Interface Reactions Manual
- 1 Introduction
- 2 Using the Interface Reactions App
- 3 Interpreting Reaction Energy Plots
- 4 Thermodynamic Methodology
- 5 Citation
- 6 References
- 7 Authors
Interfaces between solid phases are critical in determining the optical, mechanical and transport properties of the system. Interfacial reactions could occur when two contacting materials are not thermodynamically stable against each other. Information about interface reactions is valuable in various aspects: the reaction energy reflects the reactivity of two phases, and the reaction products could affect the performance of devices such as Li-ion batteries that built from these materials.
Experimentally, the investigation of interface reactions is challenging as accessing the interface between two solids is difficult and the reaction layers have only limited thickness. It is thus highly valuable to predict possible interface reactions from a computational approach.
Materials Project database provides calculated energies of a wide range of materials. By using all relevant compounds in the relevant chemical system from Materials Project database, we can construct the reaction energy plots for the interface systems at 0 K and 0 atm.
The Manual outlines the usage of the Interface Reaction App and the computational thermodynamic methods employed.
Using the Interface Reactions App
To construct the reaction energy plot for a closed system, enter the two reactants in contact into the “Reactants” fields, leave other fields as default, and click on “Search” button.
In cases where the interface system is open to a particular element at a constant chemical potential (e.g., during charge/discharge process in Li-ion batteries), additionally check "Open element?" box, and select the projected element from the drop-down list , and enter the desired relative chemical potential. Note that the relative chemical potential of an element is referenced to the chemical potential of pure substance of that element. For example, for element Li, the reference chemical potential is that of Li metal.
As the reaction energy plot is generated, it shows the reaction energy as a function of molar fraction ratio x of the first reactant. There are multiple ways to get reaction information:
- When mousing over a node on the plot, the pop-up window shows the reactivity (eV/atom) and reaction equation.
- You can zoom into a portion of the plot by defining a zoom area: click and hold at the upper-left corner of the desired area, and drag down and right, releasing the mouse at the lower-right corner of the desired area. The window should be replaced by the zoomed-in portion. To return to the original phase diagram, click “Reset axes” button at the upper-right corner.
- The reaction plot can be printed, or downloaded in PNG, JPEG, PDF, SVG format by clicking the button at the upper-right corner.
Interpreting Reaction Energy Plots
The section shows how to interpret reaction energy plot generated by Interface Reactions App. The information one can obtain from the plot includes reaction energies, reaction products and reaction equations at various mixing ratio. In the table presented below the plot, you can review, for each point in the plot, the corresponding quantities:
- mol fraction: The molar fraction of the first input reactant
- reactivity (ev/atom): The reaction energy normalized to the total number of reactant atoms
- reaction equation: A reaction equation chosen to normalize one of the reactants.
- reaction energy (kJ/mol): The reaction energy (per mol) of the displayed reaction equation.
All input reactants are converted to reduced cell formulae. For example, if you input , the app will consider the reactant to be .
Reaction Plots in Closed Systems
To illustrate the reaction information obtainable from the Interface Reactions app, we use Figure 1 as an example for system (closed to any element). and are commonly known cathode material and electrolyte material in Li-ion battery, respectively. The cathode/electrolyte interface is of particular interest in battery research as it largely affects the battery performance.
Figure 1 shows the reactivity (reaction energy normalized by atom number) as a function of molar fraction ratio x of . Table 1 lists all the critical reaction equations, and corresponding molar fraction of first reactant, reactivity, and reaction energies per mole of reaction equation. There are 8 nodes which corresponds 8 critical reactions. Each node is a kink point in the reactivity profile. For example, the second node from the left with molar fraction of 0.666 corresponds to the reaction:
The reactivity for this node is -0.417 eV/atom. The largest reaction driving force (magnitude of reactivity) is found for the reaction:
The corresponding molar fraction of is 0.74 and the reactivity is -0.426 eV/atom.
Since in reality the reaction between two phases can consume arbitrary amounts of either phase depending on the diffusion and mixing conditions, the molar fraction is not necessarily the critical ratio, but can be any value from 0 to 1. If the molar fraction is not exactly equal to the critical ratio, the reaction is a combination of the critical reactions for its left neighbor node and right neighbor node, by the lever rule. As a consequence, all reaction products in the table1 are possible phases that may be generated at the interface.
