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Scanning Thermo-Ionic Microscopy (STIM) is a technique of probing the local electrochemistry of a thermoelectric material at the nano-scale level. STIM is achieved with the use of an Atomic Force Microscopy (AFM) micro-fabricated thermal probe used for resistive heating, or with a 405nm laser used for photo-thermal heating, utilizing the Vegard strain that is induced via the thermal stress excitation. Since STIM uses thermal stress-induced oscillations as the driving force, the responses are immune to global current perturbation, thus making operando testing possible. In general, the STIM technique is best used for the probing of electrochemical functionalities at the nano-scale level. The STIM technique was developed through the University of Washington in conjunction with the Shenzhen Key Laboratory of Nanobiomechanics.

Introduction
Currently, the energy economy is shifting from a focus on fossil fuels, more towards a diverse and multi-directional network of energy sources, where there is a critical need for electrochemical materials. These electrochemical materials can be used small and large scale battery systems, fuel cells or flow batteries, electrocatalysts for efficient electrosynthesis of liquid transportation and storage of fuels, and photoelectrochemical materials that can directly convert solar energy to fuels. The current challenge in dealing with the development of these materials is the lack of knowledge of the chemical and physical process at the nano-scale level. Previous techniques of electrochemical characterization where mostly based on current measurements, which was difficult to scale down to the nano-level. There have been custom-made ion-conducting electrodes that have been used for scanning electrochemical microscopy, but the spatial resolution for these test were only on the order of micrometers. Electrostatic force microscopy and Kelvin probe force microscopy have been applied for the studies of electrochemical process, but once again the spatial resolution was not high enough and the data was often difficult to interpret. In recent years, researchers have discovered the functionality of the Vegard strain, which is the phenomenon when a large concentration of charged particles exist in the vicinity of a probe tip, changes in their concentration will cause the material to deform. This development in the Vegard strain led to electrochemical strain microscopy (ESM), which focused on the local and instantaneous fluctuation of ionic species when induced by an AC voltage that was applied through a conductive scanning probe. 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 (reference paper on Scanning thermo-ionic microscopy for probing local electrochemistry at the nanoscale). This technique allowed for considerable insight into the local chemistry, but it was often difficult to distinguish between the Vegard strain from other electromechanical mechanisms because the measured strain was electromechanical in nature. Researchers at the University of Washington have developed STIM, which is a powerful tool in probing the local electrochemical functionalities of a material at the nano-scale. This technique also utilizes the Vegard strain, but it is unique in that the strain is induced via thermal stress excitation instead of an AC electric potential, which eliminates the other electromechanical strains, as well as interference from global voltage perturbation. This technique has been accomplished using either resistive heating with an AFM thermal probe, or photo-thermal heating via a 405 nm laser. In short, the main differences between ESM and STIM is that for ESM, the ionic oscillation is driven by the electrical potential, while for STIM, it is driven by the local thermal stress.

Concept
The STIM technique is currently built on three observations: mechanical vibrations, fluctuation of ionic concentration, and local ionic species, concentration and diffusivity that all lead to electrochemistry at the nano-scale. First, when the an ionic concentration oscillates in a solid, the volume of the material in contact with the probe will fluctuate due to the Vegard strain. This results in a mechanical vibration that is measured locally by the scanning probe. Such detection of dynamic strain can be detected by a variety of scanning probe microscopy techniques such as piezoresponse force microscopy (PFM), electrochemical strain microscopy, and piezomagnetic force microscopy (PmFM). Second, the Vegard strain can be driven by an oscillation in its electrochemical potential, which is caused by gradients of ionic concentration, electric potential, or mechanical stress. And third, the characteristics of the ionic oscillation and electrochemical strain that are gathered via the scanning probe can reveal valuable information on the local ionic species, concentration, and diffusivity that tell us about the local electrochemistry at the nano-scale.

