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PowerPoint File available:. http://bl831.als.lbl.gov/ ~jamesh/powerpoint/ ACA_SINBAD_2013.ppt. Acknowledgements. Ken Frankel Alastair MacDowell John Spence Howard Padmore LBNL Laboratory Directed Research & Development (LDRD) ALS 8.3.1 creator: Tom Alber PRT head: Jamie Cate

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**PowerPoint File available:**http://bl831.als.lbl.gov/ ~jamesh/powerpoint/ ACA_SINBAD_2013.ppt**Acknowledgements**Ken Frankel Alastair MacDowell John Spence Howard Padmore LBNL Laboratory Directed Research & Development (LDRD) ALS 8.3.1 creator: Tom Alber PRT head: Jamie Cate Center for Structure of Membrane Proteins Membrane Protein Expression Center II Center for HIV Accessory and Regulatory Complexes W. M. Keck Foundation Plexxikon, Inc. M D Anderson CRC University of California Berkeley University of California San Francisco National Science Foundation University of California Campus-Laboratory Collaboration Grant Henry Wheeler The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences Division, of the US Department of Energy under contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory.**Simultaneous**INverse Beam Anomalous Diffraction**SINBAD diffractometer concept**h,k,l λ = 5 Å -h,-k,-l XFEL beam d = 3.5 Å d = 3.5 Å Nucleus Mirrors Detector Detector Synthetic light collecting structure d = 3.5 Å sample injector Detector Detector Mirrors d = 3.5 Å d = 3.5 Å**Why SINBAD?**New source of error in SFX I+ I- Different crystal volumes**Why SINBAD?**New source of error in SFX I+ I- Different crystal orientations**Why SINBAD?**New source of error in SFX I+ I- Different beam intensities**Why SINBAD?**New source of error in SFX I+ I- Different crystal positions**Why SINBAD?**New source of error in SFX I+ I- Different structures (non-isomorphism)**Why SINBAD?**New source of error in SFX I+ I- Dynamic range**Why SINBAD?**New source of error in SFX I+ I- Problem: How to get I+ and I- bothon Ewald sphere at the same time? ΔIano**Osculating Ewald Spheres**(h,k,l) Ewald sphere 2 λ* diffracted ray d* λ* θ θ λ* d* diffracted ray λ* 1 (-h,-k,-l) Ewald sphere**SINBAD diffractometer concept**h,k,l λ = 5 Å -h,-k,-l XFEL beam d = 3.5 Å d = 3.5 Å Nucleus Mirrors Detector Detector Synthetic light collecting structure d = 3.5 Å sample injector Detector Detector Mirrors d = 3.5 Å d = 3.5 Å**Tolerances:**Time: ~10% of 100 fs Distance: 3 μm Angle: ~1% of mosaicity ~100 μRad**Can’t we just use scaling?**Ispot≈ |F(hkl)|2**Vxtal**λ3 L Vcell ωVcell Darwin’s Formula I(hkl) = Ibeam re2 P A | F(hkl) |2 I(hkl) - photons/spot (fully-recorded) Ibeam - incident (photons/s/m2 ) re - classical electron radius (2.818x10-15 m) Vxtal - volume of crystal (in m3) Vcell - volume of unit cell (in m3) λ - x-ray wavelength (in meters!) ω - rotation speed (radians/s) L - Lorentz factor (speed/speed) P - polarization factor (1+cos2(2θ) -Pfac∙cos(2Φ)sin2(2θ))/2 A - attenuation factor exp(-μxtal∙lpath) F(hkl) - structure amplitude (electrons) C. G. Darwin (1914)**Vxtal**λ3 L Vcell ωVcell Darwin’s Formula I(hkl) = Ibeam re2 P A | F(hkl) |2 I(hkl) - photons/spot (fully-recorded) Ibeam - incident (photons/s/m2 ) re - classical electron radius (2.818x10-15 m) Vxtal - volume of crystal (in m3) Vcell - volume of unit cell (in m3) λ - x-ray wavelength (in meters!) ω - rotation