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Reviews a Φ c b Na3PSe4 LLZO Li O are annealed82. Predicting the exact reaction pathway that will occur between two materials at such an inter- face is difficult as it depends on the complex balance between thermodynamic driving forces and kinetically accessible mechanisms at the reaction temperature, most of which cannot currently be quantified. Instead, com- putational methods have focused on capturing the max- imal chemical driving force that can exist at an interface and the possible reaction products. At a minimum, this thermodynamic analysis can be used to classify inter- faces according to their degree of reactivity. The reaction between two solids A and B, with respective composi- tions ca and cb, at their common interface may consume an arbitrary amount of each phase, such that the aver- age composition of the interfacial products is not known a priori (fig. 2c). A method to estimate the reactivity by determining at which fraction of A and B the reaction driving force becomes maximal has been proposed64. Given the phase diagram and energy landscape of the joint chemical space of A and B, the thermodynamic reactivity is calculated by minimizing ΔE[c ,c ]=E [xc +(1−x)c ]−xE[c ] abpda b a −(1−x)E[c ] b V=0V V=2.1V O2 reservoir atμO V=3V Li2S Li3P Li3PS4 SP Li PS Li4P2S6 34 SP Li3PS4 P4S3 P2S5 P4S7 Li reservoir atμLi d Vtopo,ext = 2.75 V Na P Se Li metal Zr La Li O Li O Material A (e.g. electrode) composition ca Material B (e.g. SE) composition cb Mixing layer composition xca+(1–x)cb Fig. 2 | interface models for the evaluation of (electro)chemical stability. a | Grand potential (Φ) convex hulls of the Li–P–S system at voltage V = 0 V (left), 2.1 V (middle) and 3 V (right) versus Li metal. The x-axis gives the composition of P along the pseudo-binary S–P tie line. Note that the Li amount in each compound is variable as it is equilibrated with the voltage (chemical potential). β-Li3PS4 is coloured red when it is metastable. b | Topotactic extraction voltage (Vtopo,ext) of a Na3PSe4 solid electrolyte (SE) determined by calculating the energy cost for extracting one Na atom from the SE50. c | Schematic illustration of chemical mixing at the interface between material A and material B. The mixing layer at the interface may have an arbitrary mixing fraction x of material A. The interface system can be modelled as open to the external chemical potential of an element such as Li or O. d | Explicit atomistic model of the low-energy LLZO(001)/Li(001) interface. μLi and μO, chemical potential of Li and O, respectively; LLZO, Li7La3Zr2O12. Part d is adapted with permission from ref.85, American Chemical Society. 0 calculated to be 2.75 V using equation 3. Here, μNa is the Na chemical potential in Na metal and E[c − Na] the enthalpy of a relaxed supercell with the highest-energy Na atom removed topotactically. (3) Because no nucleation of new phases or diffusion of any element besides mobile alkali atoms is required, such oxidation and reduction decomposition reactions cannot be prevented by kinetic stabilization. Therefore, the topotactic stability method provides the widest electrochemical stability window and an estimate of the best-case scenario (the maximum degree of kinetic stabilization) for the SE. Reactivity associated with chemical mixing When considering the electrochemical stability, as in the previous sections, one only considers that the alkali ele- ment crosses the interface. However, at some interfaces (such as between the SE and cathode), chemical reac- tions may also occur via the mixing of other elements across the interface. Such chemical reactivity between the SE and electrode material has been observed after cycling at room temperature60,78 and is particularly important at elevated temperature when the electrode and SE need to be co-sintered to achieve intimate contact between particles79–81 and when the cathode and coating (4) topo,ext (0) Na over x, where Epd is the lowest energy combination of the reaction products at composition xca + (1 − x)cb. The relevant energies calculated by DFT in these large chemical spaces can be obtained from databases such as the Materials Project83, and the ability to find the mini- mum is now an explicit feature in the Materials Project. Extensions to equation 4 can easily be made by evaluat- ing the grand potential under open-system conditions for an alkali element (to study the chemical reactivity under an applied voltage) or oxygen (to study the reactiv- ity under high-temperature conditions) at a certain chemical potential64. This methodology has been used to investigate the chemical compatibility of high- voltage spinel cathodes against garnets and NASICONs during sintering80. Explicit interface calculations In the previous methodologies, the reaction free ener- gies are all treated as those of bulk solids, consistent with the fact that reaction energies are typically very large, making it reasonable to neglect the effect of interfacial energies in the reaction driving force. It is also possible to directly assess the energetics of species at the interface (either statically or dynamically) using DFT on super- cells that model the interface explicitly. Interfaces with explicit structural relaxations have been examined in several systems, including Li3PS4/Li (ref.84), Li7La3Zr2O12 (LLZO)/Li and Li2CO3/Li (refs62,85), LiCoO2/Li3PS4 and LiNbO3/Li3PS4 (ref.86), LiCrS2/Li3PS4 and LiMnS2/ Li3PS4 (ref.87), and LiPON/Li (ref.88). For example, DFT structural relaxations of LLZO/Li and Li2CO3/Li inter- faces were performed to evaluate their wetting property85. The optimized atomic structure of the low-energy inter- face LLZO(001)/Li(001) is shown in fig. 2d. Compared with the results of the previous methodologies based on bulk energies, those from explicit interface calculations V = E[c−Na]+μ −E[c] ∕e www.nature.com/natrevmatsPDF Image | Understanding interface stability in solid-state batteries
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