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[Ehsan Alibagheri](https://orcid.org/0009-0001-3005-3088), [Mohammad Khazaei](https://orcid.org/0000-0001-5093-1610), [Mehdi Estili](https://orcid.org/0000-0003-1465-8148), Alireza Seyfi, [Hiroshi Mizoguchi](https://orcid.org/0000-0002-0992-7449), Kaoru Ohno, [Hideo Hosono](https://orcid.org/0000-0001-9260-6728), [S. Mehdi Vaez Allaei](https://orcid.org/0000-0002-4713-3818)

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[LAX phases: A family of novel stable layered materials, informatics‐based discovery](https://mdr.nims.go.jp/datasets/76562c17-1005-4caa-82a0-29c19c2896b0)

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LAX phases: A family of novel stable layered materials, informatics‐based discoveryR E S E A R CH AR T I C L ELAX phases: A family of novel stable layered materials,informatics-based discoveryEhsan Alibagheri1 | Mohammad Khazaei1,2 | Mehdi Estili3 |Alireza Seyfi1 | Hiroshi Mizoguchi4 | Kaoru Ohno5 | Hideo Hosono4,6 |S. Mehdi Vaez Allaei1,71Department of Physics, University ofTehran, Tehran, Iran2School of Nano Science, Institute forResearch in Fundamental Sciences (IPM),Tehran, Iran3Research Center for Electronic andOptical Materials, National Institute forMaterials Science (NIMS), Tsukuba,Ibaraki, Japan4Research Center for MaterialsNanoarchitectonics (MANA), NationalInstitute for Materials Science (NIMS),Tsukuba, Ibaraki, Japan5Department of Physics, YokohamaNational University, Yokohama, Japan6MDX Research Center for ElementStrategy, International Research FrontiersInitiative, Yokohama, Japan7New Uzbekistan University, Tashkent,UzbekistanCorrespondenceEhsan Alibagheri, Mohammad Khazaei,and S. Mehdi Vaez Allaei, Department ofPhysics, University of Tehran, NorthKargar Avenue, Tehran 14395-547, Iran.Email: e.alibagheri@ut.ac.ir, mohammad.khazaei@ut.ac.ir, and smvaez@ut.ac.irFunding informationIran National Science Foundation,Grant/Award Number: 4025794; JapanSociety for the Promotion of Science,Grant/Award Number: 24K08211AbstractTernary MAX phases, characterized by the chemical formula M₂AX, representa group of layered materials with hexagonal lattices. These MAX phases havebeen the subject of extensive experimental and theoretical studies. Formationenergy and thermodynamic calculations indicate that MAX phases containinglate transition metals, such as Rh, Ru, Pt, Pd, Co, and Ni, are unlikely to form.Here, we introduce an alternative family of orthorhombic and monoclinicmaterials, the LAX phases, which exhibit similarities to MAX phases in termsof their layered structure and A and X elements. However, LAX materialsincorporate late transition metals in place of the early transition metals.Advanced techniques for predicting the crystal structure of materials, coupledwith data-driven materials research and machine learning algorithms, wereemployed to investigate the stable structures containing transition metals fromthe last groups of the d-block elements. The analyses revealed 207 ternary LAXsystems that demonstrate robust stability against decomposition, with 100 ofthese systems showing dynamic stability. An in-depth examination of the top10 structures revealed five LAX systems that are phase stable and exhibit supe-rior mechanical properties, outperforming MAX phase counterparts in Young'smodulus, stiffness, and hardness. These findings indicate that many LAXphase structures are viable candidates for future synthesis, highlighting thepotential of heuristic-based structure searches in material discovery.KEYWORD Sevolutionary algorithm, LAX phases, machine learning, materials discovery, materialsinformatics, MAX phasesReceived: 12 October 2024 Revised: 11 December 2024 Accepted: 16 December 2024DOI: 10.1002/inf2.12664This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, providedthe original work is properly cited.© 2025 The Author(s). InfoMat published by UESTC and John Wiley & Sons Australia, Ltd.InfoMat. 2025;e12664. wileyonlinelibrary.com/journal/infomat 1 of 11https://doi.org/10.1002/inf2.12664https://orcid.org/0009-0001-3005-3088https://orcid.org/0000-0001-5093-1610https://orcid.org/0000-0003-1465-8148https://orcid.org/0000-0001-9260-6728https://orcid.org/0000-0002-4713-3818mailto:e.alibagheri@ut.ac.irmailto:mohammad.khazaei@ut.ac.irmailto:mohammad.khazaei@ut.ac.irmailto:smvaez@ut.ac.irhttp://creativecommons.org/licenses/by/4.0/http://wileyonlinelibrary.com/journal/infomathttps://doi.org/10.1002/inf2.12664http://crossmark.crossref.org/dialog/?doi=10.1002%2Finf2.12664&domain=pdf&date_stamp=2025-02-171 | INTRODUCTIONThe study of layered materials represents a long-standingand intriguing area of research