Herein, we report on the phase stabilities and crystal structures of two newly discovered ordered, quaternary MAX phases—Mo2TiAlC2 and Mo2Ti2AlC3—synthesized by mixing and heating different elemental powder mixtures of mMo:(3-m)Ti:1.1Al:2C with 1.5 ≤ m ≤ 2.2 and 2Mo: 2Ti:1.1Al:2.7C to 1600 °C for 4 h under Ar flow. In general, for m ≥ 2 an ordered 312 phase, (Mo2Ti)AlC2, was the majority phase; for m < 2, an ordered 413 phase (Mo2Ti2)AlC3, was the major product. The actual chemistries determined from X-ray photoelectron spectroscopy (XPS) are Mo2TiAlC1.7 and Mo2Ti1.9Al0.9C2.5, respectively. High resolution scanning transmission microscopy, XPS and Rietveld analysis of powder X-ray diffraction confirmed the general ordered stacking sequence to be Mo-Ti-Mo-Al-Mo-Ti-Mo for Mo2TiAlC2 and Mo-Ti-Ti-Mo-Al-Mo-Ti-Ti-Mo for Mo2Ti2AlC3, with the carbon atoms occupying the octahedral sites between the transition metal layers. Consistent with the experimental results, the theoretical calculations clearly show that M layer ordering is mostly driven by the high penalty paid in energy by having the Mo atoms surrounded by C in a face-centered configuration, i.e., in the center of the Mn+1Xn blocks. At 331 GPa and 367 GPa, respectively, the Young's moduli of the ordered Mo2TiAlC2 and Mo2Ti2AlC3 are predicted to be higher than those calculated for their ternary end members. Like most other MAX phases, because of the high density of states at the Fermi level, the resistivity measurement over 300 to 10 K for both phases showed metallic behavior.

The MAX phases are a large family of hexagonal, ternary, carbides and nitrides with a general formula Mn+1AXn, where n = 1, 2, 3, etc., M is an early transition metal (Sc, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, etc.), A is a group 13 to 16 element (Al, Ga, In, Tl, Si, Ge, Sn, Pb, P, As, etc.) and X is carbon and/or nitrogen.1–3 Depending on the number of M layers, the shorthand notation 211, 312, and 413 is typically used, when n is 1, 2, or 3, respectively. These phases combine some of the best attributes of metals and ceramics, which can be ascribed to their thermodynamically stable nanolaminated layered structure and the metal-like nature of their bonding. Like metals, they are electrically and thermally conductive, most readily machinable,4,5 not susceptible to thermal shock, plastic at high temperatures, and exceptionally damage tolerant.6 Like ceramics, some of them are elastically rigid (Young's moduli > 300 GPa), lightweight (≈4 g/cm3), and maintain their strengths to high temperatures.1,3

Among the more than 70+ different MAX phases that have been synthesized to date, some Al-containing ones, notably Ti2AlC, have attracted the most attention due to their exceptional oxidation resistance.7–9 Crack self-healing characteristics have also been reported during the oxidation of Ti2AlC and Ti3AlC2.10–12 

More recently, we showed that by selectively etching the Al from Al-containing MAX phases, it is possible to synthesize a new family of two-dimensional (2D) materials, which we labeled MXenes. The latter have been so-called to emphasize the selective etching of the A-element from the parent MAX phase. The suffix ene was added to indicate the similarities of the resulting 2D materials to graphene. We note in passing that in contrast to hydrophobic graphene, MXenes are hydrophilic and conductive.13,14 In some cases, after etching of the Al, the resulting material behaves as a clay with capacities of the order of 1000 F/cm3.15 

To date, Al is the only A-element that has been successfully etched from the MAX phases to produce MXenes.13 It follows that MXene synthesis has been limited to Al-containing MAX phases. Although there are 10 different M elements and about 12 A elements in the MAX phase family, not all M elements bond to all A elements. For example, Al only bonds to Ti, V, Cr, Nb, and Ta. Moreover, some M elements bond to a smaller subset of A elements. We note in passing that the only Mo-containing MAX phase known to date is Mo2GaC.16–18 Very recently, a closely related phase, Mo2Ga2C, with two Ga layers instead of one, has been discovered.19 When solid solutions are taken into account, the situation is not very different. For instance, Al-containing Ti/V and Ti/Nb solid solutions exist,20 but these do not add any new elements to those already known to bond to Al. There are few exceptions, however, wherein a solid solution contains a M element, that do not generally bond to Al, such as Zr in (Nb0.8,Zr0.2)2AlC,20 and (Nb0.6,Zr0.4)2AlC,21 or Mn in (Crx,Mn1−x)2AlC.22,23 In all these examples, however, the mole fraction of the non-Al bonding M element is less that 0.5 of the total M-content.

A recent discovery in the MAX phase field is the existence of (M′,M″)n+1AlCn ordered phases, in which two M′ layers sandwich one or two M″ layers. Recently, two research groups reported that the transition metal layers in Cr2TiAlC2 and V2CrAlC2 phases were, for the most part, ordered.24,25 Spurred by this work, we very recently reported the discovery of a new Mo-containing ordered phase—isostructural with Ti3SiC24,26—Mo2TiAlC2.27 In this phase, the Ti atoms are sandwiched between two Mo-layers that, in turn, are adjacent to the Al planes resulting in a Mo-Ti-Mo-Al-Mo-Ti-Mo stacking order. The C-atoms retain their positions in the octahedral sites between the M layers.

The discovery of Mo2TiAlC2 is important for three reasons: (i) it is the first MAX phase in which Mo layers are directly bonded to Al ones; (ii) it is only the third report of a double transition metal ordered MAX phase; and (iii) probably most importantly, it now allows us to fabricate and characterize Mo-based MXenes for the first time.28 

The major goal of this study is to better understand the crystal structures and phase stabilities of Mo2TiAlC2 and Mo2Ti2AlC3. The latter is a 413 phase that has just been discovered.28 For brevity's sake, the notations Mo2TiAlC2 and Mo2Ti2AlC3 will be used. However, as shown below, the Mo:Ti ratio can deviate substantially from the nominal 2:1 or 2:2. This study is divided into two parts. In the first, we explore the phase stabilities of these new phases in general, and the effects of different Mo-Ti ratios, in particular. The temperature dependencies of the resistivities of the two phases are also presented. In the second part, the experimental results are bolstered by density functional theory, DFT, calculations of the different compositions synthesized. These calculations leave little doubt that the ordered phases are more stable than their disordered counterparts.

Elemental powders of Mo, Ti, Al, and graphite (all from Alfa Aesar, Ward Hill, MA), with mesh sizes of −250, −325, −325, and −300, respectively, were mixed in various molar ratios. The following mMo:(3-m)Ti:1.1Al:2C compositions, where m = 1.5, 1.8. 2, or 2.2, were synthesized. Like in most synthesis of Al-containing MAX phases,3 extra Al was added to compensate for its evaporation and/or conversion to alumina, Al2O3, by reaction with O contamination of starting powders.

A (Mo2,Ti2)Al1.1C2.7 composition was also synthesized. In all cases, the powder mixtures were ball milled—using zirconia milling balls in plastic jars—for 18 h. The mixtures were then placed in covered Al2O3 crucibles that, in turn, were inserted in an Al2O3 tube furnace. The latter was heated at a rate of 5 °C/min to 1600 °C and held for 4 h under flowing argon, Ar. After furnace cooling, the slightly sintered porous compacts were milled into a fine powder using a TiN-coated milling bit.

Pressureless sintered samples were fabricated for transport properties measurements. To do so, −325 mesh Mo2TiAlC2 and Mo2Ti2AlC3 powders were pressed to a load corresponding to a stress of 1 GPa at room temperature and the resulting samples were pressureless sintered under Ar flow at 1600 °C for 4 h. The relative densities of the sintered pellets were measured using Archimedes' principle and found to be 81% and 84%, for Mo2TiAlC2 and Mo2Ti2AlC3, respectively.

Powder X-ray diffraction (XRD) was carried out on a diffractometer (Rikagu Smartlab, Tokyo, Japan) in the 3°–120° 2θ range using Cu-Kα radiation (40 KV and 44 mA). The step size was 0.02° with a step time of 7 s using a 10 × 10 mm2 window slit. Prior to obtaining the XRD patterns, 10 wt. % silicon, Si, powder was added to all powders. The latter was used as an internal standard to calibrate the diffraction angles and instrumental peak broadening.

The XRD diffractograms were analyzed by the Rietveld refinement method, using the FULLPROF code.29,30 Refinement parameters were: five background parameters, scale factors from which relative phase fractions are evaluated, X and Y profile parameters for peak width limited to the major phases, lattice parameters (LPs), isotropic global atomic displacement parameter for the major phases, Mo/Ti intermixing, and atomic positions for all phases.

Powders of Mo2TiAlC2 and Mo2Ti2AlC3 were imaged using a scanning electron microscope, SEM, (Zeiss Supra 50VP, Germany) and the compositions of several individual particles were obtained with an energy-dispersive spectroscope (EDS) (Oxford Inca X-Sight, Oxfordshire, UK). High-resolution scanning transmission electron microscope (HRSTEM) micrographs and EDS spectra were obtained on individual Mo2TiAlC2 and Mo2Ti2AlC3 particles using the Linköping double corrected FEI Titan3 60–300 operated at 300 kV, equipped with the Super-X EDS system. Selected area electron diffraction (SAED) characterization was performed using a FEI Tecnai G2 TF20 UT instrument equipped with a field emission gun run at a voltage of 200 kV and a point resolution of 0.19 nm. The specimens were prepared by embedding the MAX powder in a Ti grid, reducing the Ti-grid thickness down to 50 μm via mechanical polishing and finally Ar+ ion milling to reach electron transparency.

X-ray photoelectron spectroscopy (XPS) was used to determine the chemistries of Mo2TiAlC2 and Mo2Ti2AlC3 in powder form. A Physical Electronics VersaProbe 5000 instrument was used employing a 100 μm monochromatic Al-Kα to irradiate the sample surface. Photoelectrons were collected by a 180° hemispherical electron energy analyzer. Samples were analyzed at a 45° angle between the sample surface and the path to the analyzer. Survey spectra were taken at a pass energy of 117.5 eV, with a step size of 0.1 eV, which was used to obtain the elemental analysis of the powders. High-resolution spectra of Mo 3d, Ti 2p, Al 2p, and C 1s regions were taken at a pass energy of 23.5 eV, with a step size of 0.05 eV. The spectra were taken after the samples were sputtered with an Ar beam operating at 3.8 kV and 150 μA for 1 h. All binding energies were referenced to that of the valence band edge at 0 eV.

