# X-Ray Production: Sources and Optics

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X-Ray Production: Sources and Optics
Goals develop beamline protocols (the algorithm) Describe tools Diffractometer/detector Comprehensive software R.M. Sweet Brookhaven Biology

Plan for the lecture: I. Considerations in the choice of an x-ray source A. Resolve the spots B. Optimize accuracy (decrease error) II. Types of Source A. Sealed tube and rotating Anode B. Synchrotron III. X-Ray Optics A. Monochromatization B. Collimation C. Focussing

Considerations in the choice, or design, of an x-ray beam for a diffraction experiment.
What should the source look like? How do we condition the beam: Monochromators? Focussing? Slits? How should the beam match the properties of the specimen?

What are the goals of the crystallographic experiment?
Bring all Bragg planes into diffracting position Integrate the diffraction intensity from each set of Bragg planes Over the volume of the crystal Over the crossfire of the x-ray beam Over the mosiac nature of the crystal To accomplish this, we must resolve the reflected beams: On the surface of the x-ray detector Throughout any rotation of the crystal

Here’s an example of the problem!
The longest unit-cell edge is 570Å in this photo from crystals of the Nobel-Prize winning 50S ribosomal subunit project. Ban, et al, Cell 1998

Let’s look at it in detail:
Blow this up Ban, et al, Cell 1998

Their length comes from the horizontal divergence of the focussed beam
The spots almost touch. Their length comes from the horizontal divergence of the focussed beam The kidney shape comes from defects in the optics. Ban, et al, Cell 1998

Consider the diffraction one would get from a perfect infinitesimal (point) crystal and a point source of x-rays. Intensity The crystal diffracts only at one position, and the diffracted beam is thin on the detector. rotate . . Intensity Source of x-rays The Crystal Detector Surface Rotation

The total angle of reflection is
Next, consider diffraction from a finite perfect crystal and a point source of x-rays. Intensity One must rotate the crystal to allow first its top and then its bottom to “see” the source. (F + ) s /  s Source of x-rays . F Intensity The Crystal Detector Surface Df The total angle of reflection is Df = s /  Rotation

There are perfect crystals, and then there are mosaic crystals
If the rays coming in are perfectly parallel, the whole block of the perfect crystal will diffract, but only those blocks of the mosaic crystal that are aligned with the beam will diffract. To get all of the mosaic crystal to diffract, one must: Use an x-ray beam with crossfire, or Rotate the crystal in the beam.

The total angle of reflection is
Now, consider diffraction from a finite mosaic crystal and a point source of x-rays. The crystal must be rotated over an even wider range of positions, producing a diffracted beam that is the same size on the detector, but is wider in rotation. Intensity (F + ) s /  s Source of x-rays . F Intensity The Crystal Detector Surface Df The total angle of reflection is Df = s /  +  Rotation

The total angle of reflection is
Finally, consider a finite mosaic crystal and a finite source of x-rays. Intensity The crystal diffracts over an even wider range of positions, and now the beam on the detector is wider. (F + ) s /  + F f /  Source of x-rays s f F Intensity The Crystal Detector Surface Df The total angle of reflection is Df = (s + f) /  +  Rotation

Let’s think about spot size and spot separation.
On the previous drawing we had that the spot size was: (F + ) s /  + F f /  = s + (s + f) F/  Notice that this (s + f) /  term represents all of the crossfire of the beam, whatever the source We’ll call it . So the spot size becomes s +  F

1 / d Therefore, to resolve spots, we must have that the spacing is greater than the size: F  / d > s +  F F [ / d - ] > s F > s / [ / d - ] One can see that this will work as long as the beam crossfire is small enough!! F  / d  / d 1 /  F

Plan for the lecture: I. Considerations in the choice of an x-ray source A. Resolve the spots B. Optimize accuracy (decrease error) II. Types of Source A. Sealed tube and rotating Anode B. Synchrotron III. X-Ray Optics A. Monochromatization B. Collimation C. Focussing

Accuracy - I: Statistical Precision
With photon counting, var (I) = 2 (I) = I For example, relative error is the standard deviation / the measured intensity = (I)/I = 1/I1/2 Therefore, for I = 104, (I)/I = 0.01 (1% error) There must be sufficient photons to provide the statistical precision one wants. The signal must be strong enough to rise above the noise in the counting system and other sources of “background” noise.

