Laser-driven ultrafast impedance spectroscopy

Abstract

An apparatus comprising: a source of electromagnetic radiation comprising one or more first frequencies; an input signal source comprising an alternating current (AC) electric field and comprising one or more second frequencies; a control circuit for synchronizing the application of the electromagnetic radiation and the AC electric field applied to the sample such that an output signal comprising a modulated AC electric field is output from the sample in response to: (1) the one or more second frequencies being tuned to drive ion hopping between ion sites in the sample, (2) One or more first frequencies are tuned to drive excitation of the sample interacting with the ions. The apparatus further includes a detection system that measures and / or detects a change in the output signal in response to the electromagnetic radiation, and a computer for determining at least one of a conductivity or an impedance of the sample from the output signal and from the first frequency and the second frequency.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the common assignment and common pending interest under 35 U.S.C. section 119(e) in:

[0003] U.S. Provisional Application No. 63 / 437,200, filed January 5, 2023, by Scott K. Cushing and Kim Pham, entitled “Laser-Driven Ultrafast Impedance Spectroscopy” (CIT 8941-P); and

[0004] U.S. Provisional Application No. 63 / 543,666, filed October 11, 2023, by Scott K. Cushing and Kim Pham, titled “Laser-Driven Ultrafast Impedance Spectroscopy” (CIT8941-P2);

[0005] Both of these applications are incorporated herein by reference.

[0006] Statement Regarding Federally Funded Research and Development

[0007] This invention was made with Government support under Grant No. FA9550-21-1-0022 awarded by the Air Force. The Government has certain rights in this invention. Technical Field

[0008] The present disclosure relates to spectroscopic systems and methods of making and using the same. Background Art

[0009] Modern batteries rely on solid-state and polymer electrolytes, whose conductivity can exceed that of water. To make this possible, ions must jump between vacancies on the order of picoseconds. The mobility is determined by lattice electronically screening and mechanical deformation to assist or resist these ion jumps. Current battery characterization techniques focus on measuring the overall bulk mobility by impedance spectroscopy or identifying jump points with NMR or neutron scattering. However, to date, there is no technology that can: 1) measure ultrafast ion jumps on their inherent time scale, and 2) quantify how ions interact with electronic screening clouds, phonons, or ion-ion, high-order combinations of ion-electron-phonons, or ion-phonon-phonon interactions that lead to ionic conduction. For example, using modern techniques to extrapolate these processes is estimated to be more than 9 orders of magnitude higher than studying the jump frequencies that result from the same materials. Therefore, there is a need for improved methods to study ion transport in materials. The present invention meets this need. Summary of the Invention

[0010] The present disclosure reports a new type of impedance spectroscopy in which a CW source or laser (or similar frequency tunable light source) is swept across a wide frequency range corresponding to an excitation, such as but not limited to electron, ion, phonon excitation or any combination thereof. The change in the AC field is then measured as a function of the driving frequency at frequencies covering different ion hopping regions (e.g., ranging from contact to grain boundary to bulk effects in the case of solid electrolytes). The resulting time-dependent response can measure single ion jumps on a picosecond or faster time scale. By comparing the responses at multiple driving frequencies, or combinations of pulses with different time delays at different frequencies, the relative strength of the ion jumping process is given. Overall, the quantum mechanical Hamiltonian is mapped, providing in-depth information about how ion jumping occurs, which is also the most important aspect in materials engineering. Several versions of the instrument are described with different levels of complexity and cost, depending on the depth or nature of the information to be measured. Although exemplified in the context of battery electrodes and electrolytes, the technique is also applicable to any ion-conducting or mixed-ion-conducting system.

[0011] A byproduct of the measurement technique is the realization of laser-driven increased ionic conduction, which changes the overall impedance of the cell. The ionic conductor, or any of its applications, can be modulated by light depending on the frequency. Some of these effects persist for several minutes after the picosecond excitation pulse, leading to potential technological applications.

[0012] Illustrative embodiments include, but are not limited to, the following.

[0013] 1. A system comprising:

[0014] a first source of electromagnetic radiation (EM) comprising one or more first frequencies;

[0015] a second source of input signals comprising an alternating current (AC) electric field and comprising one or more second frequencies;

[0016] a control circuit connected to the first source and the second source for synchronizing the application of the electromagnetic radiation and the AC electric field to the sample so that an output signal comprising the modulated AC electric field is output from the sample in response to:

[0017] The one or more second frequencies are tuned to drive ion hopping between ion sites in the sample, and the one or more first frequencies are tuned to drive excitation of sample-ion interactions;

[0018] a detection system positioned to measure and / or detect changes in said output signal in response to said electromagnetic radiation; and

[0019] A computer, connected to the detection system, is configured to determine at least one of conductivity or impedance of the sample based on the output signal and as a function of the first frequency and the second frequency.

[0020] 2. The system of embodiment 1, wherein the control circuit controls or further includes a control circuit for controlling:

[0021] sweeping the first frequency over a first range to drive excitation of electrons, ions and / or phonons in the sample comprising an electrolyte, and

[0022] The second frequency is swept over a second range such that the input signal drives ion hopping in the electrolyte on various ion migration time scales.

[0023] 3. The system of embodiment 2, wherein the computer determines or is programmed to determine changes in conductivity at one or more of the second frequencies associated with migration time scales in different ion hopping regions in the electrolyte, the different ion hopping regions comprising at least one of a contact region, a grain boundary, or a bulk region.

[0024] 4. The system of embodiment 3, wherein the electrolyte comprises a solid electrolyte for a battery.

[0025] 5. The system of embodiment 4, wherein the sample comprises an electrical contact to the solid electrolyte, the solid electrolyte comprising lithium ions for a lithium ion battery.

[0026] 6. The system of embodiment 1, wherein the computer determines or is programmed to determine a Hamiltonian for the sample based on the output signal, the Hamiltonian describing the interaction between excitations stimulated by the electromagnetic radiation and jumps driven by the input signal.

[0027] 7. The system of embodiment 1, wherein the first source of electromagnetic radiation comprises a pulsed or continuous wave (CW) laser configured to output the first frequency in a range between ultraviolet (UV) frequencies and THz.

[0028] 8. The system of embodiment 1, wherein the first source of electromagnetic radiation comprises a lamp for outputting electromagnetic radiation.

[0029] 9. The system of embodiment 1, wherein the second source of the input signal comprises a signal generator configured to output the second frequency in the range of 1 Hz to 1 THz.

[0030] 10. The system of embodiment 1, wherein the detection system measures or includes circuitry for measuring or detecting the output signal on a time scale of the excitation driven by the electromagnetic radiation.

[0031] 11. The system of embodiment 1, wherein the first source of electromagnetic radiation comprises a pulsed laser for outputting pulses of the electromagnetic radiation, the pulses having a full width at half maximum (FWHM) of 1 nanosecond or less, and the detection system comprises a circuit for measuring the changes with a temporal resolution of an envelope of the FWHM.

[0032] 12. The system of embodiment 1, wherein the first frequency comprises a terahertz frequency.

[0033] 13. The system of embodiment 1, further comprising a sample holder for holding the sample, wherein the sample holder comprises:

[0034] a vertical launch connector, which is used to physically connect to the microstrip on the sample;

[0035] a metal plate comprising at least one opening for inserting the sample and coupling the electromagnetic radiation into the sample; and

[0036] A fastener is used to fasten the sample between the vertical launch connector and the metal plate so that the input signal is transmitted from the vertical launch connector to the microstrip and the reflected input signal (including the output signal) is output from the microstrip to the vertical launch connector.

[0037] 14. The system of embodiment 13, further comprising a directional coupler, wherein the directional coupler connects the vertical launch connector:

[0038] a second source coupled to the input signal via a first coaxial cable; and

[0039] coupled to the detection system via a second coaxial cable.

[0040] 15. The system of embodiment 1 further comprising a time-resolved vector network analyzer comprising a second source of the input signal and comprising a signal generator, the detection system comprising an oscilloscope triggered by a photodiode that detects the electromagnetic radiation.

[0041] 16. The system of embodiment 1, wherein the detection system measures or includes circuitry for measuring the changes on a time scale over which the electromagnetic radiation is applied without time resolution, and the computer is programmed to determine the conductivity using normalization to exclude steady-state heating contributed by the input signal and for the sample comprising a thin film.

[0042] 17. The system of embodiment 1, wherein the detection system includes an IQ demodulator coupled to a photodetector for detecting the electromagnetic radiation, such that the amplitude and phase (current and voltage) of the output signal can be measured using the IQ demodulator and the output signal is associated with the temporal resolution of changes in the temporal envelope of the electromagnetic radiation.

[0043] 18. The system of embodiment 1, wherein the detection system includes circuitry for measuring or detecting the output signal to determine a change in a complex impedance of the sample, and the computer determines or is programmed to determine the conductivity based on the complex impedance.

[0044] 19. The system of embodiment 1, wherein the detection system comprises an impedance analyzer.

[0045] 20. A method for measuring electrical conductivity, comprising:

[0046] irradiating a region of the sample with electromagnetic radiation comprising one or more first frequencies;

[0047] applying an input signal to the region, the input signal comprising an alternating current (AC) electric field and comprising one or more second frequencies such that the electromagnetic radiation and the input signal are applied synchronously;

[0048] measuring and / or determining an output signal comprising the modulated AC electric field in response to:

[0049] The one or more second frequencies are tuned to drive ion hopping between sites in the sample, and the one or more first frequencies are tuned to drive excitation of the regions to interact with ions; and

[0050] The conductivity of the sample is determined based on the output signal and as a function of the first frequency and the second frequency.

[0051] 21. The method of embodiment 20, wherein the sample comprises any material system (biological or non-biological) that conducts ions. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Referring now to the drawings, wherein like reference numerals designate corresponding parts throughout:

[0053] Figure 1 : Schematic diagram of the time-resolved ultrafast impedance setup, including the laser, representative nonlinear frequency generation processes (covering the UV to THz excitation range), VNA, and sampling unit.

