Laser-driven ultrafast impedance spectroscopy

Abstract

an apparatus comprising: a source of electromagnetic radiation comprising one or more first frequencies; a source of an input signal comprising an alternating current (AC) electric field comprising one or more second frequencies; and control circuitry for synchronizing application of the electromagnetic radiation and the AC electric field to a sample, the control circuitry causing an output signal to be output from the sample comprising a modulation of the AC electric field in response to the one or more second frequencies tuned to drive hopping of ions between ion sites within the sample and the one or more first frequencies tuned to drive excitations in the sample that interact with the ions, the apparatus further comprising: a detection system for measuring and / or detecting changes in the output signal in response to the electromagnetic radiation; and a computer for determining at least one of the conductivity or impedance of the sample from the output signal as a function of the first and second frequencies.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is the latest in a series of commonly owned and concurrently pending applications: U.S. Provisional Application No. 63 / 437,200, filed January 5, 2023, entitled "LASER DRIVEN ULTRAFAST IMPEDANCE SPECTROSCOPY" (CIT 8941-P), by Scott K. Cushing and Kim Pham; and U.S. Provisional Application No. 63 / 543,666, filed October 11, 2023, entitled "LASER DRIVEN ULTRAFAST IMPEDANCE SPECTROSCOPY" (CIT 8941-P2) by Scott K. Cushing and Kim Pham; and USC §119(e) benefit is claimed based on USC §119(e) and USC §119(e) and USC §119(e) benefit of ...

[0002] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with government support under Grant No. FA9550-21-1-0022 awarded by the United States Air Force. The government has certain rights in this invention. [Technical Field]

[0003] SUMMARY OF THE INVENTION The present disclosure relates to spectroscopic systems and methods of making and using the same. [Background technology]

[0004] Current batteries rely on solid and polymer electrolytes with conductivities superior to those of water. To achieve this, ions must hop between vacant sites on the order of picoseconds. Mobility is determined by electronic screening and mechanical deformation of the lattice, which either promote or hinder this ion hopping. Current battery characterization techniques focus on measuring bulk mobility using impedance spectroscopy or identifying hopping sites using NMR or neutron scattering. However, currently, no method exists that can 1) measure ultrafast ion hopping on its native time scale, or 2) quantitatively evaluate the contributions of ion interactions with electron screening clouds and phonons, or higher-order combinations such as ion-ion, ion-electron-phonon, or ion-phonon-phonon interactions, to ionic conduction. For example, comparative studies using existing advanced techniques to estimate these processes have yielded estimates of hopping frequencies that differ by more than nine orders of magnitude for the same material. Therefore, improved methods for studying ion transport in materials are needed. The present invention fulfills this need. Summary of the Invention [Problem to be solved by the invention]

[0005] This paper reports on a new type of impedance spectroscopy, in which a CW light source or laser (or similarly frequency-tunable source) is swept over a wide frequency range corresponding to excitations such as, but not limited to, electronic, ionic, or phonon excitations, or any combination thereof. The change in an alternating current (AC) electric field at frequencies covering different ion hopping regimes (e.g., from contacts to grain boundaries to bulk effects in the case of solid electrolytes) is then measured as a function of driving frequency. The resulting time-dependent response allows for measurement of individual ion hopping on picosecond or faster time scales. Comparing responses at multiple driving frequencies, or combinations of pulses with different time delays at different frequencies, provides a measure of the relative strength of the ion hopping process. Overall, the quantum mechanical Hamiltonian is mapped, providing detailed information not only about how ion hopping occurs, but also about aspects of interest for materials engineering. Several versions of the instrument are described, with varying levels of complexity and cost, depending on the depth or nature of the information measured. While illustrated in the context of battery electrodes and electrolytes, the technique is applicable to any ionic or mixed-ion conducting system.

[0006] As a by-product of the measurement technique, a laser-driven increase in ionic conductance is realized, changing the overall impedance of the battery. The ionic conductor, or any application thereof, can be modulated by light depending on the frequency. Some of these effects persist for several minutes after the femtosecond excitation pulse, suggesting potential technological applications. [Means for solving the problem]

[0007] Exemplary embodiments include, but are not limited to, the following.

[0008] 1. a first source of electromagnetic radiation (EM) comprising one or more first frequencies; a second source of an input signal comprising an alternating current (AC) field comprising one or more second frequencies; a control circuit coupled to the first source and the second source for synchronizing application of the electromagnetic radiation and the AC electric field applied to a sample, the one or more second frequencies tuned to drive hopping of ions between ion sites within the sample; and the one or more first frequencies tuned to drive excitation in the sample that interacts with the ions; a control circuit responsive to the sample to cause an output signal comprising a modulation of the AC electric field to be output from the sample; a detection system arranged to measure and / or detect changes in said output signal in response to said electromagnetic radiation; a computer connected to the detection system for determining at least one of the conductivity or impedance of the sample from the output signal as a function of the first frequency and the second frequency.

[0009] 2. The system of embodiment 1, wherein the control circuitry: sweeping the first frequency through a first range to drive excitation of electrons, ions and / or phonons in the sample, including an electrolyte; and sweeping the second frequency over a second range such that the input signal drives ion hopping in the electrolyte over a range of ion transit time scales. The spectrometer further comprises a control circuit that controls or that controls the

[0010] 3. The system of embodiment 2, wherein the computer determines or is programmed to determine a change in conductivity at one or more second frequencies associated with a transit time scale in different ion hopping regions within the electrolyte, including at least one of a contact region, a grain boundary, or a bulk region.

[0011] 4. The system of embodiment 3, wherein the electrolyte comprises a solid electrolyte for a battery.

[0012] 5. The system of embodiment 4, wherein the sample comprises electrical contacts to the solid electrolyte containing lithium ions for a lithium ion battery.

[0013] 6. The system of embodiment 1, wherein the computer determines, or is programmed to determine, from the output signal a Hamiltonian of the sample that describes the interaction of excitations excited by the electromagnetic radiation and hopping driven by the input signal.

[0014] 7. The system of embodiment 1, wherein the first source of electromagnetic radiation comprises a pulsed or continuous wave (CW) laser that outputs the first frequency ranging from ultraviolet (UV) frequencies to THz.

[0015] 8. The system of embodiment 1, wherein the first source of electromagnetic radiation includes a lamp that outputs the electromagnetic radiation.

[0016] 9. The system of embodiment 1, wherein the second source of the input signal includes a signal generator that outputs the second frequency in the range of 1 Hz to 1 THz.

[0017] 10. The system of embodiment 1, wherein the detection system measures, or comprises circuitry for measuring or detecting, the output signal on the time scale of the excitation driven by the electromagnetic radiation.

[0018] 11. The system of embodiment 1, wherein the first source of electromagnetic radiation includes a pulsed laser that outputs pulses of electromagnetic radiation having a full width at half maximum (FWHM) of 1 nanosecond or less, and the detection system includes circuitry that measures changes in the envelope of the FWHM with time resolution.

[0019] 12. The system of embodiment 1, wherein the first frequency comprises a terahertz frequency.

[0020] 13. The system of embodiment 1, further comprising a sample holder for holding the sample, the sample holder comprising: a vertical launch connector for physically connecting to a microstrip on the sample; a metal plate with at least one opening for insertion of the sample and coupling of the electromagnetic radiation to the sample; and fasteners for securing the sample between the vertical launch connector and the metal plate such that the input signal is transmitted from the vertical launch connector to the microstrip and a reflection of the input signal (including the output signal) is output from the microstrip to the vertical launch connector.

[0021] 14. The system of embodiment 13, further comprising: via a first coaxial cable to a second source of said input signal; and to the detection system via a second coaxial cable. a coupling directional coupler for coupling the optical fiber and the optical fiber;

[0022] 15. A system as described in embodiment 1, further comprising a time-resolved vector network analyzer having a second source of the input signal including a signal generator and a detection system including an oscilloscope triggered by a photodiode that detects the electromagnetic radiation.

[0023] 16. A system as described in embodiment 1, wherein the detection system measures or comprises circuitry for measuring changes without time resolution on the time scale of application of the electromagnetic radiation, and the computer is programmed to determine the conductivity of the sample, including a thin film, using normalization to remove the contribution of steady-state heating due to the input signal.

[0024] 17. A system as described in embodiment 1, wherein the detection system comprises an IQ demodulator coupled to a photodetector that detects the electromagnetic radiation, and the amplitude and phase of the output signal (current and voltage) are measured using the IQ demodulator so that they can be correlated with a time resolution for changes in the time envelope of the electromagnetic radiation.

[0025] 18. A system as described in embodiment 1, wherein the detection system comprises circuitry for measuring or detecting the output signal to determine a change in the complex impedance of the sample, and the computer determines or is programmed to determine the conductivity from the complex impedance.

[0026] 19. The system of embodiment 1, wherein the detection system comprises an impedance analyzer.

[0027] 20. A method for measuring conductivity comprising: irradiating a region of the sample with electromagnetic radiation comprising one or more first frequencies; applying an input signal to the region, the input signal comprising an alternating current (AC) electric field comprising one or more second frequencies, such that the electromagnetic radiation and the input signal are applied synchronously; below: the one or more second frequencies tuned to drive hopping of ions between ion sites within the sample; and the one or more first frequencies tuned to drive excitation in a region that interacts with the ions; measuring and / or determining an output signal comprising a modulation of the AC field in response to the and determining from the output signal the conductivity of the sample as a function of the first frequency and the second frequency.

[0028] 21. The method of embodiment 20, wherein the sample comprises any material system (biological or non-biological) that conducts ions.

