# Interstitial segregation has the potential to mitigate liquid metal
embrittlement in iron

Ahmadian  Max-Planck-Institut fuer Eisenforschung GmbH, 40237 Düsseldorf,
Germany  A  Max-Planck-Institut fuer Eisenforschung GmbH, 40237 Düsseldorf,
Germany  Scheiber  Materials Center Leoben GmbH, 8700 Leoben, Austria  D
Materials Center Leoben GmbH, 8700 Leoben, Austria  Zhou  Max-Planck-Institut
fuer Eisenforschung GmbH, 40237 Düsseldorf, Germany  X  Max-Planck-Institut
fuer Eisenforschung GmbH, 40237 Düsseldorf, Germany  Gault  Max-Planck-
Institut fuer Eisenforschung GmbH, 40237 Düsseldorf, Germany  Department of
Materials, Royal School of Mines, Imperial College London, London, UK  B  Max-
Planck-Institut fuer Eisenforschung GmbH, 40237 Düsseldorf, Germany
Department of Materials, Royal School of Mines, Imperial College London,
London, UK  Romaner  Materials Center Leoben GmbH, 8700 Leoben, Austria
Montanuniversität Leoben, Leoben, Austria  Corresponding authors:
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>L  Materials
Center Leoben GmbH, 8700 Leoben, Austria  Montanuniversität Leoben, Leoben,
Austria  Corresponding authors<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>Darvishi Kamachali  Federal Institute for Materials
Research and Testing (BAM), Unter den Eichen 87, 12205 Berlin, Germany  R
Federal Institute for Materials Research and Testing (BAM), Unter den Eichen
87, 12205 Berlin, Germany  Ecker  Materials Center Leoben GmbH, 8700 Leoben,
Austria  W  Materials Center Leoben GmbH, 8700 Leoben, Austria  Dehm  Max-
Planck-Institut fuer Eisenforschung GmbH, 40237 Düsseldorf, Germany
Corresponding authors<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>G  Max-Planck-Institut fuer Eisenforschung GmbH, 40237
Düsseldorf, Germany  Corresponding authors<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>Liebscher  Max-Planck-
Institut fuer Eisenforschung GmbH, 40237 Düsseldorf, Germany  Corresponding
authors<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>C.
H  Max-Planck-Institut fuer Eisenforschung GmbH, 40237 Düsseldorf, Germany
Corresponding authors<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

The embrittlement of metallic alloys by liquid metals leads to catastrophic
material failure and severely impacts their structural integrity. The
weakening of grain boundaries by the ingress of liquid metal and preceding
segregation in the solid are thought to promote early fracture. However, the
potential of balancing between the segregation of cohesion-enhancing
interstitial solutes and embrittling elements inducing grain boundary
decohesion is not understood. Here, we unveil the mechanisms of how boron
segregation mitigates the detrimental effects of the prime embrittler, zinc,
in a $\Sigma 5\,[0\,0\,1]$ tilt grain boundary in $\alpha-$Fe
($4\leavevmode\nobreak\ at.\%$ Al). Zinc forms nanoscale segregation patterns
inducing structurally and compositionally complex grain boundary states. Ab-
initio simulations reveal that boron hinders zinc segregation and compensates
for the zinc induced loss in grain boundary cohesion. Our work sheds new light
on how interstitial solutes intimately modify grain boundaries, thereby
opening pathways to use them as dopants for preventing disastrous material
failure.

## Introduction

Grain boundary (GB) properties such as cohesive strength or mobility can be
significantly altered through segregation of alloying elements or impurities
1. One of the most detrimental elements impacting the properties of GBs in
iron (Fe) and steel is zinc (Zn), which promotes brittle intergranular
fracture of the material through liquid metal induced embrittlement (LMIE) 2,
3, 4, 5, 6, 7, 8, 9.

Several models were proposed to explain the underlying mechanisms leading to
LMIE 10. The Stoloff–Johnson–Westwood–Kamdar (SJWK) model considers that the
liquid metal adsorbed at the crack tip promotes crack propagation under an
applied stress by weakening the strength of the interatomic bonds 11, 12. In
contrast, stress-assisted GB diffusion preceding the crack initiation is
assumed to be the root cause for the increase in grain boundary brittleness in
the Krishtal-Gordon-An model13. DiGiovanni et. al 14 investigated the
diffusion of Zn in Fe by means of electron-probe microanalysis (EPMA) before
and after mechanical loading. Their observations confirmed that stress-
assisted diffusion in the vicinity of the crack tip is one of the dominant
mechanisms. There are various explanations on the origin of the segregation
induced GB embrittlement process. Atomic size differences in Cu-Bi, also an
LMIE system, were shown to cause local strain fields, which facilitate a
reduction in GB cohesion 15. However, the size differences between Fe and Zn
are not large enough to play a major role. Instead electronic effects such as
bonding type 16 and mobility 17, 18, 19 can be made responsible for GB
embrittlement. Peng et al. 20 performed first-principles tensile tests on a Zn
segregated $\Sigma 5\,[0\,0\,1]$ GB in ferritic Fe. They found a weakening of
the GB because of covalent bonding between Zn and Fe, which ultimately reduces
the charge density between the Fe atoms and hence their bond strength.

In order to prevent LMIE, it was proposed to introduce cohesion enhancing
alloying elements to GBs. Scheiber et al. 9 concluded from ab-initio and
thermodynamic modelling that the embrittling effect of Zn at different
symmetrical bcc-Fe tilt GBs can be reduced by Al and Si, which is related to
site-competition as well as repulsive interactions between the solutes and Zn.
Although a large body of experimental and theoretical studies on LMIE exist
21, 22, 23, a fundamental understanding on the relationships between the GB
structure, Zn segregation and its impact on embrittlement is lacking.
Especially, the role of interstitial solutes on the embrittlement of GBs by Zn
has not been considered, while for example C and B are known to act as GB
cohesion enhancers in Fe-based alloys 24, 25, 26, 27, 28, 29. Miyazawa et al.
28 have shown by first-principles based calculations that segregation of C
would increase the GB cohesion in Fe. In contrast to C, B can occupy
substitutional as well as interstitial positions in $\alpha$-Fe 30 and would
enhance the cohesion strength of the GB when taking up interstitial positions
18. Therefore, it is of great interest to understand how cohesion enhancing
solutes such as B and C impact the segregation behavior of Zn and how their
interplay affects the detrimental effect of Zn on GB cohesion on an atomistic
level.

Here, we study the local atomic structure and composition of a $\Sigma 5$ (3 1
0)[0 0 1] tilt GB in a bicrystal of body centered cubic (bcc) Fe at different
levels of Zn segregation. By atomically resolved microscopic probing
techniques, we find that Zn forms nanometer sized segregation lines in a
region preceding the former solid-liquid interface. However, both B and C are
homogeneously distributed across the GB plane. The Zn-segregation pattern
formation is explained by density-based phase-field simulations revealing a
miscibility gap of the GB, which promotes a GB phase decomposition.
Furthermore, our ab-initio calculations show that the presence of B and C
significantly reduces the segregation energy of Zn due to strong repulsive
interactions, which also leads to a reduction of the maximum Zn concentration
at the GB. Interestingly, B is capable to compensate for the reduction in the
work of separation through Zn even for high Zn GB concentrations. Our work
suggests that interstital solutes such as B and C have the potential to
mitigate the embrittling tendency of Zn. These insights provide pathways to
prevent liquid metal embrittlement in Fe by controlled addition of cohesion
enhancing elements.

