Free Electron Model Research Articles

Enhanced NIR reflectance black pigments based on CuCr2-xTixO4: Synthesis and properties

Ti-doped CuCr2O4 is an excellent black cool pigment for preventing surface overheating. Ti was introduced into the precursor in the form of tetrabutyl titanate(C16H36O4Ti) and calcined to obtain a CuCr2-xTixO4 black pigment. XRD, XPS, and EDS results showed that a portion of Ti entered the lattice of CuCr2O4, while the remaining Ti existed in the form of TiO2. The absence of TiO2 reduced the absorption of visible light. As the x value increased, the absorption of visible light by CuCr2-xTixO4 decreased and L* increased. CuCr1.1Ti0.9O4 has a maximum reflectance of 23.0% for NIR solar reflectance, and the mechanism could be determined by the following three reasons: 1) Small particles help to reflect NIR; 2) TiO2 improves the NIR reflectivity of the black pigment; and 3) According to the Drude free-electron theory, the substitution of Ti4+ for Cr3+ increases the concentration of free carriers in CuCr2O4, which increases the NIR reflectance. Application studies indicated that the CuCr1.1Ti0.9O4 coating on an alumina plate was approximately 3 °C lower than the CuCr2O4 coating after 40 minutes of irritation by an IR lamp. Therefore, CuCr1.1Ti0.9O4 pigments exhibited potential applications in insulating materials.

Spontaneous anomalous Hall effect in magnetic and non-magnetic systems

Abstract We consider two cases of spontaneous anomalous Hall current. In a non-magnetic system with spin–orbit coupling (SOC), the applied bias results in the appearance of non-equilibrium magnetization and an anomalous Hall current. The latter demonstrates non-linear dependence on the applied bias. In a magnetic system with SOC, an anomalous current appears without applied bias. We perform the calculations in the framework of the free-electron model, whereas the common approach to this type of phenomenon is based on Berry connection. We demonstrate that anomalous currents acquire a measurable magnitude for reasonable model parameters.

Tunable optical force on a perovskite-coated gold nanosphere by a polarized Bessel beam

The optical force on a perovskite-coated gold nanosphere by a polarized Bessel beam is investigated in the generalized Lorenz-Mie theory (GLMT) framework. The dielectric function of the gold core is described using the Drude-Sommerfeld model, and the cesium silver bismuth bromide (CABB) is considered for the coating. The axial optical forces F z are numerically calculated. The effects of both beam parameters (half-cone angle α0, order l, polarization) and the thickness of the coating are discussed. Numerical results show that the optical force peaks can be adjusted by changing the thickness of the coating. However, the half-cone angle α0 and order l can only change the magnitude of the optical force. The optical force can be tuned by changing beam parameters (α0, l), and the coating thickness of particles. The obtained results demonstrate potential applications for the trapped perovskite gold nanosphere.

An analytical model to ascertain A.C. electrical conductivity of metal matrix composites

ABSTRACT With regard to an inherent understanding of electrical conductivity exhibited by monolithic metals and alloys system and metal matrix composite system under alternating current field, a long-standing unresolved issue, an analytical model is developed following classical free electron theory along with a typical conceptualisation of ‘effective relaxation time’ that combines conventional relaxation time (in view of collision of free electrons with lattice defects) and the time between successive cyclic reversals of electric field (the inverse of frequency). Two prime phenomena (electron scattering and polarisation at particle–matrix interface) are further conceived for metal matrix composite system containing particles. The developed model is found to closely follow (% deviation << 10) the available experimental result in the literature on A.C. electrical conductivity of 6063Al alloy and 6063Al–TiO2 composite systems. The model further ascertains certain system-specific parameters; such as, relaxation time under A.C. field, effective scattering factor and effective relaxation time aid from interface polarisation to specify the system behaviour under alternating current field. Accordingly, the model adequately explains the declining trend of A.C. electrical conductivity with increasing frequency in monolithic alloy system and an enhancement of A.C. electrical conductivity in metal matrix composite system in the presence of particles together with a non-declining trend even on increasing frequency.

