A compact diffraction apparatus is developed with millimeter-wave propagation between two parallel plates. Two types of microfabricated model crystals are individually mounted on a rotatable structure. In contrast to previous work, the experimental results agree well with Bragg’s predictions because multiple scattering is minimized in this configuration. Factors that affect the resolution and signal strength, such as the number of scatterers, cylinder radius, and the distance between the detector and the model crystal, are analyzed. The apparatus offers a visually accessible way to teach students about crystal structure as well as scattering and diffraction.
REFERENCES
1.
W. H.
Bragg
and W. L.
Bragg
, “The reflection of x-rays by crystals
,” Proc. R. Soc. London, Ser. A
88
, 428
–438
(1913
).2.
Roland A.
Allen
, “Verification of Bragg’s law by the use of microwaves
,” Am. J. Phys.
23
, 297
–298
(1955
).3.
Robert G.
Marcley
, “Apparatus drawings project #6: Bragg diffraction apparatus
,” Am. J. Phys.
28
, 415
–417
(1960
).4.
Bailey L.
Donnally
, George
Bradley
, and Jacob
Dewitt
, “Models for microwave analogs of Bragg scattering
,” Am. J. Phys.
36
, 920
(1968
).5.
Guenter
Schwarz
and T. G.
Bullen
, “An improved mounting for the Welch–Bragg diffraction apparatus
,” Am. J. Phys.
37
, 333
(1969
).6.
Thomas D.
Rossing
, Rodney
Stadum
, and Douglas
Lang
, “Bragg diffraction of microwaves
,” Am. J. Phys.
41
, 129
–130
(1973
).7.
William H.
Murray
, “Microwave diffraction techniques from macroscopic crystal models
,” Am. J. Phys.
42
, 137
–140
(1974
).8.
M. T.
Cornick
and S. B.
Field
, “Microwave Bragg diffraction in a model crystal lattice for the undergraduate laboratory
,” Am. J. Phys.
72
, 154
–158
(2004
).9.
Joseph C.
Amato
and Roger E.
Williams
, “Rotating crystal microwave Bragg diffraction apparatus
,” Am. J. Phys.
77
, 942
–945
(2009
).10.
ANSOFT HFSS version 10.1, Ansoft Corporation, PA, USA.
11.
J. D.
Williams
and W. J.
Wang
, “Study on the postbaking process and the effects on UV lithography of high aspect ratio SU-8 microstructures
,” J. Microlithogr., Microfabr., Microsyst.
3
, 563
–568
(2004
).12.
R. W. P.
King
and T. T.
Wu
, The Scattering and Diffraction of Waves
(Harvard U. P.
, Cambridge, MA
, 1959
), p. 69
.13.
I. S.
Gradshteyn
and I. M.
Ryzhik
, Table of Integrals, Series, and Products
, 7th ed. (Academic
, San Diego
, 2000
), p. 933
.14.
A.
Sommerfeld
, Partial Differential Equations in Physics
(Academic
, New York
, 1949
), p. 193
.15.
M.
Abramowitz
and I. A.
Stegun
, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
, 10th ed. (Dover
, New York
, 1972
), p. 364
.16.
C.
Kittel
, Introduction to Solid State Physics
, 8th ed. (Wiley
, New York
, 2005
), p. 39
.17.
P. A.
Martin
, Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles
(Cambridge U. P.
, Cambridge, NY
, 2006
), pp. 1
–28
.18.
19.
J. D.
Jackson
, Classical Electrodynamics
, 3rd ed. (Wiley
, New York
, 1998
), pp. 358
–359
and 479
.20.
E. N.
Economou
, Green’s Functions in Quantum Physics
, 3rd ed. (Springer-Verlag
, Berlin
, 2006
), pp. 11
–12
.21.
Reference 13, p.
940
.22.
Reference 13, p.
659
.23.
24.
S.
Arscott
, F.
Gatet
, P.
Mounaix
, L.
Duvillatet
, J. -L.
Coutaz
, and D.
Lippens
, “Terahertz time-domain spectroscopy of films fabricated from SU-8
,” Electron. Lett.
35
, 243
–244
(1999
).25.
D. M.
Pozar
, Microwave Engineering
, 3rd ed. (Addison-Wesley
, New York
, 2005
), pp. 197
–203
.26.
H. Y.
Yao
and T. H.
Chang
, “Effect of high-order modes on tunneling characteristics
,” Prog. Electromagn. Res.
101
, 291
–306
(2010
).© 2011 American Association of Physics Teachers.
2011
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
