The investigation of structural,electronic, elastic and thermodynamic properties of Gd1−xYxAuPb alloys: A first principle study

First principle calculations have been employed to investigate the effects of Y concentration, pressure and temperature on various properties of ${\mathrm{Gd}}_{1?x}{\mathrm{Y}}_x\mathrm{AuPb}$ ($x=0,0.25,0.5,0.75,1$) alloys using density functional theory (DFT). The full potential linearized augmented plane wave (FP-LAPW) method within a framework of the generalized gradient approximation (GGA) is used to perform the calculated results of this paper. Phase stability of ${\mathrm{Gd}}_{1?x}{\mathrm{Y}}_x\mathrm{AuPb}$ alloys is studied using the total energy versus unit cell volume calculations. The equilibrium lattice parameters of these alloys are in good agreement with the available experimental results. The mechanical stability of ${\mathrm{Gd}}_{1?x}{\mathrm{Y}}_x\mathrm{AuPb}$ alloys is proved using elastic constants calculations. Also, the influence of Y concentration on elastic properties of ${\mathrm{Gd}}_{1?x}{\mathrm{Y}}_x\mathrm{AuPb}$ alloys such as Young's modulus, shear modulus, Poisson's ratio and anisotropy factor are investigated and analyzed. By considering both Pugh's ratio and Poisson's ratio, the ductility and brittleness of these alloys are studied. In addition, the total density of states and orbital's hybridizations of different atoms are investigated and discussed. Moreover, the effect of pressure and temperature on some important thermodynamic properties is investigated.     

Composition law for the Cole-Cole relaxation and ensuing evolution equations

Physically natural assumption says that any relaxation process taking place in the time interval $[t_0,t_2]$, $t_2>t_0\ge 0$ may be represented as a composition of processes taking place during time intervals $[t_0,t_1]$ and $[t_1,t_2]$ where $t_1$ is an arbitrary instant of time such that $t_0\le t_1\le t_2$. For the Debye relaxation such a composition is realized by usual multiplication which claim is not valid any longer for more advanced models of relaxation processes. We investigate the composition law required to be satisfied by the Cole-Cole relaxation and find its explicit form given by an integro-differential relation playing the role of the time evolution equation. The latter leads to differential equations involving fractional derivatives, either of the Caputo or the Riemann-Liouville senses, which are equivalent to the special case of the fractional Fokker-Planck equation satisfied by the Mittag-Leffler function known to describe the Cole-Cole relaxation in the time domain.     

Topological states in the Hofstadter model on a honeycomb lattice

We provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t,t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gapless edge modes are described in the framework of the generalized Kitaev chain formalism, which makes it possible to calculate the Hall conductance of subbands for different filling and an arbitrary magnetic flux ϕ. At half-filling the gap in the center of the fermion spectrum opens for $t>t_c=2^{\varphi }$, a quantum phase transition in the 2D-topological insulator state is realized at $t_c$. The phase state is characterized by zero energy Majorana states localized at the boundaries. Taking into account the on-site Coulomb repulsion U (where $U<<1$), the criterion for the stability of a topological insulator state is calculated at $t<<1$, $t\sim U$. Thus, in the case of $U>4\mathrm{\Delta }$, the topological insulator state, which is determined by chiral gapless edge modes in the gap Δ, is destroyed.     

Exploring new insights in BAlN from evolutionary algorithms ab initio computations

BN-AlN alloys are potential candidates to achieve wide band gap material for ultraviolet device applications. By combing density functional theory and evolutionary structure predictions, we systematically explore the thermodynamic, mechanical, dynamical and optical properties of ${\mathrm{B}}_x{\mathrm{Al}}_{1?x}\mathrm{N}$ alloys. Through structure search, three compounds (cubic ($\mathrm{B}{\mathrm{Al}}_3{\mathrm{N}}_4$, and ${\mathrm{B}}_3\mathrm{Al}{\mathrm{N}}_4$, space group P-43m), and tetragonal ($\mathrm{B}\mathrm{Al}{\mathrm{N}}_2$, space group P-42m)) have been predicted. The calculated relative large formation enthalpies suggest that large miscibility gap exists in BAlN alloys. In addition, computed elastic constants and phonon show that these structures are mechanically and dynamically stable. From the state of the art LDA-1/2 we show that the direct band gap of BN-AlN evinces strong deviation from a linear dependence on B composition. We found -in particular- giant direct band gap bowing parameter of $b～11.6$ eV for the entire range of composition, where b parameter is found to be sensitive to composition x. From a detailed analysis of the physical origin of the optical gap bowing b, we found that structural and chemical contributions play the most significant effects behind the huge optical band gap bowing parameter of BAlN alloys.     

