WO2019070523A1 - Confirmation of gas loading induced defects by complex impedance spectroscopy - Google Patents

Abstract

A method of determining whether a conduction mode is present in a sample by complex impedance spectroscopy includes: setting a sample at a first temperature; establishing a first steady state of the sample at the first temperature; obtaining a first complex impedance spectrum; calculating one or more first resistance value from the first complex impedance spectrum; setting the sample at a second temperature; establishing a second steady state of the sample at the second temperature; obtaining a second complex impedance spectrum; calculating one or more second resistance value from the second complex impedance spectrum; determining a function that relates the first and second resistance values to the first and second temperatures respectively; calculating at least one slope of the determined function; calculating at least one activation energy using the at least one calculated slope; determining whether a conduction mode is present in the sample based on the calculated activation energy.

Description

Confirmation of Gas Loading Induced Defects by Complex Impedance Spectroscopy

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority of U.S. provisional patent application no.

62/567,952, titled "Confirmation of Gas Loading Induced Defects by Complex Impedance

Spectroscopy," filed on October 4, 2017, which is incorporated herein in its entirety by this reference.

TECHNICAL FIELD

[0002] Descriptions herein relate to quantifying of loading of gaseous species onto solid material, and more particularly to the use of impedance spectroscopy to quantify adsorption and absorption of gases into solid materials for many applications including fuel cells, catalysis, and exothermic reactions.

BACKGROUND

[0003] The loading of hydrogen, any isotope thereof, into a solid material is an important technology for hydrogen fuel cells and other exothermic reaction devices. The loading of methane into metal-organic frameworks is an important, emerging technology to increase the storage capacity of this fuel source. The loading process must be controllable, quantifiable and sustainable to be repeatable and production-worthy.

[0004] The primary previously existing modalities for measuring such loading are mass change, pressure change, and/or some means of calculating the number of gas molecules which are no longer in the gas phase and therefore adsorbed on or absorbed into a solid sample. Changes in resistance are occasionally used after the resistance has been calibrated against mass change.

[0005] Some problems with previous approaches include that neither mass change nor pressure change is practical for materials which are to be loaded and activated in a continuous process. A scale cannot be implemented in a reactor. High accuracy pressure change analysis instrumentation is also very difficult to implement in a multipurpose system. The resistance measurements are either AC at a single frequency or DC. These resistance values cannot be correlated with their conduction paths.

SUMMARY

[0006] This summary is provided to introduce in a simplified form concepts that are further described in the following detailed descriptions. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it to be construed as limiting the scope of the claimed subject matter.

[0007] In at least one embodiment, a method of determining whether a conduction mode is present in a sample by complex impedance spectroscopy includes: setting a sample at a first temperature; establishing a first steady state of the sample at the first temperature; obtaining a first complex impedance spectrum; calculating one or more first resistance value from the first complex impedance spectrum; setting the sample at a second temperature; establishing a second steady state of the sample at the second temperature; obtaining a second complex impedance spectrum; calculating one or more second resistance value from the second complex impedance spectrum; determining a function that relates the first and second resistance values to the first and second temperatures respectively; calculating at least one slope of the determined function; calculating at least one activation energy using the at least one calculated slope; determining whether a conduction mode is present in the sample based on the calculated activation energy.

[0008] Establishing a first steady state of the sample at the first temperature may include establishing an isothermal and isobaric state.

[0009] The first resistance value may be determined by determining at least one axis intercept in the first complex impedance spectrum.

[00010] The second resistance value may be determined by determining at least one axis intercept in the second complex impedance spectrum.

[00011] Determining a function that relates the first and second resistance values to the first and second temperatures may include determining ln(l/R) as a function of 1/T, wherein R is resistance and T is the absolute temperature of the sample. In at least example:

1/R = B exp(-E_c/kT);

E_c is the activation energy of conductance (eV);

k is Boltzmann's Constant = 8.1673E-5 eV/K; and

B is a constant.

[00012] Calculating at least one activation energy using the at least one calculated slope may include relying on ln(l/R) as a function of 1/T having a slope of -E_c/k.

[00013] Determining whether a conduction mode is present in the sample based on the calculated activation energy may include detecting electronic conduction along grain boundaries.

[00014] The sample may be a defect free sample.

