<figure><img src="image_1.png" /></figure>

# Multiscale microstructural investigations of white and brown etching layers initiating the squat formation in pearlitic rail steels

Matteo Russo<sup>a,b,D</sup>, Aurélien Saulot<sup>a,D</sup>, Xavier Sauvage<sup>c,D</sup>, Muriel Véron<sup>d</sup>, Edgar Rauch<sup>d</sup>, Léo Thiercelin<sup>e,D</sup>, Frédéric Lebon<sup>f,D</sup>, Patrice Chantrenne<sup>b</sup>, Sophie Cazottes<sup>b,D,*</sup>

## ARTICLE INFO

### Keywords:

White etching layer

Tribological surface transformation

Pearlitic steel

Wheel-rail contact

Atom probe tomography

ACOM-TEM

## ABSTRACT

This study investigates the microstructural evolution of a pearlitic railway rail affected by squat defects, focusing on the microstructural gradients in the white and brown etching layers (WELs and BELs) below the rail surface. A multiscale characterisation of the rail microstructure is conducted using a combination of Scanning Electron Microscopy (SEM), Transmission Electron Microscopy with Automated Crystal Orientation Mapping (ACOM-TEM) mode, and Atom Probe Tomography (APT). The findings reveal that the microstructural gradient in the transformed layers consists of nanograins of carbon-saturated ferrite, twinned martensite, retained austenite, decomposed cementite, and secondary carbides. The presence of retained austenite suggests a thermal formation of the observed microstructure. The interaction between thermal driving forces and the effects of cumulative plastic deformations caused by wheel-rail interactions is discussed. It is suggested that while thermal forces drive the formation of the WEL/BEL microstructure, the tribological surface transformation (TST) occurs according to local equilibrium conditions. Specifically, the thermal driving force is enhanced by chemical driving forces resulting from the nanostructuring process of the rail microstructure prior to the WEL/BEL formation. Over subsequent wheel-rail contact cycles, the pearlitic microstructure experiences nanostructuring, leading to the formation of a dense network of grain boundaries, the fragmentation and decomposition of cementite, and the diffusion of carbon atoms (C) into ferrite by C-defects interactions. These transformations create a chemical driving force that lowers the energy barrier for austenite nucleation, ultimately resulting in the formation of martensite.

## 1. Introduction

The squat-type defect is among the most concerning railway rail defects that originate during service. Squats not only affect train dynamics by exacerbating rail degradation, but they can also evolve into catastrophic rail breaks if left untreated. Detection and treatment of squats increase maintenance costs and environmental impact, therefore, there is a growing need for optimised maintenance strategies.

A localised depression and a widening of the rail running band characterise fully developed squats. Additionally, dark lobes and V-shaped cracks, which orient toward the gauge corner, are typically present. Surrounding the squat, it is possible to observe networks of flake-like surface cracks [1]. Squats are commonly found on braking and accelerating sections of straight tracks (tangent sections) and

shallow curves, i.e., where the rails experience high traction forces. Furthermore, squats are observed more frequently on head-hardened (HH) rails compared to standard carbon (SC) rails – which is explained by a natural grinding effect by higher wear rates in milder steels – and on tracks with higher stiffness, e.g., concrete ballasts, due to their characteristic of amplifying dynamic impacts [2,3]. Several authors documented the initiation and growth of squat defects [1–16]. Steenbergen and Dollevoet [14,15] suggest that the propagation of a major leading and minor trailing crack at the rail surface drives squat formation. These cracks expand into the subsurface, enclosing a wedge-shaped rail segment. As the wedge loses its load-bearing capacity, stress redistribution causes the areas bordering the cracks to harden. The

<footnote><sup>a</sup> Univ. de Lyon, INSA Lyon, CNRS UMR 5259 LaMCoS, F-69621, Villeurbanne, France</footnote>

<footnote><sup>b</sup> Univ. de Lyon, INSA Lyon, CNRS UMR 5510, MatéIS, F-69621, Villeurbanne, France</footnote>

<footnote><sup>c</sup> Univ. Rouen Normandie, INSA Rouen Normandie, CNRS, Groupe de Physique des Matériaux, UMR6634, Rouen, France</footnote>

<footnote><sup>d</sup> Univ. Grenoble Alpes, CNRS, Grenoble INP, SIMaP, Grenoble, France</footnote>

<footnote><sup>e</sup> Arts et Métiers Institute of Technology, CNRS, Université de Lorraine, LEM3-UMR 7239, F-57078, Metz, France</footnote>

<footnote><sup>f</sup> Aix Marseille Université, CNRS, Centrale Marseille, LMA UMR 7031, F-13453, Marseille, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: sophie.cazottes@insa-lyon.fr (S. Cazottes).</footnote>
Poisson effect contributes to surface depression and widening causing a downward shift of the area above the crack planes, while differential contact pressure over the crack planes forms the double-lobed shape of the squat defect. Metallurgical studies link crack initiation with ratcheting and tribological surface transformations (TST) named white etching layers (WEL) and brown etching layers (BEL), based on their appearance under the optical microscope following chemical etching with an ethanol-nitric acid solution (Nital).

Mastering the transformation of the rail's base material into the WEL is crucial to ensure optimised maintenance strategies. Over the past four decades, it emerged different views on the formation mechanism and the nature of WEL and BEL in pearlitic rail steels [1,10,11,17–38] and in bainitic rail grades [39,40].

Two acknowledged primary driving forces leading the TST are generally proposed in the literature. Firstly, the “mechanical work” done at the rail surface by contact stresses transforms the base pearlite into a nanostructure of ferrite saturated with carbon atoms through progressive grain refinement, decomposition of cementite, and defect-assisted diffusion of carbon atoms [1,17,18,26,29,41]. The second driving force is the “thermal energy” generated in the contact area either through frictional heating or by localised plastic strain under dynamic loading, causing austenisation of the base material. Subsequent rapid cooling of the rail surface results in the formation of martensite. This mechanism, with a minor contribution of plastic strains, results in a microstructure of ultra-fine martensite, retained austenite and cementite nanoparticles [20,22,23,27]. Alternative sources of thermal energy input causing the phase transformation have been found in electrical arcing caused by current leakage between the wheels and rails [42] and rail-grinding operations [43]. Nevertheless, these mechanisms appear to have received less attention.

Identifying a single formation mechanism for WELs and BELs is challenging due to the dependence of tribological transformations on loading history. Additionally, the wheel-rail contact system features a continuous interplay between thermal and mechanical driving forces. Wojdyr et al. [25] suggested that WELs originate from thermal and mechanical driving forces. While the mechanical work drives the carbon redistribution from cementite to grain boundaries and dislocation, localised heating at the rail surface is necessary to diffuse carbon into the ferrite lattice, causing its distortion. A series of studies on squat defects in the Australian rail network [3,11,34], classified WELs based on the prevailing driving force: TP-WEL, which forms under high temperature and pressure conditions and feature a sharp transition to the unaffected pearlitic sub-structure, and SD-WEL, which develops mainly by severe plastic deformation and features a gradual transition from the transformed layer to the sheared pearlite.

Studies on Fe–C nanostructures obtained by severe plastic deformation of lamellar pearlite [24,44–47] highlight that C-defect interactions during cold-working drives the cementite dissolution and leads to local compositional changes. The introduction of a high defect density, along with compositional alterations, serves as a chemical driving force that assists non-chemical driving forces – provided by either thermal energy or mechanical work – in austenite nucleation [48]. In the wheel-rail contact scenario, such redistribution of carbon from cementite to ferrite defects may shift the thermodynamic balance of pearlite, lowering the critical temperature for austenite nucleation [36,37].

