Lithium gold boride

Lithium gold boride (chemical formula LiAu₃B) is a material with a honeycomb-like structure. that can be used to make superconducting batteries.

History

In 2018, LiAu₃B metal was discovered. Just like the other lithium boride materials, this material also is predicted to have a critical temperature where superconductivity is achieved at 5.8K.

Material

LiAu₃B is a ternary metal, consisting of the three elements lithium, gold and boron. The material is stable under extraction of its lithium atoms, during which it experiences a volume deviation of 0.42%.

Lattice structure

The unit cell consists of three formula units of LiAu₃B. The gold atoms are placed in a hexagonal structure. Together with the boron atoms, that are placed at the centre of trigonal prisms, they form the main skeleton of the material. The lithium atoms are placed at the centre of the hexagonal structure of the gold atoms.

Electronic structure

The electronic structure of the material makes it useful for battery applications. The lithium atoms at the centre of the structure behave as donors, while the Au₃B units surrounding the lithium behave as acceptors. Therefore the lithium atoms have a positive charge, whereas the host structure of gold and boron atoms has a negative charge. This follows from Mulliken charge analysis.

Mechanical stability

Under an increase of pressure, the B-Au bonds are less affected than the Au-Au bonds. Under an increase from 0 to 50 GPa, all bond lengths become smaller except those of the B-Au bonds. This is a result of the strong hybridization between the gold and boron atoms mentioned earlier. Furthermore, under increasing pressure, the electronegativity of the gold and boron atoms rises, while the electronegativity of the lithium atoms decreases. This can be explained by the fact that the length of the Au-Au bonds decreases under higher pressure. Because of the hexagonal structure of the gold atoms, the gold atoms will become closer to the lithium atoms and will be better able to 'steal' its electron. This means that the acceptation capacities of the gold and boron atoms increases under higher pressure.

Band structure

This is the band structure of the material as calculated. The total density of states can be separated into 4 regions up to the Fermi energy. The first group is a sharp peak at approximately -48 eV. This one is due to the contribution of the 1s² orbitals of the lithium atoms. The second peak is the result of the s-states of gold and boron, and is located between -11 and -9 eV. The third peak is caused by the d-states of gold and p-states of boron, located between -7 to -3 eV. The densities of both orbitals are relatively high in this region. Because the d- and p-states have approximately the same amount of energy in this region, it is easy for the electrons to hop between these two different orbitals. This, combined with the relatively high density of states in this region, will create a strong hybridization between the d-states and p-states of gold and boron respectively. The last peak is from -3 eV to the Fermi level. It is due to the p-states of gold and there is hybridization between p-states of gold and boron atoms. The hybridizations are responsible for higher covalency in Au-B bonds.

Uses

Calculations have showed that ternary metal borides promise a higher critical temperature T_c for superconductivity then.

Batteries

The flow of lithium ions from the cathode to the anode and vice versa, while facilitated by an Li⁺ conducting electrolyte, is analogous to the flow of current in ordinary batteries. It allows for simple charging and discharging of LiAu₃B batteries. Furthermore, the lattice structure is preserved even when all lithium ions are removed from the structure, to a (temporary) host structure, and only a small volumetric deviation is observed when all lithium ions are removed. The deviation is only 0.42% of the total volume when there are no lithium atoms in the Au₃B. This is because the lithium atoms are located at the centre of the hexagonal gold structures. Adding or removing the lithium atoms will not drastically change the structure of the gold and therefore also will not affect the volume too much. This is an important result for batteries because it is not desired to have batteries that change their volume while being charged or discharged. The average open-circuit voltage of 1.30V also makes the material promising to use in batteries.

Diffusion barrier

The diffusion barrier is defined as the energy difference of the system when the lithium atoms are placed inside the host structure (inside the cathode) and when the lithium atoms are outside the structure (inside the anode). So the diffusion barrier is important for batteries, as it says something about how much energy is needed to charge or discharge the system. It also depends highly on pressure, as the Au-Au bond lengthes decreases under high pressures, and thus there will be less free space for the lithium atom to be placed in. Less free space means a higher diffusion barrier. For 0 GPA the diffusion barrier is approximately 0.30 eV and increases to 0.51 eV at 15 GPa. Boltzmann's constant k_B can then be used to find a temperature dependent expression for the diffusion mobility. At room temperature at 15 GPa, the diffusion mobility is in the order of $3.4\cdot 10^{-}3$ times smaller than at 0 GPa.

Superconductivity

Like most other lithium boride metals, superconductivity is also a property of LiAu₃B. This is because the boron atoms create metal bonds. The superconductive properties can be derived from the phonon spectra of LiAu₃B at 0 hydrostatic pressure. The critical temperature where superconductivity occurs can be calculated using McMillan's equation:

$T_{c}={\frac {w_{log}}{1.2}}\exp \left({\frac {-1.04(1+\lambda )}{\lambda (1-0.62\mu ^{*})-\mu ^{*}}}\right)$.

Here, λ is given by the relation

$\lambda =\sum _{q,v}\lambda _{q,v}=2\int {\frac {\alpha ^{2}F(w)}{w}}dw$

where the individual $\lambda _{q,v}$ for a mode v at wave vector q are the electron-phonon coupling constants, and given by

$\lambda _{q,v}={\frac {\gamma _{q,v}}{\pi \hbar N(E_{F})w_{qv}^{2}}}$

with $\gamma _{q,v}$ the phonon line width, and $N(E_{F})$ the density of states at the Fermi level. Using this method, the critical temperature T_c is calculated to be 5.8K. This result is of the same order as other already known superconducting materials.

Disadvantages

One problem of LiAu₃B is that it is mostly made out of gold atoms (3 out of 5 atoms per unit cell). As gold is a relatively expensive material, these batteries will be rather costly as well. Therefore, it is not expected that LiAu₃B batteries will be used for the foreseeable future.

References

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