Peak fitting for the high-resolution spectra was performed using CasaXPS Version 2.3.16 RP 1.6. Prior to the peak fitting, the background contributions were subtracted using a Shirley function. For the Ti 2p3/2 and 2p1/2, and Mo 3d5/2 3d3/2 components, the intensity ratios of the peaks were constrained to be 2:1 and 2:3, respectively. The chemical formulas of Mo2TiAlC2 and Mo2Ti2AlC3 was determined by multiplying the total atomic percentage of each element by the fraction of that element which belongs to the MAX compound obtained from the peak fitting of the high-resolution spectra of the region of that element.

The temperature dependent DC resistivity was measured in a Quantum Design Physical Properties Measurement System in a four-point probe geometry, equipped with a custom-built setup, using a current source (Keithley 6220, Ohio) and nanovoltmeter for measurement of highly conductive samples. All resistivity measurements were carried out while the sintered samples were warmed from 2 K to 300 K. Silver paint used to make the electrical contacts. Note that the resistivity curves shown in Section III E are cropped at 10 K; below this temperature, artifacts most probably originating from the presence of superconducting impurity phases, were observed (see supplementary material).

All first-principles calculations reported here are carried out using the projector augmented wave (PAW)31 method as implemented within the Vienna ab-initio simulation package (VASP).32–34 We adopted the generalized gradient approximation (GGA) as parameterized by Perdew-Burke-Ernzerhof (PBE)35 for treating electron exchange and correlation effects. Wave functions are expanded in a plane-wave basis set, with an energy cutoff of 400 eV. For sampling of the Brillouin zone, we used the Monkhorst-Pack scheme.36 The calculated total energy for all phases is converged to within 0.1 meV/atom in terms of k-point sampling. To minimize the total energy, the unit-cell volumes, c/a ratios (when necessary), and internal parameters were optimized.

Solid solutions on the M-sites, full or partial, were modeled using the special quasi-random structure (SQS) method,37,38 where an appropriate supercell was chosen based on the criterion to mimic an atomic distribution in a random alloy, i.e., M-site correlation functions equal to zero. In this work, supercells consisting of 4 × 4 × 1 M3AX2 and M4AX3 unit cells, with a total of 96 and 128 M-sites, respectively, were considered.

For a phase to be thermodynamically stable, its energy needs to be lower than the energy of any linear combination of all other competing phases in the system. Said otherwise

ΔHcp=E(MAX)E(competingphases)<0.
(1)

In order to identify the set of relevant competing phases, for a given compound, we make use of a linear optimization procedure,38,39 which has proven successful in confirming the existence of experimentally known MAX phases, as well as predicting existence of new ones.39–44 

To calculate the elastic properties of the (M′,M″)n+1AlCn (n = 2, 3) phases, we used the method described by Fast et al.,45 where five different strains were applied to the hexagonal unit cell in order to attain the five independent elastic constants C11, C12, C13, C33, and C44. The strain values used to calculate the elastic constants were ±0.01 and ±0.02. From the elastic constants, the Voigt bulk (BV) and shear moduli (GV) were calculated, assuming

BV=29(C11+C12+2C13+C33/2)
(2)

and

GV=115(2C11+C33C122C13)+15(2C44+12(C11C12)).
(3)

In addition, the Young's modulus (E), Poisson's ratio (ν), and shear anisotropy factor (A) were calculated assuming

E=9BVGV3BV+GV,
(4)
ν=3BV2GV2(3BV+GV),
(5)
A=4C44C11+C332C13.
(6)

Before detailing the experimental and theoretical results, it is important to point out that the leitmotiv to this work is this: The lowest energy structures, and the ones that are experimentally obtained, are those in which the Mo layers are adjacent to the Al layers, with the Ti-C layers buried in between the former. Said otherwise the lowest energy configurations possess the following stacking sequence:

AlMoTiiMoAlMoTiiMoAl,

where i is 1 for the Mo2TiAlC2 phase, and 2 for the Mo2Ti2AlC3 phase. The C atoms not listed above are presumed to occupy octahedral sites between the M-elements. The ultimate reason for this state of affairs is the extreme aversion of the Mo atoms to occupy sites in which the C-atoms are not directly on top of one another, i.e., where the C-atoms are in an FCC arrangement. In all cases, Rietveld refinement suggests some intermixing (between 0 to 25 at. %) between the Ti and Mo layers.

To shed light on the stabilities of the 312 and 413 phases, five different starting compositions, listed in Table I, were reacted. The XRD patterns of the 5 different starting compositions synthesized herein are shown in Fig. 1. The weight fractions, lattice parameters, and χ2 values determined from Rietveld analysis of these patterns (see Fig. S1)46 are listed in Table I. It is crucial to note here that the starting compositions were all chosen such that either the (Mo,Ti)3AlC2 (312) or (Mo,Ti)4AlC3 (413) phase would be the majority phase obtained, as indeed observed. Note that the 312 phases detected in all the mixtures possessed quite similar lattice parameters (Table I). The same is true of the 413 phases (Table I). Schematics of both the 312 and 413 unit cells are shown in Fig. 2.

TABLE I.

Phase compositions and lattice parameters of the various starting compositions tested herein determined from Rietveld analysis of XRD data. Also, listed are the minor impurity phases and their wt. % and the χ2 of the Rietveld refinements. The numbers in parentheses are the uncertainties on the last digit.

Mo2TiAlC2Mo2Ti2AlC3Impurities
Starting compositionwt. %Lattice constants (Å)wt. %Lattice constants (Å)wt. %χ2
2.2Mo:0.8Ti: 1.1Al:2C 95(3) a: 2.99872(4) — — MoCxa 2.43 
 c: 18.6183(3) Mo < 1 
2Mo:Ti: 1.1Al:2C 91(2) a: 2.99718(3) 9(2) a: 3.0196(3) — — 2.7 
 c: 18.6614(2) c: 23.529(4) 
1.8Mo:1.2Ti: 1.1Al:2C 11(3) a: 2.9984(1) 89(3) a: 3.02076(3) Mo  < 0.7 2.6 
 c: 18.667(1) c: 23.5479(4) 
1.5Mo:1.5Ti: 1.1Al:2C — 93(3) a: 3.02119(4) Mo3Al8 1.93 
     c: 23.5461(5) Mo3Al  
2Mo:2Ti: 1.1Al:2.7C — 93(3) a: 3.02064(8) MoCxa 2.5 
Mo3Al 
c: 23.5431(7) 
Mo2TiAlC2Mo2Ti2AlC3Impurities
Starting compositionwt. %Lattice constants (Å)wt. %Lattice constants (Å)wt. %χ2
2.2Mo:0.8Ti: 1.1Al:2C 95(3) a: 2.99872(4) — — MoCxa 2.43 
 c: 18.6183(3) Mo < 1 
2Mo:Ti: 1.1Al:2C 91(2) a: 2.99718(3) 9(2) a: 3.0196(3) — — 2.7 
 c: 18.6614(2) c: 23.529(4) 
1.8Mo:1.2Ti: 1.1Al:2C 11(3) a: 2.9984(1) 89(3) a: 3.02076(3) Mo  < 0.7 2.6 
 c: 18.667(1) c: 23.5479(4) 
1.5Mo:1.5Ti: 1.1Al:2C — 93(3) a: 3.02119(4) Mo3Al8 1.93 
     c: 23.5461(5) Mo3Al  
2Mo:2Ti: 1.1Al:2.7C — 93(3) a: 3.02064(8) MoCxa 2.5 
Mo3Al 
c: 23.5431(7) 
a

The level of C occupancy cannot be determined from XRD.

FIG. 1.

XRD patterns of 5 different starting compositions—noted below each pattern. Black squares represent Si peaks, added (∼10 wt. %) as an internal standard before the XRD measurements were taken. Bragg reflections' positions of each phase are shown in Fig. S1.46 

FIG. 1.

XRD patterns of 5 different starting compositions—noted below each pattern. Black squares represent Si peaks, added (∼10 wt. %) as an internal standard before the XRD measurements were taken. Bragg reflections' positions of each phase are shown in Fig. S1.46 

Close modal
FIG. 2.

Unit cells of fully ordered (a) Mo2TiAlC2 and (b) Mo2Ti2AlC3.

FIG. 2.

Unit cells of fully ordered (a) Mo2TiAlC2 and (b) Mo2Ti2AlC3.

Close modal

When the Mo:Ti starting chemistry ratio was 2.2:0.8 (first row in Table I), the majority phase upon reaction was the 312 phase, with ≈ 4 wt. % of cubic MoCx,47 and traces of elemental Mo as impurity phases.

Similarly, when the starting Mo:Ti ratio was 2:1 (second row in Table I), the main reaction product (91(2) wt. %) was again a 312 phase. Here, 9(2) wt. % of a 413 phase was detected. We note in passing that in our initial report,27 the peaks associated with this 413 phase were marked as unknown.

When the starting Mo:Ti ratio was 1.8:1.2 (third row in Table I), and despite the fact that the overall starting chemistry corresponded to a 312 stoichiometric ratio, the final product was ∼90 wt. % 413 phase. Since the only difference between this mixture and the one above is the Mo:Ti ratio, it is reasonable to conclude that this ratio is a critical parameter in determining which of these two phases form. For reasons discussed below, reducing the Mo:Ti atomic ratio to below 2 stabilizes the 413 phase and destabilizes the 312.

To test this idea, a 312 overall starting composition, with a Mo:Ti ratio of 1.5:1.5, was reacted (4th row in Table I). In this case, the final product was mostly the 413 phase and no trace of the 312 phase was detected. The impurity phases were Mo3Al8 and Mo3Al. This again signifies that the Mo:Ti ratio is crucial in determining which of the two phases will form.

Note that for this composition, mass balance dictates that

1.5Mo+1.5Ti+1.1Al+2C=3/4(Mo2Ti2Al1.46C2.66).
(7)

Based on this reaction, it is not surprising that when the starting mixture was 2Mo:2Ti:1.1Al:2.7C, the only MAX phase formed was the 413 phase, with ∼4 wt. % Mo3Al, and ∼3 wt. % MoCx as the impurity phases. Furthermore, C-vacancies are most probably present.48 

In the rest of this study, we focus only on two starting compositions with the proper stoichiometric ratios that resulted in Mo2TiAlC2 and Mo2Ti2AlC3, viz., 2Mo:Ti:1.1Al:2C and 2Mo:2Ti:1.1Al:2.7C, respectively.

