Single Crystal Growth and Structural Characterization of Theoretically Predicted Nanolaminates M2Al2C3, Where M = Sc and Er

Single Crystal Growth and Structural Characterization of

Theoretically Predicted Nanolaminates M

₂

Al

₂

C

₃

, Where M = Sc and

Er

Quanzheng Tao,

*

Pernilla Helmer, Laurent Jouffret, Martin Dahlqvist, Jun Lu, Jie Zhou,

and Johanna Rosen

Cite This:Cryst. Growth Des. 2020, 20, 7640−7646 Read Online

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*

sı Supporting Information

ABSTRACT:

Nanolaminated materials including magnetic

ele-ments are of special interest for commonly observed nontrivial

magnetic characteristics and as potential precursors for 2D

materials. Here, we explore the previously unknown layered phase

M

2

Al

2

C

3

, where M = Sc and Er. Sc

2

Al

2

C

3

was synthesized as single

crystals of

∼mm

2

_{size, and its structure was determined by single}

crystal X-ray di

ffraction and scanning transmission electron

microscopy. Evaluation of phase stability and possible vacancy

formation based on

first-principles calculations confirms the

attained phase and suggests full occupancy on both the Al and C

sites. Potential realization of the hypothetical phase Y

2

Al

2

C

3

is also

proposed. Furthermore, we also demonstrate that Er

₂

Al

₂

C

₃

can be

synthesized in powder form, providing experimental evidence for

stoichiometries based on rare earth elements, which, in turn, suggests possible incorporation of other lanthanides.

■

INTRODUCTION

Nanolaminated materials are interesting for, e.g., their

commonly observed anisotropic properties. One such example

is the family of MAX phases, being atomically laminated metal

carbides/nitrides of the general formula M

n+1

AX

n

, where M is a

transition metal, A is an A group element, and X is carbon

and/or nitrogen (n = 1

−3).

1,2

More recently, the de

finition of

M has been expanded to also include rare earth (RE)

elements.

3,4

MAX phases show a unique combination of

ceramic and metallic properties and are promising for various

applications, such as structural materials for extreme

environ-ment and Ohmic contact for semiconductors.

5,6

Among their

interesting properties are also their diverse magnetic

character-istics, observed for Mn-based phases

7,8

as well as RE-based

MAX phase quaternaries.

3

Besides MAX phases, there are

other laminated materials with alternating metal carbide and

aluminum carbide layers, being structurally related to MAX

phases and of interest for studying magnetism. For example,

YbAl

3

C

3

, with alternating Yb layers and Al-C layers, is a

two-dimensional spin-singlet system.

9

Layered materials are also interesting as precursors for

producing 2D materials. Two-dimensional metal carbides and

nitrides, called MXene, are derived from MAX phases by

selective removal of the A layer in chemical etching

procedures.

10,11

They have shown promise for various

applications, including energy storage and catalysis.

12

About

30 MXenes have been synthesized to date, including alloy

compositions. Sc

2

C MXene has to date not been

exper-imentally realized, though several theoretical studies on Sc

₂

C

indicate potential for use in semiconductors and as

catalyst.

13−15

However, experimental realization of Sc

2

C

MXene is hindered by the lack of suitable 3D precursor

materials. The Sc-containing MAX phases, Sc

2

InC and

(Mo

2/3

Sc)

2

AlC, are not suitable for such purpose; In is

challenging to remove, while Sc as well as Al is removed when

etching (Mo

2/3

Sc)

2

AlC.

16

Other laminated materials with alternating transition metal

carbide and aluminum carbide layers have been shown suitable

for 2D materials formation. Zhou et al. produced Zr

3

C

2

MXene from Zr

3

Al

3

C

517

and a Sc-based 2D material from

ScAl

₃

C

₃

.

18

Here, we explore novel layered phases in the Sc-Al-C and

Er-Al-C systems, both for potentially interesting magnetic

properties as well as to serve as possible precursors for 2D

material formation.

