More Like this

1. Bias-Enhanced Formation of Metastable and Multiphase Boron Nitride Coating in Microwave Plasma Chemical Vapor Deposition

   https://doi.org/10.3390/ma14237167  

   Chakrabarty, Kallol; Baker, Paul A.; Vijayan, Vineeth M.; Catledge, Shane A. (December 2021, Materials)

   Boron nitride (BN) is primarily a synthetically produced advanced ceramic material. It is isoelectronic to carbon and, like carbon, can exist as several polymorphic modifications. Microwave plasma chemical vapor deposition (MPCVD) of metastable wurtzite boron nitride is reported for the first time and found to be facilitated by the application of direct current (DC) bias to the substrate. The applied negative DC bias was found to yield a higher content of sp3 bonded BN in both cubic and metastable wurtzite structural forms. This is confirmed by X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). Nano-indentation measurements reveal an average coating hardness of 25 GPa with some measurements as high as 31 GPa, consistent with a substantial fraction of sp3 bonding mixed with the hexagonal sp2 bonded BN phase. 

   more » « less
2. Intra- and intermolecular interception of a photochemically generated terminal uranium nitride

   https://doi.org/10.1039/C9SC05992J  

   Yadav, Munendra; Metta-Magaña, Alejandro; Fortier, Skye (March 2020, Chemical Science)

   The photochemically generated synthesis of a terminal uranium nitride species is here reported and an examination of its intra- and intermolecular chemistry is presented. Treatment of the U( iii ) complex L Ar UI(DME) ((L Ar ) 2− = 2,2′′-bis(Dippanilide)- p -terphenyl; Dipp = 2,6-diisopropylphenyl) with LiNIm Dipp ((NIm Dipp ) − = 1,3-bis(Dipp)-imidazolin-2-iminato) generates the sterically congested 3N-coordinate compound L Ar U(NIm Dipp ) ( 1 ). Complex 1 reacts with 1 equiv. of Ph 3 CN 3 to give the U( iv ) azide L Ar U(N 3 )(NIm Dipp ) ( 2 ). Structural analysis of 2 reveals inequivalent N α –N β > N β –N γ distances indicative of an activated azide moiety predisposed to N 2 loss. Room-temperature photolysis of benzene solutions of 2 affords the U( iv ) amide ( N -L Ar )U(NIm Dipp ) ( 3 ) via intramolecular N-atom insertion into the benzylic C–H bond of a pendant isopropyl group of the (L Ar ) 2− ligand. The formation of 3 occurs as a result of the intramolecular interception of the intermediately generated, terminal uranium nitride (L Ar )U(N)(NIm Dipp ) ( 3′ ). Evidence for the formation of 3′ is further bolstered by its intermolecular capture, accomplished by photolyzing solutions of 2 in the presence of an isocyanide or PMe 3 to give (L Ar )U[NCN(C 6 H 3 Me 2 )](NIm Dipp ) ( 5 ) and ( N , C -L Ar *)U(NPMe 3 )(NIm Dipp ) ( 6 ), respectively. These results expand upon the limited reactivity studies of terminal uranium–nitride moieties and provide new insights into their chemical properties. 

   more » « less
3. Degenerate parabolic p -Laplacian equations: Existence, uniqueness, and asymptotic behavior of solutions

   https://doi.org/10.1515/acv-2024-0060  

   Cruz-Uribe, David; Moen, Kabe; Shao, Yuanzhen (April 2025, Advances in Calculus of Variations)

   Abstract In this paper we study the degenerate parabolicp-Laplacian, ${\partial }_{t}u-v^{-1}\mathrm{div}\left({\left|\sqrt{Q}\nabla u\right|}^{p-2}Q\nabla u\right)=0${\partial_{t}u-v^{-1}\operatorname{div}(|\sqrt{Q}\nabla u|^{p-2}Q\nabla u)=0},where the degeneracy is controlled by a matrixQand a weightv.With mild integrability assumptions onQandv, we prove theexistence and uniqueness of solutions on any interval $[0,T]${[0,T]}. If we further assumethe existence of a degenerate Sobolev inequality with gain, thedegeneracy again controlled byvandQ, then we can prove bothfinite time extinction and ultracontractive bounds. Moreover, weshow that there is equivalence between the existence ofultracontractive bounds and the weighted Sobolev inequality. 