[00015] Determining whether a conduction mode is present in the sample based on the calculated activation energy may include detecting electronic conduction through bulk grains in the sample.

[00016] Determining whether a conduction mode is present in the sample based on the calculated activation energy may include detecting ionic conduction of hydrogen or deuterium ions along grain boundaries in the sample.

[00017] Determining whether a conduction mode is present in the sample based on the calculated activation energy may include detecting ionic conduction of hydrogen or deuterium ions through the bulk grains.

[00018] The method may include detecting effects of the number of hydrogen or deuterium atoms loaded into a defect free lattice on electronic and ionic conduction.

[00019] The method may include detecting effects of single atom or multi-atom defects on electronic and ionic conduction.

[00020] The method may include detecting the effects density or proximity of single atom or multi-atom defects on electronic and ionic conduction.

[00021] The method may include detecting effects of the number of hydrogen or deuterium atoms loaded into a multi-atom defect on electron and ionic conduction.

[00022] Obtaining a first complex impedance spectrum comprises obtaining electrical measurements using electrodes in electrical communication with the sample.

[00023] The electrodes may be placed on opposite sides of the sample.

[00024] The electrodes may be placed on a same side of the sample to minimize a physical distance of a surface conduction path.

[00025] Obtaining a first complex impedance spectrum may include applying alternating current perturbations to the sample over a frequency range. The frequency range may be about from 1 Hz to at least 10 MHz.

BRIEF DESCRIPTION OF THE DRAWINGS

[00026] The previous summary and the following detailed descriptions are to be read in view of the drawings, which illustrate particular exemplary embodiments and features as briefly described below. The summary and detailed descriptions, however, are not limited to only those embodiments and features explicitly illustrated.

[00027] FIG. 1 is a schematic representation of a measurement apparatus for determining electrical impedance parameters of a crystal structure sample.

[00028] FIG. 2 is a plot for demonstration purposes of an expected complex impedance spectra of the crystal structure represented in FIG. 1.

[00029] FIG. 3 is a diagram of an electric circuit model equivalent to the complex impedance spectra of FIG. 2.

[00030] FIG. 4 is another plot of complex impedance spectra for demonstration purposes.

[00031] FIG. 5 is a flowchart representing a method, according to at least one embodiment, for using CIS to confirm the presence of a defect by detecting a correlated conduction mode.

DETAILED DESCRIPTIONS

[00032] These descriptions are presented with sufficient details to provide an understanding of one or more particular embodiments of broader inventive subject matters. These descriptions expound upon and exemplify particular features of those particular embodiments without limiting the inventive subject matters to the explicitly described embodiments and features. Considerations in view of these descriptions will likely give rise to additional and similar embodiments and features without departing from the scope of the inventive subject matters. Although the term "step" may be expressly used or implied relating to features of processes or methods, no implication is made of any particular order or sequence among such expressed or implied steps unless an order or sequence is explicitly stated.

[00033] Any dimensions expressed or implied in the drawings and these descriptions are provided for exemplary purposes. Thus, not all embodiments within the scope of the drawings and these descriptions are made according to such exemplary dimensions. The drawings are not made necessarily to scale. Thus, not all embodiments within the scope of the drawings and these descriptions are made according to the apparent scale of the drawings with regard to relative dimensions in the drawings. However, for each drawing, at least one embodiment is made according to the apparent relative scale of the drawing.

[00034] Like reference numbers used throughout the drawings depict like or similar elements.

Unless described or implied as exclusive alternatives, features throughout the drawings and

descriptions should be taken as cumulative, such that features expressly associated with some particular embodiments can be combined with other embodiments.

[00035] In various embodiments, complex impedance spectroscopy is used to probe an electrochemical system with a small AC -perturbation over a range of frequencies. This non-destructive approach enables measurement of the impedance of different conduction paths and conducting species in a material. After being calibrated with the presence of a desirable conduction path or species, complex impedance is used as a confirmation or quality control tool.

[00036] The basics of complex impedance spectroscopy (CIS) are available and an

understanding thereof is an assumed precursor to these descriptions according to the knowledge of one or ordinary skill in the arts to which the inventions described herein pertain.

[00037] Two aspects of CIS are of use for measurement of gas loading in solids in embodiments described herein: the measurement of impedance for both ionic and electronic conduction; the measurement of impedance to ions and electrons conducting along different paths.

