Direct visualization of the existence of surface local chemical order in a high-entropy CoCrFeMnNi alloy

Domain: biology
Published: 2026-03-28
Editorial outcome: minor_revision

Abstract
The impacts of local chemical order (LCO) on the physical properties of high-entropy
alloys (HEAs), have been widely discussed. However, the difficulty in unambiguously observing
LCO with high precision poses a great challenge in establishing microscopic mechanisms
regarding the impacts of LCO on physical properties. Furthermore, it is still unclear whether the
LCO extends to HEA surfaces, which may impact surface-based properties, such as corrosion,
oxidation, and catalytic activities. Through the utilization of scanning tunneling microscopy
(STM), two surface LCO domains with corresponding √5×√5 𝑅 ±26.6° quasi-long-range
orderings (QLRO) are directly observed on a CoCrFeMnNi surface. Density functional theory
(DFT) calculations identify the LCO within QLRO supercells. The findings provide evidence of
the existence of surface LCO and demonstrate a method to directly observe the surface LCO of
HEAs. With the ability to unambiguously resolve elemental configuration at atomic scale, the
understanding of how LCO influences surface-based properties can be achieved, facilitating the
design of HEAs with tailored functionalities.

Introduction
Since the first realization in 20041,2, high-entropy alloys (HEAs) have gained increasing
attention due to a variety of promising properties and tunability in refractory applications3,
ductility4, mechanical strength4, creep resistance5, and electrocatalytic performance6. In addition
to having good combinations of multiple mechanical properties, HEAs host a multitude of design
options, such as changing elements and molar ratios among the elements. An emerging way to
further enhance and tune properties of HEAs is through the manipulation of local chemical order
(LCO), including chemical short-range order (CSRO) which has been shown to impact structural
stability 7, hardness8, strength9, stacking fault energy10, corrosion11, magnetization12, and
electrochemical behavior13, as well as enhance resistance to fatigue14 and irradiation damage15.
Some of the physical properties, such as corrosion resistance, oxidation resistance, and catalytic
activities, are presumably greatly impacted by the surface atoms. While the existence of the
surface LCO is still elusive, it is crucial to determine if the surface LCO does exist and, if it does,
what kind of surface LCO can be found. These types of information will facilitate the
understanding of the impact of LCO on surface-based properties of HEAs.

In equimolar HEAs, the existence of CSRO has been extensively discussed16–19. While
the formation of CSRO can be thermodynamic20 or mechanistic17, its impact on the structural
properties of HEAs is still one of the main debates in the field8,20–26. Some reports show that
CSRO has a strong impact on mechanical properties27 while others do not find a similar
conclusion24. A primary reason for these contentious results is because CSRO is very difficult to
be explicitly measured through existing characterization techniques. Most of the reported CSRO
relies on scattering-based techniques such as X-ray, neutron, and electron scattering8,23,28–30.
CSRO is proposed to appear as extra features in the regions of the reciprocal space with smaller
wavenumbers compared to the lattice Bragg peaks16,17. However, the observed extra features in
diffraction can have multiple origins19,31, resulting in challenging identification of CSRO. On the
other hand, energy dispersive X-ray spectroscopy (EDX) mapping using scanning transmission
electron microscopy (STEM) can supposedly provide atomic resolution images with elemental
sensitivity. However, since STEM measures columns of atoms that consist of all possible
elements in HEAs, it can only provide the elemental compositions in each column of atoms32,
failing to offer detailed elemental distributions at the atomic scale. Atom probe tomography
(APT) is another tool capable of revealing preferential neighbouring elements with nm-scale
resolution22,33. However, the viability of APT in deciphering the CSRO remains
inconclusive19,31,34.

In contrast, techniques using scanning tunneling microscopy (STM) are capable of
revealing atomic-scale images and sometimes element-sensitive information on the surfaces of
metals, making it potentially ideal for resolving CSRO in HEAs. STM is well-known for offering
high spatial resolution down to the atomic scale35,36. However, STM probes the electronic local
density of states (LDOS) near the Fermi energy, which typically does not contain elemental
information. Recently, by combining synchrotron X-rays with STM (namely SX-STM), SX-
STM was demonstrated to be capable of detecting core level electrons with superior spatial
resolution in various material systems37,38, including HEAs with sub-nm scale elemental
distributions mappings39. However, to clearly reveal and establish statistics of the LCO on HEA
surfaces, this requires a much larger SX-STM dataset on the elemental distributions than that
reported previously (~1.5 × 2.5 nm2)39. With limited synchrotron beamtime, it is very
challenging to reveal LCO in HEAs using SX-STM. On the other hand, although STM is
considered insensitive to elements, limited examples exhibiting element-sensitive STM images
have been reported40–46 with the following possible mechanisms: (i) differences in the work
function (Cu on Mo(110)43) ; (ii) differences in the tunneling matrix (Pt Ni (111)44);
25 75
(iii) differences in the surface states (Fe alloying with Cr(100)45); and (iv) differences in DOS near
the Fermi energy (Cu on W(110)46, PdAg(100), and PdAg(111)40). Among these element-
sensitive STM measurements, CSRO was discussed on (111) and (110) facets of Pt Co 41 and
25 75
PtNi(110) random alloys42. With these successful examples, it is argued that STM may be
capable of distinguishing elements with atomic resolution in HEAs based on the subtle
differences in the partial LDOS contributed by different elements near the Fermi energy. Here,
with the assistance of density functional theory (DFT), the contrast seen with STM can be
explained by the difference in the partial LDOS among different elements. The existence of
surface LCO on a HEA surface is revealed, and two types of LCOs with corresponding quasi-
long-range orders (QLROs) are clearly observed on the surface of a CoCrFeMnNi HEA. The
results shown here provide a foundation to understand the surface LCOs and their potential
impacts on the surface-based material properties of HEAs.

Results
Observations of the surface ordering of CoCrFeMnNi
The surface of the HEA is first characterized by low-energy electron diffraction (LEED),
as shown in Fig. 1(b). It is observed to be a predominantly single crystal square lattice matching
the pristine FCC (001) square lattice, depicted as the solid square in Fig. 1(a). The region inside
the bright Bragg diffraction spots (circled white) in the LEED pattern [Fig. 1(b)] exhibits fuzzy
features, indicating potential features on the surface with a longer length scale beyond the FCC
square lattice. LEED usually has a featureless and isotropic background near the center of the
image. This fact was used by Nascimento et. al.47 to subtract the background to reveal a small
intensity of the diffraction spots buried inside the background signal. The fuzzy features near the
center of LEED patterns were studied as diffuse LEED in literature towards the understanding of
the surface disordered atoms48,49. However, the indistinct nature of the features prohibits clear
understanding of this possible ordering. The electron beam spot size in LEED is in the order of
hundreds of μm, indicating that the hazy LEED patterns are a direct result of the multi-grain
measurements. Local measurements via STM can elucidate the origin of the ordering beyond the
FCC lattice ordering. Figure 1(c) shows a survey view of a STM topography in which two
distinct domains are observed. The fast Fourier transform (FFT) of the topography image is
shown in Fig. 1(d), where the white circled spots are FCC (001) square lattice peaks with an
atom-atom spacing 𝑑 = 2.6±0.1 Å, with additional peaks of the red and blue circled supercells
towards the center of the plot. Unlike the LEED pattern, the FFT image of the STM topography
presents sharp, bright features at wavenumbers smaller than the square lattice peaks, allowing for
a detailed analysis of this extra order. As shown in Fig. 1(d), red and blue circled spots
correspond to the two orderings in different domains where both domains show different
orientations which are shown more clearly in the FFT images [Fig. 1(g) and 1(h)] of the cropped
topography images [Fig. 1(e) and 1(f) respectively] , where only one ordering that corresponds to
one particular domain is present. The FCC(001) surface square lattice periodicity is extracted by
measuring the magnitudes of the reciprocal vectors q and q , which are defined as |𝒒| = 1.
1 2 𝑑
In both domains, four supercell periodicities, 𝑑 , are measured from the FFT images (Fig. 1(g) and
SC
(h), two 𝑑 from each domain): 𝑑 = 6.3±0.1 Å, 𝑑 = 5.8±0.1 Å, 𝑑 = 6.3±
𝑆𝐶 SC,1 SC,2 SC,3
0.1 Å,and 𝑑 = 5.6±0.1 Å, which are averaged to 𝑑̅̅̅̅̅ = 6.0±0.1 Å. The underlying FCC
SC,4 SC
square lattice can be seen in the cropped topography [Figs. 1(e) and 1(f)]. It is clear that the
square lattices in the two domains are identical, indicating that the two domains share the same
underlying FCC square lattice. This is also confirmed in Fig. 1(d), where grid lines extend from
red and blue domain peaks and meet at the FCC square lattice spots.

