MIND MAP 2
Determination of crystal structure
Measure the intern-planar spacing, the inter-planar spacing in a equivalent planes of atoms
Types of electromagnetic radiation 
To determination atomic structure or arrangement in a crystal use wave diffraction technique
sources of diffraction
primary source:X ray
Secondary sources : Neutron, electron
von Laue (1912); Crystal as 3D diffraction gartings
Electron diffractions is used for surface study of materials
Neutron diffraction is used for high precision study
X ray generation
Process 2- Non- elastic excitation of core electrons
Prosess 1 - Decelaration of electron in the metal target
example of Xray spectrum 
Diffraction pattern of an Xray from a crystal
Neutron is used to study magnetic structure of materials - based on its magnetic moment
Spectrum of slow neutron - radiation from a narrow wavelenght band selected using a monochromator
short penetration power
suitable for surface study of crystal , thin films and thin crystals
de Broglie relation for e
How diffraction works
wave interacting with a solid
crystalline material
wave interacting with a single particle
According to Bragg's Law 
similar principle to multiple slit experiments
Constructive and destructive interference patterns depends on lattice spacing (d) and wavelenght and radiation (l)
By varying wavelenght and observing diffractions pattern , information about latice spacing is obtained.
Theory , Law , Working principle 
W.L Bragg ; explained the diffracted rays form crystals .
d spacing in different crystal systems 
working principle : - X ray focused on sample at 0 - Detector opposite source read I at 20 - Incident angle increased over t while detector remain 20
Example pattern of xray diffraction 
Reciprocal Lattice
Real space and reciprocal space
Reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice )
The powder diffractomemters typically use the Bragg-Brentano geometry
A single crystal specimen in Bragg- Brentano diffractometer would produce only one family of peaks in the diffraction pattern
A polycrystalline sample should contain thousands of crystallites . Therefore, all possible diffraction peaks should be observed.
Example : Diffraction patterns
Relationship between diffraction , peaks, miller indices and lattice spacings
Indexing the peeks
Absences due to lattice centering
a beam of incident x rays are diffracted in a material 
This produce an electron diffraction pattern (example SiC).
To summarize The journey from the real lattice to the different pattern by Real lattice to real Crystal to Reciprocal lattice to Reciprocal crsytal to Diffration Pattern
The Reciprocal lattice 
Reciprocal lattice to SC, FCC and BCC 
Ewald Construction
X- Ray
Wilhelm Rontgen discovered x-ray while working at the University of Wurzburg. He assumed unknown xrays , were being emmite from the walls of the tube while the cathode ray tube was running
Bragg's law
Bragg's law comfimed the existense of real particles at the atom ic scale, as well, a providing a powerful new tool for studying crystals in the fom of X-ray and neutron diffraction .
Laue Equation and its relation with Bragg's Law
Mas Theodor in 1914 , for his first discovery of the diffraction of x-rays by crystals.The wavelengths of concern to ewald were in the visible region of the spectrum and wavelengths of concern to Ewald were in the visible region.Hence much larger than the spacing between the rosanators .
Bragg and Laue Diffraction
They both deal with elastic scattering of periodic lattice
Laue Equations 
Ewald sphere and Reciprocal lattice 
The Ewaald construction is the way to draw bragg's lawa. Crystallographers use it to visualize which reciprocal lattice point will be in diffraction condidtion for a given orientation of the crystal.
Bragg reflected ray 
When a crystal is bombarded with X-rays of a fixed wavelength (similar to spacing of the atomic-scale crystal lattice planes) and at certain incident angles, intense reflected X-rays are produced when the wavelengths of the scattered X-rays interfere constructively.
Experimental Diffraction Technique
Based on Ewald construction for crystal study, 3 technique available based on
Bragg's rule or Laue satisfied by two main methods
Laue technique
Powder technique
Crystal rotation technique 
Powder technique
Laue technique
Transmissin technique 
Reflected ray technique
Film use for recording the diffraction pattern is placed behind the sample and records the fowrad diffracted ray
Film use for recording the diffraction pattern is placed between source and sample.
Calculating Laue's angle
Ewald Construction for laue tehnique
Ewald construction diagram for crystal rotation technique
Difractometer
A diffractometer is a measuring instrument for analyzing the structure of a material from the scattering pattern produced when a beam of radiation or particles (such as X-rays or neutrons) interacts with it.
Typical diffraction pattern
Solid crystals
Liquid or amorphous solid
Sharifah Azra Bt Abdul Kadir