[0029] Referring to the drawings, like reference numbers indicate corresponding parts throughout. [Brief explanation of the drawings]

[0030] [Figure 1] Schematic of the time-resolved ultrafast impedance setup, including the laser, a representative nonlinear frequency generation process (covering the UV to THz excitation range), a VNA, and a sample cell. [Figure 2] Figures 2a-f show the calculated phonon contributions to Li-ion hopping, THz absorption, and representative modes between 0 and 6 THz for LLTO. Figure 2a shows the resolved accumulation of the normalized contributions to ion hopping. The gray dashed line indicates the experimental limit of THz generation (6 THz). Figure 2b shows the normalized contributions of 120 individual modes to Li-ion hopping. Red indicates low-energy (E) phonon modes, and blue indicates high-energy modes. Figure 2c shows the THz absorption (orange) and calculated phonon hopping contributions (bar graph) for LLTO. Figures 2d-g show the phonon modes that contribute significantly to Li-ion hopping through the front 4-O window (Figure 2g) or do not contribute at all (Figure 2d-f). [Figure 3] Figure 3a shows a photograph of the gap electrode design on the LLTO pellet. This was also used as a reference. The cell temperature was controlled using a TC-48-20 OEM temperature controller, a 12V power supply, and the corresponding TC48-20 OEM software. The heating cell was placed in a Faraday cage for all experiments to reduce noise due to electromagnetic interference. The copper mesh was custom-made with a 1.4mm copper wire spacing. Figure 3b shows a schematic diagram of the sample, including the electrodes in contact with the electrolyte. [Figure 4]Figures 4a-4d show the characterization of LLTO. Figure 4a shows the XRD pattern, Figure 4b shows the SEM image of the 1-10 μm grain size within the pellet, Figure 4c shows the bulk, and Figure 4d shows the grain boundary portion of the impedance spectrum. A 1 mm gap was placed in the center of the pellet to excite the LLTO with the light source, eliminating the effect of Au irradiation on the impedance (Figure 2). Figures 4a-4d show the XRD pattern, the 1-10 μm grain size, and a representative impedance plot. [Figure 5] Schematic of the THz field setup. OPA: Optical parametric amplifier. OAP: Off-axis paraboloid. FL: Focusing lens, P: Polarizer, PD: Photodiode. [Figure 6] Figures 6a-6d show the conductivity change of an LLTO sample from 1 Hz to 50 GHz. Excitation of charge-transfer transitions reduces the Coulomb hopping barrier, increasing the conductivity (solid black line). Figure 6a shows that the change (red region) is larger than the photoheating of the lattice (dashed black line). Figure 6b shows a unit cell of LLTO and a schematic diagram illustrating how photoexcited charge-transfer transitions dissipate electron density in the lithium-ion conduction pathway. Within the unit cell, Li ions are shown in purple, O in red, La in green, and Ti in gray at the center of the octahedron. Figure 6c shows a typical time-resolved conductivity change on the picosecond time scale. Figure 6d demonstrates the linearity of the signal response with excitation power. [Figure 7] Figures 7a–7d show the THz interaction with LLTO. The orange, blue, purple, and gray atoms correspond to oxygen, titanium, lanthanum, and lithium, respectively. Figure 7a shows the impedance analyzer recording EIS spectra before, during, and after THz excitation at t1=0. Figure 7b shows how, between t2>t1, the THz light drives resonantly contributing modes, increasing the phonon population. Figure 7c shows that continued THz irradiation results in energy transfer from phonons to Li ions and the opening of a bottleneck, thereby facilitating Li ion hopping, manifesting as a drop in impedance. Figure 7d shows that upon removal of the THz source, the phonon population and impedance return to the original state (a). [Figure 8]This diagram shows the electrochemical heating cell setup for obtaining power vs. temperature calibration curves and collecting EIS data at <32 MHz using a 1260A Solartron. The cell components are compressed and secured in place with screws through the five holes shown. Each screw is tightened with a wing nut. [Figure 9] Figure 9a shows the absorption spectrum spanning the UV-Visible to THz frequency range, demonstrating mobility enhancement with near-infrared (NIR), mid-infrared (MIR), and THz light. The change in Rbulk per change in sample temperature (K) is indicated by the orange bars and further defined by the black gradient. NIR enhancement and DC heating correspond to incoherent heating of the acoustic phonon bath. MIR excitation corresponds to coherent driving of optical phonon modes. THz light coherently drives the contributing modes and exhibits the largest relative enhancement. The width of the orange bars represents the spectral width of the excitation pulse. For comparison, Figure 9a plots the absorption spectrum spanning the UV-Visible to THz range, with the width of the orange bars representing the bandwidth of the excitation light source. This figure demonstrates that the THz light source is broader than other excitation sources. Figure 9b shows a comparison of the measured THz absorption in LLTO with the theoretically predicted contribution of the excited THz rocking modes to ionic conduction. [Figure 10] Figures 10a-10d show Nyquist plots of LLTO under targeted phonon excitation by THz at temperatures ranging from 298 K to 333 K. Figure 10a shows the grain boundary characteristics of LLTO, and Figure 10b shows the bulk characteristics. Open symbols correspond to the data. Solid lines represent fittings. Figure 10c shows the Nyquist plots of LLTO under THz excitation from 0 to 1.6 mW. The change in Z' is compared at single frequencies of 803 kHz and 32 Hz, corresponding to the bulk and grain boundary resistances. Figure 10d shows the rate of change of impedance with power. The linearity of the data refutes nonlinear effects due to the THz driving field. [Figure 11]Figure 11a is a schematic diagram of a vertical launch with exposed pins making electrical contact with the sample under investigation. Figure 11b shows that the sample is placed in a 300 μm deep, 2 mm diameter well with a 2 mm thick hole drilled in the side to allow simultaneous illumination of the sample. Figure 11c shows that the vertical launch is connected to the S12 port of a directional coupler. The S11 port allows for reflection measurements against the undisturbed reflected wave provided by the S13 port. [Figure 12] The conductivity change of an LLTO sample from 2 Hz to 110 GHz. Excitation of charge-transfer transitions reduces the Coulomb hopping barrier, increasing the conductivity (solid black line). The change shown in the red region is larger than the optical heating of the lattice (dashed black line). The dotted line shows the conductivity of LLTO when the laser is off. [Figure 13]

[0033] Figure 1 shows the conductivity change of an LLTO sample from 2 Hz to 110 GHz due to 350 nm light. Representative time-resolved conductivity changes on the picosecond time scale are shown. [Figure 14] Figures 14a-14e show the impedance change from 5 to 20 mW upon bandgap excitation with 349 nm light. Figure 14a shows the grain boundary semicircle fit to the R1+RGB / Q2 circuit. Figure 14b shows the bulk impedance semicircle fit to the R1+Rbulk / Q2 circuit. Figure 14c shows the grain boundaries, and Figure 14d shows the bulk reproducibility across three samples, showing the impedance change with 349 nm optical excitation (5-20 mW) at frequencies corresponding to each intersection of the semicircular features. Figure 14e shows the rate of impedance change as a function of 349 nm laser power, confirming a linear response at both the grain boundaries and the bulk. [Figure 15] 1 is a flowchart illustrating a device fabrication method. [Figure 16] 1 is a flow chart illustrating a method for performing spectroscopy. [Figure 17] 1 is an example of a hardware environment for performing the computer and / or control functions described herein. [Figure 18]1 is an example of a networked system for performing the computer and / or control functions described herein. [Figure 19] Figure 19a shows an exemplary detection system comprising a PLL detector, Figure 19b shows an exemplary detection system comprising an IQ modulator, and Figure 19c shows an exemplary detection system including an amplitude detector, further showing optional connections to synchronization or trigger circuitry. DETAILED DESCRIPTION OF THE INVENTION

[0031] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS In the following description of the preferred embodiments, reference is made to the drawings which form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention.

[0032] [Technical explanation] 1. System Components 1 shows a spectrometer, apparatus, device or system 100 comprising a source 102 of electromagnetic radiation comprising one or more first frequencies; a source 104 of an input signal comprising an alternating current (AC) electric field comprising one or more second frequencies; and a control circuit 106 that synchronizes the application of the electromagnetic radiation and the AC electric field to a sample 108, thereby: (1) outputting an output signal 110 comprising a modulation of an AC electric field from the sample in response to the one or more second frequencies tuned to drive hopping between ion sites in the sample; (2) The one or more first frequencies are tuned to induce excitation that interacts with ions within the sample.

[0033] The spectrometer further includes a detection system 112 that measures changes in the output signal in response to the electromagnetic radiation; and a computer that determines at least one of the conductivity or impedance of the sample from the output signal as a function of the first frequency and the second frequency.

[0034] Figure 1 shows one embodiment of a laser-driven ultrafast impedance spectrometer using a nonlinear mixer (nonlinear optical frequency generation). In an alternative configuration, a continuous-wave light source (e.g., a high-power lamp or CW laser) can be used in combination with a standard impedance analyzer (e.g., a 1260A Solartron) when measuring steady-state conditions. However, because current CW sources have difficulty achieving sufficient average power in the UV-THz range, pulsed lasers can also be used. However, this requires careful control of data acquisition due to duty-cycle averaging. In this CW version of the instrument, only relative (rather than absolute) values ​​for the second-order (electron or phonon and ion) Hamiltonian components are available, and cross-correlation terms (e.g., ion-electron-phonon) are estimated. However, this information remains important for many applications, including but not limited to the design of solid-state ionic conductors.

[0035] 2. Ionic Conductivity Calculation Example In electrochemical impedance spectroscopy (EIS), a sample is perturbed by a sinusoidal potential (Equation 1), where U(t) is the potential as a function of time t, U0 is the amplitude of the potential, and f is the frequency. 46 :

number

[0036] Interaction with the sample changes the phase and amplitude of the measured response (current or potential) as shown in Equation 2, where I(t) is the current as a function of time, I0 is the amplitude of the current, and Θ is the phase angle.

number

[0037] The complex impedance can be derived from the amplitude Z = U0 / I0 and the phase angle Θ, i.e., the phase shift between U(t) and I(t) at the measured frequency f. Although EIS cannot separate conduction caused by multiple mobile charge carriers, EIS is still a useful technique for studying ionic conduction in many solid conductors. In the literature, FFT-EIS is used to access the faster hopping regime. 47-49 , Online EIS 50,51 , and high-speed time-resolved techniques 49,52,53 have been developed, but these do not use pumps to drive ion movement.

[0038] Furthermore, this disclosure describes, to our knowledge, the first method to reach 40-110 GHz due to recent advances in electronics, whereas previous reports have only reached 1-3 GHz. 46,49,50,54,55 Ultimately, the bandwidth of the signal generator and oscilloscope determines the time and frequency resolution, and frequency extenders can be used to reach the THz range.

[0039] In one embodiment of the time-resolved impedance measurement technique, a signal generator generating frequencies from kHz to 110 GHz is used as a perturbation signal to match the time scale of the ion hopping mechanism. An oscilloscope is used to measure potential changes, current changes, and phase shifts at the same frequencies, all of which are used to derive the impedance.

