High-Throughput Survey of Ordering Configurations in MXene Alloys Across Compositions and Temperatures Teck Leong Tan,*,† Hong Mei Jin,† Michael B. Sullivan,† Babak Anasori,§ and Yury Gogotsi§ †
Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore § A.J. Drexel Nanomaterials Institute, and Department of Materials Science & Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States S Supporting Information *
ABSTRACT: 2D transition metal carbides and nitrides known as MXenes are gaining increasing attention. About 20 of them have been synthesized (more predicted) and their applications in fields ranging from energy storage and electromagnetic shielding to medicine are being explored. To facilitate the search for double-transitionmetal MXenes, we explore the structure−stability relationship for 8 MXene alloy systems, namely, (V1−xMox)3C2, (Nb 1 − x Mo x ) 3 C 2 , (Ta 1 − x Mo x ) 3 C 2 , (Ti 1 − x Mo x ) 3 C 2 , (Ti 1 − x Nb x ) 3 C 2 , (Ti 1 − x Ta x ) 3 C 2 , (Ti 1 − x V x ) 3 C 2 , and (Nb1−xVx)3C2, with 0 ≤ x ≤ 1, using high-throughput computations. Starting from density-functional theory calculated formation energies, we used the cluster expansion method to build quick-to-compute interactions, enabling us to scan through the formation energies of millions of alloying configurations. For the Mo-rich MXenes, (M11−xMox)3C2 (where M1: Ti, V, Nb, Ta) Mo atoms prefer to occupy the surface layers, and ordering persists to high temperatures, based on our Monte Carlo simulations. When Ti is alloyed with Nb or Ta, in the Ti-rich MXenes, Ti atoms prefer the surface layers (e.g., Ti−C−Nb−C−Ti sequence), and in the Nb- or Ta-rich MXenes, Ti occupies only one surface layer and the other two layers are Nb or Ta (e.g., Ti−C−Nb−C−Nb), exhibiting asymmetric ordering. However, alloying Ti with V results in solid solutions across all compositions. (Nb1−xVx)3C2 phase separates at lower temperatures but forms solid solutions at synthesis temperatures. Postsynthesis annealing at moderate temperatures (800 to 1000 K) increases the ordering for all the compositions. Lastly, by investigating the stability of their precursor MAX phases and surface-terminated MXenes, we discuss the synthesis possibilities of highly ordered MXenes. KEYWORDS: MXene, 2D material, density functional theory, alloy, ordering
T
cousins, MXenes are mostly found to be electrically conductive and hydrophilic.7,8 Being conductive, MXenes are widely studied for use as electrodes in batteries and supercapacitors.14−17 Recently, they were explored for electromagnetic interference shielding,18 electrocatalysts for the hydrogen evolution reaction,19 and as topological insulators.20,21 MXenes’ rich chemistry offers great versatility in terms of material properties design.9 While properties of graphene are often tuned via surface functionalization and that of TMDs via alloying,22−24 the electronic
wo-dimensional (2D) materials offer intriguing properties that differ from their bulk counterparts. Since the discovery of graphene, the successful isolation of monolayers of layered compounds such as transition metal dichalcogenides (TMDs)1−4 has spurred a wave of 2D materials research.5,6 More recently, the discovery of MXenes7,8 created an additional large class of 2D materials (Figure 1).9 MXenes are 2D layered transition metal carbides and/or nitrides derived mostly by selective etching of the A-element layers (mostly groups IIIA to IVA) from their parent ternary carbides and nitrides, called MAX phases. Recently, derivation from other parent laminated phases had also been successfully demonstrated.10,11 The possibility of direct large-area synthesis via chemical vapor deposition (CVD) has been suggested too.12,13 Unlike its TMD © 2017 American Chemical Society
Received: December 8, 2016 Accepted: March 15, 2017 Published: March 15, 2017 4407
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Figure 1. Schematic of the formation of MXene alloys with varying degrees of ordering, where M1 and M2 can be Ti, V, Nb, Ta, and Mo. Left: M3C2 MXenes consist of one transition metal type (blue and orange spheres) occupying the outer layers and the middle layer. C atoms (small gray spheres) occupy the space between the transition metal planes. Right: Upon alloying to form (M11−xM2x)3C2, different phases could be formed. We illustrate for the case of stoichiometric composition x = 2/3, i.e., (M11/3M22/3)3C2, the structures of the alloy MXenes with various degree of ordering. In general, the degree of disordering increases with temperature. But Mo-rich MXenes, (M11/3Mo2/3)3C2, remain close to perfect ordering even at temperatures above 1500 K. Other alloys, such as (Ti1−xVx)3C2 and (Nb1−xVx)3C2, tend to form fully disordered solid solutions.
