A first-principle study on the phase transition,electronic structure,and mechanical properties of three-phase ZrTi<Subscript>2</Subscript> alloy under high pressure*

We employed density-functional theory (DFT) within the generalized gradient approximation(GGA) to investigate the ZrTi₂ alloy, and obtained its structural phase transition,mechanical behavior, Gibbs free energy as a function of pressure, P-V equation of state,electronic and Mulliken population analysis results. The lattice parameters andP-V EOS for α, β and ω phases revealed by ourcalculations are consistent with other experimental and computational values. The elasticconstants obtained suggest that ω-ZrTi₂ and α-ZrTi₂ are mechanically stable, and that β-ZrTi₂ is mechanically unstableat 0 GPa, but becomes more stable with increasing pressure. Our calculated resultsindicate a phase transition sequence of α → ω → β forZrTi₂. Both thebulk modulus B and shear modulus G increase linearly withincreasing pressure for three phases. The G/B values illustrated goodductility of ZrTi₂alloy for three phases, with ω<α<β at0 GPa. The Mulliken population analysis showed that the increment of d electron occupancystabilized the β phase. A low value for B '₀ is the feature of EOS for ZrTi₂ and this softness in the EOS isrepresentative of pressure induced s-d electron transfer.     

On the born relation for crystals with diamond and sphalerite structure

The experimental data on the elastic constants C_ij for crystals with diamond and sphalerite structure at T=293 K were used to check the Born relation Δ4C₁₁(C₁₁?C₄₄)/(C₁₁+C₁₂)²=1. The relation was shown to be satisfied with a low accuracy for diamond due to a large scatter in the C_ij experimental values and with accuracies of 8.3, 7.6, 1.6, and 1.0% for Si, SiC, Ge, and α-Sn, respectively. For II–VI, III–V, and I–VII compounds with sphalerite structure, Λ was found to systematically deviate from unity toward lower values, and it was shown that the quantity (1-Λ) can be used to estimate the bond ionicity in these crystals. The effect of anharmonicity on the Λ values for Ge, Si, GaAs, InAs, and ZnSe was estimated; this effect was found to be insignificant.     

Ab initio calculations of B<Subscript>2</Subscript> type RHg (R = Ce,Pr, Eu and Gd) intermetallic compounds

Spin polarized ab initio calculations have been carried out to study the structural, electronic, elastic and thermal properties of RHg (R = Ce, Pr, Eu and Gd) intermetallic compounds in B₂ structure. The calculations have been performed by using both generalized gradient approximation (GGA) and local spin density approximation (LSDA). The calculated value of lattice constant (a ₀) for these compounds with GGA is in better agreement with the experimental data than those with LSDA. Bulk modulus (B), first-order pressure derivative of bulk modulus and magnetic moment (μ _B ) are also presented. The energy band structure and electron density of states show the occupancy of 4f states for light as well as heavy rare earth atom. The elastic constants are predicted from which all the related mechanical properties like Poisson’s ratio (σ), Young’s modulus (E), shear modulus (G _H ) and anisotropy factor (A) are calculated. The ductility or brittleness of these compounds is predicted from Pugh’s rule (B/G _H ) and Cauchy pressure (C ₁₂ ? C ₄₄). The Debye temperature (θ _D ) is estimated from the average sound velocity, which have not been calculated and measured yet.     

First-principles study on the electronic and optical properties of Si and Al co-doped zinc oxide for solar cell devices

Electronic and optical properties of co-doped zinc oxide ZnO with silicon (Si) and aluminum (Al), in Zn_1?2x Si _x Al _x O (0 ≤ x ≤ 0.0625) original structure forms, are investigated by the first-principles calculations based on the density functional theory (DFT). The optical constants and dielectric functions are investigated with the full-potential linearized augmented plane wave (FP-LAPW) method and the generalized gradient approximation (GGA) by WIEN2k package. The complex dielectric functions, refractive index and band gap of the pure as well as doped and co-doped ZnO were investigated, which are in good agreement with the available experimental results for the undoped ZnO. Thus, the maximum optical transmittance of the co-doped ZnO of about 95 % was achieved; it is higher than that of pure ZnO. Thus, we showed for the Si–Al co-doped ZnO with x = 0.0315 that the optical transmittance can cover a larger range in the visible light region. In addition, an occurrence of important energy levels around Fermi levels was showed, which is mainly due to doping atoms that lead to an overlap between valence and conduction bands, and consequently to the significant conductor behavior of the Si–Al co-doped ZnO. The original Zn_1?2x Si _x Al _x O structure reveals promising optical and electronic properties, and it can be investigated as good candidates for practical uses as transparent and conducting electrodes in solar cell devices.     