[0040] However, above several tens of MHz, capacitance and inductance values ​​become so small (sub-picofarad and sub-nanohenry, respectively) that direct measurement of current versus potential change becomes impractical. 56 Instead, scattering parameters are measured to determine the amplitude and phase changes related to the impedance as shown in Equation 3.1. 43,56 where VSWR is the voltage standing wave ratio, i.e., the efficiency of power transmission through the transmission line from the radio frequency power source to the load, S11 is the reflection scattering parameter, Γ is the reflection coefficient, Z0 is the reference ohm (usually 50 ohms), and Z Lis the sample impedance or load.

number

[0041] Since S11 is measured directly from the VNA, Z L can be calculated and the ionic conductivity can be further determined.

[0042] 3. Initial measurements of ultrafast ion hopping at LLTO a.Theoretical framework The basic mechanism of ionic conduction (σ) is the activation energy of ion hopping (E A ) and temperature (T), as shown in Equation 4.

number

[0043] However, σ ion also depends on many factors that become apparent after expanding the pre-Arrhenius factor σ0, as shown in Equation 5. 7 .

number

[0044] The probability of an ion hop depends on the trial frequency (ν), the jump distance (a), and the activation energy barrier (ΔH m or experimental E A ), and temperature (T). From equation 5, σ0 ∝ exp(ΔS m ) where ΔS m is the entropy of the transfer, but is expressed only as a one-body problem. In the framework of the many-body problem, ΔS m is predicted to depend on the vibrations of the host sublattice, as shown in Eq. 7 .

number

[0045] Transition state frequency (v i S ) belongs to the whole system at the beginning of the transition. The initial frequency (v i I ) is composed of normal frequencies of a system constrained by a saddle-point structure, so a multi-body treatment is required. 15,17 .v i S When is sufficiently large, e.g., for ionic conductors with large anharmonicity and soft anion sublattices, ΔS m and the subsequent large σ, which is essential for the study of phonon-coupled conduction.

[0046] Equation 6 is ΔS m Theoretically, we predict the relationship of σ to ΔS m No study has yet experimentally quantified the role of . To demonstrate the relevance of many-body coupling on ion migration, we experimentally drive correlated polyanion motion, measure the resulting effect on σ, and compare the results to driving other acoustic and optical phonon modes. While driving structural modes to change electronic and magnetic properties is common in condensed matter materials, 16,23,24 , these technologies 25,26 has not previously been applied to determining conductivity or impedance from one or more second frequencies tuned to drive ion hopping between ion sites and one or more first frequencies tuned to drive excitation in a sample that interacts with the ions, as described herein.

[0047] Using ab initio calculations, we modeled the contributions to ion hopping in LLTO based on 22 Li-ion hops, based on structural information from three LLTO configurations and experimental synchrotron diffraction data. By considering all configurations, we were able to analyze all ion migration pathways and phonon vibration types. Figure 2a shows the cumulative normalized contributions to ion hopping across frequencies from 0 to 27 THz. Further decomposition of the total modes by contribution reveals that the top 10% of modes account for 61% of the contribution to ion hopping, and the top 5% of modes account for 48% of the contribution. Below 6 THz, we found that 36% of the modes are locking types, accounting for 50% of the contribution to ion hopping.

[0048] They also calculated the amount of energy that each phonon imparts to the hopping Li ion. Although low-THz frequency modes should be high-energy, the energy of these modes is frequency-independent. In classical thermodynamics, the distribution function of the number of phonons at a particular frequency ω is given by JPEG2026504021000008.jpg1239. The total phonon energy at a given frequency is k B T, the energy of each phonon is If JPEG2026504021000009.jpg1213, then the total energy E is k B T, which is independent of frequency. Thus, at low frequencies there are many low-energy phonon modes and several high-energy phonon modes, which sum to an overall high energy.

[0049] Figure 2b plots the energy (shown by color gradation) contributed by phonon modes to the hopping ion versus its corresponding phonon frequency. Figure 2b shows that in addition to rocking modes below 6 THz, high-energy phonon modes also exist, and the contributions of both mode types are detailed in Figure 2c. We calculate that, of the top 5% contributing modes below 6 THz, >95% are rocking modes, high-energy phonon modes, or a combination thereof. Therefore, to facilitate ion transport, the surrounding polyanions must (1) transfer sufficient energy to the Li ion in the correct hopping direction and (2) possess appropriate vibrations that open the bottleneck for ion transport. The modes shown in Figures 2d–f do not satisfy both conditions, whereas the mode shown in Figure 2g does. Therefore, after confirming the existence of modes satisfying conditions (1) and (2) within the experimental THz range described herein, we hypothesize that exciting these highly contributing mode types will enhance ion transport in LLTO.

[0050] b. Spectroscopic measurement (i) Sample holder Figure 3 shows the sample holder used for battery cell testing. The heating cell allows for a temperature range of 298 K to 333 K for reference measurements of the incoherent heating of the phonon bath performed in standard impedance measurements. To allow transmission of the THz electric field, a polymethylpentene (TPX) optical window is incorporated into the heating cell. For other visible / UV sources, a quartz window, which transmits in the range of 190 nm to 2500 nm, was used. Measurements without a window were also performed for non-air- and non-moisture-sensitive samples.

[0051] (ii) Sample preparation Lithium lanthanum titanate (Li0.5La0.5TiO3, LLTO) was used as the test sample because it is stable. 1The powder was synthesized according to the method described in the previous section. Stoichiometric amounts of La2O3, Li2CO3, and TiO2 were mixed in an agate mortar and pressed into pellets under 100 MPa pressure. The pellets were placed on sacrificial powder and fired at 800 °C for 4 hours, followed by 1200 °C for 12 hours at a heating rate of 1 °C / min. The resulting powder was pressed into pellets with a diameter of 10 mm and a thickness of 0.6–0.8 mm under 2 tons of pressure. The pellets were then annealed on the mother powder at 1100 °C for 6 hours at a heating rate of 2 °C / min. A 1.6 mm wide Au film was sputtered onto one side.

[0052] Figure 4a-b shows the XRD patterns, particle size of 1-10 μm.

[0053] (iii) Equipment The laser-driven ultrafast impedance spectrometer shown in Figure 1 was constructed using a signal generator (100 GHz, Keysight, N5173B) and a high-speed oscilloscope (100 GHz, Keysight, N100A / N1046A). We compared the performance of real-time and sampling oscilloscopes, but no difference was observed because the jitter of the laser output is smaller than that of the oscilloscope. Therefore, either type of oscilloscope can be used.

[0054] The bandwidth of the signal generator and oscilloscope determines the time and frequency resolution. The smallest measurable differential signal is determined by the noise floor, so it is desirable to use a signal generator and oscilloscope with a low noise floor. -4 A noise floor of 100mW was possible.

[0055] Figure 5 shows the laser setup for THz, NIR, and MIR generation. UV-THz light was generated using a Coherent Ti:sapphire laser oscillator and amplifier (Legend Elite). In particular, UV-NIR light was generated using a Light Conversion optical parametric amplifier (TOPAS). The 5-15 μm range was covered using difference frequency generation. THz light was generated using DAST and the 1400 nm output of the optical parametric amplifier. The average power of the 1 kHz laser was several mW and was focused to a spot size of several hundred μm.

[0056] The signal generator, oscilloscope, and laser were synchronized by dividing the laser oscillator output (80 MHz) signal to 10 MHz. The laser light was focused between the surface gap electrodes. The signal was recorded on the oscilloscope and compared with the signal generator output. A picosecond rise-time photodiode measuring the 1 kHz laser amplifier output was used as the oscilloscope trigger to identify the location of the picosecond impedance modulation. The impedance change itself was then used as a trigger after narrowing the time window. The measurements were repeated at multiple laser excitation frequencies or multiple signal generator frequencies. The inter-site hopping and grain boundary frequencies within the bulk were previously determined using static impedance measurements (Figure 4c, d).

[0057] (iv) Time-resolved measurements Li at LLTO + Conduction is mediated by neighboring vacancies between bottlenecks formed by the oxygen of four corner-sharing TiO octahedra. The screening effect aids ionic conduction by minimizing electrostatic interactions between the host lattice and the mobile ions, and is found in some solid Li + and O2 2- It is predicted to enable fast ion transport in conductors. In LLTO, the 2.1 eV band gap excitation leads to ligand-to-metal charge transfer transitions, promoting single electron transport from the O 2p orbital to the Ti 3d orbital. The charge density transfer from the O 2p orbital to the Ti 3d orbital may reduce electrostatic hindrance in the ion conduction pathway, providing insight into ion-electron interactions.

[0058] Figure 6c shows the results of time-resolved ultrafast impedance measurements using a high-speed oscilloscope and the above-bandgap pulsed laser excitation. When the AC carrier frequency was removed using a Fourier filter, a clear time-resolved change in ionic conductivity was measured. 350 nm optical excitation induces a charge transfer transition from the O 2p orbital to the Ti 3d orbital. As mentioned above, ionic conduction in LLTO is theorized to occur through the rocking mode facilitating ion hopping between vacancy sites in the TiO octahedra (Figure 6b). The charge density transfer from the O 2p orbital to the Ti 3d orbital reduces electrostatic obstruction in the ionic conduction pathway, resulting in the measured increase in ionic conductivity.

[0059] Figure 6a shows the impedance change measured repeatedly in the Hz to tens of GHz range after photoexcitation of LLTO, compared with that observed with simple laser heating of an incoherent phonon bath. In Figure 6a, a CW laser was used to enable broadband AC impedance sweeps, but the rate of change in impedance was the same. The red area in Figure 6a indicates the difference between laser heating and charge transfer transitions. As expected, the increase in ionic conductivity was greatest in the intersite hopping region, as the change in charge density lowers the activation energy for ion hopping. Changes were also measured at grain boundaries and contact regions, but were less pronounced. The measured impedance change was linear with the laser beam size relative to the power and gap electrode distance (Figure 7d). Impedance changes above 10 GHz were noisy due to the gap electrode distance, but this can be improved with sample optimization.

[0060] Measuring AC impedance changes using a single excitation or driving frequency provides information on two-particle-like interaction terms, such as ion-phonon and ion-electron interactions. Using a two-pulse excitation scheme similar to 2D spectroscopy, many-body cross-correlations, such as ion-electron-phonon or ion-phonon-phonon, can be measured, with ion-ion correlations determined by cross-peaks in the 2D spectrum and comparison of the resulting relaxation dynamics between pulses. Ultimately, this instrument configuration allows for near-complete measurement of the ion-hopping Hamiltonian, as 2D spectroscopy has been used for other optically or IR-active systems.

