SB Distribution Research Articles

Collaborative effects of Zn and Sb Co-doping in magnesium silicide for thermoelectric applications

The effects of Zn and Sb co-doping in Mg2Si are investigated for thermoelectric applications, particularly focusing on the bonding with an Ni electrode and the grain boundaries. In the case of single Sb doping in Mg2Si, Sb is segregated at the interface with the Ni electrode, often accompanied by void formation due to the Kirkendall mechanism. On the other hand, in the case of Zn and Sb co-doping in Mg2Si, fast diffusion of Zn and the formation of a stable Zn-Sb alloy result in a smooth interface and void-free Zn-Sb-rich region embedded by the intermetallic ω-phase on the Mg2Si side of the interface with the Ni electrode. The thermoelectric properties and microanalyses at the grain boundaries with and without post-annealing reveal significant atomistic redistributions of Zn to form Zn-O segregation at the grain boundaries while keeping the Sb distribution uniform. Such Zn-O segregation possibly reduces the barrier height at the grain boundaries and stabilizes the grains compared to the case without post-annealing, where reactive oxygen remains. The long-term annealing test up to 1300 h under 773 K in air shows good stability of the materials with the Ni electrode. These collaborative effects will be particularly important for achieving reliable thermoelectric modules using Mg2Si.

МЕТОД СИНТЕЗА МНОГОКОМПОНЕНТНОЙ МОДЕЛИ АТРИБУТИВНЫХ ПРИЗНАКОВ ОБЪЕКТОВ

The subject matter of the article are the processes of forming of objects’ attribute features analytical descriptions for solving applied problems of statistical recognition of objects’ images on multi-channel images. The goal is to develop a multicomponent mathematical model for representing statistical information about the summation of geometric, colour and structural parameters of observational objects. The tasks to be solved are: to formalize the procedure of statistical image segmentation in conditions of incomplete a priori information about objects classes and unknown distribution densities of classification characteristics; to build effective algorithms for detection and linking contour points; to choose a universal mathematical model for describing the geometric shape of both the object and its structural components and to develop a robust method for estimating the model parameters. The methods used are: statistical methods of pattern recognition, methods of probability theory and mathematical statistics, methods of contour analysis, numerical methods for conditional optimization. The following results were obtained. The method of multicomponent model synthesis for describing colour, geometric and structural attributes of object images on multichannel images is proposed. In the model terms, the object is represented by a hierarchical set of nested contours, for the selection of which information about the colour characteristics of statistically homogeneous regions of the image is used. Methods for detecting and linking contour points have been developed, which make it possible to obtain the coordinates of the boundaries circular sweep for both convex and concave geometric objects. As a universal basis for describing the model components, the Johnson SB distribution is adopted, which allows us to describe practically any unimodal and wide class of bimodal distributions. A method for Johnson distribution parameters’ estimation from sample data, based on the method of moments and using optimization procedures for a non-linear objective function with constraints is given. Conclusions. The scientific novelty of the results obtained is as follows: the methods for describing the objects’ images in the form of a combination of several bright-geometric elements and structural connections between them have been further developed, which makes it possible to comprehensively take into account the attribute features of objects in the procedures for analyzing and interpreting images, automatically detecting and locating objects with specified characteristics

Порівняння шести функцій щільності розподілу для моделювання таксаційної будо¬ви за діаметром модальних ялицевих деревостанів Українських Карпат

Для дослідження таксаційної будови за діаметром ялицевого елемента лісу у семи підприємствах лісового господарства Українських Карпат та в НПП "Сколівські Бескиди" закладено 14 прямокутних тимчасових пробних площ та 61 кругову пробну площу (у 15 таксаційних виділах). Дані суцільного переліку дерев ялиці зі замірами їх діаметрів використано для визначення особливостей розподілу кількості дерев за діаметром. Моделювання фактичного розподілу кількості дерев здійснено за допомогою шести фунцій щільності розподілу: дво-, три-, та семипараметричного розподілу Вейбулла, гамма- та бета-розподілу, Sb розподілу Джонсона. Виявлено, що ялицеві деревостани характеризуються значною мінливістю діаметра. За результатами аналізу основних усереднених статистичних показників різних функцій розподілу за діаметром ялицевого елемента встановлено, що дво-, трипараметричний розподіл Вейбулла, гамма- та бета-розподіл завищують показники асиметрії та ексцесу порівняно із фактичним розподілом, Sb розподіл Джонсона занижує ці показники порівняно з фактичними, найближчі результати має бімодальний розподіл Вейбулла. Отримані результати непараметричної оцінки за допомогою χ² критерію Пірсона дають змогу зробити висновок, що найпридатнішою функцією для дослідження таксаційної будови модальних ялицевих деревостанів Українських Карпат є семипараметричний розподіл Вейбулла, а найменш точним – гамма-розподіл.