[00038] Many conduction paths or modes exist in a crystal lattice. Among those paths or modes, along the surface, along grain boundaries, through bulk grains and defect "hopping" are common. A crystal defect is defined as any irregularity in the crystal structure. Grain boundaries are defects since they represent a discontinuity between grains of continuous crystal structure. The term defect is also used to describe a missing atom in a crystal structure. Missing atoms represent openings in a crystal structure by which an ion could "hop" from one to another thereby permitting conduction through a crystal. Thus, each characterized defect can have a correlated conduction mode that can potentially be discerned by CIS.

[00039] CIS methods described herein are able to access the various conduction modes in a crystal structure by AC perturbations over a large frequency range, for example from 1 Hz to at least 10 MHz in at least one embodiment.

[00040] FIG. 1 is a schematic representation of a measurement apparatus 100 for determining electrical impedance parameters of simple crystal structure sample 150 having multiple grains 152. Electrodes 102 and 104 may be placed on opposite sides of the sample 150 as represented in FIG. 1 or on the same side of a sample in other embodiments. Depending upon the size of a sample, having the electrodes on the same side may be advantageous for minimizing the physical distance of the surface conduction path. Note as described above, different frequencies probe different conduction paths. Lower frequencies measure the impedance to conduction along the grain boundaries 154. Higher frequencies measure the impedance to conduction through the grains 152. Respective conducting lines 112 and 114 represent electrical connections to the electrodes 102 and 104 by which voltage and current can be applied and passed across the sample 150 and measurements thereof taken.

[00041] The apparatus 100 may include a housing 110 defining a chamber for containing, isolating, and or pressurizing the sample 150 and electrode arrangement. The chamber may be thermally controlled, for example by way of a thermal element 116, and thus may be thermally isolated from the exterior conditions such that the sample temperature can be set or varied by a controller. One or more fluidic ports may be included for use in establishing gaseous, pressured, or vacuum conditions in the chamber. One or more sensors 118 may be included in pressure and/or thermal communication or other coupling with the sample so chamber and sample conditions can be monitored and controlled. Thus, the one or more sensors 118 can include sensors that monitor temperature, pressure, IR and other light ranges, and chemical species or conditions.

[00042] In FIG. 1, a controller 120 is shown in electrical communication with each of the electrodes 102 and 104 by way of the respective conducting lines 112 and 114. The controller 120 is configured to apply voltage and current across the sample 150 and conduct measurements thereof, for example particularly for CIS, in which a small AC-perturbation is used over a range of frequencies. The controller may also be operatively coupled to the thermal element 116, and the one or more sensors 118, and may be in control of any fluidic ports by which the conditions about the sample 150 are established and controlled.

[00043] FIG. 2 is a plot of an expected complex impedance spectra of the crystal structure of

FIG. 1. Intercepts along the Z' axis represent resistances determined by the plot. For example, in FIG. 2, the first intercept R_b along the Z' axis is bulk grain resistance, whereas the second intercept is R_b+R_gb, in which R_gb is a grain boundary resistance.

[00044] An electric circuit model 300 approximately equivalent to the complex impedance spectra of FIG. 2 is shown in FIG. 3. Crystalline solids typically fit a parallel capacitor and resistor circuit model. In FIG. 3, R_b = bulk grain resistance (as in FIG. 2), C_b = bulk grain capacitance, R_gb = grain boundary resistance (as in FIG. 2), and C_gb = grain boundary capacitance.

[00045] As shown in FIG. 2, the resistance (R) of a conduction path can be taken from the lower frequency by taking the difference between the higher and lower intercepts of the semi-circular spectra with the real impedance (Ζ') axis. For example, assume that the intercepts along the Z' axis of a measured spectra are RA, RB and Rc as shown in FIG. 4. The resistance value which most likely corresponds to the surface or grain boundary resistance (R_gb) is calculated by taking the difference between the values Rc and RB along the Z' axis at the intercepts. The resistance value which most likely corresponds to the bulk resistance (R_b) of the crystalline grains is calculated by taking the difference between RB and RA-

[00046] The trapping or releasing of conducting species from a defect is affected by temperature, so it follows that both ionic and electronic conductivity are affected when crystal defects are present. The change in resistance as a function of temperature may be used to calculate activation energy of a defect as follows. So as not to introduce potential errors via changing sample or electrode dimensions, conductance (as opposed to conductivity) is calculated from Equation (1):

1/R = B exp(-E_c/kT) (1)

where R is resistance,

Ec is the activation energy of conductance (eV),

k is Boltzmann's Constant = 8.1673E-5 eV/K, T is the absolute temperature (K), and

B is a constant.

