Magnetic self-organized atomic laminate from first principles and thin film synthesis

Advancements in MAX phase materials: structure, properties, and novel applications

The MAX phase represents a diverse class of nanolaminate materials with intriguing properties that have received incredible global research attention because they bridge the divide separating metals and ceramics. Despite the numerous potential applications of MAX phases, their complex structure leads to a scarcity of readily accessible pure MAX phases. As a result, in-depth research on synthesis methods, characteristics, and structure is frequently needed for appropriate application. This review provides a comprehensive understanding of the recent advancements and growth in MAX phases, focusing on their complex crystal structures, unique mechanical, thermal, electrical, crack healing, corrosion-resistant properties, as well as their synthesis methods and applications. The structure of MAX phases including single metal MAX, i-MAX and o-MAX was discussed. Moreover, recent advancements in understanding MAX phase behaviour under extreme conditions and their potential novel applications across various fields, including high-temperature coatings, energy storage, and electrical and thermal conductors, biomedical, nanocomposites, etc. were discussed. Moreover, the synthesis techniques, ranging from bottom-up to top-down methods are scrutinized for their efficacy in tailoring MAX phase properties. Furthermore, the review explores the challenges and opportunities associated with optimizing MAX phase materials for specific applications, such as enhancing their oxidation resistance, tuning their mechanical properties, and exploring their functionality in emerging technologies. Overall, this review aims to provide researchers and engineers with a comprehensive understanding of MAX phase materials and inspire further exploration into their versatile applications in materials science and engineering.

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.

Extending the Chemistry of Layered Solids and Nanosheets: Chemistry and Structure of MAX Phases, MAB Phases and MXenes

MAX phases are layered solids with unique properties combining characteristics of ceramics and metals. MXenes are their two-dimensional siblings that can be synthesized as van der Waals-stacked and multi-/single-layer nanosheets, which possess chemical and physical properties that make them interesting for a plethora of applications. Both families of materials are highly versatile in terms of their chemical composition and theoretical studies suggest that many more members are stable and can be synthesized. This is very intriguing because new combinations of elements, and potentially new structures, can lead to further (tunable) properties. In this review, we focus on the synthesis science (including non-conventional approaches) and structure of members less investigated, namely compounds with more exotic M-, A-, and X-elements, for example nitrides and (carbo)nitrides, and the related family of MAB phases.

Optical properties of in-plane chemically ordered i-MAX structures

The prospects of novel materials with intriguing features increases with greater chemical diversity and structural complexity. In this work, we have investigated the electronic and optical characteristics of the atomically laminated i-MAX structures [(Mo_2/3Sc_1/3)₂ AC with A = Al, Ga, In, Sn] using first-principles density functional theory calculations. We demonstrate how the electronic states at the Fermi level are affected by changes in the A element, and how this has a significant impact on the electronic and optical characteristics of the i-MAX structures. Additionally, the investigated systems exhibit optical reflectivity of more than 80% in the low energy region of the electromagnetic spectrum, making them suitable for coatings that lower solar heating. The results of this theoretical investigation help us to better comprehend the i-MAX's optical characteristics.

Multiprincipal Element M2 FeC (M = Ti,V,Nb,Ta,Zr) MAX Phases with Synergistic Effect of Dielectric and Magnetic Loss

