Synthesis and Characterization of New Bismuth Lead Vanadate Pb<Subscript>2</Subscript>BiV<Subscript>3</Subscript>O<Subscript>11</Subscript>

It has been shown that BiVO₄ and Pb₂V₂O₇ react with each other, forming a new compound of the formula Pb₂BiV₃O₁₁ at molar ratio equal to 1:1. This compound has also been obtained from PbO, Bi₂O₃, and V₂O₅, mixed at a molar ratio of 4:1:3. It melts congruently at a temperature of 725 ± 5 °C and crystallizes in the triclinic system with unit-cell parameters: a = 0.710076 nm, b = 1.41975 nm, c = 1.42972 nm, α = 134.552°, β = 97.2875°, γ = 89.6083°, and Z = 4.     

Phase Equilibria in the System Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-CaO-CoO and Gibbs Energy of Formation of Ca<Subscript>3</Subscript>CoAl<Subscript>4</Subscript>O<Subscript>10</Subscript>

An isothermal section of the system Al₂O₃-CaO-CoO at 1500 K has been established by equilibrating 22 samples of different compositions at high temperature and phase identification by optical and scanning electron microscopy, X-ray diffraction, and energy dispersive spectroscopy after quenching to room temperature. Only one quaternary oxide, Ca₃CoAl₄O₁₀, was identified inside the ternary triangle. Based on the phase relations, a solid-state electrochemical cell was designed to measure the Gibbs energy of formation of Ca₃CoAl₄O₁₀ in the temperature range from 1150 to 1500 K. Calcia-stabilized zirconia was used as the solid electrolyte and a mixture of Co + CoO as the reference electrode. The cell can be represented as: From the emf of the cell, the standard Gibbs energy change for the Ca₃CoAl₄O₁₀ formation reaction, CoO + 3/5CaAl₂O₄ + 1/5Ca₁₂Al₁₄O₃₃ → Ca₃CoAl₄O₁₀, is obtained as a function of temperature: /J mol⁻¹ (±50) = −2673 + 0.289 (T/K). The standard Gibbs energy of formation of Ca₃CoAl₄O₁₀ from its component binary oxides, Al₂O₃, CaO, and CoO is derived as a function of temperature. The standard entropy and enthalpy of formation of Ca₃CoAl₄O₁₀ at 298.15 K are evaluated. Chemical potential diagrams for the system Al₂O₃-CaO-CoO at 1500 K are presented based on the results of this study and auxiliary information from the literature.     

Up-Date of a Thermodynamic Database of the ZrO<Subscript>2</Subscript>-Gd<Subscript>2</Subscript>O<Subscript>3</Subscript>-Y<Subscript>2</Subscript>O<Subscript>3</Subscript>-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> System for TBC Applications

The thermodynamic database of the ZrO₂-Gd₂O₃-Y₂O₃-Al₂O₃ system is up-dated taking into account new data on lattice stabilities of ZrO₂, Gd₂O₃ and Y₂O₃ and heat capacity measurements for the monoclinic phase Gd₄Al₂O₉ and phase with garnet structure Gd₃Al₅O₁₂. New data for the heat capacities of Gd₂Zr₂O₇ (pyrochlore) and GdAlO₃ (perovskite) as well as on the enthalpy of formation of fluorite solid solutions (Zr_1−x Gd _x )O_2−x/2 were found to be in good agreement with calculated results. In comparison with the previous assessment, taking into account new experimental data resulted in a change of the melting character of the Gd₄Al₂O₉ phase from a peritectic one to a congruent one in the Gd₂O₃-Al₂O₃ system. Correspondently, in the ternary system ZrO₂-Gd₂O₃-Al₂O₃, the melting character of the three-phase assemblage Gd₂O₃ (B), Gd₄Al₂O₉ and GdAlO₃ changed from eutectic to transition type U. The T ₀-lines for T/M and F/T diffusionless transformations and driving force of partitioning to equilibrium assemblage T + F were calculated in the ZrO₂-Gd₂O₃-Y₂O₃ system.     

