• Rollett, Anthony D.
• Hackett, Gregory A.
• Epting, William
• Litster, Shawn
• Mason, Jerry H.
• Abernathy, Harry W.
• Nuhfer, Noel T.
• Feng, Mingzhen

Abstract

<jats:p>A semi-empirical model is developed to quantitatively characterize electrode heterogeneities over the micro- and mesoscales, specifically between the relationship of the mean-squared normalized variance in the volume fraction, <jats:inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="mml-disp1" overflow="scroll"><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:msub><mml:mi>σ</mml:mi><mml:msub><mml:mi>Φ</mml:mi><mml:mi>V</mml:mi></mml:msub></mml:msub><mml:msub><mml:mover accent="true"><mml:mi>Φ</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>V</mml:mi></mml:msub></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="i0001.gif" xlink:type="simple" /></jats:inline-formula>, and the mean particle size normalized linear dimension, <jats:inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="mml-disp2" overflow="scroll"><mml:mfrac><mml:mi>L</mml:mi><mml:msub><mml:mover accent="true"><mml:mi>a</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>N</mml:mi></mml:msub></mml:mfrac></mml:math><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="i0002.gif" xlink:type="simple" /></jats:inline-formula>. The model was developed analyzing data from five large-volume physical reconstructions – collected using Xe-plasma focused ion beam with SEM (PFIB-SEM) – of several commercial cell electrodes and from unique sets of synthetic microstructures designed to have controlled distributions in particle size and local volume fractions. When comparing physical reconstructions from distinct regions of the same electrode, millimeter length scale heterogeneities are also observed, even in microstructures with limited mesoscale variability. While the model is developed using synthetic microstructures, it is used to quantify three different types of heterogeneities in the commercial cells. The potential origins are discussed with respect to variations in particle size distributions in feedstocks and to phase distributions related to fabrication processes; the potential performance impacts are discussed with respect to two effective medium theory models. The characterization and analytical methodologies and model presented can support the design and development of improved electrodes.</jats:p>

Topics

• impedance spectroscopy
• microstructure
• phase
• scanning electron microscopy
• theory
• focused ion beam
• quantitative determination method