Cathodoluminescence Characterization of Dilute Nitride GaNSbAs Alloys

The effects of ex situ annealing in N ambient and in situ annealing in As ambient on GaNSbAs/GaAs structures grown by molecular beam epitaxy were investigated by low temperature cross-sectional cathodoluminescence (CL). The amount and distribution of Sb was measured by energy dispersive spectroscopy (EDS). The cross-sectional CL analysis of all samples reveals a shift of the near band edge (NBE) emission along the growth axis, presumably associated with a non-uniform incorporation of Sb during the growth process, in agreement with the Sb distribution measured by EDS in the as-grown sample. The NBE emission in the annealed samples presents a redshift with respect to the as-grown sample. This effect might be explained by a redistribution/activation of N in the GaNSbAs lattice since the Sb distribution measured by EDS does not reveal significant changes, within the error margin, with respect to the as-grown sample. The in situ annealed in the As overpressure sample shows the best properties for solar cells applications, i.e., a NBE peak position close to 1.0 eV and the lowest full width at half maximum of this emission.

Antimony exposure and speciation in human biomarkers near an active mining area in Hunan, China

Antimony (Sb) exposure threatens human health. To identify human biomarkers for Sb exposure, we analyzed 480 environmental samples from an active Sb mining area in Hunan, China. Elevated Sb concentrations exceeding the reference level were detected in drinking water (70% of n = 83 total samples), foods (80%, n = 188), urine (95%, n = 63), saliva (44%, n = 48), hair (80%, n = 51) and nails (83%, n = 47). Drinking water contributed 85%–100% of the average daily dose (ADD) of Sb, and the total ADD (11.7 μg/kg bodyweight/day) was up to thirty times higher than the oral reference dose (0.4 μg/kg bodyweight/day) as recommended by USEPA. A positive correlation was found between ADD and Sb content in hair (p = 0.02), but not in urine (p = 0.051), saliva (p = 0.52) or nails (p = 0.85), suggesting that hair is the best non-invasive biomarker. Micro X-ray fluorescence analysis indicated that Sb is distributed in discrete spots in hair and nails, and Sb distribution is correlated with other metals. Methylated Sb species were predominant in urine (46%–100%) and saliva (74%–100%) in collected samples, implying that the human metabolic system adopts methylation as an effective pathway to detoxify and excrete Sb.

Sorption–desorption of Sb(III) in different soils: Kinetics and effects of the selective removal of hydroxides, organic matter, and humic substances

To examine the Sb(III) retention by three soils with different properties (Ferrosol, Primosol and Isohumosol), kinetic batch experiments were carried out for Sb(III) adsorption–desorption, followed by Sb release using a sequential extraction procedure. In addition, hydroxides, organic matter, and humic substances were selectively removed by washing the soil with oxalate, sodium dithionate–citrate–bicarbonate, H2O2, and NaOH. The effects of removing these substances on Sb(III) retention were investigated by comparing the Sb distribution coefficients and desorption rates. The results indicated that exogenous Sb(III) was adsorbed onto all three soils rapidly at first and then more slowly. After 168 h of adsorption, most of the adsorbed Sb(III) was irreversibly retained in stable fractions by the Ferrosol. Oxidation reactions negatively affected Sb(III) retention by the Primosol and Isohumosol, and a large proportion of the Sb adsorbed remained mobilizable. The oxalate washing markedly enhanced Sb retention but the sodium dithionate–citrate–bicarbonate washing decreased Sb retention in all three soils. The H2O2 and NaOH washings affected Sb retention by the Ferrosol more than Sb retention by the Primosol and Isohumosol. Changes in the pH and hydroxides caused by the washing strongly affected Sb sorption–desorption. The results improve our understanding of the mobility and bioavailability of exogenous Sb(III) in soils and might benefit future remediation option of Sb-contaminated soils.