The atomic occupancies—two 4f and one 2a Wyckoff sites—for the three M layers in Mo2TiAlC2 (see Fig. 2(a)), and—two 4e and two 4f—for the four M layers in Mo2Ti2AlC3 (see Fig. 2(b)) were estimated from Rietveld analysis of the XRD patterns are shown in Table II. Based on these results, we conclude that the outer layers in the 312 phase are 75(1) at. % Mo, balance Ti. The middle layers, on the other hand, are 100(1) at. % Ti. This finding confirms the strong aversion of the Mo atoms to occupy the middle M layers that are surrounded by C atoms (in FCC arrangement). In the 413 phase, the outer layers are 77(2) at. % Mo balance Ti; the inner layers are 86(1) at. % Ti, balance Mo. In other words, these compounds are ordered and their inner M layers are mostly Ti. Given that these powders were reacted at 1600 °C, and that the atomic radii of Ti and Mo—at 140 pm and 145 pm, respectively—are not too different, implies that the driving force for ordering must be substantial.

TABLE II.

Mo and Ti atomic occupancies of M sites in the Mo2TiAlC2 and Mo2Ti2AlC3 samples made from the 2Mo:Ti:1.1Al:2C and 2Mo:2Ti:1.1Al:2.7C starting compositions, respectively. The designations outer and inner refer, respectively, to M atoms adjacent to, and not adjacent to, the Al layers. The numbers in parentheses are the uncertainties on the last digit.

Occupancies of M sites (at. %)
Mo2TiAlC2Mo2Ti2AlC3
2a (inner)4f (outer)4e (outer)4f (inner)
Mo 0(1) 75(1) 77(2) 14(1) 
Ti 100(1) 25(1) 23(2) 86(1) 
Occupancies of M sites (at. %)
Mo2TiAlC2Mo2Ti2AlC3
2a (inner)4f (outer)4e (outer)4f (inner)
Mo 0(1) 75(1) 77(2) 14(1) 
Ti 100(1) 25(1) 23(2) 86(1) 

It is important to note here that the chemistry predicted from Rietveld analysis is inconsistent—especially for the 312 phase—with other observations (see below), such as EDS in SEM, XPS, EDS/HRTEM, and most importantly, our nominal starting compositions. The reason for this state of affairs is not understood at this time and more work needs to be carried out to sort out this important discrepancy. Said otherwise, the extent of ordering in the outer layers is, more likely than not, >75% Mo for the 312 phase.

The aforementioned caveats notwithstanding, it is crucial to note that regardless of which MAX phase forms (312 or 413), Rietveld analysis is consistent in that the M layers adjacent to the Al-layers are significantly richer in Mo than Ti. In contrast, the inner M layers, which are surrounded by C-atoms, are mostly Ti (with less intermixing), confirming that the presence of Mo atoms in the middle M-layers destabilizes these phases.

Figure 3(a) shows a HRSTEM micrograph of a Mo2TiAlC2 particle, synthesized starting with a 2:1 Mo:Ti ratio. Every other layer is brighter than its neighbors and can thus be associated with the heavier Mo atoms. The EDS elemental maps and their overlap (Figs. 3(b)–3(d)), in which the Mo, Ti and Al atoms are shown as red, green, and blue, respectively, confirm this conclusion. When the EDS and HRSTEM images are superimposed (Fig. 3(f)), it is obvious that every green, or Ti, layer is sandwiched between two red, or Mo layers. Figure 3(g) shows an EDS line scan along the [0001] direction on the green arrow shown in Fig. 3(f), where the Mo, Ti, and Al lines have the same coloring as in Fig. 3(e). Here, again, the line scan confirms the proposed ordering sequence.

FIG. 3.

(a) HRSTEM of Mo2TiAlC2 along the [112¯0] zone axis, EDS mapping on (a) for: (b) Mo, (c) Ti, (d) Al. (e) Overlap of (b) and (c). (f) Overlap of (a) and (e) showing the Mo atoms in red, Ti atoms in green and Al atoms in blue, (g) EDS line scan profile of Mo, Ti, and Al over the green arrow shown in g.

FIG. 3.

(a) HRSTEM of Mo2TiAlC2 along the [112¯0] zone axis, EDS mapping on (a) for: (b) Mo, (c) Ti, (d) Al. (e) Overlap of (b) and (c). (f) Overlap of (a) and (e) showing the Mo atoms in red, Ti atoms in green and Al atoms in blue, (g) EDS line scan profile of Mo, Ti, and Al over the green arrow shown in g.

Close modal

A HRSTEM image of the Mo2Ti2AlC3, sample synthesized starting with Mo:Ti:Al:C atomic ratios of 2:2:1.1:2.7 is shown in Fig. 4(a). Here, two bright atomic layers (Mo) surround two less bright layers (Ti). The 4 Mo-Ti-Ti-Mo layers are, in turn, separated by darker atomic layers that correspond to the Al layers. Similar EDS mapping was done here (Figs. 4(b) to 4(e)) and Fig. 4(f) plots the overlap of Figs. 4(a)–4(e), which clearly shows that two Ti green layers, are sandwiched between two Mo red layers. Interleaved between every 4 M-layers are Al layers, colored blue (Fig. 4(g)).

FIG. 4.

(a) HRSTEM of Mo2Ti2AlC3 along the [112¯0] zone axis, EDS mapping on (a) for: (b) Mo, (c) Ti, (d) Al. (e) Overlap of (b) and (c). (f) Overlap of (a) and (e) showing the Mo atoms in red, Ti atoms in green and Al atoms in blue, and (g) EDS line scan profile of Mo, Ti, and Al.

FIG. 4.

(a) HRSTEM of Mo2Ti2AlC3 along the [112¯0] zone axis, EDS mapping on (a) for: (b) Mo, (c) Ti, (d) Al. (e) Overlap of (b) and (c). (f) Overlap of (a) and (e) showing the Mo atoms in red, Ti atoms in green and Al atoms in blue, and (g) EDS line scan profile of Mo, Ti, and Al.

Close modal

High-resolution XPS spectra peak fitting of Mo2TiAlC2 and Mo2Ti2AlC3 for Mo 3d, Ti 2p, Al 2p, and C 1s elements are shown in Figs. 5(a)–5(d), respectively. The peak fitting results for the various species in Mo2TiAlC2 and Mo2Ti2AlC3 powders are tabulated in Tables S1 and S2,46 respectively.

FIG. 5.

XPS spectra for elements in Mo2Ti2AlC3 (413) and Mo2TiAlC2 (312) (a) Mo 3d (peaks in red correspond to the 3d5/2 and 3d3/2 components of Mo in the 413 and 312 phases), (b) Ti 2p (peaks in blue, green and orange correspond to 2p3/2 and 2p1/2 components for Ti, Ti(+2), and Ti(+3)), (c) Al 2p (peaks in red correspond to the Al component in MAX phase), and (d) C 1s regions. The blue peaks and red peak fits to the spectra emanate from C atoms in the 312 and 413 phases. The orange and green emanate from adventitious C and hydrocarbons.

FIG. 5.

XPS spectra for elements in Mo2Ti2AlC3 (413) and Mo2TiAlC2 (312) (a) Mo 3d (peaks in red correspond to the 3d5/2 and 3d3/2 components of Mo in the 413 and 312 phases), (b) Ti 2p (peaks in blue, green and orange correspond to 2p3/2 and 2p1/2 components for Ti, Ti(+2), and Ti(+3)), (c) Al 2p (peaks in red correspond to the Al component in MAX phase), and (d) C 1s regions. The blue peaks and red peak fits to the spectra emanate from C atoms in the 312 and 413 phases. The orange and green emanate from adventitious C and hydrocarbons.

Close modal

The high-resolution spectra in the Mo 3d region for Mo2TiAlC2 and Mo2Ti2AlC3, (Fig. 5(a)) were fit by 1 species with binding energies, EB's, of 227.8 eV and 227.9 eV, respectively (see Tables S1 and S2).46 These EB's are almost identical to those in Mo2C (227.8 eV) and significantly lower than Mo metal (228.5 eV).49 The fact that the measured Mo binding energies in both Mo2TiAlC2 and Mo2Ti2AlC3 are almost identical is fully consistent with the fact that the Mo-layers are on the outside and the Ti layers are on the inside, i.e., ordered.

The Ti 2p region was fit by 3 species corresponding to three Ti oxidation states species, denoted as Mo2TiAlC2, Mo2Ti(+2)AlC2, and Mo2Ti(+3)AlC2 (Fig. 5(b) and Table S1).46 The Ti EB's in Mo2TiAlC2 is 454.4 eV, which is slightly lower than that in TiC (454.9–455.1 eV),50–52 but higher than Ti metal (453.9 eV).53 Similarly, the Ti 2p region of Mo2Ti2AlC3 was also fitted by three species denoted as Mo2Ti2AlC3, Mo2Ti2(+2)AlC3 and Mo2Ti2(+3)AlC3 (Fig. 5(b) and Table S246). The EB's of the Ti components in these two Mo-containing MAX phases are almost identical to those reported for Ti3AlC2 (454.5 eV).54 This result is again consistent with the conclusion that the Ti and Mo atoms are ordered in separate layers in these structures.

The Al 2p regions for the 312 and 413 (Fig. 5(c)) were fit by single peaks at 73.4 eV and 73.8 eV, respectively. These EB's are higher than those of both elemental Al and Ti-Al alloys (72.3 and 71.5–71.4 eV, respectively).55 

The C 1s region for Mo2TiAlC2 was fit by three peaks (Fig. 5(d)), the first peak, at 282.5 eV was assigned to C atoms bonded to the outer Mo and inner Ti layers (labeled CI in Figs. 2 and 5(d)). This binding energy is higher than the corresponding energies in TiC (281.7 to 281.9 eV), Ti3AlC2 (281.5 eV),50–52,54 or Mo2C (282.7 eV).49 The other two peaks correspond to C-C and CHx species that are due to adventitious C and contamination from the atmosphere.

Crucially, in addition to a C 1s peak at 282.5 eV—with the same full width at half maximum (FWHM) as that in Mo2TiAlC2—an extra peak at 281.9 eV is observed in the 413 spectra (Fig. 5(d)). Since this EB is comparable to that of C in TiC and Ti3AlC2, we assign it to C atoms bonded to the inner Ti layers (labeled CII in Figs. 2(b) and 5(d)). The fact that the CI to CII ratio is 2 is fully consistent with their assignments.

