# Segregation at prior austenite grain boundaries: the competition between
boron and hydrogen

Guillaume Hachet<EMAIL_ADDRESS>Ali Tehranchi  Hao Shi  Manoj Prabhakar
Shaolou Wei  Katja Angenendt  Stefan Zaefferer  Baptiste Gault  Binhan Sun
Dirk Ponge<EMAIL_ADDRESS>Dierk Raabe  Department of Microstructure Physics
and Alloys Design, Max-Planck-Institut für Nachhaltige Materialien, 40237,
Düsseldorf, Germany  Key Laboratory of Pressure Systems and Safety, Ministry
of Education, School of Mechanical and Power Engineering, East China
University of Science and Technology, Shanghai, China  Department of
Materials, Royal School of Mines, Imperial College London, Prince Consort
Road, London SW7 2BP, UK

###### Abstract

The interaction between boron and hydrogen at grain boundaries has been
investigated experimentally and numerically in boron-doped and boron-free
martensitic steels using thermal desorption spectrometry (TDS) and ab initio
calculations. The calculations show that boron, which mostly segregates into
prior austenite grain boundaries (PAGBs), repels hydrogen. This behavior has
also been observed using TDS measurements, with the disappearance of one peak
when boron is incorporated into the microstructure. Additionally, the
microstructure of both boron-doped and boron-free steels has been studied
through electron backscattered diffraction, electron channeling contrast
imaging, synchrotron X-ray measurements, and atom probe tomography. While both
steels have a similar grain size, grain boundary distribution, and dislocation
densities, pronounced boron segregation into PAGBs is observed for boron-doped
steels. Therefore, the equilibrium hydrogen concentration in different
trapping sites has been evaluated using the Langmuir-McLean approximation.
This thermodynamic model shows that the distribution of hydrogen is identical
for all traps when the total hydrogen concentration is low for boron-free
steel. However, when it increases, traps of the lowest segregation energies
(mostly PAGBs) are firstly saturated, which promotes failure initiation at
this defect type. This finding partially explains why PAGBs are the weakest
microstructure feature when martensitic steels are exposed to hydrogen-
containing environments.

###### keywords:

Hydrogen , Boron , Martensitic steel , Segregation , Grain boundaries

##  1 Introduction

Hydrogen is a promising carrier molecule for a low-carbon economy and many
corresponding industrial projects are under development to use it as an energy
carrier or to develop sustainable processes like the direct reduction of iron
ore [1, 2, 3, 4]. It is also known that hydrogen easily diffuses in metals and
alloys inducing premature failure of engineering structures, a phenomenon
referred to as hydrogen embrittlement (HE). HE is well-known and has been
described by numerous models in the literature and thoroughly reviewed in
refs. [5, 6]. However, these models provide only a phenomenological
description of HE (e.g.: hydrogen enhancing the formation of vacancies [7, 8,
9], localizing plasticity [10, 11, 12], reducing the cohesive interface energy
of the system [13, 14] and so on) because the direct observation of hydrogen
at the atomic scale is quite challenging given the difficulty to locate
hydrogen in alloys experimentally [15, 16, 17].

Steel is one of the candidate materials envisaged to contain and transport
hydrogen due to its high mechanical strength, low price, flexibility to form
different microstructures from its chemical composition, and the variety of
processes that can be applied to the alloys [18]. However, it is also subject
to HE [19]. Different processes have been developed to reduce HE of steels
[20, 21], including reducing the grain size [22], which is efficient up to a
limit, and also modifies other properties of the alloy, potentially to a point
of being unsuitable for the envisaged application. Steel composition features
have also been modified, for instance, to form precipitates and reduce the
negative impact of hydrogen [23, 24]. However, once the traps inherent to the
precipitates, including interfaces with the matrix or sites inside the
precipitates, are saturated with hydrogen, they become inefficient for further
HE mitigation specifically in typical engineering loading scenarios, which are
often characterized by permanent hydrogen exposure. More recently, the
implementation of chemically heterogeneous Mn profiles in the austenite phase
of medium Mn-steels has also been proposed, improving the ductility of the
alloys in hydrogen [25]. However, such treatment is only possible for a
relatively narrow range of Mn-steel compositions. Finally, another recently
proposed solution to mitigate HE in martensitic steels is the segregation of
interstitial solutes to structural defects, being the weakest microstructure
features in hydrogen environments [26]. In the case of martensitic steels,
these weakest features are prior austenite grain boundaries (PAGBs) [27, 26].
By favoring the segregation of carbon into these defects using special heat
treatments, the negative impact of hydrogen is attenuated [26]. Thus, this
work is focused on the effect of boron localized at this structural defect and
its impact on the segregation of hydrogen.

Boron is an alloying element often incorporated in steel because it improves
the hardenability and delays the formation of ferrite [28]. It enhances the
properties of the alloy by segregating into PAGBs of the iron alloy. However,
the segregation mechanism of boron remained elusive until recently, when it
was described using equilibrium segregation and considering the precipitation
of borides or boro-carbides at GBs [29, 30]. It has also been observed
recently that boron can improve the resistance to HE of steels [31], which is
also observed in other alloy systems [32, 33]. One explanation theorized from
ab initio calculations on $\Sigma 5(310)$ GB is that boron improves grain
boundary cohesion by a strong hybridization between the Fe $s,d$-states and
the B $s,p$-states. In contrast, the hydrogen atom exhibits an ion-like
character in metals [34, 35].

While the localization and the quantification of hydrogen in metals and alloys
remain experimentally challenging, different methods have been developed to
detect this element in materials [36]. One of them is thermal desorption
spectroscopy (TDS), which allows to quantify the amount of hydrogen located in
the microstructure and estimates the trapping energy between hydrogen and
different types of crystalline defects [37, 38, 39, 40, 41, 42, 4]. These
defects acting as traps for hydrogen are usually identified from the TDS
spectra either with complementary experiments [4], simulations [43], or by
optimizing the microstructure to favor the formation of certain types of traps
[38, 44]. However, discrepancies in binding/interaction energies between
hydrogen and crystalline defects have been reported in the literature for
martensitic steels [39] or even $\alpha$-iron [45] depending on the method
used. For instance, the interaction energy of hydrogen in a single vacancy has
been estimated from diffusion analysis around -0.55 eV [46] while ab initio
calculations estimated this energy between -0.30 eV and -0.25 eV [47]). Such
energy difference makes it difficult to conclude if this crystalline defect in
$\alpha$-iron acts as a reversible or an irreversible trap for hydrogen, which
is also observed for grain boundaries in martensitic steels [39].

