Layered ternary M_n+1AX_n phases and their 2D derivative MXene: an overview from a thin-film perspective

The MAX phases [17], are carbides and nitrides (the 'X' indicating C or N) with the general formula M_n+1AX_n (n  =  1, 2, or 3), often referred to as 211 (n  =  1), 312 (n  =  2), and 413 (n  =  3) phases. The M elements are mainly group-4, group-5, and group-6 transition metals (primarily Ti, Zr, Hf, V, Nb, Ta, Cr, and Mo), while the A element is from groups 12 (Cd), 13 (Al, Ga, In, Tl), 14 (Si, Ge, Sn, Pb), 15 (P, As), or 16 (S). The origin of the label 'A' is the old American nomenclature for the periodic table [26].

Figure 1 is an illustration of the hexagonal unit cells of the 211, 312, and 413 MAX phases. The unit cells consist of M₆X octahedra, e.g. Ti₆C, interleaved with layers of A elements. In the MAX phases, the MX layers are twinned with respect to each other and separated by the A layer which acts as a mirror plane. The MAX structures are anisotropic: the lattice parameters are typically around a ~ 3 Å and c ~ 13 Å (for the 211 phases), c ~ 18 Å (for the 312 phases), and c ~ 23–24 Å (for the 413 phases). The space group is P6₃/mmc. In principle, the value of n may be higher than 3, forming the '514' phases, and higher. However, there are only a few examples of such phases, e.g. (Ti_0.5, Nb_0.5)₅AlC₄, and none have been synthesized in pure form [41].

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Intergrown MAX phases were first reported by Palmquist et al in the Ti-Si-C system [42], and soon thereafter observed also in the Ti-Ge-C and Ti-Al-C systems [43, 44]. These phases consist of alternating '211' and '312' half unit cells, to form a '523' phase, or alternating '312' and '413' half-unit cells to form a '725' phase. This stacking needs to be repeated three times to form a complete unit cell, meaning that the c-axis is three times the average unit cell of the two constituents, and that the symmetry of the P6₃/mmc space group is broken. Initially, it was believed that these intergrown phases could form only as minority or intermediate phases, primarily in thin films. However, in 2011, Scabarozi et al demonstrated that Ti₇Si₂C₅ can be synthesized as phase-pure epitaxial thin films [45]. Figure 2 (from Scabarozi et al [45]) shows a transmission electron microscopy (TEM) of the Ti₇Si₂C₅ structure; the alternating '312' and '413' layers can be seen. Somewhat later, Ti₅Al₂C₃ was synthesized as a majority phase in bulk samples [46]. Initially, the structure was reported as belonging to the P3m1 space group [46, 47], but it was soon shown that the same structure can be described with a higher symmetry in the R-3m space group [48] (refer to table 1 in [49] for the structural model of Ti₅Al₂C₃). It should also be noted that there is an erroneous report [50] on Ti₅Al₂C₃ claiming a different structure, with space group P6₃/mmc, but this proposed structure is inconsistent with the experimentally observed structure [47].

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In addition to the pure ternary phases, there is a large number of synthesized isostructural solid solutions of MAX phases, which is important for understanding the role of chemistry in controlling and ultimately tuning of physical properties. In practice, important examples of this tailoring opportunity include oxidation studies, where the excellent oxidation resistance of the alumina-formers Ti₂AlC and Ti₃AlC₂ [40, 51, 52] is retained also for solid solutions, e.g. Ti₃(Si,Al)C₂ [53–56], thermal properties, in particular tailoring of thermal expansion [57, 58], tuning magnetic characteristics [59, 60] and the possibility to stabilize new MAX phases that are not stable in their pure ternary form [41, 61–63]. For mechanical properties, solid-solution hardening effects [64–69] are generally not very pronounced, with some exceptions [70–72]. There are also some discrepancies, particularly in the Ti₃AC₂ systems (A  =  Si, Ge, Al, Sn) where several investigations [64, 65, 73–75] have demonstrated that solid solution hardening is not operative, while one study argues the opposite [72]. Most recently, Gao et al [76] demonstrated that solid solutions could play a role in increasing the hardness of coarse-grained Ti₃(Al,Si)C₂, but not for fine-grained, indicating that it is not a pure solid-solution hardening effect, but rather a microstructural effect.

