Conventional electrochemical characterization techniques based on voltage and current measurements only probe faradaic and capacitive rates in aggregate. In this work we develop a scanning thermo-ionic microscopy (STIM) to probe local electrochemistry at the nanoscale, based on imaging of Vegard strain induced by thermal oscillation. It is demonstrated from both theoretical analysis and experimental validation that the second harmonic response of thermally induced cantilever vibration, associated with thermal expansion, is present in all solids, whereas the fourth harmonic response, caused by local transport of mobile species, is only present in ionic materials. The origin of STIM response is further confirmed by its reduced amplitude with respect to increased contact force, due to the coupling of stress to concentration of ionic species and/or electronic defects. The technique has been applied to probe Sm-doped Ceria and LiFePO4, both of which exhibit higher concentrations of mobile species near grain boundaries. The STIM gives us a powerful method to study local electrochemistry with high sensitivity and spatial resolution for a wide range of ionic systems, as well as ability to map local thermomechanical response.

Electrochemistry is essential for energy conversion and storage in a wide variety of systems, including lithium ion batteries,1–3 solid oxide fuel cells,4 supercapacitors,5 and resistive switching memristors.6,7 A growing body of research suggests that electrochemical processes underpinning these applications are largely governed by phenomena occurring at the nanoscale, such as ionic defect formation and transport,8,9 interfacial chemistry and charge transfer,10–12 local cation segregation,13,14 and phase nucleation and separation.15 However, a deep fundamental understanding of these microscopic mechanisms, as well as technological advancement, is largely hampered by a lack of experimental techniques that can directly probe electrochemical processes at the nanoscale. Traditionally, many electrochemical characterization techniques are based on the measurements of current and voltage, which are very difficult to scale down to nanometer length scales, as they require detection of small currents on the order of pA that are beyond the capability of conventional charge amplifiers.16 Although scanning electrochemical microscopy (SECM) utilizes custom-made ion-conducting electrodes to study local electrochemistry,17 it is typically limited to micrometer length scales.18,19

Over the past several years, researchers have begun to employ Vegard strain,20,21 i.e., the strain associated with changes in ionic and defect concentrations, to provide an alternative imaging mechanism with high spatial resolution for electrochemical processes. For example, the topography variation of electrode material during charging and discharging of lithium ion batteries has been mapped by atomic force microscopy (AFM),22 reflecting accumulation of Vegard strain over both space and time. Likewise, electrochemical strain microscopy (ESM) is sensitive to local fluctuation in ionic species and electronic defects, induced by oscillation in potential of a conductive scanning probe tip.23–25 However, with all these techniques, it can be difficult to distinguish Vegard strain from other electromechanical mechanisms, such as piezoelectric effect, electrostatic interactions, and capacitive forces,26,27 and it is also quite challenging to carry out ESM in operando, due to the possible interference between the scanning probe potential and any global voltage perturbation applied to the device. Information about scanning probe microscopy (SPM) techniques based on dynamic strain measurement can be found in a recent review.28 

In this work, we present results of a new technique to probe local electrochemistry at the nanoscale, termed as scanning thermo-ionic microscopy (STIM), which is based on imaging of thermally induced Vegard strain. In contrast to ESM, our method probes the concentration fluctuations of ionic species or electronic defect caused directly or indirectly by temperature oscillation induced by a heated scanning probe. As a result, STIM has several potential advantages over ESM. First, the heated probe is electrically insulated from the sample and thus the measurement is not complicated by other electromechanical mechanisms such as electrostatic interactions discussed earlier. STIM also easily distinguishes nonlinear strain associated with ionic species and electronic defects from linear thermomechanical sources, such as thermal expansion, due to differences in their harmonic responses. Thus, STIM gives us a clean method to probe local ionic activities and defect structure with high sensitivity and spatial resolution that is decoupled from other strain contributions, as well as allowing mapping of local thermomechanical response. This technique can be applied to investigate a wide range of electrochemical systems, including electrode materials for lithium ion batteries and solid oxide electrolysis and fuel cells. Initial results on Sm-doped Ceria and LiFePO4 are presented here as examples.

Many solids exhibit Vegard strain defined broadly as a lattice volume change associated with a change in the concentration of one or more ionic species or electronic defects.20,21 While mechanical deformation is generally not desirable for the operation of lithium ion batteries and other solid state electrochemical devices, such strain provides an alternative imaging mechanism to probe local ionic activities with high spatial resolution, as demonstrated by ESM.23–25 From thermodynamic point of view, Vegard strain induced by concentration changes also suggests a converse effect, that diffusion of ionic and electronic species can be driven by gradients in hydrostatic stress σh in addition to gradients in concentration c and electric potential ϕ. Such a theory has been developed by Larché and Cahn in the 1970 s29,30

ct=.(Dc)+.(DFzRTcϕ).(DΩRTcσh),
(1)

where D, z, and Ω are the diffusivity, charge, and partial molar volume of an ion or defect, F and R are Faraday's constant and the ideal gas constant, and T and t are absolute temperature and time, respectively. Note that the principle of ESM is based on electro-migration, the second term in Eq. (1). What we are interested in here is if we can utilize diffusion driven by the stress gradient, the third term in the equation, for the imaging, which would allow us to overcome a number of difficulties associated with ESM, especially the coupling with other electromechanical contributions.