Enhancement of gasochromic response to hydrogen of WO3 thin films by post-process modification and catalyst selection

The gasochromic properties of WO3 thin films deposited by electron beam evaporation were investigated, focusing on their structural, morphology and optical changes caused by heat treatment. Moreover, the influence of the thickness and type of catalyst on the gasochromic properties of WO3 was examined. X-ray diffraction measurements revealed that WO3 thin films annealed up to 473 K remained amorphous, whereas annealing at 673 K and above, initiated crystallization into a monoclinic structure. Gasochromic behaviour was observed in response to hydrogen exposure, with the most significant changes occurring in films annealed at 673 K with a thin adlayer of palladium catalyst. A gasochromic response of 1.84 was achieved for H2 concentration as low as 25 ppm. The process of gasochromic colouration was correlated with the changes of free charge carrier concentration calculated based on Drude free electron theory. XPS analysis confirms WO3 reduction under hydrogen exposure, validating proposed colouration mechanisms. These comprehensive findings offer insights into optimizing gasochromic thin films for various sensing applications.

Extension of Mott Formula in the Linearized Boltzmann Transport Equation to the Study of Thermoelectric Power of Electron in Metal

The focus of this paper is to compute and study thermoelectric power of electron in metals using Mott formula based on free electron theory to get an insight on the effect of strain on electron thermoelectric power in metals. Electron density parameter of strained metals and Poisson ratio of metals is obtained and used in this work unlike some researchers that assumed a value for Poisson ratio of all metals. This assumption make the electron density parameter of strained and unstrained metals to be equal and then reduce the computation to only one input parameter. The experimental and simulated value are in good agreement. This agreement is due to the usefulness of free electron theory in theoretical forecast of some properties of metals. The Poisson ratio is involved in simulation. Result obtained revealed that thermoelectric power of electron in metals goes up as the electron density parameter rises due to high-order contributions from electron scattering theory. Electron thermoelectric power in metals increases as the temperature increases due to electron thermal excitation from their mean position. The electron thermoelectric power rises as strain rises for metals.

Development of a new analytical solution for electronic heat capacity for higher electron temperatures

A new analytical solution has been found for the electronic heat capacity of typical s-band metals. It is valid for high electron temperatures of the order of tens of kK, commonly reached in fs pulsed laser ablation. We have used the density of states (DOS) from the free-electron gas model (FEG) and a special type of function called polylogarithms. From the exact analytical solution, a third order Taylor expansion which works well up to 50kK could be derived. A new term was added to the DOS for d-band metals, which allowed us to find a new semi-analytical solution which predicts accurately the electronic heat capacity of Cu.

Thermophysical Properties of Vanadium Melts and Discussion of Thermal Diffusivity in Mott’s Theory

The temperature dependence of density, normal spectral emissivity, heat capacity at constant pressure, and thermal conductivity of the V melt were measured with high accuracy using electromagnetic levitation in a static magnetic field. Surface vibration, translational motion, and convection of the electromagnetically levitated droplet sample were suppressed by the magnetic field. In the measurement of thermal conductivity, convection in the V-melt was sufficiently suppressed by the application of a field of 7 T or higher. In this study, the measured emissivity and thermal conductivity are compared with those evaluated using the free-electron models (Drude model and Wiedemann–Franz rule). Correlations between the density of states and thermal diffusivity at the Fermi energy of transition metals in the liquid state are investigated and the applicability of Mott's s–d scattering model is discussed.

Analysis of Plasmon Loss Peaks of Oxides and Semiconductors with the Energy Loss Function.

This paper highlights the use and applications of the energy loss function (ELF) for materials analysis by using electron energy loss spectroscopy (EELS). The basic Drude-Lindhart theory of the ELF is briefly presented along with reference to reflection electron energy loss (REELS) data for several dielectric materials such as insulating high-k binary oxides and semiconductors. Those data and their use are critically discussed. A comparison is made to the available ab initio calculations of the ELF for these materials. Experimental, high-resolution TEM-EELS data on Si, SiC, and CeO2 obtained using a high-resolution, double-Cs-corrected transmission electron microscope are confronted to calculated spectra on the basis of the ELF theory. Values of plasmon energies of these three dielectric materials are quantitatively analyzed on the basis of the simple Drude's free electron theory. The effects of heavy ion irradiation on the TEM-EELS spectra of Si and SiC are addressed. In particular, the downward shifts of plasmon peaks induced by radiation damage and the subsequent amorphization of Si and SiC are discussed. TEM-EELS data of CeO2 are also analyzed with respect to the ELF data and with comparison to isostructural ZrO2 and PuO2 by using the same background and with reference to ab initio calculations.