Ordered MAX phases (M', M'')_n+1AlC_n have been a recent important development. These ordered phases differ from regular solid solutions in that the two elements on the M site are different. In the ideal case, one site is one transition metal M' (e.g. Ti) and the nonequivalent site in the structure is a different transition metal M'' (e.g. Cr). This was initially reported in the phases Cr₂TiAlC₂ and V₂CrAlC₂ [77, 78]. Ideally, these should then have a fixed stoichiometry. In practice, it appears that these phases exhibit a high degree of ordering, but not necessarily complete. A further important discovery in this topic is the ordered Mo₂TiAlC₂ [79] and Mo₂Ti₂AlC₃ [80]. In Mo₂TiAlC₂, the Ti atoms are positioned between the two Mo layers adjacent to the Al planes. Figure 3 (from Anasori et al [79]) is a high-resolution scanning TEM (HRSTEM) image with corresponding chemical analysis by energy dispersive x-ray spectroscopy (EDX) of the structure of Mo₂TiAlC₂, showing the high degree of ordering of the metal layers. The discovery of this type of structure, together with the etching of Ga from Mo₂Ga₂C (see section 4), allows for the fabrication and characterization of Mo-based MXenes.

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This section summarizes methodologies for thin-film synthesis of MAX phases, in particular chemical vapor deposition (CVD), physical vapor deposition (PVD), and solid state reaction synthesis. The summary is restricted to atomistic techniques rather than methods for growth of thick coatings such as spraying techniques, where a powder of the desired material is sprayed [81–86]. The majority of bulk synthesis methods operate (or are assumed to operate) near thermodynamic equilibrium, which is similar to the situation in CVD which is based on chemical reactions typically at high temperature. PVD, in contrast, takes place far from thermodynamic equilibrium under kinetically limited conditions. The mechanisms of film growth and the importance of substrate selection and quality are not treated here; the reader is referred to earlier reviews [26, 87].

3.1.1. CVD.

3.1.2. PVD.

3.1.3. Solid-state reaction synthesis.

3.2.1. Materials discovery.

3.2.2. Property calculations.

In 2011, a new 2D nanocrystal based on MAX phases was synthesized through immersion of Ti₃AlC₂ in hydrofluoric acid (HF). Removal of the A layer resulted in 2D M_n+1X_n layers that were labelled MXene [19], to denote the loss of the A element and emphasize the structural similarities with graphene. MXenes constitute a new family of 2D materials that, generally speaking, combine the metallic conductivity (see section 5.2) of transition metal carbides with the hydrophilic nature of their hydroxyl (OH) or oxygen (O) terminated surfaces. A common notation for the MXenes is M_n+1X_n T_x , where T_x represents the surface functional groups, mostly O, OH, and fluorine (F). The terminations originate from the choice of etching procedure, typically using HF, ammonium bifluoride (NH₄HF₂) or a solution of lithium fluoride (LiF) and hydrochloric acid (HCl).

The MXenes synthesized to date include, for example, Ti₃C₂T_x , Ti₂CT_x , V₂CT_x , Nb₂CT_x , Nb₄C₃T_x , and Ta₄C₃T_x . Zr₃C₂T_x MXenes have also been produced from laminated phases other than MAX phases, i.e. Zr₃Al₃C₅ by etching of Al-C units rather than Al etching [171]. This is important because while there are some recent reports on MAX phases in the Zr-Al-C and Hf-Al-C systems [172–174], the transition metals Zr and Hf primarily tend to form related phases of the type Zr₂Al₃C₄, Zr₃Al₃C₅, etc [31, 175]. Furthermore, solid solutions, such as Ti₃CNT_x , (Ti_0.5,Nb_0.5)₂CT_x , and (V_0.5,Cr_0.5)₃C₂T_x have been reported, in which the two transition elements are believed to randomly occupy the M-sites [176, 177]. More recently, ordered MXenes in the form of Mo₂TiC₂T_x , Mo₂Ti₂C₃T_x , and Cr₂TiC₂T_x have been presented [178], originating from the corresponding out-of-plane chemically ordered MAX phases Mo₂TiAlC₂, Mo₂Ti₂AlC₃, and Cr₂TiAlC₂, respectively, for which Ti/Ti₂C is sandwiched between two outer layers of metal (Mo/Cr) carbide layers.

Despite their young age, over 20 MXenes have been discovered, with new ones discovered continuously. They show great promise in many applications—from energy storage [179, 180], to cationic adsorption [181], conductive transparent electrodes [182–185], field effect transistors [186], and electromagnetic interference shielding [187].

