# Faceting diagram for Ag segregation induced nanofaceting at an asymmetric Cu
tilt grain boundary

Nicolas J. Peter<EMAIL_ADDRESS>Maria J. Duarte<EMAIL_ADDRESS>Christoph
Kirchlechner<EMAIL_ADDRESS>Christian H. Liebscher<EMAIL_ADDRESS>Gerhard Dehm<EMAIL_ADDRESS>Max-Planck-Institut für Eisenforschung GmbH, Max-
Planck-Strasse 1, 40237 Düsseldorf, Germany

###### Abstract

In this work, we experimentally establish the isothermal nanofacet evolution
at an asymmetric tilt grain boundary in the Cu-Ag system using a diffusion
couple approach. We investigate the nanofacet formation along the grain
boundary in dependence of the Ag solute excess concentration. The initial
grain boundary dissociates into asymmetric Ag-lean segments and Ag-rich
symmetric (210) segments. Increasing Ag excess leads to an increase in Ag-rich
facet segment length, while the length of the asymmetric facets remains
constant. From this, we construct a grain boundary nanofaceting diagram
deduced from our experiments relating local atomic structure, overall
inclination and Ag solute excess.

###### keywords:

Scanning/transmission electron microscopy (STEM), Copper, Copper alloys, Grain
boundary segregation

Grain boundaries (GBs) are interfaces separating adjoining crystals with
different misorientation. They are amongst the most important material defects
and their associated structure and properties determine their influence on the
behavior of polycrystalline materials. In early work, Gibbs established that
interfacial transitions can be described by equilibrium thermodynamics [1] and
Hart later proposed that transitions at GBs are possible and referred to them
as “two-dimensional phase transitions” [2]. The thermodynamic description of
these transitions was extended by Cahn and Rottman [3, 4] who categorized them
into faceting and congruent (all 5 degrees of freedom remain constant)
transitions. Both types, non-congruent (faceting) and congruent transitions
are referred to as GB phase transformations [5] or synonymously GB complexion
transitions [6, 7]. However, these transitions are typically studied in
perfectly symmetric and planar GBs [8, 9, 10] and mostly derived from indirect
experimental measurements [11, 12] or atomistic simulations [13]. Instances of
how complex such GB transitions can be and how factors like temperature and
chemistry can influence a GB’s structure were recently demonstrated by
scanning transmission electron microscopy (STEM). Hu et al. found a
temperature dependent segregation behavior including a first order congruent
transition at low temperatures in a planar Au-doped Si GB using atomistic
calculations [14]. Very recently, a complex co-segregation pattern including
segregation induced symmetry changes and order losses at a planar WC grain
boundary was discovered [15]. A comprehensive review on evidence of grain
boundary transitions can be found in a recent review article [16].

Already Cahn discussed that most GB transitions involve faceting [3] and such
transitions have been observed experimentally in many materials [17, 18, 19].
Faceting-roughening phenomena of GBs were recently summarized by Straumal et
al. for a great amount of different grain boundary types and in different
material systems [20]. The majority of experimental and simulation work
established a clear dependence of faceting-defaceting transitions on
temperature in pure metal GBs [21, 22, 23, 18]. Some work also focused on how
structural defects of a grain boundary (GB dislocations) may influence
faceting by pinning or dragging facets during defect motion [24]. Transitions
influenced by chemical stimulus, for instance by segregation, are much less
understood in the case of GB faceting as compared to the segregation behavior
of planar boundaries. Changing the chemistry at GBs by adsorption of solute
excess significantly changes the energy of such boundaries and consequently
structural transitions are likely to occur. Early work showed structural
transitions at a low angle grain boundary in the Fe-Au system [25]. Faceting
transitions were frequently observed in the last decades in the Cu-Bi binary
system since Bi promotes GB embrittlement [26]. Experimentally, only one
carefully performed in situ experiment conducted by Ference and Baluffi
unambiguously demonstrated that reversible faceting-defaceting can be induced
by solute adsorption [27]. However, faceting occurred on a scale of several
tens to hundreds of nanometers and the characterization of the atomic GB
structure and chemistry was not possible at that time. Four decades ago Loier
and Boos demonstrated already how small additions of Bi induce striations and
faceting of Ni grain boundaries [28]. Yu et al. recently found distinct
segregation patterns of Bi solutes at a microfaceted general GB in Ni [29]
after having shown that such patterns may be the underlying reason for
detrimental effects of Bi segregation on mechanical properties in Ni [30]. Our
recent work combining atomic resolution imaging and atomistic modelling
demonstrated that Ag segregation can act as chemical trigger promoting a
nanofaceting transition of an asymmetric tilt grain boundary in Cu [31].
However, temperature [32], pressure [33] or solute excess concentration [34,
27] strongly influence GB transitions [35] and their concentration dependence
is usually established by atomistic modeling.