within the field of mate-rials science. Graphite and MAX phases are the mostwidely recognized materials in this field. Graphite exhibitsinterlayer bonding via van der Waals forces, whereasMAX phases constitute a distinct group of layered crystalswith covalent and/or metallic interlayer interactions.MAX phases were initially discovered in the 1960s and aredescribed by the chemical formula Mnþ1AXn where M isan early transition metal (Sc, Ti, Zr, Hf, V, Nb, Ta, Cr,and Mo), A is an element from groups 13–16 (e.g., Al, Ga,In, Bi, and Tl), and X can be carbon or nitrogen.1 MAXphases are composed of block layers of Mnþ1Xn inter-leaved with layers of the A-group elements.2–8 In additionto the MAX phases, a number of other layered materialshave been the subject of extensive investigations, eachoffering distinctive exotic properties.9–11 Over the past20 years, MAX phases have attracted significant attentionfrom the materials science community due to theirunique combination of metallic- and ceramic-like proper-ties. These phases are distinguished by their adaptabilityin elemental composition and crystal engineering whilemaintaining a layered structure.12–21 This characteristichas led to the development of various innovative MAXphase structures, including out-of-plane double transitionmetals MAX phases, in-plane double transition metalsMAX phases,22 high-entropy alloy MAX phases,23 andsuperlattice MAX phases.24 While the majority of MAXphase compounds exhibit metallic characteristics, a fewsemiconducting MAX phases have been proposed in thetheoretical literature.25 The fascination with this class ofmaterials lies not only in their rich chemistry and layeredstructure, but also in their mechanical properties. Theyoffer a distinctive combination of high-temperaturestrength, damage tolerance, and thermal shock resis-tance, rendering them highly desirable for a multitude ofindustrial applications.5,26–28 Understanding and optimiz-ing the mechanical behavior of MAX phases is crucial forenhancing their performance and expanding their appli-cation in sophisticated systems.The selection of early transition metals, such as scan-dium, titanium, vanadium, or chromium, which possessvarying atomic radii, valence electron numbers, and oxida-tion states, can influence the mechanical, electronic, andmagnetic properties of the resulting MAX phases.2,29,30These metals, typically found in groups IV–VI of the peri-odic table, possess a unique combination of properties thatmake them ideal candidates for forming robust and stablestructures that are characteristic of MAX phases. Thecapacity of MAX phases to accommodate a range ofA-group elements while maintaining structural integrityfurther enriches their chemical compositions, therebyenhancing their exotic properties for potential applicationsin sophisticated technologies.29,31–36 The recent progress inadding and predicting new M, A, and X elements is attrac-tive for achieving additional new members in this fam-ily.37,38 Early transition metals are commonly employed asthe M elements in MAX phase structures, whereas middleand late transition metals are less widely used. This can beattributed to a number of factors, including the number ofvalence electrons, the atomic radii of the M, A, and X ele-ments, and the bond strength in M-X and M-A bonds.Additionally, the existence of stable competitive crystalswith the same stoichiometry may also play a role. In MAXphases, the strong M-X bonds play a pivotal rolein enhancing the structural stability of these materials.Essentially, the Mnþ1Xn blocks serve as the fundamentalbuilding blocks of MAX phases. Beyond their composi-tion and structure, the mechanical properties of MAXphase materials represent a significant area of interestand exploration.39–45By utilizing computational algorithms and data-drivenmodels, researchers can accelerate the exploration anddevelopment of new MAX phases with customized proper-ties.46,47 The analysis of structures and the identification ofpotential candidates for diverse technological applicationsare enabled by machine learning (ML) models trained onchemical datasets.34,48–50 The efficacy of ML algorithms intackling physics-related problems is evident, particularlyin their effectiveness in classification and regressionmodels, which depend on the desired properties.51–57In order to propose a novel structure for MAX phasescontaining middle and late transition metals, we conducteda comprehensive analysis of the dynamic stability of MAXphases composed of late transition metals that exhibit nega-tive phonon frequencies. Using the phonon eigenvectors ofthe negative phonon modes of these structures, we devel-oped