Thiercelin et al. [49,50] presented a thermomechanical model to predict WEL formation taking into account the interplay between the hydrostatic pressure, the shear stress and the temperature gradient at the rail subsurface. Based on the SEM-SE and SEM-EBSD analysis of several microstructures obtained from representative tests of wheel-rail contact under controlled thermomechanical conditions on an R260 rail steel [50–52] and from a WEL sample extracted from a squat zone [1], the authors described the several stages of the formation mechanism of WELs involving grain fibration and fragmentation, nanostructuring and carbon redistribution. However, the transition from the nanostructured stage to the fully developed WEL is still partially unexplained.

<table><caption>**Table 1**

Chemical composition of rail steel R260 (wt% and at%).</caption><thead><tr><th></th><th>C</th><th>Mn</th><th>Si</th><th>P</th><th>S</th><th>Cr</th><th>Al</th></tr></thead><tbody><tr><td>wt%</td><td>0.74</td><td>1.08</td><td>0.30</td><td>0.013</td><td>0.018</td><td>0.040</td><td>0.003</td></tr><tr><td>at%</td><td>3.35</td><td>0.69</td><td>0.29</td><td>0.04</td><td>0.04</td><td>0.16</td><td>0.01</td></tr></tbody></table>

To address this issue, the present study presents the microstructural characterisation of a white and brown etching layer extracted from a straight track affected by squat defects. The microstructure of the rail is studied using a combination of SEM-SE, TEM in Automated Crystal Orientation Mapping (ACOM-TEM) mode, and atom probe tomography (APT). This analysis aims to capture the carbon redistribution process at the final of the TST and elucidate the role of chemical and thermomechanical driving forces. The aim of this multi-scale characterisation is to improve the knowledge on the WEL/BEL microstructure by a complete description at the nano-metric scale of the microstructural gradient. Moreover, to fully describe the complex heterogeneous microstructure present and to assess the repeatability of the observations, four APT analyses are performed in the topmost WEL.

Section 2 outlines the characteristics of the sampling site for the reference rail sample and details the techniques used to characterise the microstructural gradient.

Section 3 presents the characterisation results, covering the microstructural gradient from the underlying pearlite to the white etching layer at the rail surface.

Section 4 discusses the role of thermal, mechanical, and chemical driving forces on the formation of the observed microstructure.

Finally, Section 5 proposes a formation mechanism for the WEL/BEL microstructure within the context of the current wheel-rail contact scenario.

## 2. Materials and methods

### 2.1. Materials

A multiscale microstructural characterisation is performed on a rail affected by a squat defect, which was taken out of service in 2009 from Paris, French suburban network, France. A tribological and metallurgical analysis performed on samples of the same area is available at [1]. The nominal chemical composition of the R260 rail steel is given in Table 1. Table 2 details the track and traffic characteristics taken from the same study. Given the track operating period, the axle load and traffic conditions, the mean tonnage accumulated before the squat defect appears is 65.7 Mt. Visual inspection of the rail track in Fig. 1(a) reveals an area affected by a single-lobe squat defect. Optical micrographs to locate the WEL were acquired on an RH-2000 microscope (Hirox) after mechanical polishing down to 1 µm and Nital etching. The optical micrograph of a longitudinal cross-section, shown in Fig. 1(b), reveals white and brown etching layers associated with crack propagation.

### 2.2. Microstructural characterisation

A TEM thin foil was prepared using a Focused Ion Beam (FIB) microscope. The thin foil was produced to cover the entire microstructural gradient of the WEL/BEL and the nearby deformed pearlite, whose location is depicted in Figs. 1 and 2(a).

At the transmission electron microscope scale (TEM), phase and orientation maps were acquired with the commercial setup ASTAR by NanoMEGAS. This TEM attachment operates by sweeping a precessing electron beam over a region of interest while the diffraction patterns are recorded with an optical camera [53]. Precession electron diffraction (PED) patterns are then analysed using a template-matching algorithm, creating a map of the crystal structure within the region. This TEM technique achieves a spatial resolution of around 1–2 nm, making
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** (a) Rail specimen exhibiting a single-lobed squat defect. A pictogram indicates the rolling direction (RD), transverse direction (TD), and normal direction to the rail surface (ND). (b) Optical micrograph of the longitudinal cross-section from sector b showing a 30 µm white and brown etching layer. ROI<sub>A</sub> and ROI<sub>B</sub> indicate regions further analysed by SEM.</figcaption></figure>

<table><caption>**Table 2**

Characteristics of sampling site. Adapted from [1].</caption><tbody><tr><td rowspan="8">Track data</td><td>Rail profile</td><td>60E1</td></tr><tr><td>Steel grade</td><td>R260</td></tr><tr><td>Track geometry</td><td>Straight line</td></tr><tr><td>Track layer</td><td>Ballast</td></tr><tr><td>Sleeper type</td><td>Twin-block</td></tr><tr><td>Track laying</td><td>2006</td></tr><tr><td>Last grinding</td><td>2006</td></tr><tr><td>Rail replacement</td><td>2009</td></tr><tr><td rowspan="2">Vehicle data</td><td>Type</td><td>MI2N/MI84<sup>a</sup></td></tr><tr><td>Axle load (t)</td><td>18/14</td></tr><tr><td rowspan="2">Traffic conditions</td><td>Speed (km/h)</td><td>80-90 Braking area</td></tr><tr><td>Mean load per day (t)</td><td>60 000</td></tr></tbody></table>

it suitable for mapping deformed regions and detecting nanograins and small carbides. This method is known under different names in the literature (ASTAR, D-STEM/PED, Automatic Crystal Orientation Mapping (ACOM-TEM)) [53–55]. In the present study, it is labelled as ASTAR. Acquisitions were carried out on a FEG TEM at 200 kV (JEOL 2100F). Ferrite (α-Fe), austenite (γ-Fe), and cementite (Fe₃C) were declared during template indexing. Due to their very close crystallographic structures, martensite is systematically indexed as ferrite during the analysis. Pixels with a confidence index of less than 15% were removed from the analysis.

All the orientation maps were post-treated with Atex software [56]. Full spike correction was applied on the maps. The detection disorientation angle for grains detection was set to 10°. For each analysed region, different maps were generated. Inverse Pole Figures (IPF) display the crystallographic orientation relative to a reference direction, chosen as the rolling direction (RD). Kernel Average Misorientation (KAM) was employed to assess the local misorientation within the microstructure. A kernel of 5 pixels was chosen to compute the average misorientation around each pixel. A threshold angle of 10° was selected to distinguish sub-granular dislocations from actual grain boundaries.

APT analyses were carried out using a CAMECA LEAP® 5000XS instrument. Needle-shaped specimens were prepared using focused ion beam milling. Specimens are aligned with their axes parallel to the rolling direction, pointing toward the transverse direction. The specimens were produced at a depth of 2.5 µm below the rail's surface within the WEL and were spaced 1 µm apart, see Fig. 3. Samples were field evaporated in voltage mode under ultra-high vacuum (10<sup>-11</sup> mbar) with electric pulses (pulse fraction of 20%, repetition rate of 200 kHz) at a temperature of 60 K. Three-dimensional (3D) reconstructions and data post-processing were performed using IVAS 6.3 Software by CAMECA.

Peaks at mass-to-charge ratios equal to 6 and 6.5 Da were assigned to carbon ions ¹²C²⁺ and ¹³C²⁺, 12 and 13 Da to ¹²C⁺ and ¹³C⁺, 18 Da to ¹²C₃²⁺, 18.5, 24.5 and 25 Da to [¹²C₂¹³C]²⁺, [¹²C₃¹³C]²⁺ and [¹²C₂¹³C₂]²⁺, 36 and 48 Da to ¹²C³⁺ and ¹²C⁴⁺. As pointed out in [57,58], there exists an ambiguity on peak assignment at 24 Da, due to overlap of C₂⁺ and C₄²⁺ peaks in the mass spectrum. In the present analysis, the upper and lower carbon atomic fractions are given by assigning the peak at 24 Da to C₂⁺ and C₄²⁺ respectively.