Unveiling the double-peak structure of quantum oscillations in the specific heat

Quantum oscillation phenomenon is an essential tool to understand the electronic structure of quantum matter. Here we report a systematic study of quantum oscillations in the electronic specific heat Cel in natural graphite. We show that the crossing of a single spin Landau level and the Fermi energy give rise to a double-peak structure, in striking contrast to the single peak expected from Lifshitz-Kosevich theory. Intriguingly, the double-peak structure is predicted by the kernel term for Cel/T in the free electron theory. The Cel/T represents a spectroscopic tuning fork of width 4.8kBT which can be tuned at will to resonance. Using a coincidence method, the double-peak structure can be used to accurately determine the Landé g-factors of quantum materials. More generally, the tuning fork can be used to reveal any peak in fermionic density of states tuned by magnetic field, such as Lifshitz transition in heavy-fermion compounds.

Effect of nano-crystallization and atomic substitution on electronic and heat properties of Bi2Te3

The specific heat of nano-crystalline (NC) Bi2Te3 (20 nm) in the temperature range of 150 K to 300 K is theoretically studied and compared with the specific heat of the bulk Bi2Te3 materials. Carrier concentration and Hall coefficient are also evaluated using free electron model and compared with experimental results. Lattice (phonon) specific heat has been observed with an overlap repulsive potential with the help of Debye model. For Nano Crystalline materials having high interface volume ratio, the Debye temperature and phonon frequencies are reasonably less at the interfaces than at the core of nano-crystal. Such softening of phonon frequencies at interfaces results in enhancement of Specific Heat in nano-structures. Total specific heat would include interface, core and electronic specific heat. The temperature derivative of the internal energy yields the electronic contribution to specific heat. The present analysis based on the softening of phonon frequencies mechanism is sufficient to describe the enhancement in specific heat by nano-crystallization.

Nanostructured Zr-Cu metallic glass thin films with tailored electrical and optical properties

Nanostructured metallic glass thin films (NMGTF) have attracted increasing attention because they are amorphous materials of tunable microstructure, which allows tailoring their properties. Herein, we provide new insights into the formation of Zr-Cu NMGTF deposited by magnetron sputtering. By varying over a wide range the working-gas pressure during the sputtering process (from 0.3 to 2 Pa) and the alloy composition (from ∼16–94 at% Cu), we show that the film microstructure can be tuned from homogeneous and compact to nanostructured, formed by nanocolumns. In particular, we demonstrate that the formation of nanocolumnar glassy films is promoted at high working pressures and low Cu contents. In addition, transmission electron microscopy and X-ray diffraction analyses reveal that the microstructural transition from homogeneous to nanocolumnar films leads to an increase in the full-width at half-maximum of the first diffraction peak, suggesting a change in the local order of the glassy alloys. Furthermore, we prove that the microstructural change allows the electrical resistivity and the optical reflectance of the films to be tailored to a large extent. We show that the amorphous films exhibit a linear relationship between their reflectance and the square root of the resistivity, according to the free electron model. However, this linear relationship breaks down for high resistivity values, for which the reflectance no longer depends on the resistivity. We highlight that, by changing the working pressure, the electrical resistivity and optical reflectance can be tuned following the same scaling law, whatever the composition of the alloy. Our results shed light on the microstructure-properties relationship of NMGTF and could serve as a platform for future applications in the field of optoelectronics.

Electronic properties of EuO and Eu2O3: FP-LAPW and LCAO computations and Compton spectroscopy strategies

Spin projected energy bands and density of states (DOS) have been deduced using full potential linearized augmented plane wave (FP-LAPW) with density functional theory (DFT) to analyze the electronic properties of EuO and Eu2O3. Whereas the Mulliken population (MP) and Compton profiles (CPs) for both the compounds have been computed using linear combination of atomic orbitals (LCAO) with pure and hybrid DFT (WC1LYP) schemes. The MP analysis indicates EuO to be more covalent than Eu2O3. Our first ever CP measurements for Eu2O3 (using 20 Ci 137Cs Compton spectrometer) indicate DFT with generalized gradient approximation and WC1LYP as successful prescriptions for predicting the electronic properties of such rare-Earth oxides. In addition, equally normalized experimental CPs of Eu2O3 are compared with other rare-Earth oxides RE2O3 (RE = Nd, Sm, Er and Yb) to decide an overall trend of localisation of f-electrons. A metallic behaviour of Eu2O3 is observed on the basis of real-space analysis of experimental, LCAO and free electron theory based CPs of Eu2O3.

