Dataset on the structure and thermodynamic and dynamic stability of Mo2ScAlC2 from experiments and first-principles calculations.

The data presented in this paper are related to the research article entitled "Theoretical stability and materials synthesis of a chemically ordered MAX phase, Mo2ScAlC2, and its two-dimensional derivate Mo2ScC" (Meshkian et al. 2017) [1]. This paper describes theoretical phase stability calculations of the MAX phase alloy MoxSc3-xAlC2 (x=0, 1, 2, 3), including chemical disorder and out-of-plane order of Mo and Sc along with related phonon dispersion and Bader charges, and Rietveld refinement of Mo2ScAlC2. The data is made publicly available to enable critical or extended analyzes.

Specifications Table

Value of the data

This data allows other researchers to calculate and predict the phase stability of new compounds within the quaternary Mo-Sc-Al-C system and related subsystem.

The data presents refined/calculated structures that can be used as input for further theoretical evaluation of properties.

The structural information can also be used for interpretation and phase identification of, e.g., attained experimental XRD, (S)TEM, and electron diffraction data.

Data

The dataset of this paper provides information for calculated phases within the quaternary Mo-Sc-Al-C system and data obtained from refinement of the XRD pattern. Table 1 provides calculated lattice parameters, formation enthalpy, and equilibrium simplex for the chemically ordered nanolaminates Mo2ScAlC2 and Sc2MoAlC2 with different atomic stacking sequences (described in detail in Fig. 7(a) in Ref. [2]). Table 2 provides information for all considered competing phases within the quaternary system. Fig. 1 show calculated phonon spectra for Mo2ScAlC2 of order A and its corresponding end members Sc3AlC2 and Mo3AlC2. Fig. 2 depicts calculated Bader charges of atoms in MoxSc3-xAlC2 (x=0, 2, 3). Table 3 shows the data obtained from refinement of the XRD pattern, see Ref. [1]; Lattice vectors a, b and c for the majority phase Mo2ScAlC2 are 3.033, 3.033 and 18.775 Å, respectively.

Table 1

Calculated lattice parameters, equilibrium total energy E0 in eV per formula unit, formation enthalpy ΔHcp in meV per atom, and identified equilibrium simplex for Mo2ScAlC2 and Sc2MoAlC2. For comparison the corresponding end members Mo3AlC2 and Sc3AlC2 are also included.

Phase	Order	a (Å)	c (Å)	E0 (eV/fu)	ΔHcp (meV/atom)	Equilibrium simplex
Mo3AlC2		3.0716	18.541	−54.830	+141	C, Mo3Al
Mo2ScAlC2	A	3.0619	19.072	−52.431	—24	(Mo2/3Sc1/3)2AlC, MoC, ScC0.875, Mo
Mo2ScAlC2	B	3.0774	19.252	−51.972	+53	(Mo2/3Sc1/3)2AlC, MoC, ScC0.875, Mo
Mo2ScAlC2	C	3.1622	18.789	−51.601	+114	(Mo2/3Sc1/3)2AlC, MoC, ScC0.875, Mo
Mo2ScAlC2	D	3.1771	18.865	−51.505	+130	(Mo2/3Sc1/3)2AlC, MoC, ScC0.875, Mo
Mo2ScAlC2	E	3.1271	19.054	−51.348	+157	(Mo2/3Sc1/3)2AlC, MoC, ScC0.875, Mo
Mo2ScAlC2	F	3.1221	19.109	−51.663	+104	(Mo2/3Sc1/3)2AlC, MoC, ScC0.875, Mo
Mo2ScAlC2	disorder	3.1252	18.861	−51.767	+87	(Mo2/3Sc1/3)2AlC, MoC, ScC0.875, Mo
Sc2MoAlC2	A	3.1798	19.819	−48.262	+28	(Mo2/3Sc1/3)2AlC, Sc3AlC, Sc3C4
Sc2MoAlC2	B	3.1808	19.845	−48.071	+60	(Mo2/3Sc1/3)2AlC, Sc3AlC, Sc3C4
Sc2MoAlC2	C	3.1886	19.696	−47.842	+98	(Mo2/3Sc1/3)2AlC, Sc3AlC, Sc3C4
Sc2MoAlC2	D	3.1892	19.770	−47.864	+94	(Mo2/3Sc1/3)2AlC, Sc3AlC, Sc3C4
Sc2MoAlC2	E	3.2279	19.802	−47.453	+162	(Mo2/3Sc1/3)2AlC, Sc3AlC, Sc3C4
Sc2MoAlC2	F	3.1898	19.700	−47.779	+108	(Mo2/3Sc1/3)2AlC, Sc3AlC, Sc3C4
Sc2MoAlC2	disorder	3.2251	19.335	−48.088	+57	(Mo2/3Sc1/3)2AlC, Sc3AlC, Sc3C4
Sc3AlC2		3.3170	20.885	−43.406	+155	Sc3AlC, Sc3C4, ScAl3C3