[0054] Figures 2a to 2f: Representative patterns of calculated phonon contributions to lithium-ion hopping, THz absorbance, and LLTO between 0 and 6 THz. Figure 2a : Normalized decomposition of the cumulative contribution of ion hopping. The grey dashed line represents the experimental limit of THz generation (6 THz). Figure 2b The normalized contributions of 120 individual modes to lithium-ion hopping are shown. Red represents low-energy (E) phonon modes, while blue represents high-energy modes. Figure 2c : LLTO absorbance (orange) versus calculated phonon hopping contribution (bar graph). Figure 2d to Figure 2g :Highly contributes to lithium ion jumping through the front 4-O window ( Figure 2g ) or not participate ( Figure 2d to Figure 2f ) phonon modes.

[0055] Figure 3a : Schematic diagram of the gap electrode design on the LLTO wafer. Also provided as a reference. The unit temperature was controlled using a TC-48-20 OEM temperature controller, a 12V power supply, and the corresponding TC48-20 OEM software. For all experiments, the heating unit was placed in a Faraday cage to reduce noise from electromagnetic interference. A custom copper mesh with 1.4mm copper wire spacing was used.

[0056] Figure 3b : Schematic diagram of a sample including electrodes in contact with an electrolyte.

[0057] Figures 4a to 4d : Characterization of LLTO, including: Figure 4a : XRD pattern, Figure 4b : SEM showing 1 μm-10 μm grain size in the wafer, and Figure 4c : block, Figure 4d : Grain boundary portion of the impedance spectrum. For a disc with a 1 mm gap in the center of the light source, LLTO was excited to eliminate the possible effect of irradiating Au (Figure 2) on the impedance. Figures 4a to 4d XRD patterns, 1 μm-10 μm grain sizes, and representative impedance plots are shown.

[0058] Figure 5 : Schematic diagram of the THz field setup. OPA: optical parametric amplifier. OAP: off-axis parabola. FL: focusing lens, P: polarizer, PD: photodiode

[0059] Figures 6a to 6d : Electrical conductivity change of LLTO sample from 1 Hz to 50 GHz. The excitation of charge transfer transition reduces the Coulomb hopping barrier and increases the conductivity (black solid line). Figure 6a This variation is shown, with the red area being larger than the optically heated lattice (black dashed line). Figure 6bSchematic diagram of the unit cell for LLTO and how the photoexcited charge transfer transition clears electron density from the lithium ion conduction path. In the unit cell, at the center of the octahedron, lithium (Li) ions are purple, oxygen (O) is red, lanthanum (La) is green, and titanium (Ti) is gray. Figure 6c Representative time-resolved changes in conductivity on the picosecond timescale are shown. Figure 6d The linearity of the signal response to the excitation power is shown.

[0060] Figures 7a to 7d : Interaction of THz with LLTO. The orange, blue, purple, and grey atoms correspond to oxygen, titanium, lanthanum, and lithium, respectively. Figure 7a : At t1=0, the impedance analyzer records EIS spectroscopy before, during and after THz excitation. Figure 7b : During t2>t1, the THz light resonantly drives the contributing modes, thereby increasing the phonon occupancy. Figure 7c : Under continuous THz irradiation, phonon-to-Li-ion energy transfer and bottleneck opening occur, leading to facile Li-ion hopping, which manifests as reduced impedance. Figure 7d : Once the THz source is removed, the phonon occupancy and impedance return to their original state ( Figure 7a ).

[0061] Figure 8 Figure 2: Electrochemical heating cell setup to obtain a power-temperature calibration curve and collect EIS data below 32 MHz using a 1260A Solartron. The cell assembly is compressed and held together with screws passing through the five holes shown. Each screw is secured with a wing nut.

[0062] Figure 9a : The absorption spectrum across the UV-Vis to THz frequency range shows the shift enhancement across near IR (NIR), mid IR (MIR) and THz light. The R caused by a unit change in sample temperature (K) is bulk The changes are represented by the horizontal orange bar and further defined by the black gradient. NIR enhancement and DC heating correspond to incoherent heating of the phonon bath. MIR excitation corresponds to coherent driving of optical phonon modes. THz light coherently drives the contributing modes, showing the maximum relative enhancement. The width of the horizontal orange bar represents the spectral width of the excitation pulse. In comparison, Figure 9a The absorption spectra spanning the UV-Vis to THz frequency range are plotted, and the width of the orange bar representing the bandwidth of the excitation source indicates that THz is broader than the other excitation sources.

[0063] Figure 9b : Comparison of measured THz absorption in LLTO with theoretical predictions of ionic conduction contributed by excited THz rocking modes.

[0064] Figures 10a to 10d : Nyquist plots of LLTO between 298 K and 333 K and the target phonon excitation with THz. Figure 10a : Grain boundary characteristics of LLTO, Figure 10b : Volume features of LLTO. Open symbols correspond to data. The line represents the fit. Figure 10c Figure 3: Yquist plots of THz-excited LLTO with 1 to 1.6 mW power. The Z' variation is compared at single frequencies of 803 kHz and 32 Hz (corresponding to bulk resistance and grain boundary resistance, respectively). Figure 10d : The percentage change in impedance versus power. The linearity of this data excludes the nonlinear effects of the drive field.

[0065] Figures 11a to 11c : Figure 11a is a schematic diagram of a vertical launch with an exposed pin making electrical contact with the sample under study. Figure 11b The sample is shown inside a well 300 microns deep and 2 mm in diameter, with a 2 mm thick hole drilled in the side to simultaneously illuminate the sample. Figure 11c The vertical launch is shown connected to the S12 port of the directional coupler. The S11 port allows reflection measurements on the reflected, undisturbed wave provided by port S13.

[0066] Figure 12 : Change in conductivity of an LLTO sample from 2 Hz to 110 GHz. The excitation of the charge transfer transition lowers the Coulomb transition barrier, thereby increasing conductivity (black solid line). The change in the red area is greater than the optical heating of the lattice (black dashed line). The dashed line shows the LLTO conductivity with a closed laser.

[0067] Figure 13 : Change in conductivity of an LLTO sample due to 350 nm light from 2 Hz to 110 GHz. Representative time-resolved change in conductivity on a picosecond timescale.

[0068] Figures 14a to 14e : Impedance changes when bandgap is excited by 349nm light at 5mW to 20mW. Figure 14a Shown is the assembly to R1+R GB / Grain boundary semicircle of Q2 circuit. Figure 14b Shown is the assembly to R1+R Bulk / The bulk impedance semicircle of the Q2 circuit. Figure 14c shows the grain boundaries, and Figure 14d Bulk replicates of three samples are shown showing the change in impedance upon excitation with 349 nm light from 5 mW to 20 mW at frequencies corresponding to the respective intercepts of the semicircular features. Figure 14eThe percent change in impedance as a function of 349 nm laser power is shown, showing a linear response for both grain boundaries and the bulk.

[0069] Figure 15 : A flow chart illustrating a method of manufacturing a device.

[0070] Figure 16 : A flow chart illustrating a method of performing spectroscopy.

[0071] Figure 17 : An exemplary hardware environment for performing the computer and / or control functions described herein.

[0072] Figure 18 : An exemplary network system for performing the computer and / or control functions described herein.

[0073] Figures 19a to 19c : An exemplary detection system including a PLL detector ( Figure 19a )、IQ modulator( Figure 19b ) and amplitude detector ( Figure 19c ), which further illustrates optional connections to synchronization or triggering circuits. DETAILED DESCRIPTION

[0074] In the following description of the preferred embodiment, reference is made to the accompanying drawings which form a part of the present invention and in which there is shown specific embodiments in which the invention may be practiced. It should be understood that other embodiments may be utilized and that structural changes may be made without departing from the scope of the invention.

[0075] Technical Description

[0076] 1. System components

[0077] Figure 1 A spectrometer, device, apparatus, or system 100 is illustrated, comprising: a source of electromagnetic radiation 102 comprising one or more first frequencies; an input signal source 104 comprising an alternating current (AC) electric field and comprising one or more second frequencies; and control circuitry 106 that synchronizes the applied electromagnetic radiation and the AC electric field applied to a sample 108 such that:

[0078] (1) outputting a modulated output signal 110 comprising an AC electric field from the sample in response to one or more second frequencies being tuned to drive ion hopping between ion sites in the sample, and

[0079] (2) One or more first frequencies are tuned to drive excitations that interact with ions in the sample.

[0080] The spectrometer also 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 conductivity or impedance of the sample based on the output signal and the first and second frequencies.

[0081] Figure 1 An embodiment of an ultrafast impedance spectrometer comprising a laser driver using a nonlinear mixer (nonlinear optical frequency generation) is illustrated. In another configuration, when measuring steady-state conditions, a continuous wave light source (e.g., a high power lamp or CW laser) can be coupled to a standard impedance analyzer (e.g., a 1260A Solartron). However, since it is difficult to obtain sufficient average power with current CW light sources across the UV to THz range, pulsed lasers can also be used, although in this case the data must be carefully controlled due to duty cycle averaging. In this CW version of the instrument, only relative values ​​(not absolute values) of the second-order (ion and electron or phonon) Hamiltonian components can be obtained by inferring cross-correlation terms (ion-electron-phonon, etc.). However, this is still important information for many applications including but not limited to the design of solid-state ion conductors

[0082] 2. Example Ionic Conductivity Calculation

[0083] In electrochemical impedance spectroscopy (EIS), a sinusoidal potential is applied to the sample of interest (Equation 1), where U(t) is the potential over time t, U0 is the amplitude of the potential, and f is the frequency 46 :

[0084] U(t)=U0sin(2πft) (1)

[0085] Interaction with the sample will cause changes in the phase and amplitude of the measured response (such as current or potential), as shown in Equation 2, where I(t) is the time-varying current, I0 is the amplitude of the current, and Θ is the phase angle.

[0086] I(t)=I0sin(2πft+Θ) (2)

[0087] The complex impedance can then be derived from the amplitude Z = U0 / I0 and the phase angle Θ, i.e., the phase shift between the measured U(t) and I(t) for frequency f. Although EIS cannot decouple the conduction caused by multiple mobile charge carriers, it is still a useful tool for studying ionic conduction in many solid-state conductors. In the literature, FFT EIS has been developed 47-49 , Online EIS 50 ,51 and fast parsing technology 49,52,53 , to access faster hopping schemes without using pumps to drive ion migration.

