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Chapter 5 High-Speed Electron Microscopy 425

Figure 5–9. Phase and amplitude contrast transfer functions (CTF’s) as simulated by the commercial

software package Java EMS [68] for the following parameters: E = 100 keV, DE = 5 eV (the maximum

allowed by the software), CS = CC = 2 mm, convergence semi-angle 10 mrad, defocus 105 nm, no objec-

tive aperture. The cross-interaction between convergence angle and aberrations is primarily respon-

sible for the low contrast. Phase contrast will be very weak, however amplitude contrast mechanisms

should produce reasonable images with better than 1 nm resolution under the assumptions in this

model. Therefore the effects that limit DTEM resolution must be among those not included in this

simulation, which was designed for conventional TEM.

426 W.E. King et al.

very important to control the convergence angle to obtain a good

DTEM image. Reasonably high-quality selected area diffraction

patterns have been achieved in DTEM over areas of some tens of

micrometers,

indicating that the convergence angles can be kept to

reasonable levels.

In short, the estimated resolution limit accounting for all known

(and measured) effects in the gun, accelerator, condenser system, and

objective lens would appear to be ∼1 nm, dramatically better than is

achieved experimentally. This suggests that the limitation is in one of

the effects not included in conventional TEM simulations; this also

suggests that if the limiting factor can be identiﬁ ed and eliminated, a

great improvement in resolution should be possible. The above argu-

ment indicates that the culprit should be either in the sample, in the

postsample lens systems, or (as indicated in Domar and Bostanjoglo

)

in the camera (including detection statistics). The balance of this section

will discuss some of these effects.

Consider the interaction of a very intense beam with a solid sample.

In conventional TEM, 1 µA would be an extremely high current at the

sample; this corresponds to roughly 1 electron per 160 fs, with an axial

spacing of ∼33 µm at 200 keV. Plasmon lifetimes are in the femtosecond

range, while TEM samples are usually less than 1 µm thick, so each

electron encounters a sample that has had time to relax since the last

electron passed through it (apart from heating and radiation damage).

DTEM currents may be four orders of magnitude larger. More than one

electron will be in the sample at a time, and at high ﬂ uences each

electron may encounter multiple previously excited plasmons on its

way through the material. The theory of electron–sample interactions

in the electron microscope always makes the one-electron-at-a-time

approximation. This theory may have to be modiﬁ ed for the DTEM.

Further, a great deal of energy will be deposited in a region highly

localized in time and space, which raises the possibility of new radia-

tion damage mechanisms. It is not clear at this time whether and how

these effects might worsen the image resolution.

The abnormally high currents in the DTEM may also affect the

behavior of the intermediate lens system, speciﬁ cally through elec-

tron–electron interactions in the intense crossovers. We have performed

rough estimates of the various effects involved (space charge, Boersch,

and stochastic particle displacement), following the formalism of Kruit

and Jansen.

Space charge effects can change the effective focal lengths and aber-

ration coefﬁ cients of each of the lenses. Space charge defocusing would

merely require a readjustment of the lens currents and a possible reca-

libration of the microscope in pulsed mode. The experience at TU

Berlin suggests that this is not a major issue. Estimating the effects of

space-charge-induced spherical aberration is somewhat more difﬁ cult

and has not yet been performed in detail. Part of the problem is that

this effect vanishes to ﬁ rst order for a circular beam of uniform inten-

sity,

so any associated distortions would have to be driven by nonsta-

tistical inhomogeneities in the beam intensity (including those due to

Chapter 5 High-Speed Electron Microscopy 427

the image contrast itself). Little more can be said without extensive

modeling, but fortunately the relevant models are already well devel-

oped in other contexts.

The Boersch effect acts to increase the energy spread of a charged

particle beam by coupling the lateral and longitudinal degrees of

freedom via statistical electron–electron interactions.

64–66

This process

will saturate when all degrees of freedom are, in some sense, in thermal

equilibrium. Saturation energy spreads depend on accelerating volt-

ages and convergence angles.

Rough estimates suggest that this effect

has adequate time to saturate in the early part of the column, and that

it may well be responsible for much of the energy spread measured by

Bostanjoglo et al.