Received: May 27, 2020 Revised: October 18, 2020 Published: November 2, 2020 Article pubs.acs.org/crystal

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■

METHOD

Experimental Details. Single crystals of Sc₂Al2C3were grown by the flux method. Elemental powders, Sc (99.9%) from Stanford Advanced Materials, Al (99.8%) from Alfa Aesar, and Graphite (99.999%) from Sigma-Aldrich, were mixed in a molar ratio of Sc:Al:C = 2:8:1 in an agate mortar and then placed in an alumina crucible that was inserted in an alumina tube furnace. An excess amount of Al served asflux for the single crystal growth. The furnace was heated at 5°C min−1up to 1600°C and held at 1600 °C for 1 h, and was thereafter cooled to 1300°C in 4 days, with subsequent cooling to 800°C at 10 °C min−1. Then the furnace is shut down to cool to room temperature.

Er2Al2C3 samples were prepared by a solid state reaction of elemental powders: Er (99.9%) from Stanford Advanced Materials, Al (99.8%) from Alfa Aesar, and Graphite (99.999%) from Sigma-Aldrich, mixed in a molar ratio of Er:Al:C = 2:2:1. The composition was chosen to avoid the formation of the competing phase ErAl3C3, which is obtained when the stoichiometric 223 ratio is used. Powders were manually mixed in an agate mortar and placed in an alumina crucible that was, in turn, inserted in an alumina tube furnace through which 5 sccm Ar wasflowing. The furnace was then heated at 5 °C min−1up to 1500°C and held at 1500 °C for 5 h, before the furnace cooling to room temperature (RT).

A specimen of Sc2Al2C3, of approximate dimensions 0.080 mm× 0.340 mm × 0.445 mm, was used for the X-ray crystallographic analysis on a Bruker APEX2 SC diffractometer equipped with an OXFORD Cryosystems 700 cooler. X-ray intensity data were measured with Mo Kα radiation (λ = 0.71073 Å) with a total exposure time of 31.92 h at 203 K. The frames were integrated with the Bruker SAINT software package using a narrow-frame algorithm.19 The integration of the data using a trigonal unit cell yielded a total of 16 084 reflections to a maximum θ angle of 47.28° (0.48 Å resolution), of which 343 were independent (average redundancy 46.892, completeness = 98.8%, Rint = 6.97%, Rsig = 1.36%) and 338 (98.54%) were greater than 2σ(F2_{). Thefinal cell} constants of a = 3.3750(3) Å, b = 3.3750(3) Å, c = 25.590(3) Å, volume = 252.43(5) Å3_{are based upon the refinement of the XYZ} centroids of 9709 reflections above 20 σ(I) with 4.778° < 2θ < 94.07°. Data were corrected for absorption effects using the Numerical Mu from Formula method (SADABS).20The calculated minimum and maximum transmission coefficients (based on crystal size) are 0.2510 and 0.7250.

X-ray powder diffraction (XRD) was carried out on a PANalytical X’Pert powder diffractometer with a Cu source (λKα ≈ 1.54 Å). Scanning transmission electron microscopy (STEM) combined with

high angle annular dark field imaging (STEM-HAADF) was

performed in the double-corrected Linköping FEI Titan3 _operated

at 300 kV. Energy dispersive X-ray spectroscopy (EDX, Oxford Instruments X-Max detector) was performed inside a scanning electron microscope (SEM, LEO 1550).

Computational Details. All calculations within this work were based on Density Functional Theory (DFT) as implemented in the Vienna Ab initio Simulation Package (VASP).21−23 The exchange-correlation (xc) energy functionals used are constructed using the Perdew−Burke−Ernzerhof (PBE)24_{generalized gradient}

approxima-tion (GGA). The projector augmented wave (PAW)25,26method was used for treating the crystal potential. All structures with full site occupation were relaxed until the forces between ions were converged to within 5 × 10−3 eV/Å per ion, and the total free energy was converged to within 5 × 10−5 eV/atom. The Brillouin zone was sampled with a k-point density of at least 10 points per Å−1and the energy cutoff for the plane wave expansion was set to 400 eV.

The stability of the M2Al2C3phases, where M denotes Sc or Y, was investigated by comparing the total energy of the 223 phase, E223, to that of any linear combination of competing phases, Ecp, for afixed 223 stoichiometry. Temperature dependent effects were not considered, since these tend to cancel out, leaving the 0 K terms to dominate also atfinite temperatures.27 Both experimentally known and hypothetical phases were considered; for more details, see

Supplementary Table 1. The phase is concluded stable if the formation enthalpy,ΔHcp, is negative

ΔHcp=E223−min (Ecp)<0 (1)

In order to identify the set of competing phases with the lowest energy, Ecp, in the following referred to as the set of most competing phases, a constrained minimization procedure was performed by constructing the convex hull as described in ref28. For this task, the python package ASE29was utilized.