[0088] In addition, previous reports only reached 1-3GHz 46,49,50,54,55 , and to the best of our knowledge, this disclosure describes the first method that can reach 40-110 GHz thanks to recent advances in electronics. Ultimately, the bandwidth of the signal generator and oscilloscope determines the time and frequency resolution, and using spectrum extenders it is possible to reach the THz range.

[0089] 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 can be used to measure potential changes, current changes, and phase shifts at the same frequencies, all of which are used to derive impedance.

[0090] However, above tens of MHz, as the values ​​of capacitance and inductance become too small (sub-picofarad and sub-nanohenry, respectively) to be measured 56 , directly measuring the change in current versus potential becomes impractical. Instead, the scattering parameters are measured to determine the magnitude and phase changes associated with the impedance, as shown in Equation 3.1 43,56 where VSWR is the voltage standing wave ratio, or how efficiently RF power is transferred through a transmission line to a load, S11 is the reflective scattering parameter, Γ is the reflection coefficient, Z0 is the reference ohm (usually 50 ohms), and Z L is the sampling impedance or load.

[0091]

[0092] Since S11 is measured directly from the VNA, Z can be calculated L And then the ionic conductivity is calculated.

[0093] 3. First exemplary measurement of ultrafast ion hopping in LLTO

[0094] a. Theoretical framework

[0095] The basic mechanism of ion conduction (σ) depends on the activation energy (E) of the ion hopping point and temperature (T). A ), as shown in Equation 4.

[0096]

[0097] However, σ ion Relying on more factors revealed after expanding the Arrhenius prefactor σ0, as shown in Equation 5. 7 shown

[0098]

[0099] The probability of an ion jumping is determined by the trial frequency (v0), the jumping distance (a0), the activation energy barrier (ΔHm or experimental E A ) and temperature (T). According to Equation 5, σ0∝exp(ΔS m ), where ΔS m is the entropy of the migration, but is only expressed as a single-body problem. In the framework of the multi-body image, the prediction ΔS m depends on the vibration of the host sublattice, as shown in Equation 6. 7 shown

[0100]

[0101] Transition state vibration frequency At the starting point of the transition belongs to the entire system. Initial state vibration frequency consists of the normal frequencies of the system constrained to a saddle point configuration, thus requiring a many-body treatment 15,17 .if Large enough, as in the case of ionic conductors with large anharmonic and soft anionic sublattices, ΔS m and subsequently σ will be large, which makes it necessary to study phonon coupled conduction.

[0102] Although Equation 6 theoretically predicts ΔS on σ m However, researchers have not yet experimentally quantified ΔS m To demonstrate the relevance of multi-body coupling for ion migration, we experimentally drive the relevant polyanion motions and measure the resulting effect on σ, comparing this result with driving other phononic and optical phonon modes. While driving structural modes that change electronic and magnetic properties is common in condensed matter materials, 16,23,24 , but such technology has not yet been applied 25,26 : Conductivity or impedance is determined based on one or more second frequencies, wherein the one or more second frequencies are tuned to drive ions to jump between ion sites in the sample, and the one or more first frequencies are tuned to drive excitation in the sample that interacts with the ions, as described herein.

[0103] Using initial calculations, the contribution of ion hopping in LLTO was modeled based on 22 unique lithium-ion hopping scenarios for three types of LLTO order and structural information from experimental synchrotron diffraction data. By considering all types of order, all possible ion migration paths and types of phonon vibrations can be analyzed. Figure 2aThe total cumulative normalized contribution to ion hopping spanning 0-27 THz is shown. When the total modes are further sorted by the most contributing modes, the top 10% of contributing modes account for 61% of the contribution to ion hopping, and the top 5% of contributing modes account for 48%. Below 6 THz, 36% of the modes are found to be wobbly in nature and contribute 50% to ion hopping.

[0104] We also calculated the energy that a single phonon exerts on a jumping lithium ion. Although low THz frequency modes should naturally be high in energy, the energy of these modes is independent of frequency. In classical thermodynamics, the distribution function of the number of phonons at a specific frequency ω is If the total energy of phonons at a given frequency is determined, and the energy of each phonon is Then the total energy E is k B T, thus becoming frequency independent. Therefore, at lower frequencies, there are many low-energy phonon modes and several high-energy phonon modes that add up to an overall high energy.

[0105] Figure 2b The energy imparted to the jumping ion by the phonon mode, represented by the color gradient, is plotted against its corresponding phonon frequency. Figure 2b shows that in addition to the rocking modes below 6 THz, there are also high-energy phonon modes, Figure 2c The percentage contributions for the two mode types are shown in more detail in . It is calculated that within the top 5% of high-contributing modes below 6 THz, >95% are either rocking modes, high-energy phonon modes, or a combination of both. Therefore, to facilitate ion transport, the surrounding polyanions must: (1) have enough energy to transfer to the lithium ions along the correct hopping direction, and (2) have the right vibrations to open the bottleneck of ion migration. Figure 2d to Figure 2f The pattern shown does not satisfy either condition, but does satisfy Figure 2g Therefore, after confirming the existence of modes satisfying conditions (1) and (2) in the experimental THz range described herein, the present inventors hypothesized that exciting these high-contribution mode types could lead to improved ion transport in LLTO.

[0106] b. Spectroscopic measurement

[0107] (i) Sample holder

[0108] FIG3 shows the sample holder used for the cell test. The heating cell allows temperatures between 298 K and 333 KT for reference measurements of an incoherently heated phonon bath, as performed for standard impedance tests. A polymethylpentene (TPX) optical window is integrated into the heating cell to allow transmission of the field. For other visible / UV light sources, a quartz window with a transparency between 190 nm and 2500 nm is used. Measurements of non-air and moisture-sensitive samples without a window are also performed.

[0109] (ii) Sample preparation

[0110] Lithium lanthanum titanate (Li0.5La0.5TiO3, LLTO) was used as the test sample because it is stable. 1 LLTO was synthesized by mixing stoichiometric amounts of La2O3, Li2CO3, and TiO2 in an agate mortar and pressing into discs under a pressure of 100 MPa. The discs were placed on a bed of sacrificial powder and calcined at 800°C for 4 hours and then at 1200°C for 12 hours at a ramp rate of 1°C / min. The resulting powder was pressed into discs with a diameter of 10 mm and a thickness of 0.6 mm to 0.8 mm under a pressure of 2 tons. The discs were then annealed at 1100°C for 6 hours at a ramp rate of 2°C / min on a bed of its parent powder. A 1.6 mm Au strip was sputtered onto one side.

[0111] Figures 4a to 4b An XRD pattern is shown, with a grain size of 1 μm to 10 μm.

[0112] (iii) equipment

[0113] Figure 1 The laser-driven ultrafast impedance spectrometer illustrated in Figure 1 was constructed using a signal generator (100 GHz, Keysight (N5173B)) and a high-speed oscilloscope (100 GHZ, Keysight, N100A / N1046A). Because the jitter of the laser output is less than that of the oscilloscope output, the performance of the real-time oscilloscope and the sampling oscilloscope were compared with no discernible difference. Therefore, either type of oscilloscope can be used.

[0114] The bandwidth of the signal generator and oscilloscope determines the time and frequency resolution. It is desirable to use a signal generator and oscilloscope with a low noise floor because this determines the lowest differential signal that can be measured. Using a signal generator and oscilloscope, you can get 10 -4 noise floor.

[0115] Figure 5Laser setups for THz, NIR, and MIR generation are shown. UV to THz light is generated using a Ti:sapphire laser oscillator and amplifier (Legend Elite) from Coherent. Specifically, UV to NIR light is created from optical conversion using an optical parametric amplifier (TOPAS). Difference frequency generation is used to cover the 5μm to 15μm range. THz light is generated using the 1400nm output of a DAST and an optical parametric amplifier. The average power for the 1kHz laser is as low as mW and is focused on a spot size of several hundred microns.

[0116] The signal generator, oscilloscope, and laser are synchronized by dividing the laser oscillator output (80 MHz) signal to 10 MHz. The light from the laser is focused between the surface gap electrodes. The signal is recorded on the oscilloscope relative to the output of the signal generator. A photodiode measuring the picosecond rise time of the 1 kHz laser amplifier output is used as an oscilloscope trigger to locate the picosecond impedance modulation. Once the time window is narrowed, the impedance change itself is used as a trigger. The measurement is then repeated for multiple laser excitation frequencies or multiple signal generator frequencies. Static impedance measurement ( Figures 4c to 4d ) predetermine bulk site-to-site hopping and grain boundary frequencies.

[0117] (iv) Time-resolved measurements

[0118] Li in LLTO + The conduction of Li is mediated by adjacent vacancies between the bottlenecks formed by the four oxygens of the corner-sharing TiO6 octahedron. The screening effect has been predicted to aid ion conduction by minimizing the electrostatic interaction between the host lattice and the migrating ions, thus enabling several solid-state Li + and O2 2- Fast ion transport in conductors. In LLTO, the ligand-to-metal charge transfer transition can occur at a 2.1 eV bandgap excitation, which promotes electron carriers from O 2p orbitals to Ti 3d orbitals. By transferring charge density from O 2p orbitals to Ti 3d orbitals, electrostatic hindrance in the ion conduction path may be reduced, providing insights into ion-electron interactions.

[0119] Figure 6c The time-resolved ultrafast impedance measurements performed using a high-speed oscilloscope and the bandgap pulsed laser excitation described above are shown. Once the AC carrier frequency is removed using a Fourier filter, clear time-resolved changes in ionic conductivity are measured. 350 nm photoexcitation induces a charge transfer transition from O 2p orbitals to Ti 3d orbitals. As described above, ionic hopping between TiO6 octahedral vacancies is promoted by rocking modes ( Figure 6b), theorized that ionic conduction in LLTO could be achieved by transferring charge density from O 2p orbitals to Ti 3d orbitals, reducing the electrostatic hindrance in the ionic conduction path and measuring an increase in ionic conductivity.