[a very rough estimate of the saturation energy

spread based on assumed parameters yields ∼10 eV, compared to the

measured 8.7 eV, while the original authors used Loefﬂ er’s formalism

(validated to within ∼20%)

to estimate a value of 7.6 eV]. In any case

it would seem that the maximal effect of chromatic spread would

already have occurred in the objective lens (with a resolution limit

∼1 nm), so that it seems doubtful that chromatic aberration in the inter-

mediate lenses is to blame for the observed resolution limit of

∼200 nm.

This brings us to the trajectory displacement effect,

65,66

which slightly

and randomly deﬂ ects electrons in and near a crossover. Suppose we

take an intermediate lens with focal length 24 mm forming an image

of radius 0.1 mm at a distance of 60 mm, with a crossover at 27 mm. The

divergence angle α

is therefore 3 mrad. These values might come up

between the ﬁ rst and second intermediate lenses of a typical TEM in a

moderate-magniﬁ cation imaging mode, with an illuminated area of

1 µm at the sample. Suppose 10

electrons are in a pulse of duration 1 ns,

for a current of 16 mA at 200 keV. Using the formulas quoted by Kruit

and Jansen,

we ﬁ nd that we are in the Gaussian regime, with an

average random trajectory displacement of 2.2 µm at the crossover and

an estimated 5 µm at the image plane. The result will be an image blur

much like what happens in projection electron lithography systems.

Referencing this displacement back to the sample plane yields a resolu-

tion limit of ∼50 nm due to this crossover alone, assuming that the rest

of the optical system faithfully transfers this image plane to the screen.

This is a very signiﬁ cant limitation to the resolution (comparable to the

quoted resolution limit of ∼200 nm in current instruments

), yet it must

be taken as only a very rough estimate of the effect in a real TEM

column. This resolution limit depends strongly on all relevant param-

eters, including the positions, intensities, and convergence angles of all

crossovers, the positions and degrees of magniﬁ cation at every image

plane, and the beam current and voltage. This means that (1) much

more involved calculations and experiments are required if we are to

understand if this is truly the resolution limit, and (2) if it is the resolu-

tion limit, then it may be possible to dramatically reduce its effects by

changing the lens excitations in the intermediate/projector lens system.

The idea would be to avoid intense crossovers with small convergence

angles at high-leverage parts of the column. A simple way to test the

428 W.E. King et al.

hypothesis would be to take the same pulsed images with and without

a small selected-area aperture. If trajectory displacement is the resolu-

tion limit, then when the aperture is inserted the electrons from outside

the region of interest will no longer be present at the intermediate lens

crossovers, and the effect should be greatly reduced.

We should also remember that the sample may well be moving,

rapidly, during the exposure. A phase front or shock wave moving at

roughly the speed of sound in the material may move several microm-

eters during a few-nanosecond electron pulse. The sample may also be

distorting from local heating or moving vertically (out of focus) due to

the effects of the pump laser. These effects must be considered in the

design of experiments. However this does not appear to be the resolu-

tion limit in the experiments to date; roughly the same resolution is

obtained in test shots on a static sample.

In summary, the observed resolution limit in DTEM may arise from

a combination of intermediate crossover interactions, motion blurring,

and low signal levels, while the effects that limit resolution in conven-

tional TEM would suggest a pulsed image resolution ∼1 nm. Various

experiments are proposed that may identify the true culprits, while

some methods of mitigating their effects are suggested. This is the

present state of knowledge at the time of writing; the near-future evolu-

tion of the understanding of these effects is likely to be rapid.

3.3 Damage

Due to the inelastic scattering of electrons in TEM, a large amount of

energy (typically some 10s of electron-volts per primary electron) is

deposited in the sample, and in many cases damage due to energy

deposition is a limiting factor in obtaining high-resolution images. For

continuous electron exposure used in standard TEM, damage is lin-

early related to the total radiation dose,

71,72

but to fully understand the

impact of damage on image quality in DTEM, the effects of higher dose

rate and the time-dependent nature of radiation damage must also be

considered. At this point, we do not know enough about either of these

subjects to conﬁ dently predict the damage-related resolution degrada-

tion in a DTEM image. Nevertheless, here we brieﬂ y review what is

known as a baseline for further investigation.

The consequences of energy deposition for TEM images depend

strongly on the nature of the sample. Although a wide variety of inor-

ganic and metallic samples can be readily imaged, sometimes with

very high resolution and contrast,

damage is the most signiﬁ cant

limiting factor for imaging less robust samples such as biomaterials.