How can we minimize background noise?
Total scanned intensity: S The integrated intensity we seek: I Intensity Intensity Scan Scan Detector noise and x-ray background The portion of the background that must be subtracted from the scan: B We have: I = S - B Standard error propagation gives 2I = 2S + 2B Since I, B, and S all are counts, 2S = S, 2B = B This gives: I / I = (S - B) / (S + B)1/2 It pays to make the reflection sharp. One wants a bright source! {Photons / (time, area, wavlelength bandwidth, crossfire)}

Detective Quantum Efficiency
DQE is a useful concept for assessing the quality of a data-collection system. Define efficiency as the double ratio: the squared output signal-to-noise (including background and detector noise) against the ideal signal-to-noise. If the output is simply a count attenuated by some factor, say the efficiency of absorption, we can see the term Efficiency makes sense.

Evaluate DQE for an Integrated Intensity
So any change in an experimental system that decreases B, whether it’s x-ray background or instrumental noise, improves the efficiency of this system.

Ways to Decrease the Background
Make the specimen mount as small as possible Use a beam no larger than the specimen Place the beamstop as close to the specimen as practicable Move the detector as far from the crystal as possible, consistent with the resolution you desire

Accuracy - II: Minimize Systematic Errors
Specimen damage: One will see usually uncorrectable variation in data Resolution limit decreases Freezing the crystal helps Consider using several x-tals with shorter total exposures on each Absorption errors: Watch for high salt solutions Make freezing loops as small as possible Because absorption varies as 3 while scattering varies as 2, it pays to use a shorter wavelength.

Plan for the lecture: I. Considerations in the choice of an x-ray source A. Resolve the spots B. Optimize accuracy (decrease error) II. Types of Source A. Sealed tube and rotating Anode B. Synchrotron III. X-Ray Optics A. Monochromatization B. Collimation C. Focussing

Conventional Sources of X-Rays
Conventional x-ray sources depend on a beam of electrons, drawn from a hot filament by a high voltage field. The electrons strike an anode, usually made from a pure elemental metal, driving an electron from an atomic orbital. The emitted radiation depends on the fluorescence spectrum of the emitting element. Anode Cathode ~10V ~40kV + -

Pseudo-Monochromatic X-Rays
There is typically a complex series of lines, with K emission being strongest K is a peak that needs to be separated from K Most of low wave-length radiation is removed with a filter that is one atomic number lower than the anode. K1 and K2 are distinct emissions. Wavelengths () are: K1 = K2 = Kave = K = E.W. Nuffield (1966) X-Ray Diffraction Methods

The Modern Laboratory X-Ray Generator
Old-style generators had a fixed anode with water cooling. Modern ones employ a rotating water-cooled anode. The “specific loading” of this sort of generator can be 4kW of electrical power through a square mm of the anode surface!! Water for cooling Motor drive Rotating anode seal X-Rays Beryllium window -40 kV relative to the anode Focusing cup Electrons Hot filament

Plan for the lecture: I. Considerations in the choice of an x-ray source A. Resolve the spots B. Optimize accuracy (decrease error) II. Types of Source A. Sealed tube and rotating Anode B. Synchrotron III. X-Ray Optics A. Monochromatization B. Collimation C. Focussing

The National Synchrotron Light Source
The NSLS can produce usable radiation from the dipole, or bending” magnets. There are two storage rings producing radiation. The lower-energy ring (750 MeV) produces light from the IR through to soft X-rays. The higher energy ring (2.6 GeV) produces hard X-rays for diffraction studies. Both rings have multi-magnet insertion devices.

It’s like flicking a string! Electron trajectory Induced Electric Vector Synchrotron Light Relativistic Electron The harder the bend, and the faster the electrons (higher energy), the shorter the wavelength is of the light. Dipole Magnet

There’s a wide spectrum of x-rays available to us for diffraction studies. Here you see the arc (dipole or bending-magnet) and wiggler sources.