degree and type of ordering. We then compare our findings on the alloys’ ordering/disordering tendencies with known experiments. At the end, we explore the ordering stabilities of MXene precursors, including their parent MAX phases and terminated MXenes. From these studies, we discuss the formation possibilities of ordered MXene alloys that are yet to be synthesized experimentally. For a given ternary MXene alloy, (M11−xM2x)3C2, different configurations of M1 and M2 atoms result in different relative stability, which can be measured by the formation energy (Ef). For a given configuration, σ, its Ef with respect to its binary MXenes M13C2 and M23C2 is given as
properties of MXenes could be tuned both via surface functionalization16,25,26 and alloying.27 For alloying, the distribution of the alloying elements (alloy structure) dictates its properties and ultimately, MXene’s performance in the intended application. As an initial step toward the rational design of MXene alloys, it is thus crucial to assess the relative stability of the different structural possibilities. Despite a large combinatorial choice of alloying elements among the transition metals, only a handful of double-transition-metal MXenes have been synthesized to date. Although most exist as random solid solution,7,8 ordered alloy MXenes were synthesized recently as well.27 Many more remain to be found, especially at off-stoichiometric compositions. It is impossible to cover the entire field of possible compositions experimentally. For structural characterization, first-principles calculations have proven to be valuable for confirming and rationalizing experimental results.27−29 Moreover, first-principles calculations could be used to predict the stability of alloy structures that have not yet been fabricated.28 However, such predictions had thus far been restricted to selected stoichiometries. Here, we construct a much more comprehensive map of the structure−stability relationship to provide insights into the phase stability of MXene alloys (i.e., disordered vs ordered) across all compositions and a large temperature range. We map the change in degree of ordering vs temperature (Figure 1) and explain why some MXene alloys prefer to order while others tend to disorder. In the spirit of high-throughput computational materials discovery, we make use of a multiscale computational platform to evaluate the relative stability of over a million possible alloy configurations for 8 selected double transition metal MXene alloys: (V 1−x Mo x ) 3 C 2 , (Nb 1−x Mo x ) 3 C 2 , (Ta 1−x Mo x ) 3 C 2 , (Ti1−xMox)3C2, (Ti1−xNbx)3C2, (Ti1−xTax)3C2, (Ti1−xVx)3C2, and (Nb1−xVx)3C2,, with 0 ≤ x ≤ 1. Utilizing accurate DFTcalculated results, the multiscale platform uses the cluster expansion method30−37 to train quick-to-compute effective atomistic interactions with high scalability. This enables computation of the thermodynamic behavior of the MXene alloys, from which, their preferred structural arrangements are mapped out versus composition and temperature. We explore three sets of alloyed MXenes. (i) Mo-containing MXenes alloyed with Ti, V, Nb, and Ta. (ii) Ti containing MXenes alloyed with group VB transition metals (V, Nb, and Ta). (iii) MXenes alloys formed from V and Nb elements only. For each alloying system, we consider the effects of composition and temperature on the
Ef (σ ) = E(σ ) − (1 − x(σ ))E(M13 C2) − x(σ )E(M 23C2) (1)
where x(σ) is the fraction of M2 atoms out of the total number of transition metal atoms. For each MXene alloy, a training set of DFT-calculated Ef(σ) is utilized to construct effective cluster interactions (ECIs) via the cluster expansion (CE) method.30−37 The construction of the ECI and MC simulations are performed using the TTK code,38−41 which is capable of generating symmetry-sorted clusters for alloy surfaces and nanostructures,42−47 where ECIs close to the surface differ from their counterparts in the bulk. The ECI values are plotted in Figure S1 (see also Figure S2 for illustration of clusters). Based on selected ECI with significant values (see Table S1), the alloying atoms’ general preference for the surface or middle layer could be deduced. The derived ECIs facilitate rapid computation of Ef(σ) and generally reproduce EDFT (σ) to within a few meV (see f Figure S3 and Table S2). Hence, using the ECIs, obtaining thermodynamically averaged quantitates, such as ⟨Ef⟩, becomes possible via Monte Carlo (MC) simulations. The MC simulations provide insights into the degree of ordering or disordering in the MXene alloy across compositions and different temperatures. Further details about the CE method, the construction of the ECIs, and MC simulations are given in the Supporting Information.
RESULTS AND DISCUSSION To study the structure−stability relationship in detail, the Ef of ∼106 alloy configurations derived from different unit cell sizes were evaluated for various alloy MXenes using the ECIs. In the following section, the structural stability and ordering of three sets of MXene alloys will be discussed: (i) Mo-based MXenes alloyed 4408
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Figure 2. Formation energy, Ef (evaluated from the cluster expansion method), versus composition plots for (M11−xMox)3C2 MXene, with M1 being (a) V, (b) Nb, (c) Ta, and (d) Ti, using ∼3 × 106 structures generated from 5 to 45-atom unit cells. Each point represents a particular structure whose relative stability is indicated by Ef. The color map indicates Mo concentration at the surface layers, where the bluer (redder) end of the spectrum toward the right (left) indicates a higher (lower) concentration of Mo. A point whose color is blue-shifted (red-shifted) with respect to the color representing its overall composition, x, indicates an elevated (depressed) Mo concentration at the surface. The dashed-line forms the groundstate hull, joining the lowest energy structures across compositions.
Figure 3. Formation energy, Ef (evaluated from the cluster expansion method), versus composition plots for (Ti1−xM2x)3C2 MXene with M2 being (a) V, (b) Nb, (c) Ta, and for (d) (Nb1−xVx)3C2, using ∼3 × 106 structures generated from 5 to 45-atom unit cells. Each point represents a particular structure whose relative stability is indicated by Ef. The color map indicates M2 concentration at the surface layers, where the bluer (redder) end of the spectrum toward the right (left) indicates a higher (lower) concentration of M2 atoms. A point whose color is blue-shifted (red-shifted) with respect to the color representing its overall composition, x, is said to have an elevated (depressed) M2 concentration at the surface. The dashed-line forms the groundstate hull, joining the lowest energy structures across compositions.