## 3. Results

### 3.1. SEM-SE characterisation of the microstructural gradient

Fig. 2 shows SEM-SE imaging of the etched microstructure corresponding to the regions of interest delimited in the optical micrograph of Fig. 1(b). In Fig. 2(a), ROI<sub>A</sub>, a WEL island of approximately 5 µm in thickness can be distinguished from the underlying BEL based on its finer texture. This texture indicates that the WEL features a nanocrystalline microstructure. The underlying BEL shows a gradient in the SE contrast, which reflect local variations in microstructural features of the BEL along the depth. Smooth and irregular islands of brighter contrast, likely corresponding to a carbon-rich phase [59], are dispersed along the BEL. Additionally, lamellar structures are visible at the BEL-pearlite transition. The deformed pearlite below the transformed layer exhibits a heterogeneous morphology with continuous cementite lamellae in some colonies, predominantly aligned parallel to the rail raceway, while a few colonies appear fragmented and curled.

<footnote><sup>a</sup> MI2N: 3 powered cars and 2 unpowered cars MI84: 2 powered cars and 2 unpowered cars.</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** SEM-SE images of the etched microstructure corresponding to the regions of interest defined in the optical micrograph of Fig. 1(b): (a) ROI<sub>A</sub>, (b) ROI<sub>B</sub>. (c) A magnified view of the region marked in blue shows bright linear features likely corresponding to cementite lamellae remnants.</figcaption></figure>

The BEL in Fig. 2(b), corresponding to ROI<sub>B</sub> in Fig. 1(b), extends approximately 40 µm. This region exhibits microstructural exhibits analogous to those observed in the BEL of ROI<sub>A</sub>: The SE contrast became brighter toward the untransformed pearlite, indicating that the BEL is composed of fine grains at the transition toward pearlite, while dispersed bright-phase islands suggest the presence of carbon-rich regions. Additionally, near the rail surface, slightly bright linear features consistently aligned parallel to the surface are observed, see the magnified view of Fig. 2(c). A matching observation is reported by Li et al. [33]. The bright lines are spaced 88 ±21 nm apart, which is roughly equivalent to the interlamellar spacing of 94 ±13 nm observed within the deformed pearlite. The direct interlamellar spacing was measured following the approach outlined in [60].

A TEM thin foil that covers the entire WEL was prepared using FIB lift-out technique. Four areas were then mapped using ACOM-TEM (ASTAR) to characterise the microstructure, see their location in Fig. 3. The microstructural gradient of the transformed layers characterised by ASTAR is presented in Fig. 4. Pictures from left to right show phase maps ((a), (d), (g) and (j)), IPF maps projected along the rolling direction ((b), (e), (h) and (k)), and KAM maps ((c), (f), (i) a,d (l)). The microstructural features of the WEL and the deformed pearlite will be discussed by analysing the microstructural gradient from the pearlite near the BEL up to the rail surface.

## 3.2. Zone 1/Deformed pearlite

Fig. 4(j)–(l) show the pearlitic microstructure beneath the transformed layer at 30 µm from the rail surface. The portion labelled upper colony in Fig. 4(k) shows well-preserved cementite lamellae parallel to the rail surface. Low KAM values and lamellae integrity suggest low plastic deformation within this area. Additionally, the grain boundaries (GBs) network of Fig. 4(l) reveals that some dislocation walls across ferrite evolve into grain boundaries. Moving downward, KAM values rise, and the density of GBs increases, indicating ongoing fragmentation in the lower colony. The observed deformation gradient from the upper to the lower region suggests that the initial orientation of the lamellae relative to the stress field dictated the degree and the deformation pattern in each colony. The upper colony appears more prone to morphological alignment, referring here to the progressive elongation and bend of the lamellae along the direction of shear stresses [61]. Simultaneously, in the lower colony, transverse grain boundaries within ferrite developed due to the accumulation of dislocation walls. This reflects the anisotropic response of pearlite colonies depending on their

initial orientation relative to the shear stresses. Colonies favourably oriented with respect to shear tend to exhibit lamellar elongation and bend, whereas misoriented colonies undergo fragmentation and subgrain formation [50].

It is worth noting that austenite was with an area fraction of 0.8% was indexed in this area. However, this is due to a phase mis-indexing. This aspect will be further addressed and clarified in the next sections.

## 3.3. Zone 2/BEL-pearlite interface

The microstructure at the pearlite to BEL transition zone is presented in Fig. 4(g)–(i). At the top and bottom of the analysed area, sharp grains in the range of tens of nanometres were indexed as austenite (Fig. 4(g)). Furthermore, in the centre of this area, remnants of lamellar cementite can be observed, indicating that the BEL comprises partially dissolved cementite. Nanostructured equiaxed ferrite grains, with diameters smaller than the interlamellar spacing, likely formed as dislocation cells resulting from severe plastic deformation, as commonly observed in HPT processed steels [61], see Fig. 4(h). Polygonal grains with a lath-like morphology, likely deformed by twinning after martensite formation, were observed. Adjacent to these twinned grains, a group of equiaxed ferrite grains, completely free of dislocations and twinning, exhibit features typically associated with recrystallised structures (Fig. 4(i)). However, considering the ultrafast heating conditions characteristic of the wheel-rail contact scenario and the limited stability of manometric-scale nuclei of ferrite, recrystallisation is unlikely to have occurred.

ASTAR analysis provides additional information using Virtual Dark-Field (VDF) mode. High-magnification VDF images of the BEL-pearlite transition zone reveal two populations of carbides with different sizes. The first group consists of spherical features that are approximately 15 nm in diameter, as shown in Fig. 5(b) and highlighted in Fig. 5(e). The carbides of this group are indexed as cementite, as indicated by the template matching of the diffraction pattern of Fig. 5(d) and (d'), while, the surrounding matrix is indexed as ferrite, see Fig. 5(c) and (c'). The second population of carbides measures approximately 5 nm in diameter (see Fig. 5(f)). Additionally, carbide-decorated dislocations with a spacing of approximately 10 nm are evident in Fig. 5(g), while dislocation-free ferrite grains are observed in the top-right corner of the same VDF image.
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Location of the regions of interest analysed by ACOM-TEM (ASTAR) and APT. (a) The TEM thin foil location is outlined by the blue box, while the four APT specimen locations are enclosed within the red box. (b) SEM-SEM image of the TEM thin foil. The cyan boxes mark the positions of four regions of interest further examined using ASTAR.</figcaption></figure>

### 3.4. Zone 3/BEL

The microstructure of the BEL at 5 µm from the surface is presented in Fig. 4(d)–(f). No evidence of residual primary cementite is found, indicating its complete dissolution. However, nanoparticles indexed as cementite are detected. Additionally, austenite islands are indexed along the grain boundaries. Identification of austenite within ferrite can be a difficult task from ASTAR mapping for two reasons. First, the diffraction patterns of the BCC and FCC phases, both possessing cubic symmetry, show similarities. Secondly, ambiguities may arise from grains that overlap within the thickness of the sample. Such overlap leads to superimposed diffraction patterns, affecting the phase and orientation identification, which is based on the analysis of the cross-correlation coefficients. This is particularly true in our case, where the grain size is smaller than the sample thickness. Therefore, the presence of austenite in this area was double checked using a cross correlation of two orientation maps of the same area, and observed with two different tilting angles. These results, presented in the Supplementary Materials, support the reliability of austenite indexation. In contrast, no consistent cementite indexing was obtained in this region. The area fraction of the austenite and ferrite phases is 8% and 91%, respectively. Based on the presence of retained austenite and twinned grains, see Fig. 4(d) and (e), it is reasonable to assume that a certain amount of indexed ferrite is, in fact, martensite. The twinning deformation is a key morphological indicator of martensitic transformation, as it is energetically favourable to accommodate the lattice-invariant deformation necessary for the γ → α' transformation [62,63]. Low internal deformation is evident from the KAM map Fig. 4(f).