√𝟓×√𝟓 𝐑±𝟐𝟔.𝟔° Quasi-long-range order (QLRO)
The nature of the observed orderings in the two domains is revealed through a detailed
analysis of the atomic-scale STM topography. Figure 2(a) shows an enlarged region of Fig. 1(c),
exhibiting an area containing two neighboring domains with atomic resolution. A disordered
region with a width of ~1 nm between the two ordered domains is observed. The domain
boundary width varies slightly but remains in the order of ~1 nm. A domain boundary can be
seen more clearly in the FFT spot-filtered topography in Fig. 2(b) (the spot-filtered process is
described further in Supplementary Fig. 2). The two ordered domains exhibit a supercell
periodicity corresponding to √5×√5 R±26.6° with respect to the FCC (001) square lattice, as
illustrated with red, blue and black squares in Figs. 2(c) and 2(d), respectively. The two patterns
cannot be obtained by symmetrical operations from one to the other, meaning that they are not
equivalent. It is worth noting that the elemental distribution of CoCrFeMnNi determined by SX-
STM39 exhibits a certain level of similarity to this ordering chemically, as depicted in
Supplementary Fig. 3. The apparent heights at each atomic location have been analyzed (see
Supplementary Figs. 5-12) and summarized in Fig. 2(e). Here, the average height of the brightest
atom (red atomic sites in Figs. 2(c) and 2(d) superlattices) in each STM image is used as a
reference point as described in Supplementary Fig. 13. In Figs. 2(c) and 2(d), atomic sites are
labeled with the ranking of the apparent heights (from highest to lowest: red, green, yellow,
purple, blue) in both supercells. Upon closer inspection, the apparent heights of the atoms vary
across different supercells, i.e. without explicit translational symmetry. Thus, the long-range
order observed here is denoted as quasi-long-range order (QLRO). This is also the reason why
the height uncertainty at each position type in Fig. 2(e) is about 3-5 pm. Considering the
uncertainty in the apparent heights, two groups are defined: (i) three bright positions (red, green,
and yellow) and (ii) two dark positions (purple and blue).

Quantifying local distortion
Furthermore, local distortions can be extracted and analyzed with the fitted atomic
positions in STM images. The deviation of the displacement (same as the standard deviation of
displacement) was used to quantify the local distortion in HEAs 50,51. From the atomic resolution
STM images, the atomic positions are determined using 2D center of mass (COM) fittings of the
spot-filtered topography images (Supplementary Fig. 2). Two quantities are defined based on the
fitted atomic positions to characterize the level of local distortion: (i) the standard deviation of
the atom-atom distance 𝜎 = √∑𝑁 1 (𝑑 −𝑑̅) 2 , where 𝑑̅ is the average atom-atom distance, 𝑑
d 𝑖=1𝑁 𝑖 𝑖
is the atom-atom distance of each pair of neighboring atoms, and N is the total number of atom-
atom pairs; and (ii) the average displacement 𝑢̅ (see Table S1) and the standard deviation of the
average displacement, 𝜎 . These two quantities are determined for domains 1, 2, and domain
𝑢
boundaries (mixed regions) separately and are summarized in Table S1. Figure 3(a) shows a
displacement mapping of the region presented in Fig. 2(a), with no clear ordering in the local
distortion observed. The atom-atom distance in domain 1, 2, and domain boundary can be
expressed as 𝑑̅ ±𝜎 : 2.69 ± 0.19 Å (domain 1), 2.67 ± 0.20 Å (domain 2), and 2.69± 0.19 Å
𝑑
(domain boundary). There is no clear difference in local distortion between the two domains and
the domain boundary. The level of local distortion can be understood with the deviation of the
atom-atom distance, which is determined to be ~7-8 % of the averaged atom-atom distance. The
local distortion in the five-element cantor alloy studied here exhibits a relatively high local
distortion compared with refractory HEAs (~4 % to ~8 % in NbTaTiV and NbTaTiVZr)50,51. On
the other hand, the statistics of the displacement 𝑢̅ ±𝜎 , is determined to be: 0.18±0.08 Å
𝑢
(domain 1), 0.20±0.08 Å (domain 2), and 0.17±0.08 Å (domain boundary). Again, there is
no clear difference in the average displacement between the two domains and the domain
boundary. The average displacement is found to be the same as the standard deviation of the
atom-atom distance, indicating that the deviation in the lattice constant (atom-atom distance) is
the direct result of the local displacement at each atomic site. The two quantities essentially
describe the same picture of local distortion in HEAs. These results indicate that the local
distortion in HEA can be studied at different grains or regions (like dendritic vs interdenritic
regions), which cannot be easily studied using scattering based techniques.

QLRO domain distributions
Three important questions remain: (i) are the two observed QLRO domains universal
across different grains? (ii) are there preferred domain sizes or preferred domain types? And (iii)
are there differences of the LCO in the dendritic or interdendritic region? For the first question,
STM measurements shown in Fig. 2(a) and Supplementary Figs. 5-12 are taken within a vicinity
of ~1 μm from each other. Figures 3(b) and 3(c) depict STM images taken at a location distanced
~sub-mm away. The same two types of QLRO (LCO) domains are observed in a different HEA
crystalline grain (Supplementary Fig. 16). For the second question, the domain sizes may vary
from a couple of nm to tens of nm as shown in Figs. 3(b) and 3(c). From the images observed,
these two domains are often observed together (neighboring to each other), indicating
energetically, no preferential domain between the two. This observation suggests that tuning
LCO between the two types of domains is expected to be achievable with external stimuli, such
as thermal treatment or mechanical loadings. More research is needed to answer these questions.
For the third question, due to the drastic difference in the length scale between the dendritic
features (tens of micron) and the STM scanning size (tens of nm to hundreds of nm), it is
challenging to determine the locations of the STM measurements belong to either dendritic or
interdendritic regions.

Origins of the QLRO
There are a few possible origins to explain the observed QLRO. First, surface structural
reconstructions occur on metal surfaces result in different surface ordering from the bulk
structures, such as missing row (1×2) reconstruction on Pt(110)52, (1×3) missing-row surface
reconstruction on Be(112̅0) surface53. These types of surface reconstructions with missing atoms
or with adatoms are ruled out. The height deviation among different sites is sub-angstrom,
indicating that the contrast originates from a difference in electronic states rather than a physical
atomic vacancy or adatom (Supplementary Fig. 17). Second, a charge density wave (CDW) is
ruled out since there is no observable transition in 𝑅-𝑇 measurements reported for the Cantor
alloy54 and a Peierls transition is not experimentally observed in STM displacement mappings
[Fig. 3(a)]. Third, the local chemical orders (LCO) may be the origin. As discussed, the contrast
among different atomic sites in the supercell is electronic in nature. Based on the STM tunneling
mechanism, it could be explained by the differences in either the tunneling matrix or the LDOS
caused by different elements. Either way, the observed QLRO is associated with LCO. For the
CoCrFeMnNi alloy, the elements have similar electron configurations near the Fermi energy.
Thus, the tunneling matrices between different elements and the tungsten tip are expected to be
similar. It is most likely that the origin of contrast is due to the subtle differences in LDOS
belonging to different elements near the Fermi energy. One may also consider this as a type of
surface structural reconstruction based on the elemental ordering. This depends on whether the
surface LCO is simply extended from the existing bulk LCO, or if the surface has its own unique
LCO due to the existence of the surface. Without detailed information about the bulk LCO, it is
inconclusive either way, and further research comparing the surface and bulk LCOs is required to
address this question. Finally, the observed QLRO may simply be due to local corrugation
(lattice distortion in the direction normal to the surface). While it is possible that the sub-
angstrom corrugation of atomic height exists, the ordered surface corrugation is likely also
associated with ordered elemental distributions, and this mechanism still ties to the existence of
the surface LCO.