Although damage in solid-state material due to direct atomic displace-

ment can be signiﬁ cant at high beam currents,

typically this is appre-

ciable only for a large integrated number of primary electrons incident

on the sample and can be avoided (in standard TEM) through the use

of a primary electron energy that is less than a sample-dependent

threshold. For a current density of 10

A/cm

through a carbon ﬁ lm

sample at between 100 and 200 keV, the sputtering rate is roughly

10 nm/s.

Although the instantaneous current density in DTEM could

Chapter 5 High-Speed Electron Microscopy 429

be considerably higher than this (as high as 10

A/cm

in future instru-

ments), this current density will be sustained only over nanoseconds.

Assuming the sputtering rate is linearly related to the current density

(which may not be the case for DTEM), sputtering would be insigniﬁ -

cant for less than millions of shots.

Since the time scale of the electron pulse can be comparable to the

thermal diffusion time, sample heating is a more signiﬁ cant issue for

DTEM than standard TEM, but this depends strongly on the sample

and beam properties. The deposited energy density can be very large.

For water irradiated by ∼200 keV electrons at a density of 10 electrons/

(a typical density for cryoEM) in a single pulse, straightforward

estimates of the inelastic cross section

result in a deposited energy

density of about 300 eV/nm

, about 10 eV per water molecule! For a

Gaussian beam with 1/e radius of 100 nm and 1/e half width of 1 ns in

water, naively assuming only standard thermal diffusion using room

temperature constants, the deposited energy density will reach 90% of

the value it would have with no diffusion. The situation is signiﬁ cantly

better with the lower heat capacity and larger thermal conductivity

found in metals. With the same beam properties, the energy density

in an aluminum sample will reach only 5% of the zero diffusion energy

density. These results depend strongly on the pulse duration. A pulse

of sufﬁ ciently short duration (less than 10s of picoseconds for a 100-nm

radius beam in aluminum) will still overwhelm diffusion within this

model. At a sufﬁ ciently short pulse duration and electron density,

sample heating may result in sample melting and lowering the atomic

displacement energy threshold. Nonetheless, questions remain as to

the actual state of the material at these early times and high tempera-

tures—it is unlikely that any standard assumptions about thermal

transport or material stability would still apply.

Biomaterials (such as proteins) are especially ill suited to examina-

tion via TEM due to their native aqueous environment, caustic species

created in the irradiation of water, low contrast, intrinsic radiolytic

susceptibility, and the relatively weakly bound tertiary and quaternary

structures of proteins. The “lifetime” of irradiated protein crystals (i.e.,

the amount of time a crystal may be irradiated until its diffraction

pattern fades) is a well-documented obstacle

to high-resolution protein

structural characterization. Yet, biology would beneﬁ t immensely from

the ability to efﬁ ciently image proteins at high resolution. Knowledge

of the detailed functioning of biomolecules and biomolecular com-

plexes is essential to our understanding of the functioning and evolu-

tion of life.

Here we focus on the imaging of biomaterials, since this

application has great scientiﬁ c beneﬁ t as well as being very challeng-

ing. Damage mechanisms would be simpler for just about any other

condensed-state sample.

Speciﬁ cally, how much will damage degrade the resolution of a

DTEM image over the time scale of the electron pulse? More optimisti-

cally, is it possible to effectively mitigate the effects of damage with

respect to a high-resolution image by using a short electron pulse?

Such an idea has already been proposed for imaging with X-rays,

where single particle diffractive protein imaging is thought to be

430 W.E. King et al.

possible using a 10-fs duration X-ray pulse. Although pulsed imaging

ultimately results in the destruction of the sample, the idea is to

obtain the image before damage has signiﬁ cantly distorted the

structure being imaged. An incidental, yet highly beneﬁ cial product of

this scheme is the ability to time-resolve structural changes, enabling

the direct visualization of nanobiostructural dynamics—a molecular

movie.

An analogous imaging scheme using electron pulses presents both

advantages and challenges. Electrons deposit much less energy per

inelastic scattering event than X-rays: less than 50 eV per event for

electrons

versus approximately 10 keV for X-rays, and the ratio of

inelastic to elastic scattering events is roughly a factor of three smaller

for electrons.