The present work focuses on the segregation of hydrogen in boron-doped steel
and boron-free steel, respectively. After a careful investigation of the
microstructure of both steels, they have been analyzed through TDS
measurements. Then, ab initio calculations have been performed to understand
the interaction between boron and hydrogen at grain boundaries. Finally, the
equilibrium concentration of hydrogen has been evaluated from TDS measurements
using the Langmuir-McLean approximation to determine the hydrogen partitioning
in the microstructure when the two steels are hydrogen-charged.

##  2 Microstructure characterization

###  2.1 Experimental details

We used two alloys named LC and B-LC steels in this work and their chemical
compositions are Fe-C0.15-B0.0005-Mn1.50-Si0.37 (wt%) and
Fe-C0.146-B0.0025-Mn1.46-Si0.40 (%wt.), respectively [48]. All steels have
been homogenized at an austenitization temperature of 1373 K for 30 seconds
and then quenched using helium gas in a Bähr DIL805 dilatometer with a cooling
rate of 200 K.s-1. The microstructures of LC and B-LC have been characterized
through electron backscatter diffraction (EBSD), synchrotron X-ray
experiments, and correlative transmission Kikuchi diffraction (TKD)-atom probe
tomography (APT) to quantify all differences between the microstructure of the
two steels.

The EBSD maps have been acquired using a high-resolution field emission GEMINI
SEM 450 (Carl Zeiss Microscopy) equipped with a Hikari XP (Ametek/EDAX, USA)
EBSD detector. An acceleration voltage of 15 kV, probe current of 2 nA, and
step size of 0.1 $\mu$m have been chosen for all mappings. The post-processing
of all images has been carried out using the TSL OIM Analysis v8 on pixels
with a confidence index above 0.1 on a surface of at least 1.5 $\times 10^{4}$
$\mu$m2. Then, the MTEX 5.11.1 software toolbox was used to identify the
misorientation angle of all grain boundaries and to reconstruct PAGBs from the
EBSD maps with MATLAB R2021b [49].

The microstructure has been analyzed using synchrotron X-ray diffraction
measurements. They were conducted at Deutsches Elektronen-Synchrotron (DESY,
Hamburg, Germany) on the Petra III P-02.1 beamline at 60 keV. A high-energy
transmission X-ray beam with a wavelength of 0.207381 Å was shed on square-
shaped specimens (10$\times$10$\times$1 mm3) to collect two-dimensional
diffractograms at a working distance of 969 mm. Before conducting quantitative
diffraction analyses, the instrumental parameters have been calibrated using
the diffraction patterns of NIST standard LaB6. All recorded two-dimensional
diffractograms have been post-processed using the GSAS-II software [50].

Finally, correlative TKD-APT measurements have been performed on PAGBs of LC
and B-LC to quantify the segregation of boron. The sample has been prepared
using a dual-beam SEM-focused ion beam (FIB) instrument (FEI Helios Nanolab
600i) using an in situ lift-out procedure. Prior to conducting the APT
measurements, specimens were analyzed using TKD to characterize the grain
boundaries with a Digiview V) EBSD detector on MERLIN SEM (Zeiss Microscopy).
The prepared APT specimens have been investigated in a CAMECA LEAP 5076XS
instrument, operated in laser mode at 60 K with a pulse rate of 200 kHz, pulse
energy of 30 pJ, and a detection rate of 50 ions per 1000 pulses. The three-
dimensional reconstructions have been performed using the AP suite 6.3
software.

###  2.2 Microstructure evolution with boron addition

The microstructure evolution with boron addition is first investigated in this
work by comparing the difference of grain size and grain boundary distribution
in boron-doped (B-LC) and boron-free (LC) steels. From the inverse pole figure
(IPF) maps provided in figs 1.a and 1.c of LC and B-LC steels, both have a
martensite microstructure after quenching. The grain size has then been
estimated from the IPF maps presented in A, is 15.4 $\mu$m $\pm$ 10.8 $\mu$m
for LC and 11.3 $\mu$m $\pm$ 10.4 $\mu$m for B-LC. These diameters have been
determined by calculating the area fraction of each grain assuming they are a
circle. A slight difference in the grain size is observed between LC and B-LC
but remains neglectable given the large fluctuations for both steels. The
reconstructed parent grains of figs 1.a and 1.c are presented in figs 1.b and
1.d, respectively. They have been obtained by regrouping grain boundaries
following the Kurdjumov-Sachs (KS) orientation relationship (OR), i.e.:
regrouping the $(111)_{\gamma}\parallel(\overline{1}01)_{\alpha}$ and
$[011]_{\gamma}\parallel[\overline{1}\overline{1}1]_{\alpha}$ [51, 52, 53, 18,
54], following the instruction provided by MTEX [55].

Figure 1: IPF maps of a) LC and c) B-LC, and d) its corresponding
reconstructed parent grains. The SGBs having a dislocation-like microstructure
(with a misorientation lower than 8°) are represented in red and the MMBs with
the KS variant misorientation and PAGB are represented in black in figs. a and
c. The PAGBs are also represented in black in figs. b and d.

Further, three categories of grain boundaries have been sorted for LC and
B-LC: (i) prior austenite grain boundaries that do not follow KS OR, (ii)
martensite-martensite boundaries with a relevant KS OR, and (iii) subgrain
boundaries (SGBs) having a misorientation lower than 8°. Table 1 presents the
length of these three types of boundaries ($l_{PAGB}$, $l_{MMB}$, and
$l_{SGB}$) for both steels. The similar percentage of all lengths suggests a
similar microstructure with boron incorporation and most of the grain
boundaries are SGBs and MMBs (more than 90% for LC and B-LC).