Investigation on Sb-doped induced Cu(InGa)Se2 films grain growth by sputtering process with Se-free annealing

In this study, the influences of doping with antimony sulfide (Sb2S3) and metallic Sb on the properties of Cu(InGa)Se2 (CIGS) films and devices have been investigated. The incorporation of metallic Sb in CIGS films has little effect on grain growth, while the incorporation of Sb2S3 could significantly increase CIGS grain size and alter the preferential orientation of CIGS films. Photoluminescence spectra reveal that the pre-deposited Sb2S3 is beneficial to reduce or passivate defects in CIGS layer. Furthermore, the effects of annealing temperature on grain size and phase structure of Sb-doped CIGS films have been explored and Sb distribution profiles in CIGS film are elucidated. These results suggest that Sb2S3 could take effects on enhancing grain growth beyond a certain critical temperature when the generated antimony selenide (Sb2Se3), rather than Sb2S3, decomposed into some volatile phases. These volatile phases could facilitate the diffusion of the atoms in grain boundaries when they pass through from the bottom to outside of CIGS films. Finally, the efficiency of solar cells increases from 8.4% for un-doped sample to 11.9% for Sb2S3-doped sample. This study provides a new approach for fabricating CIGS thin film with large grains and a potential way for non-hazardous mass production application.

Development of a statistical bivariate wind speed-wind shear model (WSWS) to quantify the height-dependent wind resource

The goal of this study was to develop a statistical bivariate wind speed-wind shear model (WSWS). The development of WSWS is based on near surface wind speed data available from 397 measurement stations distributed over Germany, as well as on ERA-Interim reanalysis wind speed data available in 1000m above ground level (a.g.l.). These data were used (1) to calculate empirical distributions of wind speed in 1000ma.g.l., (2) empirical distributions of the wind shear exponent, and (3) to fit theoretical distributions to the empirical wind speed and wind shear exponent distributions. It was found that the four parameter Johnson SB distribution reproduces the shape of the wind speed in 1000ma.g.l. empirical distributions best. The four parameter Dagum distribution provided good fits to the empirical wind shear distributions. The parameterized wind speed and wind shear marginal distributions were then linked by 16 joint copulas. Goodness-of-fit evaluation of the joint copulas demonstrates that the Gaussian-Gaussian copula reproduces the empirical bivariate wind speed-wind shear distribution most accurately. By using WSWS it is possible to continuously calculate the wind speed probability density function in hub heights between 10ma.g.l. and 200ma.g.l. This allows WSWS to be applied to virtually any power curve for computing the wind energy yield and capacity factor in the analyzed hub height range. A one-time site-specific parametrization of WSWS is sufficient for a comprehensive height-dependent exploitation of the available wind resource.

GEOCHEMICAL STUDY OF THE URBAN AND SUBURBAN AREA OF NAFPLION CITY, ARGOLIDHA PREFECTURE, HELLAS

Soil, as the primary receptor of anthropogenic urban contamination acts as a sink for a variety of toxic and other hazardous substances. It constitutes, therefore, an indicator of contamination and may be utilised geochemically to assess environmental quality of urban and suburban areas. In Nafplion, an urban and suburban area of 50 km2 , was investigated using for the first time in Hellas an integrated approach with all available geoscientific techniques to make an in-depth environmental impact assessment. One of these techniques was applied geochemistry, which mapped the geochemistry of surface soil (0-10 cm) with 144 samples, collected on a regular grid of 500 x 500 km. The following fifty determinands were measured on the soil samples: Ag, Al, As, B, Ba, Be, Bi, Ca, Cd, Ce, Co, Cr, Cu, Fe, Ga, Ge, Hg, K, La, Li, Mg, Mn, Mo, Na, Nb, Ni, P, Pb, Rb, Re, S, Sb, Sc, Se, Sn, Sr, Ta, Te, Th, Ti, Tl, U, V, W, Y, Zn, Zr, pH, electrical conductivity and grain-size distribution. The aim of the geochemical study was to distinguish, as far as possible, the origin of chemical elements, and (i) to classify them as geogenic or anthropogenic; (ii) to delineate contaminated areas, and (iii) to assess potential future impacts of human activities on soil. Interpretation of the resulting geochemical patterns has shown that those of Al, Fe, Be, Ce, Cr, Co, Ga, Ge, K, La, Li, Mg, Nb, Ni, Rb, Sc, Sr, Tl, V, Y, W and Zr are of geogenic origin, since they are directly related to parent rocks, whereas patterns of As, B, Ba, Bi, Ca, Cd, Cu, Mn, Mo, Na, P, Pb, S, Sb, Sn, Th, U and Zn are interpreted as being of dual origin, geogenic and anthropogenic. In this paper, the geochemical distribution of only five elements shall be described, i.e., Pb, Zn, Cu, Ni and Na. This case study was indeed very interesting, since for the interpretation of some patterns, even the military history of the area had to be unravelled.

