Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network

A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform（RT） method, a problem that has never been resolved before, for the Green＇s function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h_1= 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.

Ionic Conductivity of Nano-LaF_3 Bulk Material at Room Temperature

Nanocrystalline powder of LaF3 was synthesized by a method of direct precipitation from water solution. Particle size and shape of LaF3 nanocrystalline powder was analysed with TEM. Particles were mainly spherical with narrow particle size distribution （10 20 nm）. The average particle size analysed with XRD is 16.7 nm. Nano-LaF3 bulk material was prepared by compacting the powder to 1 GPa at room temperature and a vacuum of 10^-4 Pa. The ionic conductivity of nano-LaF3 bulk material was studied with complex impedance spectra at room temperature. The ionic conductivity of nano-LaF3 bulk material （1 × 10^-5 S·cm^-1 ） at room temperature is significantly increased compared to that of single crystal LaF3 （1 × 10^-6 S·cm^-1）. A special phenomenon was observed firstly time that the ionic conductivity increased gradually with multiple testing in result of relaxation.

Structural and electrical properties of single crystalline and bi-crystalline ZnO thin films grown by molecular beam epitaxy

C-oriented ZnO epitaxial thin films are grown separately on the a-plane and c-plane sapphire substrates by using a molecular-beam epitaxy technique. In contrast to single crystalline ZnO films grown on a-plane sapphire, the films grown on c-plane sapphire are found to be bi-crystalline; some domains have a 30~ rotation to reduce the large mismatch between the film and the substrate. The presence of these rotation domains in the bi-crystalline ZnO thin film causes much more carrier scatterings at the boundaries, leading to much lower mobility and smaller mean free path of the mobile carriers than those of the single crystalline one. In addition, the complex impedance spectra are also studied to identify relaxation mechanisms due to the domains and/or domain boundaries in both the single crystalline and bi-crystalline ZnO thin films.

Impedance Characteristics of MgO-ZrO_2 Ceramics Doped with CeO_2

The ultrafine CexMg0.06Zr1-xO1.94 （ x = 0 16% ） powders were synthesized by a chemical co-precipitated method. The pressed compacts were sintered in air at 1300, 1400, 1500, 1600℃ for 3 h, respectively. The phase of the ceramics was characterized by the X-ray diffraction （XRD） method. The conductivity of the ceramics was measured by the AC complex impedance technique at 700- 1200 ℃. The ratio of the cubic phase in the ceramics improves with increasing CeO2 content, leading to a enlargement of the oxygen ionic migration channel. The contact resistance between conductive phase particles decreases with increasing CeO2 content, leading to a lower migration hindrance of the oxygen ionic. Consequently, the ionic conductivity of the ceramics improves with increas- ing CeO2 content. Additionally, an analysis for this phenomenon was also presented.

Complex impedance properties of LiSr_(2)Nb_(5)O_(15) ceramic

The polycrystalline sample of LiSr2Nb5O15(LSN)was prepared by a high-temperature solid state reaction technique.The impedance parameters were studied using an impedance analyzer in a wide range of frequencies(102-106 Hz)at different temperatures(28-500℃).Nyquist plot reveals the presence of bulk effect only.The bulk resistance of the compound decreases with rise in temperature which shows the negative temperature coefficient of resistance(NTCR)like a semiconductor.The ac conductivity spectrum was found to obey Jonscher’s universal power law.DC conductivity(bulk)with temperature demonstrates that the compound exhibits Arrhenius type of electrical conductivity and the activation energy found to be 0.97 eV.

Analytical model of vertical vibrations in piles for different tip boundary conditions:parametric study and applications

In this paper,a model named fictitious soil pile was introduced to solve the boundary coupled problem at the pile tip.In the model,the soil column between pile tip and bedrock was treated as a fictitious pile,which has the same properties as the local soil.The tip of the fictitious soil pile was assumed to rest on a rigid rock and no tip movement was allowed.In combination with the plane strain theory,the analytical solutions of vertical vibration response of piles in a frequency domain and the corresponding semi-analytical solutions in a time domain were obtained using the Laplace transforms and inverse Fourier transforms.A parametric study of pile response at the pile tip and head showed that the thickness and layering of the stratum between pile tip and bedrock have a significant influence on the complex impedances.Finally,two applications of the analytical model were presented.One is to identify the defects of the pile shaft,in which the proposed model was proved to be accurate to identify the location as well as the length of pile defects.Another application of the model is to identify the sediment thickness under the pile tip.The results showed that the sediment can lead to the decrease of the pile stiffness and increase of the damping,especially when the pile is under a low frequency load.