Table 1:  Summary of the length distribution of PAGBs ($l_{PAGB}$), martensite-martensite boundaries following KS OR ($l_{MMB}$), and subgrain boundaries ($l_{LAGB}$) in LC and B-LC. |  $l_{PAGB}$ mm (%) |  $l_{MMB}$ mm (%) |  $l_{SGB}$ mm (%)
---|---|---|---
LC | 1.92 (8.3) | 10.09 (43.5) | 11.69 (48.2)
B-LC | 2.15 (7.5) | 15.68 (47.9) | 14.94 (45.6)

The synchrotron X-ray measurements show similar two-dimensional diffractograms
for LC and B-LC (figs. 2.a and 2.b, respectively). Peaks from the martensite
microstructure and the retained austenite are obtained during the measurements
when the circular integration of the two-dimensional diffractogram is
presented in logarithmic scale. This austenite phase was not detected during
the EBSD analyses, most likely because it is unstable and transforms to
martensite when it reaches the free surfaces during metallographic sample
preparation. When the synchrotron X-ray diffraction profiles are integrated,
the contribution related to the austenite phase becomes clearer (fig. 2.c).

Figure 2: Snapshots of two-dimensional diffractograms acquired for a) LC and
b) B-LC steels. c) Circular integration of the two-dimensional diffractograms
(in logarithmic scale). The major diffraction peaks are attributed to
martensite ($\alpha^{\prime}$) and retained austenite ($\gamma$) phases. The
arrows highlight fluctuations of the signal attributed to carbides. d)
Austenite phase fraction ($f_{\gamma}$) obtained for LC and B-LC e)
Dislocation density in $\alpha^{\prime}$ and $\gamma$ for both LC and B-LC
steels.

Fig 2.d presents the volume fraction of the $\gamma$ phase ($f_{\gamma}$),
which is 2.26$\pm$0.04 % for both steels and is deduced by integrating peaks
related to the martensite and austenite phases. This method was chosen over
the Rietveld refinement analysis approach because the latter neglects
fluctuations that are observed at 4.5° and 7.5° (highlighted with black arrows
in fig. 2.c). These fluctuations are related to carbides, which could be
either cementite, $\eta$-carbides, or $\varepsilon$-carbides according to the
literature [56] that some are observed through ECCI experiments (fig 10.d).
The average lattice strain from the austenite phase has been calculated using
[57]:

$\varepsilon^{ave}_{\gamma}=\frac{a_{\gamma}-a_{\gamma,0}}{a_{\gamma,0}},$ (1)

with $a_{\gamma}$ and $a_{\gamma,0}$, being the lattice constant measured from
synchrotron X-ray diffraction and the lattice constant in the unstrained
state, respectively. The unstrained lattice constant has been estimated from
the carbon content in the material using the following empirical equation:
$a_{\gamma,0}=0.35965+0.0028C_{C}$[58] and is 0.36007 nm. From eq. (1) a large
lattice strain of -0.275% is deduced. The equivalent hydrostatic stress
$\sigma_{hydro}^{\gamma}$ can subsequently be calculated using [59]:

$\sigma_{hydro}^{\gamma}=\frac{E}{1-2\nu}\varepsilon^{ave}_{\gamma},$ (2)

with $E$ and $\nu$ the Young’s modulus and Poisson’s ratio, respectively. When
the Young’s modulus and Poisson’s ratio are chosen at 172 GPa, and 0.3 [59], a
compressive hydrostatic stress $\sigma_{hydro}^{\gamma}$ of 1.2 GPa is
deduced.

Then, the crystalline size $D$ and dislocation density $\rho$ of both phases
have been determined using the Williamson-Hall approach [60, 61]:

$\beta\cos\left(\theta_{hkl}\right)=\frac{\lambda}{D}+\varepsilon_{micro}\sin\left(\theta_{hkl}\right),$
(3)

with $\beta$ the full width at half maximum of the diffraction peak at
$\theta_{hkl}$, $\lambda$ the wavelength of the beam ($\lambda$ = 0.207381 Å),
$\varepsilon_{micro}$ the micro-strain, and $\theta_{hkl}$ the position of the
$\\{hkl\\}$ reflection group. The dislocation density $\rho$ can then be
estimated using [60, 61]:

$\rho=\frac{2\sqrt{3}\varepsilon_{micro}}{bD},$ (4)

with $b$ being the magnitude of the Burgers vector of the screw dislocation in
the martensite phase (2.48 Å) and of the edge dislocation in the austenite
phase (2.54 Å). Following this approach, a similar dislocation density has
been obtained in LC and B-LC (fig. 2.d) of 1.21 $\pm$ 0.01 $\times$ 1015 m-2
in the martensite phase and 2.4 $\pm$ 0.1 $\times$ 1015 m-2 in the austenite
phase, respectively. From these measurements, boron incorporated in the steels
has a minor effect on the fraction of retained austenite and dislocation
density in both phases.

Finally, correlative TKD-APT experiments have been performed to characterize
the boron segregation at PAGBs. A site-specific lift-out has been performed
for localizing PAGB from LC and B-LC microstructures, following the procedure
presented in previous work [29] before the TKD observations. Figs 3.a and 3.d
provide the TKD maps of LC and B-LC before the APT measurements. The
orientation relationship of both GBs has first been checked to confirm that
they are PAGBs. For LC, the misorientation angle/axis between the grains is
59°/[0.542 -0.497 -0.678] and is 44°/[-0.743 0.656 -0.131] for B-LC, which are
the other grain is parallel to a $[9,4,10]$ direction. These orientation
relationships do not follow the KS OR [62, 54], thus they can be considered as
a PAGB.

Figure 3: Correlative TKD-APT analysis of PAGBs in LC (a-c) and B-LC (d-f)
steels. a) IPF map of LC with the three-dimensional reconstruction of the APT
needle showing b) boron (red atoms) and c) carbon (blue atoms). d) IPF map of
B-LC with the three-dimensional reconstruction showing e) boron (orange atoms)
and f) carbon (green atoms). g) Corresponding one-dimensional composition
profile in PAGBs.

Figs 3.b, c present three-dimensional reconstructions showing only boron and
carbon atoms for LC while figs. 3.e, f present three-dimensional
reconstructions of the same elements in B-LC. Single events have been
separated from multiple events to improve the visualization of boron and
carbon in the reconstructed data. This data filtering has been shown to
provide an improved signal-to-background ratio for species in low
concentration in Fe-based materials [63]. More details are given at B, showing
an improved quantification of boron in an interface obtained from martensitic
transformations. A pronounced segregation of both carbon and boron atoms is
observed into the GB for LC and B-LC, in agreement with the literature [64,
29, 26]. Figs 3.g plot the resulting composition profile of the interface
marked by a blue cylinder in the corresponding APT reconstruction shown inset.
While the concentration of carbon is similar for both interfaces (maximum
concentration around 2.5 at.%), the maximum boron concentration is 0.12 at.%
for LC and higher than 1.2 at.% for B-LC. This difference highlighted the
pronounced segregation of boron in PAGBs for B-LC, which is not observed for
LC, which contains almost no boron.