Microstructure Characterization of the FeAl<Subscript>2</Subscript>O<Subscript>4</Subscript>-Based Nanostructured Composite Coating Synthesized by Plasma Spraying Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>/Al Powders

The microstructure of the coating prepared by reactive plasma spraying Fe₂O₃/Al composite powders was characterized by x-ray diffraction, scanning electron microscopy, and transmission electron microscopy. The results indicated that the coating exhibited nanostructured microstructure which consisted of FeAl₂O₄, Fe or Fe solid solution, Al₂O₃ and a little FeAl. In the composite coating, spherical Fe particles (tens of nanometers to hundreds of nanometers) were distributed uniformly within the equiaxed and columnar nanograins FeAl₂O₄ matrix. There were two kinds of Al₂O₃ phases present in the composite coating. One kind was nano-sized Al₂O₃ particles uniformly dispersed within the matrix, forming eutectic structure of (FeAl₂O₄ + γ-Al₂O₃); the other was 1-1.5 μm Al₂O₃ particles embedded individually within the matrix. The composite coating had higher toughness than the conventional microstructured Al₂O₃ coating.     

Fabrication of Al matrix composite reinforced with submicrometer-sized Al<Subscript>2</Subscript>O<Subscript>3</Subscript> particles formed by combustion reaction between HEMM Al and V<Subscript>2</Subscript>O<Subscript>5</Subscript> composite particles during sintering

To fabricate an Al-V matrix composite reinforced with submicron-sized Al₂O₃ and Al_xV_y (Al₃V, Al₁₀V) phases, high energy mechanical milling (HEMM) and sintering were employed. By increasing the milling time, the size of mechanically milled powder was significantly reduced. In this study, the average powder size of 59 μm for Al, and 178 μm for V₂O₅ decreased with the formation of a new product, Al-Al₂O₃-Al_xV_y, with a size range from 1.3 μm to 2.6 μm formed by the in-situ combustion reaction during sintering of HEM milled Al and V₂O₅ composite powders. The in-situ reaction between Al and V₂O₅ during the HEMM and sintering transformed the Al₂O₃ and Al_xV_y (Al₃V, Al₁₀V) phases. Most of the reduced V reacted with excess the Al to form Al_xV_y (Al₃V, Al₁₀V) with very little V dissolved into Al matrix. By increasing the milling time and weight percentage of V₂O₅, the hardness of the Al-Al₂O₃-Al_xV_y composite sintered at 1173 K increased. The composite fabricated with the HEMM Al-20wt.%V₂O₅ composite powder and sintering at 1173 K for 2 h had the highest hardness.     

Studies on Al<Subscript>2</Subscript>O<Subscript>3</Subscript>/ZrO<Subscript>2</Subscript>/Al<Subscript>2</Subscript>O<Subscript>3</Subscript> high K gate dielectrics applied in a fully depleted SOI MOSFET

Al₂O₃/ZrO₂/Al₂O₃ gate stacks were prepared on ultrathin SOI (Silicon on insulator) substrates by ultrahigh vacuum electron beam evaporation and post-annealed in N₂ at 450°C for 30 min. Three clear nanolaminate layered structure of Al₂O₃(2.1 nm)/ZrO₂(3.5 nm)/Al₂O₃(2.3 nm) was observed with a high-resolution cross-sectional transmission electron microscope (HR-XTEM). High frequency capacitance voltage (C-V) characteristics of a fully depleted (FD) SOI MOS capacitor at 1 and 5 MHz were studied. The minority carriers determine the high frequency C-V properties, which is opposite to the case of bulk MOS capacitors. The series resistance of the SOI substrate is found to be the determinant factor of the high frequency characteristics of FD SOI MOS capacitors. This article is based on a presentation in “The 7th Korea-China Workshop on Advanced Materials” organized by the Korea-China Advanced Materials Cooperation Center and the China-Korea Advanced Materials Cooperation Center, held at Ramada Plaza Jeju Hotel, Jeju Island, Korea on August 24≈27, 2003.     