### 3.5. Zone 4/Near surface WEL

The sub-surface white etching layer features nanosized equiaxed ferritic grains, retained austenite, indexed at the grain boundaries with an area fraction of 7%, and nanocarbides, indexed with an area fraction

of 2% (Fig. 4(a)). Twinned grains are observable, as indicated by the white arrows in Fig. 4(b). Thus the WEL is expected to comprise also martensitic grains. A visual inspection of the KAM map overlaid with the grain boundary network in Fig. 4(c) reveals a fine grain size and greater internal misorientation compared to the underlying BEL, indicating a higher degree of deformation and fragmentation (see Fig. 4(f) for comparison).

APT was employed within the near-surface WEL to determine the nature of the carbides and reveal the presence of carbon supersaturated phases, complementing the earlier observations made by ASTAR. Figs. 6 to 9 depict the analysis results of four APT volumes. The 3D distribution of carbon atoms is represented by red dots in C-atom maps. The morphology and spatial distribution of C-rich clusters (carbides) are highlighted by 14 at.% C iso-composition surfaces, while C iso-composition surfaces from 2 at.% to 7 at.% highlights matrices of different carbon content.

To finely analyse the elemental composition of matrices and carbides, regions of interest were selected inside each sub-region identified by the iso-composition surfaces, and a background-corrected analysis of each ROI was performed to measure the C content. The bulk composition analysis and 1D cross-composition profiles provide the lower and upper carbon atomic fractions. These bounds were measured by assigning C₂²⁺ and C₄⁺ to the 24 Da peak.

Since partitioning of alloy manganese (Mn) and silicon (Si) is expected during the austenite-pearlite transformation (cementite has an affinity with manganese while ferrite has an affinity with silicon [64]) evidence of Mn-enrichment and Si-depletion within C-rich regions are used to differentiate primary cementite from secondary carbides, the latter forming by precipitation without Si and Mn partitioning [65].

The carbon atom maps and the corresponding iso-composition surfaces in Figs. 6 to 8(a) reveal matrices of different carbon content within the APT volumes. These matrices, represented in orange and blue, correspond to two distinct compositional families. To highlight the compositional differences between the two matrix types, the atomic
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Microstructural gradient of the White Etching Layer (WEL) and Brown Etching Layer (BEL) characterised by ASTAR. From left to right, the columns represent phase maps, inverse pole figures (IPF) parallel to RD (here, only α-Fe is represented), and KAM maps overlaid with grain boundaries (GBs) > 10°. (a)–(c) represent the WEL near the surface, (d)–(f) represent the BEL at 5 µm depth, (g)–(i) show the BEL-pearlite transition zone, and (j)–(l) depict the deformed pearlite region.</figcaption></figure>

fractions of C, Mn, and Si measured in regions of interest within each matrix are reported in Tables 3–5. The matrices corresponding to the lower carbon content group (i.e. ROI₁, ROI₃ and ROI₅) show a carbon content ranging from 0.14–0.27 at.% to 0.43–0.56 at.%, that is higher

than the solubility limit of carbon in BCC ferrite at room temperature. According to the joint results from APT and ASTAR, these matrices likely correspond to C-saturated ferrite. In contrast, the C-richer matrices (i.e., ROI₂, ROI₄, and ROI₆) display carbon contents ranging from
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** (a) VBF imaging of the microstructure at the transition zone from the pearlite to the BEL. (b) Magnified VBF image of the selected zone indicated in (a). (c) VDF image of the magnified region, with bright areas revealing spherical of 15 nm in diameter. This VDF image was constructed from the diffraction pattern shown in sub-figure (e) by selecting the spot marked in red. (d) Diffraction pattern corresponding to point d, marked by the black arrow in (b). (d') The template matching shows agreement with the ferrite template. (e) Diffraction pattern corresponding to point e, marked by the second black arrow in (b). (e') Template matching showing agreement with the cementite template. (f) The VDF image reveals a second group of smaller carbides. (f') shows the diffraction pattern collected from point f, used to construct the VDF. (g) VDF image showing the high dislocation density within the BCC matrix and (g') diffraction pattern corresponding to point g used to construct the VDF.</figcaption></figure>

2.80–3.58 at.% to 3.86–4.69 at.%. The elevated carbon content in these matrices confirms the presence of austenite, as observed in the ASTAR analysis.

**Fig. 6(b) and (c) present higher magnification views of two carbon clusters selected from the APT volume of Fig. 6(a), and the corresponding 1D composition profiles. The first cluster (b) displays a spherical**
<caption>**Table 3**</caption>

Elemental composition from $ROI_0$, $ROI_1$, and $ROI_2$ of Fig. 6. Values are reported as mean ±1 standard deviation. The lower and upper carbon atomic fractions are obtained by assigning $C_2^{2+}$ and $C_4^+$ to the 24 Da peak.

<table><caption>**Table 4**</caption><thead><tr><th></th><th>C at.%</th><th>Mn at.%</th><th>Si at.%</th></tr></thead><tbody><tr><td>ROI<sub>0</sub></td><td>15.85 ± 0.1/19.35 ± 0.1</td><td>0.24 ± 0.02</td><td>1.09 ± 0.04</td></tr><tr><td>ROI<sub>1</sub></td><td>0.43 ± 0.02/0.56 ± 0.02</td><td>0.90 ± 0.01</td><td>0.49 ± 0.01</td></tr><tr><td>ROI<sub>2</sub></td><td>3.86 ± 0.02/4.69 ± 0.02</td><td>0.53 ± 0.01</td><td>1.09 ± 0.01</td></tr></tbody></table>

Elemental composition from $ROI_3$ and $ROI_4$ of Fig. 7. Values are reported as mean ±1 standard deviation. The lower and upper carbon atomic fractions are obtained by assigning $C_2^{2+}$ and $C_4^+$ to the 24 Da peak.

<table><caption>**Table 5**</caption><thead><tr><th></th><th>C at.%</th><th>Mn at.%</th><th>Si at.%</th></tr></thead><tbody><tr><td>ROI<sub>3</sub></td><td>0.32 ± 0.02/0.45 ± 0.02</td><td>0.82 ± 0.01</td><td>0.22 ± 0.02</td></tr><tr><td>ROI<sub>4</sub></td><td>2.82 ± 0.04/3.67 ± 0.05</td><td>0.78 ± 0.02</td><td>0.57 ± 0.02</td></tr></tbody></table>

Elemental composition from $ROI_5$ and $ROI_6$ of Fig. 8. Values are reported as mean ±1 standard deviation. The lower and upper carbon atomic fractions are obtained by assigning $C_2^{2+}$ and $C_4^+$ to the 24 Da peak.

<table><thead><tr><th></th><th>C at.%</th><th>Mn at.%</th><th>Si at.%</th></tr></thead><tbody><tr><td>ROI<sub>5</sub></td><td>0.14 ± 0.01/0.27 ± 0.01</td><td>0.94 ± 0.01</td><td>0.44 ± 0.01</td></tr><tr><td>ROI<sub>6</sub></td><td>2.80 ± 0.02/3.58 ± 0.02</td><td>0.80 ± 0.01</td><td>0.26 ± 0.01</td></tr></tbody></table>

morphology with an approximate diameter of 15 nm. The corrected bulk composition from $ROI_0$ reveals a background-corrected carbon content reaching 19.35 at.% (see Table 3). Si depletion and Mn enrichment were also observed within this region (refer to Table 1 for the nominal atomic fractions of each element in R260 steel). The 1D composition profile displays a carbon content plateau extending across the thickness of the cluster. The cross-composition profile further highlights the partitioning of Mn and Si, supporting the identification of this carbide as a partially decomposed primary cementite. The blue arrow indicates a second carbon cluster of similar morphology, size, and composition in Fig. 6(a). Its detailed composition is omitted here for simplicity, as the results are analogous to the previous C-cluster. A second cluster (c) displays a flattened spherical shape, approximately 10 nm by 5 nm in size. The composition profile reveals carbon content fluctuations and the absence of a plateau, while no partitioning of Mn and Si was observed. Thus, this cluster corresponds to a secondary carbide.