EDS analysis in the SEM on individual particles showed the ratios of Mo:Ti:Al to be 2.1 ± 0.3:0.9 ± 0.2:0.9 ± 0.1 and 1.9 ± 0.1:2.0 ± 0.2:0.9 ± 0.1 for approximate chemistries of Mo2.1Ti0.9Al0.9 and Mo1.9Ti2.0Al0.9. To quantify the C- and other elements' content, we combined XPS global elemental analysis (Table S3)46 and the species extracted from the peak fitting of XPS high-resolution regions (Tables S1 and S2).46 Based on these results, the chemical formulae for Mo2TiAlC2 and Mo2Ti2AlC3 are determined to be Mo2TiAlC1.7 and Mo2Ti1.9Al0.9C2.5, respectively. These values are not too different from those determined from the EDS results lending credence to the totality of our results and methodologies. At 85%, the C-occupancy in the 413 phase is not statistically significantly different from the 83.33% in the 312 phase. Note that for the 413 phase we deliberately started with a lower C amount, as others have.56 The fact that the C-sites are not fully occupied suggests that C-vacancies may be needed to stabilize these structures.

Figure 6 shows the resistivity, ρ, versus temperature, T, results of the Mo2TiAlC2 (red, left y-axis) and Mo2Ti2AlC3 (blue, right y-axis) samples. At 150 μΩ cm, the measured resistivity value of the Mo2TiAlC2 sample at 10 K is lower than that of the Mo2Ti2AlC3 (817 μΩ cm) sample. The main reason for showing these results is to prove that—like in most MAX phases3—the conductivity is metal-like. Given the level of porosity and impurities in the samples measured, these results have to be used with caution, since they are most probably far from the intrinsic values. Note also that the resistivity curves shown are cropped at 10 K; below this temperature, artifacts originating from the possible presence of a superconducting impurity phase (e.g., molybdenum carbide) were observed (see Fig. S2).46 

FIG. 6.

Temperature dependent resistivity of Mo2TiAlC2 (red, left-side y-axis) and Mo2Ti2AlC3 (blue, right-side y-axis) measured from 10 – 300 K.

FIG. 6.

Temperature dependent resistivity of Mo2TiAlC2 (red, left-side y-axis) and Mo2Ti2AlC3 (blue, right-side y-axis) measured from 10 – 300 K.

Close modal

For the Mo2TiAlC2 composition, six different ordered structures, defined in Table S446 and schematically depicted in Fig. 7(a), and one disordered SQS (e.g., structure I in Fig. 10(a)) were considered. For the Mo2Ti2AlC3 composition, 20 different ordered structures, defined in Table S5,46 and one disordered SQS (e.g., structure I in Fig. 10(a)) were considered. Six of the 20 structures are shown schematically in Fig. 7(b). In both Figs. 7(a) and 7(b), the unit cells are sorted with increasing energy from left to right. The unit cells of type A structures are shown in Fig. 2.

FIG. 7.

Ordered structures considered theoretically, (a) all 6 possible ordered Mo2TiAlC2 unit cells and (b) 6 of 20 Mo2Ti2AlC3 ordered unit cells (see Tables III and IV). The latter are sorted from most stable on the left, to least stable on the right. The capital letters denote the various unit cells. By far the most stable configuration is the A-type.

FIG. 7.

Ordered structures considered theoretically, (a) all 6 possible ordered Mo2TiAlC2 unit cells and (b) 6 of 20 Mo2Ti2AlC3 ordered unit cells (see Tables III and IV). The latter are sorted from most stable on the left, to least stable on the right. The capital letters denote the various unit cells. By far the most stable configuration is the A-type.

Close modal
FIG. 10.

(a) Schematic of 413 unit cells for (I) a disordered distribution of Mo and Ti using the SQS method, (II) semi-ordered and, (III) complete order of type A. Here, the Mo atoms are colored red, Ti green, C black, and Al blue. (b) Formation enthalpy of Mo2TiAlC2 and Mo2Ti2AlC3 as a function of the degree of order on the M-site. This ranges from 0 for a disordered distribution of Mo and Ti (SQS) to 1 for complete order of type A. For the disordered distribution of Mo and Ti (SQS), the Gibbs free energy at 1873 K, given by the dashed lines, is estimated (only taking into account configuration entropy). The Gibbs free energy for the semi-ordered/partially ordered structures is estimated using a linear combination of the configurational entropy for the disordered and fully ordered structures.

FIG. 10.

(a) Schematic of 413 unit cells for (I) a disordered distribution of Mo and Ti using the SQS method, (II) semi-ordered and, (III) complete order of type A. Here, the Mo atoms are colored red, Ti green, C black, and Al blue. (b) Formation enthalpy of Mo2TiAlC2 and Mo2Ti2AlC3 as a function of the degree of order on the M-site. This ranges from 0 for a disordered distribution of Mo and Ti (SQS) to 1 for complete order of type A. For the disordered distribution of Mo and Ti (SQS), the Gibbs free energy at 1873 K, given by the dashed lines, is estimated (only taking into account configuration entropy). The Gibbs free energy for the semi-ordered/partially ordered structures is estimated using a linear combination of the configurational entropy for the disordered and fully ordered structures.

Close modal

A summary of the unit cell volumes, VUC, a and c lattice parameters, the calculated total energy, E0, of the quaternaries MomTi3-mAlC2 and MomTi4-mAlC2, as a function of m are listed in Tables III and IV, respectively. Also listed are the formation energies relative to the most competing phases, ΔHcp, listed in the last column. Based on the results listed in Table III, it is clear that the a lattice parameters of unit cell type A for Mo2TiAlC2 are considerably reduced (−2.1.% to −2.4%) in comparison to the end members, Ti3AlC2 and Mo3AlC2. In contradistinction, the c-lattice parameter increases (+0.6% and +1.2%). The VUC values shrink accordingly.

TABLE III.

Summary of unit cell volumes, a and c lattice parameters, the calculated total energy E0, of quaternaries in the MomTi3-mAlC2 as a function of m. Also listed are the formation energies relative to those of the most competing phases, ΔHcp, listed in the last column. The letters in brackets in the first column refer to those shown in Fig. 7(a). SQS refers to quasi random structures.

mV3/uc)a (Å)c (Å)E0 (eV/fu)aSet of most competing phasesΔHcp (meV/atom)
0 (Ti3AlC2153.46 3.0832 18.640 −49.884 Ti5Al2C3, Ti7Al2C5 −6 
3 (Mo3AlC2151.48 3.0714 18.542 −54.831 C, Mo3Al 141 
0.5 (SQS) 151.60 3.0760 18.500 −51.029 TiC, Mo3Al, Mo3Al8, Ti4AlC3 
0.75 (SQS) 150.58 3.0639 18.522 −51.575 TiC, Mo3Al, Mo3Al8, Ti4AlC3 11 
1 (A) 152.64 3.0854 18.516 −51.677 TiC, Mo3Al, Mo3Al8 91 
1 (B) 151.42 3.0713 18.537 −51.892 TiC, Mo3Al, Mo3Al8 55 
1 (C) 150.12 3.0578 18.539 −52.170 TiC, Mo3Al, Mo3Al8 
1 (D) 150.52 3.0622 18.534 −52.079 TiC, Mo3Al, Mo3Al8 24 
1 (E) 151.66 3.0546 18.768 −51.577 TiC, Mo3Al, Mo3Al8 108 
1 (F) 149.78 3.0425 18.683 −52.141 TiC, Mo3Al, Mo3Al8 14 
1 (SQS) 150.40 3.0587 18.557 −52.003 TiC, Mo3Al, Mo3Al8 37 
1.25 (SQS) 150.10 3.0539 18.580 −52.447 Ti2Mo2AlC3, TiC, Mo3Al, Mo3Al8 55 
1.5 (SQS) 149.28 3.0399 18.661 −52.954 Ti2Mo2AlC3, TiC, Mo3Al, Mo3Al8 63 
1.5 (A with partial Ti on 4f) 147.60 3.0185 18.706 −53.291 Ti2Mo2AlC3, TiC, Mo3Al, Mo3Al8 
1.75 (SQS) 149.18 3.0342 18.707 −53.339 Ti2Mo2AlC3, Mo3Al, Mo3Al8 81 
1.75 (A with partial Ti on 4f) 147.20 3.0093 18.771 −53.808 Ti2Mo2AlC3, Mo3Al, Mo3Al8 
2 (A) 147.00 3.0082 18.757 −54.305 Ti2Mo2AlC3, Mo3Al, Mo3Al8 −18 
2 (B) 148.78 3.0217 18.815 −53.762 Ti2Mo2AlC3, Mo3Al, Mo3Al8 72 
2 (C) 150.48 3.0352 18.863 −53.239 Ti2Mo2AlC3, Mo3Al, Mo3Al8 159 
2 (D) 150.64 3.0377 18.850 −53.192 Ti2Mo2AlC3, Mo3Al, Mo3Al8 167 
2 (E) 150.68 3.0632 18.542 −53.502 Ti2Mo2AlC3, Mo3Al, Mo3Al8 116 
2 (F) 151.60 3.0740 18.524 −53.271 Ti2Mo2AlC3, Mo3Al, Mo3Al8 154 
2 (SQS) 150.02 3.0442 18.683 −53.545 Ti2Mo2AlC3, Mo3Al, Mo3Al8 108 
2.25 (SQS) 150.22 3.0477 18.681 −53.887 Ti2Mo2AlC3, Mo3Al, Mo3Al8 113 
mV3/uc)a (Å)c (Å)E0 (eV/fu)aSet of most competing phasesΔHcp (meV/atom)
0 (Ti3AlC2153.46 3.0832 18.640 −49.884 Ti5Al2C3, Ti7Al2C5 −6 
3 (Mo3AlC2151.48 3.0714 18.542 −54.831 C, Mo3Al 141 
0.5 (SQS) 151.60 3.0760 18.500 −51.029 TiC, Mo3Al, Mo3Al8, Ti4AlC3 
0.75 (SQS) 150.58 3.0639 18.522 −51.575 TiC, Mo3Al, Mo3Al8, Ti4AlC3 11 
1 (A) 152.64 3.0854 18.516 −51.677 TiC, Mo3Al, Mo3Al8 91 
1 (B) 151.42 3.0713 18.537 −51.892 TiC, Mo3Al, Mo3Al8 55 
1 (C) 150.12 3.0578 18.539 −52.170 TiC, Mo3Al, Mo3Al8 
1 (D) 150.52 3.0622 18.534 −52.079 TiC, Mo3Al, Mo3Al8 24 
1 (E) 151.66 3.0546 18.768 −51.577 TiC, Mo3Al, Mo3Al8 108 
1 (F) 149.78 3.0425 18.683 −52.141 TiC, Mo3Al, Mo3Al8 14 
1 (SQS) 150.40 3.0587 18.557 −52.003 TiC, Mo3Al, Mo3Al8 37 
1.25 (SQS) 150.10 3.0539 18.580 −52.447 Ti2Mo2AlC3, TiC, Mo3Al, Mo3Al8 55 
1.5 (SQS) 149.28 3.0399 18.661 −52.954 Ti2Mo2AlC3, TiC, Mo3Al, Mo3Al8 63 
1.5 (A with partial Ti on 4f) 147.60 3.0185 18.706 −53.291 Ti2Mo2AlC3, TiC, Mo3Al, Mo3Al8 
1.75 (SQS) 149.18 3.0342 18.707 −53.339 Ti2Mo2AlC3, Mo3Al, Mo3Al8 81 
1.75 (A with partial Ti on 4f) 147.20 3.0093 18.771 −53.808 Ti2Mo2AlC3, Mo3Al, Mo3Al8 
2 (A) 147.00 3.0082 18.757 −54.305 Ti2Mo2AlC3, Mo3Al, Mo3Al8 −18 
2 (B) 148.78 3.0217 18.815 −53.762 Ti2Mo2AlC3, Mo3Al, Mo3Al8 72 
2 (C) 150.48 3.0352 18.863 −53.239 Ti2Mo2AlC3, Mo3Al, Mo3Al8 159 
2 (D) 150.64 3.0377 18.850 −53.192 Ti2Mo2AlC3, Mo3Al, Mo3Al8 167 
2 (E) 150.68 3.0632 18.542 −53.502 Ti2Mo2AlC3, Mo3Al, Mo3Al8 116 
2 (F) 151.60 3.0740 18.524 −53.271 Ti2Mo2AlC3, Mo3Al, Mo3Al8 154 
2 (SQS) 150.02 3.0442 18.683 −53.545 Ti2Mo2AlC3, Mo3Al, Mo3Al8 108 
2.25 (SQS) 150.22 3.0477 18.681 −53.887 Ti2Mo2AlC3, Mo3Al, Mo3Al8 113 
a

