Self-similar Solutions to a Kinetic Model for Grain Growth

We prove the existence of self-similar solutions to the Fradkov model for two-dimensional grain growth, which consists of an infinite number of nonlocally coupled transport equations for the number densities of grains with given area and number of neighbours (topological class). For the proof we introduce a finite maximal topological class and study an appropriate upwind-discretization of the time dependent problem in self-similar variables. We first show that the resulting finite dimensional differential system has nontrivial steady states. Afterwards we let the discretization parameter tend to zero and prove that the steady states converge to a compactly supported self-similar solution for a Fradkov model with finitely many equations. In a third step we let the maximal topology class tend to infinity and obtain self-similar solutions to the original system that decay exponentially. Finally, we use the upwind discretization to compute self-similar solutions numerically.Comment: 25 pages, several figure

On the relationship of magnetocrystalline anisotropy and stoichiometry in epitaxial L1(0) CoPt (001) and FePt (001) thin films

Two series of epitaxial CoPt and FePt films, with nominal thicknesses of 42 or 50 nm, were prepared by sputtering onto single-crystal MgO(001) substrates in order to investigate the chemical ordering and the resultant magnetic properties as a function of alloy composition. In the first series, the film composition was kept constant, while the substrate temperature was increased from 144 to 704 degrees C. In the second series the substrate temperature was kept constant at 704 degrees C for CoPt and 620 degrees C for FePt, while the alloy stoichiometry was varied in the nominal range of 40-60-at. % Co(Fe). Film compositions and thicknesses were measured via Rutherford backscattering spectrometry. The lattice and long-range order parameter for the L1(0) phase were obtained for both sets of films using x-ray diffraction. The room-temperature magnetocrystalline anisotropy constants were determined for a subset of the films using torque magnetometry. The order parameter was found to increase with increasing temperature, with ordering occurring more readily in FePt when compared with CoPt. A perpendicular anisotropy developed in CoPt for substrate temperatures above 534 degrees C and in FePt above 321 degrees C. The structure and width of the magnetic domains in CoPt and FePt, as seen by magnetic force microscopy, also demonstrated an increase in magnetic anisotropy with increasing temperature. For the films deposited at the highest temperatures (704 degrees C for CoPt and 620 degrees C for FePt), the order parameter reached a maximum near the equiatomic composition, whereas the magnetocrystalline anisotropy increased as the concentration of Co or Fe was increased from below to slightly above the equiatomic composition. It is concluded that nonstoichiometric L1(0) CoPt and FePt, with a slight excess of Co or Fe, are preferable for applications requiring the highest anisotropies

Failure of semiclassical models to describe resistivity of nanometric, polycrystalline tungsten films

The impact of electron scattering at surfaces and grain boundaries in nanometric polycrystalline tungsten (W) films was studied. A series of polycrystalline W films ranging in thickness from 10 to 310 nm and lateral grain size from 74 to 133 nm were prepared on thermally oxidized Si. The Fuchs-Sondheimer surface-scattering model and Mayadas-Shatzkes grain-boundary scattering model were employed for quantitative analyses. Predictions from the theoretical models were found to deviate systematically from the experimental data. Possible reasons for the failure of the theoretical models to describe the experimental data are explored. Finally, a discussion of the crucial features lacking from existing models is presented, along with possible avenues for improving the models to result in better agreement with experimental data

Hundredfold Enhancement of Light Emission via Defect Control in Monolayer Transition-Metal Dichalcogenides

Two dimensional (2D) transition-metal dichalcogenide (TMD) based semiconductors have generated intense recent interest due to their novel optical and electronic properties, and potential for applications. In this work, we characterize the atomic and electronic nature of intrinsic point defects found in single crystals of these materials synthesized by two different methods - chemical vapor transport and self-flux growth. Using a combination of scanning tunneling microscopy (STM) and scanning transmission electron microscopy (STEM), we show that the two major intrinsic defects in these materials are metal vacancies and chalcogen antisites. We show that by control of the synthetic conditions, we can reduce the defect concentration from above $10^{13} /cm^2$ to below $10^{11} /cm^2$. Because these point defects act as centers for non-radiative recombination of excitons, this improvement in material quality leads to a hundred-fold increase in the radiative recombination efficiency