Electromagnetic (EM) wave pollution is harmful to human health and environment, thus it is absolutely important to develop new electromagnetic wave absorbing materials. MAX phases have been attracted more attention as a potential candidate for electromagnetic wave absorbing materials due to their high conductivity and nanolaminated structure. Herein, two new magnetic MAX phases with multiprincipal elements ((Ti1/3 Nb1/3 Ta1/3 )2 FeC and (Ti0.2 V0.2 Nb0.2 Ta0.2 Zr0.2 )2 FeC) in which Fe atoms replace Al atoms in the A sites are successfully synthesized by an isomorphous replacement reaction of multiprincipal (Ti1/3 Nb1/3 Ta1/3 )2 AlC and (Ti0.2 V0.2 Nb0.2 Ta0.2 Zr0.2 )2 AlC MAX phases with Lewis acid salt (FeCl2 ). (Ti1/3 Nb1/3 Ta1/3 )2 FeC and (Ti0.2 V0.2 Nb0.2 Ta0.2 Zr0.2 )2 FeC exhibit ferromagnetic behavior, and the Curie temperature (Tc ) are 302 and 235 K, respectively. The dual electromagnetic absorption mechanisms that include dielectric and magnetic loss, which is realized in these multiprincipal MAX phases. The minimum reflection loss (RL) of (Ti1/3 Nb1/3 Ta1/3 )2 FeC is -44.4 dB at 6.56 GHz with 3 mm thickness, and the effective bandwidth is 2.48 GHz. Additionally, the electromagnetic wave absorption properties of the magnetic MAX phases indicate that magnetic loss also plays an important role besides dielectric loss. This work shows a promising composition-design strategy to develop MAX phases with good EM wave absorption performance via simultaneously regulating dielectric and magnetic loss together.

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.

From MAX Phase Carbides to Nitrides: Synthesis of V2GaC, V2GaN, and the Carbonitride V2GaC1-xNx

The research in MAX phases is mainly concentrated on the investigation of carbides rather than nitrides (currently >150 carbides and only <15 nitrides) that are predominantly synthesized by conventional solid-state techniques. This is not surprising since the preparation of nitrides and carbonitrides is more demanding due to the high stability and low diffusion rate of nitrogen-containing compounds. This leads to several drawbacks concerning potential variations in the chemical composition of the MAX phases as well as control of morphology, the two aspects that directly affect the resulting materials properties. Here, we report how alternative solid-state hybrid techniques solve these limitations by combining conventional techniques with nonconventional precursor synthesis methods, such as the "urea-glass" sol-gel or liquid ammonia method. We demonstrate the synthesis and morphology control within the V-Ga-C-N system by preparing the MAX phase carbide and nitride─the latter in the form of bulkier and more defined smaller particle structures─as well as a hitherto unknown carbonitride V₂GaC_1-xN_x MAX phase. This shows the versatility of hybrid methods starting, for example, from wet chemically obtained precursors that already contain all of the ingredients needed for carbonitride formation. All products are characterized in detail by X-ray powder diffraction, electron microscopy, and electron and X-ray photoelectron spectroscopies to confirm their structure and morphology and to detect subtle differences between the different chemical compositions.

Ab Initio Study on Dopant Relaxation Mechanism in Ti and Ce Cationically Substituted in Wurtzite Gallium Nitride

The changes in properties of materials upon introduction of impurities is well documented but less is known about the location of foreign atoms in different hosts. This study is carried out with the motivation to explore dopant location in hexagonal GaN using density functional theory based calculations. The dopant site location of the individual dopants Ti, Ce, and Ti-Ce codoped wurtzite GaN was investigated by placing the dopants at cationic lattice sites as well as off-cationic sites along the c-axis. The geometry optimization relaxed individual dopants on cationic Ga sites but in the case of codoping Ce settled at site 7.8% away along [0001 ¯] and Ti adjusted itself at site 14% away along [0001] from regular cationic sites. The analysis of the results indicates that optimized geometry is sensitive to the starting position of the dopants. The magnetic exchange interactions between Ti and Ce ions are responsible for their structural relaxation in the matrix.

Magnetic phase diagram of (Mo2/3RE1/3)2AlC, RETb and Dy, studied by magnetization, specific heat, and neutron diffraction analysis

We report the results of magnetization, heat capacity, and neutron diffraction measurements on (Mo_2/3RE_1/3)₂AlC with RE = Dy and Tb. Temperature and field-dependent magnetization as well as heat capacity were measured on a powder sample and on a single crystal allowing the construction of the magnetic field-temperature phase diagram. To study the magnetic structure of each magnetic phase, we applied neutron diffraction in a magnetic field up to 6 T. For (Mo_2/3Dy_1/3)₂AlC in zero field, a spin density wave is stabilized at 16 K, with antiferromagnetic ordering at 13 K. Furthermore, we identify the coexistence of ferromagnetic and antiferromagnetic phases induced by magnetic fields for both RE = Tb and Dy. The origin of the field induced phases is resulting from the competing ferromagnetic and antiferromagnetic interactions.