fu refers to formula unit, which is half a unit cell.

TABLE IV.

Summary of unit cell volumes, a and c lattice parameters, the calculated total energy, E0, of quaternaries in the MomTi4-mAlC3 as a function of m. Also listed are the formation energies relative to those of the most competing phases, ΔHcp, listed in the last column. The letters in brackets in the first column refer to those shown in Fig. 7(b) and Fig. 8(b). SQS refers to quasi random structures.

mV3/uc)a (Å)c (Å)E0 (eV/fu)aSet of most competing phasesΔHcp (meV/atom)
0 (Ti4AlC3194.48 3.0859 23.582 −68.413 Ti3AlC2, TiC 
4 (Mo4AlC3196.50 3.1167 23.358 −74.552 C, MoC, Mo3Al 171 
1 (A with partial Mo on 4f) 190.12 3.0543 23.534 −70.766 TiC, Mo3Al, Mo3Al8 −2 
1 (SQS) 191.48 3.0577 23.652 −71.331 TiC, Mo3Al, Mo3Al8 21 
1.5 (A with partial Mo on 4f) 188.51 3.0323 23.673 −71.902 TiC, Mo2TiAlC2, Mo3Al, Mo3Al8 −13 
1.5 (SQS) 191.31 3.0641 23.530 −70.583 TiC, Mo2TiAlC2, Mo3Al, Mo3Al8 58 
2 (type A) 187.87 3.0280 23.659 −72.969 TiC, Mo2TiAlC2 −17 
2 (type B) 194.28 3.0712 23.784 −71.453 TiC, Mo2TiAlC2 173 
2 (type C) 189.36 3.0381 23.690 −72.699 TiC, Mo2TiAlC2 17 
2 (type D) 191.09 3.0501 23.719 −72.228 TiC, Mo2TiAlC2 76 
2 (type E) 191.80 3.0559 23.716 −71.991 TiC, Mo2TiAlC2 105 
2 (type F) 191.64 3.0538 23.729 −72.063 TiC, Mo2TiAlC2 96 
2 (type G) 192.50 3.0621 23.706 −71.701 TiC, Mo2TiAlC2 142 
2 (type H) 190.24 3.0438 23.710 −72.313 TiC, Mo2TiAlC2 65 
2 (type I) 193.00 3.0668 23.694 −71.586 TiC, Mo2TiAlC2 156 
2 (type J) 193.08 3.0823 23.466 −71.838 TiC, Mo2TiAlC2 125 
2 (type K) 190.98 3.0548 23.632 −72.252 TiC, Mo2TiAlC2 73 
2 (type L) 191.49 3.0582 23.641 −72.243 TiC, Mo2TiAlC2 74 
2 (type M) 193.45 3.0797 23.552 −71.762 TiC, Mo2TiAlC2 134 
2 (type N) 190.83 3.0475 23.726 −72.446 TiC, Mo2TiAlC2 49 
2 (type O) 190.83 3.0484 23.712 −72.398 TiC, Mo2TiAlC2 55 
2 (type P) 194.40 3.0956 23.425 −71.536 TiC, Mo2TiAlC2 162 
2 (type Q) 193.52 3.0681 23.739 −71.540 TiC, Mo2TiAlC2 162 
2 (type R) 192.56 3.0601 23.744 −71.942 TiC, Mo2TiAlC2 112 
2 (type S) 193.52 3.0681 23.739 −71.540 TiC, Mo2TiAlC2 162 
2 (SQS) 191.36 3.0560 23.647 −72.267 TiC, Mo2TiAlC2 71 
2.5 (A with partial Ti on 4e) 189.76 3.0410 23.691 −73.602 Mo2TiAlC2, MoC, TiC 11 
2.5 (SQS) 191.88 3.0644 23.598 −73.090 Mo2TiAlC2, MoC, TiC 75 
3 (A with partial Ti on 4e) 191.89 3.0659 23.571 −73.991 Mo2TiAlC2, MoC 69 
3 (SQS) 193.66 3.0838 23.500 −73.450 Mo2TiAlC2, MoC 137 
mV3/uc)a (Å)c (Å)E0 (eV/fu)aSet of most competing phasesΔHcp (meV/atom)
0 (Ti4AlC3194.48 3.0859 23.582 −68.413 Ti3AlC2, TiC 
4 (Mo4AlC3196.50 3.1167 23.358 −74.552 C, MoC, Mo3Al 171 
1 (A with partial Mo on 4f) 190.12 3.0543 23.534 −70.766 TiC, Mo3Al, Mo3Al8 −2 
1 (SQS) 191.48 3.0577 23.652 −71.331 TiC, Mo3Al, Mo3Al8 21 
1.5 (A with partial Mo on 4f) 188.51 3.0323 23.673 −71.902 TiC, Mo2TiAlC2, Mo3Al, Mo3Al8 −13 
1.5 (SQS) 191.31 3.0641 23.530 −70.583 TiC, Mo2TiAlC2, Mo3Al, Mo3Al8 58 
2 (type A) 187.87 3.0280 23.659 −72.969 TiC, Mo2TiAlC2 −17 
2 (type B) 194.28 3.0712 23.784 −71.453 TiC, Mo2TiAlC2 173 
2 (type C) 189.36 3.0381 23.690 −72.699 TiC, Mo2TiAlC2 17 
2 (type D) 191.09 3.0501 23.719 −72.228 TiC, Mo2TiAlC2 76 
2 (type E) 191.80 3.0559 23.716 −71.991 TiC, Mo2TiAlC2 105 
2 (type F) 191.64 3.0538 23.729 −72.063 TiC, Mo2TiAlC2 96 
2 (type G) 192.50 3.0621 23.706 −71.701 TiC, Mo2TiAlC2 142 
2 (type H) 190.24 3.0438 23.710 −72.313 TiC, Mo2TiAlC2 65 
2 (type I) 193.00 3.0668 23.694 −71.586 TiC, Mo2TiAlC2 156 
2 (type J) 193.08 3.0823 23.466 −71.838 TiC, Mo2TiAlC2 125 
2 (type K) 190.98 3.0548 23.632 −72.252 TiC, Mo2TiAlC2 73 
2 (type L) 191.49 3.0582 23.641 −72.243 TiC, Mo2TiAlC2 74 
2 (type M) 193.45 3.0797 23.552 −71.762 TiC, Mo2TiAlC2 134 
2 (type N) 190.83 3.0475 23.726 −72.446 TiC, Mo2TiAlC2 49 
2 (type O) 190.83 3.0484 23.712 −72.398 TiC, Mo2TiAlC2 55 
2 (type P) 194.40 3.0956 23.425 −71.536 TiC, Mo2TiAlC2 162 
2 (type Q) 193.52 3.0681 23.739 −71.540 TiC, Mo2TiAlC2 162 
2 (type R) 192.56 3.0601 23.744 −71.942 TiC, Mo2TiAlC2 112 
2 (type S) 193.52 3.0681 23.739 −71.540 TiC, Mo2TiAlC2 162 
2 (SQS) 191.36 3.0560 23.647 −72.267 TiC, Mo2TiAlC2 71 
2.5 (A with partial Ti on 4e) 189.76 3.0410 23.691 −73.602 Mo2TiAlC2, MoC, TiC 11 
2.5 (SQS) 191.88 3.0644 23.598 −73.090 Mo2TiAlC2, MoC, TiC 75 
3 (A with partial Ti on 4e) 191.89 3.0659 23.571 −73.991 Mo2TiAlC2, MoC 69 
3 (SQS) 193.66 3.0838 23.500 −73.450 Mo2TiAlC2, MoC 137 
a

fu refers to formula unit, which is half a unit cell.

The same is true of Mo2Ti2AlC3 (Table IV) in comparison to its end members, Ti4AlC3 and Mo4AlC3. Here again the a lattice parameter and VUC values decrease, as the c lattice parameters increase.

The formation enthalpies, ΔHcp, calculated for MomTi3-mAlC2 relative to their most likely competing phases (listed in the last column of Table III) are plotted in Fig. 8(a) as a function of m. Also plotted, as crosses in Fig. 8, are the ΔHcp values for solid solutions of Mo and Ti. In such figures, any composition with a negative ΔHcpcan exist; those with positive ΔHcp values should not. Based on these results, only Ti3AlC2 and a type A, MomTi3-mAlC2 structure with m = 2, viz., Mo2TiAlC2 can exist as observed in this and previous work.27 Note that the −6 meV/atom value for Ti3AlC2 is different from previous work,39 since here we included more competing higher order MAX phases, such as Ti5Al2C3 and Ti7Al2C5 that are also stable. The value of ΔHcp for the ordered Mo2TiAlC2 type A structure is −18 meV/atom, which means an energetically preferred structure, consistent with experimental observations. Interestingly, the type A Mo2Ti2AlC3 structure is one of its most competing phases. Also noteworthy is the much higher energy of all other ordered structures with m = 2, wherein the Mo atoms are surrounded by C in FCC arrangement, i.e., not adjacent to the Al-layers (Fig. 8(a)). Here, again is a good example of the steep cost in energy for any structure in which the Mo atoms are surrounded by C atoms that are in an FCC arrangement.