modulated structures of MAX phases. Our detailedanalysis led to the discovery of an orthorhombic and mono-clinic lattice structure with symmetry groups 59 (Pmmn)and 11 (P2_1/m), respectively, which resembles the layeredstructure of MAX phases, as depicted in Figure 1. Two anal-ogous structures (Ni2InP58 and Ni2SnP59) were previouslysynthesized with symmetry groups 13 (P2/c) and62 (Pnma), respectively. The two structures have differentlattice parameters and are situated along the stability linewith LAX structures. The novel structure exhibitedenhanced energetic stability in comparison to the originalMAX phase structure and did not display any negativephonon modes. Henceforth, we will refer to these struc-tures as LAX phases, which exhibit similarities to MAXphases but utilize late or middle transition metals.In order to ascertain the reliability of our proposedLAX design as a viable choice for MAX phases containing2 of 11 ALIBAGHERI ET AL. 25673165, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/inf2.12664 by National Institute For, Wiley Online Library on [19/02/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensemiddle or late transition metals, we have conducted anexhaustive search of our compiled dataset of 702 ternaryL2AX structures. Computational algorithms and data-driven models were employed to expedite the investiga-tion of synthesizable L2AX phases. In particular, MLmodels trained on chemical datasets are utilized to ana-lyze structures and identify potential candidates. Uponcomparing the MAX and LAX phases with similar ele-mental compositions and extracting their energetics andstructural parameters into the ML model, we identified264 energetically stable structures. Following thedynamic stability tests, 100 of these structures were foundto be dynamically stable. Subsequently, we analyzed the10 most stable structures identified in the previous step,and subjected them to more expensive phase stabilitytests using the evolutionary algorithm. Consequently, wesucceeded in identifying five structures with dynamic,mechanical, and phase stability, which are even mechan-ically superior to the MAX phase counterparts derivedfrom the late transition metals with the symmetry groups59 (Pmmn) and 11 (P2_1/m).2 | DATA PREPARATIONIn order to identify synthesizable LAX phases, we ini-tially gathered a comprehensive collection of L2AXphases, consisting of L elements exclusively fromtransition metals (highlighted in red in Figure 1), A-siteelements primarily sourced from pnictogens, chalcogens,halogens, carbon group, boron group, and transitionmetals (highlighted in blue in Figure 1), and X elementsencompassing C, N, B, P, S, and Si (emphasized in bluein Figure 1). A total of 702 L2AX structures were subse-quently created with orthorhombic symmetry groupPmmn (space group No. 59). The unit cells of the struc-tures consist of eight atoms each. The structures werefully optimized in order to determine their formationenergy. Notably, 54% of these structures showed negativeformation energy. A positive (negative) formation energyindicates a low (high) probability of the structure beingformed from isolated components.For driving information from the structures in bothMAX and LAX phase materials, the matminner60featurizer is employed (see Supporting Information 1).Furthermore, all distances between elements in compo-nents (M-A, M-X, A-X in MAX phases and L-A, L-X, andA-X in LAX phases) were extracted from the structures asthe other descriptors.3 | RESULTS AND DISCUSSIONThe formation energies of relaxed MAX and LAX structureswere analyzed in order to gain a deeper understanding of therole of elements in each structural category. The formationenergies of LAX and MAX phases were calculated accordingto the equation: Ef ¼Et MAXorLAXð Þ�2Et MorLð Þ�EtAð Þ�Et Xð Þ, where Et MAXorLAXð Þ is the total energy ofMAX or LAX phases and Et MorLð Þ, Et Að Þ, and Et Xð Þ,are the calculated total energy of M or L, A, and X intheir ground-state crystal structures. Figure S1 illustratesFIGURE 1 Crystal structure and composition window of the discovered LAX phases. (A) The elements utilized, such as L, A, and X, arehighlighted. (B–D) The 4–2-2 structures from directions of 1–0–0, 0–0–1, and 0–1–0, respectively. (E) A 3D illustration of the unit cell.ALIBAGHERI ET AL. 3 of 11 25673165, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/inf2.12664 by National Institute For, Wiley Online Library on [19/02/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensethe variation in formation energy among 702 systemswith similar LAX structures. In 92% of cases, the forma-tion energies of LAX structures are more negative