In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow e...In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.展开更多
Calcined kaolin/TiO2 composite particle material （CK/TCPM） was prepared with TiO2 coating on the surfaces of calcined kaolin particles by the mechano-chemical method. X-ray diffraction （XRD） and scanning electron ...Calcined kaolin/TiO2 composite particle material （CK/TCPM） was prepared with TiO2 coating on the surfaces of calcined kaolin particles by the mechano-chemical method. X-ray diffraction （XRD） and scanning electron microscope （SEM） were used to investigate the microstructures and morphologies, respectively. The mechanism of the mechano-chemical reaction between calcined kaolin and TiO2 was studied by infrared spectra （IR）. The results show that TiO2 coats evenly on the surfaces of calcined kaolin particles by Si-O-Ti and Al-O-Ti bonds on their interfaces. The hiding power and whiteness of CK/TCPM are 17.12 g/m^2 and 95.7%, respectively, presenting its similarity to TiO2 in pigment properties.展开更多
CoO/CeOcomposites with high surface areas and ultrafine crystalline sizes for catalytic combustion of methane were firstly prepared by a new sol-gel method which combined ultrasonic impregnation treatment and calcinat...CoO/CeOcomposites with high surface areas and ultrafine crystalline sizes for catalytic combustion of methane were firstly prepared by a new sol-gel method which combined ultrasonic impregnation treatment and calcination in Natmosphere. The samples were characterized by various means such as nitrogen adsorption/desorption, X-ray diffraction(XRD), Htemperature-programmed reduction(H-TPR),X-ray photoelectron spectroscopy(XPS) and transmission electron microscopy(TEM). Results showed that the modified catalyst had the mesoporous structure, comparatively higher amount of surface oxygen and larger oxygen vacancies than others. As a result of the structure and surface composition merits, a high methane combustion conversion(50%) could be obtained at a low temperature of 262 °C for the modified CoO/CeOcomposites catalysts. The experimental results demonstrated that ultrasonic impregnation treatment combined with the Nthermal treatment prior to calcination in air had a promising application for preparation of CoO/CeOcomposites catalysts for low-temperature catalytic combustion of methane.展开更多
In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solution...In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.展开更多
This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)metho...This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.展开更多
This paper employs a multi-parameter multi-step chaos control method, which is built up on the OGY method, to stabilize desirable UPOs of a gear system with elastomeric web as a high-dimensional and non-hyperbolic cha...This paper employs a multi-parameter multi-step chaos control method, which is built up on the OGY method, to stabilize desirable UPOs of a gear system with elastomeric web as a high-dimensional and non-hyperbolic chaotic system, and the analyses are carried out. Three types of relations between components of a certain control parameter combination are defined in a certain control process. Special emphasis is put on the comparison of control efficiencies of the multi-parameter multi-step method and single-parameter multi-step method. The numerical experiments show the ability to switch between different orbits and the method can be a good chaos control alternative since it provides a more effective UPOs stabilization of high-dimensional and non-hyperbolic chaotic systems than the single-parameter chaos control, and according to the relation between components of each parameter combination, the best combination for chaos control in a certain UPO stabilization process are obtained.展开更多
This study explores the controllable synthesis of CuAlO_(2) using copper hydroxide and pseudo-boehmite powders as raw materials via a simple solid-phase ball milling method,along with its catalytic performance investi...This study explores the controllable synthesis of CuAlO_(2) using copper hydroxide and pseudo-boehmite powders as raw materials via a simple solid-phase ball milling method,along with its catalytic performance investigation in methanol steam reforming(MSR).Various catalysts were prepared under different conditions,such as calcination temperature,calcination atmosphere,and heating rate.Characterization techniques including BET,XRD,XPS,SEM and H2-TPR were employed to analyze the samples.The results revealed significant effects of calcination temperature on the phase compositions,specific surface area,reduction performance,and surface properties of the CA-T catalysts.Based on the findings,a synthesis route of CuAlO_(2) via the solid-phase method was proposed,highlighting the importance of high calcination temperature,nitrogen atmosphere,and low heating rate for CuAlO_(2) formation.Catalytic evaluation data demonstrated that CuAlO_(2) could catalyze MSR without pre-reduction,with the catalytic performance of CA-T catalysts being notably influenced by calcination temperature.Among the prepared catalysts,the CA-1100 catalyst exhibited the highest catalytic activity and stability.The findings of this study might be useful for the further study of the catalytic material for sustained release catalysis,including the synthesis of catalytic materials and the regulation of sustained release catalytic performance.展开更多
