# Xray Crystallography/Equipment

## Generating X-rays

### Rotating Anode

Simplified rotating anode tube schematic
• A: Anode
• C: cathode
• T: Anode target
• W: X-ray window

In house laboratory sources of X-ray radiation are typically rotating anode generators. An electron beam is focused, within a vacuum, from a metal cathode which emits electrons towards a rotating anode. The electrons accelerate between the cathode and anode due to the potential difference between them. On contact with the electrons, the metal ions in the anode release photons in the X-ray region of the EM spectrum. Photons are released of a wavelength characteristic of the metal used in the anode. For a copper anode X-rays with a wavelength of 1.54Å are produced from the K${\displaystyle \alpha }$ transition. Other possible metals are Chromium (K${\displaystyle \alpha }$ 2.29Å) and Molybdenum (K${\displaystyle \alpha }$ 0.71Å).

The anode rotates because the electrons are focused onto a small area of the anode to generate an intense X-ray source. However, this also creates very large heating effects which affect the X-ray radiation intensity.

The rotating anode tube is an improvement of the Coolidge tube. Because X-ray production is very inefficient (99% of incident energy is converted to heat) the dissipation of heat at the focal spot is one of the main limitations on the power which can be applied. By sweeping the anode past the focal spot the heat load can be spread over a larger area, greatly increasing the power rating.

The anode consists of a disc with an annular target close to the edge. The anode disc is supported on a long stem which is supported by bearings within the tube. The anode can then be rotated by electromagnetic induction from a series of stator windings outside the evacuated tube.

Because the entire anode assembly has to be contained within the evacuated tube, heat removal is a serious problem, further exacerbated by the higher power rating available. Direct cooling by conduction or convection, as in the Coolidge tube, is difficult. In most tubes, the anode is suspended on ball bearings with lead lubrication which provide almost negligible cooling by conduction.

A recent development has been liquid gallium lubricated fluid dynamic bearings which can withstand very high temperatures without contaminating the tube vacuum. The large bearing contact surface and metal lubricant provide an effective method for conduction of heat from the anode.

The anode must be constructed of high temperature materials. The focal spot temperature can reach 2500 °C during an exposure, and the anode assembly can reach 1000 °C following a series of large exposures. Typical materials are a tungsten-rhenium target on a molybdenum core, backed with graphite. The rhenium makes the tungsten more ductile and resistant to wear from impact of the electron beams. The molybdenum conducts heat from the target. The graphite provides thermal storage for the anode, and minimizes the rotating mass of the anode.

### Synchrotrons

Soleil synchrotron near Paris

Synchrotrons work differently from in-house generators. Synchrotron radiation is electromagnetic radiation generated by the acceleration of ultrarelativistic (i.e., moving near the speed of light) electrons through magnetic fields. This is achieved by the storage rings of a synchrotron.

• High brightness and high intensity, many orders of magnitude more than with X-rays produced in conventional X-ray tubes
• High brilliance, exceeding other natural and artificial light sources by many orders of magnitude: 3rd generation sources typically have a brilliance larger than 1018 photons/s/mm2/mrad2/0.1%BW, where 0.1%BW denotes a bandwidth 10-3w centered around the frequency w.
• High collimation, i.e. small angular divergence of the beam
• Low emittance, i.e. the product of source cross section and solid angle of emission is small
• Widely tunable in energy/wavelength by monochromatization (sub eV up to the MeV range)
• High level of polarization (linear or elliptical)
• Pulsed light emission (pulse durations at or below one nanosecond, or a billionth of a second);

Electrons are accelerated to high speeds in several stages to achieve a final energy that is typically in the GeV range. The electrons are stored in an ultrahigh vacuum ring on a closed loop and thus circle the ring a vast number of times. The electrons are forced to travel in a closed loop by strong magnetic fields. The magnets also need to repeatedly recompress the Coulomb-exploding space charge electron bunches. The change of direction is a form of acceleration and thus the electrons emit radiation at GeV frequencies. This is similar to a radio antenna, but with the difference that the relativistic speed changes the observed frequency due to the Doppler effect by a factor ${\displaystyle \gamma }$. Relativistic Lorentz contraction bumps the frequency by another factor of ${\displaystyle \gamma }$, thus multiplying the GeV frequency of the resonant cavity that accelerates the electrons into the X-ray range. Another dramatic effect of relativity is that the radiation pattern is also distorted from the isotropic dipole pattern expected from non-relativistic theory into an extremely forward-pointing cone of radiation. This makes synchrotron radiation sources the brightest known sources of X-rays. The planar acceleration geometry makes the radiation linearly polarized when observed in the orbital plane, and circularly polarized when observed at a small angle to that plane.

The advantages of using synchrotron radiation for spectroscopy and diffraction have been realized by an ever-growing scientific community, beginning in the 1960s and 1970s. In the beginning, storage rings were built for particle physics and synchrotron radiation was used in "parasitic mode" when bending magnet radiation had to be extracted by drilling extra holes.

As the application of synchrotron radiation became more intense and promising, devices that enhanced the intensity of synchrotron radiation were built into existing rings. Third-generation synchrotron radiation sources were conceived and optimized from the outset to produce bright X-rays.

Nowadays, fourth-generation sources that will include different concepts for producing ultrabright, pulsed time-structured X-rays for extremely demanding and also probably yet-to-be-conceived experiments are under consideration.

Working of the undulator. 1: magnets, 2: electron beam, 3: synchrotron radiation

As mentioned above, bending electromagnets are usually used to generate the radiation, but to generate stronger radiation, another kind of device, called an insertion device, is sometimes employed. Current third-generation synchrotron radiation sources are typically heavily based upon these insertion devices, when straight sections in the storage ring are used for inserting periodic magnetic structures (composed of many magnets that have a special repeating row of N and S poles) that force the electrons into a sinusoidal path or helical path. Thus, instead of a single bend, many tens or hundreds of "wiggles" at precisely calculated positions add up or multiply the total intensity that is seen at the end of the straight section. Thus these devices are called wigglers or undulators. The main difference between an undulator and a wiggler is the intensity of their magnetic field and the amplitude of the deviation from the straight line path of the electrons.

There are openings in the storage ring to let the radiation exit and follow a beam line into the experimenters' vacuum chamber. A great number of such beamlines can emerge from modern third-generation synchrotron radiation sources.

#### Beamlines

Beamlines of Soleil

At a synchrotron facility, the electrons are usually accelerated by a synchrotron, and then injected into a storage ring, in which they circulate, producing synchrotron radiation, but without gaining further energy. The radiation is projected at a tangent to the electron storage ring and captured by beamlines. These beamlines may originate at bending magnets, which mark the corners of the storage ring; or insertion devices, which are located in the straight sections of the storage ring. The spectrum and energy of X-rays differ between the two types. The beamline includes X-ray optical devices which control the bandwidth, photon flux, beam dimensions, focus, and collimation of the rays. The optical devices include slits, attenuators, crystal monochromators, and mirrors. The mirrors may be bent into curves or toroidal shapes to focus the beam. A high photon flux in a small area is the most common requirement of a beamline. The design of the beamline will vary with the application. At the end of the beamline is the experimental end station, where samples are placed in the line of the radiation, and detectors are positioned to measure the resulting diffraction, scattering or secondary radiation.

## Crystal Rotation

Crystals are rotated about one or more axis using a goniometer. Rotation, like all of data collection, is computer controlled.

The most important variables to be considered are;

• The power settings of the X-ray generator
• Exposure time for an image
• Distance between the detector and crystal
• Starting rotation angle
• Change in rotation angle during the exposure
• Number of images to be taken