Table 2

Structural information and calculated total energy for competing phases considered within the quaternary Mo-Sc-Al-C system.

Phase	Prototype structure	Pearson symbol	Space group	V (Å3/uc)	a	b	c	E0 (eV/fu)
					(Å)	(Å)	(Å)
Mo	W	cI2	Im-3m (229)	15.92	3.169			−10.850
Mo	Cu	cF4	Fm-3m (225)	16.15	4.012			−10.431
Mo	Mg	hP2	P63/mmc (194)	32.57	2.774		4.887	−10.414
Sc	Mg	hP2	P63/mmc (194)	49.25	3.321		5.157	−6.333
Sc	Sc	hP6	P6122 (178)	148.75	3.242		16.342	−6.201
Sc	Np	tP4	P4/nmm (129)	100.35	5.367		3.484	−6.223
Al	Cu	cF4	Fm-3m (225)	66.00	4.041			−3.745
Al	Mg	hP2	P63/mmc (194)	33.28	2.856		4.712	−3.712
Al	W	cI2	Im-3m (229)	16.93	3.235			−3.649
C	C (graphite)	hP4	P63/mmc (194)	38.14	2.464		7.250	−9.225
Al4C3	Al4C3	hR21	R-3m h (166)	245.00	3.355		25.129	−43.340
MoAl12	WAl12	cI26	Im-3 (204)	436.23	7.584			−57.303
MoAl5	MoAl5	hR36	R-3c h (167)	558.49	4.952		26.296	−31.001
Mo4Al17	Mo4Al17	mS84	C121 (5)	1305.85	9.187	4.939	28.974	−112.563
Mo3Al8	Mo3Al8	mS22	C12/m1 (12)	334.46	9.235	3.653	10.091	−66.170
Mo3Al	Cr3Si	cP8	Pm-3n (223)	123.48	4.980			−37.228
Sc2Al	Ni2In	hP6	P63/mmc (194)	128.50	4.902		6.176	−17.458
ScAl	CsCl	cP2	Pm-3m (221)	38.75	3.384			−10.973
ScAl	CrB	oC8	Cmcm (63)	81.00	3.338	11.101	4.371	−10.892
ScAl2	MgCu2	cF24	Fd-3m (227)	109.50	3.797			−15.277
ScAl3	AuCu3	cP4	Pm-3m (221)	69.25	4.107			−19.383
MoC	TiP	hP8	P63/mmc (194)	84.84	3.016		10.768	−19.821
MoC	NaCl	cF8	Fm-3m (225)	21.06	4.383			−19.640
MoC	η-MoC	hp12	P63/mmc (194)	126.16	3.074		15.401	−19.747
MoC	WC	hp2	P-6m2 (187)	21.00	2.928		2.829	−20.241
Mo3C2	Cr3C2	oP20	Pnma (62)	228.19	6.064	2.974	12.654	−50.938
Mo2C	β׳׳-Mo2C	hP3	P-3m1 (164)	38.06	3.068		4.669	−31.064
Mo3C	Fe3C	oP16	Pnma (62)	215.87	5.540	7.559	5.159	−40.423
Sc2C	Ti2C	cF48	Fd-3m (227)	852.33	9.481			−23.266
Sc4C3	P4Th3	cI28	I-43d (220)	188.75	7.227			−56.419
ScC0.875	NaCl	cF8	Fm-3m (225)	208.70	4.708			−14.923
ScC	NaCl	cF8	Fm-3m (225)	25.70	4.685			−15.840
Sc3C4	Sc3C4	tP70	P4/mnc (128)	851.50	7.515		15.076	−58.764
Mo3AlC	CaTiO3	cP5	Pm-3m (221)	71.70	4.154			−45.341
Mo3Al2C	Mo3Al2C	cP24	P4132 (213)	327.20	6.891			−50.299
Mo3Al2C0.9375	Mo3Al2C	cP24	P4132 (213)	1303.30	6.881			−49.691
Mo3Al2C0.875	Mo3Al2C	cP24	P4132 (213)	648.29	6.869			−49.078
Mo3Al2C0.875	Mo3Al2C	cP24	P4132 (213)	1296.87	6.870			−49.069
Mo3Al2C0.75	Mo3Al2C	cP24	P4132 (213)	321.10	6.848			−47.844
Mo2AlC	Cr2AlC	hP8	P63/mmc (194)	107.46	3.031		13.505	−35.292
Mo3AlC2	Ti3SiC2	hP12	P63/mmc (194)	151.49	3.072		18.541	−54.830
Mo4AlC3	Ti4AlN3	hP16	P63/mmc (194)	196.50	3.117		23.358	−74.552
(Mo2/3Sc1/3)2AlC	(Mo2/3Sc1/3)2AlC	mS48	C2/c (15)	689.78	9.367	5.427	13.961	−33.308
ScAl3C3	ScAl3C3	hP14	P63/mmc (194)	164.34	3.362		16.789	−47.703
Sc3AlC	CaTiO3	cP5	Pm-3m (221)	84.90	4.395			−35.023
Sc2AlC	Cr2AlC	hP8	P63/mmc (194)	141.75	3.296		15.065	−27.385
Sc3AlC2	Ti3SiC2	hP12	P63/mmc (194)	199.00	3.317		20.885	−43.406
Sc4AlC3	Ti4AlN3	hP16	P63/mmc (194)	248.50	3.296		26.414	−59.294