High performing supercapacitors using Cr2O3 nanostructures with stable channels- theoretical and experimental insights

Cr2O3 is considered to be a promising cathodic material for supercapacitor applications on the account of its fast redox kinetics, mesoporous structure, and high electrochemical stability. Using a one-step synthesis of Cr2O3, a unique cactus-like morphology can be easily obtained. Such particles improve the specific surface area and electrolyte ion diffusion, leading to enhanced capacitance values. The prepared cactus-like (Cr2O3-c) particles are able to return a specific capacitance of 68 F/g at 5 mV s−1, in three-electrode measurement. This can be attributed to the redox couple of Cr4+/ Cr3+ displayed by Cr2O3 at the electrode–electrolyte interface. Further, the electrochemical performance of cactus-like Cr2O3 material (Cr2O3-c) and solid Cr2O3 spheres (Cr2O3-s) is also compared. This study proves that much superior performance is delivered by protruded nanoparticles. The spikes on the top of the particle surface ensures that two particles are well separated, which stimulates stable channels for ion intercalation–deintercalation. The physics can be explained using a modified free electron model for three-dimensional lattice. Further, using density functional theory (DFT) calculations the electronic band structure, density of states (DOS) and their influence on the electrochemical performance of Cr2O3 are evaluated.

Geometry-Induced Spin Filtering in Photoemission Maps from WTe_{2} Surface States.

We demonstrate that an important quantum material WTe_{2} exhibits a new type of geometry-induced spin filtering effect in photoemission, stemming from low symmetry that is responsible for its exotic transport properties. Through the laser-driven spin-polarized angle-resolved photoemission Fermi surface mapping, we showcase highly asymmetric spin textures of electrons photoemitted from the surface states of WTe_{2}. Such asymmetries are not present in the initial state spin textures, which are bound by the time-reversal and crystal lattice mirror plane symmetries. The findings are reproduced qualitatively by theoretical modeling within the one-step model photoemission formalism. The effect could be understood within the free-electron final state model as an interference due to emission from different atomic sites. The observed effect is a manifestation of time-reversal symmetry breaking of the initial state in the photoemission process, and as such it cannot be eliminated, but only its magnitude influenced, by special experimental geometries.

Local field enhancement factor of spheroidal core–shell nanocomposites with passive and active dielectric cores

We studied the effects of depolarization factor (L), metal fraction (p), and dielectric function of host matrix (ε h ) on the local field enhancement factor (LFEF) of spheroidal core–shell nanocomposites (NCs) with passive and active dielectric cores. Solving Laplace’s equations in the quasi-static limit, we obtained expressions of electric potentials for spheroidal core–shell NCs. Then, by introducing L and the Drude-Sommerfeld model into these expressions, we derived the equation of LFEF in the core of spheroidal core–shell NCs. The results show that whether L, p, and/or ε h vary or kept constant, LFEF of the spheroidal core–shell NCs possesses two sets of peaks with passive dielectric core, whereas only a set of peak is observed with active dielectric core. In NCs with passive dielectric core, an increase in any of these parameters resulted in a more pronounced LFEF peaks in the first set of resonances. With both passive and active dielectric cores, increasing L increases the peaks of LFEF of spheroidal core–shell NCs, whereas increasing p shows decreasing tendency on the peaks of LFEF of the same material with active dielectric core. Moreover, the highest peak of LFEF is obtained by increasing L than p or ε h indicating that change in the geometry of spheroidal core–shell NCs has the highest effect on the LFEF than the metal concentration and host dielectric function. With the same increase in ε h , intensities of LFEF of the spheroidal core–shell NCs decrease when the dielectric core is passive and increase when the dielectric core is active. Briefly, the number and intensities of peaks of LFEF of spheroidal core–shell NCs vary greatly when its core is made either passive or active dielectric. Furthermore, by changing parameters like L, p, and ε h , adjustable LFEF could be obtained and used for applications in optical sensing, nonlinear optics, and quantum optics.

