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ii) The formation of lithium alloys

2.4 Thermodynamic and kinetic aspects of batteries

2.4.2 SEI formation

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conductivity leads to a stronger potential drop across a phase and the thickness of the phase influences the width of the potential drop. A thin phase causes a narrow drop; a thick phase causes a wide drop.

This potential decline is difficult to determine, and it is indicated as a dashed line. For simplification, a linear drop of the potential in Figure 5 is assigned, but since the potential is a function of µ̃e(the Fermi level) in the electrolyte, which is not constant, a non–linear decay can be expected. As the potential of the lithium ions µ̃Li+ is the same in all battery components, the entire potential drop across the electrolyte must be caused by the change of the electrochemical potential of the electrons (equation 10). This behavior is only valid, if the electrolyte has an (although possibly negligible) electronic partial conductivity. Only in this case can an electrochemical potential of the electrons be defined. As this is not the case in an ideal solid electrolyte, this curve is only indicated as a green dotted line.

Details about the steps of the Galvani potential at the interfaces are unknown, as they cannot be measured. The steps in Figure 5 are only schematic sketches. Their values as well as directions can be different. As at the interface the counter ions of the electrolyte are in contact with the electrode (due to surface charges), a linear potential decay analogous to the Helmholtz layer in aqueous systems should occur. A logarithmic decay is expected only in diffuse interlayers. The width of the steps should be in the range of the Debye length.

For all these considerations it is assumed that no space charge layers exist in the system. In real system they generally cannot be excluded generally [95].

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From a thermodynamic point of view, the formation of a stable reaction layer, the application of a protection layer, and the presence of impurities at the interface can be treated similarly.

Crucial for the stabilization of the interface are the ionic and electronic conductivity.

The potential difference Δ𝜑 between the two electrodes acting as the driving force for the movement of charge carriers across the electrolyte is constant. However, the change of the potential from 𝜑Anode to 𝜑Cathode is split up into two contributions, when an interlayer is present:

Δφ= ΔφSEI+ ΔφSE (13)

When a current flows during discharge of the battery, the potential drop across each phase depends on the current density i and the electronic conductivity of the SEI and the solid electrolyte according to

Δφ= ΔφSEI+ ΔφSE= – i(σ 1

el, SEI+ σ1

el,SE) . (14)

In this case, the potential drop across the electrolyte depends on the potential drop across the interlayer and vice versa. The pivotal property is the electronic conductivity in the electrolyte and the interlayer. Two general cases need to be considered (Figure 6):

 The interlayer has a larger electronic conductivity than the electrolyte.

 The interlayer has a smaller electronic conductivity than the electrolyte.

If the electronic conductivity in the interlayer is larger than the one of the electrolyte, the potential drop across the interlayer will be smaller than the potential drop across the electrolyte (Figure 6 top). If the electronic conductivity of the interlayer is smaller than the one of the electrolyte, the potential drop across the interlayer will be larger than the potential drop across the electrolyte (Figure 6 bottom).

An electron can energetically pass from the electrode into the electrolyte, if the electrochemical potential of the electrons µ̃e in the anode is higher than the LUMO in the electrolyte or if µ̃eis lower than the HOMO. If this is the case, a reaction between the anode and the electrolyte can occur. A reaction does not necessarily have to take place because electrons are only one required species and also lithium ions are needed but it is energetically possible. However, to avoid a reaction with certainty, electrons need to be prevented from

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A reaction cannot take place, if µ̃e is between the HOMO and LUMO of the electrolyte, two values that are often described as the electrochemical stability window of the electrolyte.

Similar, a reaction between lithium and an interlayer cannot take place if µ̃e lies in the stability window of the interlayer.

Equation 14 suggests that a proper selection of electrolyte and interphase materials is necessary to ensure that the potential at the SEI|electrolyte interface lies in between the stability windows of both phases. Only if the potential difference across the SEI is large enough to fulfill this requirement will the electrolyte be stable. If that is not the case, further decomposition will occur. In an ideal case, the interlayer should not have an electronic conductivity so no electrons can pass. However, if the potential drop across the SEI is too large, the strength of the electric field could lead to a decomposition of the SEI or tunneling effects (for films of only a few nanometer thickness). As the potential difference ΔµLi between the electrodes is solely depending on the electrode materials, the use of different electrodes may require a specifically tailored electrolyte multilayer structure for each combination of electrode materials in which the kind of SEI as well as its thickness are crucial. As the electrochemical stability window of most electrolytes is smaller than the potential difference between the lithium metal anode and cathode materials, a combination of different electrolytes may be required to ensure the stability of the battery. Concerning Li anodes, electrolytes that are stable at potentials of around 0 V vs. Li+/Li are needed. According to [47], only binary compounds fulfill this requirement because they cannot be further reduced.

The garnet material LLZO has a reduction potential of 0.05 V and could possibly be used as well. On the anode side, either one of these materials or an artificial layer that will react with lithium metal by forming the binary compounds should be applied.

Thus, a thermodynamic stabilization of the lithium|electrolyte interface is only possible if the interphase does not conduct electrons. Any attempt to stabilize the interface in literature that employs electronically conducting interlayers must be doomed to failure. These materials may be able to achieve a short–term kinetic stabilization but not a long–term thermodynamic stabilization.

It is important to keep in mind the influence that transport properties across an interface can have on the battery performance. A successful thermodynamic stabilization of the

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interlayer may cause another problem: unwanted lithium plating between SEI and electrolyte.

Figure 6: Schematic depiction of the changes of the potentials in a lithium ion battery with an additional SEI. The potential drop across a phase depends on the conductivity of the phase. The smaller the electronic conductivity, the higher the potential drop. Top: The SEI has a superior electronic conductivity than the electrolyte and the potential drop across the SEI is small. Bottom: The SEI has an inferior electronic conductivity than the electrolyte and the potential drop is large. As long as µ̃e at the interface is not between HOMO and LUMO, a reaction at the interface can occur, if lithium ions are present.

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