Calculation of thermic and electric properties and valence electron structure for metallic electrodes of Na||Sb-Pb-Sn liquid metal battery

<sec>The valence electron structures and thermal and electric properties of Na||Sb-Pb-Sn liquid metal battery are systematically studies with solid and molecular empirical electron theory (EET). The theoretical studies show that the thermal and electric properties are strongly related to the valence electron structure of electrode. The cathodic alloys Na_1–_<i>x</i>IA<i>_x</i>(IA = K, Rb, Cs) are designed by doping IA group alkali metals (K, Rb, Cs) into Na electrode since the melting points of IA group metals (K, Rb, Cs) are all lower than that of sodium. The theoretical bond lengths and cohesive energy of cathodic alloys Na_1–_<i>x</i>IA<i>_x</i> match the experimental ones well. The theoretical studies show the decreasing tendency of melting point, cohesive energy and electric potential with increasing doping content <i>x</i> in Na_1–_<i>x</i>IA<i>_x</i> alloys, which is due to the modulation of valence electron structure of IA group dopants. According to the analyses of valence structures, the number of lattice electrons decreases with the increasing of the doping content <i>x</i> for the cathodic alloy and causes the melting point, electric potential and cohesive energy to decline. It reveals that the IA group dopant modulates the valence electron structure of cathodic alloy, and induces the electron transformation from lattice electron to covalent electron in s orbital. </sec><sec>The anode products such as NaSb₃, NaSn, Na₁₅Sn₄ and NaPb are formed by transporting Na ions into the anode alloy Sb-Sn-Pb. The calculated bond-lengths and melting points fit the observed ones well for these anode products. Owing to their complex structures with various atomic occupations in unit cell, the thermal property or electric property is not only relative to lattice electron, but also depends on the covalent electron. The sublattice plays an important role in the forming of the four anode products. The lattice electrons are supplied by Na at 4<i>f</i> sites in Na₃Sb, Na at 16<i>e</i> and Sn at 32<i>g</i> sites in NaSn, Sn at 16<i>c</i> and Na at 48<i>e</i> sites in Na₁₅Sn₄, and Na at 16<i>f</i> and Pb at 32<i>g</i> sites in NaPb, respectively. </sec><sec>The open-gate voltage is closely related to the lattice electrons and inversely proportional to the average number of lattice electrons per atom. The open-gate voltage of NaSb₃ is the largest among the anode products, however, its averaged number of lattice electron per atom is the least. Since the lattice electron number of NaSn is the largest among the anode products, the open-gate voltage of NaSn is the least. It implies that the lattice electron plays a very important role in Na||Sb-Pb-Sn liquid metal battery, which can modulate the valence electron structures and thermal and electric properties. </sec>