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Abstract The thermal equation of state (TEOS) for solids is a mathematic model among pressure, temperature and density, and is essential for geophysical, geochemical, and other high pressure–temperature (high P–T) researches. However, in the last few decades, there has been a growing concern about the accuracy of the pressure scales of the calibrants, and efforts have been made to improve it by either introducing a reference standard or building new thermal pressure models. The existing thermal equation of state,P(V,T) = P(V,T₀) + P_th(V,T), consists of an isothermal compression and an isochoric heating, while the thermal pressure is the pressure change in the isochoric heating. In this paper, we demonstrate that, for solids in a soft pressure medium in a diamond anvil cell, the thermal pressure can neither be determined from a single heating process, nor from the thermal pressure of its calibrant. To avoid the thermal pressure, we propose to replace the thermal pressure with a well-known thermal expansion model, and integrate it with the isothermal compression model to yields a Birch–Murnaghan-expansion TEOS model, called VPT TEOS. The predicted pressure of MgO and Au at ambient pressure from Birch–Murnaghan-expansion VPT TEOS model matches the experimental pressure of zero (0) GPa very well, while the pressure prediction from the approximated Anderson PVT TEOS exhibit a big deviation and a wrong trend. 

This paper presents the numerical solution of the temperature dependent Eliashberg gap equations on the real axis for anisotropic superconductor YBa2Cu3O7 (YBCO) for below and above the calculated Tc. In those numerical calculations, the results of the first-principles electronic structure of YBCO were integrated into the Eliashberg gap equations based on the theory of many-body physics for superconductivity. As demonstrated previously,[1] the calculated Tc for YBCO was about 89 K for μ* = 0.1, which was quite close to that of experimental observations. For T < Tc, there is a large anisotropy of superconducting gap on the Fermi surface of YBCO.[2,3] Furthermore, above Tc, such as 105 K, it was found that the real part of gap function is not zero at finite frequency, although for the frequency near 0, the real part of gap function is zero. The results may be used to understand some pseudogap state properties in the material. 

Energy storage and conversion units have been considered the backbone of modern energy science and technology. In recent years, the Ni-based sulfides (NS) and mixed sulfides (NMS) have been significantly utilized as promising electrodes for various energy-related applications. This article summarizes the recent progress of NS and NMS materials in the fields of energy storage (supercapacitors) and conversion (oxygen evolution reactions). The synthetic approaches have been thoroughly discussed. A brief overview of the electrochemical performance of these materials as the electrodes for energy storage and conversion is systematically represented in the article. For such applications, these materials are frequently combined with other advanced materials, such as metal oxides, metal sulfides, and carbonaceous materials. The article ends with the existing challenges and future research directions in these research fields. 

In this work, a new canonical transformation for the Anderson lattice Hamiltonian with f–f electron coupling was developed, which was further used to identify a new Kondo lattice Hamiltonian. Different from the single impurity Kondo effect, the resulted new Kondo lattice Hamiltonian only includes the spin-flip scattering processes between conduction electrons and f-electrons, while the normal process of non-spin-flip scattering is absent in this Hamiltonian, under the second order approximation. The new Kondo lattice Hamiltonian may be used to study some anomalous physical properties in some Kondo lattice intermetallic compounds.