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1. Synthesis and Li-ion electrode properties of layered MAB phases Ni _n+1 ZnB _n ( n = 1, 2)

   https://doi.org/10.1039/c9ta12937e  

   Rezaie, Amir A.; Yan, Zheng; Scheifers, Jan P.; Zhang, Jian; Guo, Juchen; Fokwa, Boniface P. (January 2020, Journal of Materials Chemistry A)

   null (Ed.)

   Ternary MAB phases (layered transition metal borides) have recently attracted interest due to their exfoliation potential toward MBenes (analogous to MXenes), which are predicted to have excellent Li-ion battery performance. We have achieved single-phase synthesis of two MAB phases with general composition Ni n+1 ZnB n ( n = 1, 2), the crystal structures of which contain zinc layers sandwiched between thin ( n = 1) and thick ( n = 2) Ni–B slabs. Highly stacked MAB sheets were confirmed by X-ray diffraction and high-resolution scanning electron microscopy for both materials. Exposing Ni n+1 ZnB n to diluted hydrochloric acid led to the creation of crystalline microporous structures for n = 1 and non-porous detached sheets for n = 2. Both morphologies transformed the inactive bulk materials into highly active Li-ion battery anodes with capacities of ∼90 mA h g −1 ( n = 1) and ∼70 mA h g −1 ( n = 2) at a 100 mA g −1 lithiation–delithiation rate. The XPS analysis and BET surface area measurements reveal that the increased surface area and the reversible redox reaction of oxidized nickel species are responsible for this drastic increase of the lithiation–delithiation capacity. This proof of concept opens new avenues for the development of porous MAB, MAB nanosheets, MBenes and their composites for metal-ion battery applications. 

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2. Concatenating Bipartite Graphs

   https://doi.org/10.37236/8451  

   Chudnovsky, Maria; Hompe, Patrick; Scott, Alex; Seymour, Paul; Spirkl, Sophie (April 2022, The Electronic Journal of Combinatorics)

   Let $$x,y\in (0,1]$$, and let $A,B,C$ be disjoint nonempty stable subsets of a graph $$G$$, where every vertex in $$A$$ has at least $x|B|$ neighbours in $$B$$, and every vertex in $$B$$ has at least $y|C|$ neighbours in $$C$$, and there are no edges between $A,C$. We denote by $$\phi(x,y)$$ the maximum $$z$$ such that, in all such graphs $$G$$, there is a vertex $$v\in C$$ that is joined to at least $z|A|$ vertices in $$A$$ by two-edge paths. This function has some interesting properties: we show, for instance, that $$\phi(x,y)=\phi(y,x)$$ for all $x,y$, and there is a discontinuity in $$\phi(x,x)$$ when $1/x$ is an integer. For $z=1/2, 2/3,1/3,3/4,2/5,3/5$, we try to find the (complicated) boundary between the set of pairs $(x,y)$ with $$\phi(x,y)\ge z$$ and the pairs with $$\phi(x,y)1/3$. 

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3. From Metals to Semiconductors: Advancing MXY (M = Ti, Sn, Ir, X = Se, Te, Y = Se, Te) Compounds with Strain Engineering—A Computational Perspective

   https://doi.org/10.1002/adem.202401492  

   Aldaoseri, Munaf; Nourbakhsh, Zahra; Vashaee, Daryoosh (September 2024, Advanced Engineering Materials)

