Atomic Scale Design of MXenes and Their Parent Materials─From Theoretical and Experimental Perspectives.

More than a decade after the discovery of MXene, there has been a remarkable increase in research on synthesis, characterization, and applications of this growing family of two-dimensional (2D) carbides and nitrides. Today, these materials include one, two, or more transition metals arranged in chemically ordered or disordered structures of three, five, seven, or nine atomic layers, with a surface chemistry characterized by surface terminations. By combining M, X, and various surface terminations, it appears that a virtually endless number of MXenes is possible. However, for the design and discovery of structures and compositions beyond current MXenes, one needs suitable (stable) precursors, an assessment of viable pathways for 3D to 2D conversion, and utilization or development of corresponding synthesis techniques. Here, we present a critical and forward-looking review of the field of atomic scale design and synthesis of MXenes and their parent materials. We discuss theoretical methods for predicting MXene precursors and for assessing whether they are chemically exfoliable. We also summarize current experimental methods for realizing the predicted materials, listing all verified MXenes to date, and outline research directions that will improve the fundamental understanding of MXene processing, enabling atomic scale design of future 2D materials, for emerging technologies.

Experimental and Theoretical Investigations of Out-of-Plane Ordered Nanolaminate Transition Metal Borides: M4CrSiB2 (M = Mo, W, Nb).

We report the synthesis of three out-of-plane chemically ordered quaternary transition metal borides (o-MAB phases) of the chemical formula M4CrSiB2 (M = Mo, W, Nb). The addition of these phases to the recently discovered o-MAB phase Ti4MoSiB2 shows that this is indeed a new family of chemically ordered atomic laminates. Furthermore, our results expand the attainable chemistry of the traditional M5SiB2 MAB phases to also include Cr. The crystal structure and chemical ordering of the produced materials were investigated using high-resolution scanning transmission electron microscopy and X-ray diffraction by applying Rietveld refinement. Additionally, calculations based on density functional theory were performed to investigate the Cr preference for occupying the minority 4c Wyckoff site, thereby inducing chemical order.

Theoretical predictions of phase stability for orthorhombic and hexagonal ternary MAB phases.

In the quest for finding novel thermodynamically stable, layered, MAB phases promising for synthesis, we herein explore the phase stability of ternary MAB phases by considering both orthorhombic and hexagonal crystal symmetries for various compositions (MAB, M2AB2, M3AB4, M4AB4, and M4AB6 where M = Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Fe, and Co, A = Al, Ga, and In, and B is boron). The thermodynamic stability of seven previously synthesized MAB phases is confirmed, three additional phases are predicted to be stable, and 23 phases are found to be close to stable. Furthermore, the crystal symmetry preference for forming orthorhombic or hexagonal crystal structures is investigated where the considered Al-based MAB phases tend to favour orthorhombic structures whereas Ga- and In-based phases in general prefer hexagonal structures. The theoretically predicted stable MAB phases along with the structural preference is intended to both guide experimental efforts and to give an insight into the stability for different crystal symmetries of MAB phases.

Theoretical Prediction and Synthesis of a Family of Atomic Laminate Metal Borides with In-Plane Chemical Ordering.

All atomically laminated MAB phases (M = transition metal, A = A-group element, and B = boron) exhibit orthorhombic or tetragonal symmetry, with the only exception being hexagonal Ti2InB2. Inspired by the recent discovery of chemically ordered hexagonal carbides, i-MAX phases, we perform an extensive first-principles study to explore chemical ordering upon metal alloying of M2AlB2 (M from groups 3 to 9) in orthorhombic and hexagonal symmetry. Fifteen stable novel phases with in-plane chemical ordering are identified, coined i-MAB, along with 16 disordered stable alloys. The predictions are verified through the powder synthesis of Mo4/3Y2/3AlB2 and Mo4/3Sc2/3AlB2 of space group R3̅m (no. 166), displaying the characteristic in-plane chemical order of Mo and Y/Sc and Kagomé ordering of the Al atoms, as evident from X-ray diffraction and electron microscopy. The discovery of i-MAB phases expands the elemental space of these borides with M = Sc, Y, Zr, Hf, and Nb, realizing an increased property tuning potential of these phases as well as their suggested potential two-dimensional derivatives.

