EMS 162, page
1/4
Prof. Y. Takamura, 2010
UNIVERSITY OF CALIFORNIA, DAVIS
Department of Chemical Engineering and Materials Science
EMS 162: Structure and Characterization of Engineering Materials
Homework 5  SOLUTIONS
Due Date: Tuesday, Feb. 9th, 2010, in class – NO LATE HOMEWORK
Note: You must show all the steps in order to receive full credit.
Be sure to include units!
1.
Interference Function
[23 pts]
Consider the scattering of xrays from a one dimensional periodic arrangement of electrons as shown in Figure 1:
In this case, the intensity of the diffracted xrays at a scattering angle,
2
θ
, is given by the interference function:
( )
ϕ
ϕ
ϕ
2
2
sin
sin
N
I
∝
where
N
is the number of electrons in the line, and
ϕ
is the phase angle given by:
(
)
λ
θ
π
λ
θ
π
ϕ
2
sin
4
2
cos
1
2
a
a
=
−
=
where
a
is the spacing between electrons and
λ
is the wavelength of the xrays.
(a)
Using your favorite plotting software (Excel, Origin, Matlab, Mathematica), plot the interference function
as a function of phase angle (from zero to 4
π
) for the case of six, 20, and 1000 electrons in a 1D line.
(
Hint
: Be sure to use a small enough step size between data points as
N
gets large).
Hand drawings will
not be given ful
l credit.
(b)
Comment on what happens to the shape of the curves as
N
gets large.
The interference function tells us
that we expect strong diffracted intensity for certain phase angles and therefore certain scattering angles,
and low/no diffracted intensity for all other scattering angles.
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 Winter '08
 Howitt
 Sin, Crystal system, Bragg, Prof. Y. Takamura

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