This results in about 600–1000 times less energy depos-

ited in the sample per unit signal for electrons compared to X-rays.

Furthermore, electrons scatter with 10

greater probability than X-

rays, allowing imaging with a much lower electron density. Yet, elec-

trons are electrically charged fermions, which (as discussed in the

sections on photoelectron guns and resolution) limits the ﬂ uence at

the sample and both the spatial and temporal resolution. The chal-

lenge of pulsed electron microscopy will be to obtain a pulse of suf-

ﬁ cient quality and electron density to obtain a high-resolution image,

which is also short enough to avoid damage to the sample during the

pulse.

Hydrodynamic modeling of single particle diffractive imaging

with electrons (in analogy with the X-ray method above)

indicates

that 4 Å resolution is possible for a molecule of 10 nm radius with

100 keV electrons at a density of 10

electrons/(100 nm)

, with a pulse

width of 2 ps. Using the same model for the X-ray case and sufﬁ cient

photon density to achieve the same resolution, an X-ray pulse of 2 fs

is required. These results are reasonably consistent with expectations,

giving a difference in the maximum acceptable pulse length of 1000,

exactly the ratio of deposited energy per unit signal between the X-

ray and electron cases. These single particle models consider “naked”

molecules only where the damage mechanism is Coulomb explosion.

For the X-ray case, damage by this mechanism is the result of

ionized electrons exiting the sample and leaving a net positive charge,

resulting in rapid sample distortion due to electrostatic repulsion.

Charging is much less severe for an electron probe due to the much

lower kinetic energy of ionized secondary electrons. Also, it is likely

that damage will occur on a slower time scale in solution, where the

dispersion of molecules will be impeded by the presence of solution

and secondary electron transit will be signiﬁ cantly reduced, resulting

in less charging. In this case, the primary damage mechanism may

be radical chemistry and diffusion, rather than Coulomb expansion.

Although a 2-ps electron pulse width is probably beyond the capabil-

ity of DTEM using standard electron guns, sub-100-ps pulse widths

are not inconceivable at the required electron density. Attaining the

necessary spatial and temporal coherence for diffractive imaging

using such a pulse will probably be very difﬁ cult but perhaps within

the reach of foreseeable improvements in electron gun technology.

Chapter 5 High-Speed Electron Microscopy 431

Although atomic resolution may be challenging, electron gun modi-

ﬁ cations to shorten the pulses into the 10s of picoseconds may well

allow very efﬁ cient imaging of protein complexes at sufﬁ cient resolu-

tion to signiﬁ cantly contribute to our understanding of their struc-

ture and dynamics. Furthermore, the RF accelerator community is

aware of the potential for ultrashort, high brightness electron guns

in electron microscopy.

Such sources do not currently exist, but if

these were developed, they could very signiﬁ cantly improve our

ability to rapidly image biomolecules.

Currently, there is very little information directly concerning biosa-

mple radiolysis damage at the very high current densities that will be

found in DTEM. Although simulations such as those described above

can provide us with some insight into the damage process, they do not

consider the effect of an aqueous solution surrounding the sample. It

is likely that a surrounding solution will signiﬁ cantly alter the damage

process and may impede the physical diffusion of a damaged biosam-

ple long enough to obtain a high-resolution image with an electron

pulse that is longer than 2 ps. Given the available information, it is

difﬁ cult to speculate. Nonetheless, here we attempt to approach the

problem based on what is known.

First, we consider standard TEM. In some cases, the difﬁ culty in

imaging biomaterials may be overcome with standard TEM via any

of three strategies, which all depend on the mitigation of damage:

increasing sample contrast (via, for example, staining), increasing

the sample damage threshold (as in cryoelectron microscopy

), or

reducing the dose per unit sample (as in diffraction and cryoEM)

with signal averaging over many samples. Of these techniques,

cryoEM most closely approximates imaging of biosamples in a native

environment, since this method does not require contrast enhance-

ment. In cryoEM, a sample is ﬂ ash frozen such that the embedding

ice is vitreous rather than crystalline.

This minimally distorts the

sample and reduces diffractive background signal in the image. In

addition, cooling of the sample to cryogenic temperatures increases

the radiation tolerance by factors of thousands

with respect to

image-manifested damage. Although irradiation may have caused

the conditions under which sample damage would occur, the physi-

cal diffusion that would make this apparent in an image does not

occur when the sample is frozen in place.

