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

2. 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

3. 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?

4. 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

5. 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

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

7. 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

8. 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

9. 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

10. 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.

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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.

17. 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)}

18. 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.

19. 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.

20. 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

21. 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.

22. 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

23. 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 + -

24. 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

25. 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

26. 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

27. 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.

28. The Source of Synchrotron Radiation
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

29. 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.

30. 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

31. 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

32. 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.

33. 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

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

35. 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

36. 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

37. 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

38. 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.

39. 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

40. 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.

41. 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.

42. 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

43. The Future Light Source for the Northeastern US
NSLS-II

44. 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

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

46. 18 Months Total Schedule Contingency
Preliminary Summary Schedule
18 Months Total Schedule Contingency

47. 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?

48. Small beams can be used either with very small crystals... 48

49. 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