Angub, Maria Cecilia MSE 225 Problem Set 4 Cu, Jana Dela Vega,
Ma. Shanlene
1. A transmission Laue pattern is made of a cubic crystal having
a lattice parameter of 4.00 . The x-ray
beam is horizontal. The [ ] axis of the crystal points along the
beam towards the x-ray tube, the [ ] axis points vertically upward,
and the [001] axis is horizontal and parallel to the photographic
film. The film is 5.00 cm from the crystal.
a. What is the wavelength of the radiation diffracted from the
planes?
b. Where will the reflection strike the film? The Bragg angle
corresponding to any transmission Laue spot is given by:
The reflection will strike at 3.74cm above the primary beam
spot.
2. Determine and list in order of increasing angle, the values
of 2 and (hkl) for the first three lines (those of lowest 2 values)
on the powder patterns of substances with the following structure,
the incident radiation being Cu K:
Simple tetragonal (a=3.00 , c=2.00) Cu K = 1.542
(hkl) d 2
(100) 3.00 29.78
(110) 2.12 42.65
(001) 2.00 45.35
[ ]
[ ]
=
2 + 2 + 2=
.
2 + 2 + 2= .
= 2.
2 + 2 + 2= 2.
= .
2 + 2 + 2= 2. 2
= 2 sin = 1
2 = 1
.542
2 = 4.892
= 1 .542
2 2 = 22.675
= 1 .542
2 2. 2 = 2 . 26
[ ] [001]
= 1
2 + 2 + 2 2 + 2 + 2= 7 .6
= 9 7 .6 = 8.4
= 2 sin =2 4
2 + 2 + 2sin 8.4 = .8
Angle between [ ] direction and the [ ] direction:
Angle between [ ] direction and plane:
Wavelength:
= tan 2 = tan 2 8.4 5 = .74
tan 2 =
where D is 5.00 cm
[ ]
90-
5 cm
r
[ ]
