles. The previously reported [29,30] voltammetric hopping-mode SECCM protocol used in this study is shown in Fig. 1a. A single-channel nanopipet of diameter z150 nm, filled with 5 mM H 2 SO 4 (pH ¼ 2.3) and equipped with a palladiumhydrogen (PdeH 2 ) QRCE, which possessed a potential of 0.437 V vs Ag/AgCl (3.4 M KCl), was employed to perform spatially-resolved potentiodynamic polarisation measurements. The z-position of the nanopipet probe, applied potential and surface current (i surf ) measured synchronously during a single "hop" of an SECCM scan is shown in Fig. 1b. During approach of the nanopipet probe to the surface (i.e., extension in the z-direction at 3 mm/s, herein, Fig. 1bei), a potential (0.563 V vs Ag/AgCl, herein, Fig. 1beii) was applied between the QRCE and the surface (working electrode), such that when the meniscus (droplet) protruding from the end of the probe initially made contact with the surface, a current (i surf ) flowed at the substrate surface (in a 2-electrode cell), as the circuit was closed (Fig. 1beiii). This was used as a feedback signal (set point) to instantaneously halt the approach of the nanopipet, so that it did not contact the surface. Upon meniscus landing, a local potentiodynamic polarisation experiment (between 0.563 V and À1.437 V vs Ag/AgCl at 2 V s À1 , herein) was performed, before the probe was retracted and moved to a new site (pixel) with a predetermined hopping distance, d (vide infra).
The potential applied between the QRCE and the surface during the approach (0.563 V vs Ag/AgCl) was well within the passive region, where a protective passive (oxide) film was formed, for example, via the reaction: Thus, the Fe surface in contact with the meniscus would be passivated rapidly upon each meniscus landing. Once contact was established between the droplet and the surface, the potential was swept cathodically to enter the active region, where the protective passive film is removed (reduced) and the iron dissolution reaction occurs: Fe / Fe 2þ þ 2e À As mentioned above, an advantage of nanoscale electrochemical measurements is that steady-state conditions are established rapidly, which means that relatively fast voltammetric sweep rates, such as 2 V s À1 used here, can be applied [36,37]. Indeed, we have shown that under such conditions, SECCM measurements provide highly relevant data for understanding electron-transfer kinetics relevant to corrosion phenomena, as highlighted by the clear grain contrast in activity seen in electrochemical movies (SI, Movie 1). As a rule of thumb, the time to steady-state in SECCM is ca. t ss~( 10a)/ D, where a is the tip radius and D is the diffusion coefficient of Fe 2þ [51]. Thus, for the studies herein, with a ¼ 75 nm and D 10 À5 cm 2 s À1 , t ss~1 ms [36,37]. Note that a smaller voltammetric scan rate would lengthen the time to record datasets and cause more extensive local damage to the surface due to prolonged anodic dissolution at each spot (which would also expand the spot area). The ability to apply fast scan rates is advantageous in terms of limiting the perturbation of the surface.
Continuing the potential sweep into the cathodic region, the oxygen reduction reaction (ORR), Eq (4), and (to a more appreciable extent) hydrogen evolution reaction (HER), Eq (5), occur: Once the cathodic potential sweep was completed, the cycle was then reversed and the potential was swept anodically. Corrosion is a dynamic process and, as a result, the working electrode (low carbon steel) surface changes irreversibly (physically and chemically) during active dissolution. For this reason, the potential was swept from anodic to cathodic domains and only the processes occurring before (i.e., in the passive region) and in the active region during the forward potential sweep have been considered herein (vide infra).
The result of a voltammetric hopping mode experiment on the surface of low carbon steel (using the cyclic potentiodynamic polarisation protocol outlined above) is demonstrated in Fig. 1c, where each spatially-independent measurement site is seen as an array of droplet "footprints" by using scanning electron microscopy (SEM). A full matrix of the droplet footprints (60 Â 60 ¼ 3600 measurements) visible in SEM after SECCM experiments can be found in the Supporting Information, Fig. S1. The diameter of the footprints, x, defining the "working electrode area" during each measurement is consistent from point-to-point (z450 nm). The ultimate spatial-resolution of the scan is determined by d, which was conservatively set to 1.2 mm herein to ensure that each potentiodynamic polarisation measurement was independent of the last.
