Functional Materials | Neel Nadkarni

Introduction

Functional materials are a class of materials that can be controlled to exhibit specific, useful behaviors under the influence of external applied fields such as electric fields, magnetic fields, or chemical potentials. Their underlying microstructure plays a critical role in determining their response. My research focused on materials that undergo microstructural switching, resulting in a mechanical response at the macroscopic level, and how this response can be precisely controlled through externally applied fields. When a solid undergoes such a transformation or switching, it is referred to as a solid-solid phase transition. Understanding these phase transformations is essential for harnessing the unique properties of these materials, which formed the core of my research interest. Below, I have highlighted three different functional materials that I worked on and some interesting problems that I encountered during my studies.

Phase Transitions in Battery Materials

Lithium Iron Phosphate (LFP) and Lithium Cobalt Oxide (LCO) are among the most widely used cathode materials in lithium-ion batteries. During charging and discharging, lithium ions intercalate into the material to store energy. However, this intercalation process does not occur uniformly; instead, lithium ions segregate into lithium-rich and lithium-poor phases, with the charging and discharging process proceeding through this phase separation. In the case of LFP, phase separation occurs throughout the entire range of the charging process. Due to the differing lattice parameters of the two phases, misfit strain develops within the particles, creating stress that can lead to fractures and, consequently, capacity loss. Understanding this phase separation process is critical for improving the reliability and longevity of cathode materials.

In the case of Lithium Iron Phosphate (LFP), an intriguing experimental observation in nanoscale particles is the asymmetry between charging (delithiation) and discharging (lithiation) behaviors. At high rates, phase separation is suppressed during lithiation, whereas it is enhanced during delithiation. To investigate this phenomenon, we developed a continuum chemo-mechanical model that captures phase behavior and incorporates experimentally determined reaction kinetics. Our analysis revealed that the asymmetry arises from a combination of the anisotropy in the phase boundary thickness and the asymmetry in the exchange current density. The anisotropy suppresses bulk phase separation energetically, allowing surface kinetics to directly influence the bulk behavior. Simultaneously, the exchange current density dictates the asymmetry in lithiation kinetics, as demonstrated through linear stability analysis.

phase separation observed at low rates

phase separation observed at high rates

The extent of phase separation is evaluated as a function of the charge stored in the LFP nanoparticle. By incorporating anisotropy into the phase boundary modeling, the simulation successfully replicates key experimentally observed behaviors: (1) the asymmetry between charging (delithiation) and discharging (lithiation) processes, and (2) the suppression of phase separation at high rates.

The kinetics described above are reaction-driven and dominate when the particle size is on the scale of a few nanometers. For larger particles, however, lithiation becomes diffusion-driven, governed by the bulk properties of the material. Through our analysis, we identified a scaling law that predicts, for a given applied current, the transition point between reaction-limited intercalation wave-driven phase behavior and diffusion-limited shrinking-core phase behavior. This scaling theory was validated across three electrode materials: graphite, lithium iron phosphate (LFP), and lithium cobalt oxide (LCO). The results are shown below.

Furthermore, an interesting phenomenon observed in Lithium Cobalt Oxide (LCO) is its transformation from a conductor to an insulator during the phase transition. To investigate this behavior, we developed a comprehensive chemo-electro-mechanical model that captures both the phase transition and the resulting equilibrium phase separation. Additionally, the model incorporates conductivity changes, enabling us to simulate electronic transport within the material. Experimental findings reveal that the conductivity follows a metallic percolation pathway, consistent with the Hashin-Shtrikman upper bound. This model has practical applications in designing advanced battery cathodes and electrochemical memory devices.

phase separation and corresponding voltage curve of LCO

changes in conductivity of polycrystalline LCO with varying lithium concentration

Domain Wall Switching in Ferroelectrics

Ferroelectrics are a type of piezoelectric material that respond to electric fields due to their internal polarization. In widely used ferroelectric materials like PZT, below the Curie temperature, the microstructure forms multiple domains with distinct polarization vectors. When an external electric field is applied, these domains can switch from one variant to another. This polarization switching also induces mechanical deformation as a result of changes in the lattice structure driven by electromechanical coupling. The various crystal variants of PZT are illustrated in the figure below.

