The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate...The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate. An improved calculation is presented, in which two of the three parts are obtained in exact forms. A simple remedy for Landau and Lifshitz＇s qualitative calculation in the textbook is also given, which turns the qualitative result into the same one as obtained by the improved quantitative calculation. The chemical potential is solved approximately and the thermodynamic quantities are caiculated explicitly in both a weak field and a strong field. The thermodynamic quantities in a strong field obtained here contain both non-oscillating and oscillating corrections to the corresponding results derived from Landau＇s grand partition function. In particular, Landau＇s grand partition function is not sufficiently accurate to yield our nonzero results for the specific heat and the entropy. An error in the Laplace-transform method for the problem is corrected. The results previously obtained by this method are also improved.展开更多
Although the application of various nonprecious compounds as the air cathodes of Zn-air batteries has been explored, the construction of highly efficient selfsupported Co-based electrodes remains challenging and highl...Although the application of various nonprecious compounds as the air cathodes of Zn-air batteries has been explored, the construction of highly efficient selfsupported Co-based electrodes remains challenging and highly desired given their outstanding electrocatalytic activity and cost-effectiveness. Herein, we fabricated a three-dimensional(3D) self-supported electrode based on N-doped,carbon-coated Co3O4 nanosheets grown on a carbon cloth(i.e., NC-Co3O4/CC) through the electrochemical deposition and carbonization. When used as a binder-free electrode for oxygen evolution reaction(OER), the NC–Co3O4/CC electrode demonstrated excellent electrocatalytic activity with an overpotential of 210 mV at 10 mA cm^-2 and a Tafel slope of79.6 mV dec^-1. In the Zn-air battery test, the electrode delivered a small charge/discharge voltage gap(0.87 V at 10 mA cm^-2) and exhibited high durability without degradation after 93 cycles at the large current density of 25 mA cm^-2.The durability of our electrode was superior to that of a commercial Pt/C+RuO2 catalyst. The excellent performance of NC–Co3O4/CC could be attributed to the presence of 3D structures that promoted electron/ion transfer. By the absence of a binder, the carbon coating improved electron conductivity and promoted electrochemical stability. Moreover, N doping could be used to adjust the C electron structure and accelerate electron transfer. The present study provides a facile and effective route for the synthesis of various self-supported electrodes that fulfill the requirements of different energy storage and conversion devices.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10675174
文摘The free electron gas in a uniform magnetic field at low temperature is restudied. The grand partition function previously obtained by Landau＇s quantitative calculation contains three parts, which are all approximate. An improved calculation is presented, in which two of the three parts are obtained in exact forms. A simple remedy for Landau and Lifshitz＇s qualitative calculation in the textbook is also given, which turns the qualitative result into the same one as obtained by the improved quantitative calculation. The chemical potential is solved approximately and the thermodynamic quantities are caiculated explicitly in both a weak field and a strong field. The thermodynamic quantities in a strong field obtained here contain both non-oscillating and oscillating corrections to the corresponding results derived from Landau＇s grand partition function. In particular, Landau＇s grand partition function is not sufficiently accurate to yield our nonzero results for the specific heat and the entropy. An error in the Laplace-transform method for the problem is corrected. The results previously obtained by this method are also improved.
基金the support from the National Natural Science Foundation of China (21631004, 21771059 and 21571054)Heilongjiang Provincial Postdoctoral Science Foundation (LBH-Q16194)
文摘Although the application of various nonprecious compounds as the air cathodes of Zn-air batteries has been explored, the construction of highly efficient selfsupported Co-based electrodes remains challenging and highly desired given their outstanding electrocatalytic activity and cost-effectiveness. Herein, we fabricated a three-dimensional(3D) self-supported electrode based on N-doped,carbon-coated Co3O4 nanosheets grown on a carbon cloth(i.e., NC-Co3O4/CC) through the electrochemical deposition and carbonization. When used as a binder-free electrode for oxygen evolution reaction(OER), the NC–Co3O4/CC electrode demonstrated excellent electrocatalytic activity with an overpotential of 210 mV at 10 mA cm^-2 and a Tafel slope of79.6 mV dec^-1. In the Zn-air battery test, the electrode delivered a small charge/discharge voltage gap(0.87 V at 10 mA cm^-2) and exhibited high durability without degradation after 93 cycles at the large current density of 25 mA cm^-2.The durability of our electrode was superior to that of a commercial Pt/C+RuO2 catalyst. The excellent performance of NC–Co3O4/CC could be attributed to the presence of 3D structures that promoted electron/ion transfer. By the absence of a binder, the carbon coating improved electron conductivity and promoted electrochemical stability. Moreover, N doping could be used to adjust the C electron structure and accelerate electron transfer. The present study provides a facile and effective route for the synthesis of various self-supported electrodes that fulfill the requirements of different energy storage and conversion devices.