Computation of the electronic structure and direct-gap absorption spectra in Ge-rich Si<Subscript>1−x</Subscript> Ge<Subscript>x</Subscript>/Ge/Si<Subscript>1−x</Subscript>Ge<Subscript>x</Subscript> type-I quantum wells

This paper presents the results of conduction band discontinuities calculation for strained/relaxed Si_1?x Ge _x /Si_1?y Ge _y heterointerfaces in Γ _15C , Γ _2′C and L upper bands minima, as well as the room-temperature strained (vs. relaxed) band gaps deduced from the classical model-solid theory. Based upon the obtained data, we propose a type-I W-like Si_1?y Ge _y /Si_1?x Ge _x /Ge/Si_1?x Ge _x /Si_1?y Ge _y quantum wells heterostructure optimized in terms of compositions and thicknesses. Electronic states and wave functions are found by solving Schrödinger equation without and under applied bias voltage. An accurate investigation of the optical properties of this heterostructure is done by calculating the energies of the interband transitions and their oscillator strengths. Moreover, a detailed computation of the bias-voltage evolution of the absorption spectra is presented. These calculations prove the existence of type-I band alignment at Γ _2′C point in compressively strained Ge quantum wells grown on relaxed Ge-rich Si_1?y Ge _y buffers. The strong absorption coefficient (> 8 × 10³ cm^-1) and the large Stark effect (0.1 eV @ 2 V) of the Γ _2′C transitions thresholds open up perspectives for application of these heterostructures for near-infrared optical modulators.     

Estimation of changes in parameters of a crystal lattice and energy bands upon variation in the size of nanocrystals and nanofilms of silicides prepared by ion implantation

Changes in the parameters of the crystal lattice and energy bands of CoSi₂ nanofilms and nanocrystals formed in the surface Si layers by ion implantation combined with annealing are studied. It is shown that the band gap E _g of CoSi₂/Si(100) nanofilms with the thickness θ ≤ 40–50 Å is higher by ～0.1 eV than for “thick” films; in the case of nanocrystals, E _g is 0.3–0.4 eV higher than for macrocrystals.     

Electro-optical properties of strontium-barium niobate crystals and their relation to the domain structure of the crystals

The electro-optical coefficients r _ij and half-wave voltage V_λ/2 of strontium-barium niobate crystals poled in the ferroelectric phase are shown to vary along the polar axis. The r _ij (z) and V_λ/2(z) dependences indicate the presence of a residual domain density D(z) and clearly depend on the sign of the polarizing field, with r _ij being minimum (D being maximum) near the negative electrode. This character of the D(z) distribution and, hence, the r _ij (z) and V_λ/2(z) coordinate dependences can be explained by predominant domain nucleation near the negative electrode, which is revealed when the switching processes are studied using 90° (Rayleigh) light scattering from domain walls.     

Influence of Si substitution on structural,electronic and magnetic properties of Fe<Subscript>2</Subscript>MnGa Heusler compound

We investigate the electronic and magnetic properties of Fe₂MnGa_1?x Si _x alloy (x = 0, 0.25, 0.5, 0.75, and 1) using first-principles density functional theory within the generalized gradient approximation method. The lattice constant decreases linearly whereas bulk modulus increases with increasing Si content. The total magnetic moment varies linearly with increasing Si content, which follows the Slater-Pauling rule. Electronic band structure calculations indicate that the Fe₂MnGa_1?x Si _x exhibits half-metallic character for all the concentrations studied and the spin polarization and the spin-down band gap both increase with the Si content. Based on the magnetic properties calculations, the Heisenberg exchange coupling parameters give Fe-Mn ferromagnetic coupling and Mn-Mn antiferromagnetic coupling. The T _C first decreases and then increases with Si content, which is in well agreement with the experimental results.     

Electronic structure and energies of interatomic bonds in the TiSi<Subscript>2</Subscript> compound with a <Emphasis Type="Italic">C</Emphasis>49 crystal structure

Full-electron calculations of the electronic structure of the TiSi₂ compound in the structural modification C49 are performed using the augmented-plane-wave method. The total energy, the electronic band structure, and the density of states are calculated for an extended translational unit cell Ti₄Si₈, which is formed during the growth of a silicon nanowire on a p-Si substrate. Calculations are also carried out for two orthorhombic unit cells of the nonstoichiometric compositions Ti₃Si₉ and Ti₅Si₇. The energies of the interatomic bonds are determined to be E _Si-Si = 1.8 eV, E _Ti-Ti = 2.29 eV, and E _Ti-Si = 4.47 eV. The dependence of the total energy of the unit cell E _tot(V) on the unit cell volume V is obtained by optimizing the unit cell volume. The bulk modulus B ₀ = 132 GPa is determined from the Murnaghan equation of state for solids and the dependence E _tot (V). This value of the bulk modulus is used to estimate the activation energy for interstitial diffusion of silicon atoms Q _i(Si) ≈ 0.8 eV.     

