# Discovery of hexagonal ternary section Ti 2 InB 2 and its evolution to layered boride TiB

### Stability and constructions of predicted borides

Determine 1 exhibits the thermodynamic stability of potential TixAyBz compounds estimated by means of reactions of TixBz with A quite than utilizing Ti, B, and A. Within the current materials design loop, this step was realized by conducting binary variable-composition searches as applied within the USPEX code25,26,27,28 utilizing TixBz and bulk A as ending compounds. A pre-investigation to establish the construction of TixBz was carried out by using a binary construction search within the Ti-B system (Supplementary Fig. 1). For the given sorts of TixBz and elemental A, every potential mixture of TixBz and A was thought-about within the preliminary construction search, restricted solely by the full variety of atoms per unit cell. The weather Al, Ga, In, Tl, Si, Ge, Sn, Pb, and Cd have been thought-about as A candidates within the construction search. When one ternary compound, TixAyBz, was discovered to be thermodynamically secure with respect to the top compositions of TixBz and A within the binary variable-composition search, a ternary variable-composition search was began for this Ti-A-B system to estimate the worldwide stability of the expected TixAyBz construction. In any other case, the search process was initialized once more by the number of totally different pairs of TixBz and A components.

Using the technique proven in Fig. 1 resulted within the prediction of a collection of ternary compounds with the formulation Ti2AB2 and Ti3AB4 within the preliminary construction search (Fig. 2a). The ternary compounds Ti2AlB2, Ti3AlB4, Ti2GaB2, Ti3GaB4, Ti2InB2, Ti3InB4, Ti2SiB2, Ti3SiB4, Ti2GeB2, Ti3GeB4, Ti2SnB2, and Ti3SnB4 (Fig. 2a) have been thermodynamically secure with respect to bulk A and TiB or Ti3B4. Nonetheless, additional Ti-A-B ternary variable-composition searches confirmed that solely Ti2InB2 is thermodynamically extra secure than competing Ti-B, Ti-In and In-B binary phases within the Ti-In-B ternary system at ambient strain, whereas Ti2SnB2 is secure at a excessive strain of 10 GPa. Different ternary candidates steered by the binary variable-composition search have been discovered to fall barely wanting thermodynamic stability and couldn’t be synthesized beneath pressures decrease than 10 GPa.

Fig. 2

Outcomes of theoretical construction search. a Abstract of construction search outcomes utilizing binary and ternary variable-composition strategies, the place the distances for metastable phases to the convex hull are labelled within the unit of eV per method. b Crystal construction. c Calculated digital construction for secure boron-containing ternary section Ti2InB2. The projected density of states (DOS), projected band construction and partial cost map on the (110) aircraft (−zero.5 eV < E − Ef < zero.5 eV) for Ti2InB2 are proven within the left, heart, and proper panels, respectively

The optimized construction of Ti2InB2 with high-precision settings is proven in Fig. 2b. The detailed constructions of Ti2InB2 and Ti2SnB2 are proven in Supplementary Figs. 2 and three, respectively. The expected Ti2InB2 and Ti2SnB2 compounds possess typical traits of identified MAX phases: a layered hexagonal construction (house group P(bar 6)m2 (No. 187), see particulars in Supplementary Desk 1), two M (Ti) layers, and one A (In) layer shut packed alongside an HCP A-B-A sequence. As a result of the B/Ti ratio (1.zero) in Ti2InB2 and Ti2SnB2 is greater than these of X/M ratios (half, 2/three or three/four) in typical MAX phases, boron atoms occupy the X websites between M layers and kind a graphene-like layer (Supplementary Figs. 2 and three) as an alternative of a aircraft of equilateral triangles. The variety of X (B) atoms per layer in Ti2InB2 or Ti2SnB2 is 2 occasions that for C- or N-containing MAX phases, which means the existence of B–B covalent bonds that would present a stiffer construction than typical MAX phases. Theoretical calculations (Supplementary Desk 2) present that Younger’s modulus alongside the x- and y-directions, i.e., within the aircraft of the boron layer, is far bigger than these for Ti2AlC or Ti3AlC2. Phonon stability for these two constructions was additionally confirmed (Supplementary Fig. four). Due to this fact, we conclude that a 212 B-containing MAX section could be fashioned as an alternative of the normal type of Mn+1AXn.

