Abstract
When the size of a supercell employed in theoretical calculations is smaller obviously than the mean free path of electrons in metals, the computed values of the electrical conductivity and the electronic thermal conductivity show a striking finite-size effect, and such a size-dependent value cannot be used for direct comparison with that from experiments. We hereby propose an empirical law to unified describe the relation between the conductivity (including the electrical conductivity and the electronic thermal conductivity) of infinite-size crystal and that of finite-size supercell in calculations for tungsten (W). Our calculations demonstrate that it is very convenient to achieve the electrical conductivity and the electronic thermal conductivity of W metal by using this empirical law. In addition, we provide a simple power law (∼T−1.35) to describe the finite-size effects at different temperatures. Furthermore, the mean free path of electrons, which tightly correlates to the finite-size effects exhibited in the electronic transport calculations of W at different temperatures, are revealed. The proposed empirical law in this work is robust and may be valid for other metals.
Highlights
Studying the electron and thermal transport properties of solids is a very important and fundamental subject in the field of material science
The theory about electrical and thermal conductivities of a material has been established, an open obstacle in electron and thermal transport properties calculations is that the size of the supercell used in calculations is usually smaller obviously than the mean free path (MFP) of the carriers, so that the theoretically predictions cannot be available for direct comparison with the related data from experiments, this is the well-known finite-size effect
Under the assumption of the Matthiessen rule,1 the relationship between the lattice thermal conductivity of the finite-size supercell employed in calculations and the lattice thermal conductivity of the infinitesize crystal can be expressed by a simple formula, in which the calculated lattice thermal conductivity is dependent on the length of supercell
Summary
Studying the electron and thermal transport properties of solids is a very important and fundamental subject in the field of material science. The performance in the electron and thermal transport properties of a material is dependent on several factors such as the microstructure of the host, the temperature loaded on the system and the behaviors of the carriers scattered by defects and impurities. The theory about electrical and thermal conductivities of a material has been established, an open obstacle in electron and thermal transport properties calculations is that the size of the supercell used in calculations is usually smaller obviously than the mean free path (MFP) of the carriers, so that the theoretically predictions cannot be available for direct comparison with the related data from experiments, this is the well-known finite-size effect.. For the calculations of lattice thermal conductivity, the two most commonly used methods are the direct molecular dynamics method and the Green-Kubo method.. Under the assumption of the Matthiessen rule, the relationship between the lattice thermal conductivity of the finite-size supercell employed in calculations and the lattice thermal conductivity of the infinitesize crystal can be expressed by a simple formula, in which the calculated lattice thermal conductivity is dependent on the length of supercell. Recently, a new equation was proposed for the approach-to-equilibrium molecular dynamics method.
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