## Results

Global grain boundary structure

We use a bicrystal containing a $\Sigma 5$ (3 1 0)[0 0 1] tilt GB with trace
amounts of B and C to study Zn segregation from the liquid state into the GB
and the interaction of Zn with the interstitial solutes. We formed a diffusion
couple of Zn and the bicrystal, and subsequently annealed it at $800^{\circ}$C
to liquefy the Zn reservoir and enable diffusion of Zn into the solid Fe
bicrystal as schematically shown in Fig. 1a. The detailed experimental
procedure is described in the Methods and Extended Data sections. The
backscattered electron (BSE) secondary electron microscopy (SEM) image in Fig.
1b shows a two-phase region at the interface between the former liquid Zn
reservoir and the Fe bicrystal consisting of $\alpha-$Fe (bcc) and $\Gamma-$Zn
(see Extended Data). Here, we limit our observations to the GB below this two-
phase region. We specifically focus on two different GB areas indicated as
"Region $1$", which is Zn-rich with an average concentration of Zn determined
by energy-dispersive X-ray spectroscopy (EDS) in the SEM of $\sim$5 at.$\%$,
and "Region $2$" with an average Zn content of $\sim$0.5 at.$\%$ (see Fig. 1b
). Region $1$ is $\sim$5 $\mu m$ below the two-phase region and high angle
annular dark-field (HAADF) imaging along the $[0\,0\,1]$ tilt axis in the
scanning transmission electron microscope (STEM) reveals that the GB
inclination is locally deviating from the exact (310) habit plane (see Fig.
1c). Corresponding STEM-EDS measurements shown in Fig. 1d demonstrate strong
segregation of Zn to the GB and suggest that it is inhomogeneously distributed
along the GB. The GB in Region $2$, which is $\sim$30$\,\mu m$ away from the
two-phase region, is curved and exhibits a high density of local kinks as
shown in Fig. 1e. Zinc is only slightly enriched at the GB as shown in the
elemental map in Fig. 1f.

Figure 1: Overview BSE images of the $\Sigma 5\,[0\,0\,1]$ GB. a-b The
diffusion of Zn results in the formation of a two-phase region containing
$\alpha$-Fe and $\Gamma-$ Fe-Zn phases. STEM specimen were extracted from two
regions (indicated by blue rectangles). b Region 1 marks an area of the GB in
the vicinity of the two-phase region, while Region 2 is $\sim 30\,\mu m$ away
from the two-phase region. Furthermore b shows a low-angle GB (indicated by a
black arrow) intersecting with the $\Sigma$5 GB and locally bending it. c-d
Region $1$: c HAADF-STEM image of the $\Sigma 5$ GB viewed along the
$[0\,0\,1]$ tilt axis. The GB is inclined and the boundary plane can be
divided into nearly symmetric $(2\,1\,0)$, $(4\,3\,0)$ and $(3\,1\,0)$
segments. d STEM-EDS mapping of the region, which is indicated in c by a black
dashed rectangle. The GB is enriched by Zn with a weak decrease from top to
bottom. e-f Region $2$: e HAADF-STEM image shows strong inclinations of the
boundary. f Corresponding STEM-EDS map of the black dashed rectangle region
shows no clear enrichment of Zn. The scale bar in b is $10\,\mu m$, in c it is
$100\,nm$, in d, $20\,nm$, in e $50\,nm$ and in f $20\,nm$

.

Near atomic scale zinc segregation

We performed near atomic resolution STEM-EDS elemental mapping in the Zn-rich
Region $1$ of the bicrystal. Figure 2 shows atomic resolution STEM images and
the associated Zn distribution along the GB at acceleration voltages of
$300\,kV$ and $120\,kV$, respectively. The HAADF-STEM images in Fig. 2a and b
reveal that the GB structure appears disrupted by a high density of GB
defects. Measurements at $120\,kV$ shown in Fig. 2b clearly demonstrate
clustering of Zn at the GB into Zn-rich ($\sim$35 $at.\%$) and Zn-lean
($\sim$10 $at.\%$) regions having a width of $\sim$1 nm and a regular spacing
of $\sim$3-4 nm. Although Zn has a slightly higher atomic number than Fe
($\Delta$Z=4), the corresponding HAADF-STEM images do not show any indication
of regions with higher intensity. More information on the STEM-EDS
measurements will be discussed later.

To obtain further insights into the 3D arrangement of the Zn segregation and
its correlation to the distribution of the impurity elements B and C, we
performed atom probe tomography (APT) experiments from the same regions as our
STEM investigations.

Figure 2: High resolution STEM-EDS at different acceleration voltages. a The
HAADF-STEM and corresponding Zn elemental map show formation of Zn clusters
with concentrations of $\sim 30\,at.\%$. To improve the STEM-EDS resolution,
the acceleration voltage was reduced to $120\,kV$ as shown in b. The incident
electrons are scattered to lower angles due to the presence of the Zn clusters
resulting in a dark contrast in the HAADF- as well as LAADF-STEM image but a
bright contrast in the ABF-STEM image. The Zn concentration profile along the
GB shows a periodicity of $3-4\,nm$ with concentrations varying from
$10\,at.\%$ to $40\,at.\%$. The scale bar in a is $5\,nm$ and in b $1\,nm$.

Grain boundary composition

Figure 3a presents the reconstructed $3$D-volume of the needle-shaped specimen
viewed along the $[0\,0\,1]$ tilt axis extracted from Region $1$ (Zn-rich),
where the GB is positioned at a 45∘ angle $\sim$100 nm away from the apex.
Besides the segregation of Zn, B and C are also observed to segregate to the
GB. The 3D atom map of B shows a rather unusual behavior in the form of a tail
that extends into the lower grain for nearly 50 nm, although it has been
recognized that anomalies in the field evaporation of solutes can lead to
asymmetric solute distribution at GBs 31. The concentration profile of B
extracted across the GB in Fig. 3b verifies this observation, which will be
discussed later. The bulk Zn concentration of $\sim$5.5 $at.\%$ from APT
agrees with STEM-EDS measurements (Fig. 2). The averaged GB concentration of
Zn reaches a value of $\sim$10 $at.\%$. As we have seen before, the Al
concentration decreases to $\sim$2.7$at.\%$ at the GB due to the presence of B
and C 24. Both concentration profiles of B and C show a broadened and
asymmetric shape with a tail towards the left side corresponding to the lower
grain in the reconstruction (Fig. 3a). The peak concentration of B and C in
the initially investigated GB before Zn segregation was $1.8\,at.\%$ and
$2.4\,at.\%$ 24, which is reduced by a factor of $\sim$4 and $\sim$10,
respectively. A close inspection of the peak locations of the concentration
profiles reveals an offset of the B peak of $\sim$1 nm with respect to that of
the Zn concentration peak. A similar behavior was obtained in a different APT
specimen as shown in the Extended Data Figure 4.

