Several novel field emission cathodes are constructed by attaching a variety of materials to a steel substrate using multiple methods of bonding. These cathodes are tested using a pulsed relativistic (350–550 kV) vircator in a space charge limited operating regime. The viability of these cathodes as advanced or alternative components in high power microwave systems is evaluated. The currents measured from the cathodes are compared to values predicted from a 3D space charge limited flow model. The performance of the cathode is determined by how the current deviates from the model, as well as the consistency and durability.

High power electron beams are essential to a wide variety of technologies with applications in industry, medicine, defense, and scientific research. These beams are often utilized to convert electrical prime power into other forms, such as RF radiation, x rays, or particle acceleration. Thus, the efficiency and current density of the electron beam are often crucial parameters for technologies relying on them. An effective emitting cathode promotes the transition of electrons from a bound state within a conductor to the free state within a beam. Precise, efficient emitters have been the subject of research for decades;1,2 however, the focus on repetitively pulsed, relativistic, and space charge limited (SCL) cathodes, as is found in many high-power microwave (HPM) sources, is a more recent development. With increasing interest in this application space, the demand for redundancy in effective, manufacturable, and reliable emitter materials has grown. The need to strengthen the supply chain for these materials has also been realized. In the experiments documented here, we use a pulsed, relativistic Virtual Cathode Oscillator (vircator) to investigate the viability of various materials for application in HPM sources.

Electrons are bound to materials by an electric potential and must overcome this potential to form a beam. The height of this potential is known as the work function and is a material property of the cathode. The work function approximates the electric field required to liberate electrons from the material into a beam. The Fowler–Nordheim equations3 model the shape of this potential as a triangular barrier and calculate the probability of emission via quantum tunneling. They provide a calculation of the current density resulting from a cold cathode where the applied field is of similar order of magnitude as the work function. Heat can be applied to the cathode, raising the energy level of bound electrons relative to the potential barrier. The emission from this thermionic cathode is known as Schottky’s emission, and the current density is a function of both the applied field and temperature.4 The geometry of the cathode also affects the emission of current when voltage is applied. By shaping the surface of the cathode to include sharp points, such as knife edges and conducting fibers, the fields close to the surface of the cathode are enhanced, permitting emission at voltages lower than would be expected from a blunt cathode with similar gap spacings.

When the emitted current applies an electric field that suppresses further emission, a state that is typically far beyond the scale of the work function, the current enters the space charge limited regime.5,6 In this regime, the current density is limited due to the suppression of the electric field on the surface of the cathode from the electron beam itself. The Child–Langmuir law predicts the current density possible in a 1-dimensional model, given the applied voltage and the spacing between the electrodes. This relation can be expanded to two7,8 and three9 dimensions. In either of these cases, the material of the cathode has no explicit impact on the current density, as the models do not account for any throttling of the current upstream from the point of emission. This may be significant especially in cathodes that employ sharp field emission points for precise beam control, contact resistance at the bond between the emitter and substrate, or feature voids in the bulk of the material. The discrepancy between the 3D SCL model and experimental measurement will be the standard for comparison between cathodes of various geometry and materials in the analysis presented in this paper.

In this experiment, we apply various conductive emitters to a steel cathode substrate and insert the cathode into a vircator, which is driven by a Marx bank capable of delivering pulses up to 550 kV, 23 kA, for around 200 ns. An example cathode, the DOUCEL10 cathode, is pictured in Fig. 1.

FIG. 1.

Example cathode. In this case, the area of the emitter covers the entirety of the circular, 11.7 cm in diameter, steel substrate.

FIG. 1.

Example cathode. In this case, the area of the emitter covers the entirety of the circular, 11.7 cm in diameter, steel substrate.

Close modal

The vircator used to characterize cathodes in this experiment was developed at the Air Force Research Laboratory and utilizes two additional highly transparent anodes placed downstream of the primary anode that forms the vircator. These downstream anodes create a resonant cavity that stabilizes the frequency of the oscillator and forms additional virtual cathodes that work in concert to convert the beam to RF power and further improve efficiency.11,12 In the context of these experiments, the vircator provides a diagnostic regarding the direction and mean density of the emitted beam.13 Simulation and experiment have shown that this vircator requires a significant magnitude of total current to initiate oscillation. The frequency of the vircator can also be related to the density of the emitted beam. Thus, the presence of RF at the expected frequencies (2.5–3.2 GHz) can be used as an indicator that current has been emitted in the expected manner at approximately the expected density.