To model the ferroelectric switching response of PZT, our collaborators from ETH Zurich developed a temperature-dependent Landau-Devonshire model combined with stochastic, thermally-activated Allen-Cahn kinetics to capture domain wall switching behavior. The model successfully predicts key properties such as spontaneous polarization, coercive field, and the strain-electric field butterfly curve across a wide temperature range, showing strong agreement with experimental data for PZT. The resulting figures are displayed below. The diffusive nature of Allen-Cahn kinetics allows the domain wall velocity to be predicted using energy scaling laws, a concept that is derived from nonlinear transition wave propagation dynamics. Applying the energy-velocity scaling relation to this problem offers valuable insights into how the domain wall speed varies with the applied electric field. This is a critical finding, as it reveals the rate at which the ferroelectric material can be switched under an applied electric field. Such knowledge is essential for understanding the underlying actuation kinetics of the microstructure, which is a key factor in the design and optimization of ferroelectric sensors and actuators.

The spontaneous polarization vs temperature, electric field-polarization curves and strain-polarization butterfly curves are captured by the model developed. The figure on the right shows the polarization domain patterns observed in the microstructure.

Hydrogen Storage in Palladium Nanorods

Palladium nanorods have emerged as promising candidates for energy and information storage devices that utilize solute-driven phase transformations, owing to their high surface-to-volume ratio and capacity to accommodate strain. Hydrogen adsorption on the surface of these nanorods, followed by intercalation into their structure, makes them particularly interesting as hydrogen storage media. This intercalation process triggers a phase transition, leading to the coexistence of hydrogen-rich and hydrogen-poor phases, similar to what is observed in battery cathode materials. In an interesting experiment conducted by my collaborators at Stanford, hydrogen intercalation in penta-twinned palladium nanorods was investigated. They observed that, for nanorods exceeding a critical length, phase coexistence occurred with the formation of an incoherent phase boundary. Below this critical length, the nanorod fully intercalated with hydrogen. Our theoretical analysis revealed a competition between strain energy relaxation at the phase boundary, driven by the formation of an incoherent interface, and the bulk strain energy resulting from hydrogen intercalation. We demonstrated that, at thermodynamic equilibrium, a specific volume fraction corresponds to this energy balance. Furthermore, for nanorods below a critical length, it becomes energetically favorable for the entire particle to intercalate hydrogen uniformly without forming a phase boundary.

phase coexistence observed above a certain critical length of the nanorod

TEM and DADF images of the observed phase coexistence in large nanorods

References

N. Nadkarni, E. Rejovitsky, D. Fraggedakis, C.V. Di Leo, R.B. Smith, P.Bai, and M.Z.Bazant, "Interplay of phase boundary anisotropy and electro-auto-catalytic surface reactions on the lithium intercalation dynamics in LiXFePO4 platelet-like nanoparticles.", Phys. Rev. Mater., vol. 2, no. 8, p. 085406, 2018.
F. Hayee, T. C. Narayan, N. Nadkarni, A. Baldi, A. L. Koh, M. Z. Bazant, R. Sinclair, and J. A. Dionne, "In-situ visualization of solute-driven phase coexistence within individual nanorods.", Nat. Comm., vol. 9, no. 1, p. 1775, 2018.
N. Nadkarni, T. Zhou, D. Fraggedakis, T. Gao, and M. Z. Bazant, "Modeling the metal-insulator phase transition in LiXCoO2 for energy and information storage.", Adv. Func. Mater., vol. 29, no. 40, p. 1902821, 2019.
D. Fraggedakis*, N. Nadkarni*, T. Gao*, T. Zhou, Y. Zhang, Y. Han, R. M. Stephens, Y. Shao-Horn, M. Z. Bazant, "A scaling law to determine phase morphologies during ion intercalation.", Energy & Env. Sci., vol. 13, no. 7, p. 2142, 2020. (*equal authorship)
J. C. Gonzalez‐Rosillo, M. Balaish, Z. D. Hood, N. Nadkarni, D. Fraggedakis, K. J. Kim, K. M. Mullin, R. Pfenninger, M. Z. Bazant, J. L. M. Rupp, "Lithium‐battery anode gains additional functionality for neuromorphic computing through metal-insulator phase separation.", Adv. Mater., vol. 32, no. 9, p. 1907465, 2020.
R. Indergand, A. Vidyasagar, N. Nadkarni, D. M. Kochmann, "A phase-field approach to studying the temperature-dependent ferroelectric response of bulk polycrystalline PZT.", J. Mech. Phys. Solids, vol. 144, p. 104098, 2020.
B. Koo, J. Chung, J. Kim, D. Fraggedakis, S. Seo, C. Nam, D. Lee, J. Han, S. Jo, H. Zhao, N. Nadkarni, J. Wang, N. Kim, M. Weigand, M. Z. Bazant, J. Lim, "Dynamic surface phases controlling asymmetry of high-rate lithiation and delithiation in phase-separating electrodes.", Energy & Env. Sci., vol. 16, no. 8, p. 3302, 2023.