com-pared to MAX phase crystals, with only 23 exceptions(Supporting Information 1). The formation energies ofLAX phases vary depending on the specific X element pre-sent. The formation energy is approximately �0.2 eV/atomfor the carbon and nitrogen categories, while for the otherfour categories, it is higher than �0.5 eV/atom (Figure 2).The lower formation energies observed in ternary struc-tures containing carbon and nitrogen can be attributed tothe stability of the bonds formed by these elements andthe unique bonding characteristics of other elements. Cer-tain M elements in LAX structures, such as Pd and Ru,contribute to the formation of less stable structures basedon formation energy (Figure 2). On the other hand, Rh, Pt,and Ir lead to more stable structures in boron structurescontaining Al. Indeed, aluminum plays a significant rolein achieving more negative formation energy values in themajority of structures, with the exception of sulfides.From a pool of 456 structures, those with negative for-mation energy values were selected for final screening.Our process involves the execution of two-step calcula-tions to classify structures as having a high likelihood ofsynthesis or otherwise. Initially, the formation energiesof the chosen 456 systems are compared with the forma-tion energies derived from the competing phase struc-tures extracted from the quantum materials database(OQMD) repository. This screening methodology yieldssatisfactory results, as shown in previous studies.38,61 Inother words, we examine the relative formation energy(ΔH) of LAX structures in comparison to the formationenergy of the most competitive phases sourced from theOQMD materials database, where ΔH¼ELAXf �Ecomf andEcomf is the formation energy of the competing phase ofbinary structures. Furthermore, all the energies of themost competitive classes can be found in the openOQMD.62,63 In MAX system, it has been noted that MAXphases with a maximum ΔH of approximately 0.12 eV/atom have been successfully synthesized.61 Therefore, inorder to conduct a more comprehensive analysis of LAXcompounds, we have established 0.2 eV/atom as thethreshold for identifying LAX candidates with a highprobability of synthesis (see Supporting Information 1).FIGURE 2 The formation energy (eV/atom) results for all 702 LAX phase structures for the X elements of boron, carbon, nitrogen,phosphor, sulfur, and silicon. Larger formation energy is depicted with large circles.4 of 11 ALIBAGHERI ET AL. 25673165, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/inf2.12664 by National Institute For, Wiley Online Library on [19/02/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons LicenseIncreasing the threshold value will permit to retain agreater number of compounds for the subsequent stage ofour analysis, thus ensuring that no crucial LAX phase isoverlooked. In the subsequent stage, we implement theML algorithm that was efficiently crafted in our earliercomputations for haeckelite configurations.56 The modelaccurately predicted the relative formation energy in rela-tion to the convex hull. It has been demonstrated thatstructures with high synthesizability have formationenergies below Ehull+0.05 eV/atom.64,65 In this process,we utilize 52 structural descriptors and implement therandom forest regression model. The energy abovethe hull is predicted through 10-fold cross-validationusing the material project datasets. The top 264 compo-nents are selected based on their superior energy abovethe hull. Subsequently, LAX structures that satisfythe established criteria are selected for further analysis(see Supporting Information).We analyzed the differences between MAX and LAXstructures by obtaining descriptors from 702 LAX struc-tures and their corresponding stoichiometry compoundsin MAX phases. The descriptors were classified into twocategories. The first category comprised the structuralinformation, including mass density, x-ray diffractiondata, and valence band concentration of each structure.The second category involved the extrapolation of the dis-tance between each element, which was calculated usingthe following equation: dij ¼ rj� ri� �n1 . In this equation,d represents the distance between elements, r is the posi-tion of each element, and n is the number of elements inthe structures. A total of 162 features were generated andvisualized using t-distributed stochastic neighbor embed-ding (t-SNE).66 The application of t-SNE in this contextcan be extremely beneficial for uncovering complexpatterns within the dataset. Figure 3A demonstrates theexcellent distribution of MAX and LAX data clustersbased on these descriptors, revealing a distinct and