Spatially-resolved potentiodynamic polarisation experiments on low carbon steel. In order to ascertain the structuredependence of the anodic processes (iron dissolution) on low carbon steel, a 72 Â 72 mm 2 (60 Â 60 pixel 2 ) voltammetric SECCM scan was carried out. The potentiodynamic polarisation curve (only forward sweep considered, vide supra) obtained by averaging all scanning points (3600 total) is shown in Fig. 2a. A simplified Pourbaix diagram for pure iron (considered to be representative of the investigated low carbon steel, see Table 1) is also included in Fig. 2b to indicate the predicted thermodynamically stable species throughout the potential sweep [52]. The low carbon steel surface is initially in a passive state (labelled as ①, Fig. 2b) from 0.563 V vs Ag/AgCl through to ca. À0.24 V, where a small reduction peak (cathodic current) is observed (inset in Fig. 2a), attributable to passive film reduction (labelled as ②, Fig. 2b): The charge passed during this process was calculated to be 20 ± 2 pC, which corresponds to a thickness of~8 ± 1 nm, assuming an Fe 2 O 3 film. Following the reduction peak, in the potential range ca. À0.49 V to À0.94 V (active region), iron dissolution (Eq (3)) is the dominant process (labelled as ③, Fig. 2b), giving rise to large oxidation currents (peaking at z290 pA, which corresponds to a current density of z0.2 A cm À2 ). The oxidation peak (at À0.587 V) is formed as the increasing corrosion rate resulting from the removal of the protective passive film (Eq (6)) is balanced by the decreasing driving force for iron dissolution (Eq (3)), as the potential is swept cathodically. Note that due to the fine tip geometry (diameter of z150 nm) and relatively dilute supporting electrolyte (5 mM H 2 SO 4 ), ohmic (iR, where R is the tip resistance, calculated to be 320 MU, herein) drop is on the order of z90 mV at the oxidation peak. Although this may distort the shape of the potentiodynamic polarisation curve to an extent, it does not affect grain-dependent trends in i surf , considered in detail below. Upon sweeping to potentials negative of À0.937 V, the surface current is dominated by cathodic processes (labelled as ④, Fig. 2b), where iron redeposition occurs (reverse of Eq (2)), in addition to cathodic (electrocatalytic) processes such as the ORR, Eq (3), and (predominantly) HER, Eq (4). This behaviour is consistent with the macroscopic electrochemical response of similar iron-based materials in acidic media [1].
Selecting four characteristic potentials (0.063, À0.547, À0.587, À1.437 V vs Ag/AgCl, labelled in Fig. 2a), spatially-resolved i surf maps are shown in Fig. 2c. Comparison of Fig. 2c with the co-located EBSD map in Fig. 2d reveals that: (i) tens of potentiodynamic polarisation experiments (ca. 20 to 50) are carried out on each grain, statistically validating our inferences below; and (ii) some processes appear to be grain-dependent, while others are grain-independent. Starting in the passive domain (E app z 0.563 to À0.237 V vs. Ag/AgCl, Fig. 2cei), the low current values in the i surf map do not show discernible features related to the underlying crystal structure. Although this may suggest that the resistivity/protectiveness of the passive film is grain-independent, the i surf values measured in this region are dominated by the background noise (ca. 2 pA peak-to-peak, detailed in the Experimental Section), and thus it is likely that any differences between the grains are too minute to detect.
In the active domain (E app z À0.487 to À0.937 V vs. Ag/AgCl, Fig. 2c-ii and 2c-iii) there is a clear relationship between crystal orientation (Fig. 2d) and the rate of iron dissolution, evidenced by grain-dependent i surf values (vide infra). In the cathodic region (Fig. 2ceiv), where the HER is expected to be the dominant process [53], i surf shows a weaker grain-dependence. As discussed above, the preceding anodic processes are expected to have a significant influence on the processes occurring in the cathodic region due to physical changes to the surface (e.g., surface dissolution and deposition of corrosion products) and compositional changes to the surface and electrolyte (e.g., the formation of soluble Fe 2þ species within the droplet cell), and Fig. 2beiv is thus difficult to interpret. Note that in a companion study [54], we have employed a potential-pulse waveform (i.e., chronoamperometry) to reveal the structure-dependence of the HER on low carbon steel in aqueous sulfuric acid (pH 2.3), and this is a better means of elucidating HER kinetics. As such, we do not consider the HER process any further here, but focus on the anodic dissolution of Fe (vide infra).
