Distribution of hydrogen atoms at metallurgical microphases of X52 pipeline steel studied by scanning Kelvin probe force microscopy and finite element modelling

The work combined scanning Kelvin probe force microscopy measurements and finite element modelling to study the diffusion and distribution of hydrogen (H) atoms at metallurgical microphases contained in X52 pipeline steel. Results show that the pearlite contained in the steel is more stable than the ferrite during electropolishing, as indicated by the measured topographic profiles and Volta potentials. The hydrogen (H)-charging enhances the electrochemical activity of both pearlite and ferrite, as shown by increased Volta potential and thus the decreased work function. As the H-charging time increases, the Volta potentials of both phases further increase, implying that their activities increase with the H-charging time. The pearlite has a greater Volta potential and thus a lower work function than the ferrite. This is associated with more H atoms accumulating at the pearlite than at the ferrite. The H atom diffusion and accumulation are affected by H diffusivity at phase boundaries, H-trap binding energy and the number of traps in the steel.


Introduction
Hydrogen, as a "green" and "zero-emission" energy carrier, has been regarded as an ideal alternative to fossil fuels to combat climate change [1,2].Hydrogen transportation from production sites to end users is integral to the entire value chain of hydrogen economy.It is generally accepted that the most effective and economical means of transporting large amount of hydrogen over great distances is to use the existing natural gas pipelines by blending with various ratios of hydrogen [3].The compatibility of pipeline steels in high-pressure gaseous hydrogen environments has received substantial attention as hydrogen embrittlement (HE) may occur to compromise the pipeline integrity [4].
Different from the mechanism for hydrogen (H) atom generation in aqueous solutions, it is thermodynamically impossible for gaseous hydrogen molecules to spontaneously generate H atoms under pipeline operating conditions [5].However, H atoms can generate and adsorb on the steel surface in hydrogen gas environments through a dissociative adsorption mechanism [5].This preferentially occurs at emergences of dislocations and high-angle grain boundaries on the steel surface [5,6].Once entering the steels, the H atoms tend to accumulate at metallurgical features such as grain boundaries, phase boundaries and dislocations, i.e., the so-called H traps.Under an interaction between mechanical stress and H atoms that exceed a threshold concentration, hydrogen-induced cracking (HIC) can occur based on specific mechanisms developed for different H-stress-metallurgy combinations, such as hydrogen-enhanced decohesion (HEDE) and hydrogen-enhanced local plasticity (HELP) [7][8][9][10].Investigations of the H atom distribution in steels is critical to assess the HE susceptibility and locate the potential sites to initiate cracks under given conditions.
The scanning Kelvin probe force microscopy (SKPFM) has been used to "visualize" the H atom distribution at various micro-and nanoscale features contained in metals with an extremely high resolution based on measurements and mapping of Volta potential of the H-containing metals [11][12][13][14].The measured Volta potential represents the contact potential difference (CPD) between the Kelvin probe and the target metal, while the CPD is related to work function of the metal [15,16].In previously reported work [17][18][19], the relationship between the H atom concentration and work function of the test metal was established, where the work function decreased upon H atom entry, and further decreased with increasing H atom concentration.Moreover, the SKPFM can be used to determine the H atom concentration in duplex-phased metals [20], where ferrite was associated with H atom enrichment as compared with austenite.
Although experimental methods such as SKPFM can measure and determine the H atom distribution at specific sites in steels, numerical modeling such as finite element (FE) analysis can provide quantitative information about the H atom diffusion in metals.Moreover, the modeling results can help analyze the mechanism of the interaction between H atoms and metallurgical features.For example, a FE polycrystalline model was developed to study the trapping behavior of H atoms at grain boundaries [21].It was found that the H atom diffusion and trapping was remarkably affected by various types of metallurgical features.A complete numerical model describing the H atom distribution in steels can also define the microstructural parameters such as the lattice H atom diffusivity, grain boundary diffusivity and the grain boundary thickness [22].The novelty of this work is to determine the H atom diffusion and distribution at metallurgical microphases contained in a pipeline steel both quantitatively and mechanistically, explaining the H-steel interactions at a microscopic scale.
The work combined the SKPFM measurements and FE modeling to study the H atom diffusion and distribution in an X52 pipeline steel containing ferrite and pearlite.The H atoms were introduced in the steel electrochemically with various H-charging times.The SKPFM was used to measure both topographic profiles and Volta potentials of each microphase, and the FE model defined the effect of microstructural parameters on H atom diffusion and distribution in the steel.It is expected that the combined electrochemical and numerical methods can provide more mechanistic insight into the H-steel interaction.

