Ultrafast electron diffraction

The design of early ultrafast electron diffraction instruments was based on x-ray streak cameras, the first reported UED experiment demonstrating an electron pulse length of 100 ps.[1]

The electron pulses are typically produced by the process of photoemission in which a fs optical pulse is directed toward a photocathode.[2] If the incident laser pulse has an appropriate energy, electrons will be ejected from the photocathode through a process known as photoemission. The electrons are subsequently accelerated to high energies, ranging from tens of kiloelectron-volts[3] to several megaelectron-volts,[4] using an electron gun.

Generally, two methods are used in order to compress electron pulses in order to overcome pulsewidth expansion due to Coulomb repulsion. Generating high-flux ultrashort electron beams has been relatively straightforward, but pulse duration below a picosecond proved extremely difficult due to space-charge effects. Space-charge interactions increase in severity with bunch charge and rapidly act to broaden the pulse duration, which has resulted in an apparently unavoidable trade-off between signal (bunch charge) and time-resolution in ultrafast electron diffraction (UED) experiments. Radio-frequency (RF) compression has emerged has an leading method of reducing the pulse expansion in UED experiments, achieving temporal resolution well below 50 femtoseconds.[5] Shorter electron beams below 10 femtoseconds are ultimately required to probe the fastest dynamics in solid state materials and observe gas phase molecular reactions.[6]

Schematic of Ultrafast Electron Diffraction showing the pump pulse (red) exciting the sample prior to the arrival of the electron probe pulse (blue)

For studying irreversible process, a diffraction signal is obtained from a single electron bunch containing ${\displaystyle 10^{5}}$ or more particles.[7]

When studying reversible process, especially weak signals caused by, e.g., thermal diffuse scattering, a diffraction pattern is accumulated from many electron bunches, as many as ${\displaystyle 10^{8}}$.[8]

The resolution of an ultrafast electron diffraction apparatus can be characterized both in space and in time. Spatial resolution comes in two distinct parts: real space and reciprocal space. Real space resolution is determined by the physical size of the electron probe on the sample. A smaller physical probe size can allow experiments on crystals that cannot feasibly be grown in large sizes.[9]

High reciprocal space resolution allows for the detection of Bragg diffraction spots that correspond to long periodicity phenomena. It can be calculated with the following equation:[4]

${\displaystyle \Delta s={\frac {2\pi }{\lambda _{e}}}{\frac {\varepsilon _{n}}{\sigma _{x}}}}$,

where Δs is the reciprocal space resolution, λ_e is the Compton wavelength of the electrons, ϵ_n is the normalized emittance of the electrons, and σ_x is the size of the probe on the sample.

Temporal resolution is primarily a function of the bunch length of the electrons and the relative timing jitters between the pump and probe.[4]

• Ahmed Zewail
• R. J. Dwayne Miller
• Time resolved crystallography

• Srinivasan, Ramesh; Lobastov, Vladimir A.; Ruan, Chong-Yu; Zewail, Ahmed H. (2003). "Ultrafast Electron Diffraction (UED): A New Development for the 4D Determination of Transient Molecular Structures". Helvetica Chimica Acta. 86 (6): 1761. doi:10.1002/hlca.200390147.

• Sciani, Germain; Miller, R.J. Dwayne (2011). "Femtosecond electron diffraction: heralding the era of atomically resolved dynamics". Reports on Progress in Physics. 74 (9): 096101. Bibcode:2011RPPh...74i6101S. doi:10.1088/0034-4885/74/9/096101. S2CID 121497071.
• Chatelain, Robert P.; Morrison, Vance R.; Godbout, Chris; Siwick, Bradley J. (2012). "Ultrafast electron diffraction with radio-frequency compressed electron pulses". Applied Physics Letters. 101 (8): 081901. Bibcode:2012ApPhL.101h1901C. doi:10.1063/1.4747155.