MXenes have been produced as powders, flakes, and colloidal solutions. In 2014, a breakthrough was made in the synthesis of large-area epitaxial thin films of 2D Ti₃C₂, see figure 4 [182]. Depositions on transparent and insulating sapphire substrates enabled measurements of fundamental physical properties, such as optical absorption, in a broad wavelength range, conductivity and magnetoresistances down to 2 K. Most importantly, the results on electrical-transport properties unambiguously showed weak localization of charge carriers and thus proved that these materials are genuinely 2D in the sense of electronic properties.

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By varying the M and X elements, as well as the surface terminations T_x and/or the number of layers, n, in M_n+1X_n T_x , it is possible to tune the MXene properties. Most MXene compositions reported were obtained by etching the Al-layers from Al-containing MAX phases. A related hexagonal ternary nanolaminated carbide, Mo₂Ga₂C, was discovered recently in both bulk and thin-film form [188, 189]. In this phase, two Ga layers—instead of one, such as in the Mo₂GaC MAX phase—are stacked in a simple hexagonal arrangement in between Mo₂C layers, see figure 5 (left). A subsequent study [190] showed the possibility of selectively etching the Ga layers—using HF—from epitaxial Mo₂Ga₂C thin films, producing the MXene Mo₂CT_x , see figure 5 (right). The finding of Mo₂CT_x is important because it was the first MXene originating from selective etching of Ga and because it was the first MXene containing Mo. Later, both Mo₂TiC₂T_x and Mo₂Ti₂C₃T_x were discovered, as mentioned above.

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Electron microscopy has proven an indispensable tool for acquiring structural and elemental information of the MAX phases. Since the introduction of aberration corrected electron microscopy [191], it has been possible to individually detect e.g. in MAX phases, the light and typically low-contrast X elements [192] and to map the elemental distribution at atomic resolution [79, 80, 153] Although electron microscopy has been applied to a large number of studies in MXene synthesis to verify the resulting sheet-like nature, the power of the modern advanced electron microscopy is to resolve, atom by atom, the structure of individual sheets. This has been successfully applied in research on most of the other 2D materials such as graphene [193] and dichalcogenides such as MoS₂ [1].

To generalize, MXenes are most easily investigated from two perspectives; cross-section and plan-view, where with the cross-sectional (side-view) approach the observer can identify separation between sheets, stacking and gain information on the functionalization of the MXene surfaces. This approach is the most commonly used for thin films, though it is also applicable to powders. An illustrative example can be viewed in figure 6, which shows the (incomplete) etching of a thin-film MAX phase to yield MXene. The series of images clearly illustrates the interface between the MXene–MAX and how the MXene organizes itself while still attached to the MAX phase. Technically, the information gained from this investigation is hampered by the (in most cases) unknown number and elemental identity of the atoms which are projected in the atomic columns and onto the image plane. Consequently, resulting images do not reflect the individual atomic structure. Subsequently, plan-view investigations are typically more rewarding, where ideally only a single sheet is projected in the image, such as in figure 7. In this case, the M₃X₂ MXene structure projects in 2/3 of the atomic columns one M and one X atom, and only the single M atom for 1/3 of the atomic columns. For the M₂X structures each column contains a single atom M or X. The plan-view approach was first applied by Karlsson et al [194] and later also by Sang et al [195] in order to describe the structure and surface of the single Ti₃C₂ MXene sheet. These investigations have in particular yielded information on point defects (vacancies and interstitials) and the short-range organization of such defects. Detailed information on these defects is desirable as point defects are known to affect the electronic and optical properties of other 2D materials [196, 197].

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In the investigation of single sheet 2D structures, the electron beam–sample interactions and radiation damage take on a critical variable as it comes to accelerating potential in the microscope. If knock-on damage dominates the radiation damage, low-voltage microscopy (accelerating potentials at or below 60 kV) is a viable route to avoid beam-induced changes in the atomic structure [198–200]. Nevertheless, significant beam-driven dynamics are present in all of these studies, especially at contamination sites, defects, and edges. The edges of a graphene sheet are still highly dynamic at 20 kV electron irradiation [200], defects in graphene easily change their shape in 80 kV image sequences [201] and defects are introduced in molybdenum disulfide [202] under irradiation.

At present, little is known of the electron beam–MXene interactions, however, the existing investigations of the atomically resolved structures suggest that the structure of the MXene sheet is stable between 60–100 kV [191, 195]. Edges and surface functional groups on the other hand are observed to be dynamic and reorganize even at 60 kV [194]. These changes may be the effect of beam induced sample heating rather than direct interactions between the beam and surface functional groups. However, beam–MXene interactions require further investigations for optimum imaging conditions.