Material and samples
The material used in this work was an X52 pipeline steel, with a chemical composition (wt.%):C 0.24, Mn 1.4, Si 0.45, P 0.025, S 0.015, V 0.01, Nb 0.05, Ti 0.04 and Fe balance.Test samples were machined into 10 mm × 10 mm × 3 mm dimension and sealed in epoxy, leaving a working face ground by SiC papers up to 1,200 grit.To obtain the metallographic view, the working face of the sample was electropolished in a solution containing HClO 4 , glycerol and ethonal with a ratio of 1.0: 0.5: 8.5 at 30 V for 10 s.It is noted that the electropolishing time was chosen based on published work [23,24] that the microphase ferrite contained in the steel was not completely dissolved.

Electrochemical H-charging
The H-charging was conducted on the steel sample, which served as the working electrode (WE), in an electrolyte which was prepared by dissolving 600 g of borax (sodium tetraborate decahydrate) in 1 L glycerin and diluting with 20% distilled water.The H-charging was conducted under a constant cathodic current density of 2 mA/cm 2 for 0.5, 1, 2, 4 h using a Gamry Reference 400 system.A saturated calomel electrode (SCE) was used as reference electrode (RE) and a platinum wire as the counter electrode (CE).

The SKPFM measurements
After H-charging, the steel sample was washed by ethanol and wiped with ethanal to avoid contamination.The SKPFM measurements were performed on the H-charged sample using an Asylum Research atomic force microscope (AFM, MFP-3D Origin, Oxford Instruments) in air.The Kelvin probe was a NanoWorld ™ SCM-PIT conductive Pt/Ir-coated silicon tip with a resonant frequency of 60-90 kHz.The Volta potential was measured on the sample over an area of 10 μm × 10 μm with a scanning rate of 0.5 Hz at a resolution of 512 × 512 pixels.
A two-pass mode was used during SKPFM measurements.In the first pass, the topographic image of the sample was measured.In the second pass, a cantilever was lifted to a height of 50 nm above the sample surface, while an alternating current bias of 3 V was applied on the probe tip to measure the Volta potential, as described previously [25].The distance between the probe tip and the steel surface will affect the measured work function.Generally, the Volta potential measured by SKPFM will not change if the distance is maintained between 100 nm and a few microns within a so-called constant potential region [26,27].Exceeding the distance, the Volta potential decreases with the increasing distance from the sample surface.In this work, the distance between the probe tip and the steel sample surface was maintained constant at 1 micron when measuring the Volta potential.The original height difference between the two phases did not affect the results.
The topographic image of the steel sample was processed with software supplied with the equipment to remove tilts.In this work, the raw Volta potential data were present without further flattening and inversion.It is noted that, in most published works, the Volta potential signals were inverted to obtain expected polarity [28,29].Since different models of AFM have specific calibration methods, a date-inversion processing of the measured Volta potentials was not performed in this work.As stated, the measured Volta potential signals refer to the potential difference between the tip of the Kelvin probe and the steel sample.During SKPFM measurements, several Knoop indentations were used to locate the probe tip, ensuring that the mapping area was kept unchanged, as shown in Fig. 1.