A Tungsten-Based Nanolaminated Ternary Carbide: (W,Ti)4C4- x.

Nanolamellar transition metal carbides are gaining increasing interests because of the recent developments of their two-dimensional (2D) derivatives and promising performance for a variety of applications from energy storage, catalysis to transparent conductive coatings, and medicine. To develop more novel 2D materials, new nanolaminated structures are needed. Here we report on a tungsten-based nanolaminated ternary phase, (W,Ti)4C4- x, synthesized by an Al-catalyzed reaction of W, Ti, and C powders at 1600 °C for 4 h, under flowing argon. X-ray and neutron diffraction, along with Z-contrast scanning transmission electron microscopy, were used to determine the atomic structure, ordering, and occupancies. This phase has a layered hexagonal structure ( P63 /mmc) with lattice parameters, a = 3.00880(7) Å, and c = 19.5633(6) Å and a nominal chemistry of (W,Ti)4C4- x (actual chemistry, W2.1(1)Ti1.6(1)C2.6(1)). The structure is comprised of layers of pure W that are also twin planes with two adjacent atomic layers of mixed W and Ti, on either side. The use of Al as a catalyst for synthesizing otherwise difficult to make phases, could in turn lead to the discovery of a large family of nonstoichiometric ternary transition metal carbides, synthesized at relatively low temperatures and shorter times.

Synthesis of Ti3AuC2, Ti3Au2C2 and Ti3IrC2 by noble metal substitution reaction in Ti3SiC2 for high-temperature-stable Ohmic contacts to SiC.

The large class of layered ceramics encompasses both van der Waals (vdW) and non-vdW solids. While intercalation of noble metals in vdW solids is known, formation of compounds by incorporation of noble-metal layers in non-vdW layered solids is largely unexplored. Here, we show formation of Ti3AuC2 and Ti3Au2C2 phases with up to 31% lattice swelling by a substitutional solid-state reaction of Au into Ti3SiC2 single-crystal thin films with simultaneous out-diffusion of Si. Ti3IrC2 is subsequently produced by a substitution reaction of Ir for Au in Ti3Au2C2. These phases form Ohmic electrical contacts to SiC and remain stable after 1,000 h of ageing at 600 °C in air. The present results, by combined analytical electron microscopy and ab initio calculations, open avenues for processing of noble-metal-containing layered ceramics that have not been synthesized from elemental sources, along with tunable properties such as stable electrical contacts for high-temperature power electronics or gas sensors.

Theoretical Prediction and Synthesis of (Cr2/3Zr1/3)2AlC i-MAX Phase.

Guided by predictive theory, a new compound with chemical composition (Cr2/3Zr1/3)2AlC was synthesized by hot pressing of Cr, ZrH2, Al, and C mixtures at 1300 °C. The crystal structure is monoclinic of space group C2/ c and displays in-plane chemical order in the metal layers, a so-called i-MAX phase. Quantitative chemical composition analyses confirmed that the primary phase had a (Cr2/3Zr1/3)2AlC stoichiometry, with secondary Cr2AlC, AlZrC2, and ZrC phases and a small amount of Al-Cr intermetallics. A theoretical evaluation of the (Cr2/3Zr1/3)2AlC magnetic structure was performed, indicating an antiferromagnetic ground state. Also (Cr2/3Hf1/3)2AlC, of the same structure, was predicted to be stable.

Order and disorder in quaternary atomic laminates from first-principles calculations.

