X-Ray Measurement Methods From Chapter 6 of Textbook 2 and other references Diffractometer Hull/Debye-Scherrer method Pinhole method Laue Method Rotating Crystal Method 172/LectureNotes/06_Geometry,%20Detectors.pdf

S: source; C: specimen; H: goniometer; O: rotation axis; A, B: slits for collimation; F: slit; G: detector; E and H can be mechanically; coupled  2  and  relation; Schematics of a typical X-ray diffractometer:

focusing monochromator CM = 2R, OC = R Cut off the crystal behind the dotted line to a radius R

X-ray Optics: Bragg-Brentano diffractometers According to Euclid: “the angles in the same segment of a circle are equal to one another” and “the angle at the center of a circle is double that of the angle at the circumference on the same base, that is, on the same arc”.

Modern Bragg-Brentano laboratory diffractometer

Parallel beam geometry in Debye-Scherrer mode using a double monochromator (DM) and an analyzer crystal

Polycrystal Single crystal

An ideal powder sample many crystallites in random orientations; smooth and constant distribution of orientations; Crystallites < 10 μm Sample preparation: There are many methods of preparing samples: – Sample should normally be ground to < 10 μm – Sample may be sieved to avoid large or small crystallites – Sample may be loaded into a holder by pressing from the back while using a slightly rough surface at the front – Sample may be pressed in from the front – Sample may be mixed with a binder (epoxy or similar material) and then cut and polished to give a suitable surface

Hull/Debye-Scherrer method: R S S 22 22 2  =S/R Film

hole Film hole 22 22 22 22 S S 2S S S 22 R

Film hole 22 22 22 S 22 R and Resolving power

/LectureNotes/06_Geometry,%20Detectors.pdf

B S r1r1 F 22 A B r2r2 F 180 o -2  D D tan2  = r 1 /Dtan(180 o -2  = r 2 /D C C A Incident X-Ray Pinhole photographs monochromatic or white radiation and powder sample Laue methode: white radiation and single crystal

2:_Introduction_to_X-ray_diffraction Rotating Crystal Method

Concept of Ewald Sphere and Diffraction

Wavelength: incident beam = diffracted beam Magnitude of k  the same = 1/. Diffraction condition:  k = G 2B2B 2  B  k = G

Diffraction Methods: Method  Laue Variable fixed Rotating crystal Fixed Variable Powder Fixed Variable  vaied  reciprocal lattice is rotated or Ewald sphere is rotated

Reciprocal lattice of polycrystalline sample

Features of Rigaku TTRAX Ⅲ