On Bilinear Hardy–Steklov Operators

Doklady Mathematics - Sharp estimates of the best constants in bilinear weighted inequalities with Hardy–Steklov integral operators are presented.     

Effect of ion irradiation on the thermoluminescence properties of K2Ca2(SO4)3 phosphor

This paper presents the thermoluminescence (TL) studies of ion-irradiated potassium–calcium mixed sulfate phosphor. The sample was prepared by the solid-state diffusion method. The X-ray diffraction study of the prepared sample suggests an orthorhombic structure with an average particle size of 0.16 μ m. The samples were irradiated with 1.2 MeV argon ions at fluences varying between 10¹¹ and 10¹⁵ ions/cm². The argon ions penetrate to a depth of 1.93 μ m and lose their energy mainly via electronic stopping. Due to ion irradiation, a large number of defects such as oxygen vacancies, radicals and color centers are formed in the sample. TL glow curves were recorded for each of the ion fluences. A linear increase in the intensity of TL glow peaks was found with an increase in the ion dose from 72 kGy to 720 MGy. The kinetic parameters associated with the prominent glow peaks were calculated using glow curve deconvolution, different glow curve shapes and sample heating rate methods.     

Structural phase transformation in ZnS nanocrystalline thin films by swift heavy ion irradiation

Zinc sulfide (ZnS) thin films in zinc-blende (ZB) and wurtzite (W) phases have been fabricated by pulsed laser deposition. 150 MeV Ni ion beam irradiation has been carried out at different fluences ranging from 10¹¹ to 10¹³ ions/cm² at room temperature for ion induced modifications. Structural phase transformation in ZnS from W to ZB phase is observed after high energy ion irradiation which leads to the decrease in bandgap. Generation of high pressure and temperature by thermal spike during MeV ion irradiation along the ion trajectory in the films is responsible for the structural phase transformation.     

Modifications induced in the polycarbonate Makrofol KG polymer by Li (50 MeV) ion irradiation

Swift heavy ions interact predominantly through inelastic scattering while traversing any polymer medium and produce excited/ionized atoms. Here samples of the polycarbonate Makrofol of approximate thickness 20 μm, spin coated on GaAs substrate were irradiated with 50 MeV Li ion (+3 charge state). Build-in modifications due to irradiation were studied using FTIR and XRD characterizations. Considerable changes have been observed in the polymer while varying the fluence from 1E11 ion/cm² to 1E13 ion/cm² Li ions. AFM images of the surface modifications caused by ion irradiation on the polymer are also presented.      

The Manin—Drinfeld theorem and Ramanujan sums

The Manin—Drinfeld theorem asserts the finiteness of the cuspidal divisor class group of a modular curve corresponding to a congruence subgroup. The purpose of the note is to draw attention to the connection between this theorem and Ramanujan sums, and to the question of what happens for non-congruence subgroups. Research partially supported by an NSERC grant. Alfred P Sloan Fellow. Research partially supported by the NSF.     

Nano- and micro-scale patterning of Si (1 0 0) under keV ion irradiation

Evolution of Si (1 0 0) surface under 100 keV Ar⁺ ion irradiation at oblique incidence has been studied. The dynamics of surface erosion by ion beam is investigated using detailed analysis of atomic force microscopy (AFM) measurements. During an early stage of sputtering, formation of almost uniformly distributed nano-dots occurs on Si surface. However, the late stage morphology is characterized by self-organization of surface into a regular ripple pattern. Existing theories of ripple formation have been invoked to provide an insight into surface rippling.     

Effect of 100 MeV Ni ion irradiation on MOCVD grown n-GaN

Metal-organic chemical vapor deposition (MOCVD) grown n-type Gallium nitride (GaN) has been irradiated with 100 MeV Ni⁹⁺ ions at room temperature. Atomic force microscopy (AFM) images show the nano-clusters' formation upon irradiation and the irradiated GaN surface roughness increases with the increasing ion fluences. High-resolution X-ray diffraction (HR-XRD) analysis reveals the formation of Ga₂O₃ due to the interface mixing of GaN/Al₂O₃ upon irradiation. FWHM values of GaN (0 0 0 2) increases due to the lattice disorder. Photoluminescence studies show reduced band edge emission and yellow luminescence (YL) intensity with the increasing ion fluences. Change in the band gap energy between 3.38 and 3.04 eV was measured by UV-visible optical absorption spectrum on increasing the ion fluences.