We report on the phase stability of chemically ordered and disordered quaternary MAX phases - TiMAlC, TiM2AlC2, MTi2AlC2, and Ti2M2AlC3 where M = Zr, Hf (group IV), M = V, Nb, Ta (group V), and M = Cr, Mo, W (group VI). At 0 K, layered chemically ordered structures are predicted to be stable for M from groups V and VI. By taking into account the configurational entropy, an order-disorder temperature Tdisorder can be estimated. TiM2AlC2 (M = Cr, Mo, W) and Ti2M2AlC3 (M = Mo, W) are found with Tdisorder > 1773 K and are hence predicted to be ordered at the typical bulk synthesis temperature of 1773 K. Other ordered phases, even though metastable at elevated temperatures, may be synthesized by non-equilibrium methods such as thin film growth. Furthermore, phases predicted not to be stable in any form at 0 K can be stabilized at higher temperatures in a disordered form, being the case for group IV, for MTi2AlC2 (M = V, Cr, Mo), and for Ti2M2AlC3 (M = V, Ta). The stability of the layered ordered structures with M from group VI can primarily be explained by Ti breaking the energetically unfavorable stacking of M and C where M is surrounded by C in a face-centered cubic configuration, and by M having a larger electronegativity than Al resulting in a fewer electrons available for populating antibonding Al-Al orbitals. The results show that these chemically ordered quaternary MAX phases allow for new elemental combinations in MAX phases, which can be used to add new properties to this family of atomic laminates and in turn prospects for tuning these properties.

M5X4: A Family of MXenes.

MXenes are two-dimensional (2D) transition metal carbides, nitrides, and carbonitrides typically synthesized from layered MAX-phase precursors. With over 50 experimentally reported MXenes and a near-infinite number of possible chemistries, MXenes make up the fastest-growing family of 2D materials. They offer a wide range of properties, which can be altered by their chemistry (M, X) and the number of metal layers in the structure, ranging from two in M2XTx to five in M5X4Tx. Only one M5X4 MXene, Mo4VC4, has been reported. Herein, we report the synthesis and characterization of two M5AX4 mixed transition metal MAX phases, Ti2.5Ta2.5AlC4 and Ti2.675Nb2.325AlC4, and their successful topochemical transformation into Ti2.5Ta2.5C4Tx and Ti2.675Nb2.325C4Tx MXenes. The resulting MXenes were delaminated into single-layer flakes, analyzed structurally, and characterized for their thermal and optical properties. This establishes a family of M5AX4 MAX phases and their corresponding MXenes. These materials were experimentally produced based on guidance from theoretical predictions, leading to more exciting applications for MXenes.

Discovery of the ternary nanolaminated compound Nb2GeC by a systematic theoretical-experimental approach.

Since the advent of theoretical materials science some 60 years ago, there has been a drive to predict and design new materials in silicio. Mathematical optimization procedures to determine phase stability can be generally applicable to complex ternary or higher-order materials systems where the phase diagrams of the binary constituents are sufficiently known. Here, we employ a simplex-optimization procedure to predict new compounds in the ternary Nb-Ge-C system. Our theoretical results show that the hypothetical Nb2GeC is stable, and excludes all reasonably conceivable competing hypothetical phases. We verify the existence of the Nb2GeC phase by thin film synthesis using magnetron sputtering. This hexagonal nanolaminated phase has a and c lattice parameters of ∼3.24 Å and 12.82 Å.

The rise of MAX phase alloys - large-scale theoretical screening for the prediction of chemical order and disorder.

