3 Requirements for Diffraction Precise details depend on nature of sampleBragg’s law: n λ=2d sin(Θ)Collimated beam is needed to define Θ:ΔΘ should be <reflection width or mosaic spread of sampleMonochromatic beam is needed to define λ; E= hc/λ (photons)ΔE/E = - Δλ/λ; Bragg: Δλ/λ = cot(Θ) Δ ΘMAD requires tunable beam, ΔE/E < 10-4Powders may benefit from larger ΔΘLaue experiments may require bandwidth of ~ 1KeV
4 Limitations of X-ray tubes Fluorescence emission from anode that is induced by high energy electron impact produces characteristic x-ray fluorescence, superimposed on Bremsstrahlung continuumlines are not (continuously) tunablex-rays are emitted in all directionsneed special optics to collect the X-rays and redirect them into roughly collimated beam
5 Why Synchrotron Radiation? It’s far more intense (>106) than lab sourcesTunable energyNaturally collimated in vertical plane - cleanwell-matched to crystal monochromatorsundulators produce pencil beam of x-raysBrilliance is much greater than other sourcesphotons/sec/source size/angular divergenceLight comes in rapid pulses - useful for time resolution
6 Brilliance of X-ray Sources graphic courtesy of APS
7 No radiation along acceleration vector Light EmissionAccelerating charged particles emit electromagnetic radiationradio, microwave, infrared, visible, UV, X-rays, gammasThese are emitted in a dipole patternNot collimated - frequency is same as oscillation frequency - radio waves?No radiation along acceleration vector
8 Relativity changes everything When particles move at speeds close to the speed of lightit’s still a dipole pattern in their instantaneous rest framebut in lab frame, radiation pattern tilts sharply into the forward direction “headlight effect”Frequency of emitted light measured in lab frame is dramatically higher -> x-rays
9 Our Friendly Neighborhood Synchrotron Source Advanced PhotonSource Argonne, IL
10 Inside the APS:LinacSynchrotronStorage RingTextTextInsertionDevicesBeamlines!
11 Inside the ringElectrons circulate very nearly at the speed of light (at the APS, only 1.5 m/s slower than c!).Relativistic parameter γ=E/mc2Their paths are made to bend using dipole bend magnets. The beams are focussed with quadrupole and sextupole magnets“insertion devices” (wigglers and undulators) can be placed in straight sections between dipole bend magnets
12 Synchrotron Radiation Wherever the path of the electrons bends, their velocity vector changesThis acceleration causes them to produce electromagnetic radiationIn the lab rest frame, this produces a horizontal fan of x-rays that is highly collimated (to ΔΘ≈ 1/γ) in the vertical direction and extends to high energiesEnergy is put back into electron beam by “surfing” through radio frequency (RF) cavities
13 Universal Flux Curve bend magnets & wigglers εc =19.5 KeV for APS dipole bend magnetsxtTextTextSynchrotron function g1(x) (solid) and simple approximation (dashes):f(x) = 1.8 x0.3 Exp(-x), where x=ε/εc. A more accurate approximation (not shown) is g1(x)=a*xbexp(-c x), with a= , b= , c= The spectral photon flux (photons /sec/0.1% bandwidth (Δε/ε)/mA beam current/mrad) integrated over the full vertical opening angle is1.256 *107 γ g1[x], with γ=E/mc2 and εc = 3hc γ3/(4πρ)
14 Insertion Devices Text arrays of magnets of alternating polarity between which the beam travelsThe alternating magnetic field causes the path of the electrons to wiggle back and forthAcceleration causes emission of radiation at each pole (typically poles)Unlike bend magnets, ID properties can be chosen to optimize beam specifically for experimentsTwo main types: Wigglers and UndulatorsInsertion DevicesText
15 Wigglers vs Undulators Wigglers cause the electron beam to oscillate with angular deviation that is large compared to 1/γWiggler spectrum follows universal curve (like bend magnet), scaled by number of polesUndulators use smaller deflections compared to 1/γLight emitted at each pole interferes with that emitted from othersEnergy spectrum is bunched up into harmonicsRadiation pattern is a pencil of light in forward direction
18 X-ray PolarizationIn the orbital plane, the radiation is nearly 100% linearly polarizedThis can be used for polarized XAFS (x-ray linear dichroism) experiments on oriented specimensOut of the orbital plane, bend magnet radiation has some degree of left/right circular polarizationWiggler/undulator radiation is not circularly polarized (planar devices)
19 What beamlines doBeamlines are complex instruments that prepare suitable x-ray beams for experiments, and protect the users against radiation exposure.They combine x-ray optics, detector systems, computer interface electronics, sample handling/cooling, and computer hardware and software.
20 Typical Beamline Functions Radiation shielding and safety interlockSelect/scan energies/wavelengths using monochromatorsFocus the beams with x-ray mirrors, bent crystals, fresnel zone plates, or refractive opticsDefine the beams with x-ray slitsMeasure beam intensity and record diffraction pattern with suitable detectorsElectronics amplify signal and interface to the computersComputer control and data acquisition system orchestrates motion of the monochromator and other optics, controls readout of detectors, and mediates remote control alignment of samples.
26 Heat load issues Undulators pose special challenges for optics high power density makes silicon at room temperature unsuitable (mostly): need higher thermal conductivity or lower thermal expansion coefficientCooling silicon to ~100K improves both propertiesDiamonds are excellent thermal conductors and synthetic diamonds are suitable monochromator crystals
29 Mirror reflectivity vs absorptivity of surface coating
30 HarmonicsMonochromators transmit not only the desired fundamental energy, but also some harmonics of that energy. Allowed harmonics for Si(111) include 333, 444, 555, 777…These can be reduced by slightly misaligning “detuning” the second crystal using a piezoelectric transducer (“piezo”). Detuning reduces the harmonic content much more than the fundamental.If a mirror follows the monochromator, its angle can be adjusted so that it reflects the fundamental, but does not reflect the harmonics.We have developed devices called “Beam Cleaners” can be made to select particular energies
31 Focussing equations Meridional focussing (typically, vertical mirror) optic curved along beam direction2 /(R Sin(Θ)) =1/u+1/vSagittal focussing (typically, horizontal crystal or mirror)optic curved perpendicular to beam direction2 Sin(Θ)/R=1/u+1/vu,v are source to optic distance, optic to focus distanceR is local radius of curvature of opticKirkpatrick-Baez mirror or Toroidal mirror
32 ConclusionWe have covered sources, monochromators, mirrors, and focussingIn single crystal diffraction experiments, once a monochromatic beam is delivered to the sample, the goniometer and detector do most of the work.In MAD experiments, it is necessary to measure the diffraction patterns at several relatively close energies, but the principles are the sameOther variants of diffraction (e.g. DAFS) require more sophisticated control system, but the principles are the same