Bragg Scattering

Wenjun Li
Department of Physics, University of Wisconsin-Parkside
900 Wood Road, Kenosha, Wisconsin 53141 USA
Douglas Richmond
Department of Physics, University of Wisconsin-Parkside
900 Wood Road, Kenosha, Wisconsin 53141 USA

April 11, 2006

Abstract

By measuring the electron diffraction off a crystalline target, the inter-atomic spacings can be determined.

1 Introduction

Lacking, a microscope powerful enough to physically measure the spacing between atoms in a crystal structure, a caveat or two must be made. When an accelerated stream of electrons encounters a crystal lattice, the electrons are scattered towards an angle

( ) D- θ = tan - 1 |------------∘2-------------| ( 2 D- 2) L - r + r - ( 2 )

Where r = 6.6cm is the radius of curvature of the bulb. L = 14.0cm is the distance from the target to the opposite end of the bulb, and D is the diameter of the ring.

2 Procedure

2.1 Instruments and materials

1. A Teltron model 813 power supply.
2. Hewlett packard model 6218A power supply
3. Keithly 175 Auto-ranging multimeter
4. Tel-atomic diffraction tube.

2.2 Obtaining the experimental data

Varying the supply voltage to the electron gun, we were able to obtain 8 seperate data sets, comprised of the Diameter of the inner ring, diameter of the outer ring, and supply voltage. The Current is listed below as well, as a course of record.

DinnerDouterV (kV ) IμA
3.73 6.15 2.1 99.65
3.85 6.25 2.0 86.13
3.86 6.42 1.9 74.89
3.93 6.60 1.8 64.81
4.00 6.74 1.7 54.96
4.17 6.92 1.6 45.80
4.25 7.23 1.5 38.21
4.43 7.57 1.4 30.99

3 Analysis and conclusions

We plotted sinθ vs. √1- V and performed a linear regression on the data, both of which are below.

Inner Ring
sinθ √1-- V
0.13458810.02182179
0.13901440.02236068
0.13938370.02294157
0.14197060.02357023
0.14456090.02425356
0.15086620.02500000
0.15384080.02581989
0.16055160.02672612

Outer Ring
sinθ √1- V
0.22623110.02182179
0.23015510.02236068
0.23685780.02294157
0.24400080.02357023
0.24959080.02425356
0.25682440.02500000
0.26941280.02581989
0.28342640.02672612

PIC

PIC

Since the accelerated electrons are being diffracted off of two different atomic planes, and using the Bragg Condition

∘ ------ 1 2me √-----= --2--d1 sin( θ) V h

we are able to determine d1 and d2, the inter-atomic spacing of inner and outer ring, from the slope.

For the inner ring we obtained d1 = 2.37 Å with an accepted value of 2.461Å, for which our result is in an error by 3.7%.

For the outer ring we obtained d2 = 1.06Å with accepted value of 1.44Å, which suggesting that our experiment result is off by 26.4%.

References

[1]   P. Tipler, R. Llewellyn, Modern Physics 144-149 (W.H.Freeman and Company, New York, 1999)

[2]   American Institute of Physics Handbook. 3rd Ed. 9-05 (McGraw Hill Book Company, 1972)