Study on the growth of Al-doped ZnO thin films with (112̄0) and (0002) preferential orientations and their thermoelectric characteristics

In this work, using a conventional magnetron sputtering system, Al-doped ZnO (AZO) films with (11$\bar{2}$0) and (0002) preferential orientations were grown on r-sapphire and a-sapphire substrates, respectively. The effect of substrate and deposition temperature on the growth of AZO films and their preferential orientations were investigated. The crystallographic characteristics of AZO films were characterized by X-ray diffraction (XRD). The surface morphology of AZO films was studied by scanning electron microscopy (SEM) and atomic force microscopy (AFM). It is found that the lattice mismatch between AZO and substrate determines the growth of AZO films and their preferential orientations. The thermoelectric properties are strongly dependent on the crystal grain shape and the grain boundaries induced by the preferred orientation. The highly connected and elongated grains lead to high thermoelectric properties. The in-plane anisotropy performances of thermoelectric characteristics were found in the (11$\bar{2}$0) preferential oriented ZnO films. The in-plane power factor of the (11$\bar{2}$0) preferential oriented ZnO films in the [0001] direction was more than 1.5 × 10⁻³ W m⁻¹ K⁻² at 573 K, which is larger than that of the (0002) preferential oriented ZnO films.

In this work, using a conventional magnetron sputtering system, Al-doped ZnO (AZO) films with (11$\bar{2}$0) and (0002) preferential orientations were grown on r-sapphire and a-sapphire substrates, respectively.     

Unraveling the effect of Al doping on CO adsorption at ZnO(101̄0)

Understanding the effect of Al doping on CO adsorption at ZnO(10$\bar{1}$0) is crucial for designing a high-performance CO gas sensor. In this work, we investigated the adsorption properties of CO on pristine and Al-doped ZnO(10$\bar{1}$0) by performing DFT+U calculations. It is found that the doping of Al on ZnO(10$\bar{1}$0) induces the semiconductor-to-metal transition and thus enhances the conductance of the substrate. Compared to the pristine ZnO(10$\bar{1}$0), the adsorption energy of CO on the Al-doped surfaces is significantly enhanced since Al doping has the effect of strengthening the adsorption bond. The bonding analysis reveals that CO adsorbs on pristine ZnO(10$\bar{1}$0) via the sole σ-dative donation between the CO HOMO 5σ and the empty states of the Zn cation while π-back donation from filled states of Zn or Al cations to the CO 2π* LUMO is facilitated on the Al-doped surfaces. The π-back donation also results in the red-shift of the CO stretching frequency on the Al-doped surfaces, contrasting to the blue-shift on the pristine surface. The simulated results demonstrate that the doping of Al to a three-fold coordinated site on ZnO(10$\bar{1}$0) is highly beneficial for boosting the performance of the CO gas sensor. Our theoretical investigation provides fundamental insights into the effect of Al doping on the sensing mechanism for CO at the ZnO(10$\bar{1}$0) surface.

Al doping enhances the adsorption of CO on ZnO(10$\bar{1}$0) by facilitating π-back donation from the surface to CO.     

Hexagonal VO2 particles: synthesis,mechanism and thermochromic properties

Monoclinic vanadium dioxide VO₂ (M) with hexagonal structure is synthesized by hydrothermal method, and the phase evolution is evidenced. Interestingly, the hexagonal morphology comes into being as a result of the low-energy coherent interfaces, (21$\bar{1}$)₁//(2$\bar{1}$$\bar{1}$)₂ and (2$\bar{1}$$\bar{1}$)₁//(020)₂. The size of hexagonal particles is well controlled by changing the concentration of precursor solutions. Hexagonal particles exhibit excellent thermochromic properties with a narrow hysteresis of 5.9 °C and high stability. In addition, the phase transition temperature can be substantially reduced down to 28 °C by simply W doping.

Monoclinic vanadium dioxide VO₂ (M) with hexagonal structure is synthesized by hydrothermal method, and the phase evolution is evidenced.     