To further identify the origin of the observed contrast in topography, DFT calculations are
performed to assist in assigning elements to atomic sites in the two QLRO domains. DFT
calculations are performed on a slab of the alloy with randomly distributed elements, as shown in
Fig. 4(a). In the STM constant current mode measured on a particular atomic plane, the STM
apparent height is mainly determined by three factors: (i) atomic corrugation, (ii) tunneling
matrix, and (iii) LDOS. First, due to different element sizes, HEA surfaces with different
elements are expected to exhibit surface corrugation on a sub-atomic scale. The DFT calculation
of the slab [Fig. 4(a)] with surface atoms relaxed can simulate the atomic corrugation. As shown
in Supplementary Fig. 18, the surface corrugation is ~2 pm, which is smaller than the observed
height differences (~10 pm) in the STM images, as exhibited in Fig. 2(e). It is clear that the
surface corrugation is not enough to explain the observed height differences among the atomic
sites in QLRO domains. Second, typically the tunneling matrix depends on the nature of the
orbitals involved in the tunneling process. The elements in the HEA studied here are Co, Cr, Fe,
Mn, and Ni, which are neighboring transition metals in the periodic table, all with 𝑑 orbitals. It is
expected that their tunneling matrices are very similar and thus ignored here. Therefore, the STM
apparent heights 𝑧 , can be related to the integration of the available LDOS as 𝑧 ∝
STM STM
0
∫ 𝜌 (𝜖)𝑑𝜖, where 𝑉 is the STM scanning bias, and 𝜌 (𝜖) is the LDOS of the atom
−𝑉 s b s
b
underneath the STM tip as a function of energy 𝜖 with respect to the Fermi energy. The partial
LDOS near the Fermi energy from each element is calculated from DFT on the slab with
randomly distributed elements [Fig. 4(a)] and is illustrated in Fig. 4(b). It is obvious that the
partial LDOS shows clear differences between elements, while deviations can be found in each
element group. This trend indicates that the partial LDOS has an elemental identity, while the
neighboring elements may influence the details of the partial LDOS. By integrating each partial
LDOS from −75 meV to 0 meV (STM bias used in Figs. 1 and 2: −75 mV) which is depicted as
the shaded area in Fig. 4(c), the relative STM apparent height differences can be estimated. The
resulting areas under the curves (AUCs) are summarized in Fig. 4(d), revealing a ranking of
brightest (largest integrated AUC) to darkest (smallest integrated AUC): Fe, Mn, Co, Cr, then Ni.
Hence, the elemental assignments with the DFT calculated AUC are: Fe, Mn, and Co for the
bright group; and Cr and Ni for the dark group. Note that the Fe exhibits biggest uncertainty in
the AUC (Fig. 4(d)). This is due to the spectrum variation of Fe near Fermi energy is largest
among the five elements near Fermi energy, where the STM experiment tip-sample bias was set
(see Fig. 4(b)). Other elements also exhibit similar spectrum variation but away from the Fermi
energy. Thus, the AUC calculated near Fermi energy exhibit largest uncertainty for Fe. Thus, the
LCO in the two QLRO domains can be visualized in Figs. 4(e) and 4(f) for domains 1 and 2,
respectively. Figure 4(g) summarizes the elemental assignment within the supercells of the two
types of domains, while the supercells are illustrated in Fig. 4(h). The measured surface LCO
does not match the reported L or L orderings of the CoCrFeMnNi55, indicating that the
11 12
surface LCO may not be necessarily an extension of the bulk LCO.

In summary, the existence of the surface LCO on CoCrFeMnNi surfaces is directly
observed with atomic resolution STM images. Two QLRO domains with supercell periodicities
corresponding to √5×√5 R±26.6° orientations with respect to the pristine FCC (001) square
lattice and domain boundaries with randomized elemental distributions are revealed. Detailed
height analysis exhibited a bimodal distribution of superlattice position types, indicating a non-
negligible level of elemental randomness across the QLRO domains. With assistance from DFT
calculations, elemental assignments inside the QLRO domain supercells are made, as
summarized in Fig. 4(g). This work unambiguously provides direct evidence of the existence of
the surface LCO with the detailed elemental arrangements on HEA surfaces. In addition, the
results clearly demonstrated that STM is a valuable tool to study HEA systems with
unprecedented information that cannot be obtained by other characterization tools. It is expected
that this work will inspire further and more extensive studies on HEA surfaces, where future
theoretical modelling may help elucidate the origins and mechanism of surface LCO,
encouraging the HEA research community to include STM as a more commonplace
characterization tool in the understanding of the HEA systems.

Methods
HEA materials synthesis
A nearly equimolar CrMnFeCoNi alloy was synthesized using arc melting under 1 atm of
inert Ar gas, using equimolar ratios of high purity powders (>99.95%) of each constituent
element. To ensure compositional homogeneity, each sample was over- turned and re-melted five
times at ≈3500 K. The sample stayed on a water-cooled copper plate during melting and
solidification to cool it to room temperature. The HEA was cut into a 1 mm thick slice, where
one side was polished with 1200 grit sandpaper and 0.5 to 0.05 μm DIAMAT polycrystalline
diamond paste, in preparation for STM measurements.

XRD Characterization
Rigaku SmartLab X-Ray Diffractometer was used to carry out the X-ray diffraction
measurements. The XRD measurements were conducted at room temperature using Cu K𝛼
radiation (𝜆 = 1.54 Å), and 0.3 degree step size. XRD measurements determined that the bulk
crystal structure is predominantly face-centered cubic (FCC) with lattice parameter 𝑎 = 3.59±
0.01 Å [Supplementary Fig. 1(b)], which infers a nearest neighbor atom-atom distance of 𝑑 =
𝑎
= 2.54 Å [Fig. 1(a)].
√2

SEM and EDX
Scanning electron microscope energy dispersive X-ray spectroscopy (SEM-EDX)
measurements were carried out using a FEI Quanta 250 SEM equipped with tungsten electron
source, equipped with Everhart-Thornley Detector backscattered electron detector, and Oxford
Inca energy dispersive x-ray spectroscopy system (EDX). The electron acceleration energy was
set to 20 kV. SEM-EDX measurements were used to determine the bulk chemical composition of
the alloy to be Co Cr Fe Mn Ni , with EDX mappings shown in Supplementary Figs.
18 20 16 26 20
1(d)-(h) that display the typical dendritic structure for Cantor alloys fabricated via arc melting56.

STM measurements
In preparation for STM measurements, the CoCrFeMnNi alloy was cleaned in ultra-high
vacuum (UHV) via multiple cycles of warm Ar+ ion sputtering (460 °C, 30 minutes) and
annealing (510 °C, 30 minutes). The last cycle before STM measurements ended with a 24-hour
annealing at 510 °C and a slow cooling process from 510 °C to 310 °C at a cooling rate of ~1
°C/5 minute. The sample was transferred to STM chamber without exposing to air right after the
cleaning procedure. All the STM measurements were conducted using Omicron Low-
Temperature STM (LT-STM) system at liquid nitrogen temperature (77 K). The topographic
images were measured using constant current mode with the set points indicated in the figure
captions.

DFT Calculations
All DFT calculations were performed using Vienna ab initio simulation package (VASP
5.4.4) using the projected augmented wave (PAW) 57,58. A 200-atom CoCrFeMnNi-(001) supercell
with 4 layers was constructed with a vacuum spacing of 15 Å. The atomic configuration was
generated using the special quasi-random structure approach to approximate the random chemical
disorder of the HEA 59. The exchange-correlation interactions were described using the Perdew–
Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) 60. A
high plane-wave energy cutoff of 520 eV is applied, while Brillouin zone integrations are carried
out using a Γ-centered k-point mesh with a smearing width of 0.01 eV 61. The force and energy
convergence criteria for DFT self-consistent calculations were set to 10-3 eV/Å and 10-6 eV,
respectively. STM images were generated using the Tersoff-Hamann approach 62,63, which models
the STM tip as an s-wave. In this approximation, the tunneling current I at tip position r and applied
voltage V is proportional to the integrated local density of states (LDOS). The LDOS was
calculated by integrating states within an energy window of ±0.5 eV around the Fermi level to
capture the relevant tunneling states at typical experimental bias voltages.