Modeling diameter distributions of Gmelina arborea plantation in Omo Forest Reserve, Nigeria with Johnson’s SB

ABSTRACTDiameter distribution modeling is an essential tool for obtaining reliable information on the structure, growth, and yield of forests. However, this tool has not been duly utilized in many forest plantations, especially in Nigeria. Thus, this article presents the effectiveness of using the Johnson SB function for modeling diameter distributions of a Gmelina arborea plantation in Omo Forest Reserve, Nigeria. Fifty plots of 0.04 ha were randomly selected across three age series. All trees with DBH ≥ 5.0 cm in the selected plots were measured. Three fitting methods for the SB distribution were compared: conditional maximum likelihood (CML), moments (MOM), and Knoebel and Burkhart (KB) methods. The parameter recovery model (PRM) was used to recover the parameters of the distribution. The assessment was based on Kolmogorov-Smirnov (K-S), mean square error (MSE), mean absolute error (MAE), and bias. The results showed that the underlying diameter distribution of the Gmelina arborea followed the Johnson’s SB distribution fitted with MOM. The number of rejections by the K-S test was zero for MOM and CML. The mean K-S value for MOM was statistically different from CML and KB methods. The results obtained after recovering the parameters of the SB distribution were comparable with the real distributions of the Gmelina arborea stand.

Capabilities of the Johnson SB distribution in estimating rain variables

Numerous fields of atmospheric and hydrological sciences require the parametric form of the raindrop size distribution (DSD) to estimate the rainfall rate from radar observables as well as in cloud resolving and weather forecasting models. This study aims to investigate the capability of the Johnson SB distribution (JSB) in estimating rain integral parameters. Specifically, rainfall rate (R), reflectivity factor (Z) and mean mass diameter (Dmass) estimated by JSB are compared with those estimated by a three-parameter Gamma distribution, widely used by radar meteorologists and atmospheric physicists to model natural DSD. A large dataset consisting of more than 155,000 one-minute DSD, from six field campaigns of Ground Validation (GV) program of NASA/JAXA Global Precipitation Measurement mission (GPM), is used to test the performance of both JSB and Gamma distribution. The available datasets cover a wide range of rain regimes because of the field campaigns were carried out in different seasons and locations. Correlation coefficient, bias, root mean square error (RMSE) and fractional standard error (FSE) between estimated and measured integral parameters are calculated to compare the performances of the two distributions.The capability of JSB in estimating the integral parameters, especially R and Z, resulted very close to that of Gamma distribution. In particular, for light precipitation, JSB is superior to Gamma distribution in estimating R with FSE of 11% with respect to values ranging between 25% and 37% about for Gamma. Comparison of the estimated and measured DSDs shows that the JSB distribution reproduces the natural DSD quite accurately.

Particle-based Sb distribution model for Cu–Pb flotation as part of geometallurgical modelling at the polymetallic Rockliden deposit, north-central Sweden

The polymetallic Cu–Zn ore of the Rockliden massive sulphide deposit in the Skellefte District in north-central Sweden contains a number of deleterious elements in relevant concentrations. Of particular concern is the amount of antimony (Sb) reporting to the Cu–Pb concentrate. The aim of this study was to compare different model options to simulate the distribution of Sb minerals in a laboratory flotation test based on different degrees of details in the mineralogical information of the flotation feed. Experimental data obtained from four composites were used for the modelling and simulation. The following different simulation levels were run (sorted from least to highest level of detail of their mineralogical information): chemical assays, unsized bulk mineralogy, sized bulk mineralogy and particle information. It was shown that recoveries simulated based on bulk mineralogy are mostly within the error margin acceptable in the exploration stage of the Rockliden deposit. Unexpected high deviation in the simulation using particle information from the original recovery has been partly attributed to the fact that recovery of non-liberated particles cannot be modelled appropriately in the present version of the modelling and simulation software. It is expected that the implementation of full particle information in simulation will improve the Sb distribution model for the mineralogically complex Rockliden deposit.