Fabrication and Properties of Plasma-Sprayed Al<Subscript>2</Subscript>O<Subscript>3</Subscript>/ZrO<Subscript>2</Subscript> Composite Coatings

Al₂O₃ /xZrO₂ (where x = 0, 3, 13, and 20 wt.%) composite coatings were deposited onto mild steel substrates by atmospheric plasma spraying of mixed α-Al₂O₃ and nano-sized monoclinic-ZrO₂ powders. Microstructural investigation showed that the coatings comprised well-separated Al₂O₃ and ZrO₂ lamellae, pores, and partially molten particles. The coating comprised mainly of metastable γ-Al₂O₃ and tetragonal-ZrO₂ with trace of original α-Al₂O₃ and monoclinic-ZrO₂ phases. The effect of ZrO₂ addition on the properties of coatings were investigated in terms of microhardness, fracture toughness, and wear behavior. It was found that ZrO₂ improved the fracture toughness, reduced friction coefficient, and wear rate of the coatings.     

Structure and electric property comparison between Ge nanoclusters embedded in Al<Subscript>2</Subscript>O<Subscript>3</Subscript> and Al<Subscript>2</Subscript>O<Subscript>3</Subscript>/ZrO<Subscript>2</Subscript>

Metal-insulator-semiconductor (MIS) structures containing Ge nanocrystals embedded in both Al₂O₃ and ZrO₂/Al₂O₃ are fabricated by an ultra-high vacuum electron-beam evaporation method. Secondary ion mass spectroscopy (SIMS) results indicate that Ge embedded in Al₂O₃ diffuses towards the surface of the Al₂O₃ layer after annealing at 800°C in N₂ ambient for 30 min. Ge embedded in ZrO₂/Al₂O₃ is stable, thus inducing less leakage current. Capacitance voltage studies indicate that annealing can effectively passivate the negatively charged trapping centers. Memory effect of the Ge nanoclusters is verified by hysteresis in the C-V curves in the Al₂O₃/Ge+Al₂O₃/Al₂O₃ and ZrO₂/Ge+Al₂O₃/Al₂O₃ samples. This article is based on a presentation in “The 7th Korea-China Workshop On Advanced Materials” organized by the Korea-China Advanced Materials Cooperation Center and the China-Korea Advanced Materials Cooperation Center, held at Ramada Plaza Jeju Hotel, Jeju Island, Korea on August 24–27, 2003.     

Effect of Al<Subscript>2</Subscript>O<Subscript>3</Subscript> Content on Electrical Breakdown Properties of Al<Subscript>2</Subscript>O<Subscript>3</Subscript>/Cu Composite

Al₂O₃/Cu composites were prepared by external addition of Al₂O₃, and the effect of Al₂O₃ content on microstructure, density, hardness, electrical conductivity and vacuum electrical breakdown properties was studied. The results show that with increasing Al₂O₃ addition, the density of Al₂O₃/Cu composite significantly decreases, the hardness sharply increases and then slowly decreases, but the electrical conductivity invariably decreases. The vacuum breakdown test shows that with increasing Al₂O₃ addition, the breakdown strength first sharply increases and then decreases when the Al₂O₃ content exceeds 1.2 wt.%; the chopping current always exhibits a decreasing trend and the arc life first increases and then decreases. According to the morphology of arc erosion and analysis, the arc erosion resistance increases and then decreases sharply. In the range of experiments, the optimal arc erosion resistance of Al₂O₃/Cu composite can be obtained with the addition of 1.2 wt.% Al₂O₃.     

Phase Relations in the System TiO<Subscript>2</Subscript>-V<Subscript>2</Subscript>O<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> under Oxidizing and Reducing Conditions

The target of this work was to investigate the phase development in the catalyst system consisting of TiO₂ (Anatase) and V₂O₅ (Shcherbinaite) under several gas atmospheres. Thus a set of V₂O₅/TiO₂ specimens was prepared by ball milling and exposed to subsequent annealing in air and feed gas in the temperature range from 400 to 700 °C. The XRD-results showed that the initial phases Anatase and Shcherbinaite remain stable for all atmospheres containing oxygen. In the temperature range above 525 °C the formation of a Rutile solid solution (Rutile-ss) containing VO _x species takes place. However, under reducing conditions (lower oxygen partial pressure) the reduction of V₂O₅ to V₂O₃ was found by X-ray diffraction measurements. There is no miscibility up to 1300 °C followed by the formation of V₂TiO₅ (Berdesinskiite). SEM images underline the reduction by monitoring the change in morphology with respect to the V-containing phases. TiO₂ remains without much alteration. The two phases V₂Ti₇O₁₇ and V₂Ti₃O₉ (Schreyerite) as described in mineralogy have not been observed in these experiments. The knowledge of phase relations helps to find the appropriate processing conditions and to understand the aging phenomena of catalysts.     