The effect of strain on water dissociation on reduced rutile TiO2(110) surface

The effect of external uniaxial strain on water dissociation on a reduced rutile TiO₂(110) surface has been theoretically studied using first-principles calculations. We find that when the tensile strain along [1$\bar{1}$0] is applied, the energy barrier of water dissociation substantially decreases with the increase of strain. In particular, water almost automatically dissociates when the strain is larger than 3%. Besides, the water dissociation mechanism changes from indirect to direct dissociation when the compressive strain is larger than 1.3% along [1$\bar{1}$0] or 3% along [001]. The results strongly suggest that it is feasible to engineer the water dissociation on the reduced rutile TiO₂(110) surface using external strain.

The tensile strain along [1$\bar{1}$0] on the reduced TiO₂(110) surface can greatly promote the dissociation of water, the compressive strain along [001] and [1$\bar{1}$0] can change the dissociation mechanisms.     

High quality N-polar GaN films grown with varied V/III ratios by metal–organic vapor phase epitaxy

We studied the growths and characterizations of N-polar GaN films grown with constant and varied V/III ratios in high-temperature (HT) GaN growth on offcut c-plane sapphire substrates by metal–organic vapor phase epitaxy. It is found that growth with a constantly low V/III ratio resulted in a high crystallinity but a rough surface and a high oxygen concentration, whereas growth with a high V/III ratio led to a smooth surface but a high carbon concentration and a degraded crystallinity. The overall quality of the N-polar GaN epilayer cannot be effectively improved simply by tuning the V/III ratio. The growth with varied V/III ratios was conducted by lowering the V/III ratio in the initial HT-GaN growth and keeping the V/III ratio constantly high in the subsequent growth. Such a change of V/III ratio resulted in a 3D-to-2D like growth mode transition during the early stage of HT-GaN growth which helped reduce threading dislocations and suppress impurity incorporation. By optimizing the nucleation temperature and the thickness of the initial low-V/III-ratio layer, the minimum full-widths at half-maximum of (00$\bar{2}$)/(10$\bar{2}$) rocking curves obtained were 288/350 arcsec and the oxygen concentration was reduced significantly from 1.6 × 10¹⁸ cm⁻³ to 3.7 × 10¹⁷ cm⁻³ while keeping a hillock-free smooth surface morphology. The overall quality of the N-polar GaN films was considerably improved. We believe that this simple, yet effective growth technique has great application prospects for high-performance N-polar GaN-based electron devices.

N-polar GaN films (C, D, E, F) grown with varied V/III ratio show improved crystallinity and reduced impurity concentrations.     

Deformation mechanism in Al0.1CoCrFeNi Σ3(111)[11̄0] high entropy alloys – molecular dynamics simulations

High entropy alloys (HEAs), composed of multiple components with equal or near atomic proportions, have extraordinary mechanical properties and are expected to bear the impact of high-speed forces in armor protection structure materials. In order to understand the deformation behaviour of HEAs under tensile and compressive loading, molecular dynamics simulations were performed to reveal the deformation mechanism and mechanical properties of three crystal structures: Al_0.1CoCrFeNi HEAs without grain boundaries (perfect HEAs), Al_0.1CoCrFeNi HEAs with grain boundaries of Σ3(111)[1$\bar{1}$0] (GBs HEAs) and grain boundaries of Σ3(111)[1$\bar{1}$0] with chemical cluster HEAs (cluster-GBs HEAs). The mechanical properties of the three models at the same strain rate were discussed. Then, the mechanical properties at different strain rates were analyzed. The movement and direction of internal dislocations during the deformation process were investigated. The simulation results show that the GBs HEAs and the cluster-GBs both play an important role in the deformation and failure of the HEAs. Under tensile loading, three behaviour stages of deformation were observed. Cluster-GBs HEAs have a larger yield strength and Young''s modulus than that of GBs and perfect HEAs. The higher the strain rate is, the greater the stress reduction rate. Under compressive loading, there are only two behaviour stages of deformation. Cluster-GBs HEAs also have the largest yield strength. Under tensile and compressive deformation, Shockley partial dislocations of 1/6 <112> are dominant and their moving direction and effect on mechanical properties are discussed.

Build grain boundaries for Al_0.1CoCrFeNi Σ3(111)[1$\bar{1}$0] HEA and elucidate the deformation behavior under tensile and compressive loading.     