Cathode voltage is measured using a resistive voltage divider in the Marx bank. Current is measured using a shielded Rogowski coil located at the base of the cathode stalk, upon which the various cathodes are mounted. The current values reported are peak values, and current densities are assumed by dividing the current by the area of the emitter. A Pearson coil located upstream from the Rogowski coil, closer to the Marx bank output, provides a redundant current diagnostic. These diagnostics agree closely for all the data points used in the analysis in this paper, as disagreement is a sign that the pulse power has misfired. RF power is radiated into an anechoic chamber and measured using cutoff, out-of-band rectangular waveguide antennas. The signals are sent to a fast oscilloscope (Tektronix MSO 72004C) to resolve the frequency and power.

The AK-gap of the vircator is measured from the tip of the emitter to the surface of the nearest anode. It is continuously variable from 1.5 to 2.5 cm. The emitter tips are between 5 and 25 mm, proud of the stainless-steel mount that holds the cathode to isolate emission from the emitter area. The anodes used in this experiment are of three types: a tungsten honeycomb mesh, a thin (<0.1 mm) porous pyrolytic graphite sheet, and a grid woven from 0.3 mm CNT threads. They neither seemed to affect the impedance of the vircator nor its RF production. The pyrolytic graphite anodes were designed to be highly transparent to the electron beam and withstand high heat from the dissipation of beam energy. Mechanically, however, they were especially fragile and would be prone to tearing during experiments. Cutting the transparencies into them was labor intensive. The tungsten mesh and CNT threaded anode were assumed to be less transparent but mechanically much more robust. Geometric transparencies for the anodes range from ∼70% for the pyrolytic graphite, 90% for the tungsten mesh, and 99% for the CNT mesh.

These experiments tested five different cathode materials. The KULR cathode14 is a bimodal carbon fiber velvet with fibers of uniform spacing and a length of about 3 mm. This class of emitter has been used in other HPM systems15 and is relatively well characterized.16,17 The high current density, low emission threshold, and reliability make it a standard for high current applications. Its unique and proprietary fabrication methods may lead to cost and availability challenges for rapid prototyping, so other materials are of interest.

The Brazed Carbon Fabric (BCF) emitter is an alternative to the KULR cathode that uses longer, unoriented carbon fibers in a relatively dense felt.18,19 The fabric is brazed to the conductive substrate.20,21 Multiple BCF cathodes were made in varying sizes to alter the impedance of the vircator.

Carbon nanotubes were synthesized and combined into a thread, which was woven into a fabric using a novel embroidering technique.22,23 The fabric is bonded to the steel substrate so that the threads lay parallel to the surface, and emission is from the side wall of the threads.24 This gives an increased emitting area at the cost of reduced field enhancement. It is expected that the applied fields will be intense enough that enhancement is unnecessary, and the increased emission area will lead to an extended lifetime of consistent performance. Two identical fabrics were made to test the impact of the method of bonding them to the substrate. One cathode was brazed while the other employed a conductive, vacuum safe epoxy.

Duocel carbon foam, or reticulated vitreous carbon, is a commercially available material that is conductive, machinable, and features sharp edges around pores that serve as field enhancement points. The availability and low cost of the material made this material an attractive alternative to traditional flocked velvet. Despite the porous geometry, virtual leaks and loss of vacuum were no more significant for this emitter than any of the others. The material is available in multiple porosities. 60 pores per inch were used in this investigation.

The final emitter tested was a novel material developed by Tangitek®.25 The emitter consisted of ∼2 cm long carbon fibers packed tightly enough to form a dense, solid puck. The emitting end was initially roughened to create a velvet-like surface. The density of fibers could also permit better thermal management in high average power applications. The emitter was much thicker than the other materials and somewhat machinable, so varying thicknesses and surface geometries were investigated with this cathode to determine their effect on emission. A list of cathodes and their variations is provided in Table I.

TABLE I.

Summary of emitter materials and the physical parameters that were tested in this investigation.