[0061] (v) Experiments without time resolution For comparison, we tested the application of this technique without time resolution. We used a general-purpose impedance analyzer capable of measuring up to 32 MHz, just on the edge of the intersite hopping region in LLTO. A continuous-wave (CW) light source was coupled to a 1260A Solartron impedance analyzer to measure the complex impedance change from 1 Hz to 32 MHz, encompassing the tails of the grain boundary and bulk conduction regions in many materials. Ideally, a CW light source would be used to excite the sample from the UV to THz, but for the present data, we used a Ti:sapphire laser and nonlinear frequency mixing to access this region at high power.

[0062] Figure 7 shows the Li 0.5 La 0.5 A laser-driven impedance technique using THz irradiation and EIS is presented schematically to assess the relative role of coupled ion-phonon vibrational modes on the overall ionic conduction process in TiO3 (LLTO). 0.5 La 0.5 The driving effect of THz ρ modes in TiO3 (LLTO) is measured in comparison with acoustic and optical phonons across the near-infrared (NIR) and mid-infrared (MIR) regions.

[0063] (i) Normalization Because the pulsed laser repetition rate was 1 kHz, the data were duty-cycle averaged (a 1 kHz repetition rate means that the measured dynamics are time-averaged), reducing sensitivity due to the need to obtain values ​​after thermal equilibrium. We carefully considered several normalization parameters, including incident power, power density, and penetration depth for each wavelength. Ultimately, however, we used normalization of the impedance change per temperature change of the sample. This method normalizes the total absorbed power independently of the transition intensity. Because measurements are taken after several minutes of equilibrium, the penetration depth is also normalized relative to the surface electrode. This allows for direct comparison with different excitation wavelengths and DC heating, such as furnaces, which incoherently excite the phonon bath.

[0064] The normalized impedance per thermal change is independent of the intensity of the transition and accounts for the total absorbed power. Because the complex impedance measurements were performed at equilibrium after several minutes, the final value also reflects the penetration depth relative to the surface electrode. This normalization technique therefore allows for a direct comparison of laser heating and DC heating and allows for accurate calibration of the baseline of the data.

[0065] Normalization was performed using a custom heating cell (Figure 8) with a TC-48-20 OEM temperature controller and thermocouple to generate a calibration curve. The current and voltage measured between the cell and the sample were used to calculate the input power to the sample based on Watt's law, P = IV. Plotting the calculated P against the temperature readings from the TC-48-20 OEM software generated a calibration curve to determine the temperature related to the input power to the LLTO. The normalization method yielded a similar percentage change as normalizing with power density, demonstrating the validity of the proposed method. Therefore, despite the experimental limitations inherent in accurately interpreting data using CW and pulsed laser excitation, non-time-resolved measurements using commercially available impedance analyzers are feasible and can provide useful information about bond dynamics in a variety of solid-state materials without the need for custom electronics.

[0066] For time-unresolved measurements up to 32 MHz, a custom cell with a ceramic heating plate was constructed, as shown in Figure 9a, using a TC-4820 OEM heater and thermistor with temperature control operation using corresponding software. In all experiments, the heating cell was placed in a copper mesh Faraday cage with a wire spacing of 1.4 mm to reduce noise due to electromagnetic interference. THz transmission windows can be designed with a variety of organic and crystalline materials. 66 For other visible / UV light sources, a quartz window with transmission in the 190-2500 nm range was used. A windowless setup is also available for non-air-sensitive materials. The sample itself was annealed and densified as described above, and a blocking electrode such as Au, Ag, Pt, or Pd was sputtered onto the pellet using a mask to form a gap electrode. As shown in Figure 8, sputtering the Au electrode in a gap structure on the same plane as the sample pellet minimizes the sample volume probed during impedance measurements compared to full-surface sputtering on both sides, making the effects of differences in optical penetration depth and spot size more negligible. Thin film samples can also be used, which allows the effects of optical penetration depth to be ignored. The developed in-plane electrode configuration is also compatible with time-resolved setups, enabling evaluation of grain boundary and bulk conduction effects. When used as a solid electrolyte in all-solid-state batteries, the grain boundary contribution dominates the overall ionic conductivity.

[0067] (ii) Results Figure 9a compares the impedance change versus grain boundary characteristics of LLTO over a range of excitation frequencies. Over a 32 MHz frequency range, the tails of the grain boundary and bulk ion-hopping conduction regions showed identical trends, as shown in Figure 4a. The absorption features corresponding to each subsystem are shown as colored curves in Figure 9a. The height of the bar indicates the bulk impedance enhancement ratio after laser driving at that frequency, while the width of the bar indicates the bandwidth of the excitation source at that frequency. UV excitation alters electrostatic blocking within the lattice cage through ligand-to-metal charge transfer from the O 2p valence band orbitals to the Ti 3d conduction band orbitals. THz excitation represents a range of locking modes in TiO6 and was shown to be the dominant term in the bulk ion-hopping change. The NIR and DC heating plots serve as control data, as they primarily heat the material incoherently via an acoustic phonon bath. No signal was detected when optically exciting the optical phonon branch with powers comparable to those of the THz locking mode, but a higher-power DFG unit would likely provide clearer evidence.

[0068] For THz light, ΔR is 0.7% bulk / mW is measured, which is bulk / K, a 31% decrease was calculated. When the acoustic phonon bath was heated incoherently with 800 nm light, ΔR bulk / mW or 0.12% ΔR bulk This change was estimated to be 4% in ΔR / K due to DC heating. bulk / mW or 0.07% ΔR bulk This is comparable to a 3% change in r / K, within the error margin, proving that the observed changes with THz light are not solely due to laser heating of the lattice. At the same power density as when driving THz phonons, there were no detectable changes in frequencies in the optical phonon range. Because the MIR power is an order of magnitude smaller than that used for thermal heating, its relative role in this range is limited. However, this result is consistent with theoretical predictions that modes above 10 THz (approximately 30 μm) contribute little to ion hopping.

[0069] To verify the accuracy of the duty-cycle-averaged version of our device, two comparisons can be made. First, for both continuous-wave (CW) excitation shown in Figure 4a and duty-cycle-averaged excitation shown in Figure 9a, the relative change between direct current (DC) or near-infrared (NIR) heating and 350 nm optical excitation is fivefold. Second, for THz excitation, it is possible to integrate over the theoretically predicted contribution to ion hopping (Figure 9b). Using a simple Boltzmann distribution approximation and the theoretically predicted contribution of phonon modes, the 1–6 THz composite mode accounts for only about 2% of the ionic conduction at room temperature. When driven directly by THz excitation, the contribution of the THz rocking mode is about 30%. The ratio of these two values ​​is consistent with the approximately 15-fold enhancement of ionic conductance measured in Figure 9a.

[0070] More specifically, after approximate normalization between driving wavelengths from NIR to THz light, selective excitation of THz ρ modes results in a significant increase in R compared to non-resonant heating of the acoustic phonon bath or resonant driving of optical vibrational modes. bulk Yobi R gb The measurements confirm an order of magnitude decrease in , reminiscent of photomodulated ferroelectricity, magnetism, and ionic conductivity in inorganic-organic perovskites, and the enhancement is persistent and reversible, even though the recorded changes are averaged at a 500 Hz laser repetition rate.

[0071] Thus, Figure 9a accurately measures the relative contributions of the ion-hopping Hamiltonian subsystems associated with incoherent heating and uses this normalized index to perform relative comparisons between different ion-hopping Hamiltonian components. For example, Figure 9a shows that the THz rocking mode is clearly the dominant vibrational mode compared to the optical phonons or the remaining acoustic phonon bath. Second, UV excitation confirms the presence of significant electrostatic hindrance to ion hopping through the lattice cage. It is known from the literature that ionic conductivity is enhanced when LLTO is doped or compared to LLZO to reduce electrostatic hindrance. Therefore, this simplified version of the experiment is particularly useful for comparing material optimization strategies as a relative measure.

[0072] The Nyquist plots of LLTO without laser excitation are shown in Figures 10a and 10b and are shown schematically in Figure 7a. The bulk and grain boundary impedance data were individually fitted to the R1 + R2 / Q2 circuit. With increasing temperature, Z' and Z' shift to lower impedances, which corresponds to an increase in the population and mode types in the phonon bath. This leads to the transfer of E A decreases, and the ν for Li-ion hopping increases, resulting in a decrease in the measured Z'. The semicircular fitting corresponding to the grain boundary contribution has a different shape from the bulk contribution, which is thought to be due to the bulk semicircle partially overlapping with the grain boundary characteristics. Although this trend varies slightly from sample to sample, we found that the final impedance difference is consistent within the error range for all measurements.

[0073] Figures 10c and 10d show that when driven with broadband THz radiation (measured absorption spectrum of LLTO shown in the shaded area of ​​Figure 2c), Z' varies linearly with power for both bulk and grain boundary properties. This change is reversible, returning to the pre-irradiation impedance after irradiation (Figure 7d). Before normalization, the change in Z' was on the order of hundreds of Ω for average THz powers in the milliwatt range. After normalization, R bulkThe change in σ can be compared with other optical phonon modes in the MIR and with acoustic phonon modes excited incoherently by a DC-heated laser.

[0074] R using THz light bulk The relative reduction in Z' (approximately 10 times compared to incoherent DC heating) supports the hypothesis that ion migration can be enhanced by resonantly driving the contributing phonon-ion coupled modes. This enhancement is consistent with integrating the contributing modes over the THz excitation range and comparing it to the thermal regime. In the case of DC or laser-induced heating, the same power is incoherently distributed among various acoustic and high-energy phonon modes, so the overall change in measured Z' is small. Furthermore, it is unlikely that the THz field adds an electronic contribution to the overall measured conductivity or excites electronic carriers in LLTO. THz energies are generally <1 eV and in this study <0.025 eV. 35 , which is significantly lower than the band gap of LLTO (2.1 eV). 36 Therefore, it is unlikely that THz fields have enough energy to generate electron carriers or increase the electronic conductivity as is the case in materials with known superconducting transitions. 24 .

[0075] In this study, ΔS in Eq. (6) m The role of and ΔS m Selectively driving different types of phonon modes with narrowband THz pulses can be useful to further separate the ion transport dynamics caused by high-energy phonon modes from those caused by modes that distort only the local polyanion vibrations. 37 .