### Digital properties of predicted Ti2InB2

The digital constructions proven in Fig. 2c reveal that the expected B-containing ternary compound possesses typical digital options of MAX phases. Much like these identified MAX phases, this new B-containing MAX section is revealed to be metallic. It may be seen that for Ti2InB2, the bonding (antibonding) states between the d orbitals of Ti atoms and the p orbitals of B or In atoms are positioned under (above) the Fermi stage, whereas the non-bonding states of Ti are positioned between these bonding and antibonding states (close to the Fermi stage), and predominantly contribute to the metallic nature of Ti2InB2. This digital construction is qualitatively much like that for typical MAX phases. Electron localization perform (ELF) calculations confirmed that electron accumulation happens between adjoining boron atoms, which reveals the 2c–2e (two center-two electron) nature of the B–B bonds (Supplementary Fig. 5) in Ti2InB2, much like that in AlB2-type compounds, from which 2D hydrogen–boron sheets have been not too long ago obtained by way of cation trade29. Nonetheless, this case is totally different from that for typical boron clusters derived from electron-deficient multi-center 2e bonding30, the place crammed octets can’t be achieved by way of 2c–2e bonding with solely three valence electrons of boron. A Bader cost evaluation confirmed that zero.87|e| was transferred from a Ti to a B atom, which resulted within the formation of 2c–2e bonds between B atoms. It’s noteworthy to say that the cost separation of Ti and B and B–B 2c–2e bonds in Ti2InB2 is near the state of affairs in TiB2 (Supplementary Fig. 5). The boron atoms in MAB section Fe2AlB2 organize alongside B–B zig-zag chains by means of the formation of B–B 2c–2e bonding (Supplementary Fig. 5). Comparable digital options could be discovered for an additional predicted construction, Ti2SnB2, as proven in Supplementary Fig. 6.

### Chance of indium elimination from Ti2InB2

The interlayer A of MAX phases could be eliminated by etching with an acceptable acid, usually HF, which ends up in the formation of a collection of engaging supplies, MXenes6,31. To judge the potential of In elimination from Ti2InB2, the separation vitality for various interfaces alongside the [001] path of Ti2InB2 was calculated (Supplementary Fig. 7). The separation vitality for the Ti/In interface was discovered to be three.27 J m−2, whereas that for the Ti/B interface was eight.36 J m−2. Due to this fact, the bonding between A (In) and M (Ti) is far weaker than that between M (Ti) and X (B), and is much like that for the standard MAX phases that may be engineered to 2D MXenes. For a transparent comparability, the separation vitality for the Ti/Al(zero01) and Ti/C(zero01) interfaces of Ti2AlC was calculated to be 5.66 and 11.90 J m−2, respectively. The Ti–In bonding within the newly predicted MAX phases is far weaker than that for Ti-Al bonding in Ti2AlC. The Ti/In-to-Ti/B separation vitality ratio is 39%, which can be a lot smaller than the Ti/Al-to-Ti/C ratio of 48%. Consequently, the current calculations reveal the potential of acquiring 2-D MXenes from Ti2InB2 by selective elimination of indium by means of an acceptable strategy. Phonon dispersion calculations (Supplementary Fig. eight) present that the hexagonal TiB construction is dynamically secure. Nonetheless, our calculations present that the TiB orthorhombic constructions are thermodynamically extra secure (Supplementary Desk 1). This means that the elimination of indium beneath delicate situations (e.g., by chemical etching) might produce hexagonal TiB MXene, much like typical MXenes obtained by HF etching. Floor useful teams, like F, Cl, OH, and O, attributes considerably to the property modifications of typical MXenes. We studied the digital constructions of TiBX (X = F, Cl, OH, and O) and located that a metal-to-semimetal transition seems within the useful 2D TiB (Supplementary Fig. 9). Furthermore, the first-principles molecular dynamics (FPMD) simulations revealed that a section transition from hexagonal TiB to orthorhombic TiB compounds might happen because of the sturdy thermal activation of lattice vibrations beneath excessive temperature situations (Supplementary Fig. 10). The separation vitality for the Ti/Ti interface of orthorhombic TiB was calculated to be three.87 J m−2, which is comparable with that of Ti/In interface and signifies the laminated nature of TiB (Cmcm). The orthorhombic section (Cmcm) that reveals layered traits (Supplementary Fig. 11) was experimentally obtained beneath high-temperature situations and can be proven in a later part.