Lamellar-shaped C-rich zones are visible in the second APT volume illustrated in Fig. 7(a), (b), and (c). The carbide highlighted in (b) exhibits a lamellar morphology, with a thickness of approximately 8 nm. The lack of Mn and Si partitioning within this region suggests it corresponds to a precipitated carbide. Besides, a smaller precipitate characterised by C content spikes up to 10 at.% is observed. Both precipitated are embedded in the C-saturated matrix (see $ROI_3$). The second carbide displaying a lamellar structure is observed at the ferrite-austenite boundary in Fig. 7(c). Nearby, a smaller carbon content precipitate of approximately 10 at.% is visible. The lack of Mn and Si partitioning in these two clusters indicates the presence of secondary carbides.

The 3D C distribution of a third volume represented in Fig. 8(a), and the 1D composition profile across the two matrices of Fig. 8(b) indicate carbon segregation. The cluster of C atoms segregated at the boundary between matrices is highlighted by 8 % iso-concentration surfaces (in red) in Fig. 8(b). Fig. 8(c) shows a magnified view of a flat circular nano-carbide. The composition profile reveals a C content up to 20 at.%, with no significant Si and Mn partitioning, further confirming the presence of secondary carbides within the WEL.

In the fourth volume of Fig. 9 no distinct boundaries between two matrices were observed. Rather, the carbon atom map revealed regions

of carbon concentration fluctuations. These regions are pointed by the blue arrows in the C atoms map of Fig. 9(a), and enclosed by 6 at.% C iso-composition surfaces that show evenly spaced C-enriched columnar structures. To enhance the clarity of the figure, the 1D composition profiles are presented using the $C_3^+$ ion assignment for the 24 Da peak. The 1-D composition profile of Fig. 9(b) indicates that these structures exhibit carbon content fluctuations up to 10 at.% in amplitude. A 1-D composition profile along the neighbouring region of relatively lower carbon content is represented in Fig. 9(c). The C fluctuations along this ROI appear less pronounced. Moreover, two carbon-rich clusters are identified along this profile, as indicated by peaks in C content. The lack of significant Si and Mn partitioning suggests they correspond to precipitated carbides. The compositional waves resulting in the columnar structures observed in this APT volume may be attributed to the presence of martensite undergoing spinodal decomposition [66]. Moreover, the carbon distribution pattern observed along the C-rich columnar structure in Fig. 9(b) aligns with APT studies on aged martensite [67], while carbide precipitation observed along the lower carbon content region is indicative of martensite undergoing decomposition into ferrite and cementite following tempering.

## 4. Discussion

This study investigated the subsurface structure gradient of eutectoid steel in railway rails using characterisation techniques down to the atomic scale, including ASTAR and APT. The primary objective was to elucidate the mechanisms driving the formation of white and brown etching layers and to assess the relative influence of thermal and mechanical contributions.

ASTAR and APT analyses showed that the WEL, approximately 5 µm thick, and the underlying BEL, extending about 25 µm, features a variety of phases. ASTAR characterisation indicated three distinct crystallographic structures along the entire microstructural gradient of the transformed layer: BCC ($\alpha$-ferrite/$\alpha'$-martensite), FCC ($\gamma$-austenite), and orthorhombic ($\Theta$-cementite). APT analysis of the topmost WEL consistently revealed two matrix types of different C content, see Figs. 6–8(a) and (d). The low-C matrices, likely representing C-saturated ferrite, contain 0.14 to 0.56 at.% C, see $ROI_1$, $ROI_3$ and $ROI_5$. It is well established that during cementite decomposition, carbon atoms segregate at grain boundaries and dislocations. Nevertheless, studies on severely deformed carbon steels suggest that carbon can also be retained in solid solution within ferrite, which may accommodate excess carbon through lattice distortion [47,68–70]. According to these studies, the carbon content in solid solution may reach approximately 0.1 wt% at room temperature. However, artefacts related to APT analyses may also contribute to the apparent carbon content of the ferrite. For example, Tung et al. [71] measured a carbon content of 0.25 at.% in ferrite from an undeformed pearlitic rail steel using pulse-voltage APT.

Additionally, high-C matrices likely corresponding to retained austenite contain 2.80 to 4.69 at.% C homogeneously distributed, see $ROI_2$, $ROI_4$ and $ROI_6$. To the author's best knowledge, this specific partitioning of carbon has not been previously reported, while the presence of C-rich matrices with comparable carbon content has been documented elsewhere [26,36]. Carbon fluctuations and carbide precipitation observed in Fig. 9 suggest the presence of a martensitic phase undergoing decomposition in ferrite and cementite. This observation is consistent with the results and conclusions of [27,32].

APT also identified C clusters corresponding to partially decomposed cementite and secondary carbides. Remnants of primary cementite of spherical morphology of 15–20 nm in diameter, with approximately 19 at.% C content, indicates that cementite within the WEL undergoes spheroidisation during its decomposition. A comparable finding was reported by Kumar et al. [36] within the WEL/BEL transition zone on heat-treated pearlitic steels in curved tracks affected by corrugation defects. However, the authors reported primary
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** APT results of one of the four analysed volumes within the WEL. The specimens were prepared from a region located 3 µm beneath the rail surface, with analysed volumes spaced 1 µm apart. (a) The C-atom map shows the 3D distribution of carbon atoms, with areas of elevated carbon content enclosed by 14 at.% C iso-composition surfaces (in green). 3 and 7 at.% carbon (C) iso-composition surfaces, highlighting matrices with varying carbon content (depicted in orange and blue). (b) and (c) show higher magnification views and 1D composition profiles extracted along the black arrows. Partitioning of Mn and Si is observed within the 1D profile (b), indicating the presence of partially decomposed cementite. The lower and upper bounds of the carbon atomic fraction profile are obtained by assigning the 24 Da peak to $C_2^{2+}$ and $C_4^{+}$, respectively. Error bars represent ±1 standard deviation.</figcaption></figure>

cementite of stoichiometric composition. It is worth mentioning that quantification biases in carbon-enriched regions, like cementite or transition carbides, must be accounted for in APT data interpretation. Carbon is an element strongly affected by multiple-hit artefacts. C atoms are prone to field evaporate as molecular ions, therefore, their dissociation during their flight from the tip to the detector results in multi-hit events, which in turn results in a loss of C in the compositional analysis due to the so-called “dead time” between closely spaced hits [72]. Secondary carbides are present as plate-like structures of 10 nm in thickness 7 and spherical precipitates of 5 to 10 nm in Figs. 6 and 8, with a C content ranging from 15 to 19 at.%.

Additionally, carbon is found to segregate at boundary-segregated, see Fig. 8(b). Precipitation of nano-carbides and C segregation has been widely documented in previous studies [27,36,37].

