170 5.2  Electron Microscopy

be focused using electromagnetic lenses, the diffraction pattern retains phase information

from the sample in much the same way as focused rays of light in optical microscopy. This

offers an advantage over x-​ray diffraction for which phase information has to be inferred

indirectly (discussed later in this chapter).

A key biophysical application of electron diffraction is determining structural details

of lipid arrays and membrane proteins, for which 3D crystals are difficult to manufac­

ture, which is a requirement for x-​ray crystallography. Close-​packed 2D lipid–​protein

arrays are feasible to make, to determine the spacing of periodic biological structures

in the sample, using both backscattered electrons in Bragg reflection experiments and

transmitted electrons. Electrons incident on a sample having periodic features over a

characteristic length scale db can generate backscattered electrons (also known as “Bragg

reflection” or “Bragg diffraction”) by an angle θb from the normal. Since the backscattered

electrons are coherent, they can interfere, such that the condition for constructive inter­

ference generates an nth order intensity maxima, which are given by Bragg’s law, where n

is a positive integer:

(5.5)

sinθ

λ

b

b

n

d

= 2

Primary electrons may, of course, also be transmitted through the sample at an angle θt from

the normal due to electron diffraction through periodic layer features of length scale dt, with

the condition for constructive interference being

(5.6)

sinθ

λ

t

t

n

d

= 2

Selected area diffraction is often used for electron diffraction, in which a metal plate

containing different aperture sizes can be moved to illuminate different sizes and regions

of the sample. This is important in heterogeneous samples; these are potentially polycrys­

talline, which can result in difficult interpretations of electron diffraction patterns if more

than one equivalent periodic structure is present. If it is possible to spatially delimit the area

of illumination to just one diffracting periodic region, this problem can often be eradicated.

However, the strong interaction with matter of the electron beam confers a significant danger

of radiation damage of the sample, and consequently, samples need to be cooled using liquid

nitrogen or sometimes liquid helium.

Electron diffraction can also be used in ptychographic EM (Humphry et al., 2012). The

key physical principles of ptychographic diffractive imaging for EM are the same as those

discussed previously for light microscopy in Chapter 4. In essence, physical lenses used for

imaging can be replaced by an inverse Fourier transform of the diffraction data detected from

the sample.

The same method has been applied in a bespoke setup using relatively low-​energy 30

kV electrons to form a transmitted electron diffraction image. By modifying an SEM, the

primary electron is defocused to generate a broader 20–​40 nm illumination patch on the

sample. The effects of spherical aberration by the objective electron lens, which normally

focuses the beam onto the sample, are largely eradiated since it is used simply to concentrate

the electron beam into a delimited region of the sample, as opposed to acting as an imaging

component.

A CCD detector is located below the sample to detect the transmitted diffracted electrons

(the diffraction pattern formed is a type of a Gabor hologram), which is combined with a

much stronger signal from transmitted nonscattered electrons. The phases from a scattering

object can be recovered in a similar way using the ptychographic iterative engine (PIE) algo­

rithm as for optical ptychography, since the scanned electron beam moves over the sample

to generate overlap.