The influence of replacement level of calcined coal-series kaolin(CCK) on hydration of ordinary Portland cement(OPC) was studied by X-ray diffraction(XRD)/Rietveld method. X-ray diffraction/Rietveld method was used to...The influence of replacement level of calcined coal-series kaolin(CCK) on hydration of ordinary Portland cement(OPC) was studied by X-ray diffraction(XRD)/Rietveld method. X-ray diffraction/Rietveld method was used to quantify the crystalline phase composition of the hydrated samples. Additionally, the morphology of hydrated samples was observed by scanning electron microscopy(SEM). The results showed that, calcium hydroxide(CH), ettringite(AFt) and amorphous phase content in hydrated samples decreased as the replacement level of CCK increased, while AFm and str?tlingite increased, which was caused by the combination of dilute, physical and pozzolanic effects. The hydration of anhydrous cement phases was accelerated by physical effect but hindered by the retardation effect of CCK. The role of each effects was discussed in detail to analyze the mechanism of OPC hydration with CCK addition. The SEM images showed that the shortening of AFt at 1 day and the denser texture at 28 days was observed with CCK addition, which was caused by the physical and pozzolanic effects, respectively.展开更多
Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical res...Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency.Hybrid block methods for instance are specifically used in numerical integration of initial value problems.In this paper,an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations(ODEs).In deriving themethod,the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval.Furthermore,the convergence properties along with the region of stability of the method were examined.It was concluded that the newly derived method is convergent,consistent,and zero-stable.The method was also found to be A-stable implying that it covers the whole of the left/negative half plane.From the numerical computations of absolute errors carried out using the newly derived method,it was found that the method performed better than the ones with which we compared our results with.Themethod also showed its superiority over the existing methods in terms of stability and convergence.展开更多
The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of ...The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of APS were studied. Thereafter, aiming to build up a multi-step APS forecasting model that provides richer information than a conventional one-step model, the largest Lyapunov exponents(largest LEs) method was introduced into PGS. By experimental tests conducted using the same dataset, its prediction performance was compared with traditional wavelet neural network(WNN) method in both one-step and multi-step processes. Based on the results, a new multi-step forecasting model called WNN-LE method was proposed, where WNN, which enjoys a more accurate performance along with a better learning ability in short-term forecasting, was applied in the early forecast steps while the Lyapunov exponent prediction method in the latter steps precisely reflect the chaotic feature in latter forecast period. The MSE of APS forecasting for one hour time period can be reduced from 83.1 to 27.1(in a parking building with 492 berths) by using largest LEs method instead of WNN and further reduced to 19.0 by conducted the new method.展开更多
Monodispersed spheroidal SnO2 nanocrystals with the grain size of 8-30 nm were synthesized by the precipitation method using SnCl4·5H2O （stannic chloride hydrate） as raw materials.Differential scanning calorime...Monodispersed spheroidal SnO2 nanocrystals with the grain size of 8-30 nm were synthesized by the precipitation method using SnCl4·5H2O （stannic chloride hydrate） as raw materials.Differential scanning calorimetry/thermogravimetry （DSC/TG）,X-ray diffraction （XRD） and transmission electron microscope （TEM） were used to characterize the structure of SnO2 nanocrystals.The influences of the calcination temperature and time on the lattice constant,the lattice distortion and the grain size of SnO2 nanocrystals were discussed based on the XRD results.The grain growth kinetics of SnO2 nanocrystals during calcination process was simulated with a conventional grain growth model which only took into account of diffusion and with a new isothermal model proposed by our group,which took into account of both diffusion and surface reactions.Using conventional model,the grain growth rate constant of SnO2 crystals is 1.55×104nm5/min with a pre-exponential factor of 5 and an activation energy of 108.62 kJ/mol.Compared with the convention model,the new isothermal model is more realistic in reflecting the grain growth behavior of SnO2 nanocrystals during the calcination process.This indicates that the grain growth of SnO2 nanocrystals is controlled by both diffusion and reaction factors,and the effect of surface reactivity on the grain growth of SnO2 nanocrystals could not be ignored.A combined activation energy estimated with the new isothermal model is 53.46 kJ/mol.展开更多