This result indicates that

molecular diffusion, and temperature and phase-dependent chemi-

cal reactions play a role in damage,

74,75

and that damage resulting

from direct atomic displacement is insigniﬁ cant at the doses (1–10

electrons/Å

) used in cryoEM.

To further establish the relevance of diffusion in damage, an early

time diffusional dependence is indicated by electron energy loss exper-

iments that demonstrate an orders of magnitude increase in the damage

threshold with reduced excitation volume at equivalent or greater irra-

diation density. Varlot et al.

observed a change in damage threshold

of 10

between a 100 nm and 0.7 nm radius cylindrical excitation volume

irradiating polymers. Their analysis did not attribute the change in

damage threshold to temperature effects and they speculated that dif-

432 W.E. King et al.

fusion of damaged molecules (e.g., free radicals) might explain the

effect. Siangchaew et al.

also observed a substantial increase in the

damage threshold of polyethylene using a small electron probe. They

speculate that the increase in damage threshold is due to fast second-

ary electrons (of energy >50 eV) exiting the 100-nm-diameter probe

region. These electrons create damage collateral to the probe region,

but leave the probe region relatively pristine. Egerton et al.

disagree

with this interpretation, asserting that (for polyethylene) the number,

range, and energy of fast secondary electrons (FSEs) should result in

75% of the FSE energy being deposited within 2 nm of the probe beam.

Slow electrons have longer mean free paths and may exit a small probe

region,

but it is not known how damaging these low-velocity elec-

trons would be to organic samples.

Diffusion also plays a primary role in radiolysis damage. In an

aqueous environment, radiolysis damage is complex and involves

many disparate processes. The physical excitation of secondary elec-

trons through inelastic scattering is followed by electron thermaliza-

tion and diffusional transport, and trapping occurring over a time

scale on the order of 1 ps, along with the initial generation of radicals.

This is followed by equilibrium with nuclei, which occurs in a few

picoseconds. At longer time scales, chemistry begins to occur. Ioniza-

tion and energy deposition in the ﬁ rst stage result in a transient dis-

tribution of radicals and other species (including H

, OH, e

aqu

, and H

in water), which then diffuse and react with solutes and each other,

reaching a homogeneous chemistry limit within micro- to millisec-

onds.

83,84

With respect to solute interactions, pulse radiolysis studies

indicate that the primary damage mechanism in DNA is attack by

radiation-created hydroxyl radicals

and based on simulations, the

time scale of this process is thought to be hundreds of femtoseconds,

assuming low deposited energy density.

These data seem to indicate that the time scale for image manifested

damage of a biomolecule in aqueous solution would be no faster than

a few picoseconds, possibly much longer. Nonetheless, these data do

not directly address the question. Although pulse radiolysis studies

have provided a signiﬁ cant amount of information,

this information

generally concerns the time domain behavior of irradiated water (cf.

time domain spectroscopy) and stoichiometric chemistry. Such data

and corroborating simulations

83,84

can be used to aid in the understand-

ing of the diffusion of energy and radiolytic species in water, but ulti-

mately they do not tell us about structural damage in solutes,

particularly within a few picosecond time scale. More speciﬁ c experi-

mental studies of biomolecules such as DNA address damage, but

again, this typically provides information regarding the chemistry of

damage (typically via radiation-induced radicals) and the functional

viability of irradiated molecules without reference to detailed

structure.

85,88

Furthermore, the energy deposition used in pulse radi-

olysis studies is much lower (∼10 Gr)

than what is used in TEM

(>10

Gr),

and the excitation volume in TEM is correspondingly much

smaller. As a result, transport and relaxation of secondary electrons

and high-dose rate effects

will probably play a signiﬁ cant role in the

Chapter 5 High-Speed Electron Microscopy 433

damage process in DTEM. These issues are not as signiﬁ cant for con-

tinuous irradiation in conventional TEM since thermal diffusion occurs

on a faster time scale than the average time between electrons tran-

siting the sample. The instantaneous energy density in the DTEM will

be much higher, and these data do not provide information in this

regime.

