This lecture was given at the 2nd International School on Aperiodic Crystals in Bayreuth, Germany. It is an updated version of the lecture given on the 1st school, that can be found between my lectures as "TEM for incommensurately modulated materials".
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Aperiodic crystal workshop 2013: TEM
1. Diffraction by incommensurately
modulated phases
Ë Î Ì Î Í Î ÑÎ Â -2 0 0 3
Московский Государственный Университет
им. М.В. Ломоносова
Факультет Наук о Материалах
КАФЕДРА НЕОРГАНИЧЕСКОЙ ХИМИИ
Лаборатория Направленного Неорганического
Синтеза
Исаева А.А.
Í Î ÂÛ Å Í ÈÇØ ÈÅ Ñ ÅØ ÀÍ Í Û Å ÁËÎ ×Í Û Å
Ì
Õ ÀËÜÊÎ ÃÅÍ ÈÄÛ Í ÈÊÅËß
Научные руководители
д.х.н., проф. Б.А. Поповкин
к.х.н., асс. ФНМ А.И. Баранов
Joke Hadermann
2. At the end of this lecture you should be able to:
UNDERSTAND and INDEX
the reciprocal lattice of an
incommensurately modulated material.
21. Superspace groups: position and phase
(r,t) ( Rr + v, t + )
{R|v} is an element of the space group of the basic structure
is a phase shift and is ±1
Example
Pnma(01/2)s00
Space group of the components of q symmetry-operators
basic structure for the phase
26. Exercise
Index the following experimental
diffraction patterns and derive the
possible superspace group(s) from the
reflection conditions.
The example is incommensurately
modulated LaSrCuO4-x.
27. First, index the commensurate parent
structure LaSrCuO4, this will help you with
indexing the next, incommensurate one.
Given data:
cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
1/6.50 Å 1/2.61 Å
1/6.50 Å
1/1.85 Å 1/2.61 Å
1/1.85 Å
(Simulated ED patterns)
28. Given data:
cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
001
The reflection in the red box is: 002
200
1/6.50 Å 1/2.61 Å
1/6.50 Å
1/1.85 Å 1/2.61 Å
1/1.85 Å
29. Given data:
cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
001
The reflection in the red box is: 002
200
1/6.50 Å 1/2.61
2.61 Å Å
1/6.50 Å
1/1.85 Å 1/2.61
2.61 Å Å
1/1.85
1.85 Å Å
30. Given data:
cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
010
020
110
002 1/2.61 Å
002
1/1.85 Å 1/2.61 Å
1/1.85 Å
31. Given data:
cell parameters of LaSrCuO4: a=b=3.7 Å, c=13 Å.
010
020
110
002 1/2.61 Å
002
1/1.85 Å 1/2.61 Å
1/1.85 Å
82. You know cell parameters,
modulation vector and
superspace group.
83. At the end of this lecture you should be able to:
UNDERSTAND and INDEX
the reciprocal lattice of an
incommensurately modulated material.
Recap? http://www.slideshare.net/johader