Reaction Plots in Open systems
We use the same system that open to Li reservoir to illustrate the reaction plot in open system. The Li reservoir is at 3 V vs. Li metal, i.e., the chemical potential of Li in the reservoir is 3 eV/atom lower than that in Li metal.
In Figure 2, there are 16 labeled nodes that corresponds to 16 critical reactions. The reaction energy at x = 0 is negative, meaning that is not stable at 3 V vs. Li metal. The decomposition reaction (read from the table) is:
Note that Li is extracted from the reactants to the Li reservoir. In contrast, is stable at this voltage as the reaction energy is 0 eV/atom at x = 1. The interpretation of other reactions in the table is similar to that in the closed system.
By comparing Table 1 and Table 2, it could be seen that the reaction products in closed system and open system are not the same. This is because the stable materials in the phase diagram is not necessarily stable in the grand potential phase diagram, and vice versa. Users can refer to Phase Diagram App to explore the phase diagrams of the corresponding system for better understanding of these reactions.
The Interface Reactions app uses the computed energies of materials from the Materials Project database. The computational methodology, default total energy corrections and accuracy can be found in Calculations Manual.
We consider two conditions for interface systems where chemical mixing occurs: 1) interfaces closed to any element (closed system), and 2) interfaces open to a particular element in the chemical system (open system). These two scenarios are treated separately as below:
Chemical Mixing in Closed Systems
For closed systems, we calculate the reaction energy of two reactants A and B at varying mixing ratio x using the equation:
where and are compositions for reactants A and B, and are energies of ground state structures for reactants A and B, respectively. is the energy on the energy convex hull at composition .
In case where there is no structure in the database that matches the composition of reactant A or B, the energy on the convex hull or for that composition will be used instead. It should be noted that at endpoints where there is no mixing of two phases (x = 0 or 1), the reaction energies could be zero or negative, depending on whether the ground state structure energy of reactant A or B is on the hull or above the hull.
Chemical Mixing in Open Systems
In many applications, interface systems are open to a particular element at a constant chemical potential. For example, in battery conditions, the electrode/electrolyte interface is open to lithium during battery cycling. The relevant thermodynamic potential in an open system is the grand potential Φ. For instance, for a system open to Li at chemical potential , the grand potential for reactant with composition is obtained using the equation:
where is the energy of ground state structure that has composition . Again, if no such structure exists, will be used instead. and are the number of lithium and non-Li elements in composition formula , respectively. Here, PV and TS terms are ignored for systems where phase equilibria changes between solid phases. Because the system is open to Li, the grand potential should be normalized by the number of non-Li atoms. We take the convex hull of for all phases in the chemical system, and as a result the grand potential on the grand potential convex hull is a function of composition and chemical potential :
where is the number of Li atoms added to the system from the Li reservoir. In case where Li is extracted from the system to the Li reservoir, will be negative . The reaction energy in this case is given by:
Since the Interface Reactions app models based on the phase diagram of a system, compounds that are metastable may not show up in the reaction products, although they might be kinetically stabilized in real life. Other reactions with different products and smaller magnitude of reaction energies are also possible to happen. Just as in Phase Diagram App, here we also expect that reactants for which the reaction energy magnitude is small are potential candidates to form metastable interface; however, reactants with extremely high magnitude of reaction energy (i.e., 200 meV/atom) are less likely to form metastable interfaces.
To cite the Interface Reactions App, please reference the following works:
- W. D. Richards, L. J. Miara, Y. Wang, J. C. Kim, and G. Ceder., Interface Stability in Solid-State Batteries, Chemistry of Materials, vol. 28, 2016, pp. 266–273.
Note that the methodology used in this paper is slightly different from the one employed in the Interface Reactions App. In this paper, the energies for reactants are always the convex hull energy for the reactant compositions, whereas in the Interface Reactions App the reactant energies are default to be the ground state structure energies. Only when no structure in the database matches the reactant composition will the convex hull energy be used. Therefore, generally the reaction energy calculated in this App for a reaction is expected to be more negative than that in the paper.
- Yihan Xiao