MaterialEmitting area (cm2)Thickness (mm)Bond method
KULR 108.6 Proprietary 
Brazed Carbon Fabric (BCF) 108.6, 71.8, 63.1, 49.8 Brazed 
Carbon Nanotube Fabric (CNT) 108.6 Brazed, epoxied 
Duocel 108.6 Epoxied 
Tangitek 49.8 20, 10, 8, ridged Epoxied 
MaterialEmitting area (cm2)Thickness (mm)Bond method
KULR 108.6 Proprietary 
Brazed Carbon Fabric (BCF) 108.6, 71.8, 63.1, 49.8 Brazed 
Carbon Nanotube Fabric (CNT) 108.6 Brazed, epoxied 
Duocel 108.6 Epoxied 
Tangitek 49.8 20, 10, 8, ridged Epoxied 

The accuracy of the 3D space charge limited flow is a point of contention when analyzing the performance of cathodes in the vircator. The vircator, as an RF source, is not in a DC steady state, and the presence of RF oscillations may have a significant impact on the behavior of the cathode. In addition, the polished steel cathode mount may be exposed to electric fields strong enough to emit currents that are not accounted for in the analytical estimation, and the presence and expansion of plasma at either of the electrodes may significantly alter the effective geometry of the diode. The impact of RF oscillation is relatively simple to quantify. Figure 2 shows a comparison of the peak current from the KULR cathode at a fixed gap spacing to the peak RF power radiated from the vircator. The peak power measured in the shots figured represents an electronic efficiency of just over 6%. There is no detectable effect on the current emission as a function of RF power. The voltage is varied from 350 to 440 kV over these shots; however, the 3D SCL model by Koh et al. accurately accounts for that. Emission from locations other than the emitter is possible, although not expected to be especially significant. Care is taken to ensure that the highest fields in the device are located at the gap between the emitter and the transparent anode. The impedance is typically observed to be strongly correlated with the AK gap as well, further indication that this is the primary location of the current flow. The instances where this is not the case will be discussed in part C of this section.

FIG. 2.

Peak current from the KULR cathode at 1.8 cm gap spacing, normalized against the expected value from 3D space charge limited flow, showing no significant correlation with RF power.

FIG. 2.

Peak current from the KULR cathode at 1.8 cm gap spacing, normalized against the expected value from 3D space charge limited flow, showing no significant correlation with RF power.

Close modal

The presence and effect of plasma were not possible to quantify precisely in this investigation. It is strongly speculated that the expansion of plasma leads to an increase in the available emission area, a reduction in the AK gap, and a neutralization of space charge. All of these are factors that tend to increase the resulting current flow beyond the prediction of the 3D SCL model. It is observed that deviation from the SCL prediction is a function of both the emitter material and the gap spacing, as illustrated in Fig. 3. A material dependence suggests plasma may be formed from an ablated emitter, and the amount of susceptibility to ablation is material specific. The relationship between larger gap sizes and increased relative current suggests that the plasma is primarily expanding outward, perpendicular to the electric field, rather than forward toward the anode. The authors hypothesize that forward expansion would occur at a somewhat fixed and constant rate, leading to a narrower gap, which would be proportionally more significant for smaller AK gaps, leading to the opposite trend. The outer radius of the emitter features a sharp boundary where the electric field is enhanced. When strong electric fields are present on the cathode of a high impedance (high gap spacing) vircator configuration, they are amplified at the outer boundary, leading to the ablation of the emitter and an outward expanding plasma, which increases the effective emitting area of the cathode.

FIG. 3.

Deviations from the SCL predicted current for the four most effective emitters and linear fits. All data used in this figure were taken in the first ∼1000 shots of each cathode’s lifetime.

FIG. 3.

Deviations from the SCL predicted current for the four most effective emitters and linear fits. All data used in this figure were taken in the first ∼1000 shots of each cathode’s lifetime.

Close modal

Since it has been established that gap spacing has an impact on the SCL normalized current flow, a fixed geometry must be employed when comparing the performance of emitters in the vircator. Figure 4 shows a comparison of the same emitters as Fig. 3 with a fixed geometry. The emitter is circular with an area of 180.6 cm2, and the AK gap is 1.8 cm. At this gap spacing, the KULR, BCF, and CNT emitters tended to emit just below the SCL prediction, with this discrepancy tending to increase as the voltage was raised. This throttling of the current is likely due to the compression of charge flow through the fibers of the emitters, which introduces a series resistance that is more significant at higher current levels. The DUOCEL emitter has a much lower current than the others for a similar reason: its increased thickness and porous structure offer little surface area for current to flow and an increased distance required to enter the emitting surface.

FIG. 4.

Comparison of emitter materials with equally sized emitters at a 1.8 cm AK gap.

FIG. 4.

Comparison of emitter materials with equally sized emitters at a 1.8 cm AK gap.