In this section, we described the microstructure obtained in both LC and B-LC
after quenching from 1100°C in He gas (cooling rate of $\sim$200 K.s-1). A
similar microstructure is observed for LC and B-LC with an average grain size
around 13 $\mu$m (when using the grain size of spherical grains) for both
steels with the appearance of carbides, confirmed through synchrotron X-ray
experiments. Additionally, these experiments show that 2 vol.% of retained
austenite is observed in these steels. This fraction of retained austenite is
lower than the fraction deduced in medium carbon steel reported in the
literature (which is 5.5%) [65] due to the difference in carbon and silicon
content. This phase should be located at lath martensite boundaries according
to the literature [65, 66]. The dislocation density in the martensite phase
has been estimated from the synchrotron X-ray experiments as 1$\times$1015
m-2, and agrees with measurements performed in the literature [62]. In the
austenite phase, a higher dislocation density has been estimated and is
3$\times$ 1015 m-2. Finally, the APT measurements correlated with TKD analysis
reveal a major change in behavior between boron-doped and boron-free steels,
which is the segregation of boron to the PAGBs. At these interfaces, the
maximal boron concentration is $\sim$1 at.% but can increase up to 8 at.%
according to previous work [29]. In addition, previous secondary ion mass
spectroscopy analyses had demonstrated that the segregation at other
martensite boundaries is minor [29]. Since it is expected to observe the same
solute concentration for LC and B-LC at these interfaces, the trapping
behavior towards hydrogen should be similar at these interfaces. Further,
hydrogen is inserted into these microstructures and detected using TDS
measurements. According to the microstructure characterization, hydrogen could
diffuse and be potentially trapped in vacancies, dislocations (mostly screw
dislocations, in their cores and their distortion fields), grain boundaries
(martensitic laths, block and packet boundaries, PAGBs), precipitates
(carbides), and in the austenite phase.

##  3 Impact of boron segregation on the hydrogen trapping behavior

###  3.1 Experimental details

The incorporation of hydrogen into $LC$ and $B-LC$ has been performed
electrochemically, using a three-electrode system on 10$\times$10$\times$1 mm3
samples. The procedure consisted of imposing a current of -25 mA.cm-2 for 1 h
in a 0.1 M $H_{2}SO_{4}$ aqueous solution with 0.3 wt% of NH4SCN. After
charging, the oxide layers were removed from the sample using 600 SiC grinding
paper before the TDS measurements. For all conditions, the time between the
end of the electrochemical charging and the beginning of the temperature
ramping is lower than 5 min, which is performed in an infrared furnace from
298 K to 1173 K with a mass spectrometer using the G8 GALILEO apparatus from
Bruker®. The heating rate $\varphi$ varied between 8 $K.min^{-1}$ and 32
$K.min^{-1}$ to locate where hydrogen is trapped in the microstructure.

###  3.2 Results

The TDS spectrum of each condition is given in fig. 4 with the hydrogen
desorption rate $\phi$ not represented between 723 K and 1173 K because the
signal is flat.

Figure 4: TDS spectra of LC and B-LC heated for different temperature ramping
at a) 8 K.min-1, b) 12 K.min-1, c) 16 K.min-1, d) 20 K.min-1, e) 24 K.min-1,
and f) 32 K.min-1.

The absolute difference between the TDS spectra and a function being the sum
of several Gaussian distributions is then minimized using a conjugate-gradient
algorithm to determine the number of peaks for each spectrum. Following this
procedure, four peaks are detected in LC steel and only three in B-LC for all
$\varphi$. Boron mostly segregating into PAGBs [28, 29, 30], the last peak
should correspond to hydrogen trapped in this crystalline defect in $LC$
steels. This result agrees with previous studies that have shown that the
desorption of hydrogen located in HAGBs at temperature ranges higher than the
desorption of hydrogen located in dislocations [67, 68]. In these studies, the
trapping energy of hydrogen in HAGBs was estimated between -0.61 eV and -0.55
eV, whereas the trapping energy of hydrogen in average grain boundaries was
-0.27 eV [68]. However, according to the hydrogen desorption behavior observed
in LC and B-LC of this work, the difference between these two trapping
energies may be more related to PAGBs and martensite boundaries (MMBs and
SGBs) than their misorientation angle. PAGBs are GBs existing at high
temperatures (1100 °C) whereas martensite boundaries are formed in a parent
austenite grain at lower temperatures (the start of the martensite
transformation is below 450 °C), following the KS OR. Consequently, the
coherency of PAGBs is expected to be different from martensite boundaries
which can modify the trapping behavior of hydrogen even though both types of
boundaries have low and high misorientation angles.

Further, the identification of the possible trapping sites of the different
peaks is made following previous work [38, 44, 67]. In these works, the
microstructure of $\alpha$-iron and ultra-low carbon steel has been optimized
to favor the formation of certain types of traps. The segregation energy of
hydrogen in different traps, deduced from the peak shift is also compared with
results from the literature [39, 45, 40] to determine the possible trapping
sites associated with each peak.

The variation of $\varphi$ produces a shift of the different peaks. Using
Kissinger’s theory, the trapped energy of hydrogen with a defect $E^{\rm
tra}_{\rm H-def}$ can be determined using [37, 38, 69, 70, 71]:

$\frac{E^{\rm seg}_{\rm H-def}}{k_{\rm B}}=\frac{E^{\rm D}_{\rm H}+E^{\rm
tra}_{\rm H-def}}{k_{\rm
B}}=\frac{\partial\ln(\varphi/T_{pj})}{\partial(1/T_{pj})},$ (5)

where $k_{\rm B}$ being the Boltzmann constant, $E^{\rm seg}_{\rm H-def}$ the
segregation energy of hydrogen in a defect, and $E^{\rm D}_{\rm H}$ the energy
barrier for hydrogen to diffuse in lattice ($E^{\rm D}_{\rm H}$= -0.043 eV
[70, 72]).