Structure−Stability Relationship. Mo-based MXenes. Figure 2 shows the structure−stability relationship of Mo-based
with Ti, V, Nb, Ta; (ii) Ti MXenes alloyed with V, Nb, and Ta; (iii) MXenes alloys formed between Nb and V. 4409
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Figure 4. Composition of outer layer (xout) versus overall composition (x) for different MXene alloys (M11−xM2x)3C2: (a) (V1−xMox)3C2, (b) (Nb1−xMox)3C2, (c) (Ta1−xMox)3C2, (d) (Ti1−xMox)3C2, (e) (Ti1−xNbx)3C2, (f) (Ti1−xTax)3C2, (g) (Ti1−xVx)3C2, and (h) (Nb1−xVx)3C2 at various temperatures. Each line is made up of a series of points, each corresponding to a semigrand canonical MC simulation performed at fixed chemical potential (see Figure S5). Dashed lines without points refer to compositions where phase separation occurs. At low temperatures, phase segregation regions exist for some of the alloys and the corresponding ranges for x are shaded purple. At temperatures 1500 K and above, no phase segregation regions exist. Dotted lines represent the xout versus x relationships for the extreme cases of fully disordered state and the fully ordered state. As temperature increases, xout approaches the fully disordered solid solution state where the relationship xout = x holds. In the case of an ordered structure with all M2 occupying the outer layer, the relationship is defined by xout = (3/2)x for x < 2/3 and xout = 1 for x ≥ 2/3. For the ordered case with M2 fully occupying the middle layer, the relationship is defined by xout = 0 for x < 1/3 and xout = (3/2)x − 1/2 for x ≥ 1/3.
For x < 2/3, there is insufficient Mo atoms to form a purely Mo-occupied surface layers. However, in most cases, structures with higher contents of Mo atoms in the outer layers continue to have the lower Ef. For (Nb1−xMox)3C2 and (Ta1−xMox)3C2, structures with maximum Mo surface occupancy continue to exist as groundstates or close to the groundstate hull. In contrast, for (V1−xMox)3C2 and (Ti1−xMox)3C2, structures with higher Mo surface occupancies are above the groundstate hull for x < 2/3, suggesting a preference for phase segregation into adjacent groundstates at sufficiently low temperatures. Peculiar to (Ti1−xMox)3C2, structures with lower Mo surface occupancy are found to be more stable for x < 0.2, where points with low Ef are red-shifted (Figure 2d). For example, in (Ti0.9Mo0.1)3C2 (x = 0.1), Mo atoms prefer to occupy only the middle layer. This finding is opposite to the general trend, where Mo prefers to occupy the outer layers. Ti-based MXene Alloys with V, Nb, Ta. We next discuss the structure−stability relationship of MXene alloys involving Ti and a group VB transition metal (Ti1−xM2x)3C2 (M2 = V, Nb, and Ta). As shown in Figure 3b,c, (Ti1−xNbx)3C2 and
alloy MXenes (M11−xMox)3C2 with M1 = V, Nb, Ta, or Ti. In general, maximizing Mo composition in the surface layers enhances the structural stability (lower Ef) for this group of alloys. This is supported by the observation that red-shifted points have a higher Ef, while blue-shifted points have a lower Ef. The (M11−xMox)3C2 alloys manifest strong ordering tendencies for x ≥ 2/3. In this Mo-rich compositional range, structures with purely Mo-occupied surface layers are achievable. Such structures (black points) are either the groundstates or low-energy structures close to the groundstate hull and possess highly negative Ef. The groundstate hull is the dashed-line joining the different groundstates across compositions. It serves as the theoretical lower bound of the formation energy where states above the hull are not thermodynamically accessible at 0 K. The lowest energy structure occurs at x = 2/3 with perfect interlayer ordering. This lowest-energy groundstate has Mo fully occupying the surface layers and the M1 atoms fully occupying the middle layer, resulting in a low Ef of ∼ − 0.1 eV. Structures having M1 in the outer layers (red-shifted points) have a higher Ef and hence, a lower stability. 4410
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ACS Nano (Ti1−xTax)3C2 exhibit strong interlayer ordering tendencies for x ≤ 1/3. Structures with purely Ti-occupied surfaces (red colored points) exist as groundstates or close to the groundstate hull. The most stable structure occurring at x = 1/3, has perfect ordering with Ti (Nb/Ta) fully occupying the outer (middle) layers. For x > 1/3, structures that maximize the amount of Ti on surfaces continue to have higher stability. As these structures are mostly above the groundstate hull, they are only thermodynamically stable at sufficiently high temperatures. At 0 K, states above the groundstate hull will phase separate into adjacent groundstates. Interestingly, the groundstate structure at x = 2/3 has an asymmetric ordering. We note that for (Ti1/3Nb2/3)3C2 the groundstate occurs as a result of fitting error during cluster expansion and actual DFT calculated formation energy is marginally positive (see Figure S3). The asymmetric ordered structure maximizes the number of Ti on the surface by having all Ti occupying the topmost layer and Nb/Ta occupying the middle and bottommost layers (Figure S4d). In other words, Ti atoms occupy one surface layer entirely and Nb/Ta atoms occupy the central layer as well as the surface layer on the opposite side. Such asymmetric structure is intriguing, as it has not been reported thus far. In contrast, the low-energy structures in (Ti1−xVx)C2 prefer to maximize V (instead of Ti) at the surface for x ≤ 1/3. The Ef of the groundstate structures are an order of magnitude lower than those of (Ti 1−x Nb x ) 3 C 2 and (Ti1−xTax)3C2, indicating a weak ordering tendency in (Ti1−xVx)C2. For x > 1/3, all structures are above the groundstate hull, suggesting phase separation at very low temperatures. V and Nb MXene Alloys. For (Nb1−xVx)3C2, which involves the alloying of group VB transition metals, the Ef of all calculated structures are positive and thus the groundstate hull is simply the line joining Nb3C2 and V3C2. Since there are no groundstates at intermediate compositions, phase separation occurs across compositions at sufficiently low temperatures. Interlayer Ordering vs Temperature and Composition. At 0 K, the thermodynamically stable phases are the groundstates shown in the Ef vs composition plots (Figures 2 and 3) described previously. At finite temperatures, some structures above the groundstate hull are possible to form too. The disordered phase increasingly