clearseparation between them. A total of 264 compounds wereidentified in the preceding two stages and subsequentlysubjected to an assessment of their dynamic stabilitythrough phonon spectra calculations (see SupportingInformation 2). Out of these, 100 were found to bedynamically stable, with no imaginary phonon fre-quency. The structures that satisfied the stability criteriacompared to competing phases, are subjected to furtherevaluation of phase stability using evolutionary algo-rithms with the USPEX code. Out of the 10 best struc-tures identified through evolutionary algorithms search,Ir2InP, Ir2SnSi, and Pt2GaSi lie on the convex hull line.Ni2SnP and Ni2InP have a distance of 0.017 and0.013 eV/atom, while the remaining five structures aresituated at a distance of approximately 0.02–0.1 eV/atomfrom the stability line (Supporting Information 1).The electronic band structure is considered for inves-tigation of the electronic nature of the identified LAXphases. Figure 4A shows the calculated electronic bandstructure of Ir2InP. Due to the overlapping of the conduc-tion and valence bands, there is no band gap at the Fermilevel. The Fermi level crosses the valence bands and con-duction bands. The metallic behavior can be observed inall LAX structures, as shown in Figure 4 and SupportingInformation. The density of states (DOS) of the most sta-ble structure, namely Ir2InP, is predominantly influencedby the presence of Ir, as demonstrated in Figure 5A.Notably, the 5d orbitals of Ir play a significant role at theFermi level, as evidenced by their substantial orbital con-tributions, as shown in Figure 4B. Furthermore, we haveanalyzed the partial DOS (PDOS), revealing that, apartFIGURE 3 (A) The t-SNE diagram of two classes of LAX and MAX structures. (B) The convex hull diagram of Ir2InP, where the greencircle illustrates the stable structures. The range of color is in eV/atom.ALIBAGHERI ET AL. 5 of 11 25673165, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/inf2.12664 by National Institute For, Wiley Online Library on [19/02/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensefrom 5d(Ir), 3p(P), and 5 s(In) orbitals having the mostprominent contributions at the Fermi energy, otherorbitals do not actively participate in the PDOS at theFermi level. Moreover, the crystal orbital Hamilton popu-lation (COHP) analysis for Ir2InP, as illustrated inFigure 4C, demonstrates that the COHP values exhibitnegativity below the Fermi energy and positivity aboveit. The Fermi level is situated within the COHP curve,which marks the shift from bonding to antibondingareas. This signifies the presence of solely bonding statesin the respective bonds, consequently boosting the stabil-ity of the structures. As illustrated in Figure 4B, theCOHP curves for Ir2InP indicates substantial antibondinginteractions at the Fermi level. The conduction band(CB) is comprised of states formed by d(Ir), s(In), andp(P) orbitals up to approximately 2 eV, while the higher-energy states are predominantly derived from Iridium's6s, 5p, and 4f orbitals. In contrast, the valence band ispredominately influenced by the d(Ir) states within theenergy range of �5 to 0 eV.In order to gain a deeper insight into the mechanicalstability of the final LAX phase structures, we have com-puted the elastic constants of the four final structures andcompared them with their respective MAX phase struc-tures. The elastic constants were determined via thestrain-energy method. All five stable LAX phases satisfythe Born stability criteria, thereby signifying their mechan-ical robustness (see Supporting Information 1). As for theMAX phase structures, all are mechanically stable, withthe exception of the Pt2GaSi structure. The mechanicalcharacteristics of the final structures exhibit a more pro-nounced distinction between the LAX and MAX struc-tures. The elastic constants have been computed and areprovided in Supporting Information. These constantsprovide further insights into the structures. Addi-tional data may be obtained by employing the stiffnessconstants obtained. In particular, the elastic constantsC11 and C33 are indicative of the solid's stiffness in thea-axis and c-axis orientations, when pressure is appliedalong the [100] and [001] crystallographic directions,respectively.In the MAX and LAX configurations, C11 surpassesC33, suggesting greater resistance to deformation alongthe ab lattices in comparison to the c-axis. Moreover, thedifference between these constants highlights the aniso-tropic bonding strength of the configurations. In compar-ison to other elastic constants, C44 is a more reliablemeasure of hardness. With the exception of Ir2SnSi, allLAX