Structural and optical properties of cadmium magnesium zinc oxide (CdMgZnO) nanoparticles synthesized by sol–gel method

Nanoparticles of ${\mathrm{Cd}}_x{\mathrm{Mg}}_{0.12?x}{\mathrm{Zn}}_{0.88}\mathrm{O}$ $(0\le x\le 0.02)$ were synthesized by a simple sol gel route with the combination of chelating agents. Effect of cadmium on the phase, structural, morphological and optical properties of the synthesized nanoparticles has been studied and reported by using X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), energy dispersive X-ray (EDX), Fourier transform infrared spectroscopy (FTIR) and UV–Vis diffuse reflectance spectroscopy (UV–vis DRS). The crystal size, lattice parameters, unit cell volume, X-ray density, inter-planar distances and bond length were obtained and analyzed from the XRD data. The X-ray analysis reveals the formation of a single phase with a hexagonal wurtzite structure, where an increase of the cell volume was achieved as the Cd content was increased as well. Synthesized nanoparticle were nearly spherical at nano-size regime and are loosely agglomerated as observed from the SEM analysis. EDX spectra of the composition confirmed the appropriate stoichiometric ratio. A fundamental absorption peak centered at 375 nm was observed from the UV–visible absorption spectra which shifted towards a higher wavelength correlating the narrowing of the energy band gap due to increase in Cd content. The structural adjustment from the IR spectra confirmed the stretching vibration of Zn–O in the ${\mathrm{Cd}}_x{\mathrm{Mg}}_{0.12?x}{\mathrm{Zn}}_{0.88}\mathrm{O}$ lattice with Cd content.     

Exchange bias behavior and magnetocaloric effect in Ni2In-type Mn7Sn4 alloy

In this work, the exchange bias behavior and magnetocaloric effect have been studied in Mn₇Sn₄ alloy. The X-ray powder diffraction pattern recorded at room temperature indicates that the sample crystallizes in a single phase with Ni₂In-type hexagonal structure (space group $P{6}_3/\mathit{mmc}$). The maximum magnetic entropy change value across paramagnetic/ferrimagnetic transition is about 3.3 J kg⁻¹ K⁻¹ under the magnetic field change of ${\mu }_0\mathrm{\Delta }H=0\text{-}5\text{T}$. With further cooling, the reentrant spin-glass-like state is obtained below 150 K, for which the exchange bias effect has been observed. The exchange bias field is ∼7.8 mT and ∼6.7 mT at $T=10\text{K}$ when the cooling field is ${\mu }_0{H}_{\mathrm{CF}}=0.1\text{T}$ and 0.5 T, respectively. The magnetic behavior and the origin of exchange bias in Mn₇Sn₄ are discussed.     

Time-periodic quantum states of weakly interacting bosons in a harmonic trap

We consider quantum bosons with contact interactions at the Lowest Landau Level (LLL) of a two-dimensional isotropic harmonic trap. At linear order in the coupling parameter g, we construct a large, explicit family of quantum states with energies of the form $E_0+g{E}_1/4+O(g^2)$, where $E_0$ and $E_1$ are integers. Any superposition of these states evolves periodically with a period of $8\pi /g$ until, at much longer time scales of order $1/g^2$, corrections to the energies of order $g^2$ may become relevant. These quantum states provide a counterpart to the known time-periodic behaviors of the corresponding classical (mean field) theory.     

Five-body choreography on the algebraic lemniscate is a potential motion

In a remarkable paper of 2003 by Fujiwara et al. [1], a figure-eight three-body choreography on the algebraic lemniscate of Bernoulli was discovered. Such a choreography was found to be driven by the action of a pairwise potential $V(r_{ij})$, depending only on the mutual relative distances $r_{ij}$, $i,j=1,2,3$. In the present Letter we show that two different choreographies of five bodies on the same algebraic lemniscate exist and correspond to solutions of ten coupled Newton equations of motion with a pairwise interaction potential. For each choreography the explicit form of the potential is found and ten constants of motion are presented, thus, it is superintegrable.     

Molecular dynamics simulations on the effect of nanovoid on shock-induced phase transition in uranium nitride

The Angular-Dependent Potential (ADP) proposed by Tseplyaev et al. was used to study the structural behavior of uranium nitride (UN) under shock pressure by molecular dynamics (MD) simulations. Based on the calculations of shock velocity $U_S$ and particle velocity $U_P$, the results show that a pressure-induced phase transition of $\mathit{Fm}?3m\to R?3m$ structure in UN occurs at 35 GPa, and it agrees well with experimental results of 30–32 GPa. We also considered the effect of nanovoid on the phase transition of UN crystal from $Fm?3m$ to $R?3m$ structure. It is found that the pressure of phase transition decreases with the increasing nanovoid diameter. The phase transition takes place firstly around nanovoid, companied by the nanovoid collapsing, and then spreads to the void-free regions in the process of shock loading. Due to different stresses at different direction the spreading velocity of phase transition perpendicular to the direction of shock wave is observed to be far faster than the one parallel to the direction of shock wave.