X-Ray Powder Diffraction 

X-Ray Diffraction is a powerful characterization technique to quickly identify both the phase and unit cell of a crystalline material.  Some of the most common uses of X-Ray Powder Diffraction are to identify crystal structure, preferred orientation, specific phases, and other structural properties such as average grain size, percent crystallinity and phase quantification.

Crystalline samples have a distinct X-Ray diffraction pattern which serves as the DNA for a specific material and can be quickly identified through use of available databases.  It is an extremely useful tool to quantify unknown crystalline materials in the fields of geology, materials science, pharmaceuticals, environmental sciences, general engineering and biology.

Main Applications of X-Ray Diffraction

  • Quantification of crystalline materials
  • Use of rocking curve measurements to determine dislocation density and quality of thin films
  • Determination of unit cell dimensions
  • Measurement of sample purity
  • Forensic matching of investigative materials
  • Reverse engineering and competitive analysis
  • Detection of acute crystalline phases in multi-component solids
  • Crystalline size for films and other materials
  • Determination of the percentage of material in crystalline form vs amorphous
  • Determining surface off-cut in single crystal materials

 

Pros

  • Powerful and rapid testing to quantify unknown materials
  • Minimal sample preparation
  • Ambient testing conditions for analysis
  • Quantitative measurement of phase and texture orientation
  • Non-destructive

Cons

  • Generally, a bulk analysis technique
  • No depth profile data

Detailed Analysis

Phase Identification

X-rays scatter from crystalline materials in such a way to produce a unique X-ray Diffraction Pattern. By extracting the peak positions and intensities from this pattern, we can identify and quantify the amount of each phase present in the test sample. To aid in this endeavor, many advanced analytical techniques, such as Rietveld refinement have been developed to improve the accuracy.

Several hundred thousand materials have been cataloged in various diffraction databases allowing us to identify both inorganic and organic substances.

Among the common uses of this technology are:

  • Identification and quantification of multi-phase materials
  • Detection of pharmaceutical polymorphs
  • Analysis of cement and clinker phases
  • Identification of precipitates in metallic alloys
  • Analysis of corrosion products
  • Reverse engineering of competitor’s products
  • Detection of trace impurities down to 0.1 weight percent
  • Identification of silica forms in work environment such as respirable quartz
  • Analysis of erionite and asbestos in mineral deposits
  • Soil analysis
  • Verification of process streams
  • Use in quality control and validation such as Hydroxyapetite
  • Identification of catalyst phases
  • Forensic matching of investigative materials

Percent Crystallinity

There are many different and unique material structures in existence.  For certain applications it is necessary to know how much of a material is in a glassy state or amorphous and how much is a defined crystal.  Amorphous materials have a random network and are not structured in a 3D state,  while crystal structures and bonds are well defined and easily found using XRD.

Many materials, especially polymers, tend to form both crystalline and amorphous forms. Each structure produces a unique diffraction pattern that enables us to determine the relative amounts of each phase. Amorphous phases produce one or more broad humps in the diffraction pattern, while crystalline materials produce a series of sharper peaks superimposed on the amorphous humps.  Knowing the total amount of each of these phases are very important in the following areas:

  • Studies of polymers & pharmaceuticals
  • Conversion of pharmaceutical polymorphs
  • Glass content in ceramics
  • Analysis of clay & minerals
  • Rapidly solidified metallic glasses
  • Analysis of ashed samples
  • Devitrification of glass

Residual Stress

The determination of stresses within a material can be extremely important to prevent poor performance and eventual failure.   Residual stresses are known to influence the mechanical properties of a material and this can effect the time of failure due to fatigue.  XRD can measure the lattice strain and determine the amount of stress that exists by applying the appropriate materials constants.

One technique for measuring residual stress is the sin² ψ method, which is used to measure stress in fine-grained polycrystalline materials. The method relies on the measurable shift of a high-angle diffraction peak as the sample is rotated through a tilt angle ψ. Variations of the method also allow us to determine the principal stresses and the presence of shear stresses.

Among the many applications for this method are:

  • Axles, wheels, bolts, clamps, etc.
  • Cemented carbides
  • Composites
  • Ground/machined surfaces
  • Heat treated metals
  • Plated surfaces and thin films
  • Shrink fitted components
  • Tube surfaces
  • Weldments
  • Fasteners and springs

Retained Austenite

The production of carbon steel is a common practice.  Materials have different phases based on how they are formed and within carbon based steels, Austenite is one that is very stable at very high temperatures.   After the steel is quenched much of the material transforms from Austenite to Martensite, but based on the quenching conditions some can be retained within the material.  This can lead to mechanical properties that are sub-optimal that decreases the fracture toughness and/or fatigue.  In applications that require high strength the total amount of Austinite must be quantified and controlled.