Figure 3: Segregation of Zn, B, C, and depletion of Al at the $\Sigma
5\,[0\,0\,1]$ GB of Region $1$. a $3$D APT reconstruction showing the
distribution of Zn, B and C viewed along the $[0\,0\,1]$ tilt axis. Using an
isoconcentration value of $10\,at.\%$ for Zn, $0.5\,at.\%$ for B and
$0.3\,at.\%$ for C highlights the segregation of these elements to the GB. b
The composition profile extracted from a cylindrical region with diameter of
$30\,nm$ is extracted across the GB (shown in a as orange arrow). A clear
increase of Zn, B and C is shown at the GB, while the concentration of Al
decreases. The maximum concentration peak of Zn and C is at $24.7\,nm$, while
B concentration reaches the maximum already at $23.5\,nm$ same as the minimum
of Al. The Zn concentration first decreases slightly at the vicinity of the
boundary until it increases steeply. The C and B concentration do not show
such decrease at the vicinity of the GB. The B concentration shows a
continuous increase over a large range of several tens of nm before reaching
the maximum value and then it decreases abruptly to nearly $0\,at.\%$. c
Rotation of the APT reconstruction in a such that the distribution of Zn, B
and C onto the GB plane is shown, i.e. the viewing direction is along the GB
plane. While B and C show no formation of patches, Zn forms columnar patches
elongated along the tilt axis. d A concentration profile extracted along the
orange arrow in c shows the concentration and distances of Zn columns. The
scale bar in a is $50\,\text{nm}$ and $20\,\text{nm}$ in c.

Observations of the in-plane distribution of Zn within the GB obtained by APT
reveals that Zn is arranged in the form of segregation lines which are aligned
along the [001] tilt axis (see Figs. 3c and d). However, B and C show a
homogeneous distribution within the GB plane as shown in Fig. 3c. A similar
modulation in Zn concentration was observed by STEM-EDS shown in Fig. 2.

APT investigations were also performed in Region $2$ (see Extended Figure 5),
revealing a lower average bulk Zn content of $\sim$0.5 $at.\%$. Interestingly,
no clear indication for Zn segregation to the GB containing B and C with peak
concentration values of $\sim$1.8 $at.\%$ and $\sim$0.8 $at.\%$, respectively
(shown in Extended Figure 5b), is found. In comparison to the Zn-rich Region
$1$ of Fig. 3b, the peak B and C concentration at the GB in the Zn-lean Region
$2$ is nearly a factor of 4 higher, similar to values obtained in the as-grown
bicrystal 24. Furthermore, the concentration profiles of B and C adopt a
symmetric shape, in contrast to that observed in Region $1$ (Fig. 3b).

Atomic grain boundary structure

To explore the underlying atomic GB structure in both Region $1$ (Zn-rich) and
$2$ (Zn-lean), we used atomic resolution HAADF-STEM imaging as shown in Fig.
4. The HAADF-STEM overview image of the GB in Region $1$ shown in the Extended
Figure 4 a reveals a slight curvature of the GB, which leads to the formation
of different nanoscale GB facets with varying GB planes close to $(3\,1\,0)$.
The atomic resolution images of Fig. 4 a and b show that the GB structure is
composed of kite-type structural units, which are disrupted by GB defects.
Locally, the GB habit plane is varying between $(3\,1\,0)$\- and
$(2\,1\,0)$-type as well as asymmetric GB segments.

The GB in Region $2$ (Zn-lean) is composed of nanofacets with different GB
plane inclinations (see Fig. 1 e and Supplementary Figure 4 b). Figure 4 b
shows a magnified HAADF-STEM image of the GB in Region $2$, where the GB
alternates between symmetric $(2\,1\,0)$ and asymmetric segments. The atomic
GB structure in Fig. 4 c shows a near $(3\,1\,0)$ GB with kite-type structural
units, which are interrupted by GB steps or disconnections (highlighted by
dashed cyan circles) to compensate for deviations in GB inclination. In other
areas in Region $2$ the GB is dissociating into a nanofaceted structure (see
Fig. 4 d).

Figure 4: Atomic structure of the $\Sigma 5\,[0\,0\,1]$ GB in the
Fe-4at.$\%$Al bi-crystal. a, b High-resolution HAADF-STEM images from Region 1
(Zn-rich) shows the formation of kite-type structural units (purple color),
where extra atoms are introduced to shift the SU parallel and perpendicular to
the boundary plane normal. From the FFT in a the misorientation angle is
determined as $40^{\circ}$. c High-resolution HAADF-STEM images from Region 2
(Zn-lean) of the area marked by the upper dashed square in Extended Figure 4
b. The GB consists of perfect kite-type SU interrupted by GB defects, which
result in the inclination of the boundary. d High-resolution HAADF-STEM image
of the region marked by the lower dashed square in 4 b. The GB is faceting
into symmetric $(3\,1\,0)/(3\,1\,0)$ and asymmetric $(4\,3\,0)/(4\,1\,0)$. The
scale bar in a, b and c marks $1\,\text{nm}$ and in d $2\,nm$.

Grain boundary decomposition

The phase decomposition behavior of the $\Sigma 5\,(3\,1\,0)[0\,0\,1]$ GB was
further explored by density-based phase-field (DPF) modeling and simulation.
The computational details are given in the Methods section. In a first step,
we modelled the GB phase diagram in the Fe-Zn system, which is shown in Fig. 5
a. Following this thermodynamic assessment, the GB exhibits a miscibility gap,
which separates Zn-lean and Zn-rich phase regions, comparable to the Fe-Zn
bulk phase diagram (see Extended Data Figure 8). The origin of this phase
separation in the $\alpha$-Fe-Zn system is related to magnetic ordering 32.
The transition curve (blue) in Fig. 5 a represents the critical temperature
dependent bulk concentration at which the $\Sigma 5\,(3\,1\,0)$ GB is expected
to decompose into Zn-rich and Zn-lean domains. This also means that crossing
the blue curve from left to right, e.g., via a change in temperature, a low-
to-high Zn segregation transition is expected within the GB.

Interestingly, for a bulk Zn concentration of 5 at.% as observed in Region 1
in the experiment (see Fig. 1 b and 2 a) the DPF modeling predicts a GB phase
decomposition at $\sim$403∘C (highlighted by the horizontal line in Fig. 5 a)
and the GB is expected to decompose into a two-phase structure with Zn
concentrations of $\sim 17\,at.\%$ (Zn-lean) and $\sim 52\,at.\%$ (Zn-rich),
respectively. With decreasing temperature, the Zn-rich domains further enrich
in Zn up to $\sim 64\,at.\%$ at 275∘C and the concentration of the Zn-lean
regions reduces slightly to $\sim 12\,at.\%$ (shown by the dashed horizontal
line). The time dependent GB phase evolution was investigated by 3D DPF
simulations at 300∘C and a bulk Zn concentration of 5 at.% as shown in Fig. 5
b and c. Figure 5 b shows the evolution of the Zn concentration in an edge on
view at the GB for four different time steps. The in-plane evolution of the
Zn-rich and -lean domains are shown in Extended Data Figure 10. Initially, Zn
is homogeneously distributed along the GB with a concentration of $\sim
9\,at.\%$, as also seen in the concentration profiles extracted along the GB
shown in Figure 5 b (green curve). With progressing time, the GB phase
separates into Zn-rich ($\sim 60\,at.\%$) and Zn-lean ($\sim 17\,at.\%$)
domains, which are separated by $\sim 5\,nm$ consistent with the experimental
observations. For a bulk Zn concentration of 0.5 at.%, no GB decomposition is
observed according to the DPF simulations.

