1. Introduction
Many mathematical models have been developed for Li- battery cell performance. However, a critical need still do
exists for a rather simple battery performance evaluation method. In the present study, such a parameter, Integral
Average Voltage (IAV), is being introduced. Its utility, convenience and applicability are validated via existing
experimental data derived from lithiated Ni dope Mn spinel 5V cathode materials. IAV is simple to calculate using the
cell charge/discharge profile; at the same time, it offers a perceptive analysis of cell features and associated
processes.
2. Method of Calculations
3. The Applicability of the Proposed Concept
Case Study #1
 The energy spent (or gained) in course of charge transfer
through the potential difference Vcell(Qfinal)-Vcell(Qinitial) is
 Single- and double- doped spinels (M = Ni, Co, Cu, Cr, Fe, etc.) have been reported to
have operational voltages over 4V and improved cycling performance, compared to
pure LiMn2 O4 .
 The V(Q) curves for these oxides usually have a complicated shape and are
inconvenient for comparison and further consideration (figure 1).
 Figure 2 better assist identifying several correlations between different variables and
thus, allow a better comprehensive analysis of the studied electrode system.
Q final

E
V (Q)dQ
(1)
Qinitial
𝑄𝑖𝑛𝑖𝑡𝑖𝑎𝑙 (𝑄𝑓𝑖𝑛𝑎𝑙 ) stands for the charge of the cell at the
beginning (end) of the discharge/ charge process.
5.0
 The average integral voltage, over the [𝑄𝑖𝑛𝑖𝑡𝑖𝑎𝑙 , 𝑄𝑓𝑖𝑛𝑎𝑙 ]
interval is defined as:
Q final
4.6
<Voltage> (V)
Vcell 

4.8
V (Q)dQ
Qinitial
Q final  Qinitial
E

Q
(2)
3.8
<V(discharge)>; 1st run
<V(charge)>; 1st run
<V(discharge)>; 50 th run
<V(charge)>; 50 th run
Li partial intercalation energy
3.6
3.4
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55
x (Ni content)
(3)
 LiNi0.4Mn1.6O4–cathodes containing different content of conductive
additives.
5.0
13% Super P carbon
4% Super P carbon
4.8
<V(discharge)> (V)
4.0
3.0
4. The Applicability of the Proposed Concept
Case Study #2
3.
4.2
3.2
 The average over-voltage over this interval may be
defined as:
emf
Vcell  Vcell  Vcell
4.4
4.6
4.4
4.2
tg=0.13
4.0
3.8
Figure 2: 𝑉𝑐 (𝑥 ) (charge/discharge) for
Figure 1: Charge/discharge behaviour of
LiMn2−xNixO4 cycled in LiPF6 + (EC+DMC)/Li LiMn2−xNixO4/LiPF6 + (EC+DMC)/Li coin cell.
𝑉𝑐 (𝑥 ) (charge/discharge) calculated using
coin cell
data from figure 1 and equation (2). Li
partial intercalation energies resulted
from ab-initio quantum-mechanical
calculations are presented.
 Figure 2 reveals that 𝑉𝑐 (𝑥) dependence on Ni-content (x) correlates well with the
dependence of Li partial intercalation energies on nickel content.
 Li+-conductivity in LiMn2−𝑥 Ni𝑥 O4 improves with increase in nickel content and thus,
the ohmic component is expected to diminish in course of cycling.
 In course of cycling 𝑉𝑐 (charge) is practically unchanged, whereas 𝑉𝑐 (discharge)
increases for x>0.
tg=0.32
3.6
3.4
3.2
3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
5. Conclusions
Current (A/g)
Figure 3: Galvanostatic discharge
voltage curves of LiNi0.40Mn1.6O4
sample containing 4 wt % (dashed)
and 13 wt % (solid) Super P carbon
as a conductive additive
Figure 4: 𝑉𝑐
(discharge)
for
LiNi0.4 Mn1.6 O4 cathode materials for
different discharge currents and
different conductive additive contents.
𝑉𝑐 (𝑥 ) (discharge) calculated using data
from figure 3 and equation (2).
 Figure 4 clearly demonstrates that the ohmic behaviour prevails for currents
over 0.022 A/g for all conductive carbon contents.
 The conductivity of the cathode containing 13% of carbon is 2.5 higher than the
conductivity of the cathode utilizing only 4% of carbon.
 The integral average voltage (IAV) method is described and being
evaluated.
 IAV provides a convenient and robust approach presenting results of
advanced Li metal cell (Li-air) and 5 V Li-ion positive electrode (lithiated
Ni doped Mn spine) testing.
 IAV allows a deeper understanding of electrode reactions and electrode
structure.
 The method, if being adopted will be highly applicable and seems quite
useful in battery-related research.
Acknowledgments
This work was supported by The Nancy and Stephan Grand Technion Energy Program (GTEP), the Israeli Ministry of Energy and Water Resources, Israel
Science Foundation (ISF), Israel National Research for Electric Propulsion (INREP), and the Helmsley Charity Fund.
References
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023102/1 – 023102/11; [3] Copyright © Mr.WESIK Version v2.10 24/10/2001, acquired on 10-2011 from http://www.4shared.com/get/6SeK55iD/grafula3_curve_tracking.html