[00047] Note that a plot of ln(l/R) as a function of 1/T has a slope of -E_c/k allowing calculation of Ec. Accordingly, activation energy (E_c) can be calculated from the slope.

[00048] In one embodiment, physical analysis of samples by methods such as scanning tunneling electron microscopy is used to match defects with conductivity. In another embodiment, an activation energy is matched with an observed sample behavior through repeated experiment. This activation energy can then be used to confirm the presence of a certain type of defect.

[00049] FIG. 5 is a flowchart representing a method 500, according to at least one embodiment, for using CIS to confirm the presence of a defect in sample, of which the sample 150 can serve as a non-limiting example for description and illustration purposes.

[00050] In step 502, a sample temperature is set. For example, in apparatus and/or system embodiments according to FIG. 1, the temperature of the sample 150 may be set and controlled by use of the thermal element 116 operatively coupled to the controller 120.

[00051] In step 504, the sample is allowed to reach steady state. The sample may be monitored to confirm that a steady state has been established. Monitoring of the sample 150 in FIG. 1, for example, can be conducted by way of the one or more sensors 118. Steady state conditions can include stasis in temperature, pressure, chemical species and/or other conditions. Thus, steady state can refer to an isothermal state and/or an isobaric state, and other stabilized or relatively non-varying conditions as well. By reaching steady state, stimulus provided by the electrodes and the collected of CIS data are better correlated in cause and effect relationship.

[00052] In step 506, a complex impedance spectrum (CIS) is obtained, examples of which are shown in FIGS. 2 and 4. For example, the controller 120 (FIG. 1) may apply voltage and current across the sample 150 and conduct measurements thereof, according to CIS techniques, in which a small AC- perturbation is used over a range of frequencies, for example from 1 Hz to at least 10 MHz in at least one embodiment.

[00053] In step 508, resistance values are calculated from the obtained spectrum, for example by determining intercepts as described above in descriptions of FIGS. 2 and 4.

[00054] In step 510, whether resistance values have been obtained at multiple temperatures is determined. As the resistance varies as a function of temperature, multiple temperatures are to established, and respective measurements taken thereof, so as to calculate activation energy by which the defects or sample phenomena of interest are to be discerned.

[00055] Thus, in step 512, if resistance values have not been obtained at multiple temperatures as determined in step 510 ("No"), the sample temperature is increased, and further process of the method 500 returns to step 504. Iterations from step 504 to step 510 repeat (loop) until the determination in step 510 renders an affirmative. Once resistance values have been obtained at multiple temperatures as determined in step 510 ("Yes"), ln(l/R) as a function of l/T(absolute temperature in K) for analogous sets of resistance values is determined and may be plotted.

[00056] In step 516 the slope of the determined function and/or plot is calculated. In step 518, activation energy is calculated from the slope(s). Returning to Equation 1, activation energy (E_c) can be calculated by way of ln(l/R) as a function of 1/T, which has a slope of -E_c/k, thereby allowing calculation of E_c.

[00057] In step 520, a determination is made as to whether the activation energy values suggest the presence of conduction modes and thus the correlated defects, some of which may be desired. Because activation energy can be matched with an observed sample behavior, through experimentation and other analyses such as electron microscopy and other investigation techniques, the nature or presence of defects can be matched or mapped via activation energy determinations so as to confirm the presence of a certain types of conduction modes and their correlated defects.

[00058] While many types of defects, conductivities, and correlated conduction modes are within the scope of these descriptions, examples of phenomena of particular interest for LENR applications include:

Electronic conduction along the grain boundaries in a defect free sample;

Electronic conduction through the bulk grains in a defect free sample;

Ionic conduction of hydrogen or deuterium ions along the grain boundaries in a defect free sample;

Ionic conduction of hydrogen or deuterium ions through the bulk grains in defect free sample; The effects of the number of hydrogen or deuterium atoms loaded into a defect free lattice on electronic and ionic conduction;

The effects of single atom or multi-atom defects on electronic and ionic conduction;

The effects density / proximity of single atom or multi-atom defects (defect cluster) on

electronic and ionic conduction; and

The effects of the number of hydrogen or deuterium atoms loaded into a multi-atom defect on electron and ionic conduction.