[0076] Importantly, the impedance drop takes approximately 100 seconds to equilibrate and relax for both THz excitation and nonresonant heating, as shown in Figure 7d. The agreement in the rise and decay times indicates that the THz-induced impedance drop exists on a timescale much longer than the picosecond scale of the THz driving force itself. While the thermal and THz equilibration times match, the impedance changes do not, suggesting that driving a coupled phonon-ion THz mode may generate a non-equilibrium Li-ion pathway that subsequently equilibrates via thermal vibrations. Further experiments are required to clarify this aspect of our conclusions.

[0077] These results demonstrate that laser actuation can be used to control the ion-phonon states and many-body correlations that lead to fast ion transport in solids. Furthermore, this spectroscopic technique allows us to roughly identify the relative contributions of different vibrational modes to macroscopic ion hopping. Isolating the relative contributions allows us to target the dominant contributing modes and improve the design of solid electrolytes.

[0078] In other embodiments, non-time-resolved measurements can use a CW light source (e.g., a lamp or incoherent light source) and the same normalized data. High-power lamp and monochromator combinations are commonly used in various photonic spectroscopy of solar energy materials. This form of instrumentation offers a simple approach that can be implemented without requiring specialized optical knowledge or the cost of ultrafast lasers. Reaching the important far-infrared to THz region with sufficient power is more challenging, and in some embodiments, a laser light source may be required.

[0079] 4. Second Example: S11 Reflection Measurement Using SMA Connections and Vertical Launch Connectors a. Sample holder and sample preparation LLTO is a literature 59 It was synthesized according to the previous report 38 Characterization and testing was performed as described.

[0080] For S11 reflection measurements, a vector network analyzer (VNA) was used with an SMA connection to the sample, as shown in Figures 11a and 11b, and a 1000 kV sine wave (SMA) connection to the sample, as previously described in 55,57,58 The AC signal is transmitted to the sample, or load, through a directional coupler with a copper short at port S12, modeled from the model. A 2-mm-wide cavity is drilled into the side of the copper short to allow for laser excitation during time-resolved measurements. The powder sample is pressed into a 1 / 4-inch diameter pellet under high load (2 tons), annealed to achieve at least 80% of its theoretical density (composition-specific), and then polished to fit within a 300-μm recess. In addition to minimizing voids, the sample must physically contact the pins inside the vertical launch connector, forming a resonator, which is essential for accurate measurements, as shown in Figures 3a and 3b. The S11 port, which measures the reflected wave, and the S13 port, which provides the coupled reference wave, are connected to the VNA, as shown in Figure 11(c). To actually measure the S11 parameter, a microstrip, or metal strip, is deposited on or contacts the sample load, allowing high-frequency transmission from several hundred MHz to over 10 GHz. 56 The electrical connection between the microstrip and the oscilloscope is established by coaxial cable with an appropriate adapter, such as an SMA connector, for GHz range.

[0081] To measure the time-resolved impedance signal, a 40 GHz Keysight N5173B signal generator is used in combination with a 40 GHz Keysight N100A / N1046A oscilloscope. In the experiment, a 1 kHz laser with an average power of 130 mW is used, focused to a beam with a diameter of 200–300 μm, depending on the sample.

[0082] A laser clock can be used as an external reference to synchronize a custom VNA, but synchronization can be difficult because many signal generators only accept a 10 MHz reference signal, which is not output by the laser clock. Furthermore, even after frequency division, the laser clock output may not have sufficient phase stability. Therefore, to extract amplitude and phase data, an IQ demodulation method is preferred, with a picosecond photodiode assisting in the location of transient signals. S11 measurements are then performed for multiple laser excitation frequencies or multiple signal generator frequencies, depending on the experiment.

[0083] b. Steady-state measurements A Keysight N9041B UXA signal analyzer with a frequency range of 2 Hz to 110 GHz was used as the VNA for steady-state measurements.

[0084] Li at LLTO + Conduction is mediated by neighboring vacancies between bottlenecks formed by the four oxygen atoms of four corner-sharing TiO6 octahedra. 60,62 The screening effect aids ionic conduction by minimizing electrostatic interactions between the host lattice and the mobile ions, and has been shown to be effective in some solid Li + and O2 2- It is predicted to enable fast ion transport in conductors. 17-19,34 In LLTO, the 2.1 eV band gap excitation can induce ligand-to-metal charge transfer transitions that promote the transfer of electron carriers from the O2p orbitals to the Ti3d orbitals. 61 Charge density transfer from the O2p orbital to the Ti3d orbital may reduce electrostatic hindrance to the ionic conduction pathway, providing insight into ion-electron interactions.

[0085] To investigate the role of shielding on ionic conduction, we accessed the LLTO sample through a cavity in the vertical launch configuration shown in Figure 10 and optically excited the bandgap of LLTO. Although the application of the vertical launch configuration was well suited for proof-of-concept measurements, noise was observed above 10 GHz, which may be due to poor contact and pellet density. In future studies, further optimization of the cell design will improve the signal-to-noise ratio.

[0086] Steady-state measurements of LLTO were first performed using a Keysight N9041B UXA signal analyzer operating from 2 Hz to 110 GHz under 350 nm and 700 nm excitation to verify the conceptual capabilities of the device prior to more complex time-resolved experiments. Note that a vector network analyzer (VNA) is essentially a combination of a signal generator and an oscilloscope, so time-resolved electronics can also be used for this step. The S11 signal was Fourier filtered to remove the carrier frequency component, and Z was calculated using Equations 3.1-3.3. L Calculate this Z L is then used to calculate the ionic conductivity,

number

[0087] The steady-state response was first measured and used to calculate and plot Δσ / σ as a function of frequency, as shown in Figure 12. The plot shows the conductivity enhancement of LLTO after photoexcitation with a 350 nm CW laser. The red shaded area in Figure 12 shows the ionic conductivity change due to laser heating of the incoherent phonon bath with 700 nm light and the Li conductivity change due to 350 nm bandgap excitation. +The difference between the ionic conductivity change due to the modulation of the -electron coupling is shown. The largest increase in the enhancement ratio is observed in the intersite hopping region, which is attributed to the predicted lowering of the activation energy for ion hopping due to the transfer of charge density from the O2p orbital to the Ti3d orbital. Furthermore, differences are observed at the grain boundary and electrode-electrolyte interface regions by 350 nm and 700 nm, which are thought to be related to the occupancy of the thermal bath.

[0088] The generation of electron carriers is usually determined by impedance techniques such as EIS. + Many reports suggest that the enhanced ion mobility is not solely due to newly generated electron carriers, although this can complicate mobility values. 17-19 Therefore, our observation of enhanced ionic migration due to this charge transfer process appears valid even after taking into account heat generation and electron carrier generation. Even if electronic conduction also contributes, the described experiments still prove the conceptual validity of the device at steady state.

[0089] c. Time-resolved measurements using a custom VNA We measured the time-resolved enhancement of ionic conduction in LLTO by bandgap excitation using a custom-built time-resolved VNA equipped with a 40 GHz signal generator and an oscilloscope, using the sample cell configuration shown in Figure 3.

[0090] Figure 13 shows the enhancement ratio Δσ / σ as a function of frequency up to 300 ps in a time-resolved configuration using a custom VNA. The enhancement observed between 0 and 60 ps in Figure 13 is due to the Li +The decay in the enhancement ratio after 60 ps is due to the absence of the 30 fs ultrafast pulse. While Fig. 12 can be constructed from time-domain traces alone, as shown in Fig. 13, it is often useful to first perform impedance measurements over a broad frequency range in a non-time-resolved mode to identify the region of interest, as shown here.

[0091] Our time-resolved data on the picosecond timescale provide insight into how intersite hopping is affected by screening on a local scale, which, to our knowledge, has not been demonstrated before, and extends existing knowledge of how the unique local structure of hopping channels collectively affects ionic conduction.

[0092] d. Laser-driven impedance without time resolution using a commercial impedance analyzer The change in impedance due to UV excitation described above in the time-resolved case is again demonstrated in a non-time-resolved case, and the results are shown in Figure 14. The equivalent circuit fits for the bulk conduction characteristics (Figure 14(a)) and the grain boundary characteristics (Figure 7(b)) and the corresponding Nyquist plots show good agreement. The R values ​​corresponding to the grain boundary and bulk hopping regions (R GB and R bulk ) was assigned based on the capacitance value obtained from the circuit fitting. The final R extracted from the fitting GB and R bulk is plotted against the UUV power in Figure 14(c)-(e), showing that the measured impedance change is linearly proportional to the power. The continuous decreasing shift in impedance with increasing average power of UV light indicates the occurrence of a screening effect that promotes easy ion conduction, which is consistent with the results discussed above in Section II.

[0093] As mentioned in the first example, by thermally normalizing the sample as shown in Figure 7(b), lamps and non-coherent light sources can be used instead, without the need for specialized optical knowledge or the cost of ultrafast lasers. 35 and modulation of ion hopping 34、41 The measurements described in this specification are also believed to be applicable to the study of charge transport systems.

[0094] In particular, the differences in enhancement ratio values ​​between hopping time regimes across a wide frequency range indicate that each regime can exhibit significantly different behavior and that the spectroscopic techniques described herein can be used to probe unique couplings predicted to affect ion transport. Comparing the relative enhancement ratios in different hopping regimes from a range of targeted ion-phonon, ion-electron, and ion-ion excitations can reveal couplings that govern the ion conduction mechanism and pave the way for targeted design of superionic conductors.

[0095] Apparatus and Method Embodiments FIG. 16 illustrates a method for manufacturing a spectrometer system, including positioning an electromagnetic radiation source (block 1500), coupling an input signal source (block 1502); connecting a control circuit (block 1504); connecting a detection system (block 1506); and connecting a computer (block 1508).

[0096] Exemplary embodiments of devices, systems, or apparatus (block 1510) manufactured according to the methods described herein (or other methods) include, but are not limited to, the following (see also FIGS. 1-18):

[0097] 1. A spectrometer 100 (or an apparatus, system, or device useful for performing spectroscopy), comprising: a source 102 of electromagnetic radiation 102a comprising one or more first frequencies; a source 104 of an input signal 104a comprising an alternating current (AC) electric field comprising one or more second frequencies; a control circuit 106, 1700 operably connected to the sources 102, 104 and configured to synchronize (or configured, configurable, and / or programmable to synchronize) the application of the electromagnetic radiation and the AC electric field applied to the sample; the one or more second frequencies tuned to drive hopping of ions between ion sites within the sample; and the one or more first frequencies tuned to drive excitation in the sample that interacts with the ions; a control circuit 106, 1700 responsive to the signal to output an output signal (e.g., an AC signal, e.g., an electric field or voltage signal) from the sample, the output signal comprising a modulation of the AC electric field; a detection system 112, 1914 operably connected to the sample holder or positioned (or configured to measure and / or detect) a change in the output signal in response to the electromagnetic radiation; A spectrometer 100 (or an apparatus, system, or device useful for performing spectroscopy) comprising: a computer 114, 1700 operably connected to a detection system and configured / programmed to determine (or to determine) at least one of the conductivity or impedance of the sample from the output signal as a function of the first frequency and second frequency.