stabilizes against the groundstates as temperature increases. When entropic effect dominates over Ef, the MXene alloy becomes disordered (Figure 1). The thermodynamically stable phases at finite temperatures are assessed via MC simulations. Configurational entropy is considered via the ensemble averaging during MC simulation (see “Monte Carlo Simulations” section and Figure S5 in Supporting Information). Figure 4 shows the ensemble averaged outer layer concentration (xout) as a function of composition at selected temperatures. At 300 K, entropic effect is small and thus only states that are slightly above the groundstate hull are thermodynamically accessible. For compositions where no states exist close to the groundstate hull, a phase separation region is formed. For example, (Ti1−xMox)3C2 shows a phase segregation region for 0.03 < x < 2/3 at 300 K (shaded area in Figure 4d). This range corresponds to the composition range in Figure 2d where no structures were found close to the groundstate hull. On the other hand, (Nb1−xMox)3C2 and (Ta1−xMox)3C2 exhibit structures that are close to the groundstates and these structures are thermodynamically accessible at 300 K. Therefore, no phase separation regions are observed for these two cases. At higher temperatures relevant to the synthesis of their parent MAX phases (1500 to 1900 K)28,48,49 high energy states are now accessible and thus phase separation regions no longer exist in
most cases. In addition, the tendency for disordering increases as the degree of ordering diminishes. As observed in Figure 4, the outer surface concentration, xout, shifts toward the overall composition x. Because a fully disordered solid solution is represented by xout = x, the absolute difference between surface and overall compositions, |xout − x|, measures the degree of ordering/disordering in the alloy MXene at a given composition. For Mo-based alloys with strong interlayer-ordering tendencies (Figure 4a−d), high concentration of Mo in the outer layers persists at higher temperatures. For example, at 1500 to 1900 K and at x = 2/3, xout remains at around 0.9 for all Mo-based phases. For x > 2/3, xout goes above 0.9 as additional Mo is added. For x < 2/3, the surface layers remain Mo-elevated (except for (Ti1−xMox)3C2) at 1500 to 1900 K, although the degree of ordering (|xout − x|) diminishes with decreasing x. Among the Ti-based MXenes alloyed with group VB transition metals, (Ti1−xNbx)3C2 and (Ti1−xTax)3C2 show tendency to order with higher Ti (depressed Nb/Ta concentration) surface compositions (Figure 4e,f). The interlayer-ordering tendency as measured by |xout − x| is strongest at x = 1/3, indicating ordered structures with Ti occupying the outer layers and Nb/Ta occupying only the middle layer. At higher temperatures of 1500 to 1900 K, the perfect ordering is reduced by having xout ≈ 0.2 and xout ≈ 0.15 for (Ti1−xNbx)3C2 and (Ti1−xTax)3C2, respectively. For (Ti1−xVx)3C2, |xout − x| is the smallest among all alloys studied and is thus expected to form disordered solid solutions at all compositions (Figure 4g). From a substitution alloy perspective, Ti and V have similar sizes and electronic structure, thus they are expected to intermix well according to Hume−Rothery rules to form disordered solid solutions. The case of MXene alloys composing of group VB elements is exemplified by (Nb1−xVx)3C2. Figure 4h shows that V atoms prefer occupying the surface in general. For x > 2/3 and T > 1200 K, |xout − x| is small, indicating a tendency for forming highly disordered solid solutions. For 0.4 < x < 0.5, |xout − x| is the largest, indicating the tendency to form a moderately disordered solution with V-enrichment on the surface. Distribution of Alloying Elements. We next compare the effect of temperature on the degree of ordering among the alloy MXenes. At x = 2/3, the possibility of forming a perfect M1-M2M1 type ordered structure is most favorable. However, the ordering diminishes at higher temperatures. Figure 5 shows that the degree of ordering among these alloys is such that (Ti1/3Mo2/3)3C2 > (Ta1/3Mo2/3)3C2 > (V1/3Mo2/3)3C2 > (Nb1/3Mo2/3)3C2 > (Ta1/3Ti2/3)3C2 > (Nb1/3Ti2/3)3C2 > (Nb1/3V2/3)3C2 > (Ti1/3V2/3)3C2. Indeed, for Mo-based alloy MXenes, xout remains at ∼0.9 even at a high temperature of 1900 K (implying xin ∼ 0.2 in the middle layer). The strong interlayer ordering in (M11/3Mo2/3)3C2 is related to the fact that the formation energies of the perfect Mo-M1-Mo structure (Figure S4e) are the lowest. For Ti-rich surface alloys, (Ta1/3Ti2/3)3C2 and (Nb1/3Ti2/3)3C2, a high degree of intermixing of elements exists, with xout ∼ 0.8. (Ti1/3V2/3)3C2 is a solid solution. Its xout is close to the overall composition (i.e., xout ≈ x) for temperatures above 1000 K. (Nb1/3V2/3)3C2 also forms solid solution at 1500 to 1900 K with xout ∼ 0.72. Similar comparisons of the surface concentrations for other compositions are given in the S.I. (see “Distribution of Alloying Elements Versus Temperature” and Figure S6). The general trends can be summarized as follows: (i) For x > 2/3, xout increases with x. Ranking among the MXene alloys with regards to the degree of interlayer 4411
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have xout > 0.95, except for (Nb1/6Ti5/6)3C2, (Ti1/6V5/6)3C2, and (Nb1/6V5/6)3C2. (Ti1/6V5/6)3C2 and (Nb1/6V5/6)3C2 remain as solid solutions. (ii) For x < 2/3 (see Figure S6a−c), it is impossible for the outer layers to be fully occupied by one particular element type. The degree of interlayer ordering thus decreases for all alloys. However, the rate of decrease differs among them. (Ta1−xMox)3C2 and (Nb1−xMox)3C2 have the highest xout in this composition range. However, Mo atoms tendency to occupy the surface layer weakens significantly in (Ti1−xMox)3C2 as x decreases. This results in a much lower xout compared to other Mo-based MXene alloys. This reversal in Mo layer preference is consistent with our earlier discussion (see Figure 2d). The degree of ordering in (Nb1−xVx)3C2, on the other hand, decreases slowly with x. As seen in Figure S6a,b, the xout of (Nb1−xVx)3C2 is the third highest for x < 1/3. Hence, the tendency for (Nb1−xVx)3C2 to form solid solution decreases with x. Overall, the degree of interlayer ordering diminishes with increasing temperature. At synthesis temperatures corresponding to their parent MAX phases (1500 to 1900 K), some degree of mixing between the alloying elements is thus expected.