FIG. 8.

Formation enthalpy ΔHcp of, (a) MomTi3-mAlC2 and (b) MomTi4-mAlC3 phases as a function of m for ordered (filled symbols), partially disordered (open squares), and disordered distributions (crosses) of Mo and Ti. Negative ΔHcp values indicate stability compared to the set of most competing phases.

FIG. 8.

Formation enthalpy ΔHcp of, (a) MomTi3-mAlC2 and (b) MomTi4-mAlC3 phases as a function of m for ordered (filled symbols), partially disordered (open squares), and disordered distributions (crosses) of Mo and Ti. Negative ΔHcp values indicate stability compared to the set of most competing phases.

Close modal

For m = 1, or the MoTi2AlC2 composition, the type A structure is even less stable than the solid solution (+37 meV/atom). Interestingly, for m = 1, the C-type unit cell has the lowest energy.

The functional dependencies of ΔHcp on m—calculated for MomTi4-mAlC3 relative to their most likely competing phases (listed in the last column of Table IV)—are plotted in Fig. 8(b). Here again, at m = 2, with ΔHcp = −17 meV/atom, only type A structure is stable. At this composition, Mo2TiAlC2 (type A) is one of its most competing phases. At + 71 meV/atom, the solid solution of Ti and Mo on the M-sites is not stable. Furthermore, at this composition, the least stable structure is type B, where only Ti layers are adjacent to the Al-layers and all Mo layers are in between the Ti layers. Note that for the Mo2Ti2AlC3 composition, type B is the inverse of type A (compare type A and type B structures in Fig. 7(b)).

It follows that for both the MomTi3–mAlC2 and MomTi4–mAlC3 compositions, there is a strong driving force for the formation of structures where the C-Mo-C bonds, in FCC arrangement, are minimized and the Mo-Al bonds are maximized. In both systems, this occurs at m = 2 with type A layering. Another way to illustrate this important conclusion—that is well confirmed experimentally (see Table II)—is to plot ΔHcp as the fraction of Mo/(Mo + Ti) atoms surrounded by C in FCC arrangement (Fig. 9). Based on these results, it is clear that the only stable structure is type A, where C-Mo-C (in FCC) bonds do not exist, i.e., for Mo/(Mo + Ti) = 0 in Fig. 9. This does not necessarily imply that Mo and C do not form strong bonds—after all MoC is one of the most stable binary carbides known—but rather that the HCP arrangement of C is much preferred. Interestingly, Hugosson et al. also showed that while vacancies destabilized hexagonal MoC, they rendered the rock salt structure more stable.47 Some may argue that the stability of the ordered structures could be related to the presence of Mo-Al bonds. However, the fact that the Mo2AlC phase does not exist argues against this idea.

FIG. 9.

Formation enthalpy, ΔHcp, of Mo2TiAlC2, MoTi2AlC2, and Mo2Ti2AlC3 as a function of the fraction of Mo atoms, given by Mo/(Mo+Ti) facing the Al layers on the 4f (Mo2TiAlC2 and MoTi2AlC2) or 4e (Mo2Ti2AlC3) M-sites. In this figure only type A is stable and has the lowest energy compared to its most competing phases.

FIG. 9.

Formation enthalpy, ΔHcp, of Mo2TiAlC2, MoTi2AlC2, and Mo2Ti2AlC3 as a function of the fraction of Mo atoms, given by Mo/(Mo+Ti) facing the Al layers on the 4f (Mo2TiAlC2 and MoTi2AlC2) or 4e (Mo2Ti2AlC3) M-sites. In this figure only type A is stable and has the lowest energy compared to its most competing phases.

Close modal

The results, summarized in Table II, confirm there is some intermixing between the Ti and Mo layers, a not too surprising result since our samples were fabricated at 1873 K. Thus the pertinent question to ask here is by how much can the compositions deviate from m = 2 and still remain stable? To answer this question, we started with a type A structure and created solid solutions on one of the M-sites, a so-called partial SQS. The results of such calculations—shown in Figs. 8(a) and 8(b) by dashed lines—show that for both chemistries, such mixing results in less stable structures. For the MomTi3–mAlC2 compositions, ΔHcp<0 between 1.8 < m < 2.15 (see Fig. 8(a)). In the MomTi4–mAlC3 case, ΔHcp<0, over a wider m range, viz., between 1 < m < 2.3 (see Fig. 8(b)). Given the aversion of the Mo atoms to be surrounded by C atoms in an FCC arrangement, it is not surprising that the minimum in Fig. 8(b) is non-symmetric and skewed to the Ti-side. Why this is not the case for the 312 phase (Fig. 8(a)) is less clear at this time. Note that in Fig. 8, when some of the Mo atoms—on the 4f- or 4e-sites in 312 or 413 structures, respectively—are replaced by Ti, m decreases. Conversely, when some of the Ti atoms on the 2a- or 4f-sites are replaced by Mo, m increases.

As noted above, Table II reveals that there is some intermixing between the Mo and Ti layers in Mo2TiAlC2 and Mo2Ti2AlC3. This was modeled by keeping the Mo2TiAlC2 and Mo2Ti2AlC3 compositions fixed, while gradually changing the degrees of order/intermixing from complete order of type A (1) to a solid solution (0) (Fig. 9). Detailed information of the occupation of the Ti and Mo atoms on the various sites as a function of a disorder parameter is given in Table V. Figure 10(a) sketches a fully disordered structure (I), a semi-ordered structure (II) with an order parameter of 0.625, and the fully ordered Type A Mo2Ti2AlC3 structure (III).

TABLE V.

Calculated lattice parameters and atomic occupancies of Mo and Ti atoms on the M-sites for ordered, semi-ordered, and disordered distributions of Mo and Ti in the Mo2TiAlC2 and Mo2Ti2AlC3 phases.

Mo2TiAlC2
Lattice parameters2a (%)4f (%)2a (#atoms)4f (#atoms)
Degree of orderinga (Å)c (Å)TiMoTiMoTiMoTiMo
1.0000 (type A) 3.0082 18.757 100 100 
0.8125 3.0135 18.745 88 13 94 28 60 
0.6250 3.0196 18.728 75 25 13 88 24 56 
0.4375 3.0254 18.711 63 38 19 81 20 12 12 52 
0.0000 (SQS) 3.0442 18.683 34 66 33 67 11 21 21 43 
Mo2TiAlC2
Lattice parameters2a (%)4f (%)2a (#atoms)4f (#atoms)
Degree of orderinga (Å)c (Å)TiMoTiMoTiMoTiMo
1.0000 (type A) 3.0082 18.757 100 100 
0.8125 3.0135 18.745 88 13 94 28 60 
0.6250 3.0196 18.728 75 25 13 88 24 56 
0.4375 3.0254 18.711 63 38 19 81 20 12 12 52 
0.0000 (SQS) 3.0442 18.683 34 66 33 67 11 21 21 43 
Mo2Ti2AlC3
Lattice parameters4f (%)4e (%)4f (#atoms)4e (#atoms)
Degree of orderinga (Å)c (Å)TiMoTiMoTiMoTiMo
1.0000 (type A) 3.0280 23.659 100 100 
0.8125 3.0328 23.655 91 91 58 58 
0.6250 3.0376 23.648 81 19 19 81 52 12 12 52 
0.4375 3.0421 23.657 72 28 28 72 46 18 18 46 
0.0000 (SQS) 3.0560 23.647 50 50 50 50 32 32 32 32 
Mo2Ti2AlC3
Lattice parameters4f (%)4e (%)4f (#atoms)4e (#atoms)
Degree of orderinga (Å)c (Å)TiMoTiMoTiMoTiMo
1.0000 (type A) 3.0280 23.659 100 100 
0.8125 3.0328 23.655 91 91 58 58 
0.6250 3.0376 23.648 81 19 19 81 52 12 12 52 
0.4375 3.0421 23.657 72 28 28 72 46 18 18 46 
0.0000 (SQS) 3.0560 23.647 50 50 50 50 32 32 32 32 

When ΔHcp is plotted as a function of the degree of order (Fig. 10(b)), it is clear that both compounds can tolerate some disorder, with the 413 compound tolerating more disorder than its 312 counterpart. Based on the extent of intermixing between the Mo and Ti atoms in the phases listed in Table II, one can assume the order parameters for both phases are less than one. It is thus gratifying that the calculated lattice parameters for the fully ordered 312 phase—with a = 3.0135 Å and c = 18.745 Å—are slightly larger than the experimental ones, viz., 2.99718(3) and 18.6614(2) Å, respectively. For the fully ordered 413 phase, the calculated lattice parameters a = 3.0376 Å and c = 23.648 Å are again slightly larger than experiment, viz., 3.02064(8) Å and 23.5431(7) Å, respectively. Note that the use of GGA is known to generate slightly overestimated structural parameters.

Up to this point, all calculations were carried out at 0 K. The corresponding free energies are approximated as ΔGcp=ΔHcpTΔS, where ΔS=2kB[zln(z)+(1z)ln(1z)] is the configurational entropy change of an ideal solution of Ti and Mo atoms on the M-sites, where kB is the Boltzmann constant and z corresponds to the amount of Mo M-site (0 <  z < 1). For illustrative purpose, ΔGcp is calculated at 1873 K, which is the synthesis temperature used in this work. Even though ΔGcp cannot be estimated quantitatively for the intermixed structures, the contribution from configurational entropy to the free energy at elevated temperatures was estimated assuming a linear combination of the configurational entropy for the totally disordered structure and the semi/partially ordered structures. The dashed lines in Fig. 10 plot ΔGcp over the entire order domain. Not surprisingly, entropy stabilizes the slightly disordered structures. A conclusion that is again generally consistent with the results shown in Table II.