Phase relations,and mechanical and electronic properties of nickel borides,carbides, and nitrides from ab initio calculations

Based on density functional theory and the crystal structure prediction methods, USPEX and AIRSS, stable intermediate compounds in the Ni–X (X = B, C, and N) systems and their structures were determined in the pressure range of 0–400 GPa. It was found that in the Ni–B system, in addition to the known ambient-pressure phases, the new nickel boride, Ni₂B₃-Immm, stabilizes above 202 GPa. In the Ni–C system, Ni₃C-Pnma was shown to be the only stable nickel carbide which stabilizes above 53 GPa. In the Ni–N system, four new phases, Ni₆N-R$\bar{3}$, Ni₃N-Cmcm, Ni₇N₃-Pbca, and NiN₂-Pa$\bar{3}$, were predicted. For the new predicted phases enriched by a light-element, Ni₂B₃-Immm and NiN₂-Pa$\bar{3}$, mechanical and electronic properties have been studied.

Based on density functional theory and the crystal structure prediction methods, USPEX and AIRSS, stable intermediate compounds in the Ni–X (X = B, C, and N) systems and their structures were determined in the pressure range of 0–400 GPa.     

First-principles based theoretical calculations of atomic structures of hydroxyapatite surfaces and their charge states in contact with aqueous solutions

Surface charge states of biomaterials are often important for the adsorption of cells, proteins, and foreign ions on their surfaces, which should be clarified at the atomic and electronic levels. First-principles calculations were performed to reveal thermodynamically stable surface atomic structures and their charge states in hydroxyapatite (HAp). Effects of aqueous environments on the surface stability were considered using an implicit solvation model. It was found that in an air atmosphere, stoichiometric {0001} and P-rich {10$\bar{1}$0} surfaces are energetically favorable, whereas in an aqueous solution, a Ca-rich {10$\bar{1}$0} surface is the most stable. This difference suggests that preferential surface structures strongly depend on chemical environments with and without aqueous solutions. Their surface potentials at zero charge were calculated to obtain the isoelectric points (pH_PZC). pH_PZC values for the {0001} surface and the Ca-rich {10$\bar{1}$0} surface were obtained to be 4.8 and 8.7, respectively. This indicates that in an aqueous solution at neutral pH, the {0001} and Ca-rich {10$\bar{1}$0} surfaces are negatively and positively charged, respectively. This trend agrees with experimental data from chromatography and zeta potential measurements. Our methodology based on first-principles calculations enables determining macroscopic charge states of HAp surfaces from atomic and electronic levels.

Macroscopic charge states for hydroxyapatite surfaces have been quantitatively determined using an implicit solvation model based on first-principles calculations.     

Modifying structural polymorphs and tuning electronic properties in pressure-stabilized binary Ir–Sb phases

The search for novel structures and chemical stoichiometry of binary Ir–Sb compounds is of great importance in view of their catalytic applications. Based on the results of swarm structure searching technique combined with density functional theory, we proposed the hitherto unknown Ir–Sb phase diagram in a wide pressure range with various chemical compositions. Besides two ambient pressure phases of IrSb₃-Im$\bar{3}$ and IrSb₂-P2₁/c, five novel phases of IrSb-C2/c, IrSb-P$\bar{1}$, IrSb₂-P$\bar{4}$21m, IrSb₂-I4/mmm and Ir₂Sb-Pmmn were identified at high pressures. The phonon dispersion curves reveal that these phases are all dynamically stable. The calculated electronic results show that a mixed behavior of covalent, ionic and metallic bonds simultaneously exits in these novel phases. A pressure-induced electronic topological transition in Ir₂Sb-Pmmn phase occurs according to the theoretical electronic band structures, while is not shown in other stoichiometries of the Ir–Sb system. Our work provides a potential opportunity for experimental synthesis of crystal structures with different chemical stoichiometries of the binary Ir–Sb system.

Several pressure-stabilized binary Ir–Sb phases have been identified. The chemical bonding states are dramatically modified by the pressure effect. A pressure-induced electronic topological transition has been identified in Ir₂Sb.     