The identification of a single sheet is most easily performed in the (S)TEM, yet the method is treacherous. In the (S)TEM, contrast differences originate from differences in the collected dark-field signal, which is determined by Rutherford scattering of the electron beam from each partially screened atomic nucleus. The scattered intensity increases with atomic number (Z) approximately according to Z^1.7 (commonly approximated to Z²) [203]. In the plan-view approach, the double layer therefore adopts twice the intensity compared with the single layer. Despite this, the thickness of a structure cannot be unambiguously determined to a single sheet in plan-view. MXene sheets have a tendency to align themselves with M atomic columns atop M atomic columns [19, 194]. Therefore the columns contain an unknown number of M atoms. This was resolved by Karlsson et al [194] through intensity comparisons using native adatoms on the MXene sheets and by Sang et al [195] through tilting of the sheet to verify the thickness by changes in appearance.

These efforts have proven efficient in visualizing the organization of the M elements in MXene sheets, but a method for direct imaging of the surface functional groups is lacking. Potentially this can be resolved through newer methods in microscopy such as e.g. phase imaging in the STEM [204] or by annular bright field STEM [205].

One of the more promising applications for 2D materials is in the realm of energy storage, where 2D solids are particularly attractive because of their intrinsically high specific surface areas that in turn result in higher energy and power electrodes. Consequently, the intercalation of ions into layered compounds has long been exploited in energy storage devices such as batteries and electrochemical capacitors. MXenes, typically being hydrophilic and conducting, have shown great promise as electrode materials for Li-, Na-, and K-ion batteries [177, 206, 207], Li-S batteries [208], and Li-ion and aqueous supercapacitors [179, 180, 209, 210]. For example, Ti₃C₂T_x intercalated with Li+  ions have shown a steady-state capacity of ~410 mAh g⁻¹ at 1 °C for additive-free electrodes [211]. However, few host materials are known to accommodate ions much larger than lithium, though Ti₃C₂T_x have also been shown to allow spontaneous intercalation with molecules such as hydrazine, dimethyl sulfoxide (DMSO), and urea [210] as well as electrochemical intercalation of a variety of cations, including Na⁺, K⁺, $\text{NH}_{4}^{+}$, Mg²⁺, and Al³⁺ [209], the latter giving a capacitance in excess of 300 Fcm⁻³. Supercapacitor performance has been elevated by synthesizing the Ti₃C₂T_x MXene into a clay-like material, giving a volumetric capacitance of about 900 Fcm⁻³ [179]. Furthermore, recent studies also show enhanced performance for nanocomposite electrodes hybridizing polymers and MXenes [212, 213], with capacitances up to 1000 Fcm⁻³ [213]. However, the field is in its infancy, and the numbers will likely increase further as the MXene chemistry and structure, and possible hybridizing materials, are optimized.

The MAX phases are metallic conductors with typical room-temperature resistivities of the order of a few tens of µΩ cm (in comparison, the room-temperature resistivities of Ag and Ti metals are about 1.6 µΩ cm and 40 µΩ cm, respectively). In general, the electrical properties are moderately anisotropic, in the sense that the conductivity along the c-axis and along the a-axis differ but are metallic and of the same order of magnitude [26, 214–219]. There is, however, recent work with measurements on single crystals showing that some MAX phases (V₂AlC and Cr₂AlC) have a much higher degree of anisotropy [220]. Etching out the A element to form MXene results in a 2D material where, generally speaking, the metallic-like conductivity is retained. At low temperature, the electrical-transport properties of Ti₃C₂T_x thin films showed weak localization of charge carriers, i.e. a genuine 2D property [182]. Nevertheless, this depends on materials systems and terminations. The large possible variations in terminations yields a design opportunity for tuning the electronic properties and band structure, e.g. from metallic to semiconductor. This has been indicated in numerous theoretical studies, e.g. with pure O termination [221]. A challenge here is to accurately model the actual experimental termination, which is typically a complex mix of numerous termination species [222].

Measurements on Mo₂CT_x MXene [223] indicated a semiconductor-like behavior of Mo₂CT_x in contrast to metallic Ti₃C₂T_x [182], based on an increase in resistivity as the temperature is decreased from 300 K to 10 K. The result can be compared to direct thin-film synthesis of 2D α-Mo₂C by CVD, for which 3.4 nm crystals (approximately 15 metal layers) display a decrease in resistivity from 300 K to 50 K [96]. A further reduction in temperature showed a logarithmic increase in resistivity which indicates a weak 2D localization effect—similar to Ti₃C₂T_x thin films [182].