Magnetic Exchange-Coupling in CoPt/Co Bilayer thin Films

Thin film CoPt/Co bilayers have been prepared as a model system to investigate the relationship between microstructure and exchange coupling in two-phase hard/soft composite magnets. CoPt films, with a thickness of 25 nm, were sputter-deposited from a nearly equiatomic alloy target onto oxidized Si wafers. The films were subsequently annealed at 700 C and fully transformed from the FCC phase to the magnetically hard, ordered L1{sub 0} phase. The coercivity of the films increased rapidly with annealing time until it reached a plateau at approximately 9.5 kOe. Fully-ordered CoPt films were then used as substrates for deposition of Co layers, with thicknesses in the range of 2.8--225 nm, in order to produce the hard/soft composite bilayers. As predicted by theory, the magnetic coherency between the soft Co phase and the hard, ordered CoPt phase decreased as the thickness of the soft phase increased. This decrease in coupling was clearly seen in the magnetic hysteresis loops of the bilayers. At small thicknesses of Co (a few nanometers), the shape of the loop was one of a uniform material showing no indication of the presence of two phases with extremely different coercivities. At larger Co thicknesses, constricted loops, i.e., ones showing the presence of a mixture of two ferromagnetic phases of different hardnesses, were obtained. The magnetic exchange present in the bilayer samples was qualitatively analyzed using magnetic recoil curves and the dependence of exchange coupling on the soft phase dimension in the bilayer hard/soft composite magnet films is discussed

Exon and junction microarrays detect widespread mouse strain- and sex-bias expression differences

Background: Studies have shown that genetic and sex differences strongly influence gene expression in mice. Given the diversity and complexity of transcripts produced by alternative splicing, we sought to use microarrays to establish the extent of variation found in mouse strains and genders. Here, we surveyed the effect of strain and sex on liver gene and exon expression using male and female mice from three different inbred strains. Results: 71 liver RNA samples from three mouse strains - DBA/2J, C57BL/6J and C3H/HeJ - were profiled using a custom-designed microarray monitoring exon and exon-junction expression of 1,020 genes representing 9,406 exons. Gene expression was calculated via two different methods, using the 3'-most exon probe ("3' gene expression profiling") and using all probes associated with the gene ("whole-transcript gene expression profiling"), while exon expression was determined using exon probes and flanking junction probes that spanned across the neighboring exons ("exon expression profiling"). Widespread strain and sex influences were detected using a two-way Analysis of Variance (ANOVA) regardless of the profiling method used. However, over 90% of the genes identified in 3' gene expression profiling or whole transcript profiling were identified in exon profiling, along with 75% and 38% more genes, respectively, showing evidence of differential isoform expression. Overall, 55% and 32% of genes, respectively, exhibited strain- and sex-bias differential gene or exon expression. Conclusion: Exon expression profiling identifies significantly more variation than both 3' gene expression profiling and whole-transcript gene expression profiling. A large percentage of genes that are not differentially expressed at the gene level demonstrate exon expression variation suggesting an influence of strain and sex on alternative splicing and a need to profile expression changes at sub-gene resolution

Effect of microstructural evolution on magnetic properties of Ni thin films

Copyright © Indian Academy of Sciences.The magnetic properties of Ni thin films, in the range 20–500 nm, at the crystalline-nanocrystalline interface are reported. The effect of thickness, substrate and substrate temperature has been studied. For the films deposited at ambient temperatures on borosilicate glass substrates, the crystallite size, coercive field and magnetization energy density first increase and achieve a maximum at a critical value of thickness and decrease thereafter. At a thickness of 50 nm, the films deposited at ambient temperature onto borosilicate glass, MgO and silicon do not exhibit long-range order but are magnetic as is evident from the non-zero coercive field and magnetization energy. Phase contrast microscopy revealed that the grain sizes increase from a value of 30–50 nm at ambient temperature to 120–150 nm at 503 K and remain approximately constant in this range up to 593 K. The existence of grain boundary walls of width 30–50 nm is demonstrated using phase contrast images. The grain boundary area also stagnates at higher substrate temperature. There is pronounced shape anisotropy as evidenced by the increased aspect ratio of the grains as a function of substrate temperature. Nickel thin films of 50 nm show the absence of long-range crystalline order at ambient temperature growth conditions and a preferred [111] orientation at higher substrate temperatures. Thin films are found to be thermally relaxed at elevated deposition temperature and having large compressive strain at ambient temperature. This transition from nanocrystalline to crystalline order causes a peak in the coercive field in the region of transition as a function of thickness and substrate temperature. The saturation magnetization on the other hand increases with increase in substrate temperature.University Grants Commission for Centre of Advanced Studies in Physic