Finally, we note that there is actually some empirical evidence that

damage will be signiﬁ cantly reduced by the use of pulsed electron

exposure. Fryer

observed damage thresholds of 90–100 e/Å

using

10- to 100-ms pulses to image monolayer ﬁ lms of aromatic hydrocar-

bons. Using continuous exposure, the damage threshold for these

samples was 3–4 e/Å

, comparable to the damage threshold for proteins

in cryoEM. This 22–25% improvement was observed for much longer

pulses than we will use in the DTEM and points in the direction of

trying even shorter pulses.

Unfortunately, no currently available data directly address the ques-

tion of resolution smearing in DTEM due to damage from short pulses

of electrons. As far as damage is concerned, currently available simula-

tions and empirical results do not unambiguously exclude the possibil-

ity of molecular bioimaging with short electron pulses, but they do not

clearly indicate that it is possible, either. As with many aspects of

DTEM, the development and use of the instrument will ultimately

provide these answers.

4 DTEM Applications

We include a brief historical review that attempts to put electron

imaging in the context of work on electron diffraction. For the

purpose of this discussion, we limit the review to time resolutions of

micro seconds or less. Figure 5–10 provides a summary. In the mid-

1970s, Bostanjoglo et al.

16,92

developed a technique to produce strobo-

scopic images in TEM using beam blanking. In these pump-probe

studies, ultrasonics were used to pump samples that were studied

stroboscopically. This led to a number of papers studying fast

transitions.

93–101

Stroboscopic diffraction studies were carried out in the early

1980s.

102–104

Real-time gas-diffraction experiments were reported in

1984.

105

The ﬁ rst picosecond time-resolved structural studies in the

solid state occurred in the early 1980s with a streak camera used as the

basis of a diffraction instrument.

1,3

This led to the ﬁ rst picosecond time-

resolution observation of a phase transition in Al.

In the late 1980s,

pulsed photocathode,

106

multiframe movies,

107

and dynamic imaging

were demonstrated at TU Berlin.

108

In the 1990s there was work in gas-

phase energy transfer,

109

superheating of lead, and structural dynam-

ics.

110

The techniques were applied to complex transient phenomena

including dynamics of cyclohexadiene,

photo-dissociation,

111

direct

observation of ultrafast thermal lattice expansion (Ag) on picosecond

time scales,

112

melting of amorphous Si,

phase explosion in metal

ﬁ lms,

113

and melting of Al.

114

434 W.E. King et al.

TEM with high time resolution began at TU Berlin in the 1970s with

stroboscopic imaging of periodic processes using a periodically

deﬂ ected electron beam.

16,115

In this conﬁ guration, time resolutions of

200 ps were achieved for periodic processes up to 100 MHz.

116

This

technique was applied to ultrasonically driven disruption of crystals

and magnetoelastic effects

92,115

and magnetic-ﬁ eld-induced oscillations

of the domain magnetization, of domain walls, and of their substruc-

tures.

98,116,117

After 1980, the instrument was modiﬁ ed to study nonpe-

riodic processes. That instrument operated in three modes:

1980s

1970s

1990s

2000s

Melting of

Si (few ps)

Stroboscopic

electron

microscope

(200 ps)

Superheating

of Pb (200 ps)

140

Multiframe

"movie" (<10 ns

with 25 ns frames)

107

Photoreaction in gas

phase (few ps)

139

Photo-

dissociation

(few ps)

111

Time-resolved

RHEED (200 ps)

141

Stroboscopic

time-resolved

LEED (10 ns)

103

Stroboscopic

time-resolved

diffraction (100 s)

104

First time-resolved

pump-probe

diffraction (20 ps)

Pulsed cathode

TEM (20 ns)

Reflection

microscope (20 ns)

Gas phase energy

transfer (15ns)

109

First dynamic

TEM images (20 ns)

Melting of Al

(600 fs)

114

Dynamics of

cyclohexadiene

(few ps)

Electron diffraction

of Al (100ps)

"Real-time"gas

diffraction

(16 ms)

105

Stroboscopic

time-resolved

electron diffraction

(100 ns)

102

Direct observation of

lattice heating and

diffusion (Ag) on ps

time scales (<400 fs)

112

Structural

dynamics

(1.4 ps)

110

Phase change in

clusters (1 s)

142

Phase explosion in

metal films (3 ns)

Figure 5–10. Timeline showing the parallel development of ultrafast electron diffraction and DTEM

technologies.