[0098] 2. The spectrometer of embodiment 1, wherein the control circuitry is sweeping the first frequency through a first range to drive excitation of electrons, ions and / or phonons in a sample 108 including an electrolyte; and sweeping the second frequency over a second range such that the input signal drives ion hopping in the electrolyte over a range of ion transit time scales. The spectrometer further comprising a control circuit that controls, is configured to control, or controls.

[0099] 3. A spectrometer as described in embodiment 1 or 2, wherein the computer 114 is configured / programmed to determine or determine changes in conductivity at one or more second frequencies associated with travel time scales in different ion hopping regions within the electrolyte 310, including the contact region 300, the grain boundary 400, or the bulk 308 region.

[0100] 4. The spectrometer of any one of embodiments 1 to 3, wherein the electrolyte 310 comprises a solid electrolyte for a battery.

[0101] 5. The spectrometer of any of embodiments 1-4, wherein the sample comprises electrical contacts to the solid electrolyte containing lithium ions for a lithium ion battery.

[0102] 6. A spectrometer described in any of embodiments 1 to 5, wherein the computer determines (or is configured / programmed to determine) from the output signal a Hamiltonian of the sample that describes the interaction of excitations excited by the electromagnetic radiation and hopping driven by the input signal.

[0103] 7. A spectrometer described in any of embodiments 1 to 6, wherein the source of electromagnetic radiation includes a pulsed laser or continuous wave (CW) laser that outputs the first frequency in the range from ultraviolet (UV) frequencies to terahertz (THz) (e.g., including, but not limited to, frequencies corresponding to wavelengths of 100 nanometers≦wavelength≦3 millimeters).

[0104] 8. A spectrometer according to any one of the preceding embodiments, wherein the source of electromagnetic radiation comprises a lamp that outputs the electromagnetic radiation.

[0105] 9. A spectrometer as described in any of embodiments 1 to 8, wherein the source of the input signal comprises a signal generator 120 and outputs a second frequency f1, for example, in the range of 1 hertz (Hz) to 1 terahertz (THz), or 1 hertz (Hz) to 100 gigahertz (GHz) (1 Hz≦f2≦100 GHz or 1 Hz≦f≦100 THz).

[0106] 10. A spectrometer according to any one of the preceding embodiments, wherein the detection system measures or is configured to measure the change or conductivity on the time scale of the excitation driven by the electromagnetic radiation.

[0107] 11. A spectrometer described in any of embodiments 1 to 10, wherein the source of electromagnetic radiation includes a pulsed laser that outputs pulses of electromagnetic radiation having a full width at half maximum (FWHM) of 10 picoseconds (ps) or less (e.g., 1 femtosecond (fs) to 1 nanosecond (ns) or 1 fs to 10 ps, ​​e.g., 1 fs≦FWHM≦1 ns or 1 fs≦FWHM≦10 ps), and the detection system measures changes in conductivity with a time resolution of the envelope of the FWHM.

[0108] 12. The spectrometer of any one of embodiments 1-11, wherein the first frequency comprises a terahertz frequency.

[0109] 13. The spectrometer of any one of embodiments 1 to 12, further comprising a sample holder 1100 for holding the sample, the sample holder comprising: a vertical launch connector 1102 for physically connecting to a microstrip on the sample; a metal plate 1104 with at least one opening 1112 for insertion of the sample and coupling of the electromagnetic radiation to the sample; and a fastener 1104 (e.g., a pin) for securing the sample between the vertical launch connector and the metal plate such that the input signal is transmitted from the vertical launch connector to the microstrip and a reflection of the input signal (including the output signal) is output from the microstrip to the vertical launch connector.

[0110] 14. The spectrometer of embodiment 13, further comprising: via a first coaxial cable 1100 to the source of the input signal; and to the detection system via a second coaxial cable 1112. The spectrometer includes a directional coupler 1108 for coupling.

[0111] 15. A spectrometer as described in any one of embodiments 1 to 14, further comprising a time-resolved vector network analyzer having a source of the input signal including a signal generator and a detection system including an oscilloscope triggered by a photodiode that detects the electromagnetic radiation.

[0112] 16. A spectrometer as described in any of embodiments 1 to 15, wherein the detection system is configured to measure and / or detect, or measure and / or measure changes without time resolution on the time scale of application of the electromagnetic radiation, and the computer determines the conductivity of the sample, including a thin film, using normalization to remove the contribution of steady-state heating due to the input signal.

[0113] 17. A spectrometer as described in any of embodiments 1 to 16, wherein the detection system comprises an IQ demodulator coupled to a photodetector that detects or is configured to detect the electromagnetic radiation, and the amplitude and phase of the output signal (current and voltage) are measured / detected using the IQ demodulator so that they can be related to a time resolution for changes in the time envelope of the electromagnetic radiation, where I represents the in-phase component of the signal and Q represents the quadrature-phase component.

[0114] 18. A spectrometer as described in any of embodiments 1 to 17, wherein the detection system is configured to measure and / or detect the output signal to determine a change in the complex impedance of the sample, and the computer is configured / programmed to determine the conductivity from the complex impedance.

[0115] 19. The spectrometer of any of embodiments 1-18, wherein the detection system comprises an impedance analyzer.

[0116] 20. A spectrometer according to any one of embodiments 1 to 19, further comprising a vector network analyzer 1110 comprising the source of the input signal and the detection system.

[0117] 21. The spectrometer of any one of embodiments 1-20, further comprising at least one of a source of the electromagnetic radiation, a source of the input AC signal (e.g., a signal generator), or a VNA comprising the control circuit 106; the control circuit comprises a trigger output, a clock circuit, a clock output, or a synchronization circuit; The synchronization circuit outputs a signal used to synchronize the source of electromagnetic radiation and the source of the input AC signal.

[0118] 22. The spectrometer of any one of embodiments 1 to 21, wherein the control circuitry includes a synchronization circuit and / or a frequency divider circuit; The frequency divider circuit divides the repetition frequency of the pulses of electromagnetic radiation to convert it into a low frequency signal that is used to trigger or control the AC source to output the input AC signal and / or to trigger or control the detection system (e.g., an oscilloscope) to measure the output signal, in a spectrometer.

[0119] 23. A spectrometer according to any one of embodiments 1 to 22, wherein the control circuitry and / or computer comprises an application specific integrated circuit (ASIC) or integrated circuit, or a processor executing one or more programs stored in memory.

[0120] 24. A spectrometer according to any one of embodiments 1 to 23, wherein the source of electromagnetic radiation comprises a laser or a lamp.

[0121] 25. A spectrometer according to any one of embodiments 1 to 24, wherein the detection system comprises an oscilloscope and / or a detector capable of detecting the output signal and / or a vector network analyzer.

[0122] 26. The spectrometer of any one of embodiments 1 to 25, wherein the detection system 112 comprises or consists of an AC field amplitude detector / circuit 1906, a phase-locked loop detector / demodulator / circuit 1902, or an IQ demodulation circuit 1904, and optionally an impedance matching circuit 1900 for impedance matching the detector to the sample. These components can be selected or configured to detect homodyne, heterodyne, amplitude modulated (AM), or frequency modulated (FM) signals. The detector can further comprise a coaxial cable input 1908 or a microstrip or transmission line for receiving an AC signal from the sample.

[0123] 27. The spectrometer of any of embodiments 1-25, wherein the detection system is a detector comprising at least one of an amplitude detection circuit / circuitry 1906, a phase-locked loop circuit / circuitry 1902, an impedance matching circuit / circuitry 1900, and / or an IQ demodulation circuit / circuitry 1904. In various embodiments, these circuits can optionally be selected or configured to detect homodyne signals, heterodyne signals, amplitude modulated (AM) signals, or frequency modulated (FM) signals (e.g., including the output signal). The detector can optionally further comprise a coaxial cable input 1900, or a microstrip or transmission line for receiving an AC signal from the sample.

[0124] 28. The spectrometer of embodiment 26 or 27, comprising a VNA, an oscilloscope, or a lock-in amplifier within the detector or an impedance analyzer comprising at least one of the amplitude detector, an IQ modulator, or a PLL (phase-locked loop).

[0125] 29. A spectrometer as described in embodiment 27 or 28, further comprising a photodetector (e.g., a photodiode) for detecting the electromagnetic radiation, wherein the amplitude and phase of the output signal (current and voltage) can be measured using the detector and correlated with a time resolution for changes in the time envelope of the electromagnetic radiation.

[0126] 30. A method for measuring conductivity (as shown in FIG. 16): irradiating 1600 an area of ​​the sample with electromagnetic radiation comprising one or more first frequencies; applying 1602 an input signal to the region, the input signal comprising an alternating current (AC) electric field comprising one or more second frequencies, such that the electromagnetic radiation and the input signal are applied synchronously; below: the one or more second frequencies tuned to drive hopping of ions between ion sites within the sample; and the one or more first frequencies tuned to drive excitation in a region that interacts with the ions; measuring 1604 and / or determining an output signal comprising a modulation of the AC electric field in response to the and determining 1606 from the output signal the conductivity of the sample as a function of the first frequency and the second frequency.

[0127] 31. The method or spectrometer of any of embodiments 1-29, wherein the sample comprises any material system (living or non-living) that conducts ions.