Close modal

The DUOCEL and CNT emitters show reduced variation in the emitted current density when compared to the other three emitters. The discrete Marx charge voltages can be resolved from the clusters of data for only the CNT and DUOCEL emitters. To quantify this, the 1σ variation in impedance at a fixed 42 kV Marx charge voltage for the KULR cathode is 4.1%, and the same quantity is 3.0% for the CNT cathode. This difference may be significant in applications where high fidelity in beam power is essential. It is noted that significantly more data are available for the CNT cathode. This is due to a specific interest in the durability of the CNT fabrics. Other cathodes were not tested in this manner due to previous characterization in other applications and/or the strain added to the Marx performing this number of shots.

The CNT emitters were used to test the effect of the bonding method on emission. Two identical emitters were bonded to identical substrates. One was bonded using a conductive epoxy, which was also applied to other (DUOCEL, Tangitek) cathodes in this test series, and the other was brazed using a proprietary brazing compound adapted for the porosity of the CNT fabric. The cathodes performed functionally identically with regard both to current density and outgassing, well within the statistical variation of the data. The normalized current densities at various gap spacings are shown in Fig. 5.

FIG. 5.

Comparison of emission from CNT emitters bonded by brazing and by conductive epoxy. Plots are shown separately for readability, as no significant difference in performance was observed. The data in this figure were acquired early in the emitter’s life, prior to the long shot series shown in Fig. 4.

FIG. 5.

Comparison of emission from CNT emitters bonded by brazing and by conductive epoxy. Plots are shown separately for readability, as no significant difference in performance was observed. The data in this figure were acquired early in the emitter’s life, prior to the long shot series shown in Fig. 4.

Close modal

The effect of emitter geometry in the SCL regime was investigated using the BCF and Tangitek cathodes. The reduced emitting area BCF cathodes were initially designed to test the cavity stabilized vircator at higher impedances and voltages. The conducting substrates were modified to include a raised and centered circular area for the emitter to bond to. The emitter protruded about 0.4 cm to ensure the emission was contained to the emitter and not the surrounding conductor. In general, the 3D SCL model very accurately accounted for variation in the current density due to changes in the emitting area, as depicted in Fig. 6. The smallest of the four cathodes shows a significant divergence from the predicted value, as do the other BCF cathodes when the gap is greatest. In this case, the impedance of the diode is sufficiently high that a significant amount of current is directed elsewhere in the device, and the actual current density is much lower. The vircator confirms this, as no RF signal was obtained for the shots with the exceptionally high SCL normalized current densities reported in Fig. 6.

FIG. 6.

Varying emitting areas of BCF cathodes. The behavior is consistent until the small area, high gap spacing configuration, where the impedance is too great, and the discharge is redirected.

FIG. 6.

Varying emitting areas of BCF cathodes. The behavior is consistent until the small area, high gap spacing configuration, where the impedance is too great, and the discharge is redirected.

Close modal

This feature of high impedance diodes creating alternate discharge paths was also observed with the Tangitek cathode. The effect of emitter thickness was investigated by repeatedly machining away material from the same cathode. Identical parameter scans in applied voltage and gap spacing were performed for each emitter thickness. In every case, AK gap spacing was determined as the distance from the tip of the emitter to the near face of the anode. Figure 7 paradoxically suggests that the normalized current density decreases as the applied field, calculated from the peak voltage and the set gap spacing, is increased. The Tangitek emitter material applies a significant resistance to the current flow. For the thicker emitters, more field strength was required to direct current into the diode rather than diverting toward alternative discharge paths that resulted in erroneously high normalized current densities. At high field strengths, the SCL normalized current density approaches a constant value, and with thinner emitters, that value occurs at lower fields.

FIG. 7.

Performance of emitters made from varying thicknesses of the Tangitek material. SCL normalized current densities at low field strengths are very high, indicating emission beyond the emitter surface area.

FIG. 7.

Performance of emitters made from varying thicknesses of the Tangitek material. SCL normalized current densities at low field strengths are very high, indicating emission beyond the emitter surface area.

Close modal

The ridged Tangitek emitter was created by cutting 4 mm deep and 4 mm wide triangular grooves that radiate from the center of the 8 mm thick emitter. It was hypothesized that offering sharp field enhancement points would lower the field needed to contain the current emission, and the emission region would spread from the enhancement points to the entirety of the emitter. This was not observed: the normalized current density approaches its asymptotic value at an approximately equal field strength as the 8 mm emitter.