Representation of type I heterostructure junctionless tunnel field effect transistor for high-performance logic application

In this paper, a gate-all-around junctionless tunnel field effect transistor (JLTFET) based on heterostructure of compound and group III–V semiconductors is introduced and simulated. In order to blend the high tunneling efficiency of narrow band gap material JLTFETs and the high electron mobility of III–V JLTFETs, a type I heterostructure junctionless TFET adopting Ge–Al _x Ga_1?x As–Ge system has been optimized by numerical simulation in terms of aluminum (Al) composition. To improve device performance, we considered a nanowire structure, and it was illustrated that high-performance logic technology can be achieved by the proposed device. The optimal Al composition founded to be around 20 % (x = 0.2). The numerical simulation results demonstrate that the proposed device has low leakage current I _OFF of ~1.9 × 10^?17, I _ON of 4 µA/µm, I _ON/I _OFF current ratio of 1.7 × 10¹¹ and subthreshold swing SS of 12.6 mV/decade at the 40 nm gate length and temperature of 300 K.     

Observations of nanoscopic,face centered cubic Ti and TiH<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

Transmission electron microscopy has been used to study ball milled and H cycled NaAlH₄ with 10 mol% TiCl₃. Isolated from the main phases in this hydrogen storage system, nanocrystalline aggregates of fcc TiH _x (0≤x<0.67) were found. The value of x was determined based on the assumption of a linear increase of the TiH _x lattice parameter by increasing H content. The size of the TiH _x crystallites was in the range 10 to 20 nm, and the lattice parameter decreased from 4.22 Å in TiH_0.67 to 4.10 Å in pure fcc Ti. Non-equilibrium ball milling and subsequent H cycling in combination with a small crystallite size are believed to make the TiH _x phase stable. The present results are the first observations of fcc TiH _x with low hydrogen content, and the measured fcc lattice parameter of Ti matches first-principles calculations.     

Intersubband cyclotron resonance of holes in strained Ge/GeSi(111) heterostructures with germanium wide quantum wells and cyclotron resonance of 1<Emphasis Type="Italic">L</Emphasis> electrons in GeSi layers

The submillimeter (?ω=0.5–5 meV) magnetoabsorption spectra of strained Ge/Ge_1?xSi_x(111) multilayer heterostructures with thick Ge layers (d_Ge=300–850 Å, d_GeSi≈200 Å, x≈0.1) are investigated at T=4.2 K upon band-gap optical excitation. It is revealed that the absorption spectra contain cyclotron resonance lines of 1L electrons localized in GeSi solid solution layers (unlike the previously studied structures with thin Ge layers as quantum wells for 3L electrons). The absorption spectra of the samples with thick Ge layers (d_Ge=800–850 Å) exhibit cyclotron resonance lines of holes due to transitions from the lower Landau levels in the first quantum-well subband to the Landau levels belonging to the third and fifth higher subbands.     

Synthesis and characterization of Ce-doped Sm<Subscript>2</Subscript>CuO<Subscript>4 + <Emphasis Type="Italic">δ</Emphasis></Subscript> cathode for IT-SOFC applications

Single-phase solid solutions of Sm_2 ? x Ce _x CuO_4 + δ (0.05 ≤ x ≤ 0.20) with tetragonal structure are synthesized using acetate combustion followed by sintering at 1373 K for 10 h. X-ray powder diffraction and transmission electron microscopy studies confirmed the formation of solid solution in a single phase. Maximum conductivity (σ = 96.0 ± 0.5 S cm^?1 at 973 K) giving composition Sm_1.90Ce_0.10CuO₄ offers the minimum activation energy (E _a = 0.32 ± 0.004 eV) among all prepared compositions. Lowest cathode polarization resistance (R _p = 3.92 ± 0.07 Ω cm² at 973 K) and activation energy (E _a = 1.12 ± 0.03 eV) values across the measured temperature range are obtained for Sm_1.90Ce_0.10CuO₄. The impedance data fitted well to the Gerischer model indicates that a chemical-electrochemical-chemical-type reaction occurred at the mixed electronic-ionic conducting cathode.     