### Experimental synthesis and characterization of Ti2InB2

Ti2InB2 was synthesized from a combination of Ti, In and B powder by means of a solid-state response. The yield of Ti2InB2 was very delicate to the experimental situations, which have been optimized after many checks (See Strategies and Supplementary Figs. 12–17 and Desk three for particulars). Within the as-grown samples, there have been many impurities, which have been primarily TiB2 and Ti-In phases (Supplementary Figs. 13 and 14). Adjustment of the beginning compositional ratio of Ti, In and B enabled the ultimate yield of Ti2InB2 to be maximized, whereas the quantity of TiB2 was minimized (Supplementary Fig. 15). Ti–In section impurities could be eliminated by chemical etching, whereas TiB2 is extraordinarily secure (Supplementary Fig. 16). Due to this fact, after HCl acid etching, solely Ti2InB2 (93.7 wt%) and a small quantity of TiB2 (6.three wt%) remained, as proven in Fig. 3a, and the obtained Ti2InB2 was crystallized within the predicted construction (house group P(bar 6)m2). In a Rietveld evaluation, the optimum match was obtained by assuming a most well-liked orientation of (00l) for Ti2InB2, which steered a cloth with a lamellar crystal construction. A laminar construction was clearly evident from scanning electron microscopy (SEM) observations, as proven in Fig. 3b. That is in keeping with simulation outcomes, in that the separation vitality for the Ti/B interface is far bigger than that for the Ti/In interface, which means the potential of acquiring 2D TiB sheets by the selective elimination of In. The crystal construction was additional confirmed by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) (Fig. 3c). Remark alongside [001] path offers an atomic picture of Ti2InB2 within the x–y aircraft, with hexagonal patterns recording the projection of In and Ti atoms on the aircraft, which is in keeping with the prediction (Fig. 3d). A quick Fourier remodel (FFT) of the HAADF picture additionally signifies that Ti2InB2 crystallizes within the hexagonal construction. A homogenous composition ratio of Ti:In:B = 1.95:1:2.08 was confirmed by energy-dispersive X-ray spectroscopy (EDS) (Supplementary Fig. 17). The bodily properties of Ti2InB2 have been additionally measured and the outcomes are proven in Fig. 3e, f. The synthesized compound reveals metallic habits, which is in keeping with the digital construction calculations proven in Fig. 2c. Low temperature warmth capability (Cp) information (Fig. 3f) have been fitted nicely utilizing CP/T = γ + βT2, the place γ is the coefficient of the temperature-linear Cp (γT) that describes the contribution from conduction carriers, and β is the coefficient of the Debye T3 time period (βT3) related to propagating acoustic phonons.

Fig. three

Experimental characterization of synthesized Ti2InB2 compound after HCl etching. a Powder XRD sample with Rietveld evaluation utilizing GSAS bundle42. A small quantity of TiB2 is obvious. b SEM picture of a particle exhibiting a laminated construction. c HAADF-STEM picture from the [001] path. The inset exhibits the corresponding FFT sample. d Crystal construction considered from the z-direction (blue and purple spheres respectively point out Ti and In atoms). Boron just isn’t proven and the black strains characterize the unit cells. e Electrical resistivity. f Warmth capability plotted as C/T vs. T2 at low temperature. The crimson line represents a linear match to the info

### Synthesis of layered TiB

Following the standard etching methodology for producing MXenes, we first tried to acquire 2D TiB MXene by immersion of Ti2InB2 powder in 50% HF for 12 h at room temperature. This resulted in complete dissolution of the MAX section, and even TiB2 was dissolved given adequate time (Supplementary Fig. 18). Contemplating the intrinsically low melting level and excessive vapor strain of In metallic, a dealloying technique was adopted to exfoliate the In layers. SiC was used as an oxygen scavenger to forestall the oxidation of compounds in the course of the elimination of In at excessive temperature (Supplementary Fig. 19). The hypothetical dealloying response course of is described as:

$$mathrmTi_2_2 to 2 + mathrmIn(.)$$

(1)

Indium atoms have been steadily extracted from Ti2InB2 and coated on the interior wall of a silica glass tube outdoors the furnace (Supplementary Fig. 20); In was nearly utterly eliminated at 1050 °C for six days beneath vacuum situations (about 10−four Pa). The load loss for the pattern was in good settlement with the mass of In contained within the Ti2InB2 compound. Determine 4a and Supplementary Fig. 21 present that the primary dealloyed merchandise are TiB MX compounds with an orthorhombic construction (Cmcm), along with TiB2 as an impurity section within the ready Ti2InB2.

