Bi Enables the Formation of Disordered Birnessite in Rechargeable Alkaline Batteries

We have a new paper out in the Journal of the Electrochemical Society, written by Andrea Bruck. It continues our work on full 617 mAh/g rechargeability of MnO2 in alkaline batteries. Getting that full capacity reversibly enables a design pathway to get very inexpensive ($50/kWh) and high energy density (200 Wh/L) aqueous electrolyte rechargeable Zn-MnO2 batteries for the power grid. Aqueous electrolytes are desirable as an alternative to Li-ion batteries, which have flammable electrolytes, and become more of a safety risk at large scales.

Our main finding is the identification of an amorphous or “disordered” intermediate species during cycling. The figure above shows the voltage profile of the MnO2 cathode during cycling, and each section is labeled with the major material compound that is formed during that stage. (The discharge stages are labeled d1, d2, and d3. Likewise the charging stages are c1, c2, and c3.) We mix the MnO2 with bismuth oxide or Bi2O3, which is what makes it rechargeable. And during step c2, we have demonstrated a disordered compound we had never seen before. The reason we had never seen it is because all the other compounds are crystalline, and crystalline things are very easy to see. Disordered (or non-crystalline) things are often more challenging to put your finger on.

The figure above shows the structure of the layered birnessite or ẟ-MnO2, which consists of [MnO6] slabs separated by an interlayer. This data is from X-ray diffraction (XRD), which uses long-range crystallinity to produce a material fingerprint. This fingerprint is in the form of peaks or reflections, and the plot has the experimental data (black) compared to a theoretical calculation (red). We used a method called Rietveld refinement to match these and get the coordinates for all of the atoms in the material. (For example, we can tell the birnessite is hexagonal and the slab-to-slab distance is 7.131 Å)

However, you can’t observe a material by XRD if it doesn’t have good crystallinity, a.k.a. the “long-range order” to diffract X-rays. Instead we used operando Raman spectroscopy, which fingerprints materials using their response to a laser. Birnessite materials result in a series of Raman vibrational bands, the largest of which are ν1 and ν2. The figure above shows the Raman spectrum during the charge step both without Bi (top) and with Bi (bottom). In the top plots, the ν1 and ν2 bands didn’t appear until the blue dot, which is the c3 stage. However, with Bi, they appeared very early, even before the red dot, which is in the c2 stage. We know this is a disordered birnessite because it was not visible to XRD, but showed up clearly with Raman spectroscopy.

This is exciting because no one really knows why Bi makes birnessite rechargeable. Since we see it enables this formation of a disordered birnessite, that could be the key.

EDXRD review paper

We have a new paper out, which is a review paper on using energy dispersive X-ray diffraction (EDXRD) for battery characterization. EDXRD had previously been used to get crystallography data from inside diamond anvil cells, and also from the bulk interior of engineering materials like turbine blades. Using it to look inside sealed batteries was a good idea. It wasn’t my idea, but I’m one of the battery people they found to try it. I have a passion for current distributions, and EDXRD is a wonderful way to directly observe current distributions.

The paper was written with Amy Marschilok and the Takeuchi group at Stony Brook, and also with Mark Croft at Rutgers. We’re still using EDXRD to watch complex mechanisms inside batteries (without the fear that opening the battery will change anything), but since the review paper spans 2012-2020, it was a good idea to catalog past work in one place. The new HEX beamline under development at NSLS-II will be the premier EDXRD resource sometime soon. The figure below is an attempt to explain what exactly EDXRD gets you (atomic scale information, as a function of the electrode scale) and why it’s important (look how thick that electrode is). If you ever want to talk about EDXRD drop me a line.

Modeling porous electrodes: Part 3 (Newman’s BAND method)

I previously made a post about the basic formulation of porous electrode theory (part 1), and a post about how the choice of kinetic expression determines what the result will look like (part 2). The purpose of this post is to explain how to solve these basic problems using the BAND formulation found in John Newman’s textbook Electrochemical Systems (Newman and Thomas-Alyea in the Third Edition). I also provide Python code so you can get the solution yourself and modify it for your own teaching and learning needs.

As a model problem we’ll use the boundary value problem of Tafel kinetics in a concentration-independent porous electrode in Cartesian coordinates. The reason to choose this one is because Newman and Tobias provide the analytical solution in their 1962 paper “Theoretical Analysis of Current Distribution in Porous Electrodes.” You can also find this solution in Fuller and Harb’s Electrochemical Engineering, in the problems at the end of Chapter 5. The reason to choose a problem with an analytical solution is so you can check your work to know if it’s right! We lay out the problem below, which is the same as that in Newman and Tobias (1962) except one sign convention. This is four equations with four unknowns (i1, i2, Φ1, Φ2):

If you read the electrochemical engineering literature, solving problems such as this with Newman’s BAND method often comes up, and you might wonder what that is. Technically “BAND” is some Fortran code set up to solve 2-point boundary value problems in a way that is convenient for electrochemists. (My own favorite document written about BAND is “Modeling and reactor simulation” by Douglas Bennion in the AIChE symposium series 1983, Vol 79, Num 229, pp 25-36. It’s a resource meant for teachers and is somewhat hard to find so I’ve uploaded it here.) The formulation Newman uses to set up the problem casts each of the equations in this way:

Here c is a variable. The coefficients a, b, and d are those for the second derivative, first derivative, and the variable itself. And g is the constant term. When you linearize equation 2 above and then cast all of the four equations this way, you get something that looks like the tables below. I’ve collected some constants together as ß and P to keep it from looking too messy:

Once you have this, you can (a) build a block tridiagonal matrix, (b) choose initial guesses for the answers, and (c) iterate to a solution by repeatedly solving the problem until your initial guesses and final answers match. Explaining how this works is too long for a blog post, so follow these links for:

If you execute the code you should get a figure like that below, which solves the problem. (I still use Python 2.7 so you might have to do some mild editing and debugging.)

What I use this for

The reason I started writing a BAND-type method in Python is (1) I wanted to learn more about how BAND worked so I could teach it better, and (2) I wanted to model electrochemical systems without having to buy expensive software or use Fortran. It’s not exactly like Newman’s code, which also included a function to solve the matrix problem. Rather, this code lets you input the problem in Newman’s way and build the corresponding block tridiagonal matrix, then it uses SciPy to solve the matrix problem.

When I was working on the paper above in 2016, I wanted to compare experimental data to the Chen + Podlaha + Cheh alkaline battery model developed in the 1990s. Python seems like the best choice for something you can also develop as a teaching tool, so I used that to generate the results in Figure 3 of the paper. Since then I’ve used it to train some MS students getting insight into shallow-cycled MnO2 cathodes. When Zhicheng Lu’s MS thesis appeared on the internet, I received a few questions about the model by email. So this post is meant to help anyone doing similar things.

Operando study of all solid state batteries

I’m pleased to announce that Hongli Zhu’s group and ours have received an NSF award to study and improve interfacial phenomena in all solid state batteries. From the abstract:

The specific objective of this research is to improve metal sulfide stability in solid-state electrolytes for the application of all solid-state lithium batteries. In pursuit of this objective, the fundamental mechanisms of metal sulfide ion conduction and interface reactivity will be interrogated by operando characterization carried out on realistic, fully operational battery cells.

Hongli’s group does material engineering of solid state electrolytes (SSEs), while my group specializes in operando characterization, using X-rays and various other techniques. The announcement from Northeastern is here, and the NSF award page is here. We start this fall and are looking forward to it.