Fig. 1

Calculated phonon dispersion for (a) Mo2ScAlC2, (b) Sc3AlC2, and (c) Mo3AlC2.

Fig. 2

Calculated charge for atoms in Sc3AlC2, Mo2ScAlC2, and Mo3AlC2 using Bader analysis.

Table 3

Rietveld refinement of Mo2ScAlC2. The identified phases and their respective weight percentages according to the Rietveld refinement of the XRD pattern are: 1. Mo2ScAlC2 (73.9(0) wt.%), Mo2C (14.1(8) wt.%), A12O3 (7.4(0) wt.%), Mo3Al2C (3.5(0) wt.%) and, Mo3Al (1.0(2) wt.%), the total χ2 is 10.50.

Space group	P63/mmc (#194)
a (Å)	3.0334(8)
b (Å)	3.0334(8)
c (Å)	18.7750(0)
α	90.000
β	90.000
γ	120.000
Mo	4f (0.3333(3) 0.6666(7) 0.1363(2))
	Occupancy of Mo=4.00(0) and Sc=0.00(0)
Sc	2a (0.0000 0.0000 0.0000)
	Occupancy of Sc=1.83(4) and Mo=0.16(6)
Al	2b (0.0000 0.0000 0.2500) Occupancy of Al=2.00
C	4f (0.6666(7) 0.3333(3) 0.06825(5)) Occupancy of C=4.00

Experimental design, materials and methods

First-principles calculations were performed by means of density functional theory (DFT) and the projector augmented wave method [3], [4] as implemented within the Vienna ab-initio simulation package (VASP) 5.3.3 [5], [6], [7]. We adopted the non-spin polarized generalized gradient approximation (GGA) as parameterized by Perdew–Burke–Ernzerhof (PBE) [8] for treating electron exchange and correlation effects. A plane-wave energy cut-off of 400 eV was used and for sampling of the Brillouin zone we used the Monkhorst–Pack scheme [9]. The calculated total energy of all phases is converged to within 0.5 meV/atom with respect to k-point sampling and structurally optimized in terms of unit-cell volumes, c/a ratios (when necessary), and internal parameters to minimize the total energy.