   In this computational study, density functional theory (DFT) is employed to analyze the structural, electronic, elastic, and topological properties of ternary compounds MXY (M = Ti, Sn, Ir, X = Se, Te, Y = Se, Te). The effects of spin–orbit interaction and pressure‐induced strain are investigated to understand their influence on the stability, mechanical properties, and electronic behavior, paving the way for potential technological applications. The findings confirm that these compounds are inherently stable in nonmagnetic phases, with spin–orbit interaction critically influencing their energy–volume landscapes. The calculated lattice parameters, ratios of lattice constants, and bulk moduli closely align with existing data, confirming the reliability of our approach. Mechanical assessments reveal distinct behaviors: IrSe₂exhibits the highest stiffness due to pronounced covalent bonding, contrasting with SnTe₂'s elastic anisotropy and SnSeTe's nearly isotropic properties. Electronically, most compounds show metallic characteristics, except SnSe₂, which behaves as a semiconductor with an indirect, pressure‐sensitive energy bandgap. Topological analysis under varying hydrostatic pressures indicates band inversions in TiSe₂, IrSe₂, and SnSeTe, suggesting topological phase transitions absent in other compounds. This study enriches our understanding of these materials and refines the application of DFT in material design. 

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4. Triforce and corners

   https://doi.org/10.1017/s0305004119000173  

   FOX, JACOB; SAH, ASHWIN; SAWHNEY, MEHTAAB; STONER, DAVID; ZHAO, YUFEI (July 2020, Mathematical Proceedings of the Cambridge Philosophical Society)

   Abstract May the triforce be the 3-uniform hypergraph on six vertices with edges {123′, 12′3, 1′23}. We show that the minimum triforce density in a 3-uniform hypergraph of edge density δ is δ 4– o (1) but not O ( δ 4 ). Let M ( δ ) be the maximum number such that the following holds: for every ∊ > 0 and $$G = {\mathbb{F}}_2^n$$ with n sufficiently large, if A ⊆ G × G with A ≥ δ | G | 2 , then there exists a nonzero “popular difference” d ∈ G such that the number of “corners” ( x , y ), ( x + d , y ), ( x , y + d ) ∈ A is at least ( M ( δ )–∊)| G | 2 . As a corollary via a recent result of Mandache, we conclude that M ( δ ) = δ 4– o (1) and M ( δ ) = ω ( δ 4 ). On the other hand, for 0 < δ < 1/2 and sufficiently large N , there exists A ⊆ [ N ] 3 with | A | ≥ δN 3 such that for every d ≠ 0, the number of corners ( x , y , z ), ( x + d , y , z ), ( x , y + d , z ), ( x , y , z + d ) ∈ A is at most δ c log(1/ δ ) N 3 . A similar bound holds in higher dimensions, or for any configuration with at least 5 points or affine dimension at least 3. 

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5. Compositional Phase Change of Early Transition Metal Diselenide (VSe ₂ and TiSe ₂ ) Ultrathin Films by Postgrowth Annealing

   https://doi.org/10.1002/admi.202000497  

   Bonilla, Manuel; Kolekar, Sadhu; Li, Jiangfeng; Xin, Yan; Coelho, Paula Mariel; Lasek, Kinga; Zberecki, Krzysztof; Lizzit, Daniel; Tosi, Ezequiel; Lacovig, Paolo; et al (June 2020, Advanced Materials Interfaces)

   Abstract The transition metal selenides M_1+ySe₂(M = V, Ti) have intriguing quantum properties, which make them target materials for controlling properties by thinning them to the ultrathin limit. An appropriate approach for the synthesis of such ultrathin films is by molecular beam epitaxy. Here, it is shown that such synthesized V‐ and Ti‐Se₂films can undergo a compositional change by vacuum annealing. Combined scanning tunneling and photoemission spectroscopy is used to determine compositional and structural changes of ultrathin films as a function of annealing temperature. Loss of selenium from the film is accompanied by a morphology change of monolayer height islands to predominantly bilayer height. In addition, crystal periodicity and atomic structure changes are observed. These changes are consistent with a transition from a layered transition metal dichalcogenide (TMDC) to ordered intercalation compounds with V or Ti intercalated in between two layers of their respective TMDCs. These observations may clear up misconception of the nature of previously reported high‐temperature grown transition metal selenides. More significantly, the demonstrated control of the formation of intercalation compounds is a key step toward modifying properties in van der Waals systems and toward expanding material systems for van der Waals heterostructures. 

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