Quanzheng Tao
email: quanzheng.tao@liu.se

Pernilla Helmer

Laurent Jouffret

Martin Dahlqvist

Jun Lu

Jie Zhou

Johanna Rosen

Where M = Sc Er Quanzheng Tao

Single Crystal Growth and Structural Characterization of Theoretically Predicted Nanolaminates M 2 Al 2 C 3 , Where M = Sc and Er

come

■ 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 definition 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 environment and Ohmic contact for semiconductors. 5,6 Among their interesting properties are also their diverse magnetic characteristics, 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 twodimensional 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 ■ METHOD Experimental Details. Single crystals of Sc 2 Al 2 C 3 were 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 as flux for the single crystal growth. The furnace was heated at 5 °C min -1 up 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.

Er 2 Al 2 C 3 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 ErAl 3 C 3 , 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 was flowing. The furnace was then heated at 5 °C min -1 up to 1500 °C and held at 1500 °C for 5 h, before the furnace cooling to room temperature (RT).

A specimen of Sc 2 Al 2 C 3 , 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. [START_REF]SAINT V8.40A[END_REF] 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°9 (0.48 Å resolution), of which 343 were independent (average redundancy 46.892, completeness = 98.8%, R int = 6.97%, R sig = 1.36%) and 338 (98.54%) were greater than 2σ(F 2 ). The final cell constants of a = 3.3750(3) Å, b = 3.3750(3) Å, c = 25.590(3) Å, volume = 252.43(5) Å 3 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). [START_REF] Krause | Comparison of silver and molybdenum microfocus X-ray sources for single-crystal structure determination[END_REF] The 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 (λ Kα ≈ 1.54 Å). Scanning transmission electron microscopy (STEM) combined with high angle annular dark field imaging (STEM-HAADF) was performed in the double-corrected Linkoping FEI Titan 3 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). [START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] The exchangecorrelation (xc) energy functionals used are constructed using the Perdew-Burke-Ernzerhof (PBE) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] generalized gradient approximation (GGA). The projector augmented wave (PAW) [START_REF] Blochl | Projector augmented-wave method[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] method 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 -1 and the energy cutoff for the plane wave expansion was set to 400 eV.

The stability of the M 2 Al 2 C 3 phases, where M denotes Sc or Y, was investigated by comparing the total energy of the 223 phase, E 223 , to that of any linear combination of competing phases, E cp , for a fixed 223 stoichiometry. Temperature dependent effects were not considered, since these tend to cancel out, leaving the 0 K terms to dominate also at finite temperatures. [START_REF] Thore | Temperature dependent phase stability of nanolaminated ternaries from firstprinciples calculations[END_REF] Both experimentally known and hypothetical phases were considered; for more details, see C sublayers are known to be prone to hydrolysis. [START_REF] Gesing | The Crystal Structures of Zr 3 Al 3 C 5 , ScAl 3 C 3 , and UAl 3 C 3 and Their Relation to the Structures of U 2 Al 3 C 4 and Al 4 C 3[END_REF][START_REF] Fukuda | Crystal structure and thermoelectric properties of YAl 3 C 3[END_REF] Probably 193 the degradation is due to reaction with moisture in the air.

194

The structure was solved and refined using the Bruker 195 SHELXTL Software Package, [START_REF] Sheldrick | Program for structure solution; Universitaẗ of Goẗtingen[END_REF][START_REF] Sheldrick | /3 and SHELXL ver. 2018/3: Programs for crystal structure solution and refinement[END_REF] 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. [START_REF] Meshkian | W-Based Atomic Laminates and Their 2D Derivative W 1.33 C MXene with Vacancy Ordering[END_REF][START_REF] Dahlqvist | Prediction and synthesis of a family of atomic laminate phases with Kagome-like and in-plane chemical ordering[END_REF] The phase stability analysis showed Crystal Growth & Design

  177supercell size for a 5 × 5 × 1 supercell. The PHONOPY[START_REF] Togo | First principles phonon calculations in materials science[END_REF] code was 178 used for the generation of displacements and for post processing of 179 the data. Dynamical stability of a phase is indicated by the lack of 180 negative phonon frequencies. The Brillouin zone was sampled at the 181 high symmetry points for a hexagonal lattice according to the thin plate shape close to 1 × 1 mm 2 were grown 186 by the flux method. After growth, the sample was left under 187 ambient condition for 2 days. After exposure to air, the flux 188 turned into powder and the crystal can be picked out. The 189 crystals were found to degrade under ambient condition in 190 approximately 1 week, and they were therefore kept in a 191 glovebox before characterization. Layered compounds with Al-192

  confirm the structure obtained from the XRD. Figure 1 211 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 3are in good agreement with those found in ScAl 3 C 3 , except for the logical lengthening of the Al-Al and Sc-Sc distances.[START_REF] Gesing | The Crystal Structures of Zr 3 Al 3 C 5 , ScAl 3 C 3 , and UAl 3 C 3 and Their Relation to the Structures of U 2 Al 3 C 4 and Al 4 C 3[END_REF][START_REF] Tsokol | Crystal structure of ScAl 3 C 3[END_REF] 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 Figure2in 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.

Figure 1 .