Furthermore, theoretical studies have shown that under certain termination conditions, Dirac points (i.e. cones in the band structure with a zero bandgap) analogous to graphene can appear in MXenes. This was first reported by Fashandi et al [224] and opens the field for studying quantum-relativistic conduction phenomena and 'Dirac physics' in MXenes. Compared to graphene, the spin–orbit splitting at the Dirac points is much larger. Existence of topologically protected edge states is another consequence, leading to the possible application in topological insulators [224, 225–227]. These predictions remain to be experimentally verified; thus there is a need to further explore transport measurements and angle-resolved photoemission spectroscopy on single-sheet MXene.

The Seebeck coefficient (or thermopower), S, of a material is defined as ΔV/ΔT, the voltage ΔV developed over a material when exposed to a temperature gradient of ΔT. For thermoelectric energy conversion, a large Seebeck coefficient coupled with a reasonably high electrical conductivity and a low thermal conductivity is required. The MAX phases are good, metallic conductors, and thus they generally exhibit low Seebeck coefficients. In this context, however, Ti₃SiC₂ is unique: bulk samples of Ti₃SiC₂ exhibit negligible S over a very wide temperature range, from 300–850 K [228], a unique phenomenon. Based on density functional theory (DFT) calculations, Chaput et al [229, 230] predicted that two types of bands are the main contributors to the Seebeck coefficient in Ti₃SiC₂; a hole-like band in the ab-plane and an electron-like band along the c-axis, with twice the value in the c direction as that in the a direction, but with opposite sign. Therefore, the Seebeck coefficient macroscopically sums up to zero in a randomly oriented sample. This was experimentally confirmed by Magnuson et al [231], who demonstrated that the in-plane Seebeck coefficient is positive and substantial and evidenced the anisotropic states in the electronic structures, which is the underlying source of the near-zero Seebeeck coefficient in bulk, polycrystalline Ti₃SiC₂.

For MXene, the thermoelectric properties remain essentially unexplored experimentally. From theoretical predictions it can be concluded that some MXenes could exhibit very high Seebeck coefficients [232, 233], but generally they would tend to also be good thermal conductors [234, 235], which would limit their use for thermoelectric applications. Going beyond this, existing theoretical predictions are difficult to assess given the limitations on the applied methodology from Boltzmann transport theory, as described in section 3.2. For example, there are misleading predictions based on using a value of the relaxation time τ that was not determined for the specific material and assuming that τ is constant with carrier concentration [236, 237], which it is not.

A few MAX phases (notably Mo₂GaC, with a critical temperature, T_c, of ~3.9 K [238]) were reported to be superconductors already in the 1960s. However, it is a challenge to assess these results, since little or no information about the samples is accessible. Only a T_c is typically stated. It was not until 2015 that characterization on pure samples confirmed that Mo₂GaC is likely a superconductor [239]. Other reported superconductors among the MAX phases include Nb₂SC [240], Nb₂AsC [241], Nb₂InC [242] and Ti₂InC [243].

The key issue here, and the source of many discrepancies, is that measurements of superconductivity are highly sensitive to impurity phases. Anasori et al [79] demonstrated specifically the effect of a superconducting impurity phase (see section 3.4 and corresponding supplementary information of [79], and how this can lead to incorrect conclusions if care is not taken, i.e. that the presence of a superconducting impurity phase can yield an apparent superconductivity for the sample measured, even though the phase of interest is not superconducting. For example, for Nb₂SnC, there are conflicting reports [241, 244] as to whether the phase is a superconductor, likely because the samples in [241] were of higher purity, while those in [244] contained an impurity phase of (superconducting) NbC, giving a false positive result. Furthermore, it is known from measurements on highly pure bulk and thin-film samples that Ti₂GeC is not superconducting [245]. Despite this fact, there is an erroneous report [246] claiming superconductivity in that compound, where the samples in question contained a very large amount of a superconducting impurity phase. Overall, these observations emphasize the need for great care in characterizing superconductivity.

For MXenes, it was therefore an important achievement that highly phase-pure, large area 2D Mo₂C (a few nanometers thick and ~100 µm in lateral size) could be synthesized by CVD [96]. This allowed a direct measurement of the low temperature properties, and superconductivity, of ultrathin Mo₂C MXene, which as mentioned above exhibits a decrease in resistivity from 300 K to 50 K and a logarithmic increase in resistivity below 50 K, indicative of weak 2D localization effect. A superconducting transition was observed just below 3 K, with suppression of the superconducting transition for decreasing thickness, i.e. unambiguous evidence of intrinsic thickness-dependent superconductivity [96].