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Dr. P. Lucas
U of A
MSE 110
Xray diffraction:
•
Each crystal structure has a specific set of planes and dspacings
and
can be defined by this unique collection of dspacings.
•
XRD is used to determine crystal structures by measuring dspacings.
•
Xrays are energetic photons generated by atomic core electronic
transitions made possible by the creation of an electron vacancy
on the
K level (n=1).
•
Electron vacancies are created in Xray tubes by knocking off
K electrons with a high energy electron beam.
•
The beam of Xrays is reflected by subsequent atomic layers in the
crystalline sample if the path length difference between rays reflected
by subsequent atomic layers is equal to a whole number of
wavelength. All the rays are then in phase and interfere constructively.
•
The conditions for refraction are expressed in Bragg’s law
n
λ
=2d·sin
θ
•
The incident beam angle
θ
is scanned between 0 and 90º
and a peak is
recorded for the dspacing of each atomic plane.
SUMMARY FROM LAST CLASS
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View Full Document Dr. P. Lucas
U of A
MSE 110
Bragg’s Law: reflection order n
XRD
•
The reflection order
n
is equal to the number of wavelength in the path difference
between two rays reflected from subsequent atomic layers.
•
However the size of
λ
is typically of the order of d (hence n<2) so that we usually
only consider the first order reflection n=1 and Bragg’s Law reduces to:
Ray 1
Ray 2
Ray 3
n
λ
=2d·sin
θ
•
From Bragg’s law
therefore
n
λ
<2d
1
sin
2
<
=
θ
λ
d
n
λ
= 2d·sin
θ
Dr. P. Lucas
U of A
MSE 110
XRay pattern:
•
We can then calculate the set of d corresponding to the crystal structure.
XRD
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This note was uploaded on 10/06/2009 for the course MSE 110 taught by Professor Lucas during the Spring '08 term at University of Arizona Tucson.
 Spring '08
 Lucas

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