[0120] Figure 6a The impedance changes after repeated LLTO photoexcitation from Hz to tens of GHz are shown compared to laser heating of an incoherent phonon bath alone. Figure 6a A CW laser was used in the RT-PCR to allow for broadband AC impedance sweeps, but the percentage change in impedance remained the same. Figure 6a The red areas in the graph show the difference between laser heating and charge transfer transitions. As expected, the largest increase in ionic conductivity is in the site-to-site hopping region because the shift in charge density lowers the activation energy for ion hopping. Changes are also measured at grain boundaries and contact regions, but are less significant. The change in measured impedance is linear in power and linear in laser beam size relative to gap-electrode distance ( Figure 7d ). The above impedance variation is above 10 GHz due to the gap electrode distance, but can be improved through sample optimization.

[0121] Using a single excitation or drive frequency and measuring the change in AC impedance gives information about two-particle type interaction terms, namely ion-phonon and ion-electron interactions. By using a dual-pulse excitation scheme similar to 2D spectroscopy, ion-ion correlations determined by cross-peaks in the 2D spectrum and comparison of the resulting relaxation dynamics between pulses can be used to measure many-body cross-correlations such as ion-electron-phonon or ion-phonon-phonon. Ultimately, this form of instrumentation will allow nearly complete measurements of the ion-hopping Hamiltonian, just as 2D spectroscopy has been used in other optical or IR active systems.

[0122] (v) Non-time-resolved experiments

[0123] The technique's non-time-resolved adaptability was tested for comparison. Using an off-the-shelf impedance analyzer, frequencies up to 32 MHz could be measured; right at the edge of the point-to-point hopping region of LLTO. A continuous-wave (CW) light source was connected to a 1260A Solartron impedance analyzer to measure complex impedance variations between 1 Hz and 32 MHz, encompassing the tails of grain boundaries and bulk conduction mechanisms in many materials. While ideally, a CW light source would be used to excite the sample from UV to THz, the data presented here used a Ti:sapphire laser and nonlinear frequency mixing to access this regime at high power.

[0124] Figure 7 schematically illustrates the effect of coupled ion-phonon vibration modes on Li using THz irradiation and EIS measurements. 0.5 La0.5 The relative contribution of the overall ionic conduction process in TiO3 (LLTO) was investigated using a laser-driven impedance technique. The effects of driving Li ions were also measured compared to acousto-optic phonons spanning the near-infrared (NIR) and mid-infrared (MIR). 0.5 La 0.5 Effect of THzρ modes in TiO3(LLTO).

[0125] (i) Normalization

[0126] Given the 1kHz repetition rate of the pulsed laser, the data were duty cycle averaged (a 1kHz repetition rate means that any measured dynamics are time-averaged) and thermalization values ​​had to be obtained, thereby reducing sensitivity. Several normalization parameters were carefully considered, including the incident power, power density, and penetration depth at each wavelength. However, ultimately, normalization of the impedance change for each sample temperature change was used. This approach normalizes for the total absorbed power, which is independent of the transition intensity, and since the measurements are taken after several minutes in equilibrium, the penetration depth relative to the surface electrode is also measured. Therefore, different excitation wavelengths and DC heating can be directly compared, as is done in a furnace from an incoherently excited phonon bath.

[0127] The normalized impedance for each thermal transition, expressed as a fraction of the total absorbed power, is independent of the intensity of the transition. Because complex impedance measurements are taken after several minutes at equilibrium, the penetration depth relative to the surface electrode is factored into the final value. This normalization method thus allows for direct comparisons between laser and DC heating to accurately calibrate the data baseline.

[0128] By first using the TC-48-20OEM temperature controller and thermocouple Figure 8 Normalization was accomplished by constructing a calibration curve using the custom heating cell shown. Based on Watt's law, P=IV, the current and voltage across the measurement cell and through the sample were used to calculate the power input to the sample. By plotting the calculated temperature versus the temperature read out from the TC-48-20OEM software, a calibration curve was constructed to determine the temperature in relation to the power input to the LLTO. The normalization method was found to give a percentage change similar to that obtained by power density normalization, demonstrating the validity of the proposed method. Therefore, despite experimental limitations between accurately interpreting data using CW and pulsed laser excitation, non-time-resolved measurements can be achieved with commercial impedance analyzers and still provide valuable information about coupling dynamics in a variety of solid-state materials without the need for custom electronics.

[0129] For non-time-resolved measurements up to 32 MHz, a custom unit was constructed consisting of a ceramic heating plate, temperature-controlled using the corresponding software from the TC-4820 OEM heater and thermistor, as Figure 9aThe heating unit is placed in a Faraday cage made of copper mesh with a wire spacing of 1.4 mm in all experiments to reduce noise from electromagnetic interference. Various organic and crystalline materials can be used. 66 Design a THz transparent window. For other visible / UV light sources, use a quartz window with transparency between 190nm and 2500nm. A windowless setup can alternatively be used for non-air-sensitive materials. As described above, the sample itself is annealed and densified, and a barrier electrode such as Au, Ag, Pt, or Pd is sputtered onto the wafer using a mask to create a gap electrode geometry. Figure 8 Sputtering the Au electrode on the same plane of the sample disc with the gap geometry shown, rather than completely sputtering both planes, minimizes the sample volume probed during impedance measurements, making the effects of optical penetration depth and spot size-induced differences more negligible. Thin film samples can also be used, making the optical penetration depth negligible. The developed planar electrode configuration is compatible with time-resolved setups and also allows for testing grain boundary and bulk conduction effects, the grain boundary contribution of which dominates the overall ionic conductivity when used as a solid electrolyte in all solid-state batteries.

[0130] (ii) result

[0131] Figure 9a The impedance changes of the grain boundary characteristics of LLTO in the excitation frequency range are compared. For the frequency range of 32 MHz, the grain boundary and tail of the bulk ion hopping conduction mechanism show the same trend, as shown in Figure 4a The relevant absorption characteristics for each subsystem are shown as Figure 9a The colored curves in Figure 3 are shown. The height of the bars represents the enhancement ratio of the bulk impedance after laser driving at that frequency, while the width of the bars represents the bandwidth of the excitation source for that frequency. UV excitation modifies the electrostatic barrier in the lattice cage via ligand-to-metal charge transfer from the O 2p valence band orbitals to the Ti 3d conduction band orbitals. THz excitation represents a series of TiO6 rocking modes and proves to be the dominant term in modifying bulk ion hopping. NIR and DC heating curves serve as control data because they primarily heat the material incoherently via a phonon bath. No signal of photoexcited optical phonon branches with power comparable to that of the THz rocking modes was detected, but higher-power DFG units will provide more definitive evidence.

[0132] For THz light, 0.7% ΔR was measured bulk / mW, which is calculated as the bulk / K. Incoherent heating of the phonon bath with 800 nm light yields a ΔR of 0.12%. bulk / mW change or an estimated 4% ΔR bulk / K change. Within the error range, this change is consistent with the ΔR caused by DC heating. bulk 0.07% change in / mW or ΔR bulk The results are comparable to a 3% change in the power density of the THz light, demonstrating that laser heating of the lattice alone is not responsible for the observed changes induced by the THz light. For the same power density used to drive the THz phonons, there is no detectable change in the frequencies measured in the optical phonon range. MIR powers are an order of magnitude lower than thermal heating powers, so the relative contribution can only be constrained in this range. However, the results are consistent with theoretical predictions that modes above 10 THz (approximately 30 μm) are unlikely to contribute to ion hopping.

[0133] Two comparisons can be made to test the accuracy of the duty cycle averaging version of the instrument. First, for Figure 4a CW excitation and Figure 9a The duty cycle averaged in , the relative change between DC or NIR heating and 350 nm optical excitation is a factor of 5. Second, the THz excitation can be integrated over the theoretically predicted contribution to ion hopping ( Figure 9b ). Using the simplified Boltzmann distribution approximation and the theoretically predicted phonon mode contributions, the combined 1 THz to 6 THz modes will only account for about 2% of ionic conduction at room temperature. When driven directly by THz excitation, the contribution of the THz rocking modes becomes about 30%. The ratio of these two numbers is similar to Figure 9a This matches the approximately 15-fold enhancement in ionic conductivity measured in .

[0134] More specifically, after approximate normalization between the driving wavelengths from NIR to THz light, the measurements confirm that the selective excitation of THz ρ modes leads to a decrease in R compared to non-resonant heating of the phonon bath or resonant driving of optical vibrational modes. bulk and R gb This is reminiscent of light-modulated ferroelectricity, magnetism, and ionic conductivity in inorganic-organic perovskites—the enhancement is persistent and reversible, even though the recorded changes are averaged over the 500 Hz repetition rate of the laser.

[0135] therefore, Figure 9a The relative contributions of the subsystems of the ion hopping Hamiltonian associated with incoherent heating are precisely measured, and using this normalized metric, relative comparisons between different ion hopping Hamiltonian components are made. For example, Figure 9aThe results show that the THz rocking mode is clearly the dominant vibrational mode compared to optical phonons or the rest of the 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 when LLTO is doped or compared to LLZO to reduce electrostatic hindrance, increased ionic conduction is achieved. Therefore, this simplified version of the experiment should be particularly powerful when comparing material optimization strategies as a relative measure.

[0136] The Nyquist plot for LLTO without laser excitation is shown below: Figure 10a and Figure 10b and Figure 7a The impedance data for bulk and grain boundary impedances were fitted to the R1+R2 / Q2 circuit, respectively. As the temperature increases, we measure a shift towards low impedance for Z' and Z', which corresponds to an increase in the population and mode types in the phonon bath. Therefore, E for mobility A The lower v0 for lithium-ion hopping is higher, resulting in a lower measured value in Z'. The semicircle fit corresponding to the grain boundary contribution has a different shape from the bulk contribution, likely because the bulk semicircle partially overlaps with the grain boundary features. We found that this varied slightly between samples, but the final impedance difference was consistent across all measurements within the error range.

[0137] Figures 10c to 10d shows the linear variation of Z' of bulk and grain boundary features with respect to power when driven with broadband THz radiation (LLTO absorption measured at Figure 2c The change is reversible, returning to the pre-illumination impedance after illumination ( Figure 7d ). Before normalization, for average THz power in milliwatts, the variation of Z' is on the order of 100s of Ω. After normalization, R bulk The changes in are compared with other optical phonon modes in MIR and phonon modes excited incoherently by DC-heated lasers.