A hybrid choice model with a nonlinear utility function and bounded distribution for latent variables: application to purchase intention decisions of electric cars

ABSTRACTThe hybrid choice model (HCM) provides a powerful framework to account for heterogeneity across decision-makers in terms of different underlying latent attitudes. Typically, effects of the latent attitudes have been represented assuming linear utility functions. In contributing to the further elaboration of HCMs, this study suggests an extended HCM framework allowing for nonlinear utility functions of choice alternatives including not only observed but also latent variables. Box–Cox transformations are used to represent the nonlinear utility function. Johnson’s SB distribution is suggested to represent the random term of the latent variables, satisfying the constraint of the Box–Cox transformation. An empirical study using stated choice data about the intention to purchase electric cars is conducted. The empirical results show that the proposed framework can capture nonlinear effects of underlying variables including latent attitudes, thereby enhancing the explanatory power of the choice model.

Evaluation of antimony segregation in InAs/InAs1−xSbx type-II superlattices grown by molecular beam epitaxy

InAs/InAs1−xSbx type II superlattices designed for mid-wavelength infrared photo-detection have been studied using several electron microscopy methods, with specific attention directed towards interface chemical diffusion caused by Sb segregation. Reciprocal-space image analysis using the geometric phase method showed asymmetric interfacial strain profiles at the InAs-on-InAsSb interface. Measurement of local Sb compositional profiles across the superlattices using electron energy-loss spectroscopy and 002 dark-field imaging confirmed asymmetric Sb distribution, with the InAs-on-InAsSb interface being chemically graded. In contrast, the InAsSb-on-InAs interface showed a small intrinsic interface width. Careful evaluation of the experimental Sb composition profiles using a combined segregation and sigmoidal model reached quantitative agreement. Segregation dominated over the sigmoidal growth at the InAs-on-InAsSb interface, and the segregation probability of 0.81 ± 0.01 obtained from the two microscopy techniques agreed well within experimental error. Thus, 81% of Sb atoms from the topmost layers segregated into the next layer during growth causing the interfaces to be broadened over a length of ∼3 nm. This strong Sb segregation occurred throughout the whole superlattice stack, and would likely induce undesirable effects on band-gap engineering, such as blue-shift or broadening of the optical response, as well as weakened absorption.

Spatial Variability and Distribution of the Metals in Surface Runoff in a Nonferrous Metal Mine.

The spatial variation and distribution features of the metals tested in the surface runoff in Xikuangshan Bao Daxing miming area were analyzed by combining statistical methods with a geographic information system (GIS). The results showed that the maximum concentrations of those five kinds of the metals (Sb, Zn, Cu, Pb, and Cd) in the surface runoff of the antimony mining area were lower than the standard value except the concentration of metal Ni. Their concentrations were 497.1, 2.0, 1.8, 22.2, and 22.1 times larger than the standard value, respectively. This metal pollution was mainly concentrated in local areas, which were seriously polluted. The variation coefficient of Sb, Zn, Cu, Ni, Pb, and Cd was between 0.4 to 0.6, wherein the Sb's spatial variability coefficient is 50.56%, indicating a strong variability. Variation coefficients of the rest of metals were less than 50%, suggesting a moderate variability. The spatial structure analysis showed that the squared correlation coefficient (R 2) of the models fitting for Sb, Zn, Cu, Ni, Pb, and Cd was between 0.721 and 0.976; the ratio of the nugget value (C 0) to the abutment value (C + C 0) was between 0.0767 and 0.559; the semivariogram of Sb, Zn, Ni, and Pb was in agreement with a spherical model, while semivariogram of Cu and Cd was in agreement with Gaussian model, and both had a strong spatial correlation. The trend and spatial distribution indicated that those pollution distributions resulting from Ni, Pb, and Cd are similar, mainly concentrated in both ends of north and south in eastern part. The main reasons for the pollution were attributed to the residents living, transportation, and industrial activities; the Sb distribution was concentrated mainly in the central part, of which the pollution was assigned to the mining and the industrial activity; the pollution distributions of Zn and Cu were similar, mainly concentrated in both ends of north and south as well as in west; the sources of the metals were widely distributed.