The effect of the composition and pressure on the phase stability and electronic, magnetic, and elastic properties of M2AX (M = Mn, Fe; A = Al, Ga, Si, Ge; X = C, N) phases

The magnetic properties of M₂AX (M = Mn, Fe; A = Al, Ga, Si, Ge; X = C, N) phases were studied within DFT-GGA. The magnetic electronic ground state is determined. The investigation of the phase stability of M₂AX phases is performed by comparing the total energy of MAX phases to that of the set of competitive phases for calculation of the phase formation enthalpy. As the result of such an approach, we have found one stable compound (Mn₂GaC), and seven metastable ones. It is shown that several metastable MAX phases (Mn₂AlC, Fe₂GaC, Mn₂GeC, and Mn₂GeN) become stable at a small applied pressure (1.5-7 GPa). The mechanical, electronic and elastic properties of metastable MAX phases are studied.

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 Mo_4/3Y_2/3AlB₂ and Mo_4/3Sc_2/3AlB₂i-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.

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, TiO_x Cl_y , 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.

Microscopic evidence for Mn-induced long range magnetic ordering in MAX phase compounds

Zero and low field nuclear magnetic resonance measurements have been performed on MAX phase samples (Cr_1-x Mn _x )₂AC with A = Ge and Ga in order to obtain local microscopic information on the nature of magnetism in this system. Our results unambiguously provide evidence for the existence of long-range magnetic order in (Cr_0.96Mn_0.04)₂GeC and for (Cr_0.93Mn_0.07)₂GaC, but not for (Cr_0.97Mn_0.03)₂GaC. We point to a possible dependence of long range magnetic order in these MAX phase compounds on the A atom.

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 Mo_4/3Y_2/3AlB₂ and Mo_4/3Sc_2/3AlB₂ 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.

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.

Multielemental single-atom-thick A layers in nanolaminated V2(Sn, A) C (A = Fe, Co, Ni, Mn) for tailoring magnetic properties

Tailoring of individual single-atom-thick layers in nanolaminated materials offers atomic-level control over material properties. Nonetheless, multielement alloying in individual atomic layers in nanolaminates is largely unexplored. Here, we report 15 inherently nanolaminated V₂(A _xSn_1-x)C (A = Fe, Co, Ni, Mn, and combinations thereof, with x ∼ 1/3) MAX phases synthesized by an alloy-guided reaction. The simultaneous occupancy of the 4 magnetic elements and Sn in the individual single-atom-thick A layers constitutes high-entropy MAX phase in which multielemental alloying exclusively occurs in the 2-dimensional (2D) A layers. V₂(A _xSn_1-x)C exhibit distinct ferromagnetic behavior that can be compositionally tailored from the multielement A-layer alloying. Density functional theory and phase diagram calculations are performed to understand the structure stability of these MAX phases. This 2D multielemental alloying approach provides a structural design route to discover nanolaminated materials and expand their chemical and physical properties. In fact, the magnetic behavior of these multielemental MAX phases shows strong dependency on the combination of various elements.

Stability predictions of magnetic M2AX compounds

Based on high throughput density functional theory calculations, we evaluated systematically the stability of 580 M₂AX compounds. The thermodynamic, mechanical, and dynamical stability and the magnetic structure are calculated. We found 20 compounds fulfilling all three stability criteria, confirming Cr₂AlC, Cr₂GeC, Cr₂GaC, Cr₂GaN, and Mn₂ GaC, which have been synthesized. The stability trends with respect to the M- and A-elements are discussed by analyzing the formation energies, indicating that Cr and Mn containing M₂AX compounds are more stable than Fe, Co, or Ni containing compounds. Further insights on the stability are obtained by detailed analysis of the crystal orbital Hamilton population (COHP).