Here, we report the experimental assessment of GB plane and faceting evolution
in dependence on the Ag solute excess concentration at an initially asymmetric
tilt grain boundary in Cu. The concentration dependence was observed using
atomic resolution STEM in combination with energy dispersive X-ray
spectroscopy (EDS) and atom probe tomography (APT) in close vicinity to the
interface of a Cu-Ag diffusion couple. A Ag reservoir was sputter deposited on
top of a bicrystal containing the GB to create the diffusion couple. For
consistency, we refer to the surface of the bicrystal (the interface to the Ag
reservoir) as surface _._

_A pure Cu reference boundary of the bicrystal’s top surface before Ag
deposition was observed at three distinct magnifications (Fig. 1b)._
_Temperature induced faceting of that boundary was already excluded in our
previous work[31]._ The boundary appears to be entirely flat for at least 13
µm from the _top_ __ surface into the bulk as determined by STEM, even at
higher magnification. Atomic resolution imaging reveals the local atomic
arrangement and although some sub-nanometer roughness can be associated to the
asymmetric GB _;_ we refer to this boundary as flat reference boundary. The
reference GB was determined to be close to an asymmetric 34°[001] (920)/(110)
boundary _,__which is in close agreement to our previously investigated GB
showing the Ag induced nanofaceting[31]_. After Ag diffusion, the overall
macroscopic grain boundary (observed at low magnification) is no longer
straight and a seemingly continuous curvature from the bulk to the surface was
induced. A schematic representation of the grain boundary after segregation is
given in Fig. 1a) and an _experimental HAADF STEM_ micrograph of a part of the
grain boundary _close to the surface_ __ at low magnification in Fig. 2.
Micrographs were then acquired at certain locations and at high magnifications
along the segregated GB to study the overall plane evolution connected with
the nanofacet formation and the associated Ag excess. Representative locations
(_see Fig. 2 positions_ 4 to 1, _from Cu(Ag) GB close to the_ _surface_) are
marked in the overview image and are presented in more detail below. We
observe a gradual transition from a flat segregated boundary (1 in Fig. 2,
compare _STEM-EDS results_), in close resemblance to the Ag-free reference, to
a symmetric $\sum$5 (210) GB (4 in Fig. 2) as further indicated by the
adoption of the kite motif [31, 13] in the enlarged area next to the
micrograph of position 4. The intermediate GB adopts a nanofaceted state
containing Ag-rich, symmetric $\sum$5 (210) segments and newly formed,
asymmetric and Ag-lean segments with a GB plane close to (320)/(100). Almost
all kite tip positions are occupied by Ag (bright columns in HAADF STEM). In
addition, we occasionally observe image contrast indicating Ag occupation of
non-kite tip positions at the GB, as well. Therefore it is reasonable to
believe that the symmetric GB close to the surface is covered close to a
monolayer of Ag. The symmetric $\sum$5 (210) GB plane was measured to be
$\sim$ 20º inclined with respect to the non-faceted, asymmetric (920)/(110)
reference boundary plane.

