Diffraction & Interference Diffraction: spreading of waves around obstacles (EM waves, matter, or sound) Interference: the interaction of waves Diffraction in Nature
What is Interference? The resultant of several waves EM waves, matter, or sound Constructive Interference Destructive Interference Interference.5 φ =.5 φ = 45.5.5 -.5 -.5 - -.5 - -.5 φ - -.5 φ = 9.5 φ = 35.5 φ = 8.5.5.5 -.5 -.5 -.5 - -.5 φ - -.5 φ - -.5 φ - - -
Superposition phase changes with time waves travel in opposite directions different frequencies standing wave beats Both constructive and destructive interference http://www.acs.psu.edu/drussell/demos/superposition/superposition.html Diffraction Relative Intensity.8.6.4. Angle (degrees) - - L =.5m λ = 7nm a = 7 µm λl a = 5cm where - -5 - -5 5 5 R = Distance (cm) Minima occur at: n =,, 3 Assumes: L >> a (Fraunhofer) L >> R (θ v. small)
Minima at: Diffraction n =,, Relative Intensity.8.6.4. Angle (degrees) - - L =.5 m λ = 7 nm a = 7 µm d = 5 µm λl =.3cm d - -5-5 5 5 Distance (cm) single slit double slit, 5µm apart Maxima occur at ~ Assumes: L >> a (Fraunhofer) L >> R (θ v. small) Maxima at ~ Diffraction n =,, Relative Intensity.8.6.4. Angle (degrees) - - L =.5m λ= 7 nm a = 7 µm d = 5 µm N = 6 λl =.3cm d single slit six slits - -5 - -5 5 5 Distance (cm) More slits: sharper & more intense peaks maxima/minima equations more accurate Assumes: L >> a (Fraunhofer) L >> R (θ v. small)
Diffraction slit -λl/a λl/a λl/d slits -λl/a λl/a λl/d 6 slits -λl/a Distance λl/a Diffraction Intensity L =.5m λ= 7nm a = 7 µm - -5 - -5 5 5 Radial Distance (cm) We ll see later: δ = L.λ D } =sinθ R ~ θ R Assumes: L >> a (Fraunhofer) L >> R (θ v. small)
Bragg s Law d θ θ dsinθ dsinθ dsinθ = nλ X-Ray Diffraction
Filtering X-Ray Detection Proportional counter High V causes gas amplification Current in wire is proportional to number of x-rays (intensity) Reduce V to ~ V, lose gas amplification (ionisation chamber - obsolete) Increase V to ~5V, get Geiger counter, low count rate so also obsolete for diffractometry Area detector in D8 is proportional type Needs regassing every ~5 years X-rays in Argon gas Window Pulse counter electronics wire High voltage V
X-Ray Detection Scintillation counter Diffracted x-rays incident on Tl-NaI, which fluoresces violet Light photon passes to CsSb photocathode, which emits electron Electrons are drawn to several metallic dynodes, each at V more than the previous Each electron incident on dynode produces several more (photomultiplier) Final pulse is about same size as in Geiger counter Process takes less than ms, so can operate at high count rates ( 5 /s) without loss More sensitive than proportional counters to high-frequency (hard) radiation Detector in Miniflex and point detector in D8 are scintillation type X-Ray Detection Si(Li) semiconductor detector Surfaces of 3-5mm thick cylindrical B-doped Si crystal (p-type) are oppositely charged by diffusion of Li + under high reverse bias at elevated temperature Most of bulk left with equal concentrations of Li + and B 3+ and so intrinsically semiconducting Like solid-state ionization chamber: ~ e - /h + pairs created per x-ray ~kv bias sweeps charge carriers to opposite faces causing pulse in external circuit No charge amplification, so FET used to amplify signal to mv range Requires LN cooling to minimize thermal current & Li diffusion and maximize resolution of FET Better energy resolution than proportional or scintillator counters
X-Ray Detection Silicon Drift Detector (SDD) High-purity Si cooled to ~ C Chip sits atop Peltier cooling device (no need for LN) Electrons created by x-rays drift to a small collection anode Moving FET off chip reduces throughput but decreases noise so improves resolution especially for light elements Noise increase with size of crystal, so larger SDDs don't have on-chip FETs Compared to Si(Li), SDDs have: better energy resolution (3 ev for Mn Kα) higher count rates (throughput) (~75, cps) lower capacitance between anode and FET, so less noise