Synthesis of (V2/3Sc1/3)2AlC i-MAX phase and V2-xC MXene scrolls

We report the synthesis and characterization of a new laminated i-MAX phase, (V2/3Sc1/3)2AlC, with in-plane chemical ordering between the M-elements. We also present evidence for the solid solution (V2-xScx)2AlC, where x ≤ 0.05. Chemical etching of the Al and Sc results in a two-dimensional (2D) MXene counterpart: V2-xC from the latter phase. Furthermore, etching with HF yields single-sheet MXene of flat morphology, while LiF + HCl gives MXene scrolls. We also show a 4× reduction in etching time for (V2-xScx)2AlC compared to V2AlC, suggesting that traces of Sc changes the phase stability, and make the material more susceptible to etching. The results show a path for improved control of MXene synthesis and morphology, which may be applicable also for other MAX/MXene systems.

Optimizing special quasirandom structure (SQS) models for accurate functional property prediction in disordered 2D alloys

2D materials such as MXenes have garnered attention in a wide field of applications ranging from energy to environment to medical. Properties of 2D materials can be tailored via alloying and in some cases, solid-solutions (disordered alloys) are formed. To predict the disordered alloy properties via first-principles, the model structure needs to imitate the random arrangements of alloyants and yet remains computationally tractable. Using density functional theory and the cluster expansion method, we investigate the accuracy of using of special quasirandom structures (SQSs) for predicting disordered 2D alloy properties, evaluating the effect of SQS supercell size on the prediction quality of formation energies, elastic properties, and structural parameters. We illustrate the findings with 5 different disordered binary [Formula: see text] MXene alloy systems (where M  =  Ti and M'  =  Zr, Hf, V, Nb, or Ta), demonstrating that SQSs around 6-8 times the primitive cell (N  =  6-8) are sufficient to attain convergence in the property predictions versus supercell size. For formation energies, SQSs with N  >  4 are found to reproduce the formation energies of the fully disordered phase within ~2.5 meV. For the simulation of the experimentally-synthesized TiNbCO₂, we find convergence in structural parameters and elastic tensors at N ~ 6. We traced the convergence of the predictions to the convergence in the band structure-related properties via analysis of the electronic densities-of-states and the projected crystal overlap Hamilton population. Our findings suggest that modest sized SQSs would reproduce the properties of disordered MXene alloys. The results should help guide the investigations of structure-property relationships in other disordered 2D materials as well.

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 (Mo_2/3 M_1/3²)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. (Mo_2/3Sc_1/3)₂GaC and (Mo_2/3Y_1/3)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.

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 (W_2/3Sc_1/3)₂AlC and (W_2/3Y_1/3)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.

Prediction and synthesis of a family of atomic laminate phases with Kagomé-like and in-plane chemical ordering

The enigma of MAX phases and their hybrids prevails. We probe transition metal (M) alloying in MAX phases for metal size, electronegativity, and electron configuration, and discover ordering in these MAX hybrids, namely, (V_2/3Zr_1/3)₂AlC and (Mo_2/3Y_1/3)₂AlC. Predictive theory and verifying materials synthesis, including a judicious choice of alloying M from groups III to VI and periods 4 and 5, indicate a potentially large family of thermodynamically stable phases, with Kagomé-like and in-plane chemical ordering, and with incorporation of elements previously not known for MAX phases, including the common Y. We propose the structure to be monoclinic C2/c. As an extension of the work, we suggest a matching set of novel MXenes, from selective etching of the A-element. The demonstrated structural design on simultaneous two-dimensional (2D) and 3D atomic levels expands the property tuning potential of functional materials.