 1 Figure 1. (a) STEM image of Sc 2 Al 2 C 3 along [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.

Figure 5

 5 Figure 5 shows the STEM image 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 .

 2 Figure 2. Phonon calculations for Sc 2 Al 2 C 3 showing (left) phonon dispersion and (right) total and partial phonon density of states.

Figure 3 .

 3 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 quasirandom and ordered structures, respectively. The dotted lines are linear fits to the Al (red) and C (blue) disordered data, specified to include the full structure point at (0,0).

Figure 4 .

 4 Figure 4. XRD pattern of a sample containing Er 2 Al 2 C 3 . ErAl 2 is also present. The remaining peaks are not identified.

Figure 5 .

 5 Figure 5. STEM images of Er 2 Al 2 C 3 along (a) the [100] zone axis and (b) the [210] zone axis.

Table 1 .

 1 The phase is concluded stable if the 135 formation enthalpy, ΔH cp , is negative

	Δ H cp	=	E	223	-	< min ( ) 0 E cp		(1)	136
	at a specific site, ΔG z , can be estimated as	145
	Δ = Δ -Δ G H T S z z z				(2)	146
	where the formation enthalpy ΔH z is defined as ΔH cp in eq 1, but with E 223 →E z being the energy of the disordered structure with	147 148
	impurity concentration z instead of the ordered with 223	149
	stoichiometry. Since the stoichiometry of a phase with impurities	150
	can differ from that of the fully populated structure, min (E cp ) 223 does	151
	ideal disordering of the disordered structure, given by	155
	Δ = -S z	+ ( ln( ) (1 yk z z B	-	z	)ln(1	-	z	))	(3)	156

134 Supplementary 137 In order to identify the set of competing phases with the lowest 138 energy, E cp , in the following referred to as the set of most competing 139 phases, a constrained minimization procedure was performed by 140 constructing the convex hull as described in ref 28. For this task, the 141 python package ASE 29 was utilized. 142 The vacancy formation on the Al and C sites was investigated at 143 finite temperatures T for both ordered and disordered structures. The 144 Gibbs free energy of a disordered phase with impurity concentration z 152 not need to be equal to min (E cp ) z , but needs to be specifically 153 evaluated for each structure. In this work, the only type of impurity 154 considered was vacancies. ΔS z is the entropy per fomula unit for an 157 Here, z is again the impurity concentration, y the number of sites 158 per formula unit considered for the impurity (that is 2 for Al and 3 for 159 C), and k B the Boltzmann factor. The disordered structures were 160 modeled using the special quasi-random structure (SQS) method 30 to 161 generate different supercells consisting of 2 × 2 × 1 to 4 × 4 × 1 unit 162 cells. The SQS method tries to match the number of nearest 163 neighbors, second nearest neighbors, etc., for the supercell model to 164 that of the ideal disordered structure. Hence, a quasi-random 165 structure is constructed on a finite supercell. These supercells were 166 relaxed until the total free energy was converged to within 5 × 10 -5 167 eV/atom, but the previously mentioned requirement for the ionic 168 force convergence was not enforced for the larger supercells 169 considered. 170 ΔG z in eq 2 can be compared to the formation enthalpy, ΔH cp , of 171 the corresponding ordered phase, to identify at what temperature a 172 disordered phase is energetically favorable to an ordered one. 173 The dynamical stability of the Sc 2 Al 2 C 3 structure, i.e., stability with 174 respect to lattice vibrations, was studied through the phonon 175 dispersion. The phonon band structure was calculated using the 176 finite displacement method and qualitatively converged w. r. t.

  197 the final anisotropic full-matrix least-squares refinement on F 2 198 with 12 variables converged at R1 = 3.18%, for the observed 199 data, and at wR2 = 8.56% for all data. The goodness-of-fit was 200 1.318. The largest peak in the final difference electron density 201 synthesis was 2.637 e -/Å 3 , and the largest hole was -0.562 e -/ 202 Å 3 with an RMS deviation of 0.311 e -/Å 3 . On the basis of the 203 final model, the calculated density was 3.550 g/cm 3 and 204 F(000) was 258. The sample and crystal data are summarized

	t1	205 in Table 1. CCDC 1995886 contains the supplementary

giving the space group R3̅ m, 196 with Z = 3 formula units per Sc 6 Al 6 C 9 unit cell. In more detail, Crystal Growth & Design https://dx.doi.org/10.1021/acs.cgd.0c00719 Cryst. Growth Des. XXXX, XXX, XXX-XXX B 206 crystallographic data for this paper. The data can be obtained 207 free of charge from The Cambridge Crystallographic Data 208 Centre via www.ccdc.cam.ac.uk/structures.

Table 1 .

 1 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 Table1. The complete list of phases is given in Supplementary Table1. 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 Sample and Crystal Data for Sc 2 Al 2 C 3

	unit cell formula (Z = 3)	Sc 6 Al 6 C 9
	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

t2 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 f2 in Figure

2

and Supplementary Figure

3

, respectively. Neither

Table 2 .

 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

https://dx.doi.org/10.1021/acs.cgd.0c00719Cryst. Growth Des. XXXX, XXX, XXX-XXX