Anisotropic crystallite size distributions in LiFePO4 powders

The anisotropic crystallite sizes in high-performance LiFePO₄ powders were measured by XRD and compared with the particle sizes found by TEM image analysis. Lognormal particle size distribution functions were determined for all three main crystallographic axes. A procedure was developed to determine the fraction of the composite particles which consists of several crystallites and contains small- and large-angle boundaries. In a sample with the most anisotropic crystallites (ratio of volume-weighted mean crystallite sizes $\bar{L}$_V[001]/$\bar{L}$_V[010] = 1.41) the number of the composite particles was at least 30%.

Large composite particles of LiFePO₄ powders registered by TEM with at least 30% amount are recorded by XRD as smaller crystallites with at least 45% amount.     

Structural investigations of La0.6Sr0.4FeO3−δ under reducing conditions: kinetic and thermodynamic limitations for phase transformations and iron exsolution phenomena

The crystal structure changes and iron exsolution behavior of a series of oxygen-deficient lanthanum strontium ferrite (La_0.6Sr_0.4FeO_3−δ, LSF) samples under various inert and reducing conditions up to a maximum temperature of 873 K have been investigated to understand the role of oxygen and iron deficiencies in both processes. Iron exsolution occurs in reductive environments at higher temperatures, leading to the formation of Fe rods or particles at the surface. Utilizing multiple ex situ and in situ methods (in situ X-ray diffraction (XRD), in situ thermogravimetric analysis (TGA), and scanning X-ray absorption near-edge spectroscopy (XANES)), the thermodynamic and kinetic limitations are accordingly assessed. Prior to the iron exsolution, the perovskite undergoes a nonlinear shift of the diffraction peaks to smaller 2θ angles, which can be attributed to a rhombohedral-to-cubic (R$\bar{3}$c to Pm$\bar{3}$m) structural transition. In reducing atmospheres, the cubic structure is stabilized upon cooling to room temperature, whereas the transition is suppressed under oxidizing conditions. This suggests that an accumulation of oxygen vacancies in the lattice stabilize the cubic phase. The exsolution itself is shown to exhibit a diffusion-limited Avrami-like behavior, where the transport of iron to the Fe-depleted surface-near region is the rate-limiting step.

A dependence of structural transformation and iron exsolution on chemical environment and reducing conditions is proven for the perovskite La_0.6Sr_0.4FeO_3−δ.     

Adsorption of azide-functionalized thiol linkers on zinc oxide surfaces

A comprehensive understanding of the interactions between organic molecules and a metal oxide surface is essential for an efficient surface modification and the formation of organic–inorganic hybrids with technological applications ranging from heterogeneous catalysis and biomedical templates up to functional nanoporous matrices. In this work, first-principles calculations supported by experiments are used to provide the microstructural characteristics of (10$\bar{1}$0) surfaces of zinc oxide single crystals modified by azide terminated hydrocarbons, which graft on the oxide through a thiol group. On the computational side, we evaluate the specific interactions between the surface and the molecules with the chemical formula N₃(CH₂)_nSH, with n = 1, 3, 6, 9. We demonstrate that the molecules chemisorb on the bridge site of ZnO(10$\bar{1}$0). Upon adsorption, the N₃(CH₂)_nSH molecules break the neutral (Zn^δ+–O^δ−) dimers on ZnO(10$\bar{1}$0) resulting in a structural distortion of the ZnO(10$\bar{1}$0) substrate. The energy decomposition analysis revealed that such structure distortion favors the adsorption of the molecules on the surface leading to a strong correlation between the surface distortion energy and the interaction energy of the molecule. An azide-terminated thiol with three methylene groups in the hydrocarbon chain N₃(CH₂)₃SH was synthesized, and the assembly of this linker on ZnO surfaces was confirmed through atomic force microscopy. The bonding to the inorganic surface was examined via X-ray photoelectron spectroscopy (XPS). Clear signatures of the organic components on the oxide substrates were observed underlying the successful realization of thiol-grafting on the metal oxide. Temperature-dependent and angle-resolved XPS were applied to examine the thermal stability and to determine the thickness of the grafted SAMs, respectively. We discuss the high potential of our hybrid materials in providing further functionalities towards heterocatalysis and medical applications.

Studying the interaction between organic molecules and metal oxide surfaces is key to the development and modification of organic–inorganic hybrids for application in heterogeneous catalysis, biomedical implants, and functional nanoporous matrices.     