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

The data presented in this paper are related to the research article entitled “Theoretical stability and materials synthesis of a chemically ordered MAX phase, Mo₂ScAlC₂, and its two-dimensional derivate Mo₂ScC” (Meshkian et al. 2017) [1]. This paper describes theoretical phase stability calculations of the MAX phase alloy Mo_xSc_3-xAlC₂ (x=0, 1, 2, 3), including chemical disorder and out-of-plane order of Mo and Sc along with related phonon dispersion and Bader charges, and Rietveld refinement of Mo₂ScAlC₂. The data is made publicly available to enable critical or extended analyzes.

Magnetic MAX phases from theory and experiments; a review

This review presents MAX phases (M is a transition metal, A an A-group element, X is C or N), known for their unique combination of ceramic/metallic properties, as a recently uncovered family of novel magnetic nanolaminates. The first created magnetic MAX phases were predicted through evaluation of phase stability using density functional theory, and subsequently synthesized as heteroepitaxial thin films. All magnetic MAX phases reported to date, in bulk or thin film form, are based on Cr and/or Mn, and they include (Cr,Mn)2AlC, (Cr,Mn)2GeC, (Cr,Mn)2GaC, (Mo,Mn)2GaC, (V,Mn)3GaC2, Cr2AlC, Cr2GeC and Mn2GaC. A variety of magnetic properties have been found, such as ferromagnetic response well above room temperature and structural changes linked to magnetic anisotropy. In this paper, theoretical as well as experimental work performed on these materials to date is critically reviewed, in terms of methods used, results acquired, and conclusions drawn. Open questions concerning magnetic characteristics are discussed, and an outlook focused on new materials, superstructures, property tailoring and further synthesis and characterization is presented.

Phase stability of the nanolaminates V2Ga2C and (Mo1-xVx)2Ga2C from first-principles calculations

We here use first-principles calculations to investigate the phase stability of the hypothetical laminated material V₂Ga₂C and the related alloy (Mo_1–xV_x)₂Ga₂C, the latter for a potential parent material for synthesis of (Mo_1–xV_x)₂C, a new two-dimensional material in the family of so called MXenes.

We here use first-principles calculations to investigate the phase stability of the hypothetical laminated material V₂Ga₂C and the related alloy (Mo_1–xV_x)₂Ga₂C, the latter for a potential parent material for synthesis of (Mo_1–xV_x)₂C, a new two-dimensional material in the family of so called MXenes. We predict that V₂Ga₂C is thermodynamically stable with respect to all identified competing phases in the ternary V–Ga–C phase diagram. We further calculate the stability of ordered and disordered configurations of Mo and V in (Mo_1–xV_x)₂Ga₂C and predict that ordered (Mo_1–xV_x)₂Ga₂C for x ≤ 0.25 is stable, with an order–disorder transition temperature of ∼1000 K. Furthermore, (Mo_1–xV_x)₂Ga₂C for x = 0.5 and x ≥ 0.75 is suggested to be stable, but only for disordered Mo–V configurations, and only at elevated temperatures. We have also investigated the electronic and elastic properties of V₂Ga₂C; the calculated bulk, shear, and Young's modulus are 141, 94, and 230 GPa, respectively.

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.

Benefits of oxygen incorporation in atomic laminates

Atomic laminates such as MAX phases benefit from the addition of oxygen in many ways, from the formation of a protective oxide surface layer with self-healing capabilities when cracks form to the tuning of anisotropic conductivity. In this paper oxygen incorporation and vacancy formation in M 2AlC (M  =  Ti, V, Cr) MAX phases have been studied using first-principles calculations where the focus is on phase stability and electronic structure for different oxygen and/or vacancy configurations. Oxygen prefers different lattice sites depending on M-element and this can be correlated to the number of available non-bonding M d-electrons. In Ti2AlC, oxygen substitutes carbon while in Cr2AlC it is located interstitially within the Al-layer. I predict that oxygen incorporation in Ti2AlC stabilizes the material, which explains the experimentally observed 12.5 at% oxygen (x  =  0.5) in Ti2Al(C(1-x)O(x)). In addition, it is also possible to use oxygen to stabilize the hypothetical Zr2AlC and Hf2AlC. Hence, oxygen incorporation may be beneficial in many ways. Not only can it make a material more stable, but it also can act as a reservoir for internal self-healing with shorter diffusion paths.