Fig. four

Construction characterization of layered TiB. a XRD patterns for samples ready by publicity of as-obtained Ti2InB2 powder to a vacuum (about 10−four Pa) as a perform of the temperature after 6 days. b Corresponding particular floor space change of samples in a. c Typical SEM picture of the TiB section obtained at 1050 °C for six days beneath vacuum (about 10−four Pa); inset exhibits the atomic ratio for this pattern. d HRTEM picture of the TiB section alongside the [01(bar 1)] path; inset exhibits the corresponding SAED sample. e Enlarged HRTEM picture from d exhibiting the interlayer spacing for the (111) and ((bar 1)11) planes. f Simulated crystal construction of the TiB section with orthorhombic group (Cmcm) alongside the [01(bar 1)] path, the place the blue spheres characterize Ti atoms (different atoms will not be proven)

The particular floor space elevated from 2.45 to six.16 m2 g−1 with rising heating temperature, which additionally signifies that In species have been steadily extracted from Ti2InB2 (Fig. 4b). Sadly, the lateral dimension of the mum or dad Ti2InB2 was not stored after In was extracted, and the obtained TiB confirmed smaller particle measurement than the mum or dad section however nonetheless with layered construction (SEM pictures in Fig. 4c), which signifies that the unique laminated construction was modified in the course of the dealloying course of at excessive temperatures. Nonetheless, the obtained TiB could be thought-about to be a layered materials the place the layers are linked by Ti-Ti metallic bonds as we mentioned above. An EDS evaluation (Supplementary Fig. 22) indicated the presence of primarily Ti and B with a molar ratio of ~1:1 and with nearly no In residue, which is in keeping with the XRD outcomes. A high-resolution transmission electron microscopy (HRTEM) picture was acquired alongside the [01(bar 1)] path of a TiB flake, which revealed vivid atomic columns organized in a square-like sample, straight similar to the stacked Ti atoms (Fig. 4d). An enlarged HRTEM picture (Fig. 4e) and the corresponding chosen space electron diffraction (SAED) sample (Fig. 4d inset) of exfoliated TiB flakes indicated an interplanar spacing of two.162 Å for the (111) aircraft, which is in keeping with the worth of two.127 Å obtained for the simulated construction (Fig. 4f). The (zero21) and (200) interplanar spacings have been additionally measured to be 2.462 and 1.588 Å, respectively, which is in settlement with the simulation outcomes (Supplementary Fig. 23). It must be famous that top temperature typically induces recrystallization, and leads to the formation of non-layered, bulk 3D cubic section by selective lack of the A ingredient from the MAX section32,33,34,35. Nonetheless, native displacements of Ti and B atoms brought on by the excessive temperature led to the era of an orthorhombic (Cmcm) section with a layered construction throughout elimination of the In species. As proven in Supplementary Fig. 24, we take into account this orthorhombic (Cmcm) section to have originated from a section change of hexagonal (P(bar 6m)2) with the same layered construction, which could be confirmed by the simulation outcomes of FPMD at 1273 Okay for 20 ps (Supplementary Fig. 10). After the FPMD simulation of 10 ps, the house group of TiB modified from P(bar 6)m2 to Cmcm primarily because of interlayer slip. With additional simulated warmth remedy of 10 extra picoseconds, the boron hexagonal rings grew to become collapsed and boron chains as an alternative appeared, which is the standard character of orthorhombic TiB (Supplementary Figs. 1 and 10). The actual time scale of section change from hexagonal TiB to orthorhombic section (Cmcm) could be too lengthy to be repeated by the FPMD simulations. Nonetheless, the simulation outcomes could be considered a theoretical assist for the section transition within the experiment. The phonon band constructions of orthorhombic TiB constructions with house teams of Pnma and Cmcm have been calculated and proven in Supplementary Fig. 25. Each constructions are discovered to be dynamically secure. Moreover, the computed free vitality (Supplementary Fig. 25) reveals that Pnma TiB is all the time extra secure than the Cmcm section within the full temperature vary from zero to 2000 Okay although the vitality distinction could be very small (round ~zero.005–zero.01 kJ mol−1). Which means that the prospect for the transition from Cmcm to Pnma could be little because of the weak thermodynamic driving power, which explains the experimental consequence that the metastable Cmcm section is the dominant product by warmth remedy at 1050 °C.