Phase Relations in the ZrO<Subscript>2</Subscript>-Nd<Subscript>2</Subscript>O<Subscript>3</Subscript>-Y<Subscript>2</Subscript>O<Subscript>3</Subscript> System: Experimental Study and Advanced Thermodynamic Modeling

Phase equilibria in the ZrO₂-Nd₂O₃-Y₂O₃ system at 1523-1873 K have been investigated by x-ray diffraction (XRD) and scanning electron microscopy combined with energy dispersive x-ray spectroscopy (SEM/EDX). Temperatures of phase transformations were determined by differential thermal analysis. Temperatures of invariant reactions in the ZrO₂-Nd₂O₃ system F = A + Pyr and H = F + A were determined as 1763 and 2118 K respectively and thermodynamic parameters of phases were re-assessed. Phase transformations in ternary systems were determined at 1732 K for composition ZrO₂-48.46Nd₂O₃-5.38Y₂O₃ (mol%) and at 1744 and 1881 K for composition ZrO₂-79.09Nd₂O₃-2.75Y₂O₃ (mol%). They were interpreted using XRD investigation before and after DTA as Pyr + B → F, Pyr → F and A → B, respectively. The solubility of the Y₂O₃ in pyrochlore phase was found to exceed 10 mol%. The thermodynamic parameters of the ZrO₂-Nd₂O₃-Y₂O₃ system were reassessed taking into account solubility of Y₂O₃ in the Nd₂Zr₂O₇ pyrochlore phase (Pyr). It is assumed that Y³⁺ substitutes Nd³⁺ and Zr⁴⁺ in their preferentially occupied sublattices. Ternary parameter was introduced into fluorite phase (F) for better reproducing of phase equilibria. Mixing parameters were reassessed for phase A (Nd₂O₃ based solution), monoclinic phase B and cubic phase C (Y₂O₃ based solution). The isothermal sections calculated for the ZrO₂-Nd₂O₃-Y₂O₃ system are in the reasonable agreement with experimental results.     

Tunneling magnetoresistance in sintered Fe<Subscript>3</Subscript>O<Subscript>4</Subscript> samples diluted with Fe and α-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>

Electric transport and magnetoresistance characteristics were investigated for Fe₃O₄-x Fe(x=0, 10, 20 wt.%) samples and Fe₃O₄-α-Fe₂O₃ samples sintered at 500°C. For composition dependence of Fe₃O₄-x Fe samples, the largest room temperature MR, 3.3% at 10 kOe, was obtained from a Fe₃O₄-10 Fe sample. For the surface heat treatment dependence of Fe₃O₄ powders, the largest room temperature MR, 4% at 10 kOe, was obtained from a Fe₃O₄-α-Fe₂O₃ sample sintered with Fe₃O₄ powders heated at 200°C in air. It was found that these enhanced MR ratios always appear together with the appropriate excess resistance which is regarded as the tunneling barrier. These enhanced MR ratios of Fe₃O₄-10 Fe and Fe₃O₄-α-Fe₂O₃ samples can be explained by the increased interparticle contact sites and the appropriate thickness of α-Fe₂O₃, respectively.     

Thermal and structural role of additives in P<Subscript>2</Subscript>O<Subscript>5</Subscript>-ZnO-Sb<Subscript>2</Subscript>O<Subscript>3</Subscript> glass for low expansion sealing materials

A glass based on the P₂O₅-ZnO-Sb₂O₃ ternary system was modified with various additives, such as RO (R=Ca, Ba and Mn), B₂O₃ and V₂O₅, for low temperature and low expansion sealing materials. The glass transition temperature (T_g) and coefficient of thermal expansion (CTE) were monitored and reduced with additive compositions of RO. Additional incorporation of B₂O₃ at the expense of RO also showed a similar result. Significant improvement was observed when the glass was modified with V₂O_5. A glass showing T_g<350 °C along with CTE<65×10⁻⁷/°C was found, suggesting a high potential for low temperature sealing materials especially for display applications. The role of the quaternary element within the glass is discussed, along with the structural effect using Raman spectroscopy.     