The most straightforward method of applying local oscillating stress is vibrating the scanning probe mechanically. However, this implementation complicates the measurement of the resulting displacement, and it also severely limits the magnitude of stresses possible. As shown in Figure 1(a), an alternative strategy is to impose stress locally by heating the sample through a thermal probe,31,32 passing an AC through the micro-fabricated resistor localized on top of the tip. In this method, the thermal probe is heated by a sinusoidal current I[ωt]=I0cos[ωt] at an angular frequency ω=2πf. With resistance β, the resulted power dissipation p is given by

p[2ωt]=βI2=I02β2(1+cos[2ωt]),
(2)

which generates a second harmonic temperature oscillation under the heated probe around average temperature rise ΔTDC

ΔT[2ωt]=ΔTDC+ΔTACcos[2ωt+θ],
(3)

where θ is the phase delay. Such local temperature variation in turn produces a concentrated thermal expansion strain ε* and thus thermal stress σ at the second harmonic

ε*[2ωt]=αΔT[2ωt]I,σ[2ωt]=C(εε*[2ωt]),
(4)

where α and C are the thermal expansion coefficient and stiffness tensor of the material, ε is the total strain consisting of thermal strain and elastin strain, and I is the second rank unit tensor. Now substituting Eq. (4) into Eq. (1), and expanding T into Taylor series around averaging temperature T0, we obtain the local concentration oscillation driven by the thermal probe

ct=.(DΩRT0(1ΔT[2ω]T0)c0(13tr(C(εαΔT[2ωt]I)))).
(5)

From Eq. (5), it is evident that the local concentration fluctuation Δc has a second harmonic component as

Δc[2ωt]=.(DΩRT0c0(13tr(C(εαΔT[2ωt]I))))
(6)

and a fourth harmonic component as

Δc[4ωt]=.(DΩRT02c0ΔT[2ωt](13tr(C(εαΔT[2ωt]I)))),
(7)

which translate into second and fourth harmonic Vegard strains that can be measured through cantilever vibrations, as schematically shown in Fig. 1(a). Note that the second harmonic vibration consists of contributions from both thermal expansion and Vegard strain, as revealed by Eqs. (4) and (6), and it is generally dominated by thermal expansion. However, the fourth harmonic response can only arise from the nonlinear contributions of Vegard strain, and thus can be used to unambiguously detect shifts in ionic and defect concentration. It is this sensitivity of the higher harmonic response to shifts in local concentration that forms the underlying principle of STIM.

FIG. 1.

The schematics of STIM; (a) the heated scanning probe is driven by an AC at frequency f, while the second and fourth harmonics of resulted cantilever vibrations are measured, reflecting local thermal expansion and thermo-ionic activities, respectively; (b) the cantilever vibration can be approximated as a damped driven harmonic oscillator, enabling quantitative analysis near resonance with high sensitivity.

FIG. 1.

The schematics of STIM; (a) the heated scanning probe is driven by an AC at frequency f, while the second and fourth harmonics of resulted cantilever vibrations are measured, reflecting local thermal expansion and thermo-ionic activities, respectively; (b) the cantilever vibration can be approximated as a damped driven harmonic oscillator, enabling quantitative analysis near resonance with high sensitivity.

Close modal

It should be noted that the third term in Eq. (1) is only one of the possible sources of nonlinear response associated with shifts in concentration. Others not treated here include thermally-induced defect formation and thermally driven transport (Soret/Dufour effects). However, like stress-driven transport we expect strong contributions from these sources to appear in the fourth and higher order harmonic responses, and thus high sensitivity of STIM to local shifts in defect concentration.

Our current implementation of STIM utilizes an Asylum Research MFP-3D AFM equipped with Anasys ThermaLever AN2-300 thermal probe. The cantilever-sample contact resonance is determined as f0 first, and then the thermal probe is driven at f0/2 and f0/4, respectively, with the corresponding cantilever vibration measured at contact resonant frequency f0 using lock-in to enhance the sensitivity. These give us the second and fourth harmonic responses that correspond to local thermomechanical and thermos-ionic activities, respectively, as demonstrated by Eqs. (4)–(7).

