X-Ray Measurement Methods From Chapter 6 of Textbook 2 and other references

X-Ray Measurement Methods From Chapter 6 of Textbook 2 and other references http://www.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/06_Geometry,%20Detectors.pdf Diffractometer Hull/Debye-Scherrer method Pinhole method Laue Method Rotating Crystal Method

Schematics of a typical X-ray diffractometer: 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;

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

http://cheiron2008.spring8.or.jp/lec_text/Sep.30/2008_T.Matsushita_1.pdfhttp://cheiron2008.spring8.or.jp/lec_text/Sep.30/2008_T.Matsushita_1.pdf

X-ray Optics: 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”. Bragg-Brentano diffractometers

Modern Bragg-Brentano laboratory diffractometer

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

Single crystal Polycrystal

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-Scherrermethod: Film Film 2=S/R S 2 2 S R

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

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

http://www.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/06_Geometry,%20Detectors.pdfhttp://www.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/06_Geometry,%20Detectors.pdf

Pinhole photographs D D F F Incident X-Ray 2q A C A r1 C r2 S B B 180o-2q tan2q = r1/D tan(180o-2q) = r2/D monochromatic or white radiation and powder sample Laue methode: white radiation and single crystal

Rotating Crystal Method http://202.141.40.218/wiki/index.php/Unit-2:_Introduction_to_X-ray_diffraction

Concept of Ewald Sphere and Diffraction

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

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

Reciprocal lattice of polycrystalline sample

Features of RigakuTTRAXⅢ

X-Ray Measurement Methods From Chapter 6 of Textbook 2 and other references