The predicted composition of the Zn-rich GB regions is higher than determined
experimentally, since the GB phase decomposition is kinetically limited at
lower temperatures in the experiment. This is evident from the APT
measurements shown in Fig. 3 b, where depletion of Zn adjacent to the GB is
indicating incomplete segregation due to limited diffusivity during the
cooling process. Furthermore, the presence of B and C atoms at the GB may
impact the segregation behavior of Zn to the GB and ultimately affect the Zn
GB concentration.

Figure 5: Density-based GB phase diagram and phase-field simulation. a GB
phase diagram for the Fe-Zn system showing a miscibility gap separating Zn-
lean and Zn-rich GB phase regions. The solid curves represent the binodal, the
dashed curves the spindal curves, respectively. The transition curve indicates
the critical temperature and bulk Zn concentration above which the GB
decomposes into Zn-rich and -lean domains. b Edge-on view of the time
evolution of the GB phase decomposition for a bulk Zn concentration of 5 at.%
at 300∘C obtained by DPF simulations. The GB is oriented vertically and the
scale bar is 5 nm. b Concentration profiles of Zn extracted from b) for each
time step.

Co-segregation behavior of Zn and B

In order to explore the interaction of B and Zn and its impact on the
segregation behavior and GB cohesion, we performed first principles DFT
calculations of the $\Sigma 5\,(3\,1\,0)$ as well as $\Sigma 5\,(2\,1\,0)$
GBs. Details on the computational approach can be found in the Methods
section. The GB structures with all possible segregation sites considered for
Zn (green) and B (blue) atoms are displayed in Fig. 6 a and b. The same
calculations performed for C (brown) are shown in the Extended Data Figure 7.
The segregation energies of Zn $E_{seg}^{Zn}$ with and without interstitial B
for the $\Sigma 5\,(3\,1\,0)$ and $(2\,1\,0)$ GBs are shown in Fig. 6 c and d.
Zinc alone has a similarly high segregation energy for its lowest energy
position at the GB center ($z=0\leavevmode\nobreak\ \AA$) in a substitutional
site within the GB plane for both GBs of $-0.57\,eV$ and $-0.58\,eV$,
respectively. However, if B is present, the overall segregation energies of Zn
are strongly reduced (see the cyan triangles). Note that multiple possible
configurations were investigated. For example, the presence of B lowers the
segregation energy of Zn at the GB center position by a factor of $\sim$6 to
$-0.09\,eV$ for the $\Sigma 5\,(3\,1\,0)$ GB. Only for Zn farthest away from
the GB considered here at $z=\pm 2\leavevmode\nobreak\ \AA$, a slightly higher
$E_{seg}^{Zn}$ of $-0.30\,eV$ is obtained for a single configuration. A
similar trend is observed for the $\Sigma 5\,(2\,1\,0)$ GB, where the
segregation energies are reduced by a factor of $\sim$2-3 in the presence of
B. A possible configuration with Zn at the GB center with nearly the same
segregation energy as without B is found. This suggests that the $\Sigma
5\,(2\,1\,0)$ GB shows a slightly higher probability for Zn to segregate with
B being present than the $\Sigma 5\,(3\,1\,0)$ GB.

Based on the calculated segregation energies, we estimate the enrichment of Zn
at the GB at $800^{\circ}$C using the White-Coghlan isotherm 33 considering
segregation to all sites at the GB. This allows us to explore the influence of
the bulk Zn concentration and the impact of B on the expected amount of Zn at
the GB in the theoretical high temperature limit, which corresponds to the
annealing temperature of the bicrystal diffusion couple. Since both the
$\Sigma 5\,(3\,1\,0)$ and $\Sigma 5\,(2\,1\,0)$ GBs show a similar minimum
segregation energy of Zn alone, the Zn concentration is predicted to be nearly
the same at both GBs. It increases monotonically with increasing Zn bulk
content as shown in Fig. 6e (green dots). When B is also present at the GBs, a
strong reduction of the maximum Zn content can be observed for both
interfaces. For the $\Sigma 5\,(3\,1\,0)$ GB (solid lines) a reduction in the
Zn concentration from $85\,at.\%$ to $30\,at.\%$ is observed for a bulk Zn
concentration of $5.5\,at.\%$, which corresponds to the Zn-rich Region $1$ in
the experiments. A similar trend is observed for lower Zn bulk contents. The
reduction in GB Zn concentration is less pronounced for the $\Sigma
5\,(2\,1\,0)$ boundary as illustrated in Fig. 6 e (dashed lines). These
predictions indicate that B does not only strongly reduce the segregation
energies, but with this also significantly lowers the maximum attainable Zn
content at the GBs within the thermodynamic limit at the annealing
temperature.

Grain boundary cohesion

To assess the effects of co-segregation of Zn and B on GB cohesion, we
calculated the theoretical work of separation $W_{sep}$ for the $\Sigma
5\,(3\,1\,0)$ and $\Sigma 5\,(2\,1\,0)$ GBs as shown in Fig. 6 f. GB cohesive
properties were computed for each Zn concentration in the most preferential
segregation state. Both GBs show very similar cohesive properties in the pure
state without any solutes present resulting in a work of separation of
$3.5\,J/m^{2}$. With the addition of a single B atom, corresponding to half a
monolayer (ML) or $\sim 9$ at.% and $\sim 6$ at.% for the $\Sigma
5\,(3\,1\,0)$ and $\Sigma 5\,(2\,1\,0)$ GB, respectively, the cohesive energy
increases to $4.3$ and $4\,J/m^{2}$. We then investigated the effects of Zn
additions to the GBs and found that the $W_{sep}$ decreases almost linearly
for both GBs, albeit with a steeper slope for the $\Sigma 5\,(3\,1\,0)$ GB.
For the case when no B is present at the GBs, four Zn atoms ($=2$ MLs) lower
the work of separation to $2.3\,J/m^{2}$ for the $\Sigma 5\,(3\,1\,0)$ GB. The
reduction of $W_{sep}$ is less pronounced for the $\Sigma 5\,(2\,1\,0)$ GB
with $2$ ML Zn to $3\,J/m^{2}$. If both B and Zn are considered, it is found
that the cohesion reducing effects of Zn are compensated by the presence of B.
Even when 3 Zn atoms ($=1.5$ ML) are added to both GBs, the work of separation
is still higher than that of the pure interfaces. This shows that the effect
of impurity atoms on GB cohesion is to a large extent purely additive.

From these observations clear implications can be established for GB-based
alloy design to prevent LMIE. The addition of B and other impurity elements
can reduce the tendency for Zn segregation, while the presence of cohesion
enhancing elements such as B counteracts the embrittling tendency of Zn.

Figure 6: Modelling of Zn segregation to $\Sigma 5\,[0\,0\,1]$ GB with and
without B. Atomic structure of a $\Sigma 5\,[0\,0\,1](3\,1\,0)$ and b $\Sigma
5\,[0\,0\,1](2\,1\,0)$ GB with interstitial B (blue) and substitutional
positions (purple = Fe, green = Zn). c, d Zn segregation energies from DFT for
Zn to pure GB (green circles) and to GB when B is present (cyan triangles). e
Zn concentration at the GB as a function of the Zn bulk concentration modelled
for $\Sigma 5\,[0\,0\,1](3\,1\,0)$ (solid line) as well as $\Sigma
5\,[0\,0\,1](2\,1\,0)$ (dashed line) GB. For both GBs the enrichment level was
calculated with (cyan) and without (green) B. The vertical lines highlight the
observed Zn concentrations in bulk - namely $0.5\,at.\%$ and $5.5\,at.\%$. f
Modelled GB cohesion for different number of Zn atoms at $\Sigma
5\,[0\,0\,1](3\,1\,0)$ (solid line) and $\Sigma 5\,[0\,0\,1](2\,1\,0)$ (dashed
line) GB with (cyan) B and for GBs where B is not present (green).