Computational modeling
The H atom diffusion and distribution in the steel was modeled by FE analysis using a commercial software package COMSOL MultiPhysics 5.6.The topographic image of the steel sample was obtained by SKPFM measurements, as shown in Fig. 2a.Generally, the microstructure of X52 steel mainly contains ferrite (F) and pearlite (P) [30].The ferrite dissolves faster than perlite during electropolishing [25].As a result, the ferrite is deeper and the pearlite is higher in the topographic profile in Fig. 2a, where the darker areas represent ferrite, and the lighter areas represent pearlite, as labelled.Figure 2b shows the metallographic view of the steel after binarization processing to enhance visual difference between the two phases, where the black areas are ferrite, and the white areas are pearlite.Image binarization, also known as image thresholding, is a method of converting any multi-tone image (or grey-scale image) into black-white image (i.e., two tone image).To perform binarization process, the threshold value of gray scale is found to check whether a pixel has a particular gray value through complex algorithms.The main goal of the image binarization is the segmentation of a document into foreground text and background [31].To avoid the effect of other minor microstructures to make the modeling not to converge, further simplification and smoothing were performed to obtain the final model showing the microstructure of the steel in this work, as shown in Fig. 2c, where the blue areas are pearlite, the gray areas are ferrite, and the curves between them refer to phase boundaries.
In carbon steels such as X52 pipeline steel, there are various types of metallurgical features that can serve as H atom traps.In this work, dislocations and the phase boundaries between ferrite and pearlite were modeled as the main traps contained in the steel considering their dominant presence compared with other traps.The H In the presence of the effect of trapping sites on H atom diffusion, the mass transport equation from traditional Fick's law should be modified by [32]: where C L is molar concentration (mol/mm 3 ) of H atoms in lattice sites, C T is molar concentration (mol/mm 3 ) of H atoms in trapping sites, and J L is H atom flux in the lattice, which can be calculated by [22]: where D L is diffusion coefficient of H atoms in the lattice.
According to Oriani and Josephic's equation [33], the equilibrium relationship between C L and C T can be expressed as: where N T is density of trap sites, N L is number of Fe atoms per unit lattice unit volume, E b is H-trap binding energy, R is universal gas constant, and T is absolute temperature.
The number of lattice sites was reported as 5.09 × 10 29 sites/m 3 assuming tetrahedral voids as the sites to host H atoms in Fe lattice [34].The trap density N T was found in a range from 10 20 to 10 27 sites/m 3 in body-centered cubic (BCC) iron due to dislocations, and in the range from 10 25 to 10 27 sites/m 3 for grain boundaries [35][36][37].The binding energy for the traps in steels are from 20 to 70 kJ/ mol [22].The effect of the H-trap binding energies E b , relative number of trapping sites over lattice sites, N T /N L , (1) and the H atom diffusion coefficients in phase boundaries on H atom distribution were modeled in the work.
Figure 3 shows the boundary conditions and meshes used in FE modeling.Table 1 shows the input parameters used for modeling of H atom diffusion in the steel.It was assumed that the initial H atom concentration was 0 prior to H-charging.Upon H-charging, there was a constant concentration of H atoms (C in ) on the sub-surface of the steel, whereas desorption was modeled on the upper surface with a concentration of 0. Other surfaces did not have H atom flux.The phase boundaries were assumed as diffusion barriers with a thickness of 100 nm.The H atom diffusion coefficient at phase boundaries, D PB , was related to D L [22].The domain of the modeling area of 39.85 μm 2 was meshed with 271,229 elements.

Microstructure, topography and Volta potential of X52 steel
The optical views of metallographic microstructure of X52 pipeline steel under different magnifications are shown in Fig. 4. It is seen that the steel contains pearlite (P) and ferrite (F), as labelled.
Figure 5 shows the topographic profile and Volta potential map of the steel sample.It is seen that the heights of ferrite and pearlite are different.The light area represents the pearlite, which is higher in the topographic view.The dark area refers to the ferrite, which is lower in height topographically (Fig. 5a).The Volta potentials of the two phases are also different.As seen in the scale bar in Fig. 5b, the light area, i.e., ferrite, is associated with greater Volta potentials, while the dark area (pearlite) has the smaller Volta potential.
The linear scanning results of both topographic height and Volta potential along the white dotted line marked in    a more rapid dissolution during electropolishing than the pearlite [41].Overall, the Volta potential of ferrite is greater than the Volta potential of pearlite.The average Volta potential values of ferrite and pearlite over the marked line are 318.51mV (Kelvin probe, kp) and 315.19 mV (kp), respectively.As stated above, the measured Volta potential is the contact potential difference (V CPD ) between the Kevin probe tip and the steel sample: where φ Tip and φ Steel are work functions of the probe tip and the steel, respectively, and e is electron charge.The work function refers to activation energy during removal of an electron from the sample surface to a position that is far enough [42].The lower the work function, the more active the electron.According to Eq. ( 4), a smaller work (4) eV CPD = φ Tip − φ Steel function of the steel generates a greater Volta potential, V CPD .As the Volta potential of ferrite is greater than that of pearlite, the ferrite has a smaller work function than the ferrite.As the work function of a metal indicates its thermodynamic stability in service environments [43], the pearlite is more stable, and the ferrite is more active in the electropolishing electrolyte.

Volta potential of the steel upon H-charging
The topographic profiles of the steel sample before and after H-charging with various charging times are shown in Fig. 7.It is seen that the relative heights of the steel sample before and after H-charging do not change apparently.The Volta potential measurements are conducted in the same area, and the measurement results before and after H-charging of various charging times are shown in Fig. 8. Generally, as the H-charging time increases, the

h, (c) 1 h, (d) 2 h, (e) 4 h
The Volta potentials of ferrite and pearlite as a function of the H-charging time are derived from the linear scanning results along the white dotted lines as marked in Fig. 8, and the results are shown in Fig. 9.The average Volta potentials of perlite and ferrite phases with various H-charging times are listed in Table 2.The results show that the Volta potentials of both pearlite and ferrite increase with the increased H-charging time.The difference in Volta potentials between the two phases also increases with the charging time.An interesting finding is that, in the absence of H-charging, the average Volta potential of ferrite is greater than that of pearlite, as measured in Fig. 6.After a short time of H-charging such as 0.5 h, the relative values of the Volta potentials of both phases do not change.However, as the H-charging time increases, the Volta potential of pearlite becomes greater than that of ferrite, indicating a smaller work function of the pearlite than the ferrite upon a certain time of H-charging.The results imply that an extended H-charging time, i.e., an increased amount of H atoms in the steel, the pearlite becomes more active than the ferrite.