Figure 5. Composition of outer layer (xout) versus temperature for various (M11/3M22/3)3C2 MXenes. Dashed lines refer to metastable states accessed by canonical MC, where phase-separation should in fact exist (see Figure 4). For (Nb1/3V2/3)3C2, the discontinuity at ∼500 K corresponds to phase transition to a metastable ordered state.
ordering remains unchanged compared to x = 2/3. At x = 5/6 and 1900 K (see Figure S6e), all the MXene alloys
Figure 6. Atomic occupancies of representative (M11−xM2x)3C2 alloys at x = 2/3 for T = 300, 1100, and 1900 K. Larger spheres represent metallic atoms and their colors vary from red (100% occupation by M1) to blue (100% occupation by M2) depending on the average occupancies of the lattice site during MC simulation. Intermediate compositions are colored according to the color chart. Small gray spheres are C atoms. (Ti1/3Mo2/3)3C2 is representative of (M11/3Mo2/3)3C2 alloys with strong interlayer ordering, where Mo occupies the outer layer. (Ta1/3Ti2/3)3C2 represents alloy MXenes with intermediate interlayer ordering with Ti occupying the outer layer. (Ti1/3V2/3)3C2 represents a disordered solid solution. 4412
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Figure 7. Calculated electronic density of states (DOS) and projected crystal overlap Hamiltonian population (pCOHP) analysis of two different (Ti1/3Mo2/3)3C2 structures. (a) symmetric structure with Mo (blue spheres) in the top (T) and bottom (B) outer layers while Ti (red spheres) occupies the inner (I) layer; (b) asymmetric structure with Ti occupying the bottom layer and Mo occupy the top and inner layers. C atoms are shown as small gray spheres. The DOS plots show the projection onto each atomic type on different layers. For (a), only the top layers are shown because the results are the same for the bottom layers (due to structural symmetry). The negative of the pCOHP values are plotted for each type of adjacent pairs of atoms in the respective structure (except for the in-plane C−C bonds), with positive (negative) values in the vertical axis indicating bonding (antibonding) contributions. Energy values in the horizontal axes are with respective to the structure’s Fermi level, i.e., EFermi = 0.
Ordering Preference from Electronic Structure Perspective. To further understand why in Mo-based alloy MXenes Mo atoms prefer to occupy the outer layers, we investigated the changes in bonding nature of the metallic d-bands while Mo is moved from the outer layers to the inner layer. Figure 7 compares the electronic density of states (DOS) of two different ordering structures of (Ti1/3Mo2/3)3C2. Figure 7a represents a perfectly ordered symmetric structure, where Mo atoms are in the surface layers and Ti is in the middle layer (Mo−Ti−Mo). Figure 7b shows an asymmetric ordered structure of the same composition with Mo occupying one of the surface and the middle layers, while Ti is in the other surface layer (Mo−Mo−Ti). Electron states in the energy range between −8 to −2 eV correspond to covalent bonds formed between the metal atoms’ d-electrons and carbon’s valence electrons,28 as evident by the high values of the projected DOS for both metal and carbon atoms. Closer to the Fermi level (−2 to 0 eV), the DOS are mainly contributed by the d-band of the metal atoms (projected DOS from C is negligible). The inner metallic layer generally shows a lower DOS in this energy range (−2 to 0 eV) as they participate in covalent bonding with two layers of C, leading to a higher DOS in the energy range of −8 to −2 eV. The opposite is true for the outer layer metals as they interact with only one plane of C atoms. As a result, the inner (outer) layer Ti (Mo) in the symmetric structure
To help restore the maximum ordering possible, the results suggest that a postsynthesis annealing at around moderate temperatures (800 to 1000 K) to be a viable solution for most cases. It is important to distinguish interlayer ordering/disordering from the intralayer ordering/disordering within each layer. For the MXene alloys studied here, the alloying elements within each layer are randomly distributed (intralayer disordering). As illustrated in Figure 6, the atomic site occupancies belonging to the same layers are similar, regardless of the degree of interlayer ordering. For example, (Ti1/3Mo2/3)3C2 clearly has a higher interlayer ordering than (Ti1/3V2/3) 3C2. But the occupation within each layer is homogeneous nonetheless. Figure 6 also illustrates that interlayer ordering increases with decreasing temperature but no intralayer ordering is observed regardless of the temperature. The intraplane nearest-neighbor pair probability ratio in Figure S7 also supports the finding that the in-plane arrangement of alloying atoms is disordered in general. The fact that the intralayer pair ECI is much weaker than the single-body ECI for interlayer-separation (Figures S1, S2 and Table S1), also supports a weak tendency for intralayer ordering; such ordering could only be observed at lower temperatures (Figure S7). 4413