Pressure-driven thermoelectric properties of defect chalcopyrite structured ZnGa2Te4: ab initio study

The pressure induced structural, electronic, transport, and lattice dynamical properties of ZnGa₂Te₄ were investigated with the combination of density functional theory, Boltzmann transport theory and a modified Debye–Callaway model. The structural transition from I$\bar{4}$ to I$\bar{4}$2m occurs at 12.09 GPa. From the basic observations, ZnGa₂Te₄ is found to be mechanically as well as thermodynamically stable and ductile up to 12 GPa. The direct band gap of 1.01 eV is inferred from the electronic band structure. The quantitative analysis of electron transport properties shows that ZnGa₂Te₄ has moderate Seebeck coefficient and electrical conductivity under high pressure, which resulted in a large power factor of 0.63 mW m⁻¹ K⁻² (750 K). The ultralow lattice thermal conductivity (∼1 W m⁻¹ K⁻¹ at 12 GPa) is attributed to the overlapping of acoustic and optical phonon branches. As a result, the optimal figure of merit of 0.77 (750 K) is achieved by applying a pressure of 12 GPa. These findings support that ZnGa₂Te₄ can be a potential p-type thermoelectric material under high pressure and thus open the door for its experimental exploration.

ZnGa₂Te₄ is a stable vacancy ordered defect chalcopyrite structured direct band gap semiconductor which can act as a good p-type thermoelectric material with zT of 0.77 under 12 GPa applied pressure.     

Pressure-induced stability and polymeric nitrogen in alkaline earth metal N-rich nitrides (XN6, X = Ca,Sr and Ba): a first-principles study

Multi-nitrogen or polynitrogen compounds can be used as potential high energy-density materials, so they have attracted great attention. Nitrogen can exist in alkaline earth metal nitrogen-rich (N-rich) compounds in the form of single or double bonds. In recent years, to explore N-rich compounds which are stable and easy to synthesize has become a new research direction. The N-rich compounds XN₆ (X = Ca, Sr and Ba) have been reported under normal pressure. In order to find other stable crystal structures, we have performed XN₆ (X = Ca, Sr and Ba) exploration under high pressure. We found that SrN₆ has a new P$\bar{1}$ phase at a pressure of 22 GPa and an infinite nitrogen chain structure, and BaN₆ has a new C2/m phase at 110 GPa, with an N₆ ring network structure. Further, we observed that the infinite nitrogen chain and the N₆ ring network structure contain typical covalent bonds formed by the hybridization of the sp² and sp³ orbitals of N, respectively. It is found that both SrN₆ and BaN₆ are semiconductor materials and the N-2p orbital plays an important role in the stability of the crystal structure for P$\bar{1}$-SrN₆ and C2/m-BaN₆. Because of the polymerization of nitrogen in the two compounds and their stabilities under high pressure, they can be used as potential high energy-density materials. The research in this paper further promotes the understanding of alkaline earth metal N-rich compounds and provides new information and methods for the synthesis of alkaline earth metal N-rich compounds (XN₆, X = Ca, Sr and Ba).

The Fddd-SrN₆ structure can transform into P$\bar{1}$-SrN₆, and polymerized to infinite nitrogen chain structures at P = 22 GPa. For BaN₆, the Fmmm-BaN₆ structure can transform into C2/m-BaN₆, and polymerized to N₆ ring network structure at P = 110 GPa.     

High-pressure phase transition of AB3-type compounds: case of tellurium trioxide

Tellurium trioxide, TeO₃, is the only example of a trioxide adopting at ambient conditions the VF₃-type structure (a distorted variant of the cubic ReO₃ structure). Here we present a combined experimental (Raman scattering) and theoretical (DFT modelling) study on the influence of high pressure (exceeding 100 GPa) on the phase stability of this compound. In experiments the ambient-pressure VF₃-type structure (R$\bar{3}$c symmetry) is preserved up to 110 GPa. In contrast, calculations indicate that above 66 GPa the R$\bar{3}$c structure should transform to a YF₃-type polymorph (Pnma symmetry) with the coordination number of Te⁶⁺ increasing from 6 to 8 upon the transition. The lack of this transition in the room-temperature experiment is most probably connected with energetic barriers, in analogy to what is found for compressed WO₃. The YF₃-type phase is predicted to be stable up to 220 GPa when it should transform to a novel structure of R$\bar{3}$ symmetry and Z = 18. We analyse the influence of pressure on the band gap of TeO₃, and discuss the present findings in the context of structural transformations of trioxides and trifluorides adopting an extended structure in the solid state.