This is for dipoles (bending magnets)
This is for dipoles (bending magnets). For undulators, the photons emitted at the little dipoles run along beside the (relativistic) electrons. Courtesy of Wayne Hendrickson

Just like the slalom skier – see how the snow she disturbs follows along the fall line at about the same speed. Courtesy of Wayne Hendrickson

The photons interfere with the electrons, and at each undulation the electrons produce new photons that are a harmonic of the frequency of the original, thus the peaky spectrum you see here. The X25 undulator spectrum.

Plan for the lecture: I. Considerations in the choice of an x-ray source A. Resolve the spots B. Optimize accuracy (decrease error) II. Types of Source A. Sealed tube and rotating Anode B. Synchrotron III. X-Ray Optics A. Monochromatization B. Collimation C. Focussing

MSC/Rigaku/Osmic, Inc. are making “synthetic crystal” multilayer systems to be used in synchrotrons and home laboratories.

Their “confocal” system employs a “graded multilayer” on a curved backing. It gives a nice beam for most crystallographic applications. Fine spacing, high angle Coarse spacing, low angle Slight elliptical curvature gives focussing

For a synchrotron source:
Rays are nearly parallel Use a perfect crystal Si cut to use the (1,1,1) planes is a good choice Often we use two crystals: One to monochromatize One to deflect the beam back up into the horizontal plane Braggs’ law determines the wavelength

Plan for the lecture: I. Considerations in the choice of an x-ray source A. Resolve the spots B. Optimize accuracy (decrease error) II. Types of Source A. Sealed tube and rotating Anode B. Synchrotron III. X-Ray Optics A. Monochromatization B. Collimation C. Focussing

Beam Collimation (Use of Slits)
In a classic sense, collimation means “to make the rays parallel.” We generally use the term to mean limiting the beam and avoiding extra scattered rays. Specimen Limiting Aperture Source of x-rays Beamstop Guard or Scatter Aperture The beamstop must be placed to catch the scatter from the limiting aperture that is missed by the scatter aperture.

Plan for the lecture: I. Considerations in the choice of an x-ray source A. Resolve the spots B. Optimize accuracy (decrease error) II. Types of Source A. Sealed tube and rotating Anode B. Synchrotron III. X-Ray Optics A. Monochromatization B. Collimation C. Focussing

Beam Focusing (Use of a bent mirror)
Although we can’t make a lens for x-rays, we can do some optical things by total reflection at very low angles. Physically, it’s like internal reflection in a prism. These are very low angles: ~ 0.5 deg. One application is Franks (sometimes called Yale) mirrors On your local x-ray generator the distances are ~100mm.

Focussing of the X-Ray Beam
X-Rays come from the synchrotron in a fan. We’d like a more condensed beam of radiation for crystallography One should be able to focus with an ellipsoid of revolution . We can’t actually manage that, so we make a cylinder, then bend it to the shape of a toroid.

Summary I. Careful choice of an x-ray source helps to
A. Resolve the spots B. Optimize accuracy (decrease error) II. Several kinds of Source are available A. Sealed tube and rotating Anode B. Synchrotron III. X-Ray Optics condition the beam A. Monochromatization B. Collimation C. Focussing

The Future Light Source for the Northeastern US
NSLS-II

High Level Description of NSLS-II
New Capabilities Nanoprobes Diffraction Imaging Coherent Dynamics New Science A highly optimized x-ray synchrotron delivering: very high brightness and flux; exceptional beam stability; and a suite of advanced instruments, optics, and detectors that capitalize on these special capabilities. Together, these will enable: ~ 1 nm spatial resolution, ~ 0.1 meV energy resolution, and single atom sensitivity. Nanoscience Life Science Nanocatalysis

A Suite of Structural Biology Beamlines
VUV MX FP XRSS XAS 3PW hutch DW hutch Undulator hutch VUV 45 45

18 Months Total Schedule Contingency
Preliminary Summary Schedule 18 Months Total Schedule Contingency

Micro- beam diffraction
The modern 3rd generation sources easily produce beams in the 10 micrometer size range. A few can accomplish 5 micrometers, and ones are being planned in the 1 micrometer range. How might these be useful?

Small beams can be used either with very small crystals...
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Or to make multiple small-beam exposures at different points on a larger crystal.
This strategy minimizes the damage exhibited in the overall diffraction data set from the crystal. 49