The vacancy formation on the Al and C sites was investigated at finite temperatures T for both ordered and disordered structures. The Gibbs free energy of a disordered phase with impurity concentration z at a specific site, ΔGz, can be estimated as

ΔGz= ΔHz−T SΔ z (2)

where the formation enthalpyΔHzis defined as ΔHcp ineq 1, but with E223→Ez being the energy of the disordered structure with impurity concentration z instead of the ordered with 223 stoichiometry. Since the stoichiometry of a phase with impurities can differ from that of the fully populated structure, min (Ecp)223does not need to be equal to min (Ecp)z, but needs to be specifically evaluated for each structure. In this work, the only type of impurity considered was vacancies.ΔSzis the entropy per fomula unit for an ideal disordering of the disordered structure, given by

ΔSz= −yk zB( ln( )z +(1−z)ln(1−z)) (3)

Here, z is again the impurity concentration, y the number of sites per formula unit considered for the impurity (that is 2 for Al and 3 for C), and kB the Boltzmann factor. The disordered structures were modeled using the special quasi-random structure (SQS) method30to generate different supercells consisting of 2 × 2 × 1 to 4 × 4 × 1 unit cells. The SQS method tries to match the number of nearest neighbors, second nearest neighbors, etc., for the supercell model to that of the ideal disordered structure. Hence, a quasi-random structure is constructed on afinite supercell. These supercells were relaxed until the total free energy was converged to within 5× 10−5 eV/atom, but the previously mentioned requirement for the ionic force convergence was not enforced for the larger supercells considered.

ΔGzineq 2can be compared to the formation enthalpy,ΔHcp, of the corresponding ordered phase, to identify at what temperature a disordered phase is energetically favorable to an ordered one.

The dynamical stability of the Sc2Al2C3structure, i.e., stability with respect to lattice vibrations, was studied through the phonon dispersion. The phonon band structure was calculated using the finite displacement method and qualitatively converged w. r. t. supercell size for a 5× 5 × 1 supercell. The PHONOPY31code was used for the generation of displacements and for post processing of the data. Dynamical stability of a phase is indicated by the lack of negative phonon frequencies. The Brillouin zone was sampled at the high symmetry points for a hexagonal lattice according to the path suggested in ref32.

■

RESULTS AND DISCUSSION

Synthesis and Characterization of Sc

2

Al

2

C

3

. Single

crystals with a thin plate shape close to 1

× 1 mm

2

_{were grown}

by the

flux method. After growth, the sample was left under

ambient condition for 2 days. After exposure to air, the

flux

turned into powder and the crystal can be picked out. The

crystals were found to degrade under ambient condition in

approximately 1 week, and they were therefore kept in a

glovebox before characterization. Layered compounds with

Al-C sublayers are known to be prone to hydrolysis.

33,34

Probably

the degradation is due to reaction with moisture in the air.

The structure was solved and re

fined using the Bruker

SHELXTL Software Package,

35,36

giving the space group R3

̅m,

with Z = 3 formula units per Sc

6

Al

6

C

9

unit cell. In more detail,

the

final anisotropic full-matrix least-squares refinement on F

2

with 12 variables converged at R1 = 3.18%, for the observed

data, and at wR2 = 8.56% for all data. The goodness-of-

fit was

1.318. The largest peak in the

final difference electron density

synthesis was 2.637 e

−

/Å

3

_{, and the largest hole was}

_{−0.562 e}

−

_/

Å

3

with an RMS deviation of 0.311 e

−

/Å

3

. On the basis of the

final model, the calculated density was 3.550 g/cm

3

_and

F(000) was 258. The sample and crystal data are summarized

in

Table 1. CCDC

1995886

contains the supplementary

crystallographic data for this paper. The data can be obtained

free of charge from The Cambridge Crystallographic Data

Centre via

www.ccdc.cam.ac.uk/structures.

A scanning transmission electron microscope (STEM) was

used to confirm the structure obtained from the XRD.

