1. Detector 2. Crystal diffraction conditions 2-7-05

Detector in X-ray crystallography: Image plates (IP) The imaging plate (IP) is a reusable 2-D X-ray detector. Imaging plates are sensitive not only to X-rays, but other types of radiation as well: gamma radiation, alpha and beta particles, neutrons and electron beams, and serve as the primary radiation detector in many fields Advantages: high sensitivity, low noise, wide dynamic range, good linearity, good spatial resolution, modest cost. It consists of a photostimulable phosphor powder in an organic binder with a thickness between 25 and 150 mm deposited on a flexible polymer support film of about 250 mm thickness. The family of compounds comprising BaFX:Eu2+ (X = Cl, Br) have been known to have high luminescence efficiency for X-ray excitation. Phosphor Supporting film A mar detector Dia. = 345mm

Detector in X-ray crystallography: Image plates (IP) The IP is exposed to the x-ray source and stores the impinging X-rays as a latent image in the phosphor. This image is recovered by scanning a laser beam across the IP, causing photostimulated luminescence (PSL). This PSL is recorded by a photomultiplier that is scanned across the IP at the same time as the laser. The resultant signal is digitized and stored in a file for data processing.

Image plates are commonly used in academic laboratories Disadvantage: decay, high background, slow readout. Advantages: high sensitivity, low noise, wide dynamic range, good linearity, good-to-high spatial resolution, modest cost.

Detector in X-ray crystallography: CCD Charge Coupled Device (CCD) was invented in the late 1960s by researchers at Bell Labs, The CCD's  superb ability to detect light has turned it into the industry-standard image sensor technology. CCD Basics - CCD imaging is performed in a three-step process:        1. Exposure, which converts light into an electronic charge at discrete sites called pixels        2. Charge transfer, which moves the packets of charge within the silicon substrate        3. Charge-to-voltage conversion and output amplification.

Detector in X-ray crystallography: CCD The three main components of the Quantum CCD detector are phosphor screen (to convert X-rays to light), fiber-optic taper (to demagnify the light image down to the size of the CCD chip), and CCD chip to detect the light image as an electric charge image.  The electric charge image is read  out of the CCD chip and digitized (converted to binary numbers) then fed into a computer. An ADSC CCD detector used in many major synchrotron stations

Detector in X-ray crystallography: CCD The principal advantages of CCDs are their sensitivity, dynamic range and linearity. The sensitivity, or quantum efficiency, is simply the fraction of photons incident on the chip which are detected. It is common for CCDs to achieve a quantum efficiency of about 80%. Compare this figure with only a few percent for photographic plates. A typical dynamic range (that is, the ratio of the brightest accurately detectable signal to the faintest) is about 105. The corresponding figures for a photographic plate are a range of less than about 1000. Within this dynamic range the response is essentially linear: the size of the signal is simply proportional to the number of photons detected, which makes calibration straightforward. Fast readout of digitized images Disadvantages: High costs and small areas

A typical diffraction pattern

Diffraction geometry: an outline Diffraction basics Laue equations Braggs law Reciprocal space and diffraction Diffraction methods – Laue photographs – Oscillation photographs

X-ray is an electromagnetic wave The electric component: E=Acos(wt + a) Three component: amplitude, frequency, initial phase angle

Interference between waves Waves with the same frequency can interfere: (a) in phase (b) out of phase (c) partially out of phase

Double slit experiment

Diffraction at a single slit

The envelop function

Diffraction and sampling

Diffraction from crystals A crystal is a three dimensional diffraction grating The lattice periodicity of the crystal determines the sampling regions of the diffraction pattern Where the peaks appear The unit cell contents (the distribution of electron densities) give you the envelope Function The intensity of the peaks

A wave can be represented as a vector in a Argand diagram The electric component of an electromagnetic wave is: A cos(wt+a) = A cosa coswt – A sina sinwt = A cosa coswt + A sina cos(wt+90°) Acosa Asina A Real Imaginary The above vector corresponds to a wave Acosa + iAsina = Aexp[ia]

Scattering for a system with two electrons where What is S??? S is perpendicular to the imaginary reflecting plane

Scattering for a system with two electrons: origin shift does not change wave intensity The amplitude and intensity of wave T does not change

Scattering by an atom Atomic scattering factor is: Assuming centrosymmetric electron cloud distribution The electron cloud of an atom f is real if centrosymmetry is assumed f for a carbon atom

Scattering by a unit cell For each atom, the scattering is: A unit cell with three atoms For the whole unit cells, we will have: Where F(S) is called structure factor Structure factor F is the sum of scattering by all atoms

Scattering by a crystals A crystal contains a large number of unit cells For a general unit cell in a crystal, the structure factor is: The total wave scattered by the crystal is:

Scattering by a crystals A crystal does not diffract X-ray unless Not constructive interference unless all waves have the same phase This is the famous Laue condition

Laue conditions specify scattering conditions What is S??? S is perpendicular to the imaginary reflecting plane What does Laue condition mean??? a, b, c are unit vectors of crystal unit cell axes For a particular crystal unit, X-ray will only be scattered along discrete directions

Diffraction geometry: Bragg’s law A Crystal contain many lattice planes Lattice plane reflect incident X-ray Scattered X-rays interfere with each other Constructive interference results only when: 2dsinq=nl This is the Bragg’s law

Diffraction geometry: Bragg’s law From http://www.matter.org.uk Diffraction angle for a particular lattice plane can be calculated from a particular lattice plane, or vice versa.

Real space and reciprocal space

Real space and reciprocal space Imaginary reciprocal lattices are created to help us understand diffraction geometry bcsina acsinb absing a* = b* = c* = V V V

Real space vs. reciprocal space In addition: a*a=1 V=1/V*

The construction of a reciprocal lattice The reciprocal unit cell dimension is inversely related to the direct unit cell dimensions. Each reflection falls onto to a reciprocal lattice point The length of a reciprocal vector is inversely related to the distance between crystal lattice planes that give rise to that particular reflections.

Physical meaning of reciprocal lattice If Laue conditions are met, the end point of the vector S(h,k,l) are located in the reciprocal lattice points. Proof: S can always be written as S = X  a* + Y  b* + Z  c* Therefore, a S = X ( a*  a) + Y  (b*  b) + Z  (c*  c) = X Because Laue condition states: a S = h, therefore, X=h

The construction of Ewald sphere Ewald sphere is a geometric construction that allows one to visualize the diffraction directions and the properties of Bragg's law

The construction of Ewald sphere Ewald sphere is a geometric construction that allows one to visualize the diffraction directions and the properties of Bragg's law Diffraction occurs when a reciprocal lattice point intersects the Ewald sphere.

Conclusions for reciprocal lattice The reciprocal lattice rotates exactly as the crystal does. The Ewald sphere allows us to visualize a diffraction experiment The diffracted beam will "travel" from the center of the Ewald sphere through the point where its reciprocal lattice point intersects the sphere. The radius of the Ewald sphere is 1/l Diffraction only occurs when a reciprocal lattice point intersects the Ewald sphere