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MXene solid solution was synthesized8 as well as in its parent phase (Ti1/2Nb1/2)2AlC.51 In comparison, our results show its thicker M3C2 MXene counterpart, (Ti1/2Nb1/2)3C2, has a slightly Ti-enriched composition in the outer layer (see Figure 5). Likewise, for (Nb1/2V1/2)3C2, some degree of interlayer ordering is observed with V having a higher composition at the surface than the middle, although its MAX phase cousins (Nb1/2V1/2)2AlC and (Nb1/2V1/2)4AlC3 are reported to be solid solutions experimentally.51 Formation Possibilities of Ordered Alloy MXenes. To date, only (Ti1/3Mo2/3)3C2 had been synthesized among the ordered MXene alloys studied here. It is interesting to evaluate the formation possibilities of the other ordered MXene alloys. The stability analysis in this work is based on bare MXene structures. Given that MXenes are currently derived by selective etching of their parent MAX phases, it is pertinent to explore how the presence of Al atoms and surface functionalization (e.g., O, OH, or F) might alter interlayer ordering. The difference in affinity between the alloying elements with the surrounding atoms could potentially reverse the elements’ preference for the surface layers. For this purpose, we compute the relative stabilities of three structures with different outer layer compositions (xout) under the following environments: (i) in their undecorated state (bare MXene), (ii) in their respective parent MAX phase state, and (iii) in their O-functionalized-surface state. Figure 8 compares these scenarios for the ordered (M11−xM2x)3C2 alloys at x = 2/3. Comparing bare MXene alloys (Figure 8a) with their respective MAX phases (Figure 8b), different stability trends were observed for different MXene alloys. For (M11/3Mo2/3)3C2, the relative energies of the structures of bare MXene and its parent MAX are similar, suggesting that the surrounding Al atoms have little effect on the interlayer ordering. This implies that the stability trend is retained for Mo-based parent MAX phases, where Mo prefers outer layers. For (Nb1/3Ti2/3)3AlC2 and (Ta1/3Ti2/3)3AlC2, the three structures (with different xout) have comparable stabilities (Figure 8b). This suggests that Al reduces the tendency for interlayer ordering and instead encourages disordering for these alloys. The result is consistent with experimental findings that (Nb1−xTix)n+1 AlCn and (Ta1−xTix)n+1 AlCn MAX phases exist as solid solutions.51 In the case of (Ti1/3V2/3)3C2, the three structures (with different xout) have comparable stabilities both in bare MXene and in the parent MAX phases, indicating a tendency for disordering. For (Nb1/3V2/3)3C2, the tendency for ordering diminished in the presence of Al. During selective etching process to produce MXenes, their surfaces become decorated with terminations, such as O, F, and OH. We used monolayer coverage of O atoms to simulate the as synthesized state of MXene. In contrast to bare MXenes and MAX phases, Figure 8c shows no obvious trend. The perfectly ordered groundstate (M2-M1-M2 interlayer ordering with xout = 1) is found to have the lowest energy for (V1/3Mo2/3)3C2O2, (Ti1/3Mo2/3)3C2O2, and (Nb1/3Ti2/3)3C2O2. Given the feasibility of the formation of their parent MAX phases, (V1/3Mo2/3)3C2 and (Ti1/3Mo2/3)3C2 seem to have the best chances for forming ordered alloy MXenes: (i) the ordered structure (with Mo fully occupying the outer layer) is stable with respect to the lesser-ordered structures in their parent MAX phases and (ii) remains ordered even after etching. For (Nb1/3Mo2/3)3C2 and (Ta1/3Mo2/3)3C2, although the ordered MAX phase is stable, the ordering is disrupted upon addition of O to the surface. We note that the O-coverage used here may not be the thermodynamically correct one and may be higher than reality.