speed (radians/s) L - Lorentz factor (speed/speed) P - polarization factor (1+cos2(2θ) -Pfac∙cos(2Φ)sin2(2θ))/2 A - attenuation factor exp(-μxtal∙lpath) F(hkl) - structure amplitude (electrons) C. G. Darwin (1914)**Vxtal**λ3 L Vcell ωVcell Darwin’s Formula I(hkl) = Ibeam re2 P A | F(hkl) |2 I(hkl) - photons/spot (fully-recorded) Ibeam - incident (photons/s/m2 ) re - classical electron radius (2.818x10-15 m) Vxtal - volume of crystal (in m3) Vcell - volume of unit cell (in m3) λ - x-ray wavelength (in meters!) ω - rotation speed (radians/s) L - Lorentz factor (speed/speed) P - polarization factor (1+cos2(2θ) -Pfac∙cos(2Φ)sin2(2θ))/2 A - attenuation factor exp(-μxtal∙lpath) F(hkl) - structure amplitude (electrons) C. G. Darwin (1914)**Greenhough-Helliwell Formula**ΔΦ = L sin2θ (2η + Δλ/λ tanθ) + ((L2sin22θ - 1)γH2 + γV2)1/2 ΔΦ - reflecting range (radians) 2η - mosaic spread (radians) L - Lorentz factor (speed/speed) θ - Bragg angle λ - x-ray wavelength Δλ - wavelength spread γHV - horizontal and vertical beam divergence (radians) Greenhough & Helliwell (1983)**Greenhough-Helliwell Formula**ΔΦ = L sin2θ (2η + Δλ/λ tanθ) + ((L2sin22θ - 1)γH2 + γV2)1/2 ΔΦ - reflecting range (radians) 2η - mosaic spread (radians) L - Lorentz factor (speed/speed) θ - Bragg angle λ - x-ray wavelength Δλ - wavelength spread γHV - horizontal and vertical beam divergence (radians) Greenhough & Helliwell (1983)**Lorentz Factor**Ewald sphere diffracted ray spindle axis**Vxtal**λ3 L Vcell ωVcell Darwin’s Formula I(hkl) = Ibeam re2 P A | F(hkl) |2 I(hkl) - photons/spot (fully-recorded) Ibeam - incident (photons/s/m2 ) re - classical electron radius (2.818x10-15 m) Vxtal - volume of crystal (in m3) Vcell - volume of unit cell (in m3) λ - x-ray wavelength (in meters!) ω - rotation speed (radians/s) L - Lorentz factor (speed/speed) P - polarization factor (1+cos2(2θ) -Pfac∙cos(2Φ)sin2(2θ))/2 A - attenuation factor exp(-μxtal∙lpath) F(hkl) - structure amplitude (electrons) C. G. Darwin (1914)**Integral under curve**“Full” Spot intensity**Integral under curve**Spot on “Still” intensity**What is “partiality”?**Ewald sphere F(h,k,l) λ* d* diffracted ray λ***What is “partiality”?**Ewald sphere F(h,k,l) λ* d* diffracted ray λ***What is “partiality”?**Ewald sphere F(h,k,l) λ* d* diffracted ray λ***What is “partiality”?**Ewald sphere F(h,k,l) λ* d* diffracted ray λ***What is "partiality"?**100% !**Bragg, James & Bosanquet (1921). Philos. Mag. Ser. 6, 41,**309–337.**What is “partiality”?**Ewald sphere F(h,k,l) λ* d* Partiality is always 100% ! diffracted ray λ* F(0,0,0)**What is “partiality”?**Ewald sphere F(h,k,l) λ* d* Partiality is always 100% ! diffracted ray λ* F(0,0,0)**What is “partiality”?**Ewald sphere F(h,k,l) λ* d* Partiality is always 100% ! diffracted ray λ* F(0,0,0)**What is “partiality”?**Ewald sphere F(h,k,l) λ* d* Partiality is always 100% ! diffracted ray λ* F(0,0,0)**Why SINBAD?**New source of error in SFX I+ I- Different crystal orientations**F(h,k,l)**spectral dispersion λ1* Ewald sphere λ2* ~90% 100% F(0,0,0)**F(h,k,l)**spectral dispersion λ1* Ewald sphere λ2* ~45% 100% F(0,0,0)**F(h,k,l)**spectral dispersion 0% λ1* Ewald sphere λ2* 100% F(0,0,0)**beam divergence**Ewald sphere F(h,k,l) λ* d* diffracted ray λ* F(0,0,0)**beam divergence**Ewald sphere d* λ* diffracted ray F(0,0,0) λ*

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