Data Availability
Data is available upon request. The LEED, STM, and DFT calculated PDOS datasets generated
during and analyzed during the current study are available in the figshare repository64.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "LCO is considered an important factor influencing the properties of high - entropy alloys, such as mechanical, corrosion, and\ncatalytic properties. However, the characterization of LCO, especially its quantitative characterization, has not been fully\nachieved, despite some progress. In this study, STM was combined with SX technology to attempt to characterize the LCO\nof high - entropy alloys. The research direction is forward - looking, and the results are interesting. If this technology can\nachieve the characterization of LCO, especially quantitative characterization, it will promote the quantitative regulation of\nLCO and further drive its development and application in the field of property regulation. However, there are some issues in\nthis study that the authors need to address.\n1. Before using the abbreviation \"MPEA\", an explanation should be provided.\n2. STM is not sensitive to elements. Could it be that the number of elements this technology can identify is limited, meaning it\ncan only distinguish a few elements while failing to recognize the rest, which would directly affect the elemental\ncharacterization results? Or, for other alloys, the effectiveness of this technology might disappear. Relevant discussions on\nthis part need to be added.\n3. Can this technology determine the element type based on the brightness of atoms? Additionally, is there a possibility that\ntwo different elements have similar brightness? Relevant discussions on this part need to be added.\n4. The method of sample treatment in this study is the same as that used in previous studies observing LCO with Energy -\nfiltered TEM, i.e., annealing. Will different annealing temperatures and times affect LCO? Although some literature shows\nthat Energy - filtered TEM found that different temperatures and times can affect LCO, I know that the authors of these\nrelevant literatures have started to question this method.\n5. What is the method of preparing the transmission samples? Could the sample preparation method affect the\ncharacterization results, such as non - uniform thickness in different regions of the transmission sample?\n6. What is the difference between this study and the literature (10.1002/adma.202402442) cited in the paper? This literature\nalso uses the same method to study the elemental distribution on the sub - nanometer scale. If the technology is exactly the\nsame, does the study have a problem in terms of innovation?\n7. Has there been any progress in the quantitative characterization of LCO using the SX - STM technology?\n8. In this study, density functional theory (DFT) was used to verify and compare the experimental results, but the specific\ndetails of the DFT calculations were not provided. Then how can the correctness of the DFT results be proven?", "reviewer_3": "The current work demonstrates and analyses the local chemical order (LCO) on the surface of CoCrFeMnNi HEA using\nscanning tunneling microscopy (STM) techniques. The results are interesting and provide deeper insights into\nunderstanding of atomic arrangements in high entropy alloys. I recommend this work for publication, after the following\nquestions are satisfactorily answered and included in the manuscript as far as possible:\na) As authors have also hinted, there is a need to compare the LCO at the surface with that in the bulk. Can authors include\nsome discussion on the difference between bulk and surface LCO for some other alloy systems, if not for CoCrFeMnNi to\ngive further insights to the readers?\nb) The elemental arrangements in Fig. 4g suggests two domains containing Fe-Mn-Co and Ni-Cr. What tare the possible\nreasons for observing such elemental grouping? Can it be correlated to any thermodynamic interactions between the\nelements?\nc) Since CoCrFeMnNi HEA has been widely studied, does this evidence of LCO on surface provide an explanation for any\nof the observed properties for this alloy? In other words, how can understanding of surface LCO be impactful for\nunderstanding properties (atleast the surface) of this alloy?", "reviewer_4": "This manuscript presents a significant advance in the study of HEAs by directly visualizing the LCO in a CoCrFeMnNi alloy\nby STM atomic resolution observations and DFT calculations. The experimental results are well characterized, and the\nauthors have also conducted a large amount of data analysis and processing work. However, there are still some issues in\nthe manuscript regarding certain results and descriptions.\n1. The lattice constant of the famous CoCrFeMnNi matrix is about 3.59 Å, nevertheless, the author reports the atomic\nspacing as d=2.7 Å in “square lattice” (Fig. 1), which is the spacing of (110) plane. Thus, it can be inferred that the lattice\nconstant of the authors' alloy is 3.82 Å. Generally, this large deviation (more than 0.2 Å) is unacceptable. Therefore, it is\nnecessary for the authors to provide a reasonable explanation and verify it with the XRD results (Fig. S1b).\n2. Line 121-123. “As shown in Fig. 1(d), red and blue circled spots correspond to the two orderings in different domains\nwhere both domains show different orientations but the same periodicity d_SC= 6.1 ± 0.1 Å.”\nIn fact, the four points in the four blue circles (Fig. 1h) cannot lie on the same circle simultaneously, indicated two d-values.\nThus, the eight points in Fig. 1d are obviously not on the same circle, yet the authors claim the same d_SC= 6.1 ± 0.1 Å.\n3. Fig. 2: The authors divided the height and brightness into 5 groups based on 5 elements, which raises the suspicion of\n\"setting the target after shooting the arrow\" (tailoring the grouping to fit a pre-conceived outcome). Furthermore, the red dots\nlargely overlap with the green and yellow dots in most height ranges (35-40 pm). Such classification based on overlapping\nregions makes it difficult to substantiate the argument. It is suggested that the authors conduct statistical analysis on the\nheight and brightness data before proceeding with the classification.\n4. It is not clearly stated by the authors whether the observation area of the sample is from dendrites (DR) or interdendritic\nregions (IDR). Also, how about the dendritic state is after heat treatment. In addition, how the segregation in DR and IDR\naffect LCO could be an interesting research question worth exploring.\nIt is hoped that the authors could reconsider the issues regarding the above results, as it may affect the final conclusions of\nthe manuscript.\n5. Figure 1.\na) Fig. 1a lacks annotations of domain 1 and domain 2.\nb) d_SC needs to be given a specific name. Additionally, in the text, Figure 1d and d_SC are mentioned first, but there is no\nrelevant information for d_SC in Fig. 1d. The author has placed it in Figures g and h.\n6. Description in line 112: “indicating potential orderings beyond the FCC lattice”.\nThe description of the fuzzy feature is unclear, and it is suggested to cite references. In addition, does this fuzzy feature\nnecessarily refer to ordering? Is it related to the sample, equipment or parameters? Or could there be other possibilities?\n7. Line 131 “Figure 2(a) shows an enlarged region of Fig. 1(c),”\nThe atomic-scale topography in Figure 2a is derived from Figure 1c. The authors should mark the selected area in Figure 1c\nfor further discussions."}, "author_response": "Response: We sincerely thank the reviewer for recognizing the novelty and significance of our\nwork in resolving local chemical ordering (LCO) in High-Entropy Alloys (HEAs). We agree that\nthis work will indeed \"promote the quantitative regulation of LCO and further drive its\ndevelopment and application in the field of property regulation.\"\nAddressing the Methodology for Resolving LCO: To achieve this ambitious goal, we have\ncontinuously pursued techniques offering excellent spatial resolution to resolve individual\nelements. Our initial approach involved combining synchrotron X-ray with Scanning Tunneling\nMicroscopy (SX-STM), the results of which were previously published in Adv. Mater. 36,\n2402442 (2024).\nHowever, a significant drawback of the SX-STM approach is the relative scarcity of synchrotron\nbeamtime, which inherently hinders rapid progress in the systematic resolution of LCO in\nvarious HEAs.\nIn this current work, we overcome this limitation by employing a distinct and more accessible\nmethod: STM topography images coupled with Density Functional Theory (DFT) modeling.\nThis approach leverages the fundamental nature of quantum tunneling: because different\nelements in HEAs contribute uniquely to the local density of states (LDOS) near the Fermi\nenergy [as shown in Fig. 4(b)], the STM tip can detect these variations, which are then\nmanifested in the topography heights.\nAs shown in Figure 4, this method is successful in distinguishing elements (at least in groups).\nThis advancement provides a highly accessible, lab-based alternative to synchrotron methods for\nLCO analysis.\nThe Unprecedented Observation of Quasi-Long-Range Order (QLRO): Beyond the successful\nresolution of elemental arrangements, the most surprising and significant observation in this\nwork is the presence of surface quasi-long-range order (QLRO) domains. The existence of this\nimpacts on various material properties, as the reviewer has already insightfully suggested.\nFurthermore, to independently confirm this finding, we re-plotted the resolved elemental\narrangements from our previous Adv. Mater. paper (SX-STM approach) and present them in\nFigure S3. The similar QLRO ordering observed in this independent dataset strongly confirms\nthat QLRO is an intrinsic feature that can be consistently measured by two fundamentally\ndifferent techniques (SX-STM in the previous Adv. Mater. work vs. the current STM + DFT).