has a lower (higher) DOS near the Fermi level than the outer (inner) layer Ti (Mo) atoms in the asymmetric structure. Next, we analyze the bonding nature of these d-bands near the Fermi level by evaluating the projected crystal overlap Hamiltonian population (pCOHP).50 The d-bands arise from the in-plane metallic bonds and negative (positive) pCOHP values indicate bonding (antibonding) character; note that it is common to plot the negative of the pCOHP value (Figure 7). For both structures, the d-bands of the outer layer metals show a strong bonding character. The “tiebreaker” in the relative structural stability lies in the inner plane metals. For the symmetric structure, the d-bands from the in-plane Ti−Ti (Ti(I)−Ti(I)) are found to have bonding characteristics. However, in the asymmetric case, the structure is destabilized by the d-bands of the inner layer Mo (Mo(I)−Mo(I)), which shows the antibonding character. This finding could be rationalized by band filling; Ti only partially fills up its bonding states in the d-band, while Mo, having 2 valence electrons more than Ti, fully occupies the bonding part and is filling up the higher energy antibonding states as well. This was also observed for the other Mo-based MXenes (M11/3Mo2/3)3C2 (see Figure S9a,b). It is thus energetically unfavorable for Mo to occupy the inner plane,27 explaining why a perfectly symmetric ordered Mo−Ti−Mo structure is favorable. In the case of Ti and group VB elements (e.g., Nb and Ta), the antibonding argument no longer holds. With one less valence electron than Mo, the antibonding states are not filled when the group VB elements occupy the middle plane. Indeed, the inner plane atoms are found to have marginally bonding characteristics whether occupied by Ti or group VB elements (see Figure S9c−f); there is thus no clear advantage of having either element occupying the inner plane. However, comparing the in-plane metallic bonding close to the Fermi level, the d-band of outer Ti atoms seem to have a stronger bonding character than outer Nb or Ta atoms. Hence, there may be a slight preference for adopting an asymmetric structure in (Ti1/3Nb2/3)3C2 and (Ti1/3Ta2/3)3C2 with Ti occupying only one of the outer layers. The preferred asymmetry is also supported by the cluster expansion ECI values (see Table S1), which show that Ti prefers occupying the outer layer. At the same time, the negative pair and triplet ECIs in the outer layer supports clustering of similar atoms, hence Ti atoms prefer staying together on one outer plane rather than mixing with Nb/Ta atoms. Comparison with Reported Experimental Results. Our method could be used as a predictive tool for the degree of interlayer ordering and elemental mixing of MXene alloys versus synthesis temperatures. Among the ordered alloys studied here, (Ti1/3Mo2/3)3C2 has been synthesized25,27 and probably contains some degree of elemental intermixing as was reported for its parent MAX-phase synthesized at 1873 K.49 Consistent with our predictions, the experiments found the outer layers to be Mo-enriched (xout ∼ 0.75) while the inner layer is Mo-deprived (xin ∼ 0). As mentioned in that study,49 the layer compositions predicted from Rietveld analysis did not sum up to the expected overall composition of x = 2/3 but instead gives x = 1/2. Interestingly, based on the overall composition of x = 1/2, our prediction of xout = 0.67 (xin = 0.16) corresponds better with the reported experimental values. For (Ti1/2V1/2)3C2, its parent MAX phase alloy, (Ti1/2V1/2)3AlC2, had been reported to exist as a solid-solution.51 The experimental results are consistent with our finding that (Ti1−xVx)3C2 has a strong tendency to form fully disordered solid solutions across all compositions (see Figures 5 and 6). In the case of the Ti−Nb MXene, (Ti1/2Nb1/2)2C, a M2C 4414
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Figure 8. Energy comparison between structures with different xout for (a) (M11/3M22/3)3C2 (bare MXenes), (b) (M11/3M22/3)3AlC2 (MAX phases), and (c) (M11/3M22/3)3C2O2 (oxygen terminated MXenes). For each material state, S1, S2, and S3 are structures with xout = 1, 0.75, and 0.5, respectively. Energies of structures S2 and S3 are shown with respect to that of S1. Structures are illustrated on the right with atomic species differentiated by colored spheres: M1 (red), M2 (blue), C (gray), Al (magenta), and O (orange). For (c), two oxygen placements are considered: either vertically above the C atoms (C-top arrangement) or above the M atoms in the middle layer (M-top arrangement). The different scenarios are distinguished with labels A, B, and C. Case A refers to both structures adopting C-top arrangements. Case B refers to S1 adopting C-top arrangement with S2 or S3 adopting a M-top arrangement. Case C refers to both structures adopting M-top arrangements. Case D refers to S1 adopting M-top arrangement with S2 or S3 adopting a C-top arrangement. Only results from the most stable O-arrangements are shown in (c).
Lastly, we evaluate the thermodynamic feasibility of fabricating the precursor MAX phases of the highly ordered (M11/3Mo2/3)3C2 MXenes. This is important as the MAX phases could decompose into other competing phases during fabrication. The collection of competing phases that have the highest stability are called the “most competing phases”.28 In this work, these phases are selected from the list of relevant stable compounds (up to ternaries) from the Materials Project database.52 A more extensive list of compounds including MAX phases with thicker MXene layers (e.g., M4AlC3) and quaternary compounds could be considered.28 Nevertheless, our results should provide good indications of the formation possibilities of the precursor MAX phases. Table S3 shows the formation energies, Ecp f , of the MAX phases calculated with respect to the most competing phases. Given the high synthesis temperatures of MAX phases (1500 to 1900 K), configurational entropic effects on the relative stability should be considered as well. We thus estimate the free energy of formation Gcp f of the MAX phases by adding the configurational entropic contributions to Ecp f (see “Free Energy of Formation of MAX Phases“ section in S.I.). Figure 9 shows how Gfcp decreases with temperature. Even though (M11/3Mo2/3)3C2 are highly ordered alloys, entropic effects from intra-layer disordering provide significant stabilizing effects at high synthesis temperatures of its precursor MAX phase. At room temperature, (Ta1/3Mo2/3)3AlC2 is only marginally more stable than its competing phases while (V1/3Mo2/3)3AlC2 and (Nb1/3Mo2/3)3AlC2 are marginally un-
Figure 9. Formation free energies (Gcp f ) vs temperature (T) for (M11/3Mo2/3)3C2 alloys.
stable. However, at 1900 K, Gcp f is lowered to −0.04 eV, suppressing the likelihood for decomposition of the alloy MAX phases. (Ti1/3Mo2/3)3AlC2 has the lowest Gcp f among the ordered MAX phases studied, therefore, it is least likely to decompose into the competing phases. This explains the relative ease of synthesizing (Ti1/3Mo2/3)3AlC2 and why (Ti1/3Mo2/3)3C2 is one of the earlier ordered alloy MXenes to be reported.