Fig. 5.a presents the Kissinger plot of the different peaks shown in fig. 4
for LC and B-LC steels. The first peak from the TDS spectra of fig. 4 should
correspond to mobile hydrogen in the lattice (from the slope of the blue
curve). The energy obtained is -0.16 eV and is lower than the theoretically
expected activation barrier for diffusion of hydrogen in martensitic steel or
$\alpha$-iron, which is between -0.04 eV and -0.1 eV [72, 39, 70]. The main
reason is that the determination of this energy comes from the temperature at
which the hydrogen desorption rate $\phi$ is the highest. When the heating
rate ($\varphi$) is low, this temperature should come around or below room
temperature [44], the starting temperature from our experiments. The second
peak (red curves) has been attributed to hydrogen trapped at GBs in previous
work [38, 44]. Our results show a fourth peak which pertains to hydrogen
desorbing from PAGBs. Consequently, this second peak should mostly be related
to the desorption of hydrogen trapped in grain boundary from martensite
transformation, which follows the KS OR, and have the same parent austenite
grain. The trapping energy deduced from our experiment is -0.26 eV for
hydrogen segregating into this type of trapping site (deduced from the slope
of the red curve). This energy is in the range of the ones reported in the
work of Galindo et al. [40], but outside the range given in Frappart et al.
[39, 69] (fig. 5.b). The slope of the green curve gives the average trapping
energy of -0.34 eV, and should represent mostly hydrogen in dislocations
according to the literature [38, 44]. This value is in the range of the
energies given in previous studies [39, 45, 40]. The last peak, observed only
for the boron-free steel (orange curve in fig. 5.b) should be hydrogen in
PAGBs with a trapping energy of -0.37 eV. This value is close to one reported
in the work of Bhadeshia [45] but higher than the one reported in the work of
Frappart et al. [39].

Figure 5: Trapping energy deduced from the TDS spectra. a) Associated
Kissinger plot for $LC$ and $B-LC$ steels. b) Trapping energies between
hydrogen and different microstructural features in $\alpha-Fe$ [45], steel
[40] and martensite steel [39] compared to the energies determined in this
work. The shadowed points and curve correspond to the first peak which gives
an inaccurate segregation energy.

In addition, hydrogen could also be trapped in the 2% of retained austenite
observed in LC and B-LC steels and in or at carbides [45, 40, 67],
precipitates observed by ECCI and synchrotron X-ray measurements. When
hydrogen is trapped in austenite, a peak from the TDS spectra above 573 K
should be obtained [67], which is not the case, neither for LC nor for B-LC.
From the synchrotron experiments, a lattice strain of -0.275% is observed,
which is equivalent to a compressive stress of 1.2 GPa. One possible
explanation is that the austenite, which is too compressed to transform into
martensite, is becoming a repulsive site for hydrogen to segregate. Such
effect is observed in the case of edge dislocations for BCC and FCC metals,
where the stress field of the compressed area induces a negative binding
energy for hydrogen, which favors its segregation into the tensile area of the
defect [73, 74]. Additionally, the carbide concentration is too low to observe
an apparent peak by TDS measurements. A deconvolution of the TDS spectra
considering these defects could be done near peaks 2 and 3, but might lead to
an inaccurate overfit. Another peak has been found for hydrogen in microvoids
in previous works, which has an amplitude significantly lower than the other
peaks [38, 44]. However, no additional peak has been observed in either of the
two steels. One possible explanation is that hydrogen recombines in these
microvoids, making it impossible for hydrogen to desorb at the temperature
range studied in this work [44].

To summarise, an additional peak has been observed when performing TDS
measurements for different heating rates $\varphi$ on boron-free steel
compared to boron-doped steel. This peak has been attributed to HAGBs in
previous studies [68, 67]. In the previous section, we observed that both LC
and B-LC steels have similar microstructure, except for a more pronounced
segregation of boron into PAGBs. Further, ab initio calculations are performed
for a better understanding of the interaction between boron and hydrogen in
PAGBs.

##  4 Interaction energy of hydrogen and boron at grain boundaries

###  4.1 Computational details

Ab initio calculations have been performed to understand the interaction
between hydrogen and boron at grain boundaries by determining the interaction
energies between solutes and the structural defect. The structural defect
investigated is a $\alpha$-$\Sigma$5(210) grain boundary, which can also be
written as $\alpha$-39°[001](210) GB. It is a coherent site lattice grain
boundary that does not follow the KS OR, thus it should be representative of
one type of PAGBs than a boundary from martensitic transformations. The
calculations have been carried out using the Vienna Ab initio Simulation
Package (VASP) code [75, 76, 77] in the generalized gradient approximation
(GGA) using the PBE functional [78]. A plane-wave cut-off of 500 eV has been
taken for all calculations. The convergence tolerance of the atomic force is
0.01 eV/Å and the Brillouin-zone integration was made using Methfessel–Paxton
smearing [79]. The magnetic state of $\alpha$-Fe is ferromagnetic and a
$4\times 4\times 4$ supercell containing 128 Fe atoms has been used for the
bulk calculations. For the reciprocal space integration, a $\Gamma$-centered
Monkhorst-Pack [80] k-point sampling of $8\times 8\times 8$ has been used for
bulk $\alpha$-Fe calculations. The lattice constant and magnetic moments of
the ferromagnetic $\alpha$-Fe were computed as 2.834 Å and 2.2 $\mu_{\rm
B}$/atom, respectively, in agreement with the previous studies [81]. The
supercell containing the $\alpha$-$\Sigma$5(210)[001] grain boundary consisted
of 80 Fe-atoms. For the reciprocal space integration, a $\Gamma$-centered
Monkhorst-Pack [80] k-point sampling of $5\times 10\times 16$ has been used to
ensure convergence. The solute atoms H, C, and B have firstly been
incorporated in different locations of the defect (in interstitial sites
$I_{1}$ and $I_{2}$), represented in fig. 6. Then, additional calculations
have been performed to describe the interaction between a boron-doped GB with
an additional solute atom. In this situation, boron has been incorporated in
$I_{1}$ and a second solute atom (hydrogen and boron) has been incorporated in
interstitial site $I_{2}$ or in interstitial sites in the vicinity of the GB
(in octahedral and tetrahedral sites).

