One of the more powerful tools in materials screening is the computational phase stability diagram. Unfortunately, it is only utilized at the moment by a few research groups (although I do see its usage increasing), and I thought that a comic book about them might improve the situation.
So here’s that comic book! In addition, this post contains Python examples to create, plot, and analyze phase diagrams using the pymatgen library and Materials Project database. You can now do what earlier took a month of research (computing and generating an entire ternary or quaternary phase diagram) in a few seconds!
This post has three parts:
- The comic!
- Interactive phase diagram examples
- Further resources
Click here to download the full high quality PDF version (19MB) of the Phase Diagram comic.
There’s also a small file size version (3MB) for slower connections.
Interactive phase diagram examples
The Materials Project phase diagram app allows one to access a database of tens of thousands of DFT calculations and construct interactive computational phase diagrams. You can build binary, ternary, and quaternary diagrams as well as open -element diagrams. No programming required!
Python code example: Creating a phase diagram
Python code example: Creating a grand canonical phase diagram
Python code example: Checking to see if your materials is stable with respect to compounds in the MP database
“Accuracy of ab initio methods in predicting the crystal structures of metals: A review of 80 binary alloys” by Curtarolo et al.
This (somewhat epic!) paper contains data for 80 binary convex hulls computed with density functional theory. The results are compared with known experimental data and it is determined that the degree of agreement between computational and experimental methods is between 90-97%.
“A Computational Investigation of Li9M3(P2O7)3(PO4)2 (M = V, Mo) as Cathodes for Li Ion Batteries” by Jain et al.
The endpoints of a binary convex hull need not be elements. For example, in the Li ion battery field one often searches for stable intermediate phases that form at certain compositions as lithium is inserted into a framework structure. The paper above is just one example of many computational Li ion battery papers that use such “pseudo-binary” convex hulls.
“Configurational Electronic Entropy and the Phase Diagram of Mixed-Valence Oxides: The Case of LixFePO4” by Zhou et al.
Incorporating temperature into first-principles convex hulls is often possible, but not always straightforward or easy to do. Here is one example of this process that focuses on electronic entropy.
Ternary plots are not only for phase diagrams (the most creative usage I’ve ever seen is in Scott McCloud’s Understanding Comics, where it is used to explain the language of art and comics). Wikipedia does a good job of explaining the basics of how to read and interpret compositions on ternary diagrams.
Here is a nice example of the computation of a quaternary phase diagram – sliced into ternary sections – from first principles calculations.
“Accuracy of density functional theory in predicting formation energies of ternary oxides from binary oxides and its implication on phase stability” by Hautier et al.
How accurate are computational phase diagrams? The correct answer, like always, is “it’s complicated”. But based on results from this paper and some experience, colleagues of mine and I have found that an error bar of 25 meV/atom is usually a good estimate. We usually double that to 50 meV/atom when searching for materials to synthesize by conventional methods.
In an ideal world, first principles calculations would live up to their name and require no adjustable parameters. In practice, however, DFT errors do not always cancel when comparing energies of compounds with different types of electronic states. This paper shows how one can mix two DFT approximations along with some experimental data in order to produce a correct phase diagram across a changing landscape of electronic states.
“First-Principles Determination of Multicomponent Hydride Phase Diagrams: Application to the Li-Mg-N-H System” by Akbarzadeh et al.
An alternate (but equivalent) approach to the convex hull algorithm for determining phase diagrams is to use a linear programming approach. This is demonstrated by Akbarzadeh et al. in the search for H2 sorbents.
“Thermal stabilities of delithiated olivine MPO4 (M = Fe, Mn) cathodes investigated using first principles calculations” by Ong et al.
If Li ion battery cathode materials (generally oxygen-containing compounds) release O2 gas from their lattice, it can lead to runaway electrolyte reactions that cause fire. Thus, a safe cathode material resists O2 release even under extreme conditions. Stated another way, safety is the “price point” (inverse O2 chemical potential) at which a cathode material will give up its oxygen. The higher the price point, the more stable the compound. This paper compares the critical chemical potential for O2 release between MnPO4 and FePO4 cathode materials, finding that similar chemistry and structure doesn’t necessarily imply similar safety.
“CO2 capture properties of M–C–O–H (M.Li, Na, K) systems: A combined density functional theory and lattice phonon dynamics study” by Duan et al.
The CO2 capture problem is to find a compound that absorbs CO2 from an open environment at chemical potentials found in industrial processes, and then releases the CO2 back into some other open environment under sequestration conditions. This paper constructs multi-dimensional phase diagrams to predict how different chemical systems will react with CO2 under different conditions.