White and brown etching layers were found to promote a variety of railway rail defects: squats [1,6,10,11,13], corrugation [18,20,22,26, 33], head checks [35], and spalling [38,73]. Considering the inherent variability in the characteristics of WELs and BELs due to differences in contact conditions, rail grades, and the position of the contact patch between the wheel and the rail, the findings of this study are consistent with previous studies linking this tribological transformation to rail defects. New insights about the progressive transformation of
<figure><img src="image_8.png" /><figcaption>Fig. 7. APT results of a second analysed volume within the WEL. (a) The C-atom map with areas of elevated carbon content enclosed by 14 at.% C iso-composition surfaces (in green). 2 and 5 at.% carbon (C) iso-composition surfaces, highlighting matrices with varying carbon content (depicted in orange and blue). (b) and (c) show higher magnification views and 1D composition profiles extracted along the black arrows. The lack of Mn and Si partitioning across these 1D profiles indicates the presence of secondary carbides. The lower and upper bounds of the carbon atomic fraction profile are obtained by assigning the 24 Da peak to C₂²⁺ and C₄⁺, respectively. Error bars represent ±1 standard deviation.</figcaption></figure>

pearlite into the WEL/BEL microstructure can be drawn from the current ACOM-TEM and APT investigation.

## 4.1. Driving forces governing austenite nucleation

It is well-established that multiple microstructural and mechanical factors influence the $\alpha \rightarrow \gamma$ transformation by modifying the critical temperature required for austenite nucleation, $A_{C1}$. The variability in the observed phases, including partially decomposed cementite, indicates that austenite formation is governed by local equilibrium conditions and is driven by variations in the available driving forces at the sub-grain scale. The following sections explore the interplay

between thermal, mechanical, and chemical driving forces that govern austenite nucleation and growth in the wheel-rail contact scenario.

### 4.1.1. Thermal driving forces

The fundamental driving force for austenite nucleation arises from the thermal energy input due to frictional heating dissipated at the contact interface during wheel-rail slips. Based on the characteristics of the sampling site (see Table 2), the thermal energy input and temperature rise within the rail subsurface was estimated by the Ertz and Knothe’s model for an arbitrarily distributed heat load [74]:

$$T(x_k, z) = \frac{1}{\sqrt{\lambda\rho C}} \sqrt{\frac{2\alpha}{\nu}} \sum_{i=1}^{k} \dot{q}_i \times [G(x_k - x_{i-1}, z) - G(x_k - x_i, z)] \quad (1)$$
<figure><img src="image_9.png" /><figcaption>Fig. 8. APT results of a third analysed volume within the WEL. (a) The C-atom map with areas of elevated carbon content enclosed by 14 at.% C iso-composition surfaces (in green). 2 and 4 at.% C iso-composition surfaces, highlighting matrices with varying carbon content (depicted in orange and blue). (b) 8 at.% C iso-concentration surfaces (in red) highlight carbon segregation at phase boundaries. The regions of high carbon content corresponding to carbides have been omitted to improve visual clarity. (c) shows higher magnification views and 1D composition profiles of a carbide extracted along the black arrows. The lack of Mn and Si partitioning further indicates the presence of secondary carbides within the WEL. The lower and upper bounds of the carbon atomic fraction profile are obtained by assigning the 24 Da peak to C₂²⁺ and C₄⁺, respectively. Error bars represent ±1 standard deviation.</figcaption></figure>

where $T(x_k, z)$ is the temperature rise at a position $x_k$ along the rolling direction and a depth $z$ from the rail surface, $\lambda = 50$ W/mK, $\rho = 7850$ kg/m³ and $C = 450$ J/kgK are the thermal conductivity, density and the heat capacity of the rail steel respectively, supposed constant over the range of predicted temperatures, $a$ is the contact ellipse semi-axis along rolling direction, $v$ is the advancing speed of the train. $G(x, z)$ is the Green's function given by Eq. (2), representing the response of the system due to a unit impulse:

$$G(x, z) = \sqrt{\frac{2}{\pi}} \frac{x}{a} \exp \left\{ -\frac{a}{2x} \frac{z^2}{\delta^2} \right\} - \frac{z}{\delta} \operatorname{erfc} \left\{ \sqrt{\frac{a}{2x}} \frac{z^2}{\delta^2} \right\} \quad (2)$$

with $\delta = \sqrt{(2a/v) \cdot (\lambda/\rho C)}$ thermal penetration depth. Thus, the temperature rise is obtained by convolving the thermal response to a discrete heat source at a given position $(x_k, z)$, assuming that the frictional power dissipated at the contact patch is approximated using piecewise-constant steps, $\dot{q}_i$. The dissipated frictional power at the rail surface, $\dot{q}(x, y)|_{z=0}$, was modelled as a semi-ellipsoidal moving heat source:

$$\dot{q}(x, y)|_{z=0} = \epsilon_r \cdot \mu \cdot SRR \cdot v \cdot p_0 \sqrt{1 - \left(\frac{x}{a}\right)^2 - \left(\frac{y}{b}\right)^2} \quad (3)$$

where $y$ represents the transverse coordinate, $b$ is the contact ellipse semi-axis along the transversal direction, $\mu = 0.4$ is friction coefficient,
<figure><img src="image_10.png" /><figcaption>Fig. 9. APT results of a fourth analysed volume within the WEL. (a) shows an APT volume with 6 at.% C iso-composition surfaces. Blue arrows highlight regions of carbon composition fluctuations. Carbon iso-composition surfaces enclose these regions, revealing C-enriched columnar structures. (b) and (c) present 1D composition profiles from the C-enriched and adjacent lower-carbon regions, respectively. To improve visual clarity, these 1D composition profiles were obtained by counting the hits at 24 Da as three carbon atoms, providing an averaged carbon content under the assumption that C₂⁺ and C₄²⁺ contribute equally to the 24 Da peak. Error bars represent ±1 standard deviation.</figcaption></figure>

SRR = |v - v<sub>wheel</sub>|/v is the rolling sliding ratio, p₀ is the maximum con- tact pressure for a Hertzian contact, and ϵ<sub>r</sub> is the amount of frictional heating flowing into the rail given as:

$$ \epsilon_r = \frac{(\sqrt{\lambda\rho C})_{\text{rail}} \cdot \sqrt{v}}{(\sqrt{\lambda\rho C})_{\text{wheel}} \cdot \sqrt{v_{\text{wheel}}} + (\sqrt{\lambda\rho C})_{\text{rail}} \cdot \sqrt{v}} \quad (4) $$

Considering that the maximum heat flux and temperatures occur along the major axis at y = 0 [74], the temperature field and profiles are examined for this case. The Equation Eq. (1) is valid under the hypothesis of negligible heat diffusion along x and y directions, i.e. the heat flux only occurs along depth. This is the case if the ratio of the heat source's speed to the diffusion rate of heat into the solid, L = av/κ,

with κ = λ/ρC thermal diffusivity in m²/s, is greater than 10 [75]. The Hertzian contact problem was solved following Greenwood's approach [76,77] and treated independently from the thermal problem. Calculations were performed using various SRR values. Friction coefficient and thermomechanical properties were assumed constant over the whole range of temperatures. Table 6 lists the boundary conditions used for the calculations.