Effect of metallurgical phases on H atom diffusion
To model the diffusion of H atoms in the steel lattice, an initial H atom concentration of 0.04 mol/m 3 is applied.The relative number of trapping sites over lattice sites, i.e., N T /N L , is assumed as 10 -6 .The relative H atom diffusion coefficient at phase boundaries over lattice sites, i.e., D PB /D L , is assumed as 1.Since the diffusion path is extremely short (i.e., only a few microns), the H atom diffusion can easily reach a steady state.Thus, in the modeling process, the diffusion time is set as 1 s. Figure 10 shows the distribution of H atom concentration in the steel lattice as a function of time.Initially, there is no H atom in the steel (Fig. 10a).As the diffusion time increases, the H atom concentration increases.Particularly, the H atom concentration in pearlite is greater than the H atom concentration in ferrite at specific times before a steady state is reached.After a saturation state is achieved, the H atom distribution in both phases is uniform (Fig. 10d).Figure 11 shows the evolution of H atom concentrations in the lattice sites of pearlite and ferrite as a function of time.In this work, the H diffusion model was developed based on the method proposed by Sofronis and McMeeking [46].It is assumed that traps are isolated and do not form an extended network.H diffusion between the trap sites Fig. 9 Volta potentials of ferrite and pearlite as a function of the H-charging time derived from the linear scanning results along the white dashed lines as marked in Fig. 8 (a) H-free, (b) 0.5 h, (c) 1 h, (d) 2 h, (3) 4 h Table 2 Average Volta potentials of ferrite and pearlite without and with H-charging by various times along the white dashed lines as marked in Fig. 8   H is by lattice diffusion [47].The tetrahedral voids as the main sites to host H atoms in Fe lattice [5,34].However, finite element models cannot represent the sites due to limitation of the spatial scale.

Effect of microstructural parameters on H atom diffusion in the steel
Due to the wide ranges of the density of hydrogen traps contained in the steel and the H-binding energy at the traps, the H atom accumulating effect is considered.At the equilibrium state, the H accumulating factor, S, is defined as [48]: Figures 12 and 13 show the relationship between the H accumulating factor and the H-trap binding energy and that between the H accumulating factor and the relative trap site density, respectively.It is seen that the logarithm of the H accumulating factor is linearly related to both the H-trap binding energy and the relative trap site density.As the H binding energy and the trap site density increase, the H accumulating factor increases.It is noted that the considered traps are mainly dislocations and phase boundaries in this work.Thus, the derived relationships apply for the two types of H traps contained in X52 steel.Similar relationships can be derived by FE modeling for other grades of steels.Figure 14 shows the time dependence of the H atom concentration in the lattice site with various H atom diffusion coefficients at phase boundaries, D PB /D L .It is seen that, when D PB /D L is kept constant, the H atom concentration in pearlite is always greater than that in ferrite before the steady state is achieved.At the D PB /D L of 0.01, the H atom concentration in pearlite reaches 0.04 mol/ m 3 by 0.65 s; and when the D PB /D L ratios are 1 and 100, the times are 0.27 s and 0.26 s, respectively.Similarly, the times for the H atom concentration in ferrite to reach the steady-state value are 0.67 s, 0.27 s and 0.26 s, respectively.The change of D PB /D L does not change the maximum concentration of H atoms in both pearlite and ferrite lattice sites.