Investigation of magnetic and electronic properties of transition metal doped Sc2CT2(T = O, OH or F) using a first principles study

Cr- and Mn-doped Sc₂CT₂(T = OH, O, or F) systems are magnetic, which are promising two-dimensional materials in spin electronics applications.

Influence of boron vacancies on phase stability, bonding and structure of MB₂ (M = Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W) with AlB₂ type structure

Transition metal diborides in hexagonal AlB2 type structure typically form stable MB2 phases for group IV elements (M  =  Ti, Zr, Hf). For group V (M  =  V, Nb, Ta) and group VI (M  =  Cr, Mo, W) the stability is reduced and an alternative hexagonal rhombohedral MB2 structure becomes more stable. In this work we investigate the effect of vacancies on the B-site in hexagonal MB2 and its influence on the phase stability and the structure for TiB2, ZrB2, HfB2, VB2, NbB2, TaB2, CrB2, MoB2, and WB2 using first-principles calculations. Selected phases are also analyzed with respect to electronic and bonding properties. We identify trends showing that MB2 with M from group V and IV are stabilized when introducing B-vacancies, consistent with a decrease in the number of states at the Fermi level and by strengthening of the B-M interaction. The stabilization upon vacancy formation also increases when going from M in period 4 to period 6. For TiB2, ZrB2, and HfB2, introduction of B-vacancies have a destabilizing effect due to occupation of B-B antibonding orbitals close to the Fermi level and an increase in states at the Fermi level.

A critical evaluation of GGA + U modeling for atomic, electronic and magnetic structure of Cr2AlC, Cr2GaC and Cr2GeC

In this work we critically evaluate methods for treating electron correlation effects in multicomponent carbides using a GGA + U framework, addressing doubts from previous works on the usability of density functional theory in the design of magnetic MAX phases. We have studied the influence of the Hubbard U-parameter, applied to Cr 3d orbitals, on the calculated lattice parameters, magnetic moments, magnetic order, bulk modulus and electronic density of states of Cr2AlC, Cr2GaC and Cr2GeC. By considering non-, ferro-, and five different antiferromagnetic spin configurations, we show the importance of including a broad range of magnetic orders in the search for MAX phases with finite magnetic moments in the ground state. We show that when electron correlation is treated on the level of the generalized gradient approximation (U = 0 eV), the magnetic ground state of Cr2AC (A = Al, Ga, Ge) is in-plane antiferromagnetic with finite Cr local moments, and calculated lattice parameters and bulk modulus close to experimentally reported values. By comparing GGA and GGA + U results with experimental data we find that using a U-value larger than 1 eV results in structural parameters deviating strongly from experimentally observed values. Comparisons are also done with hybrid functional calculations (HSE06) resulting in an exchange splitting larger than what is obtained for a U-value of 2 eV. Our results suggest caution and that investigations need to involve several different magnetic orders before lack of magnetism in calculations are blamed on the exchange-correlation approximations in this class of magnetic MAX phases.

Experimental evidence of Cr magnetic moments at low temperature in Cr2A(A=Al, Ge)C

From x-ray magnetic circular dichroism experiments performed at low temperature on Cr2AlC and Cr2GeC thin films, it is evidenced that Cr atoms carry a net magnetic moment in these ternary phases. It is shown that the Cr magnetization of the Al-based compound nearly vanished at 100 K in agreement with what has been recently observed on bulk. X-ray linear dichroism measurements performed at various angles of incidence and temperatures clearly demonstrate the existence of a charge ordering along the c axis of the structure of Cr2AlC. All these experimental observations support, in part, theoretical calculations claiming that Cr dd correlations have to be considered to correctly describe the structure and properties of these Cr-based ternary phases.