MAX phases (M = metal, A = A-group element, X = C and/or N) are layered materials, combining metallic and ceramic attributes. They are also parent materials for the two-dimensional (2D) derivative, MXene, realized from selective etching of the A-element. In this work, we present a historical survey of MAX phase alloying to date along with an extensive theoretical investigation of MAX phase alloys (M = Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Fe, Co, and Ni, A = Al, Ga, In, Si, Ge, Sn, Ni, Cu, Zn, Pd, Ag, Pt, and Au, and X = C). We assess both in-plane chemical ordering (in the so-called i-MAX phases) and solid solution. Out of the 2702 compositions, 92 i-MAX and 291 solid solution MAX phases are predicted to be thermodynamically stable. A majority of these have not yet been experimentally reported. In general, i-MAX is favored for a smaller size of A and a large difference in metal size, while solid solution is favored for a larger size of A and with comparable size of the metals. The results thus demonstrate avenues for a prospective and substantial expansion of the MAX phase and MXene chemistries.

Investigation of out-of-plane ordered Ti4MoSiB2from first principles.

The laminated ternary boride Mo5SiB2of T2 structure have two symmetrically inequivalent metallic sites, 16l and 4c, being occupied in a 4:1 ratio. The phase was recently shown to be stable for 80% substitution of Mo for Ti, at the majority site, forming an out-of-plane chemically ordered quaternary boride: Ti4MoSiB2. Considering that the hypothetical Ti5SiB2is theoretically predicted as not stable, a key difference in bonding characteristics is indicated for full substitution of Mo for Ti at the metallic sites. To explore the origin of formation of Ti4MoSiB2, we here investigate the electronic properties and bonding characteristics of Mo5SiB2, Ti4MoSiB2and Ti5SiB2through their density of states, projected crystal orbital Hamilton population (pCOHP), Bader charge partitioning and second order force constants. The bond between the two different metallic sites is found to be key to the stability of the compounds, evident from the pCOHP of this bond showing a peak of bonding states close to the Fermi level, which is completely filled in Mo5SiB2and Ti4MoSiB2, while only partially filled in Ti5SiB2. Furthermore, the lower electronegativity of Ti compared to Mo results in charge accumulation at the Si and B sites, which coincides with a reduced bond strength in Ti5SiB2compared to Mo5SiB2and Ti4MoSiB2. Bandstructure calculations show that all three structures are metallic. The calculated mechanical and elastic properties show reduced bulk (B) and elastic (E) moduli when introducing Ti in Mo5SiB2, from 279 and 365 GPa to 176 and 258 GPa, respectively. The Pugh criteria indicates also a slight reduction in ductility, with aG/Bratio increasing from 0.51 to 0.59.

Predictions of attainable compositions of layered quaternary i-MAB phases and solid solution MAB phases.

MAB phases are layered materials combining metallic and ceramic attributes. Their ternary compositions, however, have been limited to a few elemental combinations which makes controlled and tailored properties challenging. Inspired by the recent discovery of Mo4/3Y2/3AlB2 and Mo4/3Sc2/3AlB2i-MAB phases, i.e., quaternary layered MAB phases with in-plane chemical order, we perform an extensive first-principles study to explore formation of chemical order and solid-solutions upon metal alloying of M2AB2 phases of 1092 compositions (M from group 3 to 9 and A = Al, Ga, In, Si, Ge, Sn). This large dataset provides 39 chemically ordered (i-MAB) and 52 solid solution (MAB) phases that are predicted to be thermodynamically stable at typical synthesis temperatures, of which a majority have not yet been experimentally reported. The possibility for realizing both i-MAB and solid solution MAB phases, combined with the multiple elemental combinations previously not observed in these boride-based materials, allows for an increased potential for property tuning and potential chemical exfoliation into 2D derivatives.

In-plane ordered quaternaryM4/3'M2/3″AlB2phases (i-MAB): electronic structure and mechanical properties from first-principles calculations.