To verify the concept of STIM, we first examine the harmonic responses of two types of samples, one is Sm-doped ceria, a polycrystalline solid containing both ionic and electronic defects, and the other is polytetrafluoroethylene (PTFE), an insulating polymer that serves as the control. As discussed earlier, the second harmonic response is dominated by thermal expansion that is universal in all materials, and this is indeed what we observe in both Ceria and PTFE, as shown in Fig. 2(a), where prominent resonant peaks are evident in both systems. Note that Ceria is stiffer, and thus has higher contact stiffness and resonant frequency. On the other hand, as shown in Fig. 2(b), the fourth harmonic response, which we expect to be sensitive to shifts in defect concentration, is negligible in PTFE, yet very strong in ceria. This result demonstrates the feasibility using STIM to image therm-ionic activities. It is also worth noting that the fourth harmonic response is much smaller than the second harmonic one, as expected, because it arises from the secondary effect of thermal expansion.

FIG. 2.

Comparison of (a) second and (b) fourth harmonic responses of Ceria and PTFE, demonstrating the feasibility of STIM.

FIG. 2.

Comparison of (a) second and (b) fourth harmonic responses of Ceria and PTFE, demonstrating the feasibility of STIM.

Close modal

Another consequence of Eq. (5) is that the fourth harmonic STIM response is correlated with baseline concentration c0, which can be manipulated by contact force imposed by the thermal probe—a larger contact force would increase the chemical potential, and thus reduce c0 underneath the probe, resulting in reduced STIM amplitude. This is in contrast to piezoresponse force microscopy (PFM), for example, wherein larger contact force improves electric contact between the conductive probe and sample, and thus enhances the PFM amplitude within certain extent. To verify this analysis, we probe fourth harmonic STIM response of Ceria under different contact forces, as shown in Fig. 3(a), and it is observed that the peak amplitude does decrease with increased force. To see this more clearly, the response versus frequency is fitted using the damped driven harmonic oscillator model (Fig. 1(b)),33,34 and the intrinsic amplitude, derived from the peak amplitude at resonance divided by quality factor, is plotted versus contact force (Fig. 3(b)). The overall decreasing trend with increased contact force is evident in STIM, as expected. Similar measurement is also carried out on lithium niobate using PFM for comparison, which exhibits the opposite trend (Fig. 3(c)), that higher contact force results in better electric contact, and thus higher PFM response.

FIG. 3.

The effect of contact force on STIM responses; (a) STIM responses of Ceria under different contact forces; (b) corrected STIM amplitude of Ceria versus applied force; (c) corrected PFM amplitude of lithium niobate versus applied force.

FIG. 3.

The effect of contact force on STIM responses; (a) STIM responses of Ceria under different contact forces; (b) corrected STIM amplitude of Ceria versus applied force; (c) corrected PFM amplitude of lithium niobate versus applied force.

Close modal

It is well known that nanocrystalline Ceria exhibits total conductivity that is orders of magnitude higher than bulk Ceria,35 currently understood to be caused by accumulation of mobile electrons in the diffuse space charge regions near the surface and at grain boundaries,36,37 as recently imaged by ESM.38 Using STIM, we have mapped the fourth harmonic response of Ceria as well. The topography mapping in Fig. 4(a) reveals clear grain boundaries at junctions of four grains. The fourth harmonic STIM amplitude mapping in Fig. 4(b) shows not only higher response at the grain boundaries, but also different responses in different grains, suggesting its possible dependence on grain orientation. The phase mapping in Fig. 4(c) exhibits little variation, as expected, since the phase delay is not supposed to be reversed for thermo-ionic activities, unlike PFM mapping of ferroelectric domains with opposite polarization. It is worth pointing out that during the STIM scanning, a single frequency under fixed contact force is used without tracking the shifting of resonance. As such, crosstalk with topography cannot be eliminated. Either dual frequency resonance tracking39 or band excitation40 techniques can be used to solve this problem. However, we are running out of available lock-ins for tracking in our current system, and this is a minor technical difficulty that we will overcome in the future implementation. In order to accurately reflect their different responses, we compare corrected amplitude at grain boundaries and within grains (Fig. 4(d)), averaged over ten different points probed in each area, and the higher STIM response at grain boundary is evident, due to the accumulation of space charges. This is consistent with ESM mapping we reported earlier,38 and it can also be visualized through the line scans of topography and STIM amplitude (Fig. 4(e)), revealing much higher amplitude across grain boundaries.

FIG. 4.

Fourth harmonic STIM mapping of Ceria; (a) topography; (b) amplitude; (c) phase; and (d) comparison of corrected STIM amplitudes at grain boundaries and within grains; (e) line scans of topography and STIM amplitude across a grain boundary.