## Discussion

In this study, the nanoscale segregation behaviour of Zn in the presence of B
and C at a $\Sigma 5\,(3\,1\,0)[0\,0\,1]$ bcc-Fe tilt GB was investigated. It
is found that Zn is forming a periodic, line-type segregation pattern with
nanometer periodicity in regions with $\sim$5 $at.\%$ Zn bulk concentration.
Despite the low Zn bulk concentration, strong modulation of Zn-rich ($\sim$35
$at.\%$) and Zn-lean ($\sim$15 $at.\%$) regions along the GB were observed
which originate from a phase separation of the GB during cooling from the
segregation transition at $\sim$403∘C according to our thermodynamically
informed phase-field simulations. However, we can also not exclude the role of
GB defects in the formation of this Zn segregation pattern. These Zn
modulations alone would lead to local fluctuations in the work of separation
along the GB, given the results obtained by DFT. Such local compositional
variations at GBs have not been taken into account to explain the origins of
LMIE or GB fracture 3, 4, 34, 6, 7, 8, 35. From APT it is observed that the
impurity elements B and C are homogeneously distributed within the GB plane in
the same regions. However, their peak concentration is reduced compared to the
as-grown bicrystal 24. The asymmetric segregation profiles of B and C indicate
that the GB has migrated during the annealing treatment either induced by Zn
segregation 2, 36 or through the triple line, where the GB is connected to the
liquid Zn reservoir 37.

Following our first-principles calculations, the strong repulsive interactions
between B and Zn lead to a significant reduction in the segregation tendency
of Zn in the presence of B. This ultimately leads to a reduction in the
maximum Zn concentration at the GB, which by itself has a positive effect on
GB cohesion 38, 39. Furthermore, the trends in calculated cohesive properties
of the GB clearly indicate that even lower levels of B comparable to those
observed experimentally are capable to compensate for the embrittling effects
of Zn. Since both B and C are known to enhance GB cohesion 24, 25, 26, 27, 28,
our calculated values for the work of separation only considering B are a
lower bound and it is shown in the Extended Data that C has a similarly
positive effect on GB cohesion.

While LMIE is a complex, hierarchical process leading to material failure by
the ingress of liquid metal along GBs, it has been indicated that GB
composition and local co-segregation effects ahead of the crack tip are
decisive in the underlying mechanisms 7, 14. Our investigations show that the
evolving GB composition and intrinsic elemental interactions are crucial in
understanding their effects on GB cohesion.

Our work emphasizes the role of cohesion enhancing impurity elements and how
they can be used to prevent GB failure induced during liquid metal
embrittlement. We demonstrate that impurity segregation can mitigate the
embrittling effects of Zn by hindering its segregation to GBs and leveling its
reduction in GB cohesion. This points toward a promising route for materials
design in which the controlled addition of B and C can act as efficient agent
for reducing Zn mediated LMIE in steels.

## Methods

### Experimental

For the experiments, a Fe-$4\,at.\%$Al bicrystal with a global $\Sigma
5\,[0\,0\,1]\,(3\,1\,0)$ was grown with the in-house Bridgman technique. The
bicrystal was cut into a $\sim 15\times 11\times 1\,mm$ rectangle with the GB
in the center. The steps how the bicrystal was coated with Zn are shown the
Supplementary Figure 1. First, the sample was mechanically grinded and then
chemically polished using a solution of $6\%$ HF, $14\%$H2O and $80\%$H2O2. In
order to prevent the contamination of the sample after polishing, the sample
was held with steel rods. Afterwards, the sample was immersed into a
$99.999\%$ Zn bath for $300\,s$. The temperature of the Zn bath was kept at
$\approx 467^{\circ}C$. The Zn was then grinded off the large $(0\,0\,1)$
surfaces as well as the large sides of the sample. Finally the sample was
encapsulated in a quartz tubes under vacuum ($\sim 10^{-3}-10^{-4}\,mbar$) and
annealed at $800^{\circ}C$ for $80$ hours. The Zn diffused bicrystal was
mechanically polished until reaching a mirror-like surface. Microstructural
characterization of the GB was done by EBSD (see Supplementary Figure 2a) as
well as EDS, which were simultaneously carried out by means of a ThermoFisher
Scios 2 dual beam FIB/SEM equipped with an EDAX Velocity EBSD camera and an
EDAX Octane Elite Super EDS detector. From the characterized area, TEM plane-
view specimen were prepared from two different regions using the Scios 2 FIB.
STEM imaging as well as STEM-EDS were performed on a Cs probe-corrected FEI
Titan Themis $60-300\,kV$ operated at $300\,kV$ as well as $120\,kV$ equipped
with the SuperX EDS detector system. The investigations were done with a
semiconvergence angle of $17\,mrad$, a camera length of $100\,mm$ and a probe
current of $80\,pA$. The high resolution images were processed with a
Butterworth filter and a Gaussian filter. The APT experiments were done in a
CAMECA LEAP 5000 XS operated in laser-mode.

### Computational Details

#### Atomistic Simulations

The computational details are described in more detail in Ref. 24, 39 but
encompass first principles density functional theory using the Vienna Ab-
initio Simulation Package (VASP) with projector augmented wave-functions 40,
41, 42, 43. For the exchange-correlation part, the PBE functional 44, 45 was
employed. Other parameters include the k-point mesh set as close as possible
to 40 k-points/Å for all involved simulation cells, and the energy cutoff with
400 eV. The GBs for simulations are constructed from two symmetrically
misoriented slabs that meet at the GB on one side and on the other side are
separated by a vacuum layer of at least 8 Å. Segregation energies are computed
using 46

$E_{seg,i}^{x}=\left(E_{gb,i}^{x}-E_{gb}\right)-\left(E_{bulk}^{x}-E_{bulk}\right)+\delta_{i-s}E_{Fe},$
(1)

with $E_{gb}$ being the total energy of a GB without solute $x$ while
$E_{gb,i}^{x}$ denotes the total energy of the same cell but with the solute
$x$ at GB site $i$. For the reference of the solute in the bulk, the
difference is computed between a bulk cell of 128 atoms without solute $x$ and
with solute $x$, $E_{bulk}$ and $E_{bulk}^{x}$, respectively. For considering
the change of interstitial B in the bulk to a substitutional site at the GB,
$\delta_{i-s}=1$ and $E_{Fe}$ corresponds to the total energy of a single Fe
atom in its bulk structure . Segregation energies are connected to the solute
enrichment at GBs via the White-Coghlan segregation isotherm 33 extended to
multiple solutes 47.

The work of separation was computed by separating the GB at all possible GB
planes by at least 8 Å and computing the difference of the total energies for
separated and joined GB slabs in the simulation cell 39, 9. The lowest
obtained work of separation for each segregated state is considered as the
most probable fracture plane.