We have by means of first principles density functional theory calculations studied the mechanical and electronic properties of the so calledi-MAB phases,M4/3'M″2/3AlB2, whereM' = Cr, Mo, W andM″ = Sc, Y. These phases, experimentally verified for Mo4/3Sc2/3AlB2and Mo4/3Y2/3AlB2, display an atomically laminated structure with in-plane chemical order between theM' andM″ elements. Structural properties, along with elastic constants and moduli, are predicted for different structural symmetries, including the reportedR3̄m(#166) space group. We find all consideredi-MAB phases to be metallic with a significant peak in the electronic structure at the Fermi level and no significant anisotropy in the electronic band structure. The simulations also indicate that they are rather hard and stiff, in particular the Cr-based ones, with a Young's modulusEof 325 GPa forM″ = Sc. The Mo-based phases are similar, withE= 299 GPa forM″ = Sc, which is higher than the corresponding laminated carbides (i-MAX phases).

Boridene: Two-dimensional Mo4/3B2-x with ordered metal vacancies obtained by chemical exfoliation.

Extensive research has been invested in two-dimensional (2D) materials, typically synthesized by exfoliation of van der Waals solids. One exception is MXenes, derived from the etching of constituent layers in transition metal carbides and nitrides. We report the experimental realization of boridene in the form of single-layer 2D molybdenum boride sheets with ordered metal vacancies, Mo4/3B2-xTz (where Tz is fluorine, oxygen, or hydroxide surface terminations), produced by selective etching of aluminum and yttrium or scandium atoms from 3D in-plane chemically ordered (Mo2/3Y1/3)2AlB2 and (Mo2/3Sc1/3)2AlB2 in aqueous hydrofluoric acid. The discovery of a 2D transition metal boride suggests a wealth of future 2D materials that can be obtained through the chemical exfoliation of laminated compounds.

Out-Of-Plane Ordered Laminate Borides and Their 2D Ti-Based Derivative from Chemical Exfoliation.

Exploratory theoretical predictions in uncharted structural and compositional space are integral to materials discoveries. Inspired by M5 SiB2 (T2) phases, the finding of a family of laminated quaternary metal borides, M'4 M″SiB2 , with out-of-plane chemical order is reported here. 11 chemically ordered phases as well as 40 solid solutions, introducing four elements previously not observed in these borides are predicted. The predictions are experimentally verified for Ti4 MoSiB2 , establishing Ti as part of the T2 boride compositional space. Chemical exfoliation of Ti4 MoSiB2 and select removal of Si and MoB2 sub-layers is validated by derivation of a 2D material, TiOx Cly , of high yield and in the form of delaminated sheets. These sheets have an experimentally determined direct band gap of ≈4.1 eV, and display characteristics suitable for supercapacitor applications. The results take the concept of chemical exfoliation beyond currently available 2D materials, and expands the envelope of 3D and 2D candidates, and their applications.

Impact of strain, pressure, and electron correlation on magnetism and crystal structure of Mn2GaC from first-principles.

The atomically laminated Mn2GaC has previously been synthesized as a heteroepitaxial thin film and found to be magnetic with structural changes linked to the magnetic anisotropy. Related theoretical studies only considered bulk conditions and thus neglected the influence from possible strain linked to the choice of substrate. Here we employ first principles calculations considering different exchange-correlation functionals (PBE, PW91, PBEsol, AM05, LDA) and effect from use of + U methods (or not) combined with a magnetic ground-state search using Heisenberg Monte Carlo simulations, to study influence from biaxial in-plane strain and external pressure on the magnetic and crystal structure of Mn2GaC. We find that PBE and PBE + U, with Ueff ≤ 0.25 eV, gives both structural and magnetic properties in quantitative agreement with available experimental data. Our results also indicate that strain related to choice of substrate or applied pressure is a route for accessing different spin configurations, including a ferromagnetic state. Moreover, the easy axis is parallel to the atomic planes and the magnetocrystalline anisotropy energy can be increased through strain engineering by expanding the in-plane lattice parameter a. Altogether, we show that a quantitative description of the structural and magnetic properties of Mn2GaC is possible using PBE, which opens the way for further computational studies of these and related materials.

Predictive theoretical screening of phase stability for chemical order and disorder in quaternary 312 and 413 MAX phases.