[00059] Particular embodiments and features have been described with reference to the drawings. It is to be understood that these descriptions are not limited to any single embodiment or any particular set of features, and that similar embodiments and features may arise or modifications and additions may be made without departing from the scope of these descriptions and the spirit of the appended claims.

Claims

CLAIMS s claimed is:

A method of determining whether a conduction mode is present in a sample by complex impedance spectroscopy, the method comprising:

setting a sample at a first temperature;

establishing a first steady state of the sample at the first temperature;

obtaining a first complex impedance spectrum;

calculating one or more first resistance value from the first complex impedance

spectrum;

setting the sample at a second temperature;

establishing a second steady state of the sample at the second temperature;

obtaining a second complex impedance spectrum;

calculating one or more second resistance value from the second complex impedance spectrum;

determining a function that relates the first and second resistance values to the first and second temperatures respectively;

calculating at least one slope of the determined function;

calculating at least one activation energy using the at least one calculated slope;

determining whether a conduction mode is present in the sample based on the calculated activation energy.

2. The method of claim 1, wherein establishing a first steady state of the sample at the first temperature comprises establishing an isothermal and isobaric state.

3. The method of claim 1, wherein the first resistance value is determined by determining at least one axis intercept in the first complex impedance spectrum.

4. The method of claim 3, wherein the second resistance value is determined by determining at least one axis intercept in the second complex impedance spectrum.

5. The method of claim 1, wherein determining a function that relates the first and second

resistance values to the first and second temperatures comprises determining ln(l/R) as a function of 1/T, wherein R is resistance and T is the absolute temperature of the sample.

6. The method of claim 5, wherein:

1/R = B exp(-E_c/kT);

E_c is the activation energy of conductance (eV);

k is Boltzmann's Constant = 8.1673E-5 eV/K; and

B is a constant.

7. The method of claim 1, wherein calculating at least one activation energy using the at least one calculated slope comprises relying on ln(l/R) as a function of 1/T having a slope of -E_c/k.

8. The method of claim 1, wherein determining whether a conduction mode is present in the sample based on the calculated activation energy comprises detecting electronic conduction along grain boundaries.

9. The method of claim 8, wherein the sample is a defect free sample.

The method of claim 1, wherein determining whether a conduction mode is present in the sample based on the calculated activation energy comprises detecting electronic conduction through bulk grains in the sample.

11. The method of claim 10, wherein the sample is a defect free sample.

The method of claim 1, wherein determining whether a conduction mode is present in the sample based on the calculated activation energy comprises detecting ionic conduction of hydrogen or deuterium ions along grain boundaries in the sample.

The method of claim 12, wherein the sample is a defect free sample

The method of claim 1, wherein determining whether a conduction mode is present in the sample based on the calculated activation energy comprises detecting ionic conduction of hydrogen or deuterium ions through the bulk grains.

15. The method of claim 14, wherein the sample is a defect free sample.

16. The method of claim 1, further comprising detecting effects of the number of hydrogen or deuterium atoms loaded into a defect free lattice on electronic and ionic conduction.

17. The method of claim 1, further comprising detecting effects of single atom or multi-atom defects on electronic and ionic conduction.

18. The method of claim 1, further comprising detecting the effects density or proximity of single atom or multi-atom defects on electronic and ionic conduction.

19. The method of claim 1, further comprising detecting effects of the number of hydrogen or deuterium atoms loaded into a multi-atom defect on electron and ionic conduction.

20. The method of claim 1, wherein obtaining a first complex impedance spectrum comprises obtaining electrical measurements using electrodes in electrical communication with the sample.

21. The method of claim 20, wherein the electrodes are placed on opposite sides of the sample.

22. The method of claim 20, wherein the electrodes are placed on a same side of the sample to minimize a physical distance of a surface conduction path.

The method of claim 1, wherein obtaining a first complex impedance spectrum

applying alternating current perturbations to the sample over a frequency range.

The method of claim 23, where the frequency range is about from 1 Hz to at least 10 MHz.