The precise solute excess concentration and localized elemental distribution
were determined along the boundary by APT and STEM-EDS, respectively. An APT
specimen extracted close to the sample surface (Tip 1, _position 4 in Fig. 2_)
was found to have a peak concentration of $\sim$3.6 at. % Ag (black line) as
determined from the integrated line profiles across the GB (Fig. 3a, upper
graph). A specimen extracted from below the sample surface (Tip 2, _at
position 3 in Fig. 2_) only contained a peak solute excess of $\sim$2.4 at. %
Ag (Fig. 3a, lower graph). _A depletion zone is visible for the Ag
concentration next to the enriched GB in both specimen. In the case of the
less segregated GB (Tip 2), the Ag concentration recovers towards the outer
APT needle’s surface and reaches saturation at a level of about 1.3 at. % at
about 25 nm from the GB. For Tip 1, the depletion extends much further and
saturation is not reached inside the specimen volume. From the course of the
concentration profile we expect a saturation level of around 1.7 at. % at
about 45 nm from the GB deduced from a second order polynomial fitting. To
determine the respective bulk Ag concentration more reliable, we created
cylinders of the same dimensions (25 nm x 10 nm x 40 nm) inside the two
volumes and placed them parallel to the GB at a fixed distance of 20 nm (in
saturation level of Tip 2). Bulk concentrations of 1.43_ __ ± 0.015 ___at. %
and 1.23_ __ ± 0.011 a _t. % were extracted for Tip 1 and Tip 2,
respectively._ _The precise location of the extracted tips within a few µm is
hardly possible to be determined after FIB milling preparation. The bulk Ag
concentrations appear reasonable considering the low Ag solubility according
to the equilibrium phase diagram[36]_. In addition, Ag density maps of thin
slices (1 nm thickness) through the reconstructed volumes of these two APT
tips \- one from a surface-near region (Tip 1) and one extracted from an
approximate location 3 in Fig. 2 (Tip 2) - revealed a non-faceted, Ag-rich
boundary close to the surface and further towards the bulk a faceted, Ag-rich
boundary. This transition agrees well with our experimental STEM micrographs.
Across these two boundaries we calculated the solute excess concentration
following our previously applied approach [31, 37] and revealed _for Tip 1_ a
Ag excess concentration of 4.96 at/nm2, while the faceted GB ___(Tip 2)___
showed an average excess concentration of 3.39 at/nm2. _Based on the latter,
we chose a maximum value for the color bar to qualitatively best show the
faceted GB state._ These results appear reasonable, as STEM results revealed
preferential segregation to symmetric $\sum$5 (210) GB portions, which
dominate at the surface, but contribute less for deeper measurement locations
into the bulk due to the increasing incorporation of asymmetric Ag-lean
segments. In addition, the diffusion gradient from the surface into the bulk
reduces the Ag excess concentration at the GB, which therefore appears to be
coupled with the facet lengths. The excess of the non-faceted, _symmetric_
$\sum$5 (210) boundary close to the surface is just slightly below the
monolayer solute excess of roughly 6 at/nm2, _which is calculated by the
number of atoms on a (210) plane unit area_. However, STEM micrographs at the
very surface revealed some areas in which two bright atomic columns appear
next to each other, which is why we assume to have at least monolayer coverage
at the very surface of the diffusion couple, i.e. close to the Ag reservoir.
The drawback of such compositionally sensitive APT measurements is the lack of
atomically resolved structural features in the analyzed volume. Consequently,
STEM-EDS was used in order to correlate the occurrence of the three structural
states observed with their solute excess at different locations along the
segregated boundary. Integrated intensity line profiles for the Ag-L$\alpha$
peak were extracted from EDS maps at the investigated locations and three
representative profiles (close to positions 1, 2 and 4) for the three observed
GB states are plotted after applying of a moving average algorithm for
visibility in Fig. 3b) normalized to the background intensity. The inset shows
EDS spectra integrated in a region of about 10 x 15 nm2 of the expected
Ag-L$\alpha$ peak for a GB containing area and an area inside one grain for
comparison. We would like to point out that EDS maps were acquired in zone
axis orientation immediately after image acquisition to avoid tilting and loss
of spatial correlation. In this case, quantification of the EDS data is no
longer applicable through the Cliff-Lorimer method and intensive simulation
work would have to be performed to account for effects like beam spreading and
electron channelling [38]. Therefore, we do not give absolute concentration
values from EDS but normalize our results to the concentration expected for
monolayer coverage by integrating the peak intensity and collapsing it to a GB
width of 0.12 nm, as this width provides a Ag reference concentration of 100 %
for the data set closest to the surface. This assumption is based on our
experimental _HAADF STEM results. STEM-EDS analyses_ show a clear increase of
Ag from the bulk towards the surface.

