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