[0138] R using THz light (about 10 times that of incoherent DC heating) bulk The relative reduction in Z' supports the hypothesis that resonantly driven high-contribution phonon-ion coupling modes can promote ion migration. This enhancement is consistent with integrating the contributing modes over the THz excitation range and comparing them to the thermal regime. For DC or laser-induced heating, the same power is incoherently distributed over the various acoustic and higher energy phonon modes, so the overall change in the measured Z' is lower. Furthermore, the THz field is unlikely to increase any electronic contribution to the total conductivity, the measured conductivity, or excite any electronic carriers in the LLTO. THz energies are typically less than 1 eV, and in this study were less than 0.025 35 , which is well below the 2.1eV bandgap of LLTO36 Therefore, THz fields are unlikely to generate electron carriers or have sufficient energy to promote enhanced conductivity, as is the case with known superconducting hopping materials. 24

[0139] This study can be used to clarify the ΔS in Eq. m The effect and can change ΔS m Selectively driving different phonon mode types with narrowband THz pulses will help to further decouple the ion migration dynamics caused by high-energy phonon modes from those that distort only the vibrations of the local polyanion. 37

[0140] It is important to note that for THz excitation and non-resonant heating, it takes about 100 seconds for the reduced impedance to equilibrate and relax, as Figure 7d As shown in Figure 3, the matching rise and decay times indicate that the THz-reduced impedance exists on a timescale longer than the picosecond timescale of the THz driving force itself. Matching thermal and THz equilibrium times, but non-matching impedance variations, suggests that driving coupled phonon-ion THz modes may generate non-equilibrium lithium-ion pathways, which are then balanced by thermal vibrations. Further experiments are needed to clarify this aspect of the conclusion.

[0141] These results demonstrate that laser actuation can be used to control the ion phonon states and the many-body correlations that lead to fast ion transport in solids. Furthermore, spectroscopic techniques can roughly determine the relative contributions of different vibrational modes to macroscopic ion hopping. By isolating the relative contributions, the design of solid electrolytes can be improved by identifying the key contributing modes.

[0142] In other embodiments, non-time-resolved measurements can use a CW 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 action spectra of solar materials. This form of instrumentation would represent a straightforward approach that does not require specialized optical knowledge or the cost of ultrafast lasers. Reaching the important far infrared to THz range with sufficient power is more difficult and may require a laser source in some embodiments.

[0143] 4. Second Example: S11 Reflection Measurement with SMA Connection and Vertical Launch Connector

[0144] a. Sample Holder and Sample Preparation

[0145] According to the literature 59 LLTO was synthesized and 38 It has been characterized and tested.

[0146] For S11 reflection measurements, a vector network analyzer (VNA) generates an AC signal that is transmitted to the sample or load through a directional coupler with an SMA connection into the sample and according to previous literature 55，57，58 The copper short pipe at the modeled port S12 is as follows Figure 11a and Figure 11b As shown. A 2mm wide cavity was drilled from the side of a copper stub to allow laser excitation during time-resolved measurements. The powder sample was densified under high force (2 tons) into a 1 / 4" diameter disk, annealed to reach at least 80% of its theoretical density (specific to the composition), and then polished to fit within the 300 micron well. In addition to minimizing air gaps, the sample needed to make physical contact with the pins inside the vertical launch connector to create a resonator, which is critical for accurate measurements, as shown in Figure 2. Figure 3a and Figure 3b The S11 port for measuring the reflected wave and the S13 port for providing the coupled reference wave are connected back to the VNA, as shown in Figure 11c To physically measure the S11 parameter, a microstrip or metal strip is deposited or contacted onto the sample load to achieve high-frequency transmission from hundreds of MHz to above 10 GHz. 56 The electrical connection between the microstrip and the oscilloscope is established using a coaxial cable with an appropriate adapter rated for GHz frequencies, such as an SMA connection.

[0147] To measure the time-resolved impedance signal, a 40 GHz Keysight N5173B signal generator coupled to a 40 GHz Keysight N100A / N1046A oscilloscope was used. Experimentally, a 1 kHz laser with an average power of 130 mW was used, focused into a beam with a diameter of 200 to 300 μm, depending on the sample.

[0148] A laser clock can be used as an external reference for synchronization with a custom VNA, but synchronization can be difficult in some cases because many signal generators only accept a 10 MHz reference signal, which the laser clock will not output. Furthermore, even after frequency division, the laser clock output may not have sufficient phase stability. Therefore, an IQ demodulation method is preferably used to extract amplitude and phase data using a picosecond photodiode, which is used to help locate transient signals. Next, S11 measurements are performed for multiple laser excitation frequencies or multiple signal generator frequencies, depending on the experiment.

[0149] b. Steady-state measurement

[0150] A Keysight N9041B UXA signal analyzer with a range of 2 Hz to 110 GHz was used as a VNA for steady-state measurements.

[0151] Lithium ion conduction in LLTO is achieved by corner-sharing TiO6 octahedrons. 60,62 The screening effect has been predicted to aid ion conduction by minimizing the electrostatic interaction between the host lattice and the migrating ions, thereby enabling several solid-state Li + and O2 2- Fast ion transport in conductors 17-19,34 In LLTO, the ligand-to-metal charge transfer transition can occur on a 2.1 eV bandgap excitation that promotes electron carriers from O 2p orbitals to Ti 3d orbitals. 61 By transferring charge density from O 2p orbitals to Ti 3d orbitals, the electrostatic hindrance in the ion conduction path may be reduced, providing insights into ion-electron interactions.

[0152] To test the role of shielding in ion conduction, the LLTO sample was optically excited through the cavity in a vertical emission geometry, as shown in Figure 10. While the use of a vertical emission geometry was adequate for proof-of-concept measurements, noise above 10 GHz was observed, likely due to contact issues and particle density. Further optimization of the cell design will improve the signal-to-noise ratio in future studies.

[0153] A 2Hz-110GHz Keysight N9041B UXA signal analyzer was initially used to perform steady-state measurements of the LLTO and excitation from 350nm to 700nm to develop the conceptual capabilities of the instrument before moving on to more complex time-resolved experiments. Note that a vector network analyzer (VNA) is essentially a coupled signal generator and oscilloscope, so the time-resolved electronics outlined can also be used at this stage. The S11 signal is Fourier filtered to remove the carrier signal frequency, and Z is calculated using Equations 3.1 to 3.3. L . Then you can use Z L Using the equation To calculate the ionic conductivity, where σ is the ionic conductivity, R total is processed as Z L is the impedance, l is the sample thickness, and A is the sample area.

[0154] First the steady-state response is measured and Δσ / σ is calculated and plotted as a function of frequency, as Figure 12 This figure shows the enhanced conductivity of LLTO after excitation with 350 nm CW laser light. Figure 12 The shaded red area in the figure shows the altered ionic conductivity due to laser heating of the incoherent phonon bath with 700 nm light versus the modulated Li ion from the 350 nm bandgap excitation. +Differences in electronic coupling. The largest increase in the enhancement ratio is observed in the site-to-site hopping region and is likely due to a shift in charge density from O 2p to Ti 3d orbitals, which we predict will lower the activation energy for ionic hopping. Differences are also observed at the 350 nm and 700 nm grain boundaries and across the electrode-electrolyte surface region and are likely related to the number of thermal baths.

[0155] Although the generation of electron carriers can convolute the final Li + mobility values, but many reports indicate that the enhancement of ion mobility is not solely due to the generation of newly generated electron carriers. 17-19 We therefore believe that our observations of enhanced ion mobility due to this charge transfer process hold true after accounting for both thermal and electronic carrier generation. Even in the presence of electronic conduction effects, the described experiments demonstrate the general concept of the instrument in its steady-state implementation.

[0156] c. Time-resolved measurements using a custom VNA

[0157] The time-resolved enhancement of ionic conduction due to bandgap excitation was measured using a custom-built VNA time-resolved version including a 40 GHz signal generator and an oscilloscope. The measurements were performed using the sample cell configuration shown in Figure 3.

[0158] Figure 13 The enhancement ratio Δσ / σ is shown as a function of frequency using a custom VNA time-resolving configuration up to 300 picoseconds. Figure 13 The enhancement observed between 0 and 60 picoseconds is due to the laser pulse changing the Li + The electron screening experienced. The enhancement ratio decays after 60 picoseconds due to the lack of 30-picosecond ultrafast pulses. Figure 12 It can be constructed entirely from time domain traces through automation, such as Figure 13 As shown, however, it is often useful to first determine the region of interest using wide frequency range impedance measurements in a non-time resolved manner, as shown here.

[0159] Time-resolved data on the picosecond timescale provide insights into how site-to-site hopping is affected by screening on a local scale, which, to our knowledge, has never been demonstrated before and will extend existing knowledge on how the unique local structure of hopping channels collectively influences ion conduction.

[0160] d. Non-time-resolved laser-driven impedance using a commercial impedance analyzer

[0161] Compared with the non-time-resolved method, the impedance change caused by the above UV excitation in the time-resolved case is again demonstrated, as shown in Figure 14. Figure 14a) and grain boundary characteristics ( Figure 7b ) and the corresponding Nyquist Figure 1 The capacitance values ​​corresponding to the grain boundary and bulk hopping states (R GB and R Bulk ) of the R value. Figures 14c to 14e The UUV power in the plot is the final R extracted from the fit GB and R Bulk , demonstrating that the measured impedance change is linearly proportional to the power. The sequential shift toward decreasing impedance upon increasing the UV light average power suggests that the screening effect promotes facile ion conduction, which mirrors the results previously described in Section II.

[0162] As indicated in the first example, lamps and incoherent light sources can be used instead without the need for specialized optical knowledge or the cost of ultrafast lasers, given that the sample is thermally normalized, as Figure 7b Photomodulation spectroscopy has been used in many applications, including fast charging in batteries. 35 and modulated ion hopping 34,41 , and it is believed that the measurements described in this paper can be used to study charge transfer systems.