Chemically disordered of Sc and Mo in MoxSc3-xAlC2 have been modelled using the special quasi-random structure (SQS) method [10], [11] on supercells of M3AX2 unit cells, with a total of 96 M-sites, respectively. Convergence tests with respect to total energy show that these sizes are appropriate to use, based on an energy of the unit cells being within 2 meV/atom compared to larger supercells.

Evaluation of phase stability was performed by identifying the set of most competing phases at a given composition, i.e. equilibrium simplex, using a linear optimization procedure [11], [12] including all competing phases in the system. A phase is considered thermodynamically stable when its energy is lower than the set of most competing phases, and when there is no imaginary frequencies in phonon spectra, i.e. an indicated dynamic stability. The approach has been proven successful to confirm already experimentally known MAX phases as well as to predict the existence of new ones [2], [13], [14].

Dynamical stability of the chemically ordered MoSc3-AlC2 (x=0, 2, 3) structures was evaluated by phonon calculations of supercells using density functional perturbation theory and as implemented in the PHONOPY code, version 1.9.1 [15], [16]. Calculated charges were obtained using Bader charge analysis, version 0.95a [17].

The synthesis of Mo2ScAlC2 were carried out by mixing elemental powders of Mo, Sc, Al and graphite in an agate mortar, put in an alumina crucible, and placed into a sintering furnace where it was heated up to 1700 °C and kept at that temperature for 30 min.

θ-2θ X-ray diffraction (XRD) measurements were performed on the samples using a diffractometer (Rikagu Smartlab, Tokyo, Japan), with Cu-K radiation (40 kV and 44 mA). The scans were recorded between 3° and 120° with step size of 0.02° and a dwell time of 7 s. XRD pattern was analyzed by Rietveld refinement using FULLPROF code [18], where 5 backgrounds parameters, scale factors, X and Y profile parameters, lattice parameters, atomic positions, the overall B-factor and the occupancies for the main as well as the impurity phases were fitted.

Funding sources

J. R. acknowledges funding from the Swedish Research Council (VR) under Grant no. 621-2012-4425 and 642-2013-8020, from the Knut and Alice Wallenberg (KAW) Foundation, and from the Swedish Foundation for Strategic Research (SSF) through the synergy grant FUNCASE. All calculations were carried out using supercomputer resources provided by the Swedish National Infrastructure for Computing (SNIC) at the National Supercomputer Centre (NSC), the High Performance Computing Center North (HPC2N), and the PDC Center for High Performance Computing.

Subject area	Physics, Materials science
More specific subject area	Phase stability predictions,
Type of data	Tables, Figures, Text file
How data was acquired	Density functional theory calculations using VASP 5.3.3, phonon dispersion using Phonopy 1.9.1, and atom charges using Bader charge analysis version 0.95a.
	θ-2θ X-ray diffraction (XRD) measurements were performed on the samples using a diffractometer (Rikagu Smartlab, Tokyo, Japan), with Cu-Kα radiation (40 kV and 44 mA). The scans were recorded between 3° and 120° with step size of 0.02° and a dwell time of 7 s.
Data format	Raw, Analyzed
Experimental factors	N/A
Experimental features	For synthesis of Mo2ScAlC2, elemental powders of Mo, Sc, Al and graphite were mixed in an agate mortar, put in an alumina crucible, and placed into a sintering furnace where it was heated up to 1700 °C and kept at that temperature for 30 min. Structural characterization was performed using X-ray diffraction (XRD), and for complementary structural and compositional analysis high-resolution scanning transmission electron microscopy (HRSTEM) measurement were carried out. See Ref. [1] for further information.
Data source location	Linköping, Sweden
Data accessibility	Data are available with this article.