Figure 11 plots the density of states (DOS) for type A Mo2TiAlC2. Non-bonding core states of C 2s and Al 2s are located at −13 to −10.5 eV and −8.8 to −3 eV, respectively. Between −7 and −3 eV Mo 4d and C 2p states form a hybridized bond and for Ti 3d and C 2p states this forms between −7 and −3.5 eV. The double peak just below −3 eV shows partial hybridization of Mo 4d and Al 2p states. States from −1.7 eV up to the Fermi level (Ef) are dominated by the Mo 4d states that show no clear hybridization with other elements. The peak located just below Ef can mainly be attributed to Mo 4d states.

FIG. 11.

Density of states (DOS) for type A Mo2TiAlC2. (a) Total and atomic DOS and (b) partial DOS for each unique symmetry site. Vertical solid line indicates the location of the Fermi level Ef.

FIG. 11.

Density of states (DOS) for type A Mo2TiAlC2. (a) Total and atomic DOS and (b) partial DOS for each unique symmetry site. Vertical solid line indicates the location of the Fermi level Ef.

Close modal

The DOS for type A Mo2Ti2AlC3 is shown in Fig. 12. Not surprisingly, they share many commonalities with Fig. 11. The major difference being the existence of two different C sites (2(a) and 4(f)), which results in a double peak of the non-bonding core states for C 2s located at −12.8 to −9.4 eV. The two sites also give rise to splitting of the C 2p peaks as they form hybridized bonds with both Mo 4d and Ti 3d between −7 and −1.3 eV and from −4.6 to −1.3 eV. The states located close to −2 eV are due to partial hybridization of Mo 4d and Al 2p states. From −1.3 eV to Ef, the DOS is dominated by non-bonding Mo 4d states. The latter are clearly dominant at Ef.

FIG. 12.

Density of states (DOS) for type A Mo2Ti2AlC3. (a) Total and atomic DOS and (b) partial DOS for each unique symmetry site. Vertical solid line indicates the location of the Fermi level Ef.

FIG. 12.

Density of states (DOS) for type A Mo2Ti2AlC3. (a) Total and atomic DOS and (b) partial DOS for each unique symmetry site. Vertical solid line indicates the location of the Fermi level Ef.

Close modal

Calculated electronic band structures of type A Mo2TiAlC2 and Mo2Ti2AlC3 along high-symmetry lines of the Brillouin zone are shown, respectively, in Figs. 13(a) and 13(b). Both show similar behavior, especially close to Ef, which is dominated by the Mo 4d states. Along with the DOS results shown in Figs. 11 and 12, it is reasonable to conclude that, like most other MAX phases,3 these compounds should be metallic conductors—as observed over most of the temperature range explored herein (Fig. 6)—mainly in-plane, with bands crossing Ef along various directions. The band structure also shows strong anisotropic features with less dispersion out-of-plane, i.e., along the c-axis. Near Ef this anisotropy indicates that the conductivity should be larger in-plane as compared to out-of-plane.

FIG. 13.

Electronic band structure of type A, (a) Mo2TiAlC2 and (b) Mo2Ti2AlC. Horizontal solid line at 0 represents the Fermi level Ef.

FIG. 13.

Electronic band structure of type A, (a) Mo2TiAlC2 and (b) Mo2Ti2AlC. Horizontal solid line at 0 represents the Fermi level Ef.

Close modal

The calculated elastic constants of type A Mo2TiAlC2 and Mo2Ti2AlC3 and their end members are listed in Table VI. In both cases, the ordered quaternary compounds have higher moduli than their end members. This is most pronounced for C44. Also the calculated Bv, Gv, and E moduli show improved values. For example, +36% in Bv vs. Ti3AlC2, which may be correlated to the large decrease in unit cell volume (−4.2%). As such, these ordered quaternary structures are not only highly stable, but they also seem to alter the bonding chemistry and thus improve the elastic properties with respect to their end members. The values predicted for Mo2Ti2AlC3 are noteworthily high: C11 is >420 GPa and C44 is 163 GPa.

TABLE VI.

Calculated elastic constants Cij, elastic moduli BV, GV, E, Poisson′s ratio, ν, anisotropy factor, A, and theoretical densities of Ti3AlC2, Mo3AlC2, Mo2TiAlC2 (type A) Ti4AlC3, Mo4AlC3, and Mo2Ti2AlC3 (type A).

PhaseC11C12C13C33C44BVGVEνAρ (Mg/m3)
(GPa)
Ti3AlC2 357 79 76 290 119 163 127 302 0.19 0.96 4.21 
Mo2TiAlC2–type A 386 143 140 367 150 221 132 331 0.25 1.27 6.57 
Mo3AlC2 354 143 149 352 110 216 106 274 0.29 1.08 7.43 
Ti4AlC3 385 90 86 317 131 179 137 328 0.19 0.99 4.35 
Mo2Ti2AlC3-type A 424 130 144 382 163 230 149 367 0.23 1.26 6.20 
Mo4AlC3 333 138 145 371 61 210 84 223 0.32 0.58 7.55 
PhaseC11C12C13C33C44BVGVEνAρ (Mg/m3)
(GPa)
Ti3AlC2 357 79 76 290 119 163 127 302 0.19 0.96 4.21 
Mo2TiAlC2–type A 386 143 140 367 150 221 132 331 0.25 1.27 6.57 
Mo3AlC2 354 143 149 352 110 216 106 274 0.29 1.08 7.43 
Ti4AlC3 385 90 86 317 131 179 137 328 0.19 0.99 4.35 
Mo2Ti2AlC3-type A 424 130 144 382 163 230 149 367 0.23 1.26 6.20 
Mo4AlC3 333 138 145 371 61 210 84 223 0.32 0.58 7.55 

The fact that these compounds are machinable with nothing more sophisticated that a manual hack saw, bodes well for their ultimate use in applications where high stiffness values, especially bulk moduli, are required with densities (≈6 Mg/m3) that are relatively low. Few other MAX phases have comparable elastic moduli. For example, the Ta-containing ones in general, and Ta4AlC3, in particular,57 have comparable values. The densities of the latter, however, are more than double those of Mo2Ti2AlC3.

Lastly, Liu et al. suggested that the high-order (M′,M″)3AX2 compounds form via insertion of −(M′X)m− slabs into a M2AX structure.24 However, since Mo2AlC does not exist, this formation mechanism cannot be invoked here.

Herein, we showed that despite the fact that Ti3AlC2 is stable and Mo3AlC2 is far from being stable, the quaternary Mo2TiAlC2 is quite stable. Consistent with the experimental results presented in this and previous work,27 its lowest energy configuration is when it is ordered, with the Mo-layers sandwiching both the Al and Ti-C layers. The a lattice parameter of the quaternary is lower than its end members. The opposite is true for the c lattice parameters. The unit cell volume of the quaternary is lower than its end members.

Similarly, and despite the fact the Ti4AlC3 is at the verge of being stable and Mo4AlC3 is far from being stable, the quaternary Mo2Ti2AlC3 is stable. Like its 312 counterpart, its lowest energy configuration occurs when it is ordered, with repeated Mo-Ti-Ti-Mo layering, again consistent with our experimental work.

Both Mo2TiAlC2 and Mo2Ti2AlC3 can have moderate intermixing (0 to 25 at. %), as observed experimentally and confirmed by DFT calculations. Based on our Rietveld refinement results, the outer M layers, which are richer in Mo, tolerate more intermixing than the inner M layers (Ti rich layers). The latter was explained by the fact that Mo atoms avoid being surrounded by C atoms in a FCC arrangement. The leitmotif of this work, and the driving force for ordering, is the high energetic penalty paid by the system when the Mo atoms are surrounded by C atoms in a FCC arrangement, i.e., M sites not adjacent to Al layers.

In the case of Mo2TiAlC2, the B, G, and E values are predicted to be 221, 132, and 331 GPa, respectively. For Mo2Ti2AlC3-x the B, G, and E values are predicted to be 230, 149, and 367 GPa, respectively. Like the vast majority of the MAX phases, the DOS at Ef is substantial, dominated by the Mo 4d states and explains its metallic-like conductivity.

The chemical formulae of Mo2TiAlC2 and Mo2Ti2AlC3 obtained from the XPS analysis—Mo2TiAlC1.7 and Mo2Ti1.9Al0.9C2.5—are in good agreement with those deduced from EDS. The XPS analysis shows almost no influence of Mo on the binding energy of the Ti species, whereas the binding energies of the Mo species are closer to those of Mo2C than to Mo metal. Mo2TiAlC2 has only one C species in the 1s carbon region at 242.5 eV, while Mo2Ti2AlC3 has two peaks, one of which is the same as that for Mo2TiAlC2, and the second corresponds to the C in the inner layers bonded to Ti atoms only at a binding energy of 242.1 eV. Their ratio is 2 to 1 consistent with the proposed structures and ordering.

Finally, we note that the importance of this work lies beyond the discovery of new ordered MAX phases, as exciting as that may be, but rather that the A-group element is Al, that can be readily etched in HF.13 This in turn implies that Mo-based MXenes can now be fabricated and tested. This was accomplished28 and the results are encouraging.

E.J.M. and S.J.M. were supported by the U.S. Army Research Office under Grant No. W911NF-12-1-0132. Acquisition of the PPMS was supported by the U.S. Army Research Office under Grant No. W911NF-11-1-0283. Further, we acknowledge support from the Swedish Research Council (Project Grant Nos. #621-2011-4420, 642-2013-8020, and 621-2014-4890), the Swedish Foundation for Strategic Research through the Synergy Grant FUNCASE Functional Carbides for Advanced Surface Engineering (J.R., P.E., M.W.B., and J.H.), the Future Research Leaders 5 Program (P.E. and J.L.), and the ERC Grant agreement [No. 258509] (J.R.). The Knut and Alice Wallenberg Foundation is acknowledged for a Wallenberg Academy Fellowship (J.R.) and scholar (L.H.) and for supporting the Electron Microscopy Laboratory at Linköping University operated by the Thin Film Physics Division. Calculations were performed utilizing supercomputer resources supplied by the Swedish National Infrastructure for Computing (SNIC) at the PDC Center for High Performance Computing and National Supercomputer Centre.