Pure K2Ti4O9 whiskers were prepared by KDC（Kneading-Drying-Calcination） method with TiO2 and K2CO3 as raw materials. The influences of TiO2/K2CO3 molar ratio（RT/K）, calcination temperature（TC） and cooling proces...Pure K2Ti4O9 whiskers were prepared by KDC（Kneading-Drying-Calcination） method with TiO2 and K2CO3 as raw materials. The influences of TiO2/K2CO3 molar ratio（RT/K）, calcination temperature（TC） and cooling process on phase composition and morphology of the whiskers were investigated by TG-DSC（thermo gravimetric-differential scanning calorimeter）, XRD（X-ray diffraction）, and SEM（scanning electron microscope）. Pure K2Ti4O9 potassium titanate whiskers with large length-diameter ratio（r）（over 250） can be obtained at RT/K = 2.9 and TC = 950 ℃.展开更多
The single-phase BiFeO3 powders were prepared by sol-gel method with the starting materials of bismuth nitrate and ferric nitrate, and the effect of the calcined temperature on the phases of BiFeO3 samples was studied...The single-phase BiFeO3 powders were prepared by sol-gel method with the starting materials of bismuth nitrate and ferric nitrate, and the effect of the calcined temperature on the phases of BiFeO3 samples was studied. The x-ray diffraction (XRD)showed that the single-phase BiFeO3 powders were obtained with a calcined temperature of 700 ℃. The scanning electron microscope(SEM)analysis indicated that the grain size was around 500 nm in single-phase BiFeO3 powders, and uniform particle size distribution. The FT-IR spectra showed that the BiFeO3 powders began to crystallize at 500℃.展开更多
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA019)the National Natural Science Foundation of China(11871312)。
文摘In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.
基金Funded by the National Key Technology R&D Program of China(No.2008BAE60B06)Beijing Municipal Science&Technology Commission (No.Z080003032208015)
文摘Calcined kaolin/TiO2 composite particle material （CK/TCPM） was prepared with TiO2 coating on the surfaces of calcined kaolin particles by the mechano-chemical method. X-ray diffraction （XRD） and scanning electron microscope （SEM） were used to investigate the microstructures and morphologies, respectively. The mechanism of the mechano-chemical reaction between calcined kaolin and TiO2 was studied by infrared spectra （IR）. The results show that TiO2 coats evenly on the surfaces of calcined kaolin particles by Si-O-Ti and Al-O-Ti bonds on their interfaces. The hiding power and whiteness of CK/TCPM are 17.12 g/m^2 and 95.7%, respectively, presenting its similarity to TiO2 in pigment properties.
文摘CoO/CeOcomposites with high surface areas and ultrafine crystalline sizes for catalytic combustion of methane were firstly prepared by a new sol-gel method which combined ultrasonic impregnation treatment and calcination in Natmosphere. The samples were characterized by various means such as nitrogen adsorption/desorption, X-ray diffraction(XRD), Htemperature-programmed reduction(H-TPR),X-ray photoelectron spectroscopy(XPS) and transmission electron microscopy(TEM). Results showed that the modified catalyst had the mesoporous structure, comparatively higher amount of surface oxygen and larger oxygen vacancies than others. As a result of the structure and surface composition merits, a high methane combustion conversion(50%) could be obtained at a low temperature of 262 °C for the modified CoO/CeOcomposites catalysts. The experimental results demonstrated that ultrasonic impregnation treatment combined with the Nthermal treatment prior to calcination in air had a promising application for preparation of CoO/CeOcomposites catalysts for low-temperature catalytic combustion of methane.
文摘In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.
基金the National Natural Science Foundation of China(Grant Nos.71961022,11902163,12265020,and 12262024)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(Grant Nos.2019BS01011 and 2022MS01003)+5 种基金2022 Inner Mongolia Autonomous Region Grassland Talents Project-Young Innovative and Entrepreneurial Talents(Mingjing Du)2022 Talent Development Foundation of Inner Mongolia Autonomous Region of China(Ming-Jing Du)the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region Program(Grant No.NJYT-20-B18)the Key Project of High-quality Economic Development Research Base of Yellow River Basin in 2022(Grant No.21HZD03)2022 Inner Mongolia Autonomous Region International Science and Technology Cooperation High-end Foreign Experts Introduction Project(Ge Kai)MOE(Ministry of Education in China)Humanities and Social Sciences Foundation(Grants No.20YJC860005).