Figure 1

shows STEM images along the [100] and [210] zone axes,

with corresponding schematics of the concluded crystal

structure. Due to Z-contrast, Sc appears to be brighter, Al is

weaker in contrast, and C is not visible. As shown in the

figure,

the structure consists of Sc

₂

C layers interleaved with Al

₂

C

₂

layers, resembling the stacking of a MAX phase structure (e.g.,

Sc

₂

InC) and the laminate ScAl

₃

C

₃

. Bond distances in Sc

₂

Al

₂

C

₃

are in good agreement with those found in ScAl

3

C

3

, except for

the logical lengthening of the Al

−Al and Sc−Sc distances.

33,37

In the MAX phase structure, Sc

₂

C layers are interleaved with a

single A layer, while in the ScAl

3

C

3

structure, Sc layers are

interleaved with Al

3

C

3

layers. The Sc-to-Al ratio is confirmed

by EDX, as shown in

Supplementary Figure 2

in the

Supporting Information, with an obtained Sc:Al ratio being

close to 1:1.

Theoretical Phase Stability of M

2

Al

2

C

3

, M = Sc and Y.

The theoretical evaluation for M equal to both Sc and Y was

motivated by similar elemental characteristics, and previous

observations of so-called i-MAX phases, where Sc can typically

be exchanged for Y.

38,39

The phase stability analysis showed

that Sc

2

Al

2

C

3

is predicted stable, consistent with our

experimental observations, with a formation enthalpy of

−44

meV/atom compared to its set of most competing phases, as

given in

Table 1. The complete list of phases is given in

Supplementary Table 1. Y

₂

Al

₂

C

₃

was found to have a

formation enthalpy of +4 meV/atom, and is thus predicted

to be close to stable or possibly metastable, with the set of

most competing phases found in

Table 2. Again, the complete

list of competing phases is given in

Supplementary Table 1.

The phonon dispersion for Sc

2

Al

2

C

3

and Y

2

Al

2

C

3

is shown

in

Figure 2

and

Supplementary Figure 3, respectively. Neither

Table 1. Sample and Crystal Data for Sc

2

Al

2

C

3

unit cell formula (Z = 3)

Sc6Al6C9

formula weight 539.74 g/mol temperature 203(2) K wavelength 0.71073 Å

crystal size 0.080× 0.340 × 0.445 mm crystal system trigonal

space group R3̅m

unit cell dimensions a = b = 3.3750(3) Å α = β = 90° a_calc= bcalc= 3.3845 Å αcalc=βcalc= 90°

c = 25.590(3) Å γ = 120° c_calc= 25.6309 Å γ_calc= 120° volume 252.43(5) Å3 Sc 6c (2/3, 1/3, 0.45209(2)) Al 6c (0, 0, 0.36729(3)) C1 6c (1/3, 2/3, 0.38526(8)) C2 3b (0, 0, 0.5) Z 3 density (calcd) 3.550 g/cm3 absorption coefficient 4.293 mm−1 F(000) 258

Figure 1.(a) STEM image of Sc2Al2C3along [100] zone axis, with schematic. The dashed line in the schematic indicates the size of the unit cell. (b) STEM image along [210] zone axis, with schematic.

Table 2. Formation Enthalpy for Sc

2

Al

2

C

3

and Y

2

Al

2

C

3

, and

Their Respective Set of Most Competing Phases

M2Al2C3 ΔHcp(meV/atom) most competing phases

M = Sc −44 ScAl3C3, Sc3C4, Sc3AlC

of them shows any negative frequencies, indicating that both

materials are dynamically stable.

Possible vacancy formation on the Al and C sites was

theoretically evaluated for Sc

2

Al

2

C

3

, using the fully occupied

structure without any vacancies as reference point.

Figure 3

shows the vacancy formation energy

ΔH

z

, as a function of

vacancy concentration z for C (in red) and Al (in blue). The

circles correspond to ordered vacancy con

figurations and the

diamonds to SQS con

figurations. The gray circle corresponds

to Sc

2

Al

2

C

3

without vacancies. The positive vacancy formation

energies indicate that Sc

₂

Al

₂

C

₃

is not prone to form any

vacancies. Furthermore, it costs more energy to form an Al

vacancy than a C vacancy.

The Al atoms occupy only one Wycko

ff site, while the C

atoms occupy two Wycko

ff sites, one between the Sc atoms

with three sites in the unit cell, and one next to each Al atom

with six sites in the unit cell.