Stress-Induced Diffusion
The STIM method is based on the concepts of stress-induced diffusion that was developed by Larché and Cahn in the 1970's. The equations and theories of this concept are detailed below:

$$\left ( \frac{\partial c}{\partial t} \right )=\nabla.(D \nabla c) +\nabla. ({DFz \over RT} c\nabla \phi)- \nabla. ({D\Omega \over RT}c \nabla\sigma_h)$$

where D,z, and Ω are the diffusivity, charge and partial molar volume of an ion; F and R are Faraday's and the ideal gas constants; and T and t are the absolute temperature and time respectively. As mentioned above, the three driving forces for ionic oscillation are gradients in ionic concentration (c), electric potential (φ), and hydrostatic mechanical stress ( $$\sigma_h$$). In order to impose an oscillating stress while simultaneously measuring the resulting local vibration, both of which run through the scanning probe, a local temperature oscillation with angular frequency (ω) is applied,

$$\Delta T_{AC}[\omega]=\Delta T e^{i\omega t}$$, which then results in local oscillation of therm strain Δε* and hydrostatic stress Δ $$\sigma_h$$,

$$\Delta \varepsilon *[\omega]=\alpha\Delta Te^{i\omega t} I $$

$$\Delta \sigma_h [\omega]={1 \over 3} trC(\Delta \varepsilon[\omega] -\Delta \varepsilon*[\omega])=\Delta \sigma_{h0} e^{i\omega t}$$,

where $$\alpha$$ is the thermal expansion coefficient and C is the elastic stiffness tensor of the material. ε is the total strain of consisting of thermal strain ε* and elastic strain. tr denotes the trace of the matrix, and $$\sigma_{h0}$$is the amplitude of hydrostatic stress oscillation, and I is the second rank unit tensor. Note that the hydrostatic thermal stress gradient results in a thermal vibration that is first harmonic to the temperature oscillation, which means that the first harmonic displacement response reveals the local thermomechanical properties of the material.

There are still further consequences and implications of this oscillating thermal stress, which in turn drives the oscillation in ionic concentration. The first and second harmonic components of ionic oscillation can be obtained by Taylor expanding $$T$$ around the baseline temperature $$T_0$$,

$$\Delta c[\omega]=-\nabla. ({D\Omega c_0 \over RT_0}\nabla \sigma_{h0})e^{i \omega t}$$                         $$\Delta c [2\omega]=\nabla. ({D \Omega c_0 \over RT_0^{2}}\Delta T\nabla \sigma_{h0})e^{i2\omega t},$$

which will then induce the first and second harmonic Vegard strains and the corresponding displacements. Thus, the first harmonic STIM response is made-up of contributions from both thermal expansion and Vegard strain. The response is generally dominated by the thermal expansion, and is thereafter referred to as thermal response. The second harmonic STIM response is purely caused by Vegard strain associated with ionic oscillation, and is thereafter referred to as the ionic response. Therefore, the associated thermal and ionic responses that are induced by the fluctuating thermal stress at respective harmonics, we can obtain information on both the thermomechanical and ionic properties of the material. This is the principle in using STIM.

Thermal Probe
The first component of STIM is to generate a temperature oscillation through a scanning thermal probe on the AFM machine. In the initial experiments conducted, the probe that was utilized for these experiments was an AN2-300 from Anasys Instruments, and the AFM machine was an Asylum Research model MFP-3D AFM. The thermal probe has a micro-fabricated solid state resistive heater at the end of the cantilever, which enables local heating and thus temperature oscillation when an AC current is passed through. Through this set-up, the power dissipation, which is correlated with the temperature oscillation, is second harmonic with respect to the AC current (this is due to the quadratic relationship between the power and current). This results in a thermal response at the second harmonic and a ionic response at the fourth harmonic, both in respect to the input current. From these results we can gather the thermomechanical and electrochemical properties of the material.

