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Welcome to 3.091 Lecture 18
October 21, 2009
X-Ray Diffraction Techniques
ν = R
staircase
Moseley's Law
2( (1 1 Z-γ n2f n2
i ( (
Bremsstrahlung
Figure 12.14a
O
P
P'
P''
d
d
O'
A(hkl)
(hkl)
(hkl)
B D d
C
Eα
�
α
α
Image by MIT OpenCourseWare.
Averill, B., and P. Eldredge. Chemistry: Principles, Patterns, and Applications. Flat World Knowledge, 2011. ISBN: 9781453331224.
a a
2 a 2
h+k+l even
h+k+lall all even
or all odd unmixed
Figure 12.13
diffractometry
Figure 12.13
� = 0.1542 nm (Cu K�-radiation)
0
20
40
60
80
100
Inte
nsity
(arb
itrar
y un
its)
(111)
(200)
(220) (311)
(222) (400) (331) (420)
20 30 40 50 60 70 80 90 100 110 120
2α (degrees)
Image by MIT OpenCourseWare.
Figure 12.13
Image by MIT OpenCourseWare.
(111) Averill, B., and P. Eldredge. Chemistry: Principles, Patterns, and Applications. Flat World Knowledge, 2011. ISBN: 9781453331224.
All M. C. Escher works © 2010. The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
All M. C. Escher works © 2010. The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
All M. C. Escher works © 2010. The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
All M. C. Escher works © 2010. The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
All M. C. Escher works © 2010. The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
All M. C. Escher works © 2010. The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
120° rotation
All M. C. Escher works © 2010. The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
All M. C. Escher works © 2010 The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
4-fold
90o
4-fold
90o
3-fold
120o
4-fold
90o
3-fold
120o
2-fold
180o
All M. C. Escher works © 2010 The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
All M. C. Escher works © 2010 The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com
translational symmetry without rotational symmetry
Courtesy of Ron Lifshitz. Used with permission.
Courtesy of Ron Lifshitz. Used with permission.
rotational symmetry without translational symmetry
Courtesy of Ron Lifshitz. Used with permission.
Courtesy of Ron Lifshitz. Used with permission.
Courtesy of Ron Lifshitz. Used with permission.
Courtesy of Ron Lifshitz. Used with permission.
Courtesy of Ron Lifshitz. Used with permission.
not a Bravais lattice
Courtesy of Ron Lifshitz. Used with permission.
Courtesy of Ron Lifshitz. Used with permission.
5-fold
72o
Courtesy of Ron Lifshitz. Used with permission.
Courtesy of Dan Shechtman. Used with permission.
Courtesy of Dan Shechtman. Used with permission.
5-fold
72o
“Mission Impossible” – an example of 5:4 time Courtesy of Ron Lifshitz. Used with permission.
MIT OpenCourseWare http://ocw.mit.edu
3.091SC Introduction to Solid State Chemistry Fall 2009
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