Electronica

1
1.1

X-Ray Physics
Introduction

One of the main methods to decode the structure of condensed matter on atomic scale
is x-ray diffraction. While it was originally used to analyze crystalline structures such as
metals, it can also be used to gain insights on the structure of proteins. In that case, the
protein must either be available in its crystallized form or contain crystallinecomponents,
as is the case for spider silk.
In the electromagnetic spectrum x-rays are to be found between ultraviolet light and
high energy gamma rays. The wavelength range lies between 0.01 and 10 nm and is
therefore of the order of distances between molecules and crystal lattice constants. Xrays with wavelengths longer than 1 nm are called soft x-rays, those of shorter wavelengths
areconsidered hard. Hard x-rays may range into the regime of low energy γ rays, since the
distinction between the two is derived from the source of radiation, not its wavelength.
X-rays are generated by energetic electron processes, gamma rays by transitions in atomic
nucleons.

1.2

Creation of x-rays

Today, there are two commonly used different methods to create x-rays. The first is based
ondecelerating very fast electrons by firing them at a heavy metal target. As explained by
Maxwell’s equations, the electrons will emit electromagnetic radiation upon deceleration,
which is called the Bremsstrahlung. The true interest lies, however, in the electrons that
have enough energy to knock metal electrons out of their shells. This will cause electrons
from upper shells to drop down and fill thecreated gap, thereby emitting a photon with
an energy corresponding to the energy difference between the levels (figure 1). The x-rays
produced by transitions from the n = 2 to the n = 1 levels are called Kα x-rays, those
for n = 3 → 1 are called Kβ x-rays. The energy efficiency of this process is only about
0.1%, most is lost in heat. Two of the most common elements used to create x-rays inthis fashion are copper and molybdenum.
The alternative is to use x-ray radiation from synchrotrons, which are usually linear
electron accelerators combined with storage rings. Here, the electrons are kept flying
in a circle at a well-defined speed, giving off reasonably monochromatic x-rays as they
go. The brilliance of the x-rays by far surpasses that of the ones created by characteristicradiation. Electron storage rings are huge and expansive, however, two of the most famous
ones being the DAISY in Hamburg, the ESRF in Grenoble and the CERN in Gen`ve.
e

1.3

Basics of x-ray scattering

Fig. 1: Bremsstrahlung with characteristic radiation peaks. Taken from [1].

1.3
1.3.1

Basics of x-ray scattering
Thomson scattering

In the classical description of the scatteringprocess, an electron is forced to vibrate
by the electric field of an incoming x-ray beam. Because the mass of an electron is
over a thousand times lighter than that of a nucleon, the resulting vibration and the
corresponding emitted intensities are a lot higher. This is the reason why x-rays give a
picture of the electron densities of a material and not of the nucleon positions themselves.
Toderive the scattering intensities of a material, it is therefore useful to start with the
scattering by a single electron and move from there to atoms, molecules and crystals.
Using Maxwell’s equations, it can be derived that the ratio of magnitude between radiated
and incident field of a single electron is given by:
Erad (R, t)
e2
=−
Ein
4πǫ0 mc2

eikR
cosψ.
R

The prefactor
e2
r0 == 2.82 · 10−6 nm
2
4πǫ0 mc

(1)

1.3

Basics of x-ray scattering

is called the Thomson scattering length, the angle ψ is the angle between incident and
scattered beam, R is the distance between the observer and the electron, k = (2π )/λ is
the absolute value of the wave vector, e is the elementary charge, c the speed of light, m
the mass of the electron, λ the x-ray wavelength and...