[0163] Specifically, the differences in the enhancement ratios between the hopping time regimes across a wide frequency range show how each regime behaves very differently and how the use of spectroscopy described here can be used to explore unique couplings that have been predicted to influence ion mobility. By comparing the relative enhancement rates of a range of targeted ion-phonon, ion-electron, and ion-ion excitations in different hopping states, the role of coupling in the ionic conduction mechanism is revealed, paving the way for the directed design of supersonic conductors.

[0164] Device and method embodiments

[0165] Figure 16 A method of making a spectrometer system is illustrated, 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).

[0166] Illustrative embodiments of devices, systems, or apparatuses (block 1510) made according to the methods described herein (or other methods) include, but are not limited to, the following (see also Figures 1 to 18 ).

[0167] 1. A spectrometer 100 (or a device, system, or apparatus for performing spectral analysis), comprising:

[0168] a source 102 of electromagnetic radiation 102a comprising one or more first frequencies;

[0169] a source 104 of an input signal 104a comprising an alternating current (AC) electric field and comprising one or more second frequencies;

[0170] Control circuitry 106, 1700, operatively connected to sources 102, 104, for synchronizing (or configuring, configurable, and / or being programmed to synchronize) the application of electromagnetic radiation and the application of the AC electric field to the sample such that an output signal comprising a modulated alternating electric field (e.g., an AC signal comprising an electric field or voltage signal) is output from the sample in response to:

[0171] The one or more second frequencies are tuned to drive ion hopping between ion sites in the sample, and

[0172] The one or more first frequencies are tuned to drive excitation of sample-ion interactions;

[0173] a detection system 112, 1914 operably connected to a sample holder for the sample, or positioned to measure and / or detect (or configured to measure and / or detect) a change in an output signal in response to electromagnetic radiation; and

[0174] A computer 114, 1700, operably connected to the detection system, is configured to determine at least one of conductivity or impedance of the sample based on the output signal and as a function of the first frequency and the second frequency.

[0175] 2. The spectrometer of embodiment 1, wherein the control circuit 106 controls or is configured to control, or further includes a control circuit for controlling:

[0176] sweeping a first frequency over a first range to drive excitation of electrons, ions, and / or phonons in a sample 108 comprising an electrolyte, and

[0177] The second frequency is swept over a second range such that the input signal drives ion hopping in the electrolyte on various ion migration time scales.

[0178] 3. The spectrometer of embodiment 1 or embodiment 2, wherein the computer 114 determines or is configured to / programmed to determine changes in conductivity at one or more second frequencies associated with migration time scales in different ion hopping regions in the electrolyte 310, the different ion hopping regions including the contact region 300, the grain boundary 400, and the bulk 308 region.

[0179] 4. The spectrometer of any of embodiments 1 to 3, wherein electrolyte 310 comprises a solid electrolyte for a battery.

[0180] 5. The spectrometer of any of embodiments 1 to 4, wherein the sample comprises an electrical contact to a solid electrolyte comprising lithium ions for a lithium ion battery.

[0181] 6. The spectrometer of any embodiment 1 to 5, wherein the computer determines (or is configured / programmed to determine) a Hamiltonian of the sample from the output signal, the Hamiltonian describing the interaction between excitations stimulated by the electromagnetic radiation and jumps driven by the input signal.

[0182] 7. The spectrometer of any of embodiments 1 to 6, wherein the source of electromagnetic radiation comprises a pulsed or continuous wave laser 118 that outputs a first frequency in a range between ultraviolet (UV) frequencies and terahertz (THz) frequencies (e.g., but not limited to, frequencies corresponding to 100 nm ≤ wavelength ≤ 3 mm).

[0183] 8. The spectrometer of any of embodiments 1 to 7, wherein the electromagnetic radiation source comprises a lamp for outputting electromagnetic radiation.

[0184] 9. The spectrometer of any embodiment 1 to 8, wherein the source of the input signal comprises a signal generator 120, for example, outputting a second frequency f1 in the range of 1 Hz to 1 THz or 1 Hz to 100 GHz (1 Hz ≤ f2 ≤ 100 GHz or 1 Hz ≤ f ≤ 100 THz).

[0185] 10. The spectrometer of any embodiment 1 to 9, wherein the detection system measures or is configured to measure changes in conductivity on a time scale of an excitation driven by electromagnetic radiation.

[0186] 11. The spectrometer of any embodiment 1 to 10, wherein the electromagnetic radiation source comprises a pulsed laser for outputting or being configured to output pulses of electromagnetic radiation having a full width at half maximum (FWHM) of 10 picoseconds (ps), or having a FWHM in a range of less than (e.g., 1 picosecond (fs) - 1 nanosecond (ns) or 1 fs - 10 ps, ​​1 fs ≤ FWHM ≤ 1 ns or 1 fs ≤ FWHM ≤ 10 ps), and the detection system comprises circuitry for measuring the change with a temporal resolution of an envelope of the FWHM.

[0187] 12. The spectrometer of any of embodiments 1 to 11, wherein the first frequency comprises a terahertz frequency.

[0188] 13. The spectrometer of any of embodiments 1 to 12, further comprising a sample holder 1100 for holding a sample, wherein the sample holder comprises:

[0189] a vertical launch connector 1102 for physically connecting to the microstrip on the sample;

[0190] a metal plate 1104 comprising at least one opening 1112 for inserting a sample and coupling electromagnetic radiation into the sample; and

[0191] A fastener 1106 (eg, a pin) is used to fasten the sample between the vertical launch connector and the metal plate so that the input signal is transmitted from the vertical launch connector to the microstrip, and the reflected input signal (including the output signal) is output from the microstrip to the vertical launch connector.

[0192] 14. The spectrometer of embodiment 13 further comprises a directional coupler 1108, wherein the directional coupler vertically transmits the connector:

[0193] a second source coupled to the input signal via a first coaxial cable 1100; and

[0194] The second coaxial cable 1112 is coupled to the detection system.

[0195] 15. The spectrometer of any embodiment 1 to 14, further comprising a time-resolved vector network analyzer, wherein the second source of the input signal comprises a signal generator, and the detection system comprises an oscilloscope triggered by a photodiode that detects electromagnetic radiation.

[0196] 16. The spectrometer of any embodiment 1 to 15, wherein the detection system measures and / or detects, or is configured to measure and / or detect, changes in measurement over the time scale of application of the electromagnetic radiation without time resolution of the circuit, and the computer determines the conductivity using normalization to exclude steady-state heating contributed by the input signal and for samples comprising thin films.

[0197] 17. The spectrometer of any embodiment 1 to 16, wherein the detection system includes an IQ demodulator coupled to a photodetector that detects or is configured to detect electromagnetic radiation, such that the amplitude and phase (current and voltage) of an output signal can be measured / detected using the IQ demodulator, and the output signal is associated with a temporal resolution for changing the temporal envelope of the electromagnetic radiation, where I represents the in-phase component of the signal and Q represents the quadrature-phase component.

[0198] 18. The spectrometer of any embodiment 1 to 17, wherein the detection system measures and / or detects the output signal, or is configured to measure and / or detect the output signal, to determine a change in the complex impedance of the sample, and the computer determines, or is configured / programmed to detect, the conductivity based on the complex impedance.

[0199] 19. The spectrometer of any of embodiments 1 to 18, wherein the detection system comprises an impedance analyzer.

[0200] 20. The spectrometer of any of embodiments 1 to 19, further comprising a vector network analyzer 1110 comprising an input signal source and a detection system.

[0201] 21. The spectrometer of any embodiment 1 to 20, further comprising at least one of an electromagnetic radiation source, an input AC signal source (e.g., a signal generator), or a VNA comprising a control circuit 106, wherein the control circuit comprises a trigger output, a clock circuit or a clock output, or a synchronization circuit that outputs a signal for synchronizing the electromagnetic radiation source and the input AC signal source.

[0202] 22. The spectrometer of any embodiment 1 to 21, wherein the control circuit includes a synchronization circuit and / or a divider circuit that divides the repetition rate of the electromagnetic radiation pulses into a low frequency signal for triggering or controlling the AC source to output the input AC signal, and the detection system (e.g., an oscilloscope) for measuring the output signal.

[0203] 23. The spectrometer of any of embodiments 1 to 22, wherein the control circuit and / or computer comprises an application specific integrated circuit (ASIC) or integrated circuit, or a processor for executing one or more programs stored on a memory.

[0204] 24. The spectrometer of any of embodiments 1 to 23, wherein the electromagnetic radiation source comprises a laser or a lamp.

[0205] 25. The spectrometer of any embodiment 1 to 24, wherein the detection system comprises an oscilloscope and / or a detector and / or a vector network analyzer capable of detecting the output signal.

[0206] 26. The spectrometer of any of embodiments 1 to 25, wherein the detection system 112 includes or comprises an AC electric 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 matching the detector to the sample impedance. These components can be selected or configured to detect homodyne, heterodyne, amplitude modulated (AM), or frequency modulated (FM) signals. The detector can also include a coaxial cable input 1908 or a microstrip or transmission line for receiving the AC signal from the sample.

[0207] 27. The spectrometer of any of embodiments 1 to 25, wherein the detection system is a detector comprising at least one of an amplitude detection circuit / circuit 1906, a phase-locked loop circuit / circuit 1902, an impedance matching circuit / circuit 1900, and / or an IQ demodulation circuit / circuit 1904. In various embodiments, these circuits are optionally selected or configured to detect (e.g., output signals comprising) homodyne, heterodyne, amplitude modulated (AM), or frequency modulated (FM) signals. Optionally, the detector further comprises a coaxial cable input 1900 or a microstrip or transmission line for receiving an AC signal from the sample.

[0208] 28. The spectrometer of embodiment 26 or 27, comprising a lock-in amplifier in a VNA, oscilloscope or impedance analyzer, comprising at least one of a detector or amplitude detector, an IQ modulator or a PLL (phase locked loop).

[0209] 29. The spectrometer of embodiment 27 or 28 further includes a photodetector (e.g., a photodiode) for detecting electromagnetic radiation, such that the amplitude and phase (current and voltage) of the output signal can be measured using the detector and associated with the time resolution to change the temporal envelope of the electromagnetic radiation.