   more » « less
4. Instantaneous everywhere-blowup of parabolic SPDEs

   https://doi.org/10.1007/s00440-024-01263-7  

   Foondun, Mohammud; Khoshnevisan, Davar; Nualart, Eulalia (October 2024, Probability Theory and Related Fields)

   Abstract We consider the following stochastic heat equation$$\begin{aligned} \partial _t u(t,x) = \tfrac{1}{2} \partial ^2_x u(t,x) + b(u(t,x)) + \sigma (u(t,x)) {\dot{W}}(t,x), \end{aligned}$$ $\begin{array}{c}{\partial }_{t}u(t,x)=\frac{1}{2}{\partial }_x^{2}u(t,x)+b\left(u(t,x)\right)+\sigma \left(u(t,x)\right)\dot{W}(t,x),\end{array}$defined for$$(t,x)\in (0,\infty )\times {\mathbb {R}}$$ $(t,x)\in (0,\infty )\times R$, where$${\dot{W}}$$ $\dot{W}$denotes space-time white noise. The function$$\sigma $$ $\sigma$is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the functionbis assumed to be positive, locally Lipschitz and nondecreasing. We prove that the Osgood condition$$\begin{aligned} \int _1^\infty \frac{\textrm{d}y}{b(y)}<\infty \end{aligned}$$ $\begin{array}{c}{\int }_1^{\infty }\frac{\text{d}y}{b\left(y\right)}<\infty \end{array}$implies that the solution almost surely blows up everywhere and instantaneously, In other words, the Osgood condition ensures that$$\textrm{P}\{ u(t,x)=\infty \quad \hbox { for all } t>0 \hbox { and } x\in {\mathbb {R}}\}=1.$$ $\text{P}\left\{u\right(t,x)=\infty \text{for all}t>0\text{and}x\in R\}=1.$The main ingredients of the proof involve a hitting-time bound for a class of differential inequalities (Remark 3.3), and the study of the spatial growth of stochastic convolutions using techniques from the Malliavin calculus and the Poincaré inequalities that were developed in Chen et al. (Electron J Probab 26:1–37, 2021, J Funct Anal 282(2):109290, 2022). 

   more » « less
5. 2D rare-earth metal carbides (MXenes) Mo ₂ NdC ₂ T ₂ electronic structure and magnetic properties: A DFT + U study

   https://doi.org/10.1063/5.0124167  

   Yao, Shukai; Anasori, Babak; Strachan, Alejandro (November 2022, Journal of Applied Physics)

   2D rare-earth metal carbides (MXenes) are attractive due to their novel electronic and magnetic properties and their potential as scalable 2D magnets. In this study, we used density functional theory with the Hubbard U correction to characterize the structure, termination, and magnetism in an out-of-plane ordered rare-earth containing M 3 C 2 T x MXene, Mo 2 NdC 2 T 2 (T = O or OH). We investigated the effect of the U parameter on the stability and magnetism of two possible termination sites: the hollow sites aligned with the inner Nd atoms (Nd-hollow sites) and those aligned with the closest C atoms (C-hollow sites). We found that increasing U Mo stabilized the Nd hollow sites, which minimized electrostatic repulsion between C and O atoms. Using U Mo  = 3.0 eV and U Nd  = 5.6 eV, obtained via the linear response method, we found that the energetically preferred termination site was C-hollow in Mo 2 NdC 2 O 2 and Nd-hollow in Mo 2 NdC 2 (OH) 2 . Regardless of termination and the Hubbard U value, we found Mo 2 NdC 2 O 2 and Mo 2 NdC 2 (OH) 2 to be magnetic. The C-hollow termination resulted in ferromagnetic states for all Hubbard U tested with no magnetic moment in Mo. In the case of Nd-hollow, Mo became magnetic for U Mo  ≥ 4 eV. The difference of Mo magnetism in Nd-hollow and C-hollow was explained by crystal field splitting of the Mo d orbital caused by a distorted ligand. 

   more » « less