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First Principles of Lighter, More Powerful Lithium Batteries

Gerbrand Ceder, MIT

Anton Van der Ven, MIT

T he ideal battery for a laptop computer, cell phone, or electric car would be light in weight, low in cost, high in voltage, and would lose none of its power over repeated charging and discharging. However, the most common batteries for such devices today--usually based on the chemical element lithium--are powerful but expensive. For example, the cost of lithium-based battery materials for a single electric car could be as much as $10,000. To build batteries that are lighter and less expensive, yet even more powerful, Gerbrand Ceder at MIT and graduate student Anton Van der Ven are using high-performance computers to understand and improve the active ingredients in batteries.





Lithium batteries consist of a lithium anode, an organic electrolyte that conducts the current, and a cathode. The most common cathode compound is lithium cobalt oxide, a material from which lithium can be easily removed. As the battery is charged, lithium ions are driven from the cathode into the anode; discharging lets the lithium flow back to the cathode.

While such lithium batteries can pack a lot of electrical power into a small package, the cobalt in the cathode gives the batteries substantial weight and cost. Finding a lightweight, low-cost replacement for cobalt--one that still provides the same voltage--would make portable computers lighter and electric cars less expensive. The most likely candidates for cobalt substitutes are the transition metals, the family of chemical elements to which cobalt belongs. But the number of alternatives makes it difficult to find substitute materials by experimental trial and error.

"The number of possible mixtures of lithium and transition metal oxides is almost limitless," said Ceder, an associate professor in the Department of Materials Science and Engineering and Center for Materials Science and Engineering at MIT. "But the high cost of the current cathode material is an incentive to investigate the possibilities systematically, and high-end computation provides an efficient way to direct the search."

Using NPACI's computing resources, Ceder's group has conducted first-principles calculations of the lithium-containing compounds to understand how the various substitutes for cobalt would affect the materials. They began by studying lithium cobalt oxide itself, which not only provided better understanding of how that material worked, but also predicted an alternative to simply replacing cobalt with another transition metal.

A critical finding was that the electron transfer to the cathode that accompanies lithium insertion was largely accommodated on oxygen ions, rather than on cobalt, as was traditionally believed (Figure 1). "With this finding, we were able to explain many of the surprising properties of lithium cobalt oxide," Ceder said. "When we started investigating, we were looking at how to tailor the voltage of these materials with different transition metals. However, our first-principles calculations suggested that doping of the materials with non-transition metals would increase the voltage."

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A. Van der Ven, M.K. Aydinol, G. Ceder, G. Kresse, J. Hafner, "First principles investigation of phase stability in LixCoO2,"Physical Review B, 58(6): 2975 (1998).
S.K. Mishra and G. Ceder, "Structural stability of lithium manganese oxides," Physical Review B, 59(9): 6120 (1999).

Electron MovementFigure 1. Electron Movement
Electronic changes induced by introducing lithium ions in cobalt oxide. Around the lithium ions there is a strong electron increase (yellow regions) on oxygen ions. Surprisingly only small electron increase (red) or even electron decreases (black) are found around cobalt.



With the prediction that non-transition metals could increase the voltage, Ceder's group first tried replacing half the cobalt in lithium cobalt oxide with aluminum. According to their first-principles computations, this combination would have the advantage of increasing the battery voltage while reducing the cost and weight--an advance on three fronts. They then confirmed the computational prediction experimentally in collaboration with the teams of experimental colleagues Donald Sadoway and Yet-Ming Chiang at MIT. However, further work remains to determine whether the material retains its electrical capacity and stability under repeated discharging and recharging.

The main code used by Ceder's group is the Vienna Ab initio Simulation Package (VASP), a quantum-mechanical molecular dynamics package. VASP avoids the problems with ion-electron interactions in other well-known codes, making the package ideal for transition-metal studies. A single run can take up to 70 processor hours on NPACI's Cray T90, with 10 to 15 such runs needed for statistical confidence.

After experimenting with aluminum, Ceder and his group used first-principles calculations to study the structure of lithium manganese oxides. Manganese is one of the cheapest transition metals and has a limited environmental impact. However, lithium manganese oxide has not been used in mass-produced batteries because it becomes unstable at warmer temperatures, such as those produced inside a laptop computer.

In the ideal crystal structure for the electrode material, manganese and lithium would occupy separate layers so that lithium diffusion could proceed without interacting strongly with the positively charged manganese ions (Figure 2). However, this ideal structure has only been synthesized through complex and metastable synthesis routes. Ceder's group hoped to understand why the layered structure, a very common crystal form for other transition metal oxides, was not stable in lithium manganese oxide.

Their computations suggest that the material's magnetic state and highly charged manganese ions combine to affect the stability. These factors may in fact alter the crystal structure of the oxide, which in turn determines whether the material converts to a form that can't be recharged. Ceder's group is continuing their studies of these materials. Recent articles in Physical Review B by Ceder, Van der Ven, and graduate student Snigdharaj Mishra have described the effects of varying the amount of lithium in the oxide and examined the structural stability of lithium manganese oxides.

"All of this is done from first principles because there is so little good data on these materials," Ceder said. "The area is moving so fast that there's not enough time to gather data experimentally. First-principles calculations are one of the best ways to generate those data."

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Atomic Structure
Figure 2. Atomic Structure
The preferred structure for lithium electrode materials.


Thus far, the calculations by Ceder's group have examined various properties of the compounds in isolation, so-called equilibrium properties. While this work has proved fruitful, it does not accurately depict how the materials behave inside an actual battery. One of the important properties is the rate at which a battery can be discharged and recharged, and the key factor is the transport of lithium. A battery's performance depends not only on how rapidly the lithium travels in the electrolyte, but also on the structural changes to the anode and cathode as lithium is added or removed. Rapid charging and discharging can cause strain on the oxides and break down the materials.

"Looking at non-equilibrium properties such as transport and diffusion is a difficult computational problem," Ceder said. "We are beginning large-scale simulations of lithium diffusion through these materials, and we have to look at the atomic-scale diffusion and the macroscopic structure at the same time. Nobody has ever done simulations that have coupled atomistic diffusion with macroscopic strain generation." To make matters worse, in lithium cobalt oxide, these macroscopic strains feed back into the diffusion and modify it from the unstrained state.

To perform these computationally demanding simulations, Van der Ven is just starting to use NPACI's Cray T3E at SDSC for the larger cells, more memory, and longer runs that are needed. Even Van der Ven's earliest diffusion runs are already much larger than their original first-principles calculations.

Essentially, the simulation must recalculate the lithium ion's energy four times for each "hop" that the ion makes through the electrolyte. Specifically, the elastic band method is used to calculate the energetics of the lithium ion's migration. In effect, the algorithm can be compared to the tightening of a rubber band across a saddle point between two minima of the energy landscape. In this approach, the crystal energetics with lithium at different stages of its hop are calculated simultaneously such that a global optimization of the migration path can be made. At least four stages, but preferably more, must be considered to obtain reasonably accurate information about the migration path. Since diffusion is a local phenomenon, large unit cells containing on the order of 60 or more ions must be used to minimize the effects of periodic boundary conditions.

And that's just for diffusion. Calculating other properties, such as interfaces during phase changes could require even larger computational resources, such as the teraflops IBM SP that NPACI will install later this year.

"These materials seem to be very dynamic as you use them in a battery," Ceder said. "Many decay over time, but some actually get better as they age, like a fine wine. To really understand these materials you have to simulate them in action. Such simulations would go well beyond what we can do now." --DH *

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