Investigation of electronic structure for β-Zr in the(s-d) subshell

In this paper, a theoretical study of calculating Compton profiles(CPs) for β-Zr using the renormalized-free-atom model and free electron model for different configurations (4d3-x-5s1+x),where (x= 0.1 to 1 step 0.1) is presented .The theoretical results and previously experimental data show good agreement and the best electronic configuration found was (4d2.8-5s1.2 ). The cohesive energy of β-Zr is computed by using theoretical Compton profile data and compared with available data. The band structure and density of state of (β-Zr and -Zr) phases are determined from density functional theory (DFT) with use Quantum wise Atomistix Tool Kit (ATK),Virtual Nano Lab calculations within the framework of the local density approximation (LDA).

Application of fractional Fowler-Nordheim law on field electron emission from tungsten and lanthanum hexaboride nano-scale emitters

ABSTRACT The Murphy-Good Fowler-Nordheim equation was derived for planar and smooth conducting surfaces based on the Sommerfeld free-electron theory. It is applicable to a wide range of micro-emitters. The analyses of experimental field emission data from nano-scaled emitters showed deviation from the theoretical predictions. This has either been noticed in the mismatch of the current–voltage characteristics and/or in the FN-plot behaviour. Such deviation is attributed to the non-planar character of the emitting surface and the shape of the surface potential barrier through which the emitting electrons are tunnelling. Recently, Zubair et al. derived a FN-type equation that takes into account the reduced dimensionality of the emission surface and the non-parabolic energy dispersion [Zubair et al., IEEE Transactions on Electron Devices 65(6) 2018]. In this model, the constants of the conventional FN equation become two variables that depend on the fractional parameter expressing the surface complexity. In the present work, the fractional law is applied to field electron emission from clean tungsten (W) nano-emitter and lanthanum hexaboride (LaB6) nano-protrusions. This has been accomplished in the whole range of the fractional parameter in order to find the value that reproduces a better fit with the experimental data. The application requires determining the geometrical parameter of the emitter and the field emission setup. Results show that the experimental data can easily be reproduced at certain values of the fractional parameter. These ‘certain’ values depend on the geometrical parameters and thus the method used to calculate the electric field value at the emitter surface.

Anomalous electronic energy losses in protons passing through Gd thin films

We report a theoretical analysis of recent data on the unexpectedly high electronic energy loss protons in a polycrystalline gadolinium target. These results led the authors of this data to conclude that the free electron model used to analyse these results fails. In this work we provide a quantitative explanation of the experimental results, using an approach based on density functional theory within the framework of the free electron gas model. We performed semi-classical trajectory simulations (SCTS) and employ the local-density-approximation model (LDA), using an inhomogeneous electron density distribution and the polycrystalline character of Gd samples. The good agreement obtained, delineates the need of considering a realistic description of a particle trajectory and the effective electron density ‘seen’ along it, whose description remains within a FEG model.

Analytical study of higher harmonic bunching and matrix formalism in linear high-gain free-electron laser model

Short-wavelength single-pass free electron lasers (FEL) are capable of generating transverse-coherent and high-power radiations. Compared with the self-amplified spontaneous emission (SASE) FEL scheme, seeded FEL schemes can, in principle, improve the longitudinal coherence of radiation pulses. In recent years, the research community has pursued the realization of high-repetition-rate (MHz) and high-average-power (kW) seeded FELs. To alleviate the requirements of external seeding lasers, many novel seeding schemes have been proposed, which are currently limited by the state-of-the-art laser systems. An analytical study of a recently proposed seeding scheme based on direct-amplification-enabled harmonic generation (DEHG) is presented herein. In contrast to the complete numerical simulations and optimization design, this study starts from one-dimensional FEL equations of motion and derives an analytical formula for the harmonic bunching factor at the chicane exit after the electron beam traverses the modulator undulator. Additionally, to obtain a quick estimate of downstream high-gain FEL performance, we constructed a linear high-gain FEL transport matrix, including the three-dimensional effects incorporated by the Ming-Xie formula. As an application of the analytical formulas, we discuss three different cases for designing and optimizing the seeding scheme. We expect this analytical approach to shed light on seeding designs that aim to produce the desired high-brightness mirobunched electron beam.