Figure 6: Structures of $\alpha$-Fe$\Sigma 5(210)$ GB supercell studied in
this work with the different positions where $B$, $C$, and $H$ have been
inserted. a) Full supercell structure. b) Zoom in the core of the grain with
the octahedral sites ($O_{1}$, $O_{2}$, $O_{3}$, $O_{4}$ and $O_{5}$)
represented in orange, the tetrahedral sites ($T_{1}$, $T_{2}$ and $T_{3}$) in
cyan, and interstitial sites ($I_{1}$ and $I_{2}$) represented in shade of
magenta. The grey atoms represent Fe.

The interaction energy between a solute and the Fe$\Sigma 5(210)$ GB ($E^{\rm
inter}_{\rm X-GB}$) has been determined using:

$\displaystyle E^{\rm inter}_{\rm X-GB}=(E^{\rm sp}_{\rm X-GB}-E^{\rm sp}_{\rm
GB})-(E^{\rm sp}_{\rm X}-E_{\rm bulk})$ (6)

where $E^{\rm sp}_{\rm X-GB}$, $E^{\rm sp}_{\rm GB}$ are the energies of the
supercell containing the grain boundary with and without a solute atom,
respectively. $E^{\rm sp}_{\rm X}$, $E_{\rm bulk}$ are the energies of the
supercell with a solute in its most stable position (hydrogen in tetrahedral
site, carbon in octahedral site and boron in substitutional site) and without
solute, respectively.

Then, the interaction energy between an additional solute and a boron-doped GB
($E^{\rm inter}_{\rm X-B-GB}$) has been calculated using:

$E^{\rm inter}_{\rm X-B-GB}=(E^{\rm sp}_{\rm X-B-GB}-E^{\rm sp}_{\rm
B-GB})-(E^{\rm sp}_{\rm X}-E_{\rm bulk}),$ (7)

with $E^{\rm sp}_{\rm X-B-GB}$ being the energy of the supercell containing
the grain boundary with boron inserted at site $I_{1}$ and a second solute
(either boron or hydrogen), respectively.

###  4.2 Results

Fig. 7.a presents the interaction energies of hydrogen and boron at the
different sites given in fig. 6. The most stable position for boron (and
carbon) in GB is in the site $I_{1}$ with an interaction energy of -2.38 eV
(and -1.77 eV), but a strong attraction is also observed when both solutes are
in site $I_{2}$. For hydrogen, the strongest attractive site is in the core of
the GB, in $I_{2}$ with $E^{\rm inter}_{\rm H-GB}=-0.46$ eV. This interaction
energy suggests that hydrogen can be trapped in the defect with an energy up
to -0.46 eV when the GBs are similar to a $\Sigma 5(210)[001]$ GB structure.
Since boron has the highest attraction with the grain boundaries (with an
energy lower than -2 eV), it will stay at this interface, even if other
solutes like hydrogen are in its vicinity. These results are in agreement with
the literature, where previous authors have observed the strongest attraction
for boron in $\Sigma 5(310)$ GB, compared to hydrogen and carbon [35].

Figure 7: Interaction energies between H, B, and C at boron-free and boron-
doped grain boundaries. a) $E^{\rm inter}_{\rm X-GB}$ for boron-free GB
determined using eq. (6). b) $E^{\rm inter}_{\rm X-B-GB}$ for boron-doped GB
determined using eq. (7). The shadowed points are situations where the solutes
move to their closest stable interstitial site (tetrahedral site for hydrogen
and octahedral site for boron).

The interaction energy between solutes and boron-doped GB ($E^{\rm inter}_{\rm
X-B-GB}$) is presented in fig. 7.b. In this configuration, additional boron is
attracted to the GB with interaction energies lower than -0.5 eV in $O_{2}$.
This interaction energy suggests that boron can be accumulated in GBs, which
facilitates the formation of borides when the nucleation barrier is low enough
[29, 30]. In contrast, hydrogen is repelled from the GB in this configuration
when inserted in interstitial sites. For these calculations, when hydrogen
atoms are initially inserted in octahedral sites, they are moving to their
closest stable tetrahedral site. When a second boron atom is initially
inserted in the tetrahedral site, it moves towards its closest stable
octahedral site.

The repulsive interaction between hydrogen and boron confirms the competition
between hydrogen and boron segregation observed using TDS experiments.
Discrepancies are noted between the trapping energy from TDS measurements and
the ab initio calculations because the latter determines the interaction
energy of one specific grain boundary type. In contrast, the TDS measurements
determine the average trapping energy of hydrogen in all types of PAGBs.
Additionally, the calculations do not consider carbon, which also segregates
to PAGBs. However, carbon does not saturate PAGBs when conventional heat
treatments (direct quenching from austenitization temperature to ambient
temperature) are performed [26]. Finally, the short-range interactions among
adjacent solute atoms located in GBs are not considered for these
calculations, which is an effect that could also influence the interaction
energy between a solute and a defect [72, 82, 83].

##  5 Hydrogen concentration in steels at thermodynamic equilibrium

The previous TDS measurements show that the boron-free steel has generally an
additional peak compared to the boron-doped steel and the ab initio
calculations show that hydrogen and boron have a repelling effect in GBs.
Consequently, it is possible to differentiate hydrogen trapped in PAGBs from
hydrogen trapped in other traps using TDS measurements. Further, the hydrogen
fraction in different defects $X^{\rm H}_{\rm Defect}$ is calculated from the
trapping energies determined using Kissinger’s theory. At thermodynamic
equilibrium, the hydrogen segregation in crystalline defects can be
approximated using the Langmuir-McLean formalism [84]:

$\frac{X^{\rm H}_{\rm Defect}}{1-X^{\rm H}_{\rm Defect}}=\frac{X^{\rm H}_{\rm
Bulk}}{1-X^{H}_{\rm Bulk}}\exp{\left(-\frac{E^{\rm tra}_{\rm Defect}}{k_{\rm
B}T}\right)},$ (8)

with $X^{\rm H}_{\rm Defect}$ and $X^{\rm H}_{\rm Bulk}$, fractions of
hydrogen in a crystalline defect and the matrix, respectively. $X^{\rm H}_{\rm
Bulk}$ is calculated via mass conservation from the total hydrogen
concentration $C^{\rm H}_{\rm Total}$ [83, 72, 71]:

