Transcript 投影片 1 - National Tsing Hua University

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
R cos( / 2   )
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:
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-Scherrer method:
Film
2=S/R
2
2
R
S
S
Film
Film
Film
hole
R
2
2
S
S
S
S
2
2S
4R  2 S
hole
2
2
( 2  4 ) R  2(R  S )
Film
hole
R
2
S
2
2
R  W
2
4R  2 S
2
S

 W
  tan 

S  2R  S  R 2 and 2d sin    
d
d
d
 2 R tan  Resolving

S  2 R  2 Rd tan  / d 
d
S
power
http://www.stanford.edu/group/glam/xlab/MatSci162_172
/LectureNotes/06_Geometry,%20Detectors.pdf
Pinhole photographs
Incident
X-Ray A C
D
2
B
tan2 = r1/D
D
F
r1
S
C
F
A
r2
B
180o-2
tan(180o-2) = 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/Unit2:_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
2B
2B
k = G
Diffraction Methods:
Method
Laue
Rotating crystal
Powder
 vaied 
reciprocal lattice is
rotated or Ewald
sphere is rotated

Variable
Fixed
Fixed

fixed
Variable
Variable
Reciprocal lattice of polycrystalline sample
Features of Rigaku TTRAXⅢ