Chapter 6
DESIGN OF IMPEDANCE MATCHING CIRCUITS
6.1
6.2
6.3
Impedance Matching using Lumped Elements and Transmission Lines
6.1.1 Single stub design/Lumped elementtransmission line matching
6.1.2 Double stub design
6.1.3 Single transmission line section
3 Hexagonal
NO. p 3 Patterson symmetry p6
O O
A———~——A O O
A
O
A—~—_—A O
O 0
Origin at 3
Asymmetric unit OSxSI; 0SyS§; xS(l+y)/2; ySmin(lx,(l+x)/2)
Vertices 0,0 LO Li M 0,1}
Symmetry operations
(I) l (2) 3+ 0.0 (3) 3‘ 0,0
Generators selected (1); t(1,0
Christopher C. Tisdell
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Handout 10
Data collection
Sources, detectors and methods
http:/homepages.utoledo.edu/clind/
Measurement of diffracted beams
Position of diffracted beams gives information about unit cell
dimensions and translational symmetry elements
 systematic absence
CHEM 4980/6850/8850 Midterm 2
11/12/2008
Name:_ (2 points)
1)
Give a short definition of the following (one sentence descriptions, or an
equation): (10 points).
a)
Friedels law
b)
Anomalous scattering
c)
cif
d)
Chiral solid
e)
Atomic scattering factor
2)
CHEM 4980/6850/8850 Midterm Exam I
10/4/2004
Name:_
1)
For a cubic crystal, a = 1/a*. Derive the dspacing equation for a cubic lattice.
Calculate the dspacing of the (111) reflection of a compound with a = 10 . At
which 2 value would this reflection
Handout 13
Interpreting your results
What to make of your atomic coordinates, bond
distances and angles
1
What to make of the outcome of your refinement
There are several ways of judging whether the outcome of your
refinement is any good
 low Rfactors

Fourier Syntheses, Analyses,
and Transforms
http:/homepages.utoledo.edu/clind/
The electron density
The electron density in a crystal can be described as a periodic
function
 same contents in each unit cell
 represented by a sum of cosine and sine funct
Structural Refinement based on
the Rietveld Method
An introduction to the basics by
Cora Lind
Outline
What, when and why?
 Possibilities and limitations
Examples
Data collection
Parameters and what to watch out for
Step by step guide to GSAS
Useful sourc
Structure solution
Data processing, direct methods, Patterson and
Fourier maps
Before you start
You need to have at least a pretty good idea of your unit cell
contents
 needed for data scaling
 also necessary to search for/place atoms
Elemental analysis
What is a crystal?
Historic definition before the advent of crystallography
 A solid with welldefined faces
Crystallographic definition
 A material with a regularly repeating structural motif
The strict definition is more vague
 Any material that give
Diffraction
Definition (from Cambridge Advanced Learners Dictionary):
 diffraction noun [U] SPECIALIZED
(a pattern caused by) a change in the direction of light, water or sound waves
 diffract verb [T]
to separate light into coloured strips or into ligh
Introduction
Chem 6850/8850
Xray Crystallography
The University of Toledo
[email protected]
Course Goals
To develop an understanding of basic crystallographic concepts
 Helpful if you ever need to determine a crystal structure yourself
To be able to
Structure Factors
How to get more than unit cell sizes from
your diffraction data
http:/homepages.utoledo.edu/clind/
Yet again expanding convenient concepts
First concept introduced: Reflection from lattice planes
 facilitates derivation of Braggs law

Symmetry and crystals
Imagine
 having to describe an infinite crystal with an infinite number of atoms
 or even a finite crystal, with some 1020 atoms
Sounds horrible? Well, theres symmetry to help you out! Instead
of an infinite number of atoms, you on
Handout 7
Reciprocal Space
Useful concepts for the analysis of
diffraction data
http:/homepages.utoledo.edu/clind/
Concepts versus reality
Reflection from lattice planes is just a concept that helps us to
visualize what is happening in a diffraction exper
Combining symmetry operations
An object can possess several symmetry elements
Not all symmetry elements can be combined arbitrarily
 for example, two perpendicular twofold axes imply the existence of a
third perpendicular twofold
Translational symmetry