The in-depth temperature profiles depicted in Fig. 10 indicate that a sliding rolling ratio (SRR) of at least 10% is required to fully austenitize the pearlitic steel to a depth of 15 µm under the studied conditions. Given a contact time of 0.57 ms (Fig. 10), the heating rate ranges from 1.1 ×10⁶ ° C/s at a depth of 25 µm to 1.4 × 10⁶ ° C/s at
<figure><img src="image_11.png" /><figcaption>Fig. 10. (a) Evolution of temperature profiles at rail surface over time for varying SRR values. The temperature profiles are given at the middle plane of the contact patch along the rolling direction. (b) In-depth temperature profiles at the time of the peak temperature. (c) Hydrostatic pressure at the middle plane of the contact patch.</figcaption></figure>

the rail surface. The soaking time at temperatures above $A_{C1}$ ranges from 0.25 ms to 0.45 ms. Studies on ultrafast heat treatment of carbon steels, i.e. heating rates exceeding 100 °C/s and soaking times of 100–200 ms [78,79], provide valuable insights for interpreting the current results and explaining the nucleation and growth mechanism of austenite under the wheel-rail contact scenario. At conventional heating rates, austenite formation is governed by a reconstructive process, where carbon migrates from ferrite while cementite dissolves into the growing austenite grains. Consequently, the carbon concentration in austenite corresponds to the equilibrium composition at the specific $\alpha \rightarrow \gamma$ transformation temperature. Instead, under ultrafast heating conditions, the kinetics of austenite formation is governed by a mixed mechanism which considers that austenite nucleation remains diffusion-based and initiates at the critical temperature $A_{C1}$, while austenite growth proceeds via the combination of diffusion and massive modes [78]. During the massive $\alpha \rightarrow \gamma$ transformation, once the critical temperature $T_{massive}$ is reached, the $\gamma$ phase rapidly grows into the surrounding $\alpha$ phase. Then, the atomic structure is reconfigured due to the interface movement, while carbon atoms diffuse toward the freshly formed austenite crossing the $\alpha/\gamma$ interface. The resulting austenite should display an irregular morphology and does not exhibit any crystallographic orientation relationship with the parent phase. If the interface velocity during the growth of austenite overtakes the rate of long-range diffusion, then the available driving force is entirely used for the interface movement [78]. Consequently, the austenite phase retains the chemical composition of the parent ferrite [80].

The morphology of austenite grains in ASTAR phase map (see Fig. 4(a), (d) and (g)) corroborates the hypothesis of the massive formation mechanism. Nevertheless, the APT analysis consistently revealed the presence of a C-enriched matrix corresponding to austenite, characterised by a uniform carbon distribution, suggesting diffusion took place during austenite formation. Providing an exact prediction of the kinetics of austenite growth lies beyond the scope of this study. However, estimating the characteristic diffusion length of carbon in austenite may help to elucidate the observed homogeneous C distribution. The diffusivity of C in austenite, $D_C$, is expressed by an Arrhenius equation of the form:

$$D_C = D_0 \cdot \exp \left\{ -\frac{Q}{RT} \right\} \qquad (5)$$

where $D_0 = 6.68 \cdot 10^{-5} \text{m}^2/\text{s}$ is the diffusivity coefficient, $Q = 156.73 \text{kJ/mol}$ is the activation energy for C diffusion in austenite (both taken from [81]), $R = 8.314 \cdot 10^{-3} \text{kJ/mol}$ is the gas constant and $T$ is the absolute temperate in kelvin. The diffusion length of C in austenite, $L_C$ was calculated as:

$$L_C = \sqrt{D_C \cdot t} \qquad (6)$$

where $t$ is the diffusion time. Diffusivity values were calculated by considering only the portions of the temperature profiles at various depths where the predicted temperature exceeded $A_{C1}$ (723 °C). The diffusion length of carbon in austenite during the thermal cycle due to a single wheel-rail contact is estimated following the methodology outlined by [36]. The diffusion lengths are computed for each time step of the temperature profile derived from the thermal calculations. These values are subsequently integrated to determine the overall diffusion length at a specific depth. The diffusion length in austenite was found to vary between 84 nm at the rail surface and 8 nm at 14 µm, while at the depth of the APT volumes, i.e. 3 µm, was found to be 70 nm. It is worth mentioning that Eq. (5) may underestimate the carbon diffusion length in austenite, as it does not account for the diffusivity's dependence on carbon content, which could further extend the diffusion range near carbon-enriched regions [81]. The estimated diffusion length offers a plausible explanation for the homogeneous carbon distribution observed in the APT analysis. However, it cannot be concluded whether carbon homogenisation by diffusion occurred during austenite growth or after its formation. Thus, two scenarios arise: (i) austenite of relatively high carbon content forms via a mixed diffusional-massive mechanism during a single wheel-rail heating cycle, or (ii) it may nucleate through a pure massive mechanism, inheriting the carbon content of the parent ferrite. Then subsequent wheel-rail heating cycles and the C content gradient provide a driving force for carbon to diffuse from the neighbouring cementite particles.

### 4.1.2. Chemical driving forces

The formation of WELs occurs through distinct pathways [34,50, 82], involving grain fibration and fragmentation, followed by nanostructuring at the grain scale [50,82], and cementite decomposition at the atomic scale [37]. These processes provide a chemical driving force that assists the non-chemical driving forces in the phase transformation [48]. In the current case, evidence of fibration and fragmentation stages was observed in untransformed regions adjacent to the WEL/BEL islands (Supplementary Material, Figure S2). Given that the rail was installed in 2006 and retired in 2009 (as detailed in Table 2), it is plausible that nanostructuring processes were initiated before forming the WEL, and catalysed its formation. In addition to the thermal driving force needed for austenite nucleation and growth, several factors affect the equilibrium between the parent pearlite and the newly formed austenite. In the context of wheel-rail contact, the accumulation of defects in the crystal lattice over successive contact cycles, along with local changes in chemical composition and hydrostatic pressure [83], may decrease the energy barrier between the parent and new phases. This process can consequently lower the $A_{C1}$ temperature. The presence of spherical nano-cementite, approximately 15–20 nm in diameter, observed in Fig. 6(b), combined with the increased density of grain boundaries at the rail subsurface, see the GBs network
in Fig. 4(c), (f), and (I), may have destabilised the microstructure. From a thermodynamic perspective, the refinement of carbide particles enhances the Gibbs–Thomson effect, reducing the activation energy barrier for austenite nucleation. Additionally, smaller carbide particles (10–20 nm) increase the density of nucleation sites at ferrite/carbide junctions, where the activation energy barriers for austenite nucleation are even lower than at $\alpha/\alpha$ interfaces [84].

As cementite decomposes through the interaction of carbon with dislocations and vacancies introduced by plastic deformations [37], carbon atoms are released into the ferrite matrix and segregate at dislocation sites (Fig. 5). This segregation raises the Gibbs free energy of ferrite, further lowering the energy barrier for austenite nucleation. The APT analysis further revealed that primary cementite with a carbon content below 19 at.% is absent within the WEL. A similar cut-off was observed in eutectoid carbon steel subjected to twin-disc experiments and subsequent annealing at 250 °C [71]. Removing carbon atoms from $Fe_3C$ lattice by interactions with defects shifts cementite away from its ideal stoichiometric composition. Consequently, the Gibbs free energy of cementite deviates from its local energy minimum, making dissolution energetically favourable [71]. In the present wheel–rail contact scenario, deformation-induced cementite decomposition progresses until the Gibbs free energy of cementite and sufficient carbon atom mobility lead to a redistribution of carbon within the ferritic matrix. It can be speculated that in scenarios where the temperature for austenite nucleation is not met due to lower rolling sliding ratios, carbon redistribution through ferrite still occurs by the pipe diffusion mechanism [85], which becomes a feasible mechanism in pearlitic rail steels for temperatures greater than 250 °C.

Additionally, a high density of grain boundaries as observed in Fig. 4(c) enhances the kinetics of austenite formation through two main mechanisms. First, the stored energy at these interfaces provides an additional driving force for transforming ferrite and carbides into austenite [86,87]. Second, grain boundaries serve as rapid diffusion channels, facilitating the redistribution of carbon from decomposing cementite [45] and acting as sites for austenite nucleation.

In addition to the microstructural changes catalysing the formation of the white etching layer, the hydrostatic pressure experienced by the rail decreases the onset temperature for austenite nucleation. The recent work by Al-Juboori [83] demonstrated that high hydrostatic pressure facilitates the phase transformation of rail steel into martensite at temperatures below the critical $A_{C1}$ temperature for pearlite–austenite transformation. Specifically, the authors report that applying 1 GPa of hydrostatic pressure led to martensite formation at temperatures as low as 550 °C during a Gleeble thermo-mechanical test. In the current scenario, a hydrostatic pressure of 1 GPa is predicted along the entire thickness of the transformed layer. Therefore, this hydrostatic pressure may have assisted the transformation process, allowing it to occur at a lower temperature than would typically be required. However, uncertainties relative to the assessment of local temperature in Gleeble tests – due to uneven heating conditions, increased resistivity due to dislocation density and contact resistance between the sample and the anvils – require a cautious interpretation of the reported transformation temperatures. Moreover, the literature [88, 89] and thermodynamic calculations from the same study [83] suggest that hydrostatic pressure lowers the transformation temperature by 25 °C/GPa.