$C^{\rm H}_{\rm Total}=N_{\rm L}X^{\rm H}_{\rm Bulk}+N_{\rm P_{2}}X^{\rm
H}_{\rm P_{2}}+N_{\rm P_{3}}X^{\rm H}_{\rm P_{3}}+N_{\rm P_{4}}X^{\rm H}_{\rm
P_{4}}.$ (9)

with $N_{\rm L}$, $N_{\rm P_{2}}$, $N_{\rm P_{3}}$ and $N_{\rm P_{4}}$ being
the number of possible trap sites in the lattice and from peaks 2, 3, and 4,
respectively. The number of trap sites in the matrix is $N_{\rm L}=6$ [85, 72]
and $N_{\rm Defect}$ is estimated using [85]:

$N_{\rm Defect}=N_{\rm L}\times\left(\frac{D_{\rm L}}{D_{\rm
eff}}-1\right)\exp{\left(\frac{E^{\rm tra}_{\rm Defect}}{k_{\rm B}T}\right)},$
(10)

where $D_{\rm L}$ is the lattice diffusion of hydrogen in $\alpha$-Fe ($D_{\rm
L}=1.45\times 10^{-9}$ m2.s-1 at 298 K [39]). Eq. (10) has been chosen in this
work because it is not directly dependent on the trapped hydrogen
concentration and its validity was verified in previous work by Monte-Carlo
simulations [86, 85]. The effective diffusion of hydrogen $D_{\rm eff}$ in LC
and B-LC steels is determined through permeation tests at 298 K, which are
presented in fig. 8.

Figure 8: Permeation curves of different samples (named S1, S2, and S3) for LC
and B-LC steels with the lagging time ($t_{lag}$) deduced from the slope of
the different curves.

The hydrogen permeation study has been conducted with a Kelvin probe-based
detection method developed in-house [87, 88]. On the side of the sample
designated for hydrogen detection, a dry nitrogen atmosphere is maintained,
and a 100 nm Pd coating was applied using a Leybold Univex 450 physical vapor
deposition apparatus. The hydrogen-entry side of the sample has been subjected
to the same galvanostatic condition as samples for TDS measurements. Time lags
of 11.6 min, 15.1 and 17.6 min are obtained for LC and 6.8 min, 8.0 and 12.7
min for B-LC. These time lags give an effective diffusion coefficient of
hydrogen of 5.81 $\pm$ 1.02 $\times$ 10-10 m2.s-1 and 9.74 $\pm$ 2.37 $\times$
10-10 m2.s-1 for LC and B-LC, respectively. These effective diffusion
coefficients are one order higher than the ones reported in the literature
(4.5 $\times$ 10-11 m2.s-1 [89] and 7.4 $\times$ 10-11 m2.s-1 [39]) because of
the charging conditions in this present work (high current density and acidic
solution with NH4SCN). It results in a higher activity of hydrogen and traps
are faster filled compared to the corresponding observations reported in
previous studies [89, 39]. Additionally, since boron has a repulsive
interaction with hydrogen, fewer traps need to be filled in B-LC, which
explains the difference in the effective diffusion coefficient of hydrogen
between LC and B-LC. Then, the number of possible traps can be determined
using equation (10), and the results are presented in table 2.

Table 2: Number of trap sites (in at-1) in different microstructural defects deduced from eq. (10) for LC and B-LC. | LC | B-LC
---|---|---
$N_{\rm P_{2}}$ | 2.52 $\times$ 10-3 | 8.23 $\times$ 10-4
$N_{\rm P_{3}}$ | 1.65 $\times$ 10-4 | 5.39 $\times$ 10-5
$N_{\rm P_{4}}$ | 2.35 $\times$ 10-5 |

Incorporating eq. (9) in eq. (8), the latter equation can be solved self-
consistently. Fig. 9 presents the fraction of hydrogen in different
crystalline defects for a total hydrogen concentration of 10 appm, 100 appm,
and 1000 appm as a function of the temperature for LC and B-LC.

Figure 9: hermodynamic equilibrium hydrogen fraction in the different
crystalline defects as a function of the temperature for total hydrogen
concentration of 10 appm (dotted lines), 100 appm (dashed lines), and 1000
appm (solid lines) in a) LC and b) B-LC. The blue lines correspond to the
fraction of hydrogen from peak 1 (mostly in the lattice), the red lines
correspond to the fraction of hydrogen into the trapping sites of peak 2, the
green lines correspond to the fraction of hydrogen into trapping sites of peak
3 and the orange lines correspond to the fraction of hydrogen in trapping
sites of peak 4. Figures c and d are zooms of figures a and b for low hydrogen
fraction, respectively. Hydrogen distribution at different trapping sites for
different total hydrogen concentrations for e) LC and f) B-LC.

Figs. 9.a-d show that all traps are not filled at thermodynamic equilibrium
when the total hydrogen concentration is below 1000 appm for the two steels.
For comparison, the total hydrogen concentration determined from the peak
integration and presented in C is below 700 appm. For the LC steel, hydrogen
segregates into trap sites of peak 4 because the trapping energy is lower
compared to the other trapping sites. Trap sites of peak 4 are mostly located
where boron is segregating (i.e.: PAGBs). This observation also explains why
this type of GB is the weakest microstructure feature in hydrogen environments
for steels [27, 26]. In addition, even if the permeation experiments revealed
fewer possible trap sites ($N_{P_{2}}$ and $N_{P_{3}}$) for B-LC compared to
LC, the fraction of hydrogen in trap sites 2 and 3 are higher in B-LC than in
LC. Consequently, similar concentrations of hydrogen in traps from peaks 2 and
3 are obtained in the two steels at thermodynamic equilibrium

Then, the hydrogen distribution into the different trap sites and the lattice
has been estimated in LC and B-LC and presented in figs 9.e and 9.f. For LC
steel, when the total hydrogen concentration is low ($C^{\rm H}_{\rm Total}$ =
10 appm), $X^{\rm H}_{\rm Def}$ is similar for trapping sites and lattice,
showing no preferential segregation. When the total hydrogen concentration
increases, traps of lowest energy are firstly saturated (i.e.: peak 4), and
the hydrogen concentration increases in other defects to possibly saturate
them. In the situation where boron protects the trapping sites of the lowest
segregation energy, hydrogen is localized in the lattice with a similar
concentration of hydrogen in other microstructure features. This effect can
lead to other failure mechanisms in the materials that have been suggested in
terms of specific models in the literature describing hydrogen embrittlement
in metals and alloys [19, 5, 6].