The combination of structural and compositional characterization of the
observed faceting evolution enables a comprehensive view on the evolution of
individual facet segments. In fact, we composed a segregation-induced GB
faceting diagram for the investigated GB under the chosen diffusion conditions
(Fig. 4). Plotting the facet segment length against the relative Ag monolayer
coverage (Fig. 4a) as determined by EDS along the GB (Fig. 3b) reveals a
concentration window for faceting to occur. While the asymmetric facet segment
length was found to be independent of the Ag excess and remained at a length
$l$ of about 1 nm, the symmetric facet segments almost linearly grew with
increasing excess concentration starting from 1 nm (R-square of 0.96).
Therefore, the reason for an increasing global GB inclination lies in growing
symmetric facet segments. Thus there are three clearly distinguishable GB
states as a function of overall Ag excess solute: (i) non-faceted, asymmetric
and Ag-lean (Figure 2-1), (ii) preferentially Ag segregated and nanofaceted
(Figure 2-2 and 2-3) as well as (iii) non-faceted, symmetric and Ag-rich
(Figure 2-4).

The present results confirm our previous findings [31] that after Ag
segregation induced facet formation there is preferential segregation
occurring to only the symmetric facet segments, while the asymmetric segments
remain Ag-lean. To make a better connection between facet segment length, Ag
segregation and especially overall GB inclination, we plotted the relative Ag
excess concentration as obtained by EDS under the assumption of full monolayer
coverage for the symmetric $\sum$5 (210) GB close to the surface (Fig. 4b). At
this point, the boundary was about 20° inclined from the asymmetric reference
GB. _To describe the relation between Ag concentration and facet length, we
normalize the ratio of the asymmetric segment length (ASL) and the symmetric
facet segment length (SSL) using the “facet segment ratio” parameter FSR. FSR
is calculated as $FSR=SSL/(ASL+SSL)$._ Consequently, the ___Ag-rich,
symmetric_ $\sum$5 (210) GB close to the surface does not show any faceting
and FSR = 1 (ASL = 0). The purely asymmetric reference GB at inclination 0°
has consequently no symmetric segments and thus FSR = 0. The ASL was
determined above to be _approximately_ __ constant with a length of $\sim$1 nm
_for the faceted GB_. Under the assumption of full monolayer coverage for FSR
= 1 supported by STEM observations, we drew a dashed line (red) to indicate an
anticipated linear decrease of Ag excess with a linearly decreasing amount of
the symmetric segment fraction. Our experimental results are given as
individual data points and are linearly fitted (white) with a R-square value
of 0.93. Indeed, our results follow the anticipated, ideal line in reasonable
agreement (compare red and white lines), which leads us to the conclusion that
for the nanofaceted boundary portion symmetric facet segments always are at
least close to monolayer coverage, while it indicates that asymmetric segments
of the nanofaceted grain boundary section are close to being Ag-free. This
extends our previous findings deduced from a GB faceted at a single Ag
concentration to the entire faceting range. No faceting was observed below FSR
= 0.5, which means below these equisized nanofacets, faceting disappears and a
purely asymmetric GB takes up the Ag excess. However, the excess uptake does
not exceed about 30 % of the symmetric $\sum$5 (210) GB’s excess. This does
not necessarily imply a generally fixed saturation level, as it depends on the
local chemical potential, which is influenced also by the annealing
temperature and subsequent cooling/quenching conditions. In light of an
extrapolation of the facet data to FSR = 0 in Figure 4b _(white dashed line)_
, the asymmetric GB should have a _Ag_ concentration of around 16 % of a
$\sum$5 (210) boundary. As this is less than the actually observed 30 %, the
asymmetric GB seems much more favorable to be preserved compared to inducing a
GB dissociation. This agrees well with our previous MD simulation results,
which indicate Ag solute excess being absorbed at the asymmetric boundary
already starting at a chemical potential around $\mu=0.35\,eV$, while the
symmetric $\sum$5 (210) boundary starts taking up Ag only above chemical
potentials of $\mu=0.5\,eV$ [31]. Thus, Ag uptake of the asymmetric boundary
before the threshold concentration seems to be a prerequisite to induce the
nanofaceting. Finally, the jump from about 30 % relative Ag monolayer coverage
(FSR = 0) to about 50 % when nanofaceting is induced, strongly indicates a
first order GB transition occurring.