Oxidation Behavior of NiFe<Subscript>2</Subscript>O<Subscript>4</Subscript> Spinel-Coated Interconnects in Wet Air

Corrosion of boilers and heat exchangers is accelerated in the presence of vanadium, sodium, and sulfur from low-grade fuels. Several iron- and nickel-based alloys were immersed in 60 mol% V₂O₅–40Na₂SO₄ salt for 1000 h in order to investigate their degradation behavior at 600 °C in air. Materials performance was analyzed by means of substrate recession rate and metallographic characterization. Their corrosion mechanism is characterized by the formation of a sulfide/oxide layer adjacent to the metal, the dissolution of scale oxides in the molten deposit, and their precipitation near the outer surface of the deposit. High Ni- and Cr-containing alloys show the lowest metal loss rates. Al addition was detrimental due to low-melting eutectic AlVO₄–V₂O₅ formation. Fe–Cr-based alloys showed the highest metal loss rates. In such alloys, high Cr additions (above 20%) did not improve the performance due to the negative synergetic effect by simultaneous dissolution of Fe₂O₃ and Cr₂O₃. The predominant salt composition at the corrosion front varied from vanadate rich to sulfate rich during the exposure. This change in the attacking salt makes it difficult to find a protective material for mixed sulfate–vanadate-induced corrosion.     

Dependence of Al<Subscript>2</Subscript>O<Subscript>3</Subscript> coating thickness and annealing conditions on microstructural and electrochemical properties of LiCoO<Subscript>2</Subscript> film

We studied the dependence of Al₂O₃ coating thickness and annealing conditions on the surface morphology and electrochemical properties of Al₂O₃ coated LiCoO₂ films. The optimum coating thickness allowing for the highest capacity retention was about 24 nm. A sample consisting of Al₂O₃ coated on annealed LiCoO₂ film with additional annealing at 400 °C had a uniform coating layer between the coating materials and cathode films. This sample showed the best capacity retention of ∼91 % with a charge-cut off of 4.5 V after 30 cycles, while the bare cathode film showed a capacity retention of ∼32 % under the same conditions. The formation of second phases such as Co-Al-O was observed in the coating films by X-ray photoelectron spectroscopy (XPS). The Co-Al-O containing samples showed a higher initial capacity because of their smaller grain size, but less capacity retention than the Al₂O₃ containing samples.     

Phase Formation of the Yttrium Aluminates in the Y<Subscript>2</Subscript>O<Subscript>3</Subscript>-Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiC System

Phase formation sequence of the yttrium aluminates in the Y₂O₃-Al₂O₃-SiC ternary system as temperature increases were investigated via x-ray diffraction (XRD). Results showed that YAM (monoclinic), YAP (perovskite) and YAG (garnet) were the yttrium aluminates presented in the solid-state reacted samples at a fixed Al₂O₃:SiC ratio of 1:1. Formation of the yttrium aluminates depended on the temperature. The YAM, YAP and YAG started to form below 1150 °C, at 1300 °C, and at 1450 °C, respectively. Accordingly, two behavior phase diagrams of the Y₂O₃-Al₂O₃-SiC ternary system were recognized, one is in the temperature range of 1150-1300 °C and the other is in 1300-1450 °C, respectively. Thereafter, the phase equilibrium was reached in the temperature range of 1450-1700 °C. Effects of SiC on the phase formation processes in the ternary system were discussed.     

Influence of Feedstock Powder Modification by Heat Treatments on the Properties of APS-Sprayed Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-40% TiO<Subscript>2</Subscript> Coatings