405nm Laser
STIM has also been implemented through a photothermal approach to induce local heating and temperature fluctuation. The photothermal excitation module utilizes a 405 nm laser with modulated intensity aligned at the base of a gold coated cantilever. Under the photothermal excitation, the laser power, which is directly correlated with the local temperature, is modulated directly. This leads to first harmonic thermal responses and second harmonic ionic responses. At the University of Washington the cantilever was a Multi75GD-G cantilever from Budget Sensors, and this was implemented on an Asylum Research Cypher ES AFM that was equipped with a blueDrive photothermal module.

Lock-In Amplifier
A lock-in amplifier is used to detect the various harmonic responses of the deflected cantilever due to the fact that the deflections are usually very small in magnitude, so the lock-in amplifier is necessary to pick up these responses with much accuracy. This is necessary to enhance the signal to noise ratio by orders of magnitude. A dual amplitude resonance tracking (DART) technique is applied to avoid topography cross-talks during the STIM scanning. DART is used to track the contact resonance through implementation of the thermal probe. In total, four lock-ins are required to measure the thermal (off-resonance) and ionic response (resonance-enhanced) mappings simultaneously via photothermal or Joule heating excitation. The responses at the two frequencies across the resonance allow us to solve for the quality factor and the contact resonance frequency of the system. This is based on the damped driven simple harmonic oscillator model, which enables more accurate quantitative analysis.

Point-wise Studies
To demonstrate the feasibility of STIM, listed below is an examination of the point-wise thermal and ionic responses of two types of samples at respective harmonics. For this example the two samples are a nanocrystalline Sm-doped ceria, which is a good ionic conductor; and the other is a polytrtrafluoroethylene (PTFE), which serves as the control sample as it has no ionic conductivity.

Thermal Responses
When subjected to the STIM technique, we can clearly see in the figure to the right that both samples exhibit substantial thermal response measured at the second harmonic, which is expected in any material regardless of its ionic characteristics. A seen in the figure, we notice that ceria has a higher contact resonance frequency as compared to PTFE, which indicates a higher elastic modulus as expected. Through this procedure, the experimental data can also be fitted with a damped driven simple harmonic oscillator to obtain the quality factors of ceria and PTFE (57.7 and 46.4 respectively), which indicate higher viscous energy dissipation in PTFE. Once the intrinsic thermal response amplitudes are corrected using the quality factors, it is suggested that the thermal expansion of PTFE is higher than that of ceria, as expected. Through these observations, it is concluded that the local thermomechanical properties of solid materials can indeed be obtained from the STIM thermal response.

Ionic Responses
Further insights can be be gained from the ionic responses that are measured at the fourth harmonics, which is shown in the right image in the figure above. Most obviously, it is noted that the ceria exhibits a much higher response than that of PTFE, which is almost negligible due to its non-ionic nature. When the data is once again analyzed with a damped driven simple harmonic model, the quality factors of ceria and PTFE are 49.52 and 55.95 respectively. From this the intrinsic response of each can be calculated, such that ceria has a response of 3.31 pm, and PTFE has a response of 0.31 pm. Both of these reassure the fact that ceria has good ionic conductivity, and PTFE is non-ionic in nature. Overall, the quality factors and resonance frequencies obtained from both the thermal and ionic responses are in good agreement, which confirms the reliability of the measurements. The ionic response of ceria is an order of magnitude smaller as compared to its thermal response, but the the signal is sufficiently strong and clean for sensitive detection. Thus, this set of data proves the feasibility of STIM.

Advantages

 * Powerful tool for probing local electrochemical activities based on atomic force microscopy
 * Mapping ionic and thermal properties at nanoscale using both heated probes and regular AFM probes. With this, the probes do not need to be electrically conductive
 * In contrast to ESM, the responses are insensitive to the electrochemical, electrostatic, and capacitive effects
 * In-operando spectroscopy of battery materials is possible because STIM is immune to global current perturbations
 * Experimental measurement of ionic conductivity based on spectroscopic studies
 * Easily distinguishes nonlinear strain associated with ionic species and electronic defects from linear thermomechanical sources due to differences in their harmonic responses