Our experimental findings enable us to propose a mechanistic picture of the
observed faceting phenomenon. We showed previously experimentally and by
simulations that heat treatment at 800°C (1073 K) does not induce nanofaceting
at the asymmetric GB studied here, while Ag segregation does. Consequently,
heating the boundary to 800ºC leaves the boundary intact, possibly with
increased disorder. Mishin and co-workers showed in a series of studies on Cu-
Ag GBs that increasing temperature, but also increasing Ag solute excess can
significantly influence how ordered a GB is referred to the perfect bulk
lattice [39, 40, 41, 42]. At such high temperatures, Ag atoms are going almost
completely in solid solution and diffuse from the surface through the bulk and
along the boundary creating a Ag concentration gradient. The solidus line was
likely not crossed, as no homogeneous nucleation of Ag precipitates was
observed inside the grains. Upon cooling, the disordered grain boundary
restores its low temperature structure, while still remaining in the solid
solubility region according to the equilibrium phase diagram [36]. Judging
from the determined bulk Ag concentration of about 1.5 at. %, the solidus line
is crossed at around 550°C (823 K). At this point, Ag starts to segregate
towards the GB upon further cooling to minimize the energy of the system. The
amount of Ag segregating to the boundary is depth dependent due to the created
concentration gradient. Eventually, a critical threshold concentration is
reached to initiate nucleation of the symmetric $\sum$5 (210) facets, since
the observed normal kite structure (Fig. 2, 2-4) can absorb the highest amount
of Ag excess and leads to the largest reduction in energy compared to
segregation to the initial asymmetric GB [31]. The nucleation of symmetric Ag-
rich facets is the initial step dissociating the asymmetric GB into a
nanofaceted boundary. The local amount of Ag solute excess at the boundary,
which is dictated by the concentration gradient in the bulk, determines the
density of nucleation sites and provides the driving force for facet growth.
Following the trend of having more Ag towards the surface, symmetric facets
grow longer towards the surface until a continuous $\sum$5 (210) GB is formed
close to the surface. Below an estimated critical Ag threshold concentration
of around 0.6 at.% for the bulk Ag content faceting will not occur considering
a constant segregation factor
($\beta=\frac{GBconcentration}{Bulkconcentration})$. However, as the bulk
diffusion gradient cannot be quantified here accurately, the threshold
concentration cannot be determined precisely neither. The nucleation of the
Ag-rich $\sum$5 (210) facet segments at the initially asymmetric GB is
accompanied by the nucleation of the asymmetric facet segment and the
associated GB disconnections or facet junctions, which are also necessary to
migrate the boundary to compensate for the overall change in inclination
towards the surface. The defects are likely involved in the migration of the
GB to compensate for the inclination change induced by nucleation the
symmetric facet segments. For instance, the migration of a flat, symmetric GB
was shown theoretically for an Al $\sum$7 GB to function via a nucleation
process of islands on the grain boundary plane [43] (also regarded as
disconnection nucleation for $\sum$13 and $\sum$17 Cu boundaries [44, 45]) and
to be highly temperature dependent between 500 K to 700 K [43], which is close
or even in the temperature range we expect our facet nucleation to occur. The
question remains, why a nanofaceted GB portion is found instead of coarse
facets or even just a curved GB. In general, the energy of faceted GB
following Hamilton et al. is composed of two parts: (i) the contribution of
the GB energies of the two facet segments $\gamma_{1,2}$ along with the
contribution of facet junctions $\gamma_{j}$ as well as (ii) the interaction
between facet junctions $\gamma_{j-j}$. The overall GB energy $\gamma_{GB}$
can thus be described as
$\gamma_{GB}=\gamma_{1}+\gamma_{2}+\frac{2\gamma_{j}}{\varLambda}+\frac{\gamma_{j-j}}{\Lambda}$,
with $\varLambda$ being the facet period (length). For our purposes we neglect
the interaction of the junction term here leading to
$\gamma_{GB}=\gamma_{1}+\gamma_{2}+\frac{2\gamma_{j}}{\varLambda}$. Hamilton
et al. demonstrated by simulation work that the GB inherently wants to create
equal sized, coarse facets to reduce the spacing of the GB facet junctions and
thus $\gamma_{GB}$ as much as possible [46]. Although this theory was
confirmed experimentally by Medlin et al. [47] and atomistic simulations by Wu
et al. [48], this analysis does not consider segregation and kinetic effects.
Wu et al. found that migration kinetics during facet coarsening can promote
the formation of finite sized facets. Instead of a continuous decrease in
energy for increasing facet periods, migration of facet segments can impose a
multitude of energy barriers depending on the structure of the facet segment
resulting in the inhibition of further migration and therefore stabilization
of finite length facets. Here, the energy change due to segregation can be
expressed generally through
$\Delta\gamma_{GB}=\Delta\gamma_{ASL}+\Delta\gamma_{SSL}+\frac{2\Delta\gamma_{j}}{\varLambda}$.
However, considering the preferential segregation only to the symmetric
portion and no noticeable segregation to facet segment junctions, the energy
reduction is mainly attributed to the reduction in energy due to the formation
of symmetric $\sum$5 (210) segments thus following
$\Delta\gamma_{GB}=\Delta\gamma_{2}$. Nevertheless, it would be interesting to
study effects of segregation to junctions and how they influence the
energetics of the systems including the interaction between junctions, which
was neglected here. Segregation to facet junctions was for example recently
observed at faceted Si [49] and Cu GBs [50].