\n1. Before using the abbreviation \"MPEA\", an explanation should be provided.\nResponse: We thank the reviewer for pointing out this matter. Since we only use MPEA once in\nthe manuscript and it can be replaced with HEA in this sentence, we have replaced it with\n“HEA” to create consistent terminology throughout the manuscript.\n2. STM is not sensitive to elements. Could it be that the number of elements this technology\ncan identify is limited, meaning it can only distinguish a few elements while failing to\nrecognize the rest, which would directly affect the elemental characterization results? Or,\nfor other alloys, the effectiveness of this technology might disappear. Relevant discussions\non this part need to be added.\nResponse: We appreciate the reviewer's thoughtful comment regarding the conventional\ncapability of scanning tunneling microscopy (STM) in resolving elements. We certainly\nacknowledge that STM is generally not the go-to technique for elemental mapping. Despite this,\nas noted in the original manuscript, there are foundational reports from the 1990s demonstrating\ntheir capability of distinguishing dissimilar elements, particularly in simpler binary alloy\nsystems.\nIn this work, we push the frontier of this technique by utilizing STM topography in conjunction\nwith Density Functional Theory (DFT) calculations to successfully distinguish the elements in\nthe complex, five-component Cantor alloy into two main elemental groups.\nRationale for Grouping Elements. The limitation to resolving only two groups, rather than five\nindividual elements, stems from the necessary trade-off between atomic resolution and\nspectroscopic range in STM measurements:\n1. Requirement for Atomic Resolution: Achieving true atomic resolution in STM requires an\nextremely small tip-sample distance, which is achieved with an extremely small tip-sample\nbias (near zero bias).\n2. Reliance on Local Density of States (LDOS): Under these low-bias conditions, the\ntopography contrast is overwhelmingly dominated by the partial density of states (DOS)\ncontributed by each atom very near the Fermi energy, as detailed in Figure 4(c).\n2\n3. Grouping Result: Because the usable range of DOS near the Fermi energy is limited at low\nbias, the elements in the Cantor alloy could only be reliably separated into two main groups:\no Bright (Tall) Topography: The three elements Fe, Mn, and Co.\no Dark (Low) Topography: The two elements Cr and Ni.\nWe recognize that one could suggest using a higher tip-sample bias to integrate over a wider\nrange of the partial DOS for better distinction. However, a larger bias concurrently increases the\ntip-sample distance, which would inevitably lead to the loss of the essential atomic resolution.\nThe data presented in the manuscript represents the optimal balance we achieved: providing\natomic resolution images with sufficient elemental resolving power to observe the main\ndifference in the LDOS.\nFuture Directions and Method Versatility. The elemental similarities in the Cantor alloy\n(Cr, Co, Ni, Mn, and Fe) are significant, as they are neighbors in the periodic table and all\npossess similar 3d orbitals as their outermost shells near the Fermi energy.\nThe STM tunneling current (I) is fundamentally simplified as 𝐼 ∝ |𝑀|2∫ 0 𝜌 (𝜖)𝑑𝜖, where 𝜌\n−𝑉𝑏 𝑠 𝑠\nis the partial DOS from the element at the location of the STM tip tunneling, and |𝑀|2 is the\ntunneling matrix element. While we successfully leveraged the differences in 𝜌 near the Fermi\n𝑠\nenergy to distinguish elements, the tunneling matrix term, |𝑀|2 is expected to be very similar for\nthis specific group of elements due to their identical outermost 3d orbitals.\nFor HEAs with more dramatically different elemental compositions (e.g., elements far apart on\nthe periodic table with varying orbital contributions), we anticipate the topography contrast\nwould be significantly more distinguishable by leveraging the differences in the tunneling matrix\nelement |𝑀|2, in addition to the differences in the partial DOS. We are actively pursuing this line\nof research in our laboratory.\nFurthermore, a potentially superior method for resolving more elements, which is beyond the\nscope of this initial work, is to utilize the full dI/dV spectrum across a wider energy range, where\nthe elemental differences are much more distinct, as illustrated in Figure 4(b). This is the focus\nof our next manuscript.\nCrucially, the success of this method in revealing the elemental groups was sufficient to enable\nour other main novel finding: the unprecedented observation of the quasi-long-range order\n(QLRO) on the Cantor alloy surface.\n3. Can this technology determine the element type based on the brightness of atoms?\nAdditionally, is there a possibility that two different elements have similar brightness?\nRelevant discussions on this part need to be added.\noriginal manuscript, the primary method for resolving elements in this work relies on the STM\ntopography height (i.e., the brightness or apparent height of the atoms).\nAs discussed extensively in the context of Figure 4 (and recapped in our previous point), the\ncurrent data successfully allows us to distinguish the elements into two main groups:\n1. The Bright Group: The elements Fe, Mn, and Co are all observed by STM as bright atoms.\nThe differences in their individual apparent heights are too small to be reliably separated\nfrom the experimental noise, so they are grouped together.\n2. The Dark Group: Similarly, Cr and Ni are observed as dark atoms. The small difference in\ntheir individual brightness is also comparable to the noise level, preventing further separation\ninto distinct elemental species.\nTherefore, while the method effectively separates the five elements into two chemical groups\nbased on the differences in their Local Density of States (LDOS) near the Fermi level, we\nacknowledge the limitation imposed by the signal-to-noise ratio in resolving individual species\nwithin these groups.\n4. The method of sample treatment in this study is the same as that used in previous studies\nobserving LCO with Energy - filtered TEM, i.e., annealing. Will different annealing\ntemperatures and times affect LCO? Although some literature shows that Energy - filtered\nTEM found that different temperatures and times can affect LCO, I know that the authors\nof these relevant literatures have started to question this method.\nResponse: We thank the reviewer for this insightful and highly relevant comment. We agree that\nthe question of whether annealing conditions or other synthesis methods can truly alter Local\nChemical Ordering (LCO) remains a significant and active debate within the high-entropy alloy\n(HEA) community.\nA major challenge contributing to this debate is the difficulty in reliably detecting LCO [often\nreferred to as Short-Range Order (SRO)]. As the reviewer notes, even previously accepted\nmethods, such as energy-filtered TEM, are facing scrutiny.\nThis manuscript directly addresses the detection challenge by establishing a novel, high-\nresolution methodology - the first application of Scanning Tunneling Microscopy (STM) to study\nLCO/SRO in HEAs, to our knowledge. The core emphasis of the current work is twofold:\n1. Methodology: Demonstrating a new, reliable technique for visualizing elemental ordering.\n2. Unprecedented Observation: Reporting the first observation of LCO and the surprising\nQuasi-Long-Range Order (QLRO) on the surface of a Cantor alloy.\naddress the reviewer's excellent question regarding the effect of thermal treatment.\nFor future research directions, we fully agree that understanding how to manipulate LCO is a\ncritical topic that will \"promote the quantitative regulation of LCO.\" In fact, investigating how\nsynthesis and thermal treatment conditions affect the observed LCO/QLRO is an active and\ncentral component of our ongoing research.\nHowever, a comprehensive and clear discussion on the influence of annealing conditions on\nLCO requires extensive, systematic comparisons across numerous samples and varying synthesis\nparameters. To maintain the focus and integrity of the current manuscript - which emphasizes the\nmethodological breakthrough and the novel QLRO observation - it would be more prudent to\ndedicate a separate, thorough study to this complex topic.\nWe greatly appreciate the reviewer for pointing out this important future direction, which is\nentirely aligned with the efforts currently underway in our laboratory.\n5. What is the method of preparing the transmission samples? Could the sample\npreparation method affect the characterization results, such as non - uniform thickness in\ndifferent regions of the transmission sample?\nResponse: We thank the reviewer for the question. We would appreciate it if the reviewer could\nclarify the term \"transmission samples,\" as we do not clearly understand what \"transmission\"\nrefers to in this context.\nAll measurements in this work were performed using Scanning Tunneling Microscopy (STM),\nwhich is a highly surface-sensitive technique.\nThe samples were prepared from a polycrystalline Cantor alloy with a bulk thickness on the\norder of millimeters. We do not anticipate that this macroscopic thickness (or any minor non-\nuniformity) is a factor influencing the surface LCO (Local Chemical Ordering) that we observe.\nThis is because the surface LCO is determined by the meticulous, in situ preparation under ultra-\nhigh vacuum (UHV): Sputtering & annealing: The samples underwent multiple cycles of Ar+ ion\nsputtering (460 °C, 30 minutes) and annealing (510 °C, 30 minutes). This process was followed\nby slow cooling to promote optimal surface crystallinity and a well-defined structure for the\nSTM measurement.