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X-Ray Diffraction
Principle: interference of photons by reflection by ordered structures
Interference positive for:

2
n = 2d sin 

Bragg’s law

d sin 
d
So, identification compound
In real catalysts: line broadening
the smaller the crystals the more line broadening
So, from XRD crystallite diameter
D can be estimated
D = K / (b cos )
b = peak width
K = constant; usually ca. 1
Catalysis and Catalysts - X-Ray Diffraction (XRD)
Schematic of X-Ray Diffractometer
Ionisation chamber
rotates 2 degrees when
the crystal rotates 
Crystal

X-ray source
XRD patterns: fingerprints of
ordered solids
2
Detector
Catalysis and Catalysts - X-Ray Diffraction (XRD)
XRD: unambiguous
information on crystal
structure
Active Phase of Industrial Catalysts is Microcrystalline
a.
2 =
b.
180o
Photographic film
111
200
Diffraction line
Undeviated X-rays
200
220
220
222
Sample
400
311
222
420
400
422
331
420
422
511
333
440
531
600
442
620
533
622
440
600
442
620
622
444
640
642
444
Incident X-rays
711
551
640
2 = 0o
Catalysis and Catalysts - X-Ray Diffraction (XRD)
X-Ray Diffraction Data:
KCl
NaCl
X-Ray Diffraction Patterns
WO3/SiO2-W
wt% WO3
100
37
WO3/SiO2
WO3
20
12
(1.5 -100 wt%)
6
3
1.5
60
50
40
30
20
10
2 (degrees)
WO3/Al2O3-D
wt% WO3
29
WO3
13
7.4
WO3/Al2O3
3.6
1.8
(0 -29 wt%)
0.9
0
70
60
50
40
2 (degrees)
Catalysis and Catalysts - X-Ray Diffraction (XRD)
30
20
10
Solid-State Diffusion of Co into Al2O3
9.1 wt% CoO/Al2O3
* bulk CoAl2O4
Calcination T:
o
1290 K
n
m
l
1025
k
j
i
h
875
g
f
e
675
d
c
b
a
380
80
70
60
50
2 (degrees)
Catalysis and Catalysts - X-Ray Diffraction (XRD)
40
30
20
2-line position of “Al2O3 and CoAl2O4”
diffraction line at about 80 degrees
Above 900 K the intensity of spinel lines increases,
Al2O3 lines shift:
2 (degrees)
79.6
79.4
79.2
79.0
78.8
600
800
1000
Calcination temperature (K)
1200
Conclusion: above 800 K Co2+ diffuses into the bulk
Catalysis and Catalysts - X-Ray Diffraction (XRD)
Thermal Stability of NiO-WO3/Al2O3
 Does Ni2+ diffuse into alumina?
 If so, does WO3 influence the rate of diffusion?
unit cell size
2d sin  = n
T
Catalysis and Catalysts - X-Ray Diffraction (XRD)
Change of Unit Cell Size vs Calcination Temperature
791.0
NiO(4.1)/Al2O3
792.7
a
NiO(5.1)WO3/Al2O3
794.4
796.0
797.7
calculated
675
875
1075
Calcination temperature (K)
Catalysis and Catalysts - X-Ray Diffraction (XRD)
Calculated Concentration Profiles of Ni in Al2O3 Crystallites
t=0
5
Al2O3
a
4
b
C/Ce 3
NiAl2O4
c
2
 C 
 r 2

C
1
r 
 D   
t
r
r
925 K
975 K
d
1025 K
1
0
 E 
D  D0 exp 

 RT 
875 K
0
251 kJ/mol
2.910-9 m2/s
Catalysis and Catalysts - X-Ray Diffraction (XRD)
1
2
3
r (nm)
4
5
6
Summary of XRD




A “must” in catalyst characterisation
structure of crystalline phases (nm range)
Crystal dimension
Hydrotreatment:
– diffusion of Ni and Co follows Fick’s law
– Ni rate of diffusion not influenced by W oxide
– Ni and Co diffusion during reaction negligible
Catalysis and Catalysts - X-Ray Diffraction (XRD)