In conclusion, we present the first GB faceting diagram by studying the
influence of Ag solute excess concentration on facet formation in an
asymmetric tilt grain boundary via aberration corrected STEM, STEM-EDS and
APT. After having established a Ag concentration gradient by a diffusion
couple approach, we were able to distinguish different structural arrangements
(faceting states) along the boundary as a function of Ag solute excess
concentration. _The total length of the $\sum$5 GB increases by more than 15%
compared to its initial (Ag-free) position, revealing a lower energy state
after Ag segregation._ In the bulk at low Ag solute excess relative to the
surface, the initially asymmetric GB remains structurally unaffected but takes
up Ag. Exceeding a threshold amount of solute excess, the boundary undergoes a
first order transition and becomes nanofaceted. One facet segment ___changes
its grain boundary plane, but_ remains asymmetric, Ag-lean and constant in
length, while the other segment was determined to be a symmetric $\sum$5 (210)
type, with increasing length towards the surface and being enriched in Ag. At
the surface, highest amounts of available Ag allow for a planar $\sum$5 (210)
GB containing close to a monolayer of Ag. Similar GB phase diagrams have been
established for different transitions like GB premelting, intergranular film
formation or for multilayer segregation patterns as a function of
concentration [16]. However, only few such GB phase diagrams could be
established, yet. We present here the first experimental GB nanofaceting
diagram as a function of solute excess concentration, similar to GB
segregation diagrams as proposed by Lejček and Hofman for iron GBs [51] or
Watanabe et al.’s hardening/segregation GB diagrams in iron alloys [52], but
focusing on the atomic grain boundary structure evolution. Establishing such
diagrams, analogous to bulk phase diagrams, may offer new possibilities for
microstructure engineering in order to tune macroscopic materials properties.
Although the preferential segregation might appear as an exception from the
Langmuir McLean adsorption behavior in terms of homogeneous GB decoration, the
individual segments still follow Langmuir McLean. Regarding the asymmetric
segregated and the symmetric $\sum$5 (210) GB, we were able to use the
Langmuir McLean relation to deduce the ratio of their respective segregation
energies and found that the Gibbs segregation energy of the symmetric boundary
is approximately 1.08 times the energy of the asymmetric GB. Nevertheless,
adjusted segregation models accounting for such faceting transitions are
becoming necessary for these cases. It has to be noted that a continuously
curved grain boundary, in contrast to a faceted boundary may be connected
differently to physical properties such as mobility or plastic deformation. In
fact, continuous curvatures at lower magnifications might be related to
nanofaceting transitions as observed in the present study more often for doped
material systems. Still, such phenomena would only be resolved with adequate
characterization techniques of highest resolution.

