11. Essential Parts of the Diffractometer
X-ray Tube: the source of X Rays
Incident-beam optics: condition the X-ray beam before it hits the sample
The goniometer: the platform that holds and moves the sample, optics, detector, and/or tube
The sample & sample holder
Receiving-side optics: condition the X-ray beam after it has encountered the sample
Detector: count the number of X Rays scattered by the sample

12. Instrumentation Production of X-Rays Collimator Monochromator Detector
Filter
Crystal monochromator
Detector
Photographic methods
Counter methods

13. The wavelength of X rays is determined by the anode of the X-ray source.
Electrons from the filament strike the target anode, producing characteristic radiation via the photoelectric effect.
The anode material determines the wavelengths of characteristic radiation.
While we would prefer a monochromatic source, the X-ray beam actually consists of several characteristic wavelengths of X rays. K L M

18. Bragg’s law is a simplistic model to understand what conditions are required for diffraction.
dhkl
For parallel planes of atoms, with a space dhkl between the planes, constructive interference only occurs when Bragg’s law is satisfied.
In our diffractometers, the X-ray wavelength l is fixed.
Consequently, a family of planes produces a diffraction peak only at a specific angle q.
Additionally, the plane normal must be parallel to the diffraction vector
Plane normal: the direction perpendicular to a plane of atoms
Diffraction vector: the vector that bisects the angle between the incident and diffracted beam
The space between diffracting planes of atoms determines peak positions.
The peak intensity is determined by what atoms are in the diffracting plane.

23. XRD-Methods Laue photographic method Braggs X-Ray spectrometer
Rotating crystal method
Powder method

24. Laue photographic method
In his first experiments, Max von Laue (Nobel Prize in Physics in 1914) used continuous radiation (with all possible wavelengths) to impact on a stationary crystal. With this procedure the crystal generates a set of diffracted beams that show the internal symmetry of the crystal. In these circumstances, and taking into account Bragg's Law, the experimental constants are the interplanar spacings d and the crystal position referred to the incident beam. The variables are the wavelength λ and the integer number n:
n λ = 2 dhkl sin θnh,nk,nl
Thus, the diffraction pattern will contain (for the same spacing d) the diffracted beams corresponding to the first order of diffraction (n=1) of a certain wavelength, the second order (n=2) of half the wavelength (λ/2), the third order (n=3) with wavelength λ/3, etc. Therefore, the Laue diagram is simply a stereographic projection of the crystal

26. The Laue method in transmission mode
The Laue method in reflection mode
Laue diagram of a crystal

27. Braggs X-Ray spectrometer

28. When x-rays are scattered from a crystal lattice, peaks of scattered intensity are observed which correspond to the following conditions:
The angle of incidence = angle of scattering.
The pathlength difference is equal to an integer number of wavelengths.
The condition for maximum intensity contained in Bragg's law above allow us to calculate details about the crystal structure, or if the crystal structure is known, to determine the wavelength of the x-rays incident upon the crystal.

29. X-radiation for diffraction measurements is produced by a sealed tube or rotating anode.
Sealed X-ray tubes tend to operate at 1.8 to 3 kW.
Rotating anode X-ray tubes produce much more flux because they operate at 9 to 18 kW.
A rotating anode spins the anode at 6000 rpm, helping to distribute heat over a larger area and therefore allowing the tube to be run at higher power without melting the target.
Both sources generate X rays by striking the anode target wth an electron beam from a tungsten filament.
The target must be water cooled.
The target and filament must be contained in a vacuum.

30. Rotating crystal method

31. Most of our powder diffractometers use the Bragg-Brentano parafocusing geometry.
A point detector and sample are moved so that the detector is always at 2q and the sample surface is always at q to the incident X-ray beam.
In the parafocusing arrangement, the incident- and diffracted-beam slits move on a circle that is centered on the sample. Divergent X rays from the source hit the sample at different points on its surface. During the diffraction process the X rays are refocused at the detector slit.
This arrangement provides the best combination of intensity, peak shape, and angular resolution for the widest number of samples.
F: the X-ray source
DS: the incident-beam divergence-limiting slit
SS: the Soller slit assembly
S: the sample
RS: the diffracted-beam receiving slit
C: the monochromator crystal
AS: the anti-scatter slit

33. What is X-ray Powder Diffraction (XRD)
X-ray powder diffraction (XRD) is a rapid analytical technique primarily used for phase identification of a crystalline material and can provide information on unit cell dimensions.
The analyzed material is finely ground, homogenized, and average bulk composition is determined.