Figure 3

shows a large spread in

formation enthalpy for the structures with C vacancies at the

same vacancy concentration. This is due to the di

fference in

binding energy of the two sites, where it costs more energy to

remove a C atom in the Sc layers compared to in the Al layers.

The data also show that, for the energetically most favorable Al

vacancy structures, the penalty in going from 8% to 17%

vacancy concentration, and from 25% to 33%, is very small.

These structures at 17% and 33% each correspond to

completely emptying an Al-C layer of Al atoms, which, for

the 8% and 25% structures, were only half-empty. This resulted

in a relaxed structure where the C atoms had considerably

rearranged themselves to compensate for the Al vacancies in a

way they did not for the half-empty layers.

The Gibbs free energy,

ΔG

_z

, at non-zero temperature for the

disordered vacancy structures can be estimated by

eq 2. Thus,

a disordered structure becomes more favorable the higher the

temperature, and could become stable at elevated

temper-atures. The entropic contributions at T = 2000 K for Sc

₂

Al

₂

C

₃

are between 26

−47 and 14−31 meV/atom for the C and Al

vacancy structures, respectively, depending on the vacancy

concentration. Thus, the vacancy structures only start to be

comparable in energy per atom to the fully occupied structure

at temperatures far above those reached during synthesis.

Synthesis and Characterization of Er

2

Al

2

C

3

. After

identi

fication of the structure of Sc

2

Al

2

C

3

, we also attempted

to synthesize RE-containing compounds with the same

structure by solid state reaction of elemental powders.

In the ternary Er-Al-C phase diagram, Er

₂

Al

₂

C

₃

is located

close to ErAl

3

C

3

. When the initial elemental powder ratios

were close to the stoichiometry of ErAl

₃

C

₃

, for example, with a

stoichiometry ratio of Er

2

Al

2

C

3

, ErAl

3

C

3

was found to be the

majority phase. A simpli

fied phase diagram of the Er-Al-C

ternary system is shown in

Supplementary Figure 4. The initial

power compositions were therefore chosen to avoid the

ErAl

3

C

3

phase, resulting in an optimized elemental powder

ratio of Er:Al:C = 2:2:1.

Figure 4

shows the X-ray powder

di

ffraction pattern of Er

₂

Al

₂

C

₃

. The major peaks are indexed

with Er

2

Al

2

C

3

and ErAl

2

, while the origin of the remaining

peaks is not identi

fied. Due to limited sample purity, we herein

only show evidence of the Er

2

Al

2

C

3

phase and save more

detailed analysis of the sample for future investigations.

Figure 5

show the STEM images of Er

2

Al

2

C

3

along the

[100] and [210] zone axes. Due to the Z-contrast, Er appears

the brightest, Al is very weak, and C is not visible at all.

After analysis of the here reported novel laminate phases

Sc

2

Al

2

C

3

and Er

2

Al

2

C

3

, we can conclude that the structure

consists of M

₂

C layers interleaved with Al

₂

C

₂

layers and is as

such closely related to the MAX phase structure (e.g., Sc

2

InC)

and other MAX phase like laminates (ScAl

₃

C

₃

). Considering

their structural similarity, similar properties may be expected,

Figure 2. Phonon calculations for Sc2Al2C3 showing (left) phonon dispersion and (right) total and partial phonon density of states.

Figure 3.Formation enthalpy (at zero temperature) for structures with vacancies at the Al (red data) or C sites (blue data) at different vacancy concentrations. Diamond shapes and circles indicate quasi-random and ordered structures, respectively. The dotted lines are linearfits to the Al (red) and C (blue) disordered data, specified to include the full structure point at (0,0).

Figure 4.XRD pattern of a sample containing Er2Al2C3. ErAl2is also present. The remaining peaks are not identified.

such as anisotropic character and mixed ceramic and metallic

properties. This remains to be explored. Furthermore, the

i-MAX phases based on RE include Er as well as 11 other

lanthanide elements. This strongly indicates that more

M

2

Al

2

C

3

phases may exist, with RE elements beyond Er.

Consequently, Er

₂

Al

₂

C

₃

along with other possible

RE-containing analogues would be highly interesting for

investigations of magnetism in nanolaminated structures, in

line with previous systematic studies on RE-based i-MAX

phases.

3

Finally, another promising prospect of these materials

is for potential conversion into the 2D counterparts, by either

selective etching or mechanical exfoliation. If the Al-C layers

would be removed, M

2

C layers would be produced, which

would lead to a structure and composition identical to those of

a conventional MXene.