## 4.2. Factors influencing retained austenite stability

ASTAR phase maps and APT compositional analysis consistently identified retained austenite coexisting with cementite particles and ferritic structures. Several factors may contribute to the stability of austenite at room temperature: (i) chemical stabilisation due to carbon enrichment of ferrite. As previously mentioned, the decomposition of cementite and the subsequent release of carbon within the ferritic matrix during the nanostructuring process enhances the stability of

<table><caption>**Table 6**
Reference values for the estimation of contact temperature.</caption><tr><td>Normal load</td><td>9 (t)</td></tr><tr><td>Vehicle speed</td><td>80 (km/h)</td></tr><tr><td>SRR</td><td>2 – 5 – 10 (%)</td></tr><tr><td>E<sub>wheel/rail</sub></td><td>210 (GPa)</td></tr><tr><td>v<sub>wheel/rail</sub></td><td>0.3</td></tr><tr><td>α<sub>wheel/rail</sub></td><td>1.42E-5 (m<sup>2</sup>/s)</td></tr><tr><td>friction coefficient</td><td>0.4</td></tr><tr><td>Wheel diameter</td><td>890 (mm)</td></tr><tr><td>Rail crown radius</td><td>300 (mm)</td></tr><tr><td colspan="2"><b>computed</b></td></tr><tr><td>P<sub>MAX</sub></td><td>1.2 (GPa)</td></tr><tr><td>semi-axes of the contact ellipse</td><td></td></tr><tr><td>in rolling direction:</td><td>6.7 (mm)</td></tr><tr><td>in transversal direction:</td><td>5.3 (mm)</td></tr></table>

austenite compared to ferrite. (ii) nanostructuring promotes thermal and mechanical stability. Reduced grain size promotes carbon partitioning during the austenite formation stage, as the higher density of phase boundaries promotes this process. The high carbon content in the newly formed austenite raises the strain energy required for the martensitic transformation [90–92]. Furthermore, reducing grain size increases the energy barrier for the plastic deformation needed for martensitic transformation, as predicted by the Hall–Petch effect. This further heightens the driving force required to convert austenite into martensite [93]. On the contrary, reduced grain size can also provide grain-boundary nucleation sites for the $\gamma \rightarrow \alpha'$ transformation, thus increasing the temperature for athermal phase transformation via quenching, $M_s$. The exact balance between these effects cannot be determined solely based on the available data. A significant drop in the $M_s$ temperature can hinder the athermal $\gamma \rightarrow \alpha'$ transformation. Additionally, subsequent heating cycles would be necessary for the precipitation of secondary carbides. (iii) An additional factor determining austenite stability is the strain partitioning resulting from the variability of microconstituents within the WEL and BEL. Ferrite grains can mitigate strain localisation, thus improving the mechanical stability of retained austenite [79].

## 4.3. Formation mechanism of WEL

In continuity with the formation mechanism of WELs proposed by Thiercelin et al. [49,50], a thermal scenario aided by the chemical driving forces introduced by the cumulative effect of deformations induced by rail wheel contact is outlined in Fig. 11. In the early stages of the TST the initial pearlitic microstructure, Fig. 11(a)–(b), undergoes fibration and fragmentation. At this stage, it is assumed that plastic deformations primarily control the evolution of the microstructure. At the scale of grains, a grain size reduction and an increase in the aspect ratio of grains is observed, Fig. 11(b) – [82]. At the sub-grain scale, cementite fragmentation, morphological reorientation, bending and interlamellar space reduction are observed at the rail subsurface (see Supplementary material, Figs. S2 and S3). Since the early stages of fibration and fragmentation, grain boundaries may evolve from dense dislocation walls, as supported by studies on cold rolled pearlite [94], Fig. 11 (b’). The pearlitic microstructure evolves toward a nanostructured state. Grain size is further reduced and grain disorientation increased [82], Fig. 11(c). At the sub-grain scale, the cementite is further fragmented and its decomposition progresses through interaction with defects formed in the microstructure. Phenomena of carbon migration, such as pipe diffusion, may be favoured by thermal effects. The nanostructuring process makes the ferrite–cementite microstructure more thermodynamically unstable than austenite. Chemical driving forces and hydrostatic pressure lower the energy barrier for austenite nucleation, i.e. the $A_{C1}$ temperature is lowered. From a wheel–rail contact perspective, a lower SRR than that expected by thermal calculations is suitable for austenite nucleation, Fig. 11 (c’). Once the energy barrier for austenite growth
<figure><img src="image_12.png" /><figcaption>Fig. 11. Schematic illustration depicting the progressive TST of the original pearlitic microstructure.</figcaption></figure>

is exceeded by the combination of chemical and non-chemical driving forces, the tribological transformation leads to the formation of martensite either by athermal, Fig. 11(d)-(d'). Further heating cycles may be needed to precipitate nano-carbides in C-saturated ferrite [95] and martensite.

## 5. Conclusion

This study examines the formation mechanisms and driving forces behind white and brown etching layers at the nanometric scale, using a combination of SEM, ASTAR and APT. The characterisation of the microstructural gradient in the transformed layer through ASTAR and APT has revealed the relationship between thermal effects and the gradual process of nanostructuring in the subsurface of the rail. The APT results underscore the importance of performing multiple analyses in each region to fully capture the heterogeneity of such a complex nanostructure.

The key findings of the current study include:

1. The white and brown etching layers observed in a R260 rail steel belonging to a straight track affected by squat defects feature nanograins of ferrite, martensite, retained austenite, partially decomposed cementite, and secondary carbides.

2. The presence of lamellar cementite remnants within the BEL and spherical cementite indicates that the tribological transformation, while a thermal force drives it, takes place according to the local equilibrium conditions; the white etching layer can be regarded as fully formed even before the cementite is entirely dissolved.

3. Cementite decomposition and carbon redistribution occur during the life cycle of the rail. These phenomena constitute a chemical driving force assisting the thermal effect induced during wheel slip events on the rail.

### CRediT authorship contribution statement

**Matteo Russo:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation,

Conceptualization. **Aurélien Saulot:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Xavier Sauvage:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Muriel Véron:** Writing – review & editing, Writing – original draft, Visualization, Validation, Resources, Methodology, Investigation, Formal analysis, Data curation. **Edgar Rauch:** Writing – review & editing, Writing – original draft, Visualization, Validation, Investigation, Formal analysis, Data curation, Conceptualization. **Léo Thiercelin:** Writing – review & editing, Writing – original draft, Visualization, Validation, Resources, Methodology, Investigation, Data curation, Conceptualization. **Frédéric Lebon:** Writing – review & editing, Writing – original draft, Visualization, Validation, Investigation, Formal analysis, Data curation, Conceptualization. **Patrice Chantrenne:** Writing – original draft, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

### Declaration of Generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors used ChatGPT from OpenAI to improve English readability and language clarity. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Aurelien Saulot reports financial support was provided by Carnot Institutes Network. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
## Acknowledgements

FIB experiments were supported by the French RENATECH network, the CPER Hauts de France project IMITECH and the Métropole Européenne de Lille.

This study was performed within the OPTIMRAIL project, funded by Carnot Ingénierie@Lyon institute.

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.matchar.2025.115477.

## Data availability

Data will be made available on request.

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