### Prospect of layered TiB as anode materials for ion batteries

Though impurities, akin to TiB2 and 3D TiB (Pnma), have been current, a brand new layered materials, TiB (Cmcm), was efficiently ready by dealloying the brand new Ti2InB2 MAX section. Though the layered TiB (Cmcm) just isn’t comparable with 2D MXenes, the profitable elimination of In atoms suggests the chance to acquire TiB MXene at delicate situations. Due to this fact, it’s mandatory to analyze the potential purposes of 2D TiB prematurely. To judge the thermal stability of the 2D TiB construction at elevated temperatures for purposes, we carried out FPMD simulations at 1273 and 1773 Okay for 10 ps (Supplementary Fig. 26). No signal of disruption or structural decomposition even within the 1773 Okay simulation. Due to this fact, it’s anticipated that 2D TiB can be secure at temperatures as excessive as 1773 Okay for sensible purposes. The intercalation of Li+ or Na+ ions between MXene sheets makes them promising supplies for Li- or Na-ion batteries. The cost/discharge response that ought to happen on the anode is: TiBLi(Na) ↔ TiB + Li+(Na+) + e−. To substantiate the potential of layered TiB as an anode materials for Li/Na ion batteries, adsorption of Li and Na atoms on the floor of a TiB monolayer was first studied utilizing DFT calculations. These calculations revealed that every TiB primitive cell (Ti2B2) can accommodate as much as two Li or two Na atoms (the adsorption of additional Li/Na atom can be thermodynamically unfavored.), which corresponds to a composition of TiBLi or TiBNa (Fig. 5a). Due to this fact, the theoretical particular capability of TiB for Li or Na ions was calculated to be 480 mAh g−1, which is considerably greater than these of the standard MXenes Ti3C2 (320 mAh/g for Li+)11, Ti2C (359 mAh g−1 for Na+)36 and even greater than that of the business anode materials, graphite (372 mAh g−1 for Li+)11. The open circuit voltage (OCV) for the intercalation reactions involving Li+ and Na+ ions on a TiB floor was respectively estimated to be as little as zero.33 and zero.17 V, respectively, that are each a lot smaller than that for Ti3C2 (zero.62 V for Li+) and comparable with that for graphite (about zero.2 V for Li+) and the hypothetical TiC3 (zero.18 V for Na+)11,36. The calculated ELF throughout the absorbed Li/Na atoms and TiB monolayer present that the electron cloud unfold out within the metallic layers can display screen the repulsion between the constructive metallic ions (Fig. 5a). A Bader cost evaluation revealed that the cost switch from absorbed Li atoms to the TiB monolayer was zero.80 |e|/Li, whereas one Na atom misplaced zero.48 |e| upon adsorption. Due to this fact, Li/Na atoms could be stabilized by the coulombic attraction between negatively charged B and positively charged Li/Na atoms.

Fig. 5

Adsorption and diffusion habits of Li and Na on 2D TiB (Cmcm). a ELF maps of a pristine TiB monolayer with one layer of Li atoms and one layer of Na atoms. b Thought-about diffusion paths for Li and Na on the TiB monolayer. c Calculated diffusion vitality obstacles alongside the paths in b. The purple and yellow spheres characterize Li and Na atoms, respectively

The diffusion vitality barrier for Li or Na on the TiB floor is important for figuring out the cost−discharge price in Li/Na ion batteries. The diffusion vitality barrier alongside three totally different pathways (Fig. 5b) between essentially the most secure nearest-neighboring adsorption websites of Li and Na on a three × three TiB supercell was calculated utilizing the climbing-image nudged elastic band (CI-NEB) methodology37. Determine 5b, c present that Li ions transfer alongside Path 1 and a couple of with decrease vitality obstacles of zero.11 and zero.16 eV, whereas Path three has the very best vitality barrier of zero.22 eV. Equally, for Na diffusion on the TiB floor, the vitality obstacles alongside Paths 1, 2, and three are respectively zero.08, zero.11, and zero.17 eV. Due to this fact, the brand new TiB monolayer ought to have a excessive charge-discharge price because of these computed low vitality obstacles for Li and Na diffusion, that are very aggressive with these for typical MXenes (e.g. zero.18 eV for Li diffusion on Ti3C2), graphite (zero.30 eV for Li diffusion), anatase TiO2 (zero.35–zero.65 eV for Li diffusion) and the expected TiC3 (zero.18 eV for Na diffusion)11,36. We famous that the diffusion activation vitality for Li+ and Na+ ions on oxidized TiB floor will get elevated (zero.31~zero.68 eV for Li+ and zero.22~zero.50 eV for Na+) however remains to be aggressive to the reported typical supplies (Supplementary Fig. 27). Contemplating the excessive particular capability, low OCV and low vitality obstacles for Li+ and Na+ ions, the 2D- TiB (Cmcm) could possibly be a promising various materials to the business graphite anode in Li/Na ion batteries. Furthermore, the diffusion of Li+/Na+ ions on hexagonal TiB floor was investigated (Supplementary Fig. 27), as a result of the current analysis signifies the chance to acquire TiB MXene at delicate situations. It exhibits that the diffusion vitality obstacles of Li+/Na+ ions on clear hexagonal TiB floor could be as little as round zero.02 eV. On the oxidized surfaces, the calculated vitality obstacles for Li+ and Na+ are, respectively, zero.23 and zero.19 eV.