configurations exhibit higher hardness values thantheir respective MAX phases.67Moreover, the mechanical properties of the LAXphase exhibit significantly superior characteristics incomparison to the MAX phase. Additionally, the incorpo-ration of late transition metals enhances interlayer bond-ing, contributing to enhanced stability and mechanicalperformance (Supporting Information 1). For instance, inthe LAX phase Ni2SnSi, the Young's modulus rangesfrom 52.05 to 229.89GPa with an average value of133.13GPa (Hill average for polycrystal). This high valueindicates a significant resistance to deformation. In con-trast, the Young's modulus for the MAX phase exhibits arange of 23.18 to 129.95GPa, with an average Hill valueof 59.70GPa. This reflects a markedly lower stiffness andstructural resilience. The Vickers hardness of the LAXphase is in the range of 4.10 to 5.58GPa on average. Incontrast, the MAX phase shows a lower hardness range,typically from negative values (which suggests non-ductile behavior in some samples) up to 1.84GPa. TheFIGURE 4 (A) The band structure, DOS, projected DOS (PDOS (states/eV/cell)), and (B) crystal orbital Hamilton population (COHP(1/eV)) analysis for Ir2InP. The Fermi is set at zero.6 of 11 ALIBAGHERI ET AL. 25673165, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/inf2.12664 by National Institute For, Wiley Online Library on [19/02/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons LicenseLAX phase thus demonstrates superior wear resistance,which is essential for applications involving mechanicalstress. The bulk modulus of the LAX phase ranged from97.49 to 221.16GPa, in comparison to the MAX phase,which spans from 55.24 to 245.96GPa. The consistency ofthe LAX values indicates a more stable structure underFIGURE 5 The Young's modulus distribution of the two synthesizable systems of (A, B) Ir2InP and (C, D) Ni2SnP having the LAX andMAX structures.TABLE 1 The mechanical parameters of synthesizable LAX structures in comparison to their similar MAX structures.Structure Formula B (GPa) Y (GPa) S (GPa) v (GPa) B/G Debye (K) VH (GPa) Pc (GPa)Space groupnumberLAX Ir2InP 170.151 180.667 68.278 0.32 2.49 298 6.48 51.2 59Ir2SnSi 200.963 224.223 85.322 0.31 2.36 331.1 8.09 69.0 59Ni2SnP 128.485 136.071 51.406 0.32 2.50 356.1 5.283 31.5 59Ni2InP 136.137 127.797 47.560 0.34 2.86 343.9 4.285 47.1 59Ni2SnSi 148.063 133.133 49.304 0.35 3.00 349.5 4.162 65.9 11Pt2GaSi 170.988 185.704 70.396 0.32 2.43 309.6 6.818 97.4 11MAX Ir2InP 116.459 101.354 37.401 0.36 3.11 221.1 3.285 72.9 194Ir2SnSi 191.669 185.507 69.287 0.34 2.77 299.2 5.815 102.5 194Ni2SnP 98.9490 64.470 23.167 0.39 4.27 241.2 1.634 92.2 194Ni2SnSi 122.007 59.702 21.045 0.42 5.80 230.9 1.078 118.1 194Ni2InP 115.240 80.683 29.163 0.38 3.95 270.9 2.101 103.8 194Note: The bold structure is situated at a distance of 0.038 eV/atom distance from the convex hull, while the remaining five structures are positioned along theconvex energy line. Similar structures in MAX phases are unavailable due to their mechanical instability.ALIBAGHERI ET AL. 7 of 11 25673165, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/inf2.12664 by National Institute For, Wiley Online Library on [19/02/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensepressure. Similarly, the average shear modulus for LAX is49.30GPa, in comparison to the MAX phase, whichreports values from 6.30 to 46.75GPa, indicating anenhanced capacity to withstand shear stress in LAX. Themechanical superiority of LAX phases can be attributedto their unique layered crystal structure incorporatinglate transition metals, which are known for higher bond-ing strength and improved load-bearing capabilities. Theincreased anisotropy observed in LAX phases (withanisotropic ratios of 4.417 for Young's modulus in com-parison to 5.605 for the MAX phase) suggests that themechanical properties can be extensively tailoredaccording to the loading direction, thereby offeringgreater flexibility in application. Similarly, this compara-tive analysis repeated in other final structures highlightsthe mechanical advantages of LAX materials. The bulkmodulus and shear modulus are frequently employed toanalyze how materials respond to pressure and rigidityunder pressure, respectively. These moduli are employedto study pure deformations, including changes in volumeand shape. According to Table 1, MAX phases have lowerbulk moduli than LAX systems with similar composition,indicating the lowest resistance to hydrostatic pressure.On the other hand, Ni2SnP demonstrates the lowest resis-tance to plastic deformation among the compoundsunder investigation. Young's modulus, represented by Y,is