##  6 Conclusion

In this work, the effect of boron segregation on the trapping behavior of
hydrogen has been investigated in steel both experimentally and theoretically.
First, the microstructure of boron-doped (B-LC) and boron-free (LC) steels has
been studied using EBSD, synchrotron X-ray measurements, and correlative TKD-
APT measurements to observe any change due to the presence of boron. While the
dislocation density, grain size, and grain boundary distributions are similar
for LC and B-LC, a pronounced segregation of boron in PAGBs is observed for
the B-LC steel. When both steels are pre-charged with hydrogen and measured
through TDS measurements, fewer peaks are detected for B-LC. From this
behavior, the peak corresponding to hydrogen being trapped in PAGBs can be
distinguished from hydrogen trapped in the other microstructural defects. Ab
initio calculations demonstrate a strong attraction between boron and GBs
(interaction energy of -2.38 eV for a $\Sigma 5(210)[001]$ GB structure),
stronger than the interaction between hydrogen and GBs (interaction energy of
-0.46 eV for the same GB structure). Additionally, when the GB contains boron
solute, the interaction between hydrogen and this defect becomes repulsive.
Finally, the equilibrium hydrogen concentration in different defects has been
approximated using the McLean formalism with the trapping energy deduced from
the TDS measurements and the effective hydrogen diffusion coefficients
obtained from the permeation tests. The latter experiment has shown that
hydrogen has a higher diffusion coefficient in B-LC compared to LC because
fewer traps can be filled by hydrogen in B-LC. Different hydrogen partitioning
is observed depending on temperature and total hydrogen concentration. We
observed that the concentration of hydrogen in the lattice will be increased
for B-LC compared to LC at thermodynamic equilibrium because boron influences
the fraction of hydrogen in trap sites pertaining to PAGBs. This effect can
induce different failure mechanisms described in different models proposed to
explain hydrogen embrittlement. In a situation where traps of the lowest
trapping energies like PAGBs are passivated by the presence of boron, it can
modify the material’s resistance against hydrogen embrittlement, which is a
planned future investigation.

Acknowledgments \- The authors thank Dr. A. Oudriss, and Dr. E. Clouet for
fruitful discussions and the help of M. Adamek, A. Sturm, and U. Tezins for
technical support. Synchrotron X-ray diffraction experiments have been
conducted on Beamline P02.1, PETRA III at DESY (proposal No. I-20230183), with
technical support from Dr. Alba San Jose Mendez and Dr. Alexander Schökel.
G.H. and S.L.W. acknowledge the financial support from the Alexander von
Humboldt Foundation through grant n°3.3-FRA-1227460-HFST-E and
n°3.1-USA-1237011-HFST-P, respectively.

##  Appendix A EBSD and ECCI mapping of LC and B-LC

The measurements of the average grain size of LC and B-LC have been performed
with the EBSD maps from 10.a and 10.b, respectively. For a better
representation, a larger surface has been analyzed (surface of at least 2.7
$\times 10^{5}$), and a step size of 0.4 $\mu$m has been used for the
acquisition of both maps. For the ECCI, the scanning electron microscope (SEM)
was operated with an acceleration voltage of 30 kV and a probe current of 5
nA. We inverted the signal from the backscattered electron detector to obtain
an image contrast similar to bright-field conditions for transmission electron
microscopy images [90].

Figure 10: EBSD inverse pole figure (IPF) maps of steels a) LC and b) B-LC. c)
ECCI of the area highlighted by a green square in b), showing in detail the
lath microstructure, and d) carbides with all variants highlighted by white
arrows.

Figs. 10.c and 10.d show ECC images of B-LC. The distance between martensitic
laths is around 200 nm. When the distance between laths becomes too large
(more than 500 nm), the formation of carbides is observed, which has been
investigated using synchrotron X-ray measurements.

##  Appendix B Single and multiple events to improve the detection of boron
using APT measurements

The three-dimensional reconstruction presented in fig. 3 has been subjected to
a data filtering process based on the multiplicity of the detection events, as
described by Yao et al. [63]. This appendix compares the concentration of
carbon and boron at an interface in the boron-doped steel which has been
determined with and without this filtering. The experiment has been carried
out using a LEAP 5000 XS instrument, operated in voltage mode at 60 K with a
pulse rate of 200 kHz, a pulse fraction of 15 %, and a detection rate of 50
ions per 1000 pulses. Fig. 11.a plots the mass spectrum of the specimen
analyzed by APT and 11.c plots the single and multiple events detected during
the same experiments. Multiple events are when a single pulse leads to
multiple ions hitting the detector and have differences on the y-axis scale
compared to the single events. Most of the carbon and boron are detected as
part of multiple events and in the mass spectrum for single hits, there is
barely any detectable signal for boron. This filter on the data improves the
signal-to-background ratio specifically for boron and hence facilitates
visualization of the boron distribution and quantitative analysis.
Additionally, several shoulders are observed around different peaks (e.g.: for
Fe2+ or C2+). These shoulders are mostly due to the dissociation of molecular
ions, which has been discussed in previous work [91].

Figure 11: Impact on the data filtering on the detection of boron in B-LC. a)
Mass spectrometer of the unfiltered data process with the corresponding b) 1D
concentration profiles of boron and carbon c) Mass spectra of the single event
and b) multiple events detected during the same analysis with the
corresponding d) concentration profile of carbon and boron.

The corresponding one-dimensional concentration profiles of boron and carbon
are then presented in figs 11.b and 11.d, with and without this filtering
process applied. With this multiplicity filter used, a maximum boron
concentration up to 0.045 at% is obtained from fig. 11.d. However, there is
barely any observable increase in boron due to the high level of background in
fig. 11.b, when the data are unfiltered.

##  Appendix C Hydrogen concentration from peak integration of all heating
rates.

Fig. 4 provided the TDS spectrum of different heating rates for hydrogen pre-
charged LC and B-LC steels. The hydrogen concentration in both steels can be
estimated by integrating all curves. Fig. 12 presents the deduced hydrogen
concentration from peak integration. For each point, two measurements have
been performed.

Figure 12: Hydrogen concentration deduced from peak integration from the TDS
spectra presented in fig. 4.

In general, the total hydrogen concentration deduced is similar for both
steels for all heating rates ($\varphi$). However, when the heating rate
$\varphi$ increases, the total hydrogen concentration is increased showing
that more hydrogen is desorbed when $\varphi$ is the highest, a phenomenon
that can be described by modeling the TDS spectrum. [70, 41].

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