Electrical properties of bulk and nano Li_(2)TiO_(3) ceramics:A comparative study

Nanocrystalline and bulk Li_(2)TiO_(3) having monoclinic structure were prepared by mechanical alloying as well as conventional ceramic route.Complex impedance analysis in the frequency range of 100 Hz-1 MHz over a wide range of temperature(50-500℃)indicates the presence of grain boundary effect along with the bulk contribution.The frequency-dependent conductivity plots exhibit power law dependence,suggesting three types of conduction in the material:low-frequency(100 Hz-1 kHz)conductivity showing long-range translational motion of electrons(frequency independent),mid-frequency(1-10 kHz)conductivity showing short-range hopping of charge carriers and high-frequency(10 kHz-1 MHz)conductivity showing conduction due to localized orientation of hopping mechanism.The electrical conductivity measurement of nanocrystalline and bulk Li_(2)TiO_(3) with temperature shows the negative temperature coefficient of resistance(NTCR)behavior.The activation energy(0.77 eV for nano sample and 0.88 eV for bulk sample)study shows the conduction mechanism in both samples.The low activation energies of the samples suggest the presence of singly ionized oxygen vacancies in the conduction process.

Electrical transport properties of V_(2)O_(5)-added Ni-Co-Zn ferrites

Frequency-dependent dielectric constant,dielectric loss,AC conductivity values and complex impedance spectra of V_(2)O_(5)-added Ni-Co-Zn ferrites(Ni_(0.62)Co_(0.03)Zn_(0.35)Fe_(2)O_(4)+xV_(2)O_(5),where x=0,0.5,1 and 1.5 wt.%)have been investigated at room tempera-ture.The dielectric properties of the samples follow the Maxwell-Wagner polarization model.An inverse relationship was found between dielectric constant and AC electrical resistivity for all the samples.The dielectric constants decreased with the addition of V_(2)O_(5),while the electrical resistivities of V_(2)O_(5)-added Ni-Co-Zn ferrites are found to be larger than that of pure Ni-Co-Zn ferrite.The AC conductivity was reduced with the addition of V_(2)O_(5)to Ni-Co-Zn ferrite at lower-frequency region.However,AC conductivity shows a sharp increase at higher-frequency region,which could be attributed to the enhancement of electron hopping between the Fe2+and Fe3+ions in the ferrite matrix due to the activity of the grains.The complex impedance spectroscopy results through Cole-Cole/Nyquist plot have demonstrated a single semicircular arc.It indicates that conduction mechanism takes place predominantly through the grain/bulk property,which could be ascribed to the larger grain size of V_(2)O_(5)-added Ni-Co-Zn ferrites.

Structural,microstructural and dielectric properties of Ba_(1-x)La_(x)Tie_(1-x/4)O_(3)prepared by sol gel method

Detailed structural and dielectric properties of Lanthanum-doped barium titanate Ba_(1-x)La_(x)Tie_(1-x/4)O_(3)ceramic powders BLTx(where x=0:00;0.10;0.20;0.30 and 0.40)/BT,BLT10,BLT20,BLT30 and BLT40,synthesized by the sol gel process,calcined at 900℃for 3 h and sintered at 1250○C for 6 h,have been investigated.The phase formation and crystal structure of the samples were checked by X-ray diffraction(XRD)and Raman spectroscopy.The samples crystallize in the pure perovskite structure that transforms from tetragonal to pseudocubic under doping with La;results that have been confirmed by Rietveld Refinement technique.The estimated average crystallite size of the samples was about 23 nm.Dielectric parameters(dielectric permittivity and losses)were determined in the temperature range room temperature(RT)-280℃and in the frequency range 500 Hz-2 MHz.La doping gives rise to a strong decrease of the ferro-to-paraelectric transition temperature,and the frequency dependence of the permittivity shows that the samples with x=0.00 and x=0.10 reach their resonance frequency.The frequency dependence of impedance and electric modulus properties were studied over a wide frequency range from 1 kHz to 2MHz at various temperatures to confirm the contributions from grains and grain-boundaries.The complex impedance analysis data have been presented in the Nyquist plot which is used to identify the corresponding equivalent circuit and fundamental circuit parameters;it was found that the grain boundaries resistance is dominant at room temperature.The frequency dependence of the parameters permittivity,losses and AC conductivity reveals that the relaxation process is of the Maxwell-Wagner type of interfacial polarization.