文摘This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.
基金Sponsored by the National High Technology Research and Development Program of China(Grant No.2009AA04Z404)
文摘This paper employs a multi-parameter multi-step chaos control method, which is built up on the OGY method, to stabilize desirable UPOs of a gear system with elastomeric web as a high-dimensional and non-hyperbolic chaotic system, and the analyses are carried out. Three types of relations between components of a certain control parameter combination are defined in a certain control process. Special emphasis is put on the comparison of control efficiencies of the multi-parameter multi-step method and single-parameter multi-step method. The numerical experiments show the ability to switch between different orbits and the method can be a good chaos control alternative since it provides a more effective UPOs stabilization of high-dimensional and non-hyperbolic chaotic systems than the single-parameter chaos control, and according to the relation between components of each parameter combination, the best combination for chaos control in a certain UPO stabilization process are obtained.
基金supported by the Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology(2023yjrc51)the National Natural Science Foundation of China(22172184)+2 种基金the Foundation of State Key Laboratory of Coal Conversion(J24-25-603)the Fundamental Research Project of ICC-CAS(SCJC-DT-2023-01)Weiqiao-UCAS Special Projects on Low-Carbon Technology Development(GYY-DTFZ-2022-015)。
文摘This study explores the controllable synthesis of CuAlO_(2) using copper hydroxide and pseudo-boehmite powders as raw materials via a simple solid-phase ball milling method,along with its catalytic performance investigation in methanol steam reforming(MSR).Various catalysts were prepared under different conditions,such as calcination temperature,calcination atmosphere,and heating rate.Characterization techniques including BET,XRD,XPS,SEM and H2-TPR were employed to analyze the samples.The results revealed significant effects of calcination temperature on the phase compositions,specific surface area,reduction performance,and surface properties of the CA-T catalysts.Based on the findings,a synthesis route of CuAlO_(2) via the solid-phase method was proposed,highlighting the importance of high calcination temperature,nitrogen atmosphere,and low heating rate for CuAlO_(2) formation.Catalytic evaluation data demonstrated that CuAlO_(2) could catalyze MSR without pre-reduction,with the catalytic performance of CA-T catalysts being notably influenced by calcination temperature.Among the prepared catalysts,the CA-1100 catalyst exhibited the highest catalytic activity and stability.The findings of this study might be useful for the further study of the catalytic material for sustained release catalysis,including the synthesis of catalytic materials and the regulation of sustained release catalytic performance.
基金Funded by the Academician Workstation of Yichang Huilong Science and Technology Co.,Ltd.Association of Science and Technology of Hubei Province(No.2013]104-22)
文摘The influence of replacement level of calcined coal-series kaolin(CCK) on hydration of ordinary Portland cement(OPC) was studied by X-ray diffraction(XRD)/Rietveld method. X-ray diffraction/Rietveld method was used to quantify the crystalline phase composition of the hydrated samples. Additionally, the morphology of hydrated samples was observed by scanning electron microscopy(SEM). The results showed that, calcium hydroxide(CH), ettringite(AFt) and amorphous phase content in hydrated samples decreased as the replacement level of CCK increased, while AFm and str?tlingite increased, which was caused by the combination of dilute, physical and pozzolanic effects. The hydration of anhydrous cement phases was accelerated by physical effect but hindered by the retardation effect of CCK. The role of each effects was discussed in detail to analyze the mechanism of OPC hydration with CCK addition. The SEM images showed that the shortening of AFt at 1 day and the denser texture at 28 days was observed with CCK addition, which was caused by the physical and pozzolanic effects, respectively.
基金This research was funded by Fundamental Research Grant Scheme(FRGS)under the Ministry of Higher Education Malaysia,grant number with project ref:FRGS/1/2019/STG06/UTP/03/2.
