Research ArticleAPPLIED SCIENCES AND ENGINEERING

Pascalammetry with operando microbattery probes: Sensing high stress in solid-state batteries

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Science Advances  08 Jun 2018:
Vol. 4, no. 6, eaas8927
DOI: 10.1126/sciadv.aas8927
  • Fig. 1 Scheme for pascalammetry with microbattery probes.

    (A) Cross-sectional schematic of a solid-state battery. (B) Cross-sectional schematic of the solid-state microbattery used for pascalammetry measurements. The full cell consists of a microbattery probe in contact with an oxide-free Si cathode. (C) Cross-sectional schematic of the scan-probe experimental geometry. The separation distance between the Si cathode and microbattery probe is denoted as z. Negative values of z correspond to compressive forces/stresses on the full cell. Initial approach is made with a coarse mechanical motor, while compressive forces/stresses are applied via piezo actuator. (D) Schematic of signals/protocols used to establish a stable microbattery junction for subsequent pascalammetry measurements. The variables z, P, and I denote separation, applied pressure, and current during approach (left of vertical pink line), initial contact (vertical pink line), validation of diffusion-limited current (current decay obeys Cottrell equation to the right of vertical pink line), and establishment of a more stable junction (right of the vertical dashed gray line). (E) Schematic of the biased microbattery probe approaching and contacting the oxide-free Si counter electrode before pascalammetry measurements. Constant bias voltage (V) is applied to promote charging. Solid, dashed, and dotted outlines of the microbattery probe represent different time windows during the approach and after the initial contact with low stress. A corresponding plot of charge versus time1/2 is adjacent. The transition from a null signal (solid and dashed) to a linear signal (dotted) indicates an initial contact (pink vertical line) sufficient to establish a full-cell battery and demonstrate diffusion-limited current (time right of the vertical pink line). (F) Illustration of microbattery probe/Si cathode junction and signals during two sequential stress-step pascalammetry measurements. In the junction illustration, applied compressive forces (black arrows), stress (clear to red color scale), and mechanical degradation (cracking of the electrolyte coating) are depicted. The pascalammetry signals illustration shows applied stress (pressure) in blue and induced faradaic current transients in gray. Note how this stress-step pascalammetry is analogous to potential-step voltammetry.

  • Fig. 2 Pascalammetry and SEM measurement data.

    Displayed on the left-hand side is a chronology of the experimental measurements that interleave SEM imaging of the junction (center) with pascalammetry measurements (right). Gray boxes on the timeline indicate data shown in this figure. SEM images are color-matched to the material colors in Fig. 1 and show the microbattery probe/Si cathode junction before pascalammetry (top), after pascalammetry (middle), and after retraction of the microbattery probe (bottom). Representative pascalammetry data sets (P-sets) under various constant charging or discharging bias conditions are shown. Each pascalammetry plot traces normalized applied stress/pressure in blue on top and induced faradaic current transients in color on bottom. Current color designates different bias conditions (provided on the time line in corresponding gray boxes). Note that stress-step pascalammetry induces current transients, analogous to potential-step voltammetry. Note also that electrolyte fracture is observed after pascalammetry measurements (middle SEM image), as highlighted with arrows, and pulverization of portions of the microbattery probe is observed after retraction (lower SEM image), consistent with the application of high stresses.

  • Fig. 3 Faradaic currents in highly stressed microbatteries deviate from Cottrellian behavior and signal SAD.

    (A) Charge (time-integrated current) versus time is plotted for the minimally/non-stressed initial contact (dashed black) and a representative stress-step pascalammetry experiment (dashed red). Power law fitting of form Q = atγ (blue traces overlaid) demonstrates that the minimally/non-stressed microbattery follows the time dependence of the Cottrell equation, while the stressed microbattery deviates. (B) Plots of the same data from (A) versus time1/2, with linear fits overlaid (blue traces). (C) Plot of the fitting parameter γ (± 6σ) for non-stressed initial contact (gray) and all pascalammetry measurements (color coded by P-set). Without exception, all stress-step pascalammetry experiments induce current transients that exhibit non-Cottrellian evolution.