#### Phase-field Simulations

The composition- and temperature-dependent GB phase behavior as well as GB
segregation evolution are explored using the thermodynamically-informed phase-
field modelling. The derivation and computational details of the model can be
found in 48. The CALPHAD integrated density-based free energy functional of
the Fe-Zn system reads

$\displaystyle G(\rho,X_{Zn},T)=X_{Fe}G_{Fe}(\rho,T)+X_{Zn}G_{Zn}(\rho,T)$
$\displaystyle+\rho^{2}\Delta H_{mix}^{B}(X_{Zn},T)-T\Delta
S_{mix}^{B}(G_{Zn},T)$ $\displaystyle+\frac{\kappa_{X_{Zn}}}{2}(\nabla
X_{Zn})^{2}$ (2)

with
$G_{i}(\rho,T)={\rho^{2}}E_{i}^{B}+{{\rho}}(G_{i}^{B}(T)-E_{i}^{B})+{\frac{\kappa_{i}^{\rho}}{2}\left(\nabla\rho\right)^{2}}$
and the atomic density $\rho\in[\rho^{GB},1]$ ($\rho=1$ for the bulk and
$\rho=\rho^{GB}$ at the GB plane). Here the superscript $B$ indicates bulk
properties extracted from TCFE11 Thermo-Calc database: $G_{i}^{B}$ is the free
energy, $E_{i}^{B}$ the potential energy and $\Delta H_{mix}^{B}$ and $\Delta
S_{mix}^{B}$ are the mixing enthalpy and entropy, respectively. The gradient
energy coefficients $\kappa_{i}^{\rho}$ and $\kappa_{X_{Zn}}$ accounts for the
structural and chemical heterogeneity with the GB region.

The GB phase diagram is calculated for $\rho^{GB}=0.92$ which corresponds to
the current $\Sigma 5\ [0\,0\,1]$ GBs. Figure 9 shows the density profiles
across the GBs computed from previous atomistic simulations 49. The chemical
spinodal and miscibility gaps are computed using a robust implementation of
the Maxwell construction and verified versus Thermo-Calc calculations. The
density-based phase-field simulations were performed using an Openmp parallel
C++ code with adaptive time-stepping. The simulation domain has been 17x17x3.4
nm3 with dx = 0.17 nm. Further details of simulation methods can be found in
50.

## Data Availability

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

## Code Availability

The code that support the findings of this study are available from the
corresponding author upon reasonable request.

## Extended Data

Diffusion couple

The steps to introduce Zn into the GB is shown in Fig. 1. First, the bicrystal
was mechanically grinded with SiC paper upon a grit size of
$15\leavevmode\nobreak\ \mu m$. Next, the bicrystal was chemically polished
with a acidic solution of $6\%$ HF, $14\%$ H2O and $80\%$ H2O2. In order to
avoid contamination, the sample was clamped by a steel rod. Immediately after
the polishing step, the bicrystal was immersed into a Zn bath, whose
temperature was measured to $467^{\circ}C$. The bicrystal was kept for
$300\,s$ into the bath. Afterwards, the Zn layers onto the (001) surfaces and
the large edges were mechanically removed, so that only Zn at the short edges
remained. Under this condition, the Zn coated bicrystal was encapsulated in a
quartz capsule under vacuum with $p\sim 10^{-3}\text{to}10^{-4}\,mbar$ and
annealed at $800^{\circ}C$ for $80$ hours. A backscattered electron (BSE)
micrograph from the region below the Fe-Zn interface shown in Fig. 2a reveals
the formation of a two-phase layer containing $\alpha-$ Fe and the solid-
solution phase of Zn. The orientation of the two-phase layer was determined by
electron backscatter diffraction (EBSD) having an orientation close to
$[0\,1\,2]$. The boundary type was identified as a symmetric $40^{\circ}\Sigma
5\,(3\,1\,0)[0\,0\,1]$ high angle GB. STEM investigations of the two phase
region are shown in Fig. 2b and c. Figure 2b shows the ABF-STEM image and the
corresponding STEM-EDS elemental maps for Fe and Zn around the GB. As it can
be seen, the GB is dewetted with Zn. A concentration profile across the
dewetted boundary results in a Zn concentration of $\geq 60\,at.\%$ (see
Figure 2c).

Extended Data Figure 1: Zn diffusion into the Fe bicrystal. a Mechanically
grinding the bicrystal up to $1200$ SiC grit paper and subsequent chemical HF
polishing. The GB is indicated by a black line. b The polished sample was
immersed into a liquid Zn bath. The temperature of the bath was measured with
a thermocouple to be $467^{\circ}C$. The inset shows the bicrystal completely
coated with Zn. Extended Data Figure 2: Microstructural characterisation a A
BSE image shows the formation of a two-phase region, which extended up to
$\sim 150\,\mu m$. The out-of plane inverse pole figure shows orientation of
the two-phase region to be close to $[0\,1\,2]$, while the $\alpha-$Fe region
maintained the $[0\,0\,1]$ direction. TEM specimen were extracted from the
black dashed box. b ABF-STEM image and corresponding STEM-EDS mapping of the
GB show the GB completely dewetted and transformed into a Zn-rich phase. The
line profile in c shows a concentration of $\sim 70\,at.\%$ Zn. The scale bars
in a) are $50\,\mu m$ (left) and $2\,\mu m$ (right) and in b it is $100\,nm$

Influence of temperature on GB structure
STEM investigations of the GB showed mesoscale inclinations with symmetric
$(2\,1\,0)$ and asymmetric segments. In order to understand whether the high
temperature annealing was causing it, a Zn-free bicrystal was annealed at
$800^{\circ}C$ for $80$ hours under similar high vacuum conditions ($p\sim
10^{-5}\,mbar$). As shown in Fig. 3a and b, the GB is flat and straight with
no inclinations or kinks. The ABF-STEM shows dislocations nucleated within the
grains, which can be caused during FIB milling. High-resolution HAADF-STEM
images at different regions of the GB are shown in Fig. 3c. The GB is a
symmetric $\Sigma 5\,[0\,0\,1]\,(3\,1\,0)$ and its structure shows kite-type
structural units similar as investigated in previous studies 24. This confirms
that the annealing does not affect the orientation of the boundary planes.
Therefore, the observed inclinations needs to be related to the diffusion of
Zn and the formation of the two-phase layer.