Taking all of the i surf maps (every 2 mV) over the entire potential range (0.563 to À1.437 V vs Ag/AgCl), a spatially-resolved i surf ÀE movie was constructed, shown in the Supporting Information, Movie S1. Note that throughout the movie, a small number of individual pixels appear to be far more active than the rest, which are labelled in Fig. 3a and further examined (i.e., pixel-resolved iÀE curves shown) in detail in Fig. 3b. For these "active pixels", the onset potential for active dissolution is ca. 100 mV (95e125 mV) more positive, and the anodic peak currents are larger (312e836 pA) compared to the surface average iÀE curve (black trace, peak current of 290 pA). Multiple processes appear to contribute to the anodic current, giving rise to a "split peak", with the process occurring at more positive potentials giving rise to unstable current fluctuations (also seen in the passive region, at E > 0.2 V vs Ag/AgCl). These additional processes are thought to arise from the oxidation (and dissolution) of manganese sulfide (MnS) inclusions, which has been addressed in our previous study [33], highlighting MnS inclusions as possible initiation sites for localised corrosion. Under anodic dissolution conditions, the presence of MnS inclusions cannot be confirmed with EDS, after experiments, as the inclusions undergo partial or complete dissolution as the potential sweeps through the active region. However, SEM images after experiments (e.g. Fig. 3c and d) shows a larger deposit of corrosion products and/or greater damage to the surface at these "active pixel" sites.
Movie S1 and Fig. 2ceii convincingly show that electrochemical iron dissolution is influenced by surface structure (i.e., crystallographic orientation), which is further explored in Fig. 4. Three characteristics of the anodic peak are considered, labelled in Fig. 4a: the reduction pre-peak potential ðV red p Þ; the oxidation peak current (i p ); and the oxidation peak potential ð V ox p Þ, maps of which are shown in Fig. 4b, c, and d, respectively. The charge passed during oxidation (Q Ox ), which is proportional to the amount of iron dissolved during oxidation and; the full width half maximum of the oxidation peak (FWHM), which indicates the range of potentials over which active dissolution occurs, are also presented in the Supporting Information, Fig. S2. Other areas of the low carbon steel surface were also mapped using the same SECCM protocol; examples of the spatially-resolved i p maps are plotted alongside colocated EBSD maps in the Supporting Information, Fig. S3, to highlight the reproducibility of the method.
The cathodic process prior to the active region ðsignified by V red p Þ is attributable to the reduction of the passive film (Eq (5)), which leaves the unprotected low carbon steel surface exposed for active dissolution. In other words, V red p indicates the potential above which the passive film is stable, or conversely, below which active dissolution will occur. Clearly, the graindependence of V red p indicates that the nature of the passive film, formed during the passive region of the potential sweep, varies between crystallographic facets. This may arise due to variations in the thickness and/or structure of the passive film, both of which could perceivably lead to differing film reduction behaviour. The anodic peak, the position (V ox p , Fig. 4d), magnitude (i p , Fig. 4c), charge passed (Q Ox , taken as the integral of the peak, see Supporting Information, Fig. S2), width (taken as the full width at half maximum, FWHM, see Supporting Information, Fig. S2) are all grain-dependent. Comparing the maps, the grains that possess passive films that are easiest to reduce (most-positive V red p , Fig. 2b) undergo the highest rates of dissolution (highest i p , Fig. 2c) over the widest potential range (largest FWHM, Fig. S2c).