  • Fig. 4 Analytic solution to a diffusion/activation equation quantifies pascalammetry data, identifies stress-assisted diffusion, and elucidates degradation mechanisms within highly stressed solid-state electrolytes.

    (A) Expression for time-integrated current (charge “Q”) for the diffusion/activation theory for stress-assisted diffusion, and plots of the fitting parameters for all pascalammetry measurements. I0 ± 6σ (left hand side) and γ ± 6σ (right hand side). (B) Plots in this pane share a common horizontal axis corresponding to electrolyte thickness from x = 0 to x = L. Top: Cross-sectional schematic of an operando solid-state electrochemical storage device. A constant applied potential difference promotes active species to reduce at the cathode/electrolyte interface. Middle: Evolution (0 to 200 s) of active species concentration profiles within the solid-state electrolyte for stress-assisted diffusion/activation (colored) and Cottrellian diffusion (gray). Concentrations are normalized by C(x, t)/C(L, 0), and the early-time curves are dashed. Bottom: Evolution (0 to 200 s) of active species fluxes within the solid-state electrolyte for stress-assisted diffusion/activation (colored) and Cottrellian diffusion (gray). Fluxes are normalized by j(x, t)/j(0, tmin), and the early-time curves are dashed. (C) Plots in this pane share a common horizontal axis of time from t = 0 s to t = 200 s. Top: Sketch showing the applied stress step of a potential pascalammetry measurement. Middle: Evolution of the normed total active species within the electrolyte [integral of C(x, t)/C(x, 0), from x = 0 to x = L] for Cottrellian diffusion (gray) and stress-assisted diffusion as described by the diffusion/activation theory (orange). In the diffusion/activation theory for stress-assisted diffusion, the total active species within the electrolyte increases in time. Bottom: Evolution of the normed time-dependent diffusion coefficient, D(t)/D(0), for various fractions of latent species activation.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/6/eaas8927/DC1

    Supplementary Text

    Derivation of Eq. 1 in the main text

    Derivation of the analytical solution to the diffusion/activation equation in the main text

    Derivations of all equations in main text

    Derivation of SAD current, main text Eq. 5, and constant Θ

    Derivation of max/initial faradaic current density inequality, Eq. 6 in the main text

    General formulation of the DAT

    Time constant for capacitive charging/discharging

    Capacitive time constant is independent of contact area

    Applied compressive forces and stresses by piezo actuator

    SAD and liquid electrolyte battery systems

    Plotting parameters

    fig. S1. Current and charge evolution for SAD (experiment), non-stressed diffusion (Cottrell), and diffusion plus a driving force demonstrate distinctness of SAD.

    fig. S2. Diffusion plus driving force current evolution and power law with γ < 0.5, both decay faster than diffusion-limited current (Cottrell).

    fig. S3. Temporal evolution of active species concentration within electrolyte during SAD.

    fig. S4. Evolution of ionic active species current density within electrolyte during SAD.

    Reference (42)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Derivation of Eq. 1 in the main text
    • Derivation of the analytical solution to the diffusion/activation equation in the main text
    • Derivations of all equations in main text
    • Derivation of SAD current, main text Eq. 5, and constant Θ
    • Derivation of max/initial faradaic current density inequality, Eq. 6 in the main text
    • General formulation of the DAT
    • Time constant for capacitive charging/discharging
    • Capacitive time constant is independent of contact area
    • Applied compressive forces and stresses by piezo actuator
    • SAD and liquid electrolyte battery systems
    • Plotting parameters
    • fig. S1. Current and charge evolution for SAD (experiment), non-stressed diffusion (Cottrell), and diffusion plus a driving force demonstrate distinctness of SAD.
    • fig. S2. Diffusion plus driving force current evolution and power law with γ < 0.5, both decay faster than diffusion-limited current (Cottrell).
    • fig. S3. Temporal evolution of active species concentration within electrolyte during SAD.
    • fig. S4. Evolution of ionic active species current density within electrolyte during SAD.
    • Reference (42)

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