## Methods

Bicrystal growth and sample preparation. To achieve the structure-chemistry
correlation for Ag segregation induced nanofaceting, we grew a Cu bicrystal
containing the asymmetric grain boundary using the Bridgman technique. The
[001] crystallographic directions of the two seed crystals were aligned
parallel with a misorientation of 54∘ around this common axis to ensure the
formation of a tilt GB with a common [001] zone axis orientation, important
for the STEM analysis. Additionally, an asymmetric inclination of 31∘ was
chosen for the as-grown reference boundary. From the grown bicrystal, discs
were cut perpendicular to the [001] growth direction and metallographically
prepared to obtain best surface quality with a final electropolishing step. A
reference lamella was extracted from this disc for STEM investigations using
focused ion beam (FIB) preparation. Segregation was achieved by thermal
annealing at 800∘C under high vacuum conditions for 120 hours. In our previous
work we could exclude already that these conditions influence the pure, Ag-
free, grain boundary structure [31]. Ag was sputter deposited to a thickness
of 500 nm onto the same disc used as reference, to extract a Ag segregated GB
as close to the reference state as possible. In this way a diffusion couple
arrangement was created between Ag and the GB-containing Cu. No additional
metallographic preparation was performed to not alter the state of the GB
artificially. Thus, although a slight spatial misalignment, we believe to
examine the same GB before and after the diffusion process.

Scanning transmission electron microscopy. The FIB prepared lamella was
investigated after thermal treatment using a probe-corrected STEM in a Thermo
Fischer Scientific Titan Themis 60-300 STEM machine. A schematic overview of
the crystallography and diffusion couple geometry is provided in Fig. 1(a).
The shown micrographs were acquired in high-angle annular dark field imaging
conditions to benefit from its Z-contrast conditions, i.e. the semi-collection
angle was set to 76 - 200 mrad. EDS maps were acquired at selected locations
to correlate nanofaceting with Ag solute excess concentration in zone axis
orientation immediately after image acquisition to avoid tilting and thus loss
of spatial correlation. A Super-X windowless EDS detector was used at an
acceleration voltage of 300 kV.

Atom probe tomography. Quantification of Ag excess concentration at the GB
with respect to the matrix was obtained from atom probe tomography (APT)
reconstructions at specific regions of interest. APT tips were prepared by FIB
(same instrument used for TEM lamellae) [53], applying a final cleaning at 5
kV and 41 pA, ensuring a Ga content <0.1 at.% in the analyzed regions. APT
data was collected using a local electrode atom probe, LEAP 5000XS by Cameca
Instruments. The measurements were performed at a temperature of 50 K, in
laser mode with an energy of 60 pJ, using a pulse repetition rate of 250 kHz
and a detection rate of 0.007 atoms per pulse.

## Acknowledgments

The authors cordially thank Tobias Oellers from the Ruhr University Bochum for
Ag deposition on our Cu bicrystals to create the investigated diffusion
couples. The funding and support by the European Research Council (ERC) under
the EU’s Horizon 2020 Research and Innovation Programme is gratefully
acknowledged by NJP, MJD and GD (ERC Advanced Grant, GB-Correlate, Grant No.
787446).

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Figure 1: (a) Schematic representation of the diffusion couple’s arrangement
and the crystallography of the grown bicrystal containing the asymmetric tilt
grain boundary and how the boundary behaves after segregation. (b) HAADF-STEM
micrographs of the asymmetric, Ag-free, reference boundary at different
magnifications. Micrographs are in [001] zone axis orientation. Figure 2: The
curved Ag segregated GB as an overview image at lower magnification along with
micrographs along a boundary over a distance of about 15 µm indicating the
changes from an asymmetric GB (bulk) over the nanofaceted state with
increasing symmetric facet segments to a solely symmetric GB (surface) and an
atomic resolution micrograph to capture the symmetric (210) GB’s kite
structure. All HAADF-STEM micrographs were acquired in [001] zone axis
orientation. Figure 3: (a) APT results of the Ag segregated GB. The extracted
concentration profile across the boundary is given, while Ag density maps are
shown representative for two different samples - one at the surface, one
deeper into the bulk - highlighting the different GB states. (b) STEM-EDS
results across the GB at three representative locations. In the nanofaceted
case, EDS information is collected across the GB containing multiple facets.
EDS data was collected in zone axis orientation at the exact location where
micrographs were recorded.  Figure 4: (a) GB faceting diagram presenting the
facet segment length evolution along the boundary as a function of Ag solute
excess concentration. Three distinct GB states appear: (i) asymmetric and not
faceted for low Ag excess, (ii) nanofaceted, preferentially segregated
boundary within a solute excess window and (iii) symmetric and not faceted
boundary for high Ag excess. (b) Correlation between faceting, inclination and
overall inclination of the GB including a linear fit through recorded data
points (white line), a straight line to highlight an expected linear
dependence of Ag content in facets (red) and the boundary specific Ag excess
at the asymmetric GB.