FIG. 8.

Current density data and moving average (black) from the brazed CNT fabric cathode showing an initial loss of ∼17% of the peak SCL normalized current density before stabilizing around 1500 shots.

FIG. 8.

Current density data and moving average (black) from the brazed CNT fabric cathode showing an initial loss of ∼17% of the peak SCL normalized current density before stabilizing around 1500 shots.

Close modal

The carbon nanotube emitters are of specific interest due to the resilience of the material and its flexibility, allowing them to be formed into cathodes of irregular shape. For these experiments, CNT threads were woven into a layered textile, with individual threads creating field enhancement lines to facilitate emission. To test resilience, ∼3000 total shots were performed at varying voltages and constant gap spacing (1.8 cm). This number was limited by the lifetime of the components in the Marx. It was observed that the SCL normalized current density tended to decrease for the first ∼1500 shots before stabilizing. It is hypothesized that this is due to the presence of volatile chemical impurities in the emitter or bonding agent that are vaporized and liberated by the current and pumped out of the system. Figures 3 and 5 feature brazed CNT cathode data that was acquired prior to the long 3000 shot test. The data cover the first ∼100 shots of the cathode, and little change is observed over ranges of that scale. This change is readily observable in the CNT data in Fig. 8.

After testing was completed in the vircator, the CNT emitters were imaged using a scanning electron microscope (SEM) to assess the level of destruction to the fibers. Some selected images are shown in Figs. 9(a)9(d). The images reveal what appear to be individual and collections of discrete rupture sites on the surface of fibers. These sites, which were only observed on emitters subjected to field emission experiments, are thought to be the result of a Coulomb explosion.26,27 The diameters of the craters left by these Coulombic explosions are typically around 5  μm in diameter, approximately a factor of 10 smaller than those found by Li et al., which analyze Coulomb explosions from vertically oriented carbon nanofibers. This is likely due to differences in the geometry of the emission point, which is the sidewall of a relatively thick fiber in this experiment, leading to a reduction in field enhancement compared to emission from a nanofiber tip. Heating also played a significant role, which is assumed to be insignificant in our experiment but not in Li’s, where higher average power density led to measured temperature increases and a weakening of the atomic and intermolecular bonds of the CNT emitter.

FIG. 9.

(a) (Top left): Overview of a site at the top layer, representing the level of structural degradation at ∼3000 shots. (b) (Top right): View of the surface layer where Coulomb explosions have collected, leaving a roughened surface. (c) (Bottom left): View of the second layer, where ruptures are typically individual, although some small collections are present. (d) (Bottom right): Close view of an individual rupture site showing its scale and jagged geometry.

FIG. 9.

(a) (Top left): Overview of a site at the top layer, representing the level of structural degradation at ∼3000 shots. (b) (Top right): View of the surface layer where Coulomb explosions have collected, leaving a roughened surface. (c) (Bottom left): View of the second layer, where ruptures are typically individual, although some small collections are present. (d) (Bottom right): Close view of an individual rupture site showing its scale and jagged geometry.

Close modal

It is hypothesized that individual rupture sites create a preferential emission point for subsequent shots, leading to the formation of well-defined regions of more intense damage to the fibers. As expected, the most severe damage is found on the outermost layer of the CNT fibers, while only a few individual rupture sites are found on lower layers. Overall, the structural degradation at ∼3000 shots can be considered superficial. Damage is limited to a small fraction of the emitter’s surface, and even in the most damaged locations, the structure of the fiber is intact.

A relativistic vircator has been used to compare the performance of various emitter materials for application in single shot HPM devices. The key performance parameters included current density, consistency, cost, and durability. The impact of the geometry of the emitter and its effect on performance were also analyzed. Multiple materials were identified in this investigation that could provide an advantage over existing technologies in some aspect or provide a more available alternative. In particular, the CNT fabric emitters showed current densities comparable to the KULR and BCF emitters, with reduced variability between shots. The DUOCEL emitters provided an inexpensive and reliable alternative, at the cost of reduced current.

The authors would like to express their gratitude to Steven Fairchild, Dmitri Tsentalovich, Kent Averett, and Alán Martinez for their help with the procurement and analysis of the CNT cathodes.

The authors have no conflicts to disclose.

S. C. Exelby: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Project administration (lead); Resources (equal); Writing – original draft (lead). C. J. Leach: Conceptualization (equal); Funding acquisition (lead); Investigation (supporting); Methodology (equal); Resources (equal); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author, S. C. Exelby, upon reasonable request.

