174 5.3  X-Ray Tools

(5.9)

r

mv

qB

m r

qB

mfr

qB

f

qB

m

E

mv

q B r

m

=

=

=

∴

=

≈

=

ω

π

π

2

2

1

2

2

2

2

2

2

Thus, f is independent of v, assuming nonrelativistic effects, which is the case for cyclotrons.

Synchrotrons have larger values of r than cyclotrons and therefore greater values of E, which

can exceed 20 MeV after which noticeable relativistic effects occur; thus, f must be varied

with v to produce a stable circular beam.

A synchrotron is a large-​scale infrastructure facility but produces brighter beams than x-​

ray tubes, with a greater potential range of wavelength ultimately permitting greater spatial

resolution. The use of major synchrotron facilities for providing dedicated x-​ray beamlines

for crystallography has increased enormously in recent years. In the two decades, since 1995,

the number of molecular structures solved using x-​ray crystallography, which were deposited

each year in the Protein Data Bank archive (see Chapter 7) from nonsynchrotron x-​ray crys­

tallography has remained roughly constant at ~1000 structures every year, whereas those

solved using synchrotron x-​ray sources has increased by a factor of ~20 over the same period.

Synchrotrons can generate a continuum of highly collimated, intense radiation from lower

energy infrared (~10⁻⁶ m wavelength) up to a much higher energy hard x-​rays (10⁻¹² m wave­

length). Their output is thus described as polychromatic. The spectral output from a typical

x-​ray tube is narrower at a wavelength of ~10⁻¹¹ m, but both synchrotron x-​ray and x-​ray tube

will often propagate through a monochromator to select a much narrower range of wave­

length from the continuum.

Monochromatic x-​rays simplify data processing significance and improve the effective

resolution and signal-​to-​noise ratio of the probe beam, as well as minimize damage to

the sample from extraneous satellite lines. An x-​ray monochromator typically consists of

a quartz (SiO2) crystal, often fashioned into a cylindrical geometry, which results in con­

structive interference at specific angles on for a very narrow range of wavelength due to Bragg

reflection at adjacent crystal planes. For a small region of the crystal, the difference in optical

path length between the backscattered rays emerging at an angle θ from two adjacent layers,

which are separated by a spacing d of an x-​ray scattering sample is 2d sin θ, and so the con­

dition for constructive interference is that this difference is equal to a whole integer number

n of wavelengths λ, hence 2d sin θ =​ nλ. Quartz has a rhombohedral lattice with an interlayer

spacing of d =​ 0.425 nm; the Ka line of aluminum has a wavelength of λ =​ 0.834 nm; there­

fore, this specific beam can be generated at an angle of θ =​ 78.5°. The typical bandwidth of a

monochromatic beam is ~10⁻¹² m.

A recent source of x-​rays for biophysics research has been from the x-​ray free-​electron

laser (XFEL). Although currently not being in sufficient mainstream use to act as a direct

alternative to synchrotron-​derived x-​rays, the XFEL may enable a new range of experiments

not possible with synchrotron beams. With x-​ray tubes and conventional synchrotron radi­

ation, the x-​ray source is largely incoherent, that is, a random distribution of phases of the

output photons. However, high-​energy synchrotron electrons can be made to emit coherently

TABLE 5.1  Wavelength Values of Typical Kα

Lines of Common Metal Targets

Used in the Generation of X-​Rays

Element

Kαλ (nm)

Mo

0.071

Cu

0.154

Co

0.179

Fe

0.194

Cr

0.229

Al

0.834