Extended Data Figure 3: Influence of annealing on GB structure a HAADF as well
as ABF-STEM overview images of the GB show no inclinations of the GB, but the
nucleation of many dislocations. A magnified image confirms that the GB did
incline at the mesoscale (b). c Atomic-resolved HAADF-STEM images show the
kite-type SU of the GB with a symmetric $(3\,1\,0)$ boundary plane. The GB
contains few defects. The Scale bar in a is $500\,nm$, b it is $100\,nm$ and
in c it is $1\,nm$. Extended Data Figure 4: HAADF-STEM of the $\Sigma
5\,[0\,0\,1]$ GB from Region 1 and 2. a Overview HAADF-STEM image showing the
inclinations of the GB from nearly symmetric $(2\,1\,0)$ into an asymmetric
configuration of $(3\,2\,0)/(3\,1\,0)$ boundary planes. The dashed square
indicates the region analyzed at atomic level shown in Fig. 4a and b. b
Overview HAADF-STEM image of the GB from the Region 2. The GB inclinates from
symmetric $(2\,1\,0)$ into an asymmetric configuration of
$(0\,1\,0)/(1\,1\,0)$ boundary planes. The Scale bar in a and b is $20\,nm$.
Extended Data Figure 5: Segregation of Zn, B, and C at the $\Sigma
5\,(2\,1\,0)[0\,0\,1]$ GB of Region $2$. a $3$D APT reconstruction showing the
distribution of Zn, B and C. The $[0\,0\,1]$ tilt axis shows upwards. Using an
isoconcentration value of $0.5\,at.\%$ for Zn and B and $0.3\,at.\%$ for C
highlights the segregation of these elements to the GB. b The composition
profile extracted from a cylindrical region with diameter of $30\,nm$ is
extracted across the GB (shown as orange arrow in a). A clear increase of B
and C is shown at the GB, while the concentration of Zn stays unchanged. The
maximum concentration peak of B and C is at the same position of $\sim
18.5\,nm$. Both elements show a symmetric concentration profile. The scale bar
in a is $40\,\text{nm}$. Extended Data Figure 6: Segregation of Zn, B, and C
at the $\Sigma 5\,[0\,0\,1]$ GB of Region 1. a 3D APT reconstruction of
showing the segregation of Zn, B and C at the GB. The GB is split into two
parts connected through a large step, which is also enriched with Zn. b A
concentration profile across the bottom GB is shown. Strong segregation of Zn
and a moderate enrichment level of B and C of $\leq 0.5\,at.\%$. The Zn
distribution shows a stronger depletion into the right grain, where the
concentration peak of B and C are located. The latter elements show a tail
into the right grain. The scale bar in a is $20\,nm$. Extended Data Figure 7:
Modelling of Zn segregation to $\Sigma 5\,[0\,0\,1]\,(3\,1\,0)$ GB with and
without C a Zn segregation energy from DFT for Zn to pure (green circles) and
to GB when C is present (brown triangles). The segregation energy of Zn and
therefore its tendency decreases with the presence of C. b Calculated work of
separation of the boundary for different number of Zn atoms with (brown) and
without C (cyan). The presence of C shows an enhancement of the boundary
strength. Extended Data Figure 8: Fe-Zn bulk phase diagram. Bulk phase diagram
of Fe and Zn determined by CALPHAD-based thermodynamic modelling. The shaded
gray region represents the miscibility gap due to magnetic ordering. Extended
Data Figure 9: GB density profiles atomic density and its fluctuations across
the a $\Sigma 5\,[0\,0\,1](3\,1\,0)$ and b $\Sigma 5\,[0\,0\,1](2\,1\,0)$ GBs
in $\alpha$-Fe. 3D atomic simulation results from 49 are used to compute the
density profiles. All values are coarse-grained and averaged in planes
parallel to the GB plane. The bars show the density fluctuation in the planes.
Extended Data Figure 10: GB in-plane segregation and phase decomposition from
DPF simulation a the time evolution of Zn segregation and interfacial phase
decomposition within the GB plane are shown. The scale bar is 4 nm. The
results show the Zn segregation variation initiated by the GB density
variations followed by a segregation transition and interfacial phase
decomposition. b shows the 3D simulation domain.