1.
M. W.
Barsoum
and
M.
Radovic
,
Annu. Rev. Mater. Res.
41
,
195
(
2011
).
2.
P.
Eklund
,
M.
Beckers
,
U.
Jansson
,
H.
Högberg
, and
L.
Hultman
,
Thin Solid Films
518
,
1851
(
2010
).
3.
M. W.
Barsoum
,
MAX Phases: Properties of Machinable Ternary Carbides and Nitrides
(
John Wiley & Sons
,
2013
).
4.
M. W.
Barsoum
and
T.
ElRaghy
,
J. Am. Ceram. Soc.
79
,
1953
(
1996
).
5.
M. W.
Barsoum
,
D.
Brodkin
, and
T.
ElRaghy
,
Scr. Mater.
36
,
535
(
1997
).
6.
M. W.
Barsoum
, in
Encyclopedia of Materials Science and Technology
, edited by
K. H. J.
Buschow
,
R. W.
Cahn
,
M. C.
Flemings
,
E. J.
Kramer
,
S.
Mahajan
, and
P.
Veyssiere
(
Elsevier
,
Amsterdam
,
2006
).
7.
M.
Sundberg
,
G.
Malmqvist
,
A.
Magnusson
, and
T.
El-Raghy
,
Ceram. Int.
30
,
1899
(
2004
).
8.
X. H.
Wang
and
Y. C.
Zhou
,
Oxid. Met.
59
,
303
(
2003
).
9.
D. J.
Tallman
,
B.
Anasori
, and
M. W.
Barsoum
,
Mater. Res. Lett.
1
,
115
(
2013
).
10.
G. M.
Song
,
Y. T.
Pei
,
W. G.
Sloof
,
S. B.
Li
,
J. T. M.
De Hosson
, and
S.
van der Zwaag
,
Scr. Mater.
58
,
13
(
2008
).
11.
H.
Yang
,
Y.
Pei
,
J.
Rao
, and
J. T. M.
De Hosson
,
J. Mater. Chem.
22
,
8304
(
2012
).
12.
A.-S.
Farle
,
C.
Kwakernaak
,
S.
van der Zwaag
, and
W. G.
Sloof
,
J. Eur. Ceram. Soc.
35
,
37
(
2015
).
13.
M.
Naguib
,
V. N.
Mochalin
,
M. W.
Barsoum
, and
Y.
Gogotsi
,
Adv. Mater.
26
,
982
(
2014
).
14.
J.
Halim
,
M. R.
Lukatskaya
,
K. M.
Cook
,
J.
Lu
,
C. R.
Smith
,
L.-Å.
Näslund
,
S. J.
May
,
L.
Hultman
,
Y.
Gogotsi
,
P.
Eklund
, and
M. W.
Barsoum
,
Chem. Mater.
26
,
2374
(
2014
).
15.
M.
Ghidiu
,
M. R.
Lukatskaya
,
M.-Q.
Zhao
,
Y.
Gogotsi
, and
M. W.
Barsoum
,
Nature
516
,
78
(
2014
).
16.
L. E.
Toth
,
J. Less Common Met.
13
,
129
(
1967
).
17.
R.
Meshkian
,
A. S.
Ingason
,
M.
Dahlqvist
,
A.
Petruhins
,
U. B.
Arnalds
,
F.
Magnus
,
J.
Lu
, and
J.
Rosen
,
Phys. Status Solidi RRL
9
,
197
(
2015
).
18.
C.
Hu
,
C.
Li
,
J.
Halim
,
S.
Kota
,
D. J.
Tallman
, and
M. W.
Barsoum
,
J. Am. Ceram. Soc.
(published online).
19.
C.
Hu
,
C.-C.
Lai
,
Q. Z.
Tao
,
J.
Lu
,
J.
Halim
,
L.
Sun
,
J.
Zhang
,
J.
Yang
,
B.
Anasori
,
J.
Wang
,
Y.
Sakka
,
L.
Hultman
,
P.
Eklund
,
J.
Rosen
, and
M. W.
Barsoum
,
Chem. Commun.
51
,
6560
(
2015
).
20.
M.
Naguib
,
G.
Bentzel
,
J.
Shah
,
J.
Halim
,
E.
Caspi
,
J.
Lu
,
L.
Hultman
, and
M.
Barsoum
,
Mater. Res. Lett.
2
,
233
240
(
2014
).
21.
H.
Nowotny
,
P.
Rogl
, and
J. C.
Schuster
,
J. Solid State Chem.
44
,
126
(
1982
).
22.
A.
Mockute
,
J.
Lu
,
E. J.
Moon
,
M.
Yan
,
B.
Anasori
,
S. J.
May
,
M. W.
Barsoum
, and
J.
Rosen
,
Mater. Res. Lett.
3
,
16
22
(
2015
).
23.
A.
Mockute
,
M.
Dahlqvist
,
J.
Emmerlich
,
L.
Hultman
,
J.
Schneider
,
P. O. Å.
Persson
, and
J.
Rosen
,
Phys. Rev. B
87
,
094113
(
2013
).
24.
Z.
Liu
,
E.
Wu
,
J.
Wang
,
Y.
Qian
,
H.
Xiang
,
X.
Li
,
Q.
Jin
,
G.
Sun
,
X.
Chen
,
J.
Wang
, and
M.
Li
,
Acta Mater.
73
,
186
(
2014
).
25.
E. N.
Caspi
,
P.
Chartier
,
F.
Porcher
,
F.
Damay
, and
T.
Cabioc'h
,
Mater. Res. Lett.
3
,
100
106
(
2015
).
26.
W.
Jeitschko
and
H.
Nowotny
,
Monatsh. Chem.
98
,
329
(
1967
).
27.
B.
Anasori
,
J.
Halim
,
J.
Lu
,
C. A.
Voigt
,
L.
Hultman
, and
M. W.
Barsoum
,
Scr. Mater.
101
,
5
(
2015
).
28.
B.
Anasori
,
Y.
Xie
,
M.
Beidaghi
,
J.
Lu
,
B. C.
Holser
,
L.
Hultman
,
Y.
Gogotsi
, and
M.
Barsoum
,
ACS Nano
(published online).
29.
H. M.
Rietveld
,
J. Appl. Crystallogr.
2
,
65
(
1969
).
30.
J.
Rodríguez-Carvajal
,
Phys. B: Condens. Matter
192
,
55
(
1993
).
31.
P. E.
Blöchl
,
Phys. Rev. B
50
,
17953
(
1994
).
32.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
48
,
13115
(
1993
).
33.
G.
Kresse
and
D.
Joubert
,
Phys. Rev. B
59
,
1758
(
1999
).
34.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
49
,
14251
(
1994
).
35.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
36.
H. J.
Monkhorst
and
J. D.
Pack
,
Phys. Rev. B
13
,
5188
(
1976
).
37.
A.
Zunger
,
S. H.
Wei
,
L. G.
Ferreira
, and
J. E.
Bernard
,
Phys. Rev. Lett.
65
,
353
(
1990
).
38.
M.
Dahlqvist
,
B.
Alling
,
I. A.
Abrikosov
, and
J.
Rosén
,
Phys. Rev. B
81
,
024111
(
2010
).
39.
M.
Dahlqvist
,
B.
Alling
, and
J.
Rosén
,
Phys. Rev. B
81
,
220102
(
2010
).
40.
P.
Eklund
,
M.
Dahlqvist
,
O.
Tengstrand
,
L.
Hultman
,
J.
Lu
,
N.
Nedfors
,
U.
Jansson
, and
J.
Rosén
,
Phys. Rev. Lett.
109
,
035502
(
2012
).
41.
A. S.
Ingason
,
A.
Mockute
,
M.
Dahlqvist
,
F.
Magnus
,
S.
Olafsson
,
U. B.
Arnalds
,
B.
Alling
,
I. A.
Abrikosov
,
B.
Hjörvarsson
,
P. O. Å.
Persson
, and
J.
Rosen
,
Phys. Rev. Lett.
110
,
195502
(
2013
).
42.
A. S.
Ingason
,
A.
Petruhins
,
M.
Dahlqvist
,
F.
Magnus
,
A.
Mockute
,
B.
Alling
,
L.
Hultman
,
I. A.
Abrikosov
,
P. O. Å.
Persson
, and
J.
Rosen
,
Mater. Res. Lett.
2
,
89
(
2014
).
43.
A.
Petruhins
,
A.
S.
Ingason
,
J.
Lu
,
F.
Magnus
,
S.
Olafsson
, and
J.
Rosen
,
J. Mater. Sci.
50
,
4495
(
2015
).
44.
A.
Mockute
,
P. O. Å.
Persson
,
F.
Magnus
,
A. S.
Ingason
,
S.
Olafsson
,
L.
Hultman
, and
J.
Rosen
,
Phys. Status Solidi RRL
8
,
420
(
2014
).
45.
L.
Fast
,
J. M.
Wills
,
B.
Johansson
, and
O.
Eriksson
,
Phys. Rev. B
51
,
17431
(
1995
).
46.
See supplementary material at http://dx.doi.org/10.1063/1.4929640 for XRD Rietveld refinement and further resistivity, XPS and theoretical analysis.
47.
H. W.
Hugosson
,
O.
Eriksson
,
L.
Nordström
,
U.
Jansson
,
L.
Fast
,
A.
Delin
,
J. M.
Wills
, and
B.
Johansson
,
J. Appl. Phys.
86
,
3758
(
1999
).
48.
M. W.
Barsoum
,
L.
Farber
,
I.
Levin
,
A.
Procopio
,
T.
El-Raghy
, and
A.
Berner
,
J. Am. Ceram. Soc.
82
,
2545
(
1999
).
49.
L.
Kiwi-Minsker
and
A.
Renken
,
Catal. Today
110
,
2
(
2005
).
50.
J. E.
Krzanowski
and
R. E.
Leuchtner
,
J. Am. Ceram. Soc.
80
,
1277
(
1997
).
51.
J.
Luthin
and
C.
Linsmeier
,
Phys. Scr.
2001
,
134
(
2001
).
52.
Y.-H.
Chang
and
H.-T.
Chiu
,
J. Mater. Res.
17
,
2779
(
2002
).
53.
M. C.
Biesinger
,
L. W. M.
Lau
,
A. R.
Gerson
, and
R. S. C.
Smart
,
Appl. Surf. Sci.
257
,
887
(
2010
).
54.
S.
Myhra
,
J. A. A.
Crossley
, and
M. W.
Barsoum
,
J. Phys. Chem. Solids
62
,
811
(
2001
).
55.
D. E.
Mencer
, Jr.
,
T. R.
Hess
,
T.
Mebrahtu
,
D. L.
Cocke
, and
D. G.
Naugle
,
J. Vac. Sci. Technol. A
9
,
1610
(
1991
).
56.
J.
Etzkorn
,
M.
Ade
, and
H.
Hillebrecht
,
Inorg. Chem.
46
,
7646
(
2007
).
57.
C.
Hu
,
Z.
Lin
,
L.
He
,
Y.
Bao
,
J.
Wang
,
M.
Li
, and
Y.
Zhou
,
J. Am. Ceram. Soc.
90
,
2542
(
2007
).

Supplementary Material