[0210] 30. A method for measuring electrical conductivity (e.g. Figure 16 shown), including:

[0211] irradiating 1600 a region of the sample with electromagnetic radiation comprising one or more first frequencies;

[0212] applying 1602 an input signal to a region, the input signal comprising an alternating current (AC) electric field and comprising one or more second frequencies such that the electromagnetic radiation and the input signal are applied synchronously;

[0213] Measuring 1604 and / or detecting a modulated output signal comprising an AC electric field in response to:

[0214] The one or more second frequencies are tuned to drive ion hopping between sites in the sample, and

[0215] The one or more first frequencies are tuned to drive excitation of the region to interact with ions; and

[0216] The conductivity of the sample is determined (eg, calculated) 1606 from the output signal and as a function of the first frequency and the second frequency.

[0217] 31. The method or spectrometer of any of embodiments 1-29, wherein the sample comprises any material system (biological or non-biological) that conducts ions.

[0218] 32. In one embodiment, including any of embodiments 1 to 30, the method comprises a laser-driven ultrafast impedance method that can directly measure bulk ionic conduction on a picosecond timescale based on subcomponents of the ion-hopping Hamiltonian. This technique exploits the advantages of communication-based signal generators and oscilloscope-based AC impedance measurements to over 100 GHz. These frequencies are comparable to picosecond ion hopping in site-to-site states, although lower frequencies can certainly be used to measure other hopping states, such as at grain boundaries. Using these electronics, the time-resolved change in impedance is then measured as a function of a picosecond pulsed drive laser that sweeps from UV to THz. Within this frequency range, energy gaps are set for the subcomponents of the entire ion-hopping Hamiltonian. For example, UV can photoexcite charge transfer transitions to modulate electrostatic blocking of ion channels or generate nonequilibrium carrier distributions to modulate screening effects. Near-infrared to THz light can be used to resonantly excite optical phonons or rocking and paddlewheel modes. Phonon modes can be selected by anharmonic or Raman interactions, or simply heated incoherently as a reference channel. Comparing the amplitudes of these perturbations maps the relative contribution of each subcomponent to the bulk ion hopping, while comparing the temporal decays provides insight into correlation and memory effects.

[0219] 33. A version of the instrument was also described and tested that still maps the ion-hopping Hamiltonian, but at the expense of temporal resolution. This second version actually doesn't even require an ultrafast laser and could therefore be used as a form of action spectroscopy for battery characterization experiments. This technique would then be suitable for rapidly comparing material modifications, such as doping or grain size, for a given material.

[0220] 34. The spectrometer of 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, wherein the application is executed by the one or more processors to determine impedance and / or conductivity.

[0221] 35. The spectrometer of any embodiment 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, wherein the application is executed by the one or more processors to achieve the synchronization or output a signal for synchronization.

[0222] In these examples (eg, Examples 1 to 35), the term "spectrometer" may be replaced with device, system, or apparatus.

[0223] 30. A system 100 comprising:

[0224] a source 102 of electromagnetic radiation 102a comprising one or more first frequencies;

[0225] a source 104 of an input signal 104a comprising an alternating current (AC) electric field and comprising one or more second frequencies;

[0226] A synchronization circuit or means for synchronization 106, 1700, operatively connected to the sources 102, 104, for synchronizing the application of electromagnetic radiation and the application of the alternating electric field to the sample such that an output signal comprising a modulated AC electric field is output from the sample in response to:

[0227] The one or more second frequencies are tuned to drive ion hopping between ion sites in the sample, and

[0228] The one or more first frequencies are tuned to drive excitation of sample-ion interactions;

[0229] a detector or detector means or means for detecting 112 operatively connected to said sample holder for said sample or positioned for measuring and / or detecting changes in said output signal (e.g., an AC signal comprising an electric field or voltage signal) in response to said electromagnetic radiation; and

[0230] A computer or computing unit or computer unit 114, 1700, operatively connected to the detection system, is configured to determine at least one of conductivity or impedance of the sample based on the output signal and in dependence on the first frequency and the second frequency.

[0231] 31. The system of embodiment 30, wherein the means for synchronizing and the means for detecting comprise the apparatus described herein and their equivalents.

[0232] 32. The system of embodiment 30 or 31, further comprising any one of embodiments 1 to 29.

[0233] 33. The system, spectrometer, or method of any embodiment 1 to 32, wherein the detector or detection system 1914 includes an input terminal 1918 for receiving a trigger or synchronization signal, or is connected to at least one of the synchronization circuit / control circuit 106, 1912, or photodetector of electromagnetic radiation that outputs the trigger or synchronization signal.

[0234] 34. The system or spectrometer of any of embodiments 1 to 33, wherein:

[0235] The connection 124 between the control circuit or synchronization circuit and the source is wired (eg, including cables, coaxial cables, or transmission lines for transmitting electrical signals) or wireless.

[0236] The connection 120 between the detector and the sample is wired (eg, comprising an electrical cable, coaxial cable, or transmission line for transmitting electrical signals) or wireless.

[0237] The connection 122 between the detector 1102, 1914 and the computer 114, 1700 is wired (eg, including an electrical cable, coaxial cable, or transmission line for transmitting electrical signals) or wireless.

[0238] 35. The system or spectrometer of any embodiment 1 to 34, wherein the output signal and the input signal comprise an AC electric field or voltage, the amplitude and / or phase of which can be measured by the detector 1914.

[0239] Hardware environment

[0240] Figure 17 1700 (referred to as a computer-implemented system and / or computer-implemented method) for implementing one or more embodiments of the present invention and may be used as control circuitry or 106 or computer 114 in one or more embodiments. The hardware and software environment includes a computer 1702 and may include peripheral devices. Computer 1702 may be a user / client computer, a server computer, or a database computer. Computer 1702 includes a hardware processor 1704A and / or a dedicated hardware processor 1704B (hereinafter collectively referred to as processor 1704) and memory 1706, such as random access memory (RAM). Computer 1702 may be coupled 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 include a multi-touch device, mobile phone, or other Internet-enabled device that executes on various platforms and operating systems.

[0241] In one embodiment, computer 1702 executes instructions defined by a computer program 1710 (e.g., a conductivity calculation, control, or Hamiltonian calculation application) by a hardware processor 1704A under the control of an operating system 1708. The computer program 1710 and / or the operating system 1708 may be stored in memory 1706 and may interface with a user 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 the computer program 1710 and the operating system 1708.

[0242] The output / results may be presented on a display 1722 or provided to another device for presentation or further processing or action. Images may be provided by a graphical user interface module 1718. Although the graphical user interface module 1718 is depicted as a separate module, the instructions for performing the graphical user interface functionality may reside or be distributed within the operating system 1708, the computer program 1710, or implemented using dedicated memory and processors.

[0243] In one or more embodiments, the display 1722 is integrated with / integrated into the computer 1702 and includes a multi-touch device having a touch sensing surface (e.g., a track box or a touch screen) that has the ability to recognize that there are two or more points of contact with the surface.

[0244] Some or all of the operations performed by the computer 1702 according to the computer program 1710 instructions can be implemented in a special-purpose processor 1704B. In this embodiment, some or all of the computer program 1710 instructions can be implemented by firmware instructions stored in a read-only memory (ROM), a programmable read-only memory (PROM), or a flash memory within the special-purpose processor 1704B or within the memory 1706. The special-purpose processor 1704B can also be hard-wired to perform some or all of the operations to implement the present invention through circuit design. In addition, the special-purpose processor 1704B can be a hybrid processor that includes dedicated circuits for performing a subset of functions, as well as other circuits for performing more general functions such as responding to computer program 1710 instructions. In one embodiment, the special-purpose processor 1704B is an application-specific integrated circuit (ASIC) or a field-programmable gate array (FPGA).

[0245] The computer 1702 may also implement a compiler 1712 that allows an application or computer program 1710 written in a programming language such as C, C++, assembly, SQL, Python, Prolog, MATLAB, Ruby, Rails, Haskell, or other language to be translated into processor 1704 readable code. Alternatively, the compiler 1712 may be an interpreter that directly executes instructions / source code, translates source code into an intermediate representation for execution, or executes stored precompiled code. Such source code may be written in various programming languages ​​such as Java, JavaScript, Perl, BASIC, etc. Upon completion, the relationships and logic used by the application or computer program 1710 (generated using the compiler 1712) access and manipulate data received from I / O devices and stored in the memory 1706 of the computer 1702.

[0246] Computer 1702 may also optionally include external communication devices such as a modem, satellite link, Ethernet card, or other device for accepting input from other computers 1702 and providing output to other computers 1702 .

[0247] In one embodiment, the instructions for implementing the operating system 1708, computer program 1710, and compiler 1712 are tangibly embodied in a non-transitory computer-readable medium (e.g., 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. Furthermore, the operating system 1708 and computer program 1710 consist of computer program 1710 instructions that, when accessed, read, and executed by the computer 1702, cause the computer 1702 to perform the steps required to implement and / or use the present invention or to load the instruction program into the memory 1706, thereby generating special-purpose data structures that cause the computer 1702 to operate as a specially programmed computer that performs the method steps described herein. The computer program 1710 and / or operating instructions may also be tangibly embodied in the memory 1706 and / or data communication device 1730, thereby creating a computer program product or article of manufacture according to 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.

[0248] Of course, those skilled in the art will recognize that any combination of the above components, or any number of different components, peripherals, and other devices, may be used with the computer 1702 .

[0249] Figure 18 A typical distributed / cloud-based computer system 1800 is schematically shown using a network 1804 to connect client computers 1802 to server computers 1806. A typical combination of resources may include the network 1804, which includes the Internet, a LAN (local area network), a WAN (wide area network), an SNA (system network architecture) network, etc., as well as a personal computer or workstation (such as Figure 17 As shown) client 1802, and as a personal computer, workstation, small computer, main frame (such as Figure 17 However, it may be noted that different networks such as a cellular network (e.g., GSM (Global System for Mobile Communications) or other), a satellite-based network, or any other type of network may be used to connect the client 1802 and the server 1806 according to embodiments of the present invention.