\nThis established UHV cleaning and annealing protocol ensures that the observed surface\nphenomena are characteristic of the prepared surface and are decoupled from the bulk geometry.\n6. What is the difference between this study and the literature (10.1002/adma.202402442)\ncited in the paper? This literature also uses the same method to study the elemental\n5\ndistribution on the sub - nanometer scale. If the technology is exactly the same, does the\nstudy have a problem in terms of innovation?\nResponse: We appreciate the reviewer's comment, but it's important to clarify that this work\nutilizes a fundamentally different methodology than the literature referenced (our previous Adv.\nMater. paper). Let’s start by summarizing the main differences between the two methods\n(previous Adv. Mater. and this work)\nMethod Core Mechanism for Elemental Distinction Drawback\nCurrent Local Density of States (LDOS) near the Fermi Limited to resolving\nWork (STM energy, probed by the STM tip and assisted by DFT elements into groups due\n+ DFT) calculated DOS. to low-bias requirements.\nCore-level electrons and their distinct elemental\nPrevious fingerprints, probed using Synchrotron X-ray STM. Scarcity of synchrotron\nWork (SX- The X-ray assisted tunneling mechanism provides beamtime and limited\nSTM) both excellent spatial resolution and elemental sample area.\nsensitivity\nThe significant limitation of the Synchrotron X-ray STM (SX-STM) approach is the scarcity of\nbeamtime. For instance, two weeks of beamtime yielded elemental maps over an area of only\n2.5 nm×1.5 nm. This limited area is simply too small to reliably recognize the periodic or\nrepeating patterns that Local Chemical Ordering (LCO) and Quasi-Long-Range Order (QLRO)\nentail.\nThe key advantage of the current STM + DFT method is its ability to produce elemental maps\nover a much larger area. This increased statistical sampling and field-of-view enabled us to, for\nthe first time, clearly observe and characterize the surface LCO in the Cantor alloy. While we did\nfind evidence of the same QLRO pattern when re-examining the elemental distribution from the\nprevious SX-STM data (as shown in Figure S3), the original small-area results were insufficient\nto recognize and report the existence of this extended QLRO.\nTherefore, the greater accessibility and larger imaging area of the STM + DFT method in this\nwork were crucial for the novel observation of the surface LCO and QLRO.\n7. Has there been any progress in the quantitative characterization of LCO using the SX -\nSTM technology?\nResponse: We thank the reviewer for the interest in our previous work involving Synchrotron X-\nray Scanning Tunneling Microscopy (SX-STM), which was published in Adv. Mater.\nspecifically concerning the facility where the experiments were conducted:\n1. APS Upgrade: The Advanced Photon Source (APS) at Argonne National Laboratory\nunderwent a major upgrade, which halted user access for over a year.\n2. Beamline Changes: The specific SX-STM beamline used for our prior work was\ndecommissioned as part of the APS upgrade.\nWhile the core STM equipment may potentially be adapted for use at a different beamline, this\nwould require a new user proposal, extensive technical communication, and the resolution of\nengineering challenges with the APS beamline scientists. We encourage continued interest from\nthe High-Entropy Alloy (HEA) community to be expressed to APS, ANL. It would be beneficial\nin encouraging the APS administration to support the reintegration of this unique instrument.\nWhile we appreciate the curiosity about this related area, we must emphasize that these external\nfacility issues are irrelevant to the work presented in this manuscript. The present study\nsuccessfully establishes and utilizes an independent, lab-based methodology (STM + DFT) that\novercomes the accessibility limitations of synchrotron beamtime and leads to the novel findings\nreported herein. In a different view, this method without using synchrotron can be seen as a new\nprogress toward resolving elements in HEA using STM.\n8. In this study, density functional theory (DFT) was used to verify and compare the\nexperimental results, but the specific details of the DFT calculations were not provided.\nThen how can the correctness of the DFT results be proven?\nResponse: We thank the reviewer’s comments about the quality and the details of the DFT\ncalculations. We have added a section in the SI document that clarifies the specific details of the\nDFT calculations, which will help demonstrate the validity of the DFT results. This SI section\nincludes references that were used to make DFT calculations.\nResponse: We appreciate the reviewer’s time and feedback, as well as their recognition of the\nnovelty of our work presented in this manuscript.\na) As authors have also hinted, there is a need to compare the LCO at the surface with that\nin the bulk. Can authors include some discussion on the difference between bulk and\nsurface LCO for some other alloy systems, if not for CoCrFeMnNi to give further insights\nto the readers?\nResponse: We thank the reviewer for this valuable comment. Bringing up the difference between\nbulk and surface ordering is indeed important, and we agree that it enhances the manuscript's\ncontext.\nIt is a well-established principle in surface science that surface ordering is often distinct from\nbulk ordering due to the broken symmetry at the surface. To minimize surface energy, atoms\noften adopt different atomic locations or arrangements, leading to phenomena like surface\nreconstruction. Classic examples include as missing row (1×2) reconstruction on Pt(110) [Phys\nRev B 38, 10197–10204 (1988)], (1×3) missing-row surface reconstruction on Be(112̅0) surface\n[Surf Sci 269/270, 7–13 (1992)].\nIn High-Entropy Alloys (HEAs), the sheer number of component elements and the role of high\nconfigurational entropy further complicate this scenario. It is thus naturally expected that the\nsurface Local Chemical Ordering (LCO) and bulk LCO are not necessarily identical.\nWhile addressing how LCO differs between the bulk and the surface is a critical and fascinating\ntopic, it requires an in-depth, dedicated study that goes beyond the scope of our current\nmanuscript. Given that:\n1. The understanding of bulk LCO in HEAs is still in its infancy.\n2. The surface LCO in HEAs is first observed in the present work.\nIt is currently highly challenging to provide definitive insights into how the bulk and surface\nordering differ.\nTo immediately benefit the readers and address this point, we have revised Lines 204-206 of the\nmanuscript to include a brief discussion on the general physical principles that drive differences\nbetween bulk and surface structures, referencing well-known examples from pure metal systems.\nThis inclusion provides the necessary context without overextending the claims of the current\nmethodology paper.\nb) The elemental arrangements in Fig. 4g suggests two domains containing Fe-Mn-Co and\nNi-Cr. What tare the possible reasons for observing such elemental grouping? Can it be\ncorrelated to any thermodynamic interactions between the elements?\nResponse: We thank the reviewer for posing this excellent question regarding the origin of the\nobserved surface Local Chemical Ordering (LCO).\nWe must honestly state that a clear, definitive answer to the mechanism driving this surface LCO\nis not available within the scope of this work. This question is, in fact, the same fundamental\nchallenge facing the study of LCO/Short-Range Order (SRO) in bulk High-Entropy Alloys\n(HEAs), which is primarily proposed to result from thermodynamic equilibrium [as suggested by\nJ. Phase Equilib. Diffus. (2017) 38:391–403].\nOpportunity for Theoretical Modeling: For surface LCO, the broken symmetry inherent to the\nsurface likely plays an additional and complex role beyond bulk thermodynamics.\nHowever, the clear, well-defined patterns and observations provided in this manuscript offer a\ncrucial advantage: we believe that our results give theoretical and computational researchers an\nunprecedented opportunity to validate models and finally resolve the origin of LCO in a more\ndefinitive manner than is currently possible for bulk cases.\nTo emphasize this critical next step, we have added a sentence to the manuscript's Summary\nsection, making an explicit call for further theoretical modeling to address the origin of the\nsurface LCO observed here.\nc) Since CoCrFeMnNi HEA has been widely studied, does this evidence of LCO on surface\nprovide an explanation for any of the observed properties for this alloy? In other words,\nhow can understanding of surface LCO be impactful for understanding properties (atleast\nthe surface) of this alloy?\nResponse: We thank the reviewer for bringing up this important point. The observation of surface\nLocal Chemical Ordering (LCO) and Quasi-Long-Range Order (QLRO) domains provides a\ncritical new foundation for understanding several key properties studied in this High-Entropy\nAlloy (HEA), specifically oxidation resistance, mechanical properties, and catalytic\nperformance.\nOxidation Resistance\nThe ordered domains offer a compelling new research direction for understanding the alloy's\noxidation behavior.\n• Existing Literature: First-principles calculations show that Cr and Mn exhibit a strong\ntendency for surface segregation in oxygen-containing environments, forming protective\noxide layers (Ferrari and Kormann, 2020 [https://doi.org/10.1016/j.apsusc.2020.147471]).\n• QLRO Impact: The observed QLRO domains may directly impact oxide nucleation and\ngrowth kinetics, potentially providing a structural explanation for the exceptional oxidation\nresistance and the formation of the reported dual-layer oxide structure (external Mn O and\n2 3\ninternal Cr O ). Our ability to visualize this surface ordering provides a clear pathway for\n2 3\nsystematic study.