Modeling of LiFePO4

At the end of 2009, as a postdoc, I began applying phase-field methods to lithium iron phosphate (LiFePO4), a phase-separating battery material that is popular for its high-rate capabilities and long cycle life. This page highlights the main results from the papers I published on this work. The first major result was an unexpected rate-dependent phase-separation, which we referred to as suppression of phase-separation. These videos show simulations of a single particle at increasing discharge rates. The phase-separating behavior disappears above a critical current. At the slowest discharge, the phase boundaries form orderly striped domains, which are a result of elastic coherency strain. As the current is increased, the phase separation becomes less pronounced. Just below the critical current (third video), only a small degree of phase separation is visible and no stable phases are formed before the particle is filled.

The second important observation came during the study of coherency strain. Because the two different phases have slightly different lattice constants, strain develops at the phase boundaries. By analyzing the anisotropic mismatch strain and elastic constants, I was able to rationalize that the phase boundaries should tend to align along the (101) family of crystallographic planes. Additionally in finite-size particles, coherency strain leads to the formation of stripes. By studying the periodicity of experimentally observed stripes, I was able to back out the phase boundary energy. To the right is a video of the formation of stripes.

The final key to understanding lithium iron phosphate was the realization that the surface energy of the particles plays an important role. Generally in solids, the surface energy cab be strongly affected by adsorbed atoms. Ab initio calculations reveal that some surfaces of LiFePO4 have a strong positive change in energy when lithium is added, while others have a strong negative energy change. The surfaces with the negative energy change can act as a heterogeneous nucleation site. With the phase field model, we were able to derive that the nucleation barrier is size-dependent, proportional to a particle’s area to volume ratio. To the right is a simulation of the lithiation of a single LiFePO4 particle with surface energy included. Instead of forming stripes, the lithiated phase is begins growing at the surface of the particle.