[0128] 32. In one embodiment, including any of embodiments 1-30, the method includes a laser-driven ultrafast impedance measurement method capable of directly measuring bulk ionic conduction on the picosecond time scale for subcomponents of the ion hopping Hamiltonian. This technique leverages advances in communications-based signal generators and oscilloscopes to extend AC impedance measurements to over 100 GHz. These frequencies correspond to picosecond ion hopping in the intersite regime, although lower frequencies can of course be used to measure other hopping regimes, such as grain boundaries. Using this electronics, time-resolved impedance changes are measured as a function of a femtosecond pulse-driven laser sweeping from UV to THz. This frequency range includes energy gaps corresponding to each subcomponent of the overall ion hopping Hamiltonian. For example, UV light can photoexcite charge-transfer transitions to modulate electrostatic blocking of ion channels or generate non-equilibrium carrier distributions to modulate screening effects. Near-infrared to THz light can be used to resonantly excite optical phonons or rocking and paddlewheel modes. Acoustic phonon modes can be selected through anharmonic or Raman interactions, or simply by incoherent heating as a reference channel. Comparing the amplitudes of these perturbations maps the relative contribution of each subcomponent to bulk ion hopping, and comparing their time decays provides insight into correlation and memory effects.

[0129] 33. We also describe and test another version of the device that retains the ability to map the ion-hopping Hamiltonian but sacrifices time resolution. This second version does not require an ultrafast laser in practice, making it accessible to battery characterization laboratories as a form of action spectroscopy. This technique is therefore suitable for the rapid comparison of material modifications, such as doping or particle size, for a given material.

[0130] 34. A spectrometer as described in any of embodiments 1 to 33, wherein the computer 114 comprises one or more processors; one or more memories; and an application / program stored in the one or more memories, and the application executed by the one or more processors determines impedance and / or conductivity.

[0131] 35. A spectrometer described in any of embodiments 1 to 34, wherein the control circuit comprises one or more processors; one or more memories; and an application / program stored in the one or more memories, and the application executed by the one or more processors performs synchronization or outputs a signal used for synchronization.

[0132] In these examples (eg, embodiments 1-35), the term "spectrometer" can be replaced with device, system, or apparatus.

[0133] 30. The system 100, a source 102 of electromagnetic radiation 102a comprising one or more first frequencies; a source 104 of an input signal 104a comprising an alternating current (AC) electric field comprising one or more second frequencies; a synchronization circuit or means 106, 1700 operatively connected to said sources 102, 104 for synchronizing the application of said electromagnetic radiation and said AC electric field applied to the sample, the one or more second frequencies tuned to drive hopping of ions between ion sites within the sample; and the one or more first frequencies tuned to drive excitation in the sample that interacts with the ions; a synchronizing circuit or means 106, 1700 responsive to the sample voltage to cause an output signal comprising a modulation of the AC field to be output from the sample; a detector or detector means or detection means 112 operably connected to a sample holder for said sample or arranged to measure and / or detect a change in an output signal (e.g., including an AC signal, e.g., an electric field or voltage signal) in response to said electromagnetic radiation; a computer or computing unit, or computer unit 114, 1700, operably connected to the detection system and configured to determine at least one of the conductivity or impedance of the sample from the output signal as a function of the first frequency and second frequency;

[0134] 31. The system of embodiment 30, wherein the synchronization means and detection means include devices described herein and equivalents thereof.

[0135] 32. The system of embodiment 30 or 31, further comprising any of embodiments 1 to 29.

[0136] 33. A system, spectrometer, or method according to any one of embodiments 1 to 32, wherein the detector or detection system 1914 has an input 1918 for receiving a trigger signal or synchronization signal, or is connected to the synchronization circuit / control circuit 106, 1912, or at least one of the photodetectors of the electromagnetic radiation that outputs the trigger signal or synchronization signal.

[0137] 34. A system or spectrometer according to any one of embodiments 1 to 33, the connection 124 between the control or synchronization circuitry and the source is wired (e.g., including a cable, coaxial cable, or transmission line for transmitting electrical signals) or wireless; the connection 120 between the detector and the sample is wired (e.g., including a cable, coaxial cable, or transmission line for transmitting an electrical signal) or wireless; The connection 122 between the detector 1102, 1914 and the computer 114, 1700 may be wired (eg, including a cable, coaxial cable, or transmission line for transmitting electrical signals) or wireless.

[0138] 35. A system or spectrometer according to any of the preceding embodiments, wherein the output and input signals comprise AC fields or voltages whose amplitude and / or phase can be measured by the detector 1914.

[0139] Hardware Environment FIG. 17 illustrates an example of a hardware and software environment 1700 (referred to as a computer-implemented system and / or computer-implemented method) that may be used to implement one or more embodiments of the present invention and that may be used as the control circuit 106 or the computer 114 in one or more embodiments. The hardware and software environment includes a computer 1702 and may include peripheral devices. The computer 1702 may be a user / client computer, a server computer, or a database computer. The computer 1702 includes a hardware processor 1704A and / or a dedicated hardware processor 1704B (hereinafter, alternatively collectively referred to as processor 1704) and memory 1706, such as random access memory (RAM). The computer 1702 may be connected to and / or integrated with other devices, including input / output (I / O) devices, such as a keyboard 1714, a cursor control device 1716 (e.g., a mouse, pointing device, pen and tablet, touch screen, multi-touch device, etc.), and a printer 1728. In yet another embodiment, computer 1702 may comprise a multi-touch device, a mobile phone, or other Internet-enabled device that operates on a variety of platforms and operating systems.

[0140] In one embodiment, computer 1702 operates by hardware processor 1704A executing instructions defined by computer program 1710 (e.g., a conductivity calculation, control, or Hamiltonian calculation application) under the control of operating system 1708. Computer program 1710 and / or operating system 1708 may be stored in memory 1706 and interface with users and / or other devices to accept input and commands and provide output and results based on such input and commands and the instructions defined by computer program 1710 and operating system 1708.

[0141] The output / results may be displayed on a display 1722 or provided to another device for display or further processing or action. Images may be provided via a graphical user interface (GUI) module 1718. Although the GUI module 1718 is illustrated as a separate module, the instructions to perform GUI functions may be resident or distributed within the operating system 1708, the computer program 1710, or may be implemented by dedicated memory and a processor.

[0142] In one or more embodiments, display device 1722 is integrated into computer 1702 and includes a multi-touch device having a touch-sensitive surface (e.g., a trackpad or touchscreen) capable of recognizing the presence of more than one contact on the surface.

[0143] Some or all of the processing performed by computer 1702 pursuant to instructions of computer program 1710 may be implemented by special purpose processor 1704B. In this embodiment, some or all of the instructions of computer program 1710 may be implemented as firmware instructions stored in read-only memory (ROM), programmable read-only memory (PROM), or flash memory within special purpose processor 1704B or within memory 1706. Special purpose processor 1704B may be hardwired by circuit design to perform some or all of the operations for implementing the present invention. Furthermore, special purpose processor 1704B may be a hybrid processor including dedicated circuitry for performing a subset of functions and other circuitry for performing more general-purpose functions, such as in response to instructions of computer program 1710. In one embodiment, special purpose processor 1704B is an application-specific integrated circuit (ASIC) or a field-programmable gate array (FPGA).

[0144] The computer 1702 may implement a compiler 1712 for converting an application or computer program 1710 written in C, C++, Assembly, SQL, PYTHON, PROLOG, MATLAB, RUBY, RAILS, HASKELL, or other programming language into code readable by the processor 1704. Alternatively, the compiler 1712 may be an interpreter that executes instructions / source code directly, converts source code into an intermediate representation that is executed, or executes stored pre-compiled code. Such source code may be written in a variety of programming languages, such as JAVA, JAVASCRIPT, PERL, BASIC, etc. Once completed, the application or computer program 1710 uses the relationships and logic generated using the compiler 1712 to access and manipulate data received from I / O devices and stored in the memory 1706 of the computer 1702.

[0145] Computer 1702 may also optionally include external communications devices such as a modem, satellite link, Ethernet card, or other device that accepts input from, and provides output to, other computers 1702 .

[0146] In one embodiment, instructions implementing operating system 1708, computer program 1710, and compiler 1712 are tangibly embodied in a non-transitory computer-readable medium, such as data storage device 1720, which may include one or more fixed or removable data storage devices, such as a zip drive, floppy disk drive 1724, hard drive, CD-ROM drive, tape drive, etc. Additionally, operating system 1708 and computer program 1710 include computer program 1710 instructions that, when accessed, read, and executed by computer 1702, cause computer 1702 to perform the steps necessary to implement and / or use the present invention, or to load the instruction program into memory 1706, thereby generating specialized data structures such that computer 1702 operates as a specially programmed computer that performs the method steps described herein. Computer program 1710 and / or operating instructions may also be tangibly embodied in memory 1706 and / or data communication device 1730, thereby creating a computer program product or article of manufacture in accordance with the present invention. Accordingly, the terms "article of manufacture," "program storage device," and "computer program product" as used herein are intended to encompass a computer program accessible from any computer-readable device or media.

[0147] Of course, one skilled in the art will recognize that any combination of the above components, or a different number of components, peripherals, and other devices, may be used in conjunction with computer 1702 .

[0148] 18 schematically illustrates a typical distributed / cloud-based computer system 1800 that uses a network 1804 to connect a client computer 1802 to a server computer 1806. A typical combination of resources may include the network 1804 (including the Internet, a LAN (Local Area Network), a WAN (Wide Area Network), an SNA (Systems Network Architecture) network, etc.), the client 1802 (a personal computer or workstation as shown in FIG. 17), and the server 1806 (a personal computer, workstation, minicomputer, or mainframe as shown in FIG. 17). Note, however, that different networks, such as a cellular network (e.g., GSM [Global System for Mobile Communications], etc.), a satellite-based network, or other types of networks, may be used to connect the client 1802 and the server 1806 in accordance with embodiments of the present invention.

[0149] The client 1802 is connected to a server computer 1806 by a network 1804, such as the Internet. The network 1804 may provide and connect communications between the client 1802 and the server 1806 using Ethernet, coaxial cable, wireless communication, radio frequency (RF), etc. Furthermore, in a cloud-based computing system, resources (e.g., storage, processors, applications, memory, infrastructure, etc.) in the client 1802 and the server computer 1806 may be shared among the client 1802, the server computer 1806, and users via one or more networks. Resources may be shared by multiple users and dynamically reallocated based on demand. In this respect, cloud computing can be described as a model for enabling access to a shared pool of configurable computing resources.

[0150] The client 1802 may execute a client application or web browser and communicate with a server computer 1806 executing a web server 1810. Such a web browser is typically a program such as MICROSOFT INTERNET EXPLORER / EDGE, MOZILLA FIREFOX, OPERA, APPLE SAFARI, or GOOGLE CHROME. Additionally, software executed on the client 1802 may be downloaded to the client computer 1802 from the server computer 1806 and installed as a web browser plug-in or an ACTIVEX control. Thus, the client 1802 may utilize ACTIVEX Component / Component Object Model (COM) or Distributed COM (DCOM) components to present a user interface on the client's 1802 display. The web server 1810 is typically a program such as MICROSOFT's INTERNET INFORMATION SERVER.