## References

  * 1 Lejček, P. & Šob, M.  An analysis of segregation-induced changes in grain boundary cohesion in bcc iron.  _J. Mater. Sci._ 49, 2477–2482 (2014).
  * 2 Hillert, M. & Purdy, G. R.  Chemically induced grain boundary migration.  _Acta Metal._ 26, 333–340 (1978).
  * 3 Beal, C., Kleber, X., Fabregue, D. & Bouzekri, M.  Liquid zinc embrittlement of twinning-induced plasticity steel.  _Scr. Mater._ 66, 1030–1033 (2012).
  * 4 Cho, L., Kang, H., Lee, C. & De Cooman, B. C.  Microstructure of liquid metal embrittlement cracks on Zn-coated 22MnB5 press-hardened steel.  _Scr. Mater._ 90–91, 25–28 (2014).
  * 5 Ashiri, R. _et al._ Supercritical area and critical nugget diameter for liquid metal embrittlement of Zn-coated twining induced plasticity steels.  _Scr. Mater._ 109, 6–10 (2015).
  * 6 Razmpoosh, M. H. _et al._ Liquid metal embrittlement in laser beam welding of Zn-coated 22MnB5 steel.  _Mater. Des._ 155, 375–383 (20185).
  * 7 Razmpoosh, M. H., Macwan, A., Goodwin, F., Biro, E. & Zhou, Y.  Role of Random and Coincidence Site Lattice Grain Boundaries in Liquid Metal Embrittlement of Iron (FCC)-Zn Couple.  _Metall Mater Trans A_ 51, 3938–3944.
  * 8 Ikeda, Y. _et al._ Early stages of liquid-metal embrittlement in an advanced high-strength steel.  _Materials Today Advances_ 13, 100196 (2022).
  * 9 Scheiber, D., Prabitz, K., Romaner, L. & Ecker, W.  The influence of alloying on Zn liquid metal embrittlement in steels.  _Acta Mater._ 195, 750–760 (2020).
  * 10 Fernandes, P. J. L. & Jones, D. R. H.  Mechanisms of liquid metal induced embrittlement.  _Int. Mater. Rev._ 42, 251–261 (1997).
  * 11 Stoloff, N. S. & Johnston, T. L.  Crack propagation in a liquid metal environment.  _Acta Metal._ 11, 251–256 (1963).
  * 12 Westwood, A. R. C. & Kamdar, M. H.  Concerning liquid metal embrittlement, particularly of zinc monocrystals by mercury.  _Philos. Mag. A_ 8, 787–804 (1963).
  * 13 Gordon, P. & An, H. H.  The mechanisms of crack initiation and crack propagation in metal-induced embrittlement of metals.  _Metal. Mater. Trans. A_ 13, 457–472 (1982).
  * 14 DiGiovanni, C., Ghatei Kalashami, A., Biro, E. & Zhou, N. Y.  Liquid metal embrittlement transport mechanism in the Fe/Zn system: Stress-assisted diffusion.  _Materialia_ 18, 101153 (2021-08-01).
  * 15 Schweinfest, R., Paxton, A. T. & Finnis, M. W.  Bismuth embrittlement of copper is an atomic size effect.  _Nature_ 432, 1008–1011 (2004).
  * 16 Senel, E., Walmsley, J. C., Diplas, S. & Nisancioglu, K.  Liquid metal embrittlement of aluminium by segregation of trace element gallium.  _Corrosion Science_ 85, 167–173 (2014).
  * 17 Yuasa, M. & Mabuchi, M.  Bond mobility mechanism in grain boundary embrittlement: First-principles tensile tests of Fe with a P-segregated $\Sigma$3 grain boundary.  _Phys. Rev. B_ 82, 094108 (2010).
  * 18 Wu, R., Freeman, A. J. & Olson, G. B.  First Principles Determination of the Effects of Phosphorus and Boron on Iron Grain Boundary Cohesion.  _Science_ 265, 376–380 (1994).
  * 19 Wu, R., Freeman, A. J. & Olson, G. B.  Nature of phosphorus embrittlement of the Fe $\Sigma$3[11¯0](111) grain boundary.  _Phys. Rev. B_ 50, 75–81 (1994).
  * 20 Peng, W., Peng, H., Wu, G. & Zhang, J.  Effect of zinc-doping on tensile strength of $\Sigma$5 bcc Fe symmetric tilt grain boundary.  _Computational Materials Science_ 171, 109204 (2020).
  * 21 Geng, W. T., Freeman, A. J. & Olson, G. B.  Influence of Alloying Additions on Grain Boundary Cohesion of Transition Metals: First-Principles Determination and Its Phenomenological Extension.  _Phys. Rev. B_ 63, 165415 (2001).
  * 22 Razmpoosh, M., DiGiovanni, C., Zhou, Y. & Biro, E.  Pathway to understand liquid metal embrittlement (lme) in fe-zn couple: From fundamentals toward application.  _Progress in Materials Science_ 121, 100798 (2021).
  * 23 Bhattacharya, D. _et al._ Influence of the starting microstructure of an advanced high strength steel on the characteristics of Zn-Assisted liquid metal embrittlement.  _Mater. Sci. and Eng. A_ 804, 140391 (2021).
  * 24 Ahmadian, A. _et al._ Aluminum depletion induced by co-segregation of carbon and boron in a bcc-iron grain boundary.  _Nat Commun_ 12, 6008 (2021).
  * 25 Wu, R., Freeman, A. J. & Olson, G. B.  Effects of Carbon on Fe-Grain-Boundary Cohesion: First-Principles Determination.  _Phys. Rev. B_ 53, 7504–7509.
  * 26 Fraczkiewicz, A.  Influence of Boron on the Mechanical Properties of B2-Ordered FeAl Alloys.  _Mater. Trans. JIM_ 41, 166–169 (2000).
  * 27 Wang, J., Janisch, R., Madsen, G. K. H. & Drautz, R.  First-Principles Study of Carbon Segregation in Bcc Iron Symmetrical Tilt Grain Boundaries.  _Acta Mater._ 115, 259–268 (2016).
  * 28 Miyazawa, N., Hakamada, M. & Mabuchi, M.  Atomic bond-breaking behaviour during grain boundary fracture in a C-segregated Fe grain boundary.  _Phil. Mag. Let._ 97, 311–319.
  * 29 Kholtobina, A. S., Ecker, W., Pippan, R. & Razumovskiy, V. I.  Effect of alloying elements on hydrogen enhanced decohesion in bcc iron.  _Computational Materials Science_ 188, 110215 (2021).
  * 30 Fors, D. H. R. & Wahnström, G.  Nature of Boron Solution and Diffusion in $\alpha$-Iron.  _Phys. Rev. B_ 77, 132102 (2008).
  * 31 Felfer, P. J. _et al._ A New Approach to the Determination of Concentration Profiles in Atom Probe Tomography.  _Microscopy and Microanalysis_ 18, 359–364 (2012).
  * 32 Su, X., Tang, N.-Y. & Toguri, J. M.  Thermodynamic evaluation of the fe–zn system.  _Journal of Alloys and Compounds_ 325, 129–136 (2001).
  * 33 White, C. L. & Coghlan, W. A.  The Spectrum of Binding Energies Approach to Grain Boundary Segregation.  _Met. Mat Trans A_ 8, 1403–1412.
  * 34 Ashiri, R. _et al._ Liquid metal embrittlement-free welds of Zn-coated twinning induced plasticity steels.  _Scripta Materialia_ 114, 41–47 (2016).
  * 35 Scheiber, D., Prabitz, K., Romaner, L. & Ecker, W.  The Influence of Alloying on Zn Liquid Metal Embrittlement in Steels.  _Acta Materialia_ (2020).
  * 36 Rabkin, E. _et al._ High-Temperature Diffusion-Induced Grain Boundary Migration in an Fe-5 at.% Al Bicrystal during Zinc Diffusion.  _Mater. Sci. Forum_ 126–128, 321–324.
  * 37 Dohie, J. S., Cahoon, J. & Caley, W.  The grain-boundary diffusion of zn in $\alpha$-fe.  _JPED_ 28, 322–327 (2007).
  * 38 Tahir, A., Janisch, R. & Hartmaier, A.  Hydrogen embrittlement of a carbon segregated $\sigma$5 (310)[001] symmetrical tilt grain boundary in $\alpha$-fe.  _Mater. Sci. Eng. A_ 612, 462–467 (2014).
  * 39 Scheiber, D., Romaner, L., Pippan, R. & Puschnig, P.  Impact of Solute-Solute Interactions on Grain Boundary Segregation and Cohesion in Molybdenum.  _Phys. Rev. Mater._ 2, 093609.
  * 40 Kresse, G. & Hafner, J.  Ab Initio Molecular Dynamics for Liquid Metals.  _Phys. Rev. B_ 47, 558 (1993).
  * 41 Kresse, G. & Furthmüller, J.  Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set.  _Comput. Mater. Sci._ 6, 15–50 (1996).
  * 42 Kresse, G. & Furthmüller, J.  Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set.  _Phys. Rev. B_ 54, 11169–11186 (1996).
  * 43 Kresse, G. & Joubert, D.  From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method.  _Phys. Rev. B_ 59, 1758–1775 (1999).
  * 44 Perdew, J. P., Burke, K. & Ernzerhof, M.  Generalized Gradient Approximation Made Simple.  _Phys. Rev. Lett._ 77, 3865.
  * 45 Perdew, J., Burke, K. & Ernzerhof, M.  Perdew, Burke, and Ernzerhof Reply.  _Phys. Rev. Lett._ 80, 891.
  * 46 Ebner, A. S. _et al._ Grain boundary segregation in Ni-base alloys: A combined atom probe tomography and first principles study.  _Acta Mater._ 221, 117354 (2021).
  * 47 Scheiber, D., Jechtl, T., Svoboda, J., Fischer, F. & Romaner, L.  On Solute Depletion Zones along Grain Boundaries during Segregation.  _Acta Mater._ 182, 100–107.
  * 48 Kamachali, R. D.  A model for grain boundary thermodynamics.  _RSC Adv._ 10, 26728–26741 (2020).
  * 49 Ratanaphan, S. _et al._ Grain boundary energies in body-centered cubic metals.  _Acta Mat_ 88, 346–354 (2015).
  * 50 Darvishi Kamachali, R. _et al._ Segregation-assisted spinodal and transient spinodal phase separation at grain boundaries.  _npj Comput. Mater._ 6, 191 (2020).

## Acknowledgments

The authors gratefully acknowledge the financial support under the scope of
the COMET program within the K2 Center “Integrated Computational Material,
Process and Product Engineering (IC-MPPE)” (Project No 886385). This program
is supported by the Austrian Federal Ministries for Climate Action,
Environment, Energy, Mobility, Innovation and Technology (BMK) and for Digital
and Economic Affairs (BMDW), represented by the Austrian Research Promotion
Agency (FFG), and the federal states of Styria, Upper Austria and Tyrol. X. Z.
is supported by the Alexander-Humboldt-Stiftung. R. D.K. gratefully
acknowledges support from German Research Foundation (DFG) through projects DA
1655/2-1 and DA 1655/3-1. G. D. gratefully acknowledges support by the ERC
Advanced Grant GB-Correlate (Grant Agreement 787446).

## Author contribution

G. D., W. E. and L. R. secured funding. C.H. L. and A. A. designed the
experiments and C.H. L. supervised the project. A. A. conducted the electron
microscopy experiments including STEM and FIB/SEM.
X. Z. conducted the APT experiments. D. S. performed the atomistic
simulations. R. D. K. executed the thermodynamic and phase-field simulations.
C.H. L., L. R. and B. G. contributed to the data analysis. A. A., D. S. and
C.H. L. wrote the paper. X. Z., B. G., R. K. D., W. E., L. R. and G. D.
revised the paper.

## Competing interests

The authors declare no competing interests.