34. Fundamental Principles of X-ray Powder Diffraction (XRD)
Max von Laue, in 1912, discovered that crystalline substances act as three-dimensional diffraction gratings for X-ray wavelengths similar to the spacing of planes in a crystal lattice.
X-ray diffraction is now a common technique for the study of crystal structures and atomic spacing.
X-ray diffraction is based on constructive interference of monochromatic X-rays and a crystalline sample.
These X-rays are generated by a cathode ray tube, filtered to produce monochromatic radiation, collimated to concentrate, and directed toward the sample. The interaction of the incident rays with the sample produces constructive interference (and a diffracted ray) when conditions satisfy Bragg's Law (nλ=2d sin θ).

35. This law relates the wavelength of electromagnetic radiation to the diffraction angle and the lattice spacing in a crystalline sample.
These diffracted X-rays are then detected, processed and counted.
By scanning the sample through a range of 2θangles, all possible diffraction directions of the lattice should be attained due to the random orientation of the powdered material.
Conversion of the diffraction peaks to d-spacings allows identification of the mineral because each mineral has a set of unique d-spacings. Typically, this is achieved by comparison of d-spacings with standard reference patterns.

36. All diffraction methods are based on generation of X-rays in an X-ray tube. These X-rays are directed at the sample, and the diffracted rays are collected.
A key component of all diffraction is the angle between the incident and diffracted rays. Powder and single crystal diffraction vary in instrumentation beyond this.

37. Applications of XRD XRD is a nondestructive technique
To identify crystalline phases and orientation
To determine structural properties:
Lattice parameters (10-4Å), strain, grain size, expitaxy, phase composition, preferred orientation (Laue) order-disorder transformation, thermal expansion
To measure thickness of thin films and multi-layers
To determine atomic arrangement
Detection limits: ~3% in a two phase mixture; can be
~0.1% with synchrotron radiation
Spatial resolution: normally none

38. Applications
X-ray powder diffraction is most widely used for the identification of unknown crystalline materials (e.g. minerals, inorganic compounds). Determination of unknown solids is critical to studies in geology, environmental science, material science, engineering and biology. Other applications include
characterization of crystalline materials
identification of fine-grained minerals such as clays and mixed layer clays that are difficult to determine optically
determination of unit cell dimensions measurement of sample purity

39. With specialized techniques, XRD can be used to:
determine crystal structures using Rietveld refinement
determine of modal amounts of minerals (quantitative analysis)
make textural measurements, such as the orientation of grains, in a polycrystalline sample
characterize thin films samples by:
determining lattice mismatch between film and substrate and to inferring stress and strain
determining dislocation density and quality of the film by rocking curve measurements
measuring superlattices in multilayered epitaxial structures
determining the thickness, roughness and density of the film using glancing incidence X-ray reflectivity measurements

40. Strengths and Limitations of X-ray Powder Diffraction (XRD)?
Powerful and rapid (< 20 min) technique for identification of an unknown mineral
In most cases, it provides an unambiguous mineral determination
Minimal sample preparation is required
XRD units are widely available
Data interpretation is relatively straight forward

41. Limitations
Homogeneous and single phase material is best for identification of an unknown
Must have access to a standard reference file of inorganic compounds (d-spacings, hkls)
Requires tenths of a gram of material which must be ground into a powder
For mixed materials, detection limit is ~ 2% of sample
For unit cell determinations, indexing of patterns for non-isometric crystal systems is complicated
Peak overlay may occur and worsens for high angle 'reflections'

42.
THANK YOU