[0151] Web server 1810 may host Active Server Pages (ASP) or Internet Server Application Programming Interface (ISAPI) applications 1812, which may execute scripts. These scripts invoke objects (called business objects) that perform business logic. The business objects then manipulate data in a database 1816 via a database management system (DBMS) 1814. Alternatively, database 1816 may be part of or directly connected to client 1802, instead of communicating / retrieving information from database 1816 over network 1804. When developers encapsulate business functionality in objects, the system is sometimes referred to as a Component Object Model (COM) system. Thus, scripts running on web server 1810 (and / or application 1812) invoke COM objects that implement the business logic. Additionally, server 1806 may utilize MICROSOFT TRANSACTION SERVER (MTS) through interfaces such as ADO (Active Data Objects), OLE DB (Object Linking and Embedding DataBase) or ODBC (Open DataBase Connectivity) to access the required data stored in database 1816.

[0152] Generally, all of these components 1800-1816 include logic and / or data embodied in or obtainable from a device, medium, signal, or carrier, such as a data storage device, a data communication device, a remote computer device or devices connected to a computer via a network or another data communication device, etc. Furthermore, this logic and / or data, when read, executed, and / or interpreted, performs the steps necessary to implement and / or use the present invention.

[0153] Although the terms "user computer," "client computer," and / or "server computer" are used herein, it is understood that such computers 1802 and 1806 are interchangeable and may further include thin client devices having limited or full processing capabilities, mobile phones, laptop computers, pocket computers, multi-touch devices, and / or any other devices having suitable processing, communication, and input / output capabilities.

[0154] Of course, one skilled in the art will recognize that any combination of the above components, or different components, peripherals, and other devices, may be used with computers 1802 and 1806. Embodiments of the present invention are implemented as software / CAD applications on client 1802 or server computer 1806. Additionally, as described above, client 1802 or server computer 1806 may include thin client devices or handheld devices with multi-touch based displays.

[0155] Advantages and Improvements Pump-probe spectroscopy involves the impulsive initiation of what would otherwise be a rare event near equilibrium, consistent with the description of thermally activated ion hops. However, the technique described here must differ in an important way from standard pump-probe spectroscopy. Unlike conventional pump-probe approaches, the exemplary embodiment of this technique does not attempt to directly induce or initiate ion conduction using ultrafast laser pulses and then measure changes in other measurable parameters, such as DC current, voltage, or diffraction. Instead, a high-frequency AC field is used to continuously and periodically drive ion hops within a sample (e.g., a solid electrolyte). An ultrafast laser is then used to perturb the subsystems (electrons, vibrational modes, displacement fields) that modulate the ion hopping process. Changes in the amplitude and phase of the AC field represent changes in bulk impedance or conductivity due to such perturbations. In this study, measuring the AC field perturbations was key to success because it allowed us to generate an ultrafast DC field that drives ion motion throughout the device without worrying about battery charge-discharge cycles. It also avoids the problem of simply measuring ion hopping by measuring the lifetime of photoexcited perturbations and assuming that their dynamics coincide with the dynamics of bulk ion hopping.

[0156] The data presented herein demonstrate that the laser-driven impedance method can measure the relative roles of different components of the many-body ion-hopping Hamiltonian through frequency-selective perturbations. For example, we measured a 10-fold enhancement in ion transport compared to incoherent heating by directly driving strongly contributing phonon modes. These results are consistent with ab initio calculations and support its use in exploring phonon-mediated hopping. The methodology demonstrated herein will be useful for the design of future solid electrolytes and other ion-hopping materials driven by vibrational modes. Furthermore, our results suggest the possibility of metastable photoinduced states for ion transport, potentially leading to new applications and scientific advances.

[0157] Furthermore, the laser-driven ultrafast impedance technique presented here can directly measure ion hopping on picosecond and longer time scales, allowing comparison of the absolute and relative roles of ions and their coupling with phonons, electrons, and other ions. This technique overcomes the challenges of other ultrafast time-resolved methods by utilizing the laser as a probe for AC measurements, rather than as a pump source to initiate ionic conduction, thus ensuring that the resulting transient response or signal directly probes ionic conduction. This work focuses on one species, Li, which has a small contribution to electronic conduction. + Although we focus on conductors, extension to mixed ionic-electronic conducting systems or any solid or polymeric ionic conductor is feasible. Additionally, cost-effective light-modulated or action spectrum-like techniques can leverage cost-effective light sources, such as monochromated high-power broadband lamps, providing a more laboratory-friendly means to probe complex ionic binding. Even if time-domain information on binding and correlation is lost, the relative influence of different electronic and vibrational interactions can still be compared.

[0158] [References] The following references are incorporated herein by reference:

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[0161] Further information about one or more embodiments of the present invention can be found in references 38-39.

[0162] conclusion This completes the description of the preferred embodiments of the present invention. The foregoing description of one or more embodiments of the present invention has been presented for purposes of illustration and example. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teachings. It is intended that the scope of the invention be limited not by this detailed description, but rather by the appended claims.

Claims

1. a first source of electromagnetic radiation (EM) comprising one or more first frequencies; a second source of an input signal comprising an alternating current (AC) field comprising one or more second frequencies; a control circuit connected to the first source and the second source for synchronizing application of the electromagnetic radiation and the AC electric field applied to a sample, the one or more second frequencies tuned to drive hopping of ions between ion sites within the sample; and the one or more first frequencies tuned to drive excitation in the sample that interacts with the ions; a control circuit responsive to the sample to cause an output signal comprising a modulation of the AC electric field to be output from the sample; a detection system arranged to measure and / or detect changes in said output signal in response to said electromagnetic radiation; a computer connected to the detection system for determining at least one of the conductivity or impedance of the sample from the output signal as a function of the first frequency and the second frequency.

2. 10. The spectrometer of claim 1, wherein the control circuit comprises: sweeping the first frequency through a first range to drive excitation of electrons, ions and / or phonons in the sample, including an electrolyte; and sweeping the second frequency over a second range such that the input signal drives ion hopping in the electrolyte over a range of ion transit time scales. The spectrometer further comprises a control circuit that controls or that controls the

3. 3. The system of claim 2, wherein the computer determines, or is programmed to determine, a change in conductivity at one or more second frequencies associated with transit time scales in different ion hopping regions within the electrolyte, including at least one of a contact region, a grain boundary, or a bulk region.

4. The system of claim 3 , wherein the electrolyte comprises a solid electrolyte for a battery.

5. 5. The system of claim 4, wherein the sample comprises an electrical contact to the solid electrolyte containing lithium ions for a lithium ion battery.

6. 10. The system of claim 1, wherein the computer determines, or is programmed to determine, from the output signal a Hamiltonian of the sample that describes the interaction of excitations excited by the electromagnetic radiation and hopping driven by the input signal.

7. 10. The system of claim 1, wherein the first source of electromagnetic radiation comprises a pulsed or continuous wave (CW) laser that outputs the first frequency in the range from ultraviolet (UV) frequencies to THz.

8. The system of claim 1 , wherein the first source of electromagnetic radiation comprises a lamp that outputs the electromagnetic radiation.

9. The system of claim 1 , wherein the second source of the input signal comprises a signal generator that outputs the second frequency in the range of 1 Hz to 1 THz.

10. 2. The system of claim 1, wherein the detection system measures or comprises circuitry for measuring or detecting the output signal on a time scale of an excitation driven by the electromagnetic radiation.

11. 2. The system of claim 1, wherein the first source of electromagnetic radiation includes a pulsed laser that outputs pulses of electromagnetic radiation having a full width at half maximum (FWHM) of 1 nanosecond or less, and the detection system includes circuitry that measures changes in the envelope of the FWHM with time resolution.

12. The system of claim 1 , wherein the first frequency comprises a terahertz frequency.

13. 10. The system of claim 1, further comprising a sample holder for holding the sample, the sample holder comprising: a vertical launch connector for physically connecting to a microstrip on the sample; a metal plate having at least one opening for insertion of the sample and coupling of the electromagnetic radiation to the sample; and a fastener for securing the sample between the vertical launch connector and the metal plate such that the input signal is transmitted from the vertical launch connector to the microstrip and a reflection of the input signal (including the output signal) is output from the microstrip to the vertical launch connector.

14. 14. The system of claim 13, further comprising: via a first coaxial cable to a second source of the input signal; and via a second coaxial cable to the detection system. a coupling directional coupler for coupling the optical fiber and the optical fiber;

15. 10. The system of claim 1, further comprising a time-resolved vector network analyzer comprising a second source of the input signal comprising a signal generator and a detection system comprising an oscilloscope triggered by a photodiode to detect the electromagnetic radiation.

16. 10. The system of claim 1, wherein the detection system measures or comprises circuitry for measuring changes without time resolution on the time scale of application of the electromagnetic radiation, and the computer is programmed to determine the conductivity of the sample, including a thin film, using normalization to remove the contribution of steady-state heating due to the input signal.

17. 2. The system of claim 1, wherein the detection system comprises an IQ demodulator coupled to a photodetector that detects the electromagnetic radiation, and wherein the amplitude and phase of the output signal (current and voltage) are measured using the IQ demodulator so that they can be related to a time resolution for changes in the temporal envelope of the electromagnetic radiation.

18. 10. The system of claim 1, wherein the detection system comprises circuitry for measuring or detecting the output signal to determine a change in complex impedance of the sample, and the computer determines, or is programmed to determine, conductivity from the complex impedance.

19. The system of claim 1 , wherein the detection system comprises an impedance analyzer.

20. 1. A method for measuring conductivity comprising: irradiating a region of the sample with electromagnetic radiation comprising one or more first frequencies; applying an input signal to the region, the input signal comprising an alternating current (AC) electric field comprising one or more second frequencies, such that the electromagnetic radiation and the input signal are applied synchronously; below: the one or more second frequencies tuned to drive hopping of ions between ion sites within the sample; and the one or more first frequencies tuned to drive excitation in a region that interacts with the ions; measuring and / or determining an output signal comprising a modulation of the AC field in response to the and determining from the output signal the conductivity of the sample as a function of the first frequency and the second frequency.

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