Galvanomagnetic properties of Heusler alloys Co<Subscript>2</Subscript>Fe<Emphasis Type="Italic">Z</Emphasis> (Z = Al,Si, Ga,Ge, In,Sn, Sb)

The magnetization, Hall effect, and resistivity of Heusler alloys Co₂FeZ (where Z = Al, Si, Ga, Ge, In, Sn, and Sb are s- and p-elements) have been studied at T = 4.2 K in magnetic fields H ≤ 100 kOe. In strong fields (H > 20 kOe), magnetization can be described by the Stoner model. The normal R ₀ and anomalous R _S Hall effect coefficients have been determined. The coefficient RS is positive for almost all the studied alloys and represents a “linearly quadratic” resistivity function incorporating linear and quadratic terms. The constant R ₀ is negative for most alloys, and its absolute value is two or three orders of magnitude smaller than for R _S . The magnetoresistivity of the studied alloys does not exceed several percent and may be both positive and negative for different specimens.     

Photoionization of the Xe atom and Xe@C<Subscript>60</Subscript> molecule

Photoionization of the Xe atom and Xe@C₆₀ molecule have been studied usingthe random phase approximation with exchange (RPAE) method. The Xe atom was described byrelaxed orbitals including overlap integrals. The C₆₀ fullerene has beenrepresented by an attractive short range spherical well with potentialV(r), given byV(r) =  ?V ₀ forr _i  < r < r _o ,otherwise V(r) = 0 wherer _i andr _o are respectively, the inner and outerradii of the spherical shell. The time independent Schrödinger equation was solved usingboth regular and irregular solutions and the continuous boundary conditions atr _i andr _o . The results demonstrate improvementto previous calculations for both the Xe atom and Xe@C₆₀ molecule and comparevery well with the recent experimental data.     

Ground State of <Emphasis Type="Italic">N</Emphasis> Coupled Nonlinear Schrödinger Equations in <Emphasis Type="Italic">R</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>,<Emphasis Type="Italic">n</Emphasis>≤3

We establish some general theorems for the existence and nonexistence of ground state solutions of steady-state N coupled nonlinear Schrödinger equations. The sign of coupling constants β _ij ’s is crucial for the existence of ground state solutions. When all β _ij ’s are positive and the matrix Σ is positively definite, there exists a ground state solution which is radially symmetric. However, if all β _ij ’s are negative, or one of β _ij ’s is negative and the matrix Σ is positively definite, there is no ground state solution. Furthermore, we find a bound state solution which is non-radially symmetric when N=3.     

The electronic and optical properties of InGaN-based solar cells alloys: First-principles investigations via mBJLDA approach

First-principles calculations of the electronic and optical properties of the bulkIn _x Ga_1 ? x N alloys aresimulated within the framework of full-potential linearized augmented plane-wave (FP-LAPW)method. To this end, a sufficiently adequate approach, namely modified Becke-Johnson(mBJLDA) exchange correlation potential is employed for calculating the energy band gapand optical absorption of InGaN-based solar cells systems. The quantities such as theenergy gap, density of states, imaginary part of dielectric function, refractive index andabsorption coefficient are determined for the bulkIn _x Ga_1?x N alloys, in thecomposition range from x = 0 to x = 1. It is found thatthe indium composition robustly controls the variation of band gap. From the examinationof the density of states and optical absorption ofIn _x Ga_1?x N ternary alloys,the energy gaps are significantly reduced for largest In concentration. The computed bandgaps vary nonlinearly with the composition x. It is also surmised thatthe significant variation in the band gaps elaborated via the experimental crystallinegrowth process, is originated by altering the In composition. Interestingly, it isworthwhile to perform InGaN solar cells alloys with improved efficiencies, because oftheir entire energy gap variation from 0.7 to 3.3 eV.     

Effect of pressure on the elastic properties of silicon carbide

The pressure dependences of the second-order elastic constants C _ij and the velocity of sound in 3C-SiC and 2H-SiC crystals are calculated in the framework of the Keating model. The third-order elastic constants C _ijk for 3C-SiC are determined from the dependences of the second-order elastic constants C _ij on the pressure p.     

On the Negative Spectrum of the Two-Dimensional Schrödinger Operator with Radial Potential

For a two-dimensional Schrödinger operator H _{α V}  = ?Δ ?αV with the radial potential V(x) = F(|x|), F(r) ≥ 0, we study the behavior of the number N _?(H _{α V} ) of its negative eigenvalues, as the coupling parameter α tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth N _?(H _{α V} ) = O(α) and for the validity of the Weyl asymptotic law.