Raman spectrum of molten cryolite was recorded. Based on the new understanding of the scattering coefficients, contents of various structural entities in acidic NaF-AlF3 melts at 942-1 024 ℃ in previous research were...Raman spectrum of molten cryolite was recorded. Based on the new understanding of the scattering coefficients, contents of various structural entities in acidic NaF-AlF3 melts at 942-1 024 ℃ in previous research were reanalyzed. The new quantitative analysis results show that when cryolite ratio（CR） is less than 2, AlF4- is the dominant anion in the melts, and its mole fraction is about 0.70 for melts with CR=1.5 and 0.50 for melts with CR=2. When CR is more than 2.5, the mole fraction of AlF6^3- is relatively large, which is around 0.45 for melts with CR=2.5. Ionic structure of Na3AlF6-Al2O3 melts was investigated by UV-Raman spectroscopy. Octahedral AlF6^3- and tetrahedral AlF4- are proved to exist with possible partial replacement of F- by O^2-. Al2O2F4^2- with a large scattering coefficient also exists in the melts in which alumina concentration is more than 4% （mass fraction）. The increase of temperature causes blue-shift of the bands in the Raman spectra.展开更多
A rigorous approach is proposed to model the mean ion activity coefficient for strong electrolyte systems using the Poisson-Boltzmann equation. An effective screening radius similar to the Debye decay length is introd...A rigorous approach is proposed to model the mean ion activity coefficient for strong electrolyte systems using the Poisson-Boltzmann equation. An effective screening radius similar to the Debye decay length is introduced to define the local composition and new boundary conditions for the central ion. The crystallographic ion size is also considered in the activity coefficient expressions derived and non-electrostatic contributions are neglected. The model is presented for aqueous strong electrolytes and compared with the classical Debye-Hfickel （DH） limiting law for dilute solutions. The radial distribution function is compared with the DH and Monte Carlo studies. The mean ion activity coefficients are calculated for 1：1 aqueous solutions containing strong electrolytes composed of alkali halides. The individual ion activity coefficients and mean ion activity coefficients in mixed sol- vents are predicted with the new equations.展开更多
The infinite-horizon linear quadratic regulation （LQR） problem is settled for discretetime systems with input delay. With the help of an autoregressive moving average （ARMA） innovation model, solutions to the unde...The infinite-horizon linear quadratic regulation （LQR） problem is settled for discretetime systems with input delay. With the help of an autoregressive moving average （ARMA） innovation model, solutions to the underlying problem are obtained. The design of the optimal control law involves in resolving one polynomial equation and one spectral factorization. The latter is the major obstacle of the present problem, and the reorganized innovation approach is used to clear it up. The calculation of spectral factorization finally comes down to solving two Riccati equations with the same dimension as the original systems.展开更多
基金Project (51004034) supported by the National Natural Science, ChinaProject(N090302009) supported by the Fundamental Research Funds for the Central Universities, China
文摘Raman spectrum of molten cryolite was recorded. Based on the new understanding of the scattering coefficients, contents of various structural entities in acidic NaF-AlF3 melts at 942-1 024 ℃ in previous research were reanalyzed. The new quantitative analysis results show that when cryolite ratio（CR） is less than 2, AlF4- is the dominant anion in the melts, and its mole fraction is about 0.70 for melts with CR=1.5 and 0.50 for melts with CR=2. When CR is more than 2.5, the mole fraction of AlF6^3- is relatively large, which is around 0.45 for melts with CR=2.5. Ionic structure of Na3AlF6-Al2O3 melts was investigated by UV-Raman spectroscopy. Octahedral AlF6^3- and tetrahedral AlF4- are proved to exist with possible partial replacement of F- by O^2-. Al2O2F4^2- with a large scattering coefficient also exists in the melts in which alumina concentration is more than 4% （mass fraction）. The increase of temperature causes blue-shift of the bands in the Raman spectra.
基金Supported by the National Natural Science Foundation of China(21206010)
文摘A rigorous approach is proposed to model the mean ion activity coefficient for strong electrolyte systems using the Poisson-Boltzmann equation. An effective screening radius similar to the Debye decay length is introduced to define the local composition and new boundary conditions for the central ion. The crystallographic ion size is also considered in the activity coefficient expressions derived and non-electrostatic contributions are neglected. The model is presented for aqueous strong electrolytes and compared with the classical Debye-Hfickel （DH） limiting law for dilute solutions. The radial distribution function is compared with the DH and Monte Carlo studies. The mean ion activity coefficients are calculated for 1：1 aqueous solutions containing strong electrolytes composed of alkali halides. The individual ion activity coefficients and mean ion activity coefficients in mixed sol- vents are predicted with the new equations.
基金the National Natural Science Foundation of China under Grant No.60574016
文摘The infinite-horizon linear quadratic regulation （LQR） problem is settled for discretetime systems with input delay. With the help of an autoregressive moving average （ARMA） innovation model, solutions to the underlying problem are obtained. The design of the optimal control law involves in resolving one polynomial equation and one spectral factorization. The latter is the major obstacle of the present problem, and the reorganized innovation approach is used to clear it up. The calculation of spectral factorization finally comes down to solving two Riccati equations with the same dimension as the original systems.