FIG. 4.

Fourth harmonic STIM mapping of Ceria; (a) topography; (b) amplitude; (c) phase; and (d) comparison of corrected STIM amplitudes at grain boundaries and within grains; (e) line scans of topography and STIM amplitude across a grain boundary.

Close modal

STIM can also be applied to study electrode materials for lithium ion batteries as well, and we use LiFePO4 as an example. The fourth harmonic amplitude and phase versus driving frequency is shown in Fig. 5(a), exhibiting a clear resonant peak as expected in an ionic system. The topography mapping is shown in Fig. 5(b), wherein the grain structure is evident. The STIM amplitude mapping in Fig. 5(c) again reveals higher response near grain boundaries, consistent with what we observed before using ESM,24 though some of the regions inside grains have large STIM response as well. As such, this technique can be applied to study a wide range of electrochemical systems.

FIG. 5.

STIM mapping of LiFePO4; (a) amplitude and phase versus driving frequency; (b) topography mapping; and (c) amplitude mapping.

FIG. 5.

STIM mapping of LiFePO4; (a) amplitude and phase versus driving frequency; (b) topography mapping; and (c) amplitude mapping.

Close modal

Finally, we compare the mappings of second and fourth harmonic STIM responses in a triple grain boundary junction of Sm-dope ceria, overlaid on topography, as shown in Fig. 6. It is reiterated that the second harmonic response consists of contributions from both thermal expansion and charge activities, while the fourth harmonic one solely reflects the local charge activities. As seen in Figs. 6(a) and 6(c), the mapping are in general similar, partially due to the cross-talk with topography, as we are not tracking the shifting in resonant frequency, and partially due to the fact that both responses contain information about ionic and electronic defects. In particular, variation within grains is evident in both second and fourth harmonic responses, and interfaces within each of the grains are visible. The origin of such variation requires further investigation. To appreciate the advantage of fourth harmonic response over second harmonic one in probing local ionic and electronic defects, we compare the respective amplitudes measured point-wise at grains boundaries and within grains, as this eliminates the influence of cross-talk with topography. From Figs. 6(c) and 6(d), it is clear that the grain boundaries have higher second harmonic response than grains, yet the contrast is modest, and the ratio is 1.32. On the other hand, the ratio of grain boundaries versus grains in fourth harmonic response is 2.26, which is much higher. In other words, fourth harmonic response is much more sensitive to local ionic and electronic activities.

FIG. 6.

Comparison of second and fourth harmonic responses of STIM in Sm-doped ceria; ((a) and (b)) second harmonic amplitude mapping overlaid on topography, and comparison of corrected amplitudes at grain boundaries (averaged over 10 points) versus grains (averaged over 30 points); ((c) and (d)) fourth harmonic amplitude mapping overlaid on topography, and comparison of corrected amplitudes at grain boundaries (averaged over 10 points) versus grains (averaged over 30 points).

FIG. 6.

Comparison of second and fourth harmonic responses of STIM in Sm-doped ceria; ((a) and (b)) second harmonic amplitude mapping overlaid on topography, and comparison of corrected amplitudes at grain boundaries (averaged over 10 points) versus grains (averaged over 30 points); ((c) and (d)) fourth harmonic amplitude mapping overlaid on topography, and comparison of corrected amplitudes at grain boundaries (averaged over 10 points) versus grains (averaged over 30 points).

Close modal

In the past a few years, it has been realized that electrically induced Vegard strain can provide an imaging mechanism for electrochemical processes with high spatial resolution, though it is difficult to distinguish Vegard strain from other electromechanical sources. In this work, we develop a new STIM technique to probe local electrochemistry at the nanoscale via imaging of thermally induced Vegard strain, based on the fluctuation of ionic and defect concentrations resulting from local temperature oscillation driven by a heated scanning probe. The thermal probe is electrically insulated from the sample and thus there is no electric interference as in ESM, and the measurement is not complicated by electrostatic forces or other electromechanical mechanisms. By decoupling second harmonic thermal expansion and fourth harmonic Vegard strain, both local thermomechanical and electrochemical properties can be mapped, and it has been applied to probe Sm-doped Ceria and LiFePO4, revealing higher ionic and defect activities near grain boundaries. The STIM gives us a powerful method to probe local electrochemistry with high sensitivity and spatial resolution, as well as local thermomechanical properties, and it can be applied to investigate a wide range of electrochemical systems.

This material is based, in part, upon work supported by National Science Foundation (Nos. CBET 1435968 and DMR 1337173) and the State of Washington through the University of Washington Clean Energy Institute. We also acknowledge the support of the Natural Science Foundation of China (11472236) and Shenzhen Science and Technology Innovation Committee (ZDSYS20140509162754023).

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