■

CONCLUSION

In summary, we synthesized two novel nanolaminated

materials of the general formula, M

2

Al

2

C

3

, M = Sc and Er.

We determined the structure of single crystal Sc

2

Al

2

C

3

by

single crystal XRD and STEM, while the crystal structure of a

powder sample of Er

2

Al

2

C

3

was determined by STEM. Both

phases crystallize in the R3

̅m structure with alternating M

2

C

and Al

2

C

2

layers. The structure is closely related to MAX phase

structures and other nanolaminates with intermediate Al-C

layers. We also studied the theoretical phase stability of the

Sc

2

Al

2

C

3

and the hypothetical Y

2

Al

2

C

3

phase, and possible

vacancy formation in Sc

2

Al

2

C

3

, based on

first-principles

calculations. The phases were predicted stable, respectively,

metastable, with no driving force for vacancy formation in

Sc

₂

Al

₂

C

₃

. These materials are interesting for further

explora-tion with respect to fundamental properties, and as potential

precursors for 2D materials. Furthermore, Er

₂

Al

₂

C

₃

, along with

suggested possible other RE-based analogues, may display

interesting magnetic characteristics.

■

ASSOCIATED CONTENT

*

sı Supporting Information

The Supporting Information is available free of charge at

https://pubs.acs.org/doi/10.1021/acs.cgd.0c00719.

Digital image of a single crystal, EDX spectrum, phonon

calculations for Y

₂

Al

₂

C

₃

, phase diagram, and considered

competing phases used for the stability calculation

(PDF)

Accession Codes

CCDC

1995886

contains the supplementary crystallographic

data for this paper. These data can be obtained free of charge

via

www.ccdc.cam.ac.uk/data_request/cif, or by emailing

data_request@ccdc.cam.ac.uk, or by contacting The

Cam-bridge Crystallographic Data Centre, 12 Union Road,

Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

■

AUTHOR INFORMATION

Corresponding Author

Quanzheng Tao − Thin Film Physics Division, Department of

Physics, Chemistry, and Biology (IFM), Linko

̈ping University,

SE-581 83 Linko

̈ping, Sweden;

orcid.org/0000-0002-4073-5242; Email:

quanzheng.tao@liu.se

Authors

Pernilla Helmer − Thin Film Physics Division, Department of

Physics, Chemistry, and Biology (IFM), Linko

̈ping University,

SE-581 83 Linköping, Sweden

Laurent Jouffret − Univ. Grenoble Alpes, CNRS, Grenoble INP,

LMGP, 38000 Grenoble, France

Martin Dahlqvist − Thin Film Physics Division, Department of

Physics, Chemistry, and Biology (IFM), Linko

̈ping University,

SE-581 83 Linko

̈ping, Sweden;

orcid.org/0000-0001-5036-2833

Jun Lu − Thin Film Physics Division, Department of Physics,

Chemistry, and Biology (IFM), Linköping University, SE-581

83 Linko

̈ping, Sweden

Jie Zhou − Thin Film Physics Division, Department of Physics,

Chemistry, and Biology (IFM), Linko

̈ping University, SE-581

83 Linköping, Sweden

Johanna Rosen − Thin Film Physics Division, Department of

Physics, Chemistry, and Biology (IFM), Linköping University,

SE-581 83 Linko

̈ping, Sweden;

orcid.org/0000-0002-5173-6726

Complete contact information is available at:

https://pubs.acs.org/10.1021/acs.cgd.0c00719

Notes

The authors declare no competing

financial interest.

■

ACKNOWLEDGMENTS

This work was supported by the Knut and Alice Wallenberg

(KAW) Foundation through a Fellowship Grant, Project

funding (KAW 2015.0043), and by support to the Linköping

Ultra Electron Microscopy Laboratory. The Swedish Research

council is gratefully acknowledged through Project

642-2013-8020. This work was also

financially supported by the

Flag-ERA JTC 2017 project entitled

“MORE-MXenes”, and the

Swedish Foundation for Strategic Research (SSF) through a

synergy grant (EM16-0004). The calculations were carried out

using supercomputer resources provided by the Swedish

National Infrastructure for Computing (SNIC) at the National

Supercomputer Centre (NSC) and the High Performance

Computing Center North (HPC2N).

■

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