X-Ray Measurement Methods From Chapter 6 of Textbook 2 and other references Diffractometer Hull/Debye-Scherrer method Pinhole method Laue Method Rotating.

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

DiffractometerHull/Debye-Scherrer method

Pinhole methodLaue Method

Rotating Crystal Method

http://www.stanford.edu/group/glam/xlab/MatSci162_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:

)2/cos( R

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.pdf

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

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

22

2=S/RFilm

Film

Filmhole

Film

hole

22 22

S

S

2S

S

S2

SR 24

R

)(2)42( SRR

Filmhole

222

S

2R

SR 24 WR W

S

2

22 RSRSdd

d tan

sin2

and

ddRRS /tan22 S

R

d

d

tan2 Resolving

power

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

B S

r1

F2q

A

Br2

F

180o-2q

D D

tan2q = r1/D tan(180o-2 )q = r2/D

C C AIncidentX-Ray

Pinhole photographs

monochromatic or white radiation and powder sampleLaue methode: white radiation and single crystal

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

Rotating Crystal Method

Concept of Ewald Sphereand Diffraction

Wavelength: incident beam = diffracted beamMagnitude of k the same = 1/.

Diffraction condition: k = G

2B

2B k = G

k = G

Diffraction Methods:

Method Laue Variable fixedRotating crystal Fixed Variable Powder Fixed Variable

vaied reciprocal lattice isrotated or Ewaldsphere is rotated

Reciprocal lattice of polycrystalline sample

Features of Rigaku TTRAXⅢ