a measure of the rigidity of solids and establishes arelationship between this characteristic and thermalshock resistance (TSR) in an inversely proportional man-ner. Thus, a solid with a high Y value indicates highrigidity and low TSR. Consequently, the Y values of theLAX structures are higher than those of the MAX struc-tures (Table 1, Figure 5). While these moduli do notdirectly reflect hardness, they tend to be higher for mate-rials with greater rigidity.68 Furthermore, the stiffnessconstants are utilized to predict whether MAX phasesexhibit ductile or brittle properties by calculating CauchyPressure (CP). The difference between C11 and C44 repre-sents the CP, whereby a negative or positive value indi-cates brittle or ductile behavior, respectively. Moreover,negative and positive values indicate the existence ofdirectional covalent and ionic bonds, respectively. InTable 1, all MAX and LAX materials possess covalentbonds and exhibit ductile characteristics. The Vickershardness (VH) of a solid gauges its ability to withstanddeformation under extreme conditions, primarily deter-mined by the strength of atomic bonds within the mate-rial. A variety of factors, including atomic arrangement,defects, and other related characteristics, also affect theVH of solids.69 The VH of LAX structures is significantlygreater, being two to three times higher than that of theMAX components. This distinction can be attributed tothe bond overlap population, which is particularlysuitable for partial metallic systems. The increased VH ofthese structures may be attributed to the robust covalentbonding between L-X atoms, as opposed to M-X atoms.In MAX phases, the M-A bond is weaker than the cova-lent M-X bond due to electron interactions within thematerial.70–72 MAX phases exhibit weaker M-A bondsthan the covalent M-X bonds due to electron interactionsin the material. The d electrons of M atoms interact withthe s and p orbitals of X atoms, which results in strongcovalent bonds in MAX structures. Conversely, the M-Abonds are predominantly metallic, leading to a weakerbond than the M-X bond. The bond distances of the M-Xand M-A bonds in MAX phases are greater than those ofL-X and L-A in LAX structures, indicating stronger bondstrengths in LAX structures. Furthermore, the electronconcentration in the structures also affects the bondingcharacteristics of MAX phases and, similarly, of LAXphases, influencing the filling of bonding, nonbonding,and antibonding states. A deficiency of electrons canresult in partially unfilled bonding, while an excess ofvalence electrons can lead to overly filled antibondingstates, which in turn causes instability in both cases.4 | CONCLUSIONOur investigation has led to the discovery of a novel fam-ily of ternary layered transition metal compounds, desig-nated as LAX phases. These materials present themselvesas a viable alternative to MAX phase structures by incor-porating late transition metals from the last groups of thed-block elements. Through utilizing advanced crystalstructure prediction techniques, data-centric materialsresearch, and the potential of ML, we have successfullyidentified several synthesizable LAX compounds thatboast superior mechanical properties compared to tradi-tional MAX phase materials. Our comprehensive stabilityevaluations, which encompass dynamic, mechanical, andphase stability in conjunction with structural characteris-tics, have provided a detailed insight into the potential ofthese innovative materials. A key distinguishable differ-ence between the MAX and LAX structures is thatwhen P, S, and Si are used as the X elements in combina-tion with the last transition metals as the M elements,the stable structures converge toward the LAX systemsrather than the MAX phases. Furthermore, analogous tothe process of deriving MXenes from MAX phases via thechemical elimination of A elements, it is anticipated thatby etching A elements from LAX phases, 2D materials,designated as LXenes, can be synthesized. It is antici-pated that LXenes, like their MXene counterparts, willexhibit outstanding characteristics, including enhancedsurface area and tunable electronic properties, rendering8 of 11 ALIBAGHERI ET AL. 25673165, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/inf2.12664 by National Institute For, Wiley Online Library on [19/02/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensethem suitable for various energy and device technologyapplications. It is noteworthy that LXenes, which are com-posed of late transition metals, are predicted to demon-strate superior catalytic performance suitable for variouscatalytic applications. Late transition metals are