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13.4 Cycling Efficiency of Lithium Anode  381

               13.4
               Cycling Efficiency of Lithium Anode
               13.4.1
               Measurement Methods

               Lithium deposited on an anode during a charge is chemically active and reacts
               with organic electrolytes after deposition. Thus, the lithium is consumed during
               cycling. The cycling efficiency (percent) of a lithium anode (Eff) is basically defined
               by Equation 13.1 [23], where Q p is the amount of electricity needed to plate lithium
               and Q s is the amount of electricity needed to strip all the plated lithium. As Eff is
               less than 100%, an excess of lithium is included in a practical rechargeable cell to
               compensate for the consumed lithium.
                    Eff = 100 × Q s /Q p                                  (13.1)
               The figure of merit (FOM) for lithium cycling efficiency [24] is also often used
               to evaluate the cyclability of a lithium cell. The FOM is defined as the number
               of cycles completed by one atom of lithium before it becomes electrochemically
               inactive. Equation 13.2 is derived from the above definition.
                           sum of each discharge capacity to the end of cycle life
                    FOM =                                                 (13.2)
                                    capacity of lithium anode cell
               We can calculate the FOM from Eff, using Equation 13.3 [25].
                              1
                    FOM =                                                 (13.3)
                          1 − Eff/100
               The value of Eff is affected by many experimental conditions other than the
               electrolyte and anode materials. The experimental conditions include such factors
               as the cell configuration, electrode orientation, electrode surface area, working
               electrode substrate, charge–discharge currents, charge quantity, and amount of
               electrolyte.
                When Al, Pt, Ni, or Cu is used as the substrate of lithium plating with 1 mol L −1
               LiClO 4 –PC/1,2-dimethoxyethane (DME), Eff decreases in the order is A1 > Pt >
               Ni > Cu [26]. Lithium is easily alloyed electrochemically with many metals [27]; the
               Eff values measured in these experiments could include those of lithium alloys.
                Lithium cycling on a lithium substrate (Li-on-Li cycling) is another frequently
               used Li half-cell test [28], in which an excess of lithium (Q ex is plated on a metal
               working electrode, and then constant-capacity cycling (Q ps ); Q ps is smaller than
               Q ex ) is continued until all the excess lithium is consumed. The FOM can be
               evaluated as shown in Equation 13.4.

                          (cycling life) × Q ps
                    FOM =                                                 (13.4)
                                Q ex
               The influence of the amounts of lithium deposited in Li-on-Li cycling has been
               examined by Foos et al.[29].Theyused a cell (I)witha Q ex of 3.4C cm −2  and a Q ps
               of 1.1C cm −2  and a cell (II) with a Q ex of 18–23 C cm −2  and a Q ps of 5–10 C cm −2
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