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Register a new userThe role of Hume-Rotherys rules play in the MAX phases formability
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MAX phases are a family of layered, hexagonal-structure ternary carbides or nitrides of a transitional metal and an A-group element. What makes this type of material fascinating and potentially useful is their remarkable combinations of metallic and ceramic characteristics; as well as the indispensable role in top-down synthesis of their 2D counterparts, MXenes. To enhance the efficiency in the successful search for potential novel MAX phases, the main efforts could go toward creating an informationprediction system incorporating all MAX phases databases, as well as generally valid principles and the high-quality regularities. In this work, we employ structure mapping methodology, which has shown its merit of being useful guides in materials design, with Hume-Rothery parameters to provide guiding principles in the search of novel MAX phases. The formable/non-formable data on MAX phases can be ordered within a twodimensional plot by using proposed expression of geometrical and electron concentration factors.
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Chemical exfoliation of MAX phases into two-dimensional (2D) MXenes can be considered as a major breakthrough in the synthesis of novel 2D systems. To gain insight into the exfoliation possibility of MAX phases and to identify which MAX phases are promising candidates for successful exfoliation into 2D MXenes, we perform extensive electronic structure and phonon calculations, and determine the force constants, bond strengths, and static exfoliation energies of MAX phases to MXenes for 82 different experimentally synthesized crystalline MAX phases. Our results show a clear correlation between the force constants and the bond strengths. As the total force constant of an A atom contributed from the neighboring atoms is smaller, the exfoliation energy becomes smaller, thus making exfoliation easier. We propose 37 MAX phases for successful exfoliation into 2D Ti$_2$C, Ti$_3$C$_2$, Ti$_4$C$_3, $Ti$_5$C$_4$, Ti$_2$N, Zr$_2$C, Hf$_2$C, V$_2$C, V$_3$C$_2$, V$_4$C$_3$, Nb$_2$C, Nb$_5$C$_4$, Ta$_2$C, Ta$_5$C$_4$, Cr$_2$C, Cr$_2$N, and Mo$_2$C MXenes. In addition, we explore the effect of charge injection on MAX phases. We find that the injected charges, both electrons and holes, are mainly received by the transition metals. This is due to the electronic property of MAX phases that the states near the Fermi energy are mainly dominated by $d$ orbitals of the transition metals. For negatively charged MAX phases, the electrons injected cause swelling of the structure and elongation of the bond distances along the $c$ axis, which hence weakens the binding. For positively charged MAX phases, on the other hand, the bonds become shorter and stronger. Therefore, we predict that the electron injection by electrochemistry or gating techniques can significantly facilitate the exfoliation possibility of MAX phases to 2D MXenes.
The stability of Cr, V, Al carbide MAX phases, materials of interest for a variety of magnetic as well as high temperature applications, has been studied using density-functional-theory first-principles calculations. The enthalpy of mixing predicts these alloys to be unstable towards unmixing at 0 K. The calculations also predict, however, that these phases would be thermally stabilised by configurational entropy at temperatures well below the values used for synthesis. The temperature Ts below which they become unstable is found to be quite sensitive to the presence of magnetic moments on Cr ions, as well as to the materials magnetic order, in addition to chemical order and composition. Allowing for magnetism, the value of Ts for helf V and half Cr with chemically disordered Cr and V atoms, is estimated to be between 516 K and 645 K depending on the level of theory, while, if constrained to spin-paired, Ts drops to 142 K. Antiferromagnetic spin arrangements are found to be favoured at low temperatures, but they are most likely lost at synthesis temperatures, and probably at room temperature as well. However, the combination of antiferromagnetic frustration and configurational disorder should give rise to interesting spin textures at low temperatures.
A most basic and puzzling enigma in surface science is the description of the dissociative adsorption of O2 at the (111) surface of Al. Already for the sticking curve alone, the disagreement between experiment and results of state-of-the-art first-principles calculations can hardly be more dramatic. In this paper we show that this is caused by hitherto unaccounted spin selection rules, which give rise to a highly non-adiabatic behavior in the O2/Al(111) interaction. We also discuss problems caused by the insufficient accuracy of present-day exchange-correlation functionals.
Two dimensional (2D) ferromagnetic materials have attracted much attention in the fields of condensed matter physics and materials science, but their synthesis is still a challenge given their limitations on structural stability and susceptibility to oxidization. MAX phases nanolaminated ternary carbides or nitrides possess a unique crystal structure in which single-atom-thick A sublayers are interleaved by two dimensional MX slabs, providing nanostructured templates for designing 2D ferromagnetic materials if the non-magnetic A sublayers can be substituted replaced by magnetic elements. Here, we report three new ternary magnetic MAX phases (Ta2FeC, Ti2FeN and Nb2FeC) with A sublayers of single-atom-thick 2D iron through an isomorphous replacement reaction of MAX precursors (Ta2AlC, Ti2AlN and Nb2AlC) with a Lewis acid salts (FeCl2). All these MAX phases exhibit ferromagnetic (FM) behavior. The Curie temperature (Tc) of Ta2FeC and Nb2FeC MAX phase are 281 K and 291 K, respectively, i.e. close to room temperature. The saturation magnetization of these ternary magnetic MAX phases is almost two orders of magnitude higher than that of V2(Sn,Fe)C MAX phase whose A-site is partial substituted by Fe. Theoretical calculations on magnetic orderings of spin moments of Fe atoms in these nanolaminated magnetic MAX phases reveal that the magnetism can be mainly ascribed to intralayer exchange interaction of the 2D Fe atomic layers. Owning to the richness in composition of MAX phases, there is a large compositional space for constructing functional single-atom-thick 2D layers in materials using these nanolaminated templates.
A fundamental component of networking infras- tructure is the policy, used in routing tables and firewalls. Accordingly, there has been extensive study of policies. However, the theory of such policies indicates that the size of the decision tree for a policy is very large ( O((2n)d), where the policy has n rules and examines d features of packets). If this was indeed the case, the existing algorithms to detect anomalies, conflicts, and redundancies would not be tractable for practical policies (say, n = 1000 and d = 10). In this paper, we clear up this apparent paradox. Using the concept of rules in play, we calculate the actual upper bound on the size of the decision tree, and demonstrate how three other factors - narrow fields, singletons, and all-matches make the problem tractable in practice. We also show how this concept may be used to solve an open problem: pruning a policy to the minimum possible number of rules, without changing its meaning.
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