文摘Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency.Hybrid block methods for instance are specifically used in numerical integration of initial value problems.In this paper,an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations(ODEs).In deriving themethod,the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval.Furthermore,the convergence properties along with the region of stability of the method were examined.It was concluded that the newly derived method is convergent,consistent,and zero-stable.The method was also found to be A-stable implying that it covers the whole of the left/negative half plane.From the numerical computations of absolute errors carried out using the newly derived method,it was found that the method performed better than the ones with which we compared our results with.Themethod also showed its superiority over the existing methods in terms of stability and convergence.
基金Project(2012CB725402)supported by the National Key Basic Research Program of ChinaProjects(51338003,50908051)supported by the National Natural Science Foundation of China
文摘The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of APS were studied. Thereafter, aiming to build up a multi-step APS forecasting model that provides richer information than a conventional one-step model, the largest Lyapunov exponents(largest LEs) method was introduced into PGS. By experimental tests conducted using the same dataset, its prediction performance was compared with traditional wavelet neural network(WNN) method in both one-step and multi-step processes. Based on the results, a new multi-step forecasting model called WNN-LE method was proposed, where WNN, which enjoys a more accurate performance along with a better learning ability in short-term forecasting, was applied in the early forecast steps while the Lyapunov exponent prediction method in the latter steps precisely reflect the chaotic feature in latter forecast period. The MSE of APS forecasting for one hour time period can be reduced from 83.1 to 27.1(in a parking building with 492 berths) by using largest LEs method instead of WNN and further reduced to 19.0 by conducted the new method.
基金Funded by the International Cooperation of Science and Technology Ministry PRC (2005DFBA028)the Nation Undergraduate Innovation Experimentation Plan of Education Ministry PRC (LA08025)
文摘Monodispersed spheroidal SnO2 nanocrystals with the grain size of 8-30 nm were synthesized by the precipitation method using SnCl4·5H2O （stannic chloride hydrate） as raw materials.Differential scanning calorimetry/thermogravimetry （DSC/TG）,X-ray diffraction （XRD） and transmission electron microscope （TEM） were used to characterize the structure of SnO2 nanocrystals.The influences of the calcination temperature and time on the lattice constant,the lattice distortion and the grain size of SnO2 nanocrystals were discussed based on the XRD results.The grain growth kinetics of SnO2 nanocrystals during calcination process was simulated with a conventional grain growth model which only took into account of diffusion and with a new isothermal model proposed by our group,which took into account of both diffusion and surface reactions.Using conventional model,the grain growth rate constant of SnO2 crystals is 1.55×104nm5/min with a pre-exponential factor of 5 and an activation energy of 108.62 kJ/mol.Compared with the convention model,the new isothermal model is more realistic in reflecting the grain growth behavior of SnO2 nanocrystals during the calcination process.This indicates that the grain growth of SnO2 nanocrystals is controlled by both diffusion and reaction factors,and the effect of surface reactivity on the grain growth of SnO2 nanocrystals could not be ignored.A combined activation energy estimated with the new isothermal model is 53.46 kJ/mol.
基金Funded by the Natural Science Foundation Key Project of Hubei Province(No.2011CDA060)
文摘Pure K2Ti4O9 whiskers were prepared by KDC（Kneading-Drying-Calcination） method with TiO2 and K2CO3 as raw materials. The influences of TiO2/K2CO3 molar ratio（RT/K）, calcination temperature（TC） and cooling process on phase composition and morphology of the whiskers were investigated by TG-DSC（thermo gravimetric-differential scanning calorimeter）, XRD（X-ray diffraction）, and SEM（scanning electron microscope）. Pure K2Ti4O9 potassium titanate whiskers with large length-diameter ratio（r）（over 250） can be obtained at RT/K = 2.9 and TC = 950 ℃.
文摘The single-phase BiFeO3 powders were prepared by sol-gel method with the starting materials of bismuth nitrate and ferric nitrate, and the effect of the calcined temperature on the phases of BiFeO3 samples was studied. The x-ray diffraction (XRD)showed that the single-phase BiFeO3 powders were obtained with a calcined temperature of 700 ℃. The scanning electron microscope(SEM)analysis indicated that the grain size was around 500 nm in single-phase BiFeO3 powders, and uniform particle size distribution. The FT-IR spectra showed that the BiFeO3 powders began to crystallize at 500℃.