\nMechanical Properties\nOur findings offer a mechanistic basis for previously reported surface-influenced mechanical\nbehavior.\n• Existing Literature: Surface segregation in CoCrFeMnNi has been shown to influence the\nnucleation of plasticity, where Mn-enriched surfaces exhibit altered yield stress and elastic\nlimits (Korchuganov et al., 2020 [http://dx.doi.org/10.1088/1742-6596/1556/1/012049]).\n• QLRO Impact: The QLRO structure may provide a physical explanation for these\nobservations. The quasi-ordered domains likely increase the activation energy for dislocation\nnucleation at the free surface, while the domain boundaries may act as obstacles to\ndislocation glide. This potential surface strengthening mechanism could contribute to\nenhanced fatigue and wear properties reported for CoCrFeMnNi alloys.\nCatalytic Performance\nThe identified surface ordering provides a more fundamental structural context for the alloy's\ncatalytic activity.\n• Existing Literature: CoCrFeMnNi nanoparticles have demonstrated promising\nelectrocatalytic activity, such as for the oxygen reduction reaction (Waag et al., 2019\n[https://doi.org/10.1039/C9RA03254A]). While performance is generally attributed to high-\nentropy and synergistic effects, the precise active sites remain ambiguous.\n• QLRO Impact: Our identification of surface LCO/QLRO suggests a more specific\nexplanation: the quasi-ordered surface structures may create well-defined active sites with\noptimal geometric and electronic configurations, moving the understanding beyond\ngeneralized \"synergistic interactions.\"\nConclusion and Future Work\n• This work firmly establishes the critical importance of surface characterization in\nunderstanding HEA properties, especially given computational predictions indicating\nsignificant deviations between surface and bulk compositions (Mazitov et al., 2024\n[https://doi.org/10.1088/2515-7639/ad2983]).\n• It is prudent, however, to acknowledge that while our observed surface LCO/QLRO can\nexplain and correlate with these phenomena, we cannot yet make direct, quantitative claims\nabout their causal impact. To establish this direct link, we have planned future experiments\non nano-indented HEA samples, which will allow us to directly relate the observed LCO and\nstrain to local physical properties.\nResponse: We thank the reviewer for seeing the novelty of this work.\n1. The lattice constant of the famous CoCrFeMnNi matrix is about 3.59 Å, nevertheless, the\nauthor reports the atomic spacing as d=2.7 Å in “square lattice” (Fig. 1), which is the\nspacing of (110) plane. Thus, it can be inferred that the lattice constant of the authors' alloy\nis 3.82 Å. Generally, this large deviation (more than 0.2 Å) is unacceptable. Therefore, it is\nnecessary for the authors to provide a reasonable explanation and verify it with the XRD\nresults (Fig. S1b).\nResponse: We thank the reviewer for clearly identifying the discrepancy between the lattice\nconstant measured in the STM images and the value determined by XRD.\nSources of STM Measurement Error: The bulk lattice constant measured by XRD (X-ray\nDiffraction) in the Supplementary Information is 3.59 Å, which corresponds to an expected\nsurface square lattice constant (atom-atom distance) of 2.54 Å (3.59 Å/√2).\nSTM measurements are susceptible to two primary sources of error that affect the accurate\ndetermination of this real-space length scale:\n1. Calibration Error: The conversion of the piezo scanning voltage to a physical distance is\ngoverned by a calibration factor. This factor can drift with the scanning temperature, and\nrequires regular checking against a known standard crystal (e.g., graphite or silicon).\n2. Thermal Drift: Temperature fluctuations or imbalances in the system often induce image\nartifacts such as skewing, stretching, or compression of the image aspect ratio, directly\nimpacting the measured real-space dimensions.\nCorrection and Recalibration: We have conducted a thorough review and found that the\nprevious STM calibration factor was not properly set. We have since updated and improved the\naccuracy of our calibration factor by meticulously re-measuring known standards.\nWith this updated calibration, the atom-atom spacing measured is 𝑑 = 2.6±0.1 Å. While this\ncorrected value (2.64 Å) is still slightly larger than the expected 2.54 Å, the difference (0.1 Å) is\nwithin the typical uncertainty of the measurement, which is primarily constrained by the residual\nthermal drift.\nWe confirm that all scale bars and reported measurements derived from the STM topography\nhave been re-calibrated in the revised manuscript. Although the reported numerical values have\nshifted slightly, these changes do not alter the fundamental results or conclusions of this work. A\nfull list of changes is provided in the document below.\n2. Line 121-123. “As shown in Fig. 1(d), red and blue circled spots correspond to the two\norderings in different domains where both domains show different orientations but the\nsame periodicity d_SC= 6.1 ± 0.1 Å.”\nIn fact, the four points in the four blue circles (Fig. 1h) cannot lie on the same circle\nsimultaneously, indicated two d-values. Thus, the eight points in Fig. 1d are obviously not\non the same circle, yet the authors claim the same d_SC= 6.1 ± 0.1 Å.\nResponse: We thank the reviewer on the comment and have carefully inspected our data. In STM\nimages, the drift effect may skew the image and result in different distance from the square\nlattice points. This makes the square lattice appear elongated in a rectangular fashion (together\nwith the FFT images). The value quoted in the previous manuscript is the average of the four\npairs of spots (two in red and two in blue). The four d_SC values are: 𝑑 = 6.3± 0.1 Å and\n𝑆𝐶,1\n𝑑 = 5.8± 0.1 Å [Fig. 1(h)] and 𝑑 = 6.3± 0.1 Å and 𝑑 = 5.6± 0.1 Å [Fig. 1(g)].\n𝑆𝐶,2 𝑆𝐶,3 𝑆𝐶,4\nThe averaged values in Fig. 1(h) is 6.05 ± 0.1 Å; while the averaged value in Fig. 1(g) is 5.95 ±\n0.1 Å. For reader’s benefit, we have listed all four numbers and their averaged value.\n3. Fig. 2: The authors divided the height and brightness into 5 groups based on 5 elements,\nwhich raises the suspicion of \"setting the target after shooting the arrow\" (tailoring the\ngrouping to fit a pre-conceived outcome). Furthermore, the red dots largely overlap with\nthe green and yellow dots in most height ranges (35-40 pm). Such classification based on\noverlapping regions makes it difficult to substantiate the argument. It is suggested that the\nauthors conduct statistical analysis on the height and brightness data before proceeding\nwith the classification.\nResponse: We appreciate the reviewer's comment regarding the height analysis. However, we\nmust strongly disagree with the assertion that our data analysis was designed to achieve a pre-\nconceived outcome. Our analytical approach was entirely driven by the experimental\nobservations of the surface ordering.\nOur analysis followed a clear, sequential process:\n1. Initial Observation: We first identified the existence of the √5×√5𝑅26.6° Quasi-Long-\nRange Order (QLRO) domains in the STM topography, characterized by a specific, recurring\nsupercell structure.\n2. Supercell Definition: This supercell contains five unique atomic positions (P1-P5). At this\nstage, no elements were assigned to any position, nor was there any presumption regarding\ntheir relative brightness. Note that originally, the five position types are simply labeled P1-P5\nrandomly inside the supercell during our analysis, the color assignment was done after we\nhave the ranking of the height for readers’ benefit (in step 4 later).\n3. Height Analysis: We then performed a statistical height analysis on these five unique atomic\npositions in the supercells, as presented in Figure 2(e), with the corresponding histograms in\nFigures S14(d) and (e) for the two domains.\n4. Grouping by Height: The five positions were ranked and initially color-coded based purely\non their average height. We then observed that the top three atomic sites (denoted by red,\ngreen, and yellow) and the bottom three atomic sites (denoted as purple and blue) exhibited\ntwo groups of heights indistinguishable from each other due to the overlap in their height\nhistograms.\n5. Elemental Assignment: Only after establishing these two distinct height groups did we\ncorrelate them with the element groups predicted by our DFT calculations [as summarized in\nFigure 4(g)].\nThe inability to separate the top three sites (red, green, and yellow) into individual elements is\nprecisely what forces us to group them together (Fe, Mn, and Co). Similar reason for the bottom\ntwo sites. Furthermore, this overlapping of height histograms among the distinct supercell sites is\na key piece of evidence that emphasizes the inherent disorder within the determined quasi-\nperiodic structure, which is why we correctly describe the phenomenon as \"quasi-\"long-range\norder (QLRO). Our analysis, therefore, accurately reflects the disorder observed in the data.\n4. It is not clearly stated by the authors whether the observation area of the sample is from\ndendrites (DR) or interdendritic regions (IDR). Also, how about the dendritic state is after\nheat treatment. In addition, how the segregation in DR and IDR affect LCO could be an\ninteresting research question worth exploring.\nResponse: We thank the reviewer for raising this valuable and interesting research question.