Tellurium trioxide, TeO₃, is the only example of a trioxide adopting at ambient conditions the VF₃-type structure (a distorted variant of the cubic ReO₃ structure).     

Allotropes of tellurium from first-principles crystal structure prediction calculations under pressure

We investigated the allotropes of tellurium under hydrostatic pressure based on density functional theory calculations and crystal structure prediction methodology. Our calculated enthalpy-pressure and energy-volume curves unveil the transition sequence from the trigonal semiconducting phase, represented by the space group P3₁21 in the range of 0–6 GPa, to the body centered cubic structure, space group Im$\bar{3}$m, stable at 28 GPa. In between, the calculations suggest a monoclinic structure, represented by the space group C2/m and stable at 6 GPa, and the β-Po type structure, space group R$\bar{3}$m, stable at 10 GPa. The face-centered structure is found at pressure as high as 200 GPa. As the pressure is increased, the transition from the semiconducting phase to metallic phases is observed.

Through first-principles simulations, we suggest the phase stability of the allotropic transition sequence of tellurium from the trigonal structure up to the cubic structure.     

Theoretical predictions for low-temperature phases,softening of phonons and elastic stiffnesses,and electronic properties of sodium peroxide under high pressure

High-pressure phase stabilities up to 600 K and the related properties of Na₂O₂ under pressures up to 300 GPa were investigated using first-principles calculations and the quasi-harmonic approximation. Two high-pressure phases of Na₂O₂ that are thermodynamically and dynamically stable were predicted consisting of the Amm2 (distorted P$\bar{6}$2m) and the P2₁/c structures, which are stable at low temperature in the pressure range of 0–22 GPa and 22–28 GPa, respectively. However, the P$\bar{6}$2m and Pbam structures become the most stable instead of the Amm2 and P2₁/c structures at the elevated temperatures, respectively. Interestingly, the softening of some phonon modes and the decreasing of some elastic stiffnesses in the Amm2 structure were also predicted in the pressure ranges of 2–3 GPa and 9–10 GPa. This leads to the decreasing of phonon free energy and the increasing of the ELF value in the same pressure ranges. The HSE06 band gaps suggest that all phases are insulators, and they increase with increasing pressure. Our findings provide the P–T phase diagram of Na₂O₂, which may be useful for investigating the thermodynamic properties and experimental verification.

High-pressure phase stabilities up to 600 K and the related properties of Na₂O₂ under pressures up to 300 GPa were investigated using first-principles calculations and the quasi-harmonic approximation.     

Estimation of Jones matrix,birefringence and entropy using Cloude-Pottier decomposition in polarization-sensitive optical coherence tomography: erratum

