Abstract: In this work, we study the behavior of introducing
atomic size vacancy in a graphene nanoribbon superlattice. Our
investigations are based on the density functional theory (DFT) with
the Local Density Approximation in Atomistix Toolkit (ATK). We
show that, in addition to its shape, the position of vacancy has a
major impact on the electrical properties of a graphene nanoribbon
superlattice. We show that the band gap of an armchair graphene
nanoribbon may be tuned by introducing an appropriate periodic
pattern of vacancies. The band gap changes in a zig-zag manner
similar to the variation of band gap of a graphene nanoribbon by
changing its width.
Abstract: Given a bivariate normal sample of correlated variables,
(Xi, Yi), i = 1, . . . , n, an alternative estimator of Pearson’s correlation
coefficient is obtained in terms of the ranges, |Xi − Yi|.
An approximate confidence interval for ρX,Y is then derived, and
a simulation study reveals that the resulting coverage probabilities
are in close agreement with the set confidence levels. As well, a
new approximant is provided for the density function of R, the
sample correlation coefficient. A mixture involving the proposed
approximate density of R, denoted by hR(r), and a density function
determined from a known approximation due to R. A. Fisher is shown
to accurately approximate the distribution of R. Finally, nearly exact
density approximants are obtained on adjusting hR(r) by a 7th degree
polynomial.
Abstract: We report the electronic structure and optical
properties of NdF3 compound. Our calculations are based on density
functional theory (DFT) using the full potential linearized augmented
plane wave (FPLAPW) method with the inclusion of spin orbit
coupling. We employed the local spin density approximation (LSDA)
and Coulomb-corrected local spin density approximation, known for
treating the highly correlated 4f electrons properly, is able to
reproduce the correct insulating ground state. We find that the
standard LSDA approach is incapable of correctly describing the
electronic properties of such materials since it positions the f-bands
incorrectly resulting in an incorrect metallic ground state. On the
other hand, LSDA + U approximation, known for treating the highly
correlated 4f electrons properly, is able to reproduce the correct
insulating ground state. Interestingly, however, we do not find any
significant differences in the optical properties calculated using
LSDA, and LSDA + U suggesting that the 4f electrons do not play a
decisive role in the optical properties of these compounds. The
reflectivity for NdF3 compound stays low till 7 eV which is
consistent with their large energy gaps. The calculated energy gaps
are in good agreement with experiments. Our calculated reflectivity
compares well with the experimental data and the results are analyzed
in the light of band to band transitions.
Abstract: This calculation focus on the effect of exchange
interaction J and Coulomb interaction U on spin magnetic moments
(ms) of MnO by using the local spin density approximation plus the
Coulomb interaction (LSDA+U) method within full potential linear
muffin-tin orbital (FP-LMTO). Our calculated results indicated that
the spin magnetic moments correlated to J and U. The relevant
results exhibited the increasing spin magnetic moments with
increasing exchange interaction and Coulomb interaction.
Furthermore, equations of spin magnetic moment, which h good
correspondence to the experimental data 4.58μB, are defined ms =
0.11J +4.52μB and ms = 0.03U+4.52μB. So, the relation of J and U
parameter is obtained, it is obviously, J = -0.249U+1.346 eV.
Abstract: In this project electrical and optical properties of
BaZrO3 have been accomplished through the full-potential
linear augmented plane wave (FP-LAPW) by applying Wein2k
software. In this study band structure, density of state, gap energy,
refractive index and optical conduction have been studied. The results
of calculations show that BaZrO3 is an insulator with an indirect gap
in which 3.2 ev and studied refractive index equal 2.07. These results
are in accordance with the ones obtained in experimental researches.
Abstract: The spin (ms) and orbital (mo) magnetic moment of
the antiferromagnetic NiO and MnO have been studied in the local
spin density approximation (LSDA+U) within full potential linear
muffin-tin orbital (FP-LMTO method with in the coulomb interaction
U varying from 0 to 10eV, exchange interaction J, from 0 to 1.0eV,
and volume compression VC in range of 0 to 80%. Our calculated
results shown that the spin magnetic moments and the orbital
magnetic moments increase linearly with increasing U and J. While
the interesting behaviour appears when volume compression is
greater than 70% for NiO and 50% for MnO at which ms collapses.
Further increase of volume compression to be at 80% leads to the
disappearance of both magnetic moments.
Abstract: The density estimates considered in this paper comprise
a base density and an adjustment component consisting of a linear
combination of orthogonal polynomials. It is shown that, in the
context of density approximation, the coefficients of the linear combination
can be determined either from a moment-matching technique
or a weighted least-squares approach. A kernel representation of
the corresponding density estimates is obtained. Additionally, two
refinements of the Kronmal-Tarter stopping criterion are proposed
for determining the degree of the polynomial adjustment. By way of
illustration, the density estimation methodology advocated herein is
applied to two data sets.