In this work we systematically explore a class of atomically laminated materials, Mn+1AXn (MAX) phases upon alloying between two transition metals, M' and M'', from groups III to VI (Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W). The materials investigated focus on so called o-MAX phases with out-of-plane chemical ordering of M' and M'', and their disordered counterparts, for A = Al and X = C. Through use of predictive phase stability calculations, we confirm all experimentally known phases to date, and also suggest a range of stable ordered and disordered hypothetical elemental combinations. Ordered o-MAX is favoured when (i) M' next to the Al-layer does not form a corresponding binary rock-salt MC structure, (ii) the size difference between M' and M'' is small, and (iii) the difference in electronegativity between M' and Al is large. Preference for chemical disorder is favoured when the size and electronegativity of M' and M'' is similar, in combination with a minor difference in electronegativity of M' and Al. We also propose guidelines to use in the search for novel o-MAX; to combine M' from group 6 (Cr, Mo, W) with M'' from groups 3 to 5 (Sc only for 312, Ti, Zr, Hf, V, Nb, Ta). Correspondingly, we suggest formation of disordered MAX phases by combing M' and M'' within groups 3 to 5 (Sc, Ti, Zr, Hf, V, Nb, Ta). The addition of novel elemental combinations in MAX phases, and in turn in their potential two-dimensional MXene derivatives, allow for property tuning of functional materials.

Electronic structure, bonding characteristics, and mechanical properties in (W2/3Sc1/3)2AlC and (W2/3Y1/3)2AlC i-MAX phases from first-principles calculations.

With the recent discovery of in-plane chemically ordered MAX phases (i-MAX) of the general formula ([Formula: see text])2 AC comes addition of non-traditional MAX phase elements. In the present study, we use density functional theory calculations to investigate the electronic structure, bonding nature, and mechanical properties of the novel (W2/3Sc1/3)2AlC and (W2/3Y1/3)2AlC i-MAX phases. From analysis of the electronic structure and projected crystal orbital Hamilton populations, we show that the metallic i-MAX phases have significant hybridization between W and C, as well as Sc(Y) and C states, indicative of strong covalent bonding. Substitution of Sc for Y (M 2) leads to reduced bonding strength for W-C and Al-Al interactions while M 2-C and M 2-Al interactions are strengthened. We also compare the Voigt-Reuss-Hill bulk, shear, and Young's moduli along the series of M 1 = Cr, Mo, and W, and relate these trends to the bonding interactions. Furthermore, we find overall larger moduli for Sc-based i-MAX phases.

Origin of Chemically Ordered Atomic Laminates ( i-MAX): Expanding the Elemental Space by a Theoretical/Experimental Approach.

With increased chemical diversity and structural complexity comes the opportunities for innovative materials possessing advantageous properties. Herein, we combine predictive first-principles calculations with experimental synthesis, to explore the origin of formation of the atomically laminated i-MAX phases. By probing (Mo2/3 M1/32)2 AC (where M2 = Sc, Y and A = Al, Ga, In, Si, Ge, In), we predict seven stable i-MAX phases, five of which should have a retained stability at high temperatures. (Mo2/3Sc1/3)2GaC and (Mo2/3Y1/3)2GaC were experimentally verified, displaying the characteristic in-plane chemical order of Mo and Sc/Y and Kagomé-like ordering of the A-element. We suggest that the formation of i-MAX phases requires a significantly different size of the two metals, and a preferable smaller size of the A-element. Furthermore, the population of antibonding orbitals should be minimized, which for the metals herein (Mo and Sc/Y) means that A-elements from Group 13 (Al, Ga, In) are favored over Group 14 (Si, Ge, Sn). Using these guidelines, we foresee a widening of elemental space for the family of i-MAX phases and expect more phases to be synthesized, which will realize useful properties. Furthermore, based on i-MAX phases as parent materials for 2D MXenes, we also expect that the range of MXene compositions will be expanded.