[0250] A network 1804, such as the Internet, connects the client 1802 to the server computer 1806. The network 1804 can utilize Ethernet, coaxial cable, wireless communication, radio frequency (RF), etc. to connect and provide communication between the client 1802 and the server 1806. In addition, in a cloud-based computing system, resources (e.g., storage, processors, applications, memory, infrastructure, etc.) in the client 1802 and server computer 1806 can be shared by the client 1802, the server computer 1806, and users across one or more networks. Resources can be shared by multiple users and can be dynamically reallocated based on demand. In this regard, cloud computing can be referred to as a model for allowing access to a shared pool of configurable computing resources.

[0251] Client 1802 can execute a client application or web browser and communicate with server computer 1806 executing web server 1810. Such web browsers are typically programs such as Microsoft Internet Explorer / Edge, Mozilla FireFox, Opera, Apple Safari, Google Chrome, and the like. Furthermore, software executing on client 1802 can be downloaded from server computer 1806 to client computer 1802 and installed as a web browser plug-in or ActiveX control. Thus, client 1802 can utilize ActiveX components / Component Object Model (COM) or Distributed COM (DCOM) components to provide a user interface on the display of client 1802. Web server 1810 is typically a program such as Microsoft's Internet Information Server.

[0252] Web server 1810 can host an Active Server Pages (ASP) or Internet Server Application Programming Interface (ISAPI) application 1812 that can execute scripts. The scripts call objects (referred to as business objects) that implement business logic. The business objects then manipulate data in database 1816 via a database management system (DBMS) 1814. Alternatively, database 1816 can be part of client 1802 or directly connected to client 1802, rather than communicating with / retrieving information from database 1816 via network 1804. When developers encapsulate business functionality into objects, the system can be referred to as a Component Object Model (COM) system. Thus, scripts executed on web server 1810 (and / or application 1812) call COM objects that implement business logic. Furthermore, server 1806 can utilize Microsoft's Transaction Server (MTS) to access required data stored in database 1816 via interfaces such as ADO (Active Data Objects), OLEDB (Object Linking and Embedding), or ODBC (Open Database Connectivity).

[0253] In general, these components 1800-1816 all include logic and / or data embodied in or retrievable from a device, medium, signal, or carrier wave, such as a data storage device, a data communications device, a remote computer or a device coupled to a computer via a network or via another data communications device, etc. Furthermore, this logic and / or data, when read, executed, and / or interpreted, causes the execution of steps necessary to implement and / or use the present invention.

[0254] Although reference is made herein to the terms "user computer," "client computer," and / or "server computer," it will be understood that such computers 1802 and 1806 may be interchangeable and may further include thin client devices having limited or full processing capabilities, such as cellular telephones, notebook computers, pocket computers, multi-touch devices, and / or any other device having appropriate processing, communication, and input / output capabilities.

[0255] Of course, those skilled in the art will recognize that any combination of the above components, or any number of different components, peripherals, and other devices, may be used with computers 1802 and 1806. Embodiments of the present invention are implemented as a software / CAD application on a client 1802 or server computer 1806. Furthermore, as described above, the client 1802 or server computer 1806 may comprise a thin client device or a portable device with a multi-touch based display.

[0256] Advantages and improvements

[0257] In pump-probe spectroscopy, ultrafast laser pulses induce rare near-equilibrium events that fit the description of thermally activated ion hopping. However, the technique presented here needs to be clearly distinguished from standard pump-probe spectroscopy. Unlike previous pump-probe iterations, the illustrative embodiment of our technique does not attempt to directly trigger or induce ion conduction using ultrafast laser pulses and then measure changes in DC current, voltage, or some other metric (such as diffraction). Instead, a high-frequency AC electric field is used to constantly and cyclically drive ion hopping within a sample (e.g., a solid-state electrolyte). An ultrafast laser is then used to perturb the various subsystems (electronics, vibrational modes, displacement fields) that modulate the ion hopping process. Changes in the amplitude and phase of the AC electric field represent changes in bulk impedance or conductivity caused by this perturbation. In our tests, measuring perturbations to the AC electric field proved key to success because it overcomes the problems of trying to create ultrafast DC electric fields that generate ion motion in the device without having to worry about battery charge and discharge cycling. It also avoids the problems of simply trying to measure ion hopping by measuring the lifetime of the photoexcited perturbation and assuming its dynamics match those of bulk ion hopping.

[0258] Our data demonstrate that the laser-driven impedance method can be used to measure the relative contributions of different components of the many-body ion-hopping Hamiltonian through frequency-selective perturbations. For example, by directly driving high-contribution phonon modes, we measured a 10-fold enhancement in ion migration relative to incoherent heating. This result is consistent with ab initio calculations, validating its application in exploring phonon-mediated hopping. The method demonstrated here will aid in the design of future solid-state electrolytes and other ion-hopping materials driven by vibrational modes. These results also hint at the potential of metastable photoinduced states for ion transport, which will lead to new applications and science.

[0259] In addition, the laser-driven ultrafast impedance technique proposed in this paper can directly measure ion hopping on picosecond and longer time scales, and compare the absolute and relative effects of ion coupling to phonons, electrons and other ions. Because this technique overcomes the challenges of other ultrafast time-resolved methods by using the laser as a probe in AC measurements, rather than using the laser as a pump source to initiate ion conduction, this method ensures that the generated transient or signal directly probes ion conduction. Although this study focuses on a Li-ion with low contribution to electronic conductivity, +conductors, but extension to mixed ion-electron conducting systems or any solid or polymer ionic conductors is clearly possible. Furthermore, cost-effective photomodulation or action spectroscopy-like methods offer a more laboratory-friendly route to probing complex ionic couplings, utilizing cost-effective light sources such as high-power, broad-spectrum lamps with monochromators. Even if the temporal information about coupling and correlation is lost, the relative contributions of different electronic and vibrational interactions can still be compared.

[0260] References

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[0436] Further information regarding one or more embodiments of the present invention can be found in references 38-39.

[0437] in conclusion

[0438] This summarizes 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 description. The present invention is not intended to be exhaustive or limited to the precise forms disclosed. Many modifications and variations are possible in light of the above teachings. The scope of the present invention is not limited by this detailed description, but is defined by the appended claims.

Claims

1. A system comprising: a first source of electromagnetic radiation (EM) comprising one or more first frequencies; a second source of input signals comprising an alternating current (AC) electric field and comprising one or more second frequencies; a control circuit connected to the first source and the second source for synchronizing the application of the electromagnetic radiation and the AC electric field to the sample so that an output signal comprising the modulated AC electric field is output from the sample in response to: The one or more second frequencies are tuned to drive ion hopping between ion sites in the sample, and The one or more first frequencies are tuned to drive excitation that interacts with ions in the sample; a detection system positioned to measure and / or detect changes in said output signal in response to said electromagnetic radiation; and A computer, connected to the detection system, is configured to determine at least one of conductivity or impedance of the sample based on the output signal and as a function of the first frequency and the second frequency.

2. The spectrometer according to claim 1, wherein The control circuit controls or further includes a control circuit for controlling: sweeping the first frequency over a first range to drive excitation of electrons, ions and / or phonons in the sample comprising an electrolyte, and The second frequency is swept over a second range such that the input signal drives ion hopping in the electrolyte on various ion migration time scales.

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

4. The system according to claim 3, wherein: The electrolyte includes a solid electrolyte for a battery.

5. The system according to claim 4, wherein: The sample includes electrical contacts to the solid electrolyte, which includes lithium ions for use in a lithium-ion battery.

6. The system according to claim 1, wherein: The computer determines or is programmed to determine a Hamiltonian for the sample from the output signal, the Hamiltonian describing the interaction between excitations stimulated by the electromagnetic radiation and jumps driven by the input signal.

7. The system according to claim 1, wherein: The first source of electromagnetic radiation comprises a pulsed or continuous wave (CW) laser configured to output the first frequency in a range between ultraviolet (UV) frequencies and THz.

8. The system according to claim 1, wherein: The first source of electromagnetic radiation comprises a lamp for outputting electromagnetic radiation.

9. The system according to claim 1, wherein: The second source of the input signal includes a signal generator configured to output the second frequency in the range of 1 Hz to 1 THz.

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

11. The system according to claim 1, wherein: The first source of electromagnetic radiation comprises a pulsed laser for outputting pulses of the electromagnetic radiation, the pulses having a full width at half maximum (FWHM) of 1 nanosecond or less, and the detection system comprises circuitry for measuring the changes with a temporal resolution of an envelope of the FWHM.

12. The system according to claim 1, wherein: The first frequency comprises a terahertz frequency.

13. The system of claim 1 , further comprising a sample holder for holding the sample, wherein the sample holder comprises: a vertical launch connector, which is used to physically connect to the microstrip on the sample; a metal plate comprising at least one opening for inserting the sample and coupling the electromagnetic radiation into the sample; and A fastener is used to fasten the sample between the vertical launch connector and the metal plate so that the input signal is transmitted from the vertical launch connector to the microstrip and the reflected input signal (including the output signal) is output from the microstrip to the vertical launch connector.

14. The system of claim 13, further comprising a directional coupler that couples the vertical launch connector: a second source coupled to the input signal via a first coaxial cable; and coupled to the detection system via a second coaxial cable.

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

16. The system of claim 1, wherein: The detection system measures or includes circuitry for measuring the change without time resolution over the time scale of application of the electromagnetic radiation, and the computer is programmed to determine the conductivity using normalization to exclude steady-state heating contributed by the input signal and for the sample comprising a thin film.

17. The system of claim 1, wherein: The detection system comprises an IQ demodulator coupled to a photodetector for detecting the electromagnetic radiation such that the amplitude and phase (current and voltage) of the output signal can be measured using the IQ demodulator and the output signal is correlated to the temporal resolution of changes in the temporal envelope of the electromagnetic radiation.

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

19. The system of claim 1, wherein: The detection system includes an impedance analyzer.

20. A method for measuring electrical 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 and comprising one or more second frequencies such that the electromagnetic radiation and the input signal are applied synchronously; measuring and / or determining an output signal comprising the modulated AC electric field in response to: The one or more second frequencies are tuned to drive ion hopping between sites in the sample, and The one or more first frequencies are tuned to drive excitations that interact with ions in the region; and determining the conductivity of the sample based on the output signal and as a function of the first frequency and the second frequency.

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