1.
P.
Zhang
,
A.
Valfells
,
L. K.
Ang
,
J. W.
Luginsland
, and
Y. Y.
Lau
,
Appl. Phys. Rev.
4
,
011304
(
2017
).
2.
D.
Shiffler
,
M.
Haworth
,
K.
Cartwright
,
R.
Umstattd
,
M.
Ruebush
,
S.
Heidger
,
M.
LaCour
,
K.
Golby
,
D.
Sullivan
,
P.
Duselis
, and
J.
Luginsland
,
IEEE Trans. Plasma Sci.
36
,
718
(
2008
).
3.
R. H.
Fowler
and
L.
Nordheim
,
Proc. R. Soc. A
119
,
173
(
1928
).
4.
C. H.
Hinrichs
,
W. A.
Mackie
,
P. A.
Pincosy
, and
P.
Poulsen
,
IEEE Trans. Electron Devices
37
,
2575
(
1990
).
8.
J. W.
Luginsland
,
Y. Y.
Lau
, and
R. M.
Gilgenbach
,
Phys. Rev. Lett.
77
,
4668
(
1996
).
9.
W. S.
Koh
,
L. K.
Ang
, and
T. J. T.
Kwan
,
Phys. Plasmas
12
,
053107
(
2005
).
10.
See https://ergaerospace.com for ERG, Duocel® Reticulated Vitreous Carbon, 60 PPI,
2022
.
11.
J.
Benford
,
D.
Price
,
H.
Sze
, and
D.
Bromley
,
J. Appl. Phys.
61
,
2098
(
1987
).
12.
S.
Champeaux
,
P.
Gouard
,
R.
Cousin
, and
J.
Larour
,
IEEE Trans. Plasma Sci.
43
,
3841
(
2015
).
13.
W.
Jiang
and
M.
Kristiansen
,
Phys. Plasmas
8
,
3781
(
2001
).
14.
See https://kulrtechnology.com/cathode/ for Kulr Technology Group, Inc., Carbon Fiber Velvet Cathodes,
2023
.
15.
D.
Shiffler
,
M.
Ruebush
,
M.
Haworth
,
R.
Umstattd
,
M.
LaCour
,
K.
Golby
,
D.
Zagar
, and
T.
Knowles
,
Rev. Sci. Instrum.
73
,
4358
(
2002
).
16.
C. A.
Schlise
,
Explosive Emission Cathodes for High Power Microwave Devices: Gas Evolution Studies
(
Naval Postgraduate School
,
2004
).
17.
D.
Shiffler
,
M.
LaCour
,
K.
Golby
,
M.
Sena
,
M.
Mithcell
,
M.
Haworth
,
K.
Hendricks
, and
T.
Spencer
,
IEEE Trans. Plasma Sci.
29
,
445
(
2001
).
18.
B. W.
Hoff
et al,
Rev. Sci. Instrum.
91
,
064702
(
2020
).
19.
S-bond Technologies
, S-Bond ® Joining Graphite and Carbon to Metals, Lansdale, PA,
2009
.
20.
R. W.
Smith
,
U. S. Patent 6,047,876 (11 April 2000
).
21.
See www.Ceramaterials.Com for CeraMaterials, Activated Carbon Felt, Port Jervis, NY.
22.
N.
Behabtu
,
C. C.
Young
,
D. E.
Tsentalovich
,
O.
Kleinerman
,
X.
Wang
et al,
Science
339
,
182
(
2013
).
23.
L. W.
Taylor
,
O. S.
Dewey
,
R. J.
Headrick
,
N.
Komatsu
,
N. M.
Peraca
et al,
Carbon
171
,
689
(
2021
).
24.
S. B.
Fairchild
,
C. E.
Amanatides
,
T. A.
deAssis
,
P. T.
Murray
,
D.
Tsentalovich
et al,
J. Appl. Phys.
133
,
094302
(
2023
).
25.
TangiTek®
, Tangible Technologies, Portland, OR,
2023
.
26.
Y.
Li
,
Y.
Sun
,
D. A.
Jaffray
, and
J. T. W.
Yeow
,
RSC Adv.
7
,
40470
(
2017
).
27.
P. E.
Mason
,
F.
Uhlig
,
V.
Vaněk
,
T.
Buttersack
,
S.
Bauerecker
, and
P.
Jungwirth
,
Nat. Chem.
7
,
250
(
2015
).