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daughterduckUrban and Civil

Nov 15, 2013 (3 years and 4 months ago)

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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

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

= 2
R
,
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

2


2


2

=S/R

Film

Film

Film

hole

Film

hole

2


2


2


2


S

S

2S

S

S

2


S
R
2
4


R

)
(
2
)
4
2
(
S
R
R






Film

hole

2


2


2


S

2


R

S
R
2
4


W
R


W
S



2


2
2





R
S
R
S
d
d
d




tan
sin
2






and

d
d
R
R
S
/
tan
2
2








S
R
d
d






tan
2
Resolving

power

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

B

S

r
1

F

2


A

B

r
2

F

180
o
-
2


D

D

tan2


= r
1
/D

tan(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

http://202.141.40.218/wiki/index.php/Unit
-
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

B

2

B


k

=
G


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