(∂EOCP / ∂T)p,x = -(1 / nF)(∂S(x) / ∂x)p,T
in which p = pressure, x = amount of intercalated Li, n = number of electrons, F = Faraday constant, and S(x) is the entropy arising primarily from Li/vacancy configurations within the lattice. In Li-ion half cells, it has been shown that the measured profiles correlate with order/disorder transitions at the cathode [1-4]. The advantage of this method is its structural sensitivity, since it naturally includes the entropic information arising from the Li/vacancy structure, which has proved challenging to probe even with the most advanced in-situ neutron scattering based techniques [5,6]. There is a need to develop a more quantitative understanding of the results obtained from entropy profiles and relate these results to the changes observed during cell aging. The unintentional formation of point defects has been proposed as one explanation for the change in the entropy profiles with successive cell charge/discharge cycles.
Here, we combine Monte Carlo (MC) models with experimental entropy profiles of a cathode material of current commercial interest, LixMn2O4 (0 < x < 1). This paper describes and builds upon work that we have recently published . Intentionally introduced defects M (M = Li, Ni, Cr) in LixMyMn2-yO4 (where y= defect concentration) pin lithium atoms into the lattice, as shown by density functional theory (DFT) calculations. We examine and quantify the effect of defect concentration on entropy profiles, as shown in the figure below. We compare the results to ones we have obtained experimentally and analyse the trends from both data sets. Our simulations show the same trend that is observed in experiment: a suppression of the entropy peaks with increasing defect content. We relate the peak amplitudes to the number of configurations available due to Li ordering, which can be visualised as shown below. Experimentally validated MC data are ideal to illustrate the microscopic origins of the entropy change peaks, yielding narratives of their positions and amplitudes.
Apart from the entropy change profiles, we also discuss the how the simulated absolute (integrated) configurational entropy varies with the defect content, as demonstrated in the figure below. This analysis provides additional insight into how the order/disorder transition becomes suppressed with increasing defect substitution. Furthermore, it reveals that the two peaks are affected unequally by the presence of the defects.
In summary, our work provides additional microscopic understanding of entropy profiles and a quantitative relationship between the peak amplitude and structure, which provides insight into the origins of the changes observed during entropy profiling of aged Li-ion cells.
 Y. Reynier, J. Graetz, T. Swan-Wood, P. Rez, R. Yazami, B. Fultz, Phys. Rev. B 70 (2004) 174304.
 K. Maher, R. Yazami, Electrochim. Acta 101 (2013) 71-78.
 S. -W. Kim, S. -I. Pyun, Electrochim. Acta 46 (2001) 987-997.
 P. J. Osswald, M. del Rosario, J. Garche, A. Jossen, H. E. Hoster, Electrochim. Acta 177 (2015) 270-276.
 M. Bianchini, E. Suard, L. Croguennec, C. Masquelier, J. Phys. Chem. C 118(2014) 25947-25955.
 N. Sharma, D. Yu, Y. Zhu, Y. Wu, V.K. Peterson, Chem. Mater. 25 (2013) 754-760.