\nUnfortunately, we cannot definitively identify whether the observed images were captured within\na dendrite region (DR) or an interdendritic region (IDR). This limitation stems from the vast\ndifference in scale between our measurement technique and the characteristic features of the\nsample:\n1. Scale Disparity: Our STM imaging is limited to a nanoscale regime (typically less than\n100 nm). Conversely, the DR and IDR features typically exist on the microscale (tens of\nmicrons), which is beyond the largest scanning window achievable by our STM instrument.\n2. Visualization: It is currently unclear how DR and IDR would manifest or be distinguishable\nin STM topography at the microscale.\nThus, with the current information, it is unknown whether the observed patterns related to DR or\nIDR and it is still an active research topic to understand the differences in the LCO in the two\ndistinct regions. We agree with the reviewer that “how the segregation in DR and IDR affect\nLCO could be an interesting research question worth exploring” We have added a couple\nsentences in the manuscript to clearly describe this (lines 199-202).\nIt is hoped that the authors could reconsider the issues regarding the above results, as it\nmay affect the final conclusions of the manuscript.\n5. Figure 1.\na) Fig. 1a lacks annotations of domain 1 and domain 2.\nResponse: Labels have been added to figure 1(e), (f) to denote which cropped region from Figure\n1(a) is domain 1 and 2.\nb) d_SC needs to be given a specific name. Additionally, in the text, Figure 1d and d_SC are\nmentioned first, but there is no relevant information for d_SC in Fig. 1d. The author has\nplaced it in Figures g and h.\nResponse: We thank the reviewer for the careful reading of our manuscript. d_SC is the supercell\nperiodicity. In the text, this name is given when first mentioning d_SC (lines 131-134). The first\nmention of Figure 1(d) now includes a mention of the d_SC peaks in comparison to the FCC\nsquare lattice peaks, and the specific information about d_SC is still in Figures 1(g),(h).\n6. Description in line 112: “indicating potential orderings beyond the FCC lattice”.\nThe description of the fuzzy feature is unclear, and it is suggested to cite references. In\naddition, does this fuzzy feature necessarily refer to ordering? Is it related to the sample,\nequipment or parameters? Or could there be other possibilities?\nResponse: We thank the reviewer for the suggestion to use a more careful statement regarding\nthe features in our Low-Energy Electron Diffraction (LEED) image. We agree that based solely\non the fuzzy features near the center, it is not conclusive to imply a specific type of ordering\nbeyond the fundamental face-centered cubic (FCC) lattice.\nClarification and Context on Diffuse LEED. The central background in LEED patterns, often\ndescribed as diffuse scattering, is a recognized phenomenon in surface science.\n• This background is generally attributed to scattering from surface atoms with non-ideal,\nlonger-range order or disorder.\n• The study of these features, known as \"diffuse LEED,\" has been established in literature as a\ntool for understanding surface order/disorder on crystalline surfaces (e.g., [PRL 55, 2312\n(1985)] and [PRB 31, 1216 (1985)]).\n• In some cases, this background is processed for enhanced analysis. For instance, Nascimento\net al. [PRL 103, 076104 (2009)] utilized the naturally featureless, isotropic background to\nsubtract noise and reveal diffraction spots of weak intensity buried within the signal.\nRevised Manuscript Statement. Our original intention for including the LEED image was to\nserve as a qualitative precursor, prompting the detailed, conclusive measurements conducted by\nScanning Tunneling Microscopy (STM), which revealed the specific Quasi-Long-Range Order\n(QLRO) domains.\nTo provide accurate context and to benefit the reader, we have modified the statement in the\nmanuscript as follows:\n1. Original Text: \"The region inside the bright Bragg diffraction spots (circled white) in the\nLEED pattern [Fig. 1(b)] exhibits fuzzy features, indicating potential orderings beyond the\nFCC lattice.\"\n2. Revised Text: \"The region inside the bright Bragg diffraction spots (circled white) in the\nLEED pattern [Fig. 1(b)] exhibits fuzzy features, indicating potential features on the\nsurface with a longer length scale beyond the FCC square lattice.\"\nThen the following sentences are added after this sentence:\n“LEED usually has a featureless and isotropic background near the center of the image. This fact\nwas used by Nascimento et al. [PRL 103, 076104 (2009)] to subtract the background to reveal a\nsmall intensity of the diffraction spots buried inside the background signal. The fuzzy features\nnear the center of LEED patterns were studied as “diffuse LEED” in literature towards the\nunderstanding of the surface disordered atoms [PRL 55, 2312 (1985), and PRB 31, 1216\n(1985)].”\n7. Line 131 “Figure 2(a) shows an enlarged region of Fig. 1(c),”\nThe atomic-scale topography in Figure 2a is derived from Figure 1c. The authors should\nmark the selected area in Figure 1c for further discussions.\nResponse: We thank the reviewer for pointing this out. A dotted box has been added to Figure 1c\nfor clarity of the selected region in Figure 2(a), and the figure caption has been adjusted.\nList of changes:\nAll text changes in the manuscript and SI are red.\n1. Section S12 has been added to the supplementary information to further describe and\ncharacterize the DFT calculation method.\n2. Discussion of metal surface reconstructions was added to lines 205-207.\n3. Discussion of the surface and bulk LCO was added to the end of the Results section.\n4. A call for theoretical work to explore the origins of surface LCO are added to the\nSummary.\n5. Additional sentences have been added to lines 199-201 about the dendritic vs.\ninterdendritic regions.\n6. Labels for the supercell periodic distances (𝑞 ,𝑞 ,𝑞 ,𝑞 ) are added to Figure\n𝑆𝐶,1 𝑆𝐶,2 𝑆𝐶,3 𝑆𝐶,4\n1(g)-(h) with clarified supercell periodicity distances 𝑑 ,𝑑 ,𝑑 ,𝑑 ). Scale bars\n𝑆𝐶,1 𝑆𝐶,2 𝑆𝐶,3 𝑆𝐶,4\nin Figure 1(c)-(h) are adjusted for correct calibration factor. Figures 1(e),(f) have been\nlabelled as domains 1 and 2.\n7. Reported values in the text for the atom-atom spacing d, and supercell periodicity d_SC,\nhave been adjusted.\n8. Scale bars in Figure 2(a)-(b) are adjusted for correct calibration factor. A dotted black box\naround Figure 2(a) has been added to denote the corresponding boxed region in Figure\n1(c).\n9. Scale of displacement vector and image scale bars in Figure 3(a)-(c) are adjusted for\ncorrect calibration factor.\n10. Scale bars in Figure S2(a)-(f) are adjusted for correct calibration factor.\n11. Scale of displacement vector in Figure S4 is adjusted for correct calibration factor.\n12. Values in Table S1 are adjusted for correct calibration factor.\n13. Reported values from Table S1 in the main text have been adjusted for correct calibration\nfactor.\n14. Scale bars in Figures S5(a)-(b) are adjusted for correct calibration factor.\n15. Scale bars in Figures S6(a)-(b) are adjusted for correct calibration factor.\n16. Scale bars in Figures S7(a)-(b) are adjusted for correct calibration factor.\n17. Scale bars in Figures S8(a)-(b) are adjusted for correct calibration factor.\n18. Scale bars in Figures S9(a)-(b) are adjusted for correct calibration factor.\n19. Scale bars in Figures S10(a)-(b) are adjusted for correct calibration factor.\n20. Scale bars in Figures S11(a)-(b) are adjusted for correct calibration factor.\n21. Scale bars in Figures S12(a)-(b) are adjusted for correct calibration factor.\n22. Scale bar in Figure S14(a) is adjusted for correct calibration factor.\n23. Scale bars in Figure S15 are adjusted for correct calibration factor.\n24. Line profiles and the scale bar in Figure S16 are re-plotted with the correct calibration\nfactor.\n25. Figure 1 and Figure 2 captions have been adjusted to describe the cropped region in\nFigure 2(a).\n26. Reported values of d and d_SC have been adjusted in the main text. Additionally, the\ndescription of the text of Figure 1(d) was made to be more detailed.\n27. Additional sentences in the main text and additional references were added in the\ndiscussion of Figure 1(b), the fuzzy LEED features.\n28. Figure 1(c) has an additional black dotted box that denotes the topography of Figure 2(a),\nand the captions of Figures 1 and 2 have been adjusted."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The author has satisfactorily addressed my questions, and the manuscript can be published.", "reviewer_4": "Overall, the authors have comprehensively and rigorously addressed the questions raised in the previous review. Key issues such as the lattice constant measurements, drift effect, d_SC, and annotations have been effectively resolved and revised. The authors have also candidly acknowledged the limitations in distinguishing dendritic and interdendritic regions and clearly outlined relevant future research directions, demonstrating a rigorous academic attitude.\nAlthough the authors' grouping logic and supporting data are sufficient, it is suggested to add a global raw data statistical graph: horizontal axis (atomic height), vertical axis (count or probability density), with no classification identifiers for data points/lines/columns (e.g., color, shape). This allows readers to clearly see the obvious peaks in the raw data, which is of great concern to them.\nIt is recommended that the manuscript be published after the authors provide the raw statistical graph."}, "author_response": "Response: We thank the reviewer for agreeing to our explanation and revision and\nsuggestion for publication.\nResponse: We thank the reviewer for agreeing to our explanation and revision.\nResponse: We thank the reviewer for the great suggestion. We have added this figure into\nthe supporting information document.\nResponse: We thank the reviewer for suggesting publication after we add the statistical\ngraph."}]

Decision letter