Grain dependent anodic iron dissolution at low carbon steel. In order to gain an insight into which grains facilitate anodic iron dissolution and further explain these dependencies, we focus on the grains of low-index crystal orientation [i.e., the (100), (101) and (111) crystal facets]. All grains within 10 of the (100), (101) and (111) orientations are shown in Fig. 5aei, ii and iii, respectively, and average potentiodynamic polarisation curves obtained from each of the grains are shown in Fig. 5b. In total, 130, 264 and 365 individual measurements were taken on the (100), (101) and (111) grains, respectively. Evidently, from Fig. 5b, the variation in the potentiodynamic polarisation curves within a family of grains [i.e., compare the red curves for (100)] is much less than that between families of grains [i.e., compare the red and green curves for (100) and (101), respectively], demonstrating the strong crystallographicdependence of anodic iron dissolution. The average LSVs also show that the difference in dissolution current between grains is greater on the right hand side of the oxidation peak compared to the left hand side. In other words, sweeping the potential from positive to negative, the potential at which anodic iron dissolution initiates (e.g., Figs. 4b and 5b, inset) is more strongly graindependent than the potential at which iron dissolution ceases.
V red p increases in the order (101) < (111) < (100), from which it can be inferred that the passive (oxide) film is the thinnest and/or least protective on the (100) grains. This grain-dependent film composition/structure is consistent with previous studies, where it has been shown that the oxide films electrochemically grown on the (100) and (110) crystal facets of iron have different crystallographic structures [55]. Taking i surf at À0.581 V vs Ag/AgCl as an indicator of the relative rates of iron dissolution in the active region, histograms were constructed from the grain-resolved potentiodynamic polarisation curves, shown in Fig. 4c. Note that À0.581 V vs Ag/AgCl (indicated in Fig. 4b) was chosen to minimise the influence from the protective passive film (assumed to be completely removed at ca. 100 mV more negative than V red p ) and cathodic processes. Average i surf values increase in the order 218 ± 23, 252 ± 22, and 334 ± 26 pA (mean ± standard deviation) for the (101), (111) and (100) facets, respectively, which follows the same In a previous study on iron, the grain dependence of iron dissolution was studied with atomic force microscopy (AFM), where it was shown that the (100) grains exhibited the largest dissolution rate during electropolishing in acidic media at a constant current density of 0.3 A cm -2 . In a different study on iron single crystals in pH 1 sulfuric acid, it was also found that the dissolution rate for the low index planes increased in the sequence (100) > (111) > (101) [56]. Our results, using a different approach, are consistent with this prior work. Furthermore in a study carried out on a light weight ferritic steel, an EDC technique revealed a critical current density (i.e., maximum current during active dissolution) that was ca. 50% larger at (100) grains compared to the (111) orientation (compared to ca. 31%, herein) in 0.5 M H 2 SO 4 . Although the material studied herein (low carbon steel) was different to those considered [3,8], these studies lend weight to our observation of higher active dissolution currents on the (100) grains compared to the (101) or (111) grains.
There is much speculation in the literature as to why grains exhibit different anodic dissolution rates. For example, it has been theorised [8] that the surface density of the atoms of each grain governs corrosion susceptibility/resistance (also applied to other metals, such as magnesium [57]), where anodic metal dissolution rates decrease with increasing packing density (i.e., densely packed surface atom layers 'shield' the sub-surface layers from interaction with the corrosive electrolyte). For the case of ferrite steel (i.e., the structure of low carbon steel), surface atom density increases in the order 1.2 Â 10 15 , 1.7 Â 10 15 and 1.9 Â 10 15 atoms cm À2 for the (100), (101) and (111) planes, respectively. While this certainly fits our observations for the (100) grains (Fig. 5b, red traces), such a naïve analysis cannot explain the higher rates of dissolution observed at the (111) compared to the (101) planes (Fig. 5b, blue and green traces, respectively). This suggests that there are likely other factors that affect the active dissolution rate of the individual grains, explored further below.
STEM inspection of individual SECCM scanning sites. To visualise the physical changes to the low carbon steel that occur during SECCM-induced anodic corrosion, FIB milling was used to extract a section of the surface containing individual scanning sites (i.e., individual SECCM "pixels"). Note that a pipet probe of diameter z2 mm was used in this particular experiment to enable the more ready preparation of the cross-section. The step-by-step guide of the FIB milling procedure is shown in Fig. 6 and is also described in detail in the Experimental Section.