Lateral Placement of Vehicles on Horizontal Curves

The deterioration of pavement is a significant factor which adds to its life cycle cost. This is mainly due to wear and tear of the pavement caused due to wheels of vehicle and environmental factors. This deterioration is mainly observed at maximum wheel path on the pavement. The maximum wheel path is identified by conducting placement survey of vehicles. A review of literature indicates that lot of studies related to placement of vehicle in straight stretch is available whereas on curves it is very less. This has motivated the authors to conduct a placement study on horizontal curves. About 8 locations (paved and unpaved) in Bangalore city was identified for the present study. The data was analyzed for general placement and placement with respect to the type of vehicles for varying width and radius. It was found that as the curve radius increases the percentage shift was found to decrease. The vehicles were generally observed to shift towards center with increase in road width on curves. The placement of commercial vehicles was modeled by a probability distribution function and this was modeled as Johnson SB distribution.

Statistical Analysis of Breakdown Voltages in Virgin and Aged LDPE Using Johnson S<sub>B</sub> and Weibull Distribution

Polymeric material such as low density polyethylene (LDPE) has been used for decades as insulating material. Any polymeric material will experience degradation after prolonged application of high electrical stresses. Deeper understanding of the long term electrical degradation of the insulating material is necessary to predict the life of high voltage cable. Electroluminescence method (EL) is used to detect the breakdown voltages of thin film LDPE. This method utilizes a Peltier cooled electron multiplying charge coupled device (EMCCD) camera to detect the breakdown of the sample. Statistical distribution of the AC breakdown voltages of 100μm virgin and aged LDPE has been analysed. Comparison for the best fitted distribution was made for Weibull distribution and Johnson SB distribution using Anderson-Darling (A2) goodness-of-fit and Kolmogorov-Smirnov (D) goodness-of-fit (GOF). Johnson SB is rarely used in high voltage engineering application. The probability density function (PDF) and the cumulative density function (CDF) for both distributions are defined in this article. The statistical parameters used are estimated based on Maximum Likelihood Estimation (MLE) for both distributions. Based on the statistical analysis, it is observed that Johnson SB provide better fitting than Weibull distribution with lower fitting error and that 3-parameter Weibull is much better fitting than 2-parameter Weibull distribution for most cases. It is also found that the median breakdown voltage of LDPE samples decreases with increasing aging temperature.

New class of Johnson distributions and its associated regression model for rates and proportions

By starting from the Johnson SB distribution pioneered by Johnson (), we propose a broad class of distributions with bounded support on the basis of the symmetric family of distributions. The new class of distributions provides a rich source of alternative distributions for analyzing univariate bounded data. A comprehensive account of the mathematical properties of the new family is provided. We briefly discuss estimation of the model parameters of the new class of distributions based on two estimation methods. Additionally, a new regression model is introduced by considering the distribution proposed in this article, which is useful for situations where the response is restricted to the standard unit interval and the regression structure involves regressors and unknown parameters. The regression model allows to model both location and dispersion effects. We define two residuals for the proposed regression model to assess departures from model assumptions as well as to detect outlying observations, and discuss some influence methods such as the local influence and generalized leverage. Finally, an application to real data is presented to show the usefulness of the new regression model.

Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

Abstract Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.

Numerical simulation and experimental characterization of the performance evolution of a liquid antimony anode fuel cell

A solid oxide fuel cell (SOFC) with a liquid antimony anode is fabricated based on a smooth single crystal YSZ electrolyte substrate and a porous Pt cathode. The performance of the liquid antimony anode was tested under “battery mode”, with the anode chamber shielded in argon throughout the test and the cathode exposed to air. Polarization curves were taken and a long term constant potential discharging test was carried out afterwards. Taking electrochemical reaction, mass transport and microstructure of the liquid Sb anode into consideration, a one dimensional mathematical model was built and then validated by the polarization curve and the constant potential discharging performance curve obtained during the test. This model analyzes the metallic Sb distribution in the anode during cell operation, explains the cell performance evolution base on the microstructural development of the liquid Sb anode and simulates how the anode microstructure affects the cell performance.