An erratum is presented to correct errors in the equations in [Biomed. Opt. Express 7(9), 3551–3573 (2016)].OCIS codes: (110.4500) Optical coherence tomography, (170.4500) Optical coherence tomography, (170.4470) Ophthalmology, (120.2130) Ellipsometry and polarimetryIn our paper [1], several errors in the equations have been found and are corrected as below.Equation (22) of [1] should read Hnoise(Ei¯)=∑j=12−ζj(i)log4(ζj(i)),(22) where the negative sign and the base 4 of the logarithm were described correctly. We note that the same base of the logarithm has to be used for the entropy throughout the processing flow.In addition, Eq. (28) was erroneously presented in [1], which algebraically resulted in 1 regardless of the signals and noises. It was related to the erroneous definition of Eq. (27) in [1]. Equation (27) should be defined to include the bias of the noises as [s0″(1)s1″(1)s2″(1)s3″(1)]:=[|g1H|2¯+|g1V|2¯|g1H|2¯−|g1V|2¯2Re[g1Hg1V*¯]2Im[g1Hg1V*¯]]=[|g1H|2¯+|g1V|2¯|g1H|2¯−|g1V|2¯2Re[E1HE1V*¯]2Im[E1HE1V*¯]]=[|g1H|2¯+|g1V|2¯|g1H|2¯−|g1V|2¯2|E1H|¯|E1V|¯cosδ2|E1H|¯|E1V|¯sinδ]=[|g1H|2¯+|g1V|2¯|g1H|2¯−|g1V|2¯2|g1H|2¯−|n1H|2¯|g1V|2¯−|n1V|2¯cosδ2|g1H|2¯−|n1H|2¯|g1V|2¯−|n1V|2¯sinδ],(27) which is based on Eq. (25) of [1]. Equation (28) of [1] should then read P(1)={s1″(1)}2+{s2″(1)}2+{s3″(1)}2s″0(1)=(|g1H|2¯−|g1V|2¯)2+4(|g1H|2¯−|n1H|2¯)(|g1V|2¯−|n1V|2¯)|g1H|2¯+|g1V|2¯.(28)Consequently, Eqs. (43)-(46) of [1] should readP(ε1¯)=(|ε1H|2¯−|ε1V|2¯)2+4(|ε1H|2¯−Var(ε1H))(|ε1V|2¯−Var(ε1V))|ε1H|2¯+|ε1V|2¯,(43)P(ε2¯)=(|ε2H|2¯−|ε2V|2¯)2+4(|ε2H|2¯−Var(ε2H))(|ε2V|2¯−Var(ε2V))|ε2H|2¯+|ε2V|2¯,(44)P(ε1¯|ε2¯)=(|ε1H|2¯−|ε1V|2¯)2+4(|ε1H|2¯−Var(ε1H|ε2¯))(|ε1V|2¯−Var(ε1V|ε2¯))|ε1H|2¯+|ε1V|2¯,(45)P(ε2¯|ε1¯)=(|ε2H|2¯−|ε2V|2¯)2+4(|ε2H|2¯−Var(ε2H|ε1¯))(|ε2V|2¯−Var(ε2V|ε1¯))|ε2H|2¯+|ε2V|2¯.(46)In Eq. (28), |g1H|2¯−|n1H|2¯ and |g1V|2¯−|n1V|2¯ should be non-negative in principle, but can be negative in practice. If these parameters are negative in the data processing, they are set as zero to avoid physically undefined values of P⁽¹⁾. Similar operations are also applied to Eqs. (43)-(46).In addition, the last sentence of Section 2.5 shown in the following should be deleted because it was presented incorrectly and did not make sense in [1]; “The absolute-squared expected values of the matrix elements in Eq. (24) or (29) that are used in Eqs. (35)-(42) are calculated as |g1H|2¯−|n1H|2¯ and similarly for all other elements.”Since all of the equations were correctly implemented in our processing software of [1], no change is required in the results.     

Structural,optical, electric and dielectric characterization of a NaCu0.2Fe0.3Mn0.5O2 compound

The compound NaCu_0.2Fe_0.3Mn_0.5O₂ was synthesized using a solid-state method and it crystallized in a hexagonal system with a R$\bar{3}$m space group in an O3-type phase. The optical properties were measured using UV-Vis absorption spectrometry to determine the absorption coefficient α and the optical band gap E_g. The optical band gap energy of this sample is 2.45 eV, which indicates that it has semiconductor characteristics. Furthermore, the electrical and dielectric properties of the material were investigated using complex impedance spectroscopy between 10⁻¹ Hz and 10⁶ Hz at various temperatures (333–453 K). The permittivity results prove that there are two types of polarization, dipolar polarization and space charge polarization. The Nyquist diagrams show the contribution of the effects of the grain, grain boundary, and electrode properties. The frequency dependence of the conductivity was interpreted in terms of Jonscher''s law. The DC conductivity follows both the Mott and Arrhenius laws at low and high temperature, respectively. The temperature dependence of the power law exponent(s) suggests that the overlapping large polaron tunneling (OLPT) model is the dominant transport process in this material. The optimum hopping length of the polaron (4 Å) is large compared with the interatomic spacing (2.384 Å for Na–O and 2.011 Å for Cu, Fe, Mn–O).

The compound NaCu_0.2Fe_0.3Mn_0.5O₂ was synthesized using a solid-state method and it crystallized in a hexagonal system with a R$\bar{3}$m space group in an O3-type phase.