An STEM analysis of the cross-sectional structure and composition of a typical area where SECCM measurements were made is shown in Fig. 6c. There is a deep recess relative to the surrounding areas resulting from the removal of Fe 2þ during the active dissolution process (Eq (2)). Corrosion products are re-deposited over the top of this site (highlighted with a dotted line, thickness of ca. 140 nm), producing a layer that contains iron, sulphur and oxygen (electron dispersive spectroscopy, EDS). The EDS map for platinum is included to identify the protective layer from the FIB milling procedure. These corrosion products are likely comprised of iron (II) and iron (III) oxysulfate species, as calculated with the HYDRA and MEDUSA software, which consider the thermodynamically stable (equilibrium) solid products under a given set of experimental conditions (further details can be found in the Experimental Section).
Density functional theory calculations. To explore the possible factors governing the grain-dependent iron dissolution rates, density functional theory (DFT) calculations were performed that consider the binding energies of iron atoms at the surface of a lattice. In brief, we consider the thermodynamic properties for each of the low index crystal planes by calculating the energy required to remove (ionise) one monolayer of iron using the following (simplified) equation: where E Fe-Fe represents the binding energy of Fe on the surface of a particular plane, normalised by the number of atoms for a monolayer, E n is the total energy stored in n monolayers of iron atoms, E (n-1) is the surface energy after removing one monolayer, E Fe 2þ is the energy of an Fe 2þ ion liberated from the surface and N is the number of atoms per monolayer. Further details of the calculations can be found in the Experimental Section. The measured i surf values (at À0.581 V), 218, 252 and 334 pA scale with the calculated E Fe-Fe values, À24.253, À24.237 and À24.216 eV for the (101), (111) and (100) planes, respectively (plot shown in the Supporting Information, Fig. S4). This means that crystal orientations where Fe atoms are thermodynamically easier to remove (and ionise), evidenced by less negative E Fe-Fe values, correlate with higher active iron dissolution rates, evidenced by larger i surf values at active potentials (Fig. 4). Note that the convergence error for each calculation was ±0.001 eV showing that despite the very subtle differences in energy between orientations, the calculations were sufficiently precise to confirm any trends between the dissolution behaviour of different crystal planes.
Dissolution of a crystalline solid in a solution is complex, involving a number of interacting processes in parallel at different characteristic sites [58,59]. Nonetheless, the above analysis suggests a correlation of the anodic dissolution kinetics with the free energy of ionization, consistent with a general semi-empirical framework for predicting dissolution rates based on free energy relations [58,60]. It must be emphasized that the DFT calculations are performed for a simplified system (i.e., a plane of Fe atoms on a lattice, undergoing uniform dissolution/corrosion). The influence of anions (as well as other species present in solution) is not explicitly considered, which are known to influence the corrosion behaviour of steel, the most well-known example being Cl À ions inducing localised (pitting) corrosion [61]. In reality, the grain-dependent corrosion susceptibility/resistance of low carbon steel is likely to be dependent on solution conditions [2] (i.e., pH, electrolyte composition, etc.) which, as demonstrated herein, is amenable to analysis through SECCM, again highlighting the potential of this technique in corrosion research.

Conclusions
In this study, we have advanced the understanding of the dependence of anodic iron dissolution on the underlying crystallographic structure of low carbon steel in aqueous sulfuric acid (pH 2.3). This was achieved through the combination of local potentiodynamic polarisation experiments from SECCM (>100 measurements analysed on each low-index plane) with co-located structural information from EBSD, which revealed grain-dependent anodic iron dissolution rates that increase in the order (100) > (111) > (101). Local cross-sectional analysis with STEM imaging revealed a build-up of corrosion products within the dissolved area of an individual droplet "footprint" site, which was suggested to comprise insoluble iron oxysulfate species, formed during the active dissolution of iron. The grain-dependent anodic dissolution rates derived from SECCM were rationalized through complementary DFT calculations, which showed that the rate of iron dissolution, and hence corrosion susceptibility, increases with increasing (i.e., less-negative) E Fe-Fe values (i.e., the energy required to remove a monolayer of iron from the surface of a lattice). Overall, this study further positions SECCM as an effective tool for analysing the structure-dependent corrosion-related behaviour of metal alloys at the nanoscale, particularly when combined with complementary structural characterisation (e.g., EBSD and STEM) and computational analysis (e.g., DFT calculations).