renownedfor their superior catalytic activities, highlighting their vastpotential for diverse applications in catalysis. This studypushes the boundaries of existing layered materials andunderscores the impact of informatics-driven materialexploration in catalyzing innovation and breakthroughs inmaterials science. The success of our heuristic-based struc-ture searches suggests a promising avenue for future mate-rials discovery, paving the way for expedited explorationand creating cutting-edge materials with unparalleledproperties for sophisticated applications.5 | EXPERIMENTAL SECTIONIn this research, we conducted first-principles calcula-tions using the Perdew–Burke–Ernzerhof (PBE)73 func-tional within the generalized gradient approximation(GGA) framework and the projector augmented wavemethod (PAW) potentials74 with the Vienna Ab initioSimulation Package (VASP).75 Using the conjugate gradi-ent method, we used a plane wave cutoff energy of520 eV to expand the wave functions and optimizeatomic positions and lattice parameters. The total energyconverged to a value less than 0.00001 meV/cell, and theacting force on each atom in the optimized structureswas below 0.0005 eV/Ǻ. We used fine Monkhorst–Pack76k-point meshes of 2π � 0.04 Å�1to thoroughly samplethe Brillouin zone for structural optimizations and totalenergy calculations. Furthermore, we obtained phonondispersion spectra based on the finite displacementmethod using the PHONOPY code.77,78 Phonon calcula-tions utilized a 3� 3� 1 or 4� 4� 1 supercell, whichprovided comprehensive insight into the material's vibra-tional properties.The USPEX, an evolutionary algorithm, was employed toperform structural investigations. It is a well-established soft-ware known for accurately anticipating new phases of bulkor 2D materials.79–83 The minimum global structure of bulksystems, a population size of 200 individuals per generation,was employed, with the number of generations ranging from220 to 250 based on the seed structure's contribution. In sub-sequent generations, a particle swarm optimization schemedetermined 50% of the population from the previous genera-tion's best structure, while the remaining 50% was randomlygenerated to maintain population diversity.An ML model was utilized to examine the phase sta-bility of structures. The Materials Project datasets weretrained to predict the energy above the hull of LAXphases using a nine-regression model with 52 descriptors.The model achieved a mean absolute error (MAE) of0.05 eV/atom for energy above the hull, which wasreported in our previous work.56ACKNOWLEDGMENTSThe authors sincerely thank the crew of the Center for Com-putational Materials Science of Institute for MaterialsResearch, Tohoku University, for their continuous support ofthe supercomputing facilities (Project No. 202112-SCKXX-0501). M.K. acknowledges the support of the Iran NationalScience Foundation (INSF) through grant number 4025794.M.E. acknowledges the support of the JSPS Kakenhi Grant-in-Aid for Scientific Research (24K08211).CONFLICT OF INTEREST STATEMENTThe authors declare no conflict of interest.ORCIDEhsan Alibagheri https://orcid.org/0009-0001-3005-3088Mohammad Khazaei https://orcid.org/0000-0001-5093-1610Mehdi Estili https://orcid.org/0000-0003-1465-8148Hideo Hosono https://orcid.org/0000-0001-9260-6728S. Mehdi Vaez Allaei https://orcid.org/0000-0002-4713-3818REFERENCES1. Nowotny VH. Strukturchemie einiger Verbindungen derÜbergangsmetalle mit den elementen C, Si, Ge, Sn. Prog SolidState Chem. 1971;5:27-70.2. Barsoum MW. The MN+1AXN phases: a new class of solids.Prog Solid State Chem. 2000;28(1):201-281.3. Khazaei M, Arai M, Sasaki T, Estili M, Sakka Y. 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Phys Chem Chem Phys. 2021;23(46):26178-26184.SUPPORTING INFORMATIONAdditional supporting information can be found onlinein the Supporting Information section at the end of thisarticle.How to cite this article: Alibagheri E,Khazaei M, Estili M, et al. LAX phases: A family ofnovel stable layered materials, informatics-baseddiscovery. InfoMat. 2025;e12664. doi:10.1002/inf2.12664ALIBAGHERI ET AL. 11 of 11 25673165, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/inf2.12664 by National Institute For, Wiley Online Library on [19/02/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licenseinfo:doi/10.1002/inf2.12664info:doi/10.1002/inf2.12664 LAX phases: A family of novel stable layered materials, informatics‐based discovery Abstract 1  |  INTRODUCTION 2  |  DATA PREPARATION 3  |  RESULTS AND DISCUSSION 4  |  CONCLUSION 5  |  EXPERIMENTAL SECTION ACKNOWLEDGMENTS CONFLICT OF INTEREST STATEMENT ORCID REFERENCES SUPPORTING INFORMATION