The formation and decomposition of aluminum titanate (Al₂TiO₅, tialite) in feedstock powders and coatings of the binary Al₂O₃-TiO₂ system are so far poorly understood. A commercial fused and crushed Al₂O₃-40%TiO₂ powder was selected as the feedstock for the experimental series presented in this paper, as the composition is close to that of Al₂TiO₅. Part of that powder was heat-treated in air at 1150 and 1500 °C in order to modify the phase composition, while not influencing the particle size distribution and processability. The powders were analyzed by thermal analysis, XRD and FESEM including EDS of metallographically prepared cross sections. Only a maximum content of about 45 wt.% Al₂TiO₅ was possible to obtain with the heat treatment at 1500 °C due to inhomogeneous distribution of Al and Ti in the original powder. Coatings were prepared by plasma spraying using a TriplexPro-210 (Oerlikon Metco) with Ar-H₂ and Ar-He plasma gas mixtures at plasma power levels of 41 and 48 kW. Coatings were studied by XRD, SEM including EDS linescans of metallographically prepared cross sections, and microhardness HV1. With the exception of the powder heat-treated at 1500 °C an Al₂TiO₅-Ti₃O₅ (tialite–anosovite) solid solution Al_2?xTi_1+xO₅ instead of Al₂TiO₅ existed in the initial powder and the coatings.     

Comparative analysis of the kinetics of dissolution of oxides Y<Subscript>2</Subscript>O<Subscript>3</Subscript> and Fe<Subscript>2</Subscript>O<Subscript>3</Subscript> in the iron matrix upon mechanical alloying

The kinetics of low-temperature dissolution of oxides Y₂O₃ and Fe₂O₃ in an iron matrix during mechanical alloying has been studied using electron microscopy. It has been shown that the dissolution rate upon deformation of primary coarse oxides Fe₂O₃ in α iron (and, hence, saturation of the α matrix with oxygen) during treatment in a ball mill for up to 10 h is several times higher than the dissolution rate of Y₂O₃ oxides. The high-temperature (1100°C) annealing of a mechanoalloyed mixture of Fe + 1.5% Y + 1.35% Fe₂O₃ leads to the precipitation of 60% (of the total number of particles) secondary oxides 2–5 nm in size and only of 5–7% secondary nanooxides in a mechanoalloyed mixture of Fe + 2% Y₂O₃.     

High-Temperature Oxidation of Nickel-Based Cermet Coatings Containing WC and Al<Subscript>2</Subscript>O<Subscript>3</Subscript> Nanosized Particles

This paper investigates the high-temperature oxidation of cermet coatings composed of two types of nanosized particles (WC and a mixture of WC and Al₂O₃) incorporated in nickel and produced by co-electrodeposition. For this purpose, high-temperature oxidation tests were conducted at three temperatures (500, 600, and 700 °C) in dry air with 6 time intervals up to 96 h and mass changes at each specific time interval was measured. Statistical techniques were used to calculate the oxidation rate constants (k) and growth-rate time constants (a) for all coatings. The confidence intervals associated with tests were also calculated. The results showed linear to sub-parabolic oxidation rates for coatings composed of only WC particles and sub-liner to liner oxidation rates for coating with both WC and Al₂O₃ particles. The reduction in oxidation rates for coatings with both WC and Al₂O₃ particles were correlated to the addition of Al₂O₃ particles in the matrix.     

Solid Solution and Phase Relations in SiC-AlN-Pr<Subscript>2</Subscript>O<Subscript>3</Subscript> System

The phase relations in the Si-Al-Pr-O-N-C systems, involving SiC-AlN-Pr₂O₃, AlN-Pr₂O₃-Al₂O₃ and SiC-AlN-Pr₂O₃-Al₂O₃ systems were determined by XRD phase analyses of the solid-state reacted samples from powder mixtures of SiC, AlN, Pr₂O₃, as well as Al₂O₃. Pr₂Al(Si)O₃N(C) solid-solution (1:1 ss) between SiC and Pr₂AlO₃N (1:1 compound) was discovered with the limited solubility of 0.6 SiC at 1650 °C. Subsolidus phase diagram of SiC-AlN-Pr₂O₃ system was presented, SiC was compatible with AlN, Pr₂O₃ and 1:1 ss, respectively. Two-aluminates PrAlO₃ (PrAP) and PrAl₁₁O₁₈ [β(Pr), β-Al₂O₃ type] were formed when Al₂O₃ impurity was introduced in AlN powder. They establish the equilibrium relationships respectively with SiC, AlN, Pr₂O₃ and Pr₂AlO₃N. Accordingly, the phase relations in the AlN-Pr₂O₃-Al₂O₃ ternary system and SiC-AlN-Pr₂O₃-Al₂O₃ quaternary system containing four quaternary phases compatible tetrahedrons were presented.