CONCLUSIONS Coupling first-principles DFT calculations with the cluster expansion (CE) method, we elucidated the degree of ordering 4415
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cut-offs are set to 500 eV. All atomic coordinates are fully relaxed until the absolute value of the forces acting on each atom is less than 0.01 eV/Å. During structural relaxation, the supercell volume remains fixed, although its shape is allowed to change. To minimize spurious interactions between periodic images, a vacuum of at least 15 Å along the z-direction is ensured. Spin polarized calculations are performed, although the magnetic moments are found to be negligible for structures that do not contain Ti, namely, (V1−xMox)3C2, (Nb1−xMox)3C2, (Ta1−xMox)3C2, and (Nb1−xVx)3C2. Monkhorst−Pack sampling58 with 12 × 12 × 1 k-point grids is used for the 5-atom primitive cell of M3C2. For larger unit cells, the numbers of k-points in the planar directions are reduced accordingly, maintaining a k-point density of around 40 k-points per Å−1. Selected structures of MAX phases are calculated with similar settings, although the k-point grid is doubled in the z-direction. The bonding characteristics of selected structures are analyzed using the projected crystal overlap Hamiltonian population (pCOHP) derived from the LOBSTER code.50,59,60
across composition and temperature for 8 different (M11−xM2x)3C2 ternary MXenes. CE constructs effective atomistic interactions for each alloy, enabling formation energies of millions of possible alloy structures (configurations) to be computed in a highthroughput fashion. From Monte Carlo simulations, MXene alloys incorporating Mo (i.e., (V1−xMox)3C2, (Nb1−xMox)3C2, (Ta1−xMox)3C2, and (Ti1−xMox)3C2) show strong interlayer ordering with Mo generally preferring outer layers. Even at high temperatures (1400 to 1900 K), the Mo composition in the outer layers is ∼0.9 (implying a M1 concentration of 0.8 in the middle layer). Interestingly, for (Ti1−xMox)3C2 at very low Mo concentration (x < 0.1), Mo atoms tendency to occupy the surface layer is reversed and they prefer to occupy the middle layer. However, in the case of group VB transition metals (V, Nb, and Ta) alloying with Mo in (M11/3, Mo2/3)3C2, Mo prefers the outer layers throughout the entire composition range. For Ti alloying with group VB transition metals, Nb and Ta prefer the middle layer and the majority of Ti atoms occupy the outer layers. In general, the degree of interlayer ordering is less than that observed for the Mo-rich alloy MXenes. Ordering does not exist for Ti−V MXenes, with (Ti1−xVx)3C2 forming random solid solutions at synthesis temperatures across all compositions. For alloys from Nb and V elements, (Nb1−xVx)3C2 intermixes well at synthesis temperatures to form solid solutions, although at lower temperatures the alloy is expected to segregate forming a layered MXene. In general, our work shows how the degree of interlayer ordering diminishes with increasing temperature. At synthesis temperatures of MXenes’ parent MAX phases (1500 to 1900 K), some degree of mixing between the alloying elements is expected. Based on the ordering in the MXenes, we can deduce that Mo-based MAX phases keep their interlayer ordering at the synthesis temperature, while others are less ordered. To help restore close-to-perfect ordering, we suggest a postsynthesis annealing for the ordered MXenes at moderate temperatures (800 to 1000 K). In contrast to the interlayer ordering, we observed a complete intralayer disordering even for alloys with strong interlayer ordering. In other words, within each atomic layer, there are no atomic position preferences for the majority or minority elements of the layer. Among the ordered MXenes, we show why (Ti1/3, Mo2/3)3C2 has been the “easiest” to synthesize. (i) The precursor MAX phase is stable against decomposition to other competing phases. (ii) The interlayer ordering is maintained even in the presence of surface terminations. On the other hand, the MAX phases of the other ordered Mo-rich MXenes, (M11/3, Mo2/3)3C2 (M1 = V, Nb, or Ta) are either marginally stable or unstable with respect to the competing phases at 0 K. However, at sufficiently high temperatures, these MAX phases are stabilized as a result of configurational entropic effects. The findings suggest higher synthesis temperatures for these parent ordered MAX phases to avoid decomposition into other phases. Our predictions here cover a wide range of compositions and temperatures for a variety of MXene alloys and can guide synthesis of multielement MXene alloys in the future.
ASSOCIATED CONTENT S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b08227. Computational details including the cluster expansion method, the construction of a reliable cluster expansion, Monte Carlo simulations and free energy of formation of MAX phases, discussion on distribution of alloying element versus temperature, diagrams of the effective interactions and their values, plots of formation energies of structure vs composition calculated via DFT, crystal structures of groundstates, plot of results from semigrand canonical MC simulations, plot of outer layer composition vs temperature, plot of nearest-neighbor pair probabilities vs temperature, plot of outer layer compositional difference vs temperature, plot of DOS and pCOHP of selected ordered MXenes, table of values for selected effective cluster interactions, table of the fitting error for the cluster expansion method, and table of formation energies of alloy MAX phases against their most competing phases (PDF)
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. ORCID
Teck Leong Tan: 0000-0002-7089-8966 Yury Gogotsi: 0000-0001-9423-4032 Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS The authors acknowledge the use of high-performance computing facilities in A*STAR Computational Resource Centre (ACRC) and National Supercomputing Centre (NSCC) in Singapore for the DFT computations performed in this work. B.A. and Y.G. acknowledge the support of the Fluid Interface Reactions, Structures, and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, for their work on stability of MXenes.
COMPUTATIONAL METHODS Geometry optimization and formation energy (Ef) calculations of the various (M11−xM2x)3C2 alloy structures are performed using DFT implemented in the Vienna ab initio Simulation Package (VASP)53,54 within a Projected Augmented Wave (PAW)55 basis and with the Perdew, Burke, and Ernzerhof (PBE) functional.56,57 Plane-wave
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DOI: 10.1021/acsnano.6b08227 ACS Nano 2017, 11, 4407−4418
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DOI: 10.1021/acsnano.6b08227 ACS Nano 2017, 11, 4407−4418