Discussion
This work demonstrates that, in X52 pipeline steel, the pearlite is more stable than the ferrite during the electropolishing process, as indicated by the topographic and Volta potential measurements.Upon electropolishing, the pearlite dissolves less and has a greater height than ferrite (Figs. 5 and 6).Moreover, the pearlite has the smaller Volta potential and thus the greater work function than the ferrite.Generally, a great work function indicates a high stability of valence electrons and thus a low electrochemical activity in aqueous solutions [49].The different dissolution activities of the two phases are attributed to their compositions.The pearlite is an aggregate of ferrite and cementite [50], where a high content of cementite is associated with a great work function [51].
It is also confirmed that H-charging can enhance the electrochemical activity of both pearlite and ferrite contained in the steel, as indicated by the increased Volta potential (Fig. 9 and Table 2) and thus a decreased work function.As the H-charging time increases, it is expected that more H atoms will be introduced in the steel.The Volta potentials of both pearlite and ferrite further increase, indicating that their work functions decrease and thus the increased electrochemical activity.The results are consistent with published works that the work function of metals was related to the amount of H atoms adsorbed, and a higher H atom concentration caused a smaller work function [52].As the pearlite has a greater Volta potential and thus a lower work function than the ferrite (Fig. 9), more H atoms are expected to accumulate at pearlite.The measurement result is well consistent with the modeling results of the H atom distribution in pearlite and ferrite, as seen in Fig. 10.Before a saturation state is achieved, the pearlite contains more H atoms than the ferrite.This work further investigates the effect of microstructural parameters of the steel on H atom diffusion by FE modeling.When the H atom diffusivity at phase boundaries is extremely small (i.e., the D PB /D L ratio is Fig. 11 Evolution of H atom concentrations in the lattice sites of pearlite and ferrite as a function of time much smaller than 1), the phase boundaries will hinder the diffusion of H atoms so that the process for H atom concentration to reach a steady state is delayed.When the D PB /D L is much larger than 1, the phase boundaries can promote the H atom diffusion, making the H atom concentration reach the steady value rapidly.More important, the H atom diffusivity at phase boundaries does not affect the distribution of H atoms in the two phases.With a given D PB /D L , the H atom concentration in pearlite is always greater than that of ferrite.Furthermore, the H-trap binding energy and relative number of trapping sites are directly related to the H atom concentration at the traps.When the binding energy is high enough and there are sufficient trap sites, a large amount of H atoms will be accumulated in the traps so that the local H atom concentration can exceed a threshold value, causing crack initiation under given stressing conditions.Fig. 12 Relationship between the H accumulating factor and the H-trap binding energy Fig. 13 between the H accumulating factor and the relative trap site density Furthermore, for diffusion of species in solids, the time required to reach a steady state depends on the square of the length scale over which diffusion must take place [53].The H diffusion lengths are different in experimental testing and numerical modeling.In the modeling, the diffusion length is tens of microns, while the length scale in the tests is several centimeters.As a result, the diffusion time to reach the steady state is much different, and the diffusion time in modeling is much shorter than the time in the tests.

Conclusions
A combination of SKPFM and FE modeling enables measurements of H atom distribution in microphases in steel and analysis of the H atom diffusion that is affected by different metallurgical parameters.In X52 pipeline steel, the pearlite is more stable than the ferrite, as indicated by the topographic and Volta potential measurements by SKPFM.Upon electropolishing, the pearlite dissolves less and has a greater height, a smaller Volta potential and thus a greater work function than the ferrite.All of them indicate an electrochemical stability of the pearlite than the ferrite.
The H-charging can enhance the electrochemical activity of both pearlite and ferrite contained in the steel, as indicated by the increased Volta potential and thus the decreased work function.As the H-charging time increases, the Volta potentials of both phases further increase, indicating that their work functions decrease and thus the increased electrochemical activity.The pearlite has a greater Volta potential and thus a lower work function than the ferrite.It is expected that more H atoms accumulate at pearlite, as confirmed by the modeling results.
When the H atom diffusivity at phase boundaries is small, the phase boundaries will hinder the diffusion of H atoms so that the process for H atom concentration to reach a steady state is delayed.When the H diffusivity at phase boundaries is large, the phase boundaries can promote the H atom diffusion.Furthermore, a high H-trap binding energy and more trap sites contained in the steel favor the H atom accumulation at the traps.

Fig. 1
Fig. 1 Schematic diagram illustrating the SKPFM measurements conducted in a defined area on the sample surface

Fig. 2 a
Fig. 2 a Topographic profile of the steel sample obtained by SKPFM measurements, b A view of the steel after binarization processing to enhance the visualization quality, c The developed geometrical model of the steel microstructure in this work

Fig. 3
Fig. 3 The boundary conditions (a) and meshes (b) used in FE modeling in this work

HFig. 4
Fig. 4 Optical views of metallographic microstructure of X52 pipeline steel under different magnifications

Fig. 10
Fig. 10 Distributions of H atom concentration in the steel lattice as a function of time (a) 0, (b) 0.03 s, (c) 0.06 s, (d) 0.1 s

Fig. 14
Fig. 14 Time dependence of the H atom concentration in the lattice site with various H atom diffusion coefficients at phase boundaries, D PB /D L

Table 1
Input parameters used for FE modeling of H atom diffusion in the steel