XRD provides is the characterization technique of choice for this type of specific testing, especially when the total concentration of Austenite is less than 15%.  Standard techniques and protocols exist that produce results down to 0.5% or less.  When there are additional carbide phases in the steel, this is reduced to 1%, which is still enough accuracy to determine the chances of failure.  The main applications of this technique are as follows:

  • Quality control
  • Optimization of heat treating process
  • Avoiding grinding burn and shot-peening damage
  • Control premature failure
  • Dimensional control
  • Suppression of crack growth during spalling

 

 

 

 

 

Rocking Curves

Rocking Curves are used to determine defects and in-homogeneity’s  in single crystals and thin films.  In lattice matched thin films, rocking curves can be used to study the film thickness, strain profiles, lattice mismatch and even relaxation.  By fixing the detector at the center of the expected Bragg reflection and following the diffracted intensity as the sample is independently rotated (or “rocked”), one can gain valuable information. The full width at half maximum intensity (FWHM) is related to the dislocation density in the film and to the curvature of the sample. High Resolution variations of the method also allow us to determine misfit strain, the periodicity in artificial super-lattices, the quality of the inter-facial region, layer thickness, composition, and degree of mosaicity.

Rocking Curves can also be used to study polycrystalline materials. Key characteristic information that can be obtained are the particle or grain size and the degree of deformation in ductile materials.

Preferred Orientation

Preferred orientation occurs when there is a stronger tendency for the majority of crystallites in a powder or texture to be oriented in the same direction than all others.  A classic example of this is when a metal is rolled in order to form a sheet.  This creates a preferred orientation within the structure.  In most cases, this will lead to anisotropic distribution of properties such as modulus, strength, ductility, toughness, electrical conductivity, thermal expansion, etc. Therefore, it is important to monitor and quantify changes in the texture.

X-ray diffraction is an ideal tool to examine preferred orientation. In a conventional θ/2θ coupled scan, preferred orientation will cause a change in the intensity distribution. Such changes can be quantified with the Texture Coefficient, which compares the oriented sample to the ideal unoriented sample. A more complete picture of the orientation is obtained by the use of Pole Figures and Orientation Distribution Functions.

Among the many uses of Texture Analysis are:

  • Properties in thin films
  • Forgings
  • Surface coatings
  • Optimizing growth conditions
  • Formation of epitaxial layers
  • Surface and bulk deformation

Particle Size Analysis

Using XRD is another tool to determine the particle size within a specimen.  The particle sizes analysis is performed by measuring the broadening of a specific X-ray diffraction peak within the crystal unit cell.  By examining the full width at half maximum (FWHM) the size can be calculated.  In general, the width of the peak is inversely related to the particles size, so as the peak becomes more narrow, the particle size increases.

In the Simplest case where the domains are stress free, the size can be estimated from a single diffraction peak. But in those cases where stress may be present, a more robust method is required such as the Warren-Averbach or Rietveld methods that utilize several diffraction peaks.

Among the many uses of this method are:

  • Catalyst size analysis
  • Studies of precipitation processes
  • Nanoscale composites
  • Pigments
  • Pharmaceuticals
  • Phase transformation kinetics
  • Fibers and composites
  • Quality control
  • Forensic analysis

Thin Film Analysis

Thin film analysis is not a specific test that is performed but rather a group of X-ray diffraction methods that are used in epitaxial and polycrystalline thin films and substrates.  Semiconductor materials are most prevalent, but other materials can be analyzed as well.  Using the precision lattice parameter measurement methods, the lattice mismatch of an epitaxial layer can be determined very precisely.   Many other types of tests can be performed on thin films including the following:

  • Orientation of an epitaxial film
  • Crystallite size and micro-strain
  • Rocking curves

Lattice Parameters

Lattice parameters refer to the physical dimensions of unit cells in a crystal structure.  In general, lattices are consisted of 3 dimensions and contain 3 lattice constants (a, b, & c) to go along with the 3 angles between them (α, β, γ).  These parameters are defined for specific materials at known conditions, such as temperature and pressures.  This information is useful as it can characterize the material in question can provide the user with additional information such as the thermal properties, measure of the strain state or analysis of defect structures if the lattice constants and angles differ from known values.  The lattice constants are measured at the Angstrom level, so increased accuracy of the measurement is needed.  X-ray diffraction permits for this level of accuracy and can achieve accuracy to several significant digits at the Angstrom level.

Two common methods are in use to compute the lattice parameters. If crystallographic information about the crystal structure is incomplete, then a least squares method is commonly used. This method takes into account the systematic errors caused by misalignment and sample placement. If more complete information is known about the crystal structure, then a Rietveld refinement is commonly used. This method is a whole pattern fitting procedure utilizing all of the diffraction peaks and their shapes.

Among the common uses of precision lattice parameters are:

  • Material synthesis
  • Analysis of solid solutions
  • Thermal expansion
  • Strain/stress determination
  • Misfit strains
  • Zeolite framework composition

Corrosion Product Identification

In everyday life there are examples of corrosion of metals that are seen.  Metal based equipment such as pipes and screws are exposed to the atmosphere and the corrosion can be seen physically.  In these cases they are replaced with new parts, but in certain fields, the corroded parts are sent for a failure analysis to determine the root cause so the behavior can be fixed for future iterations.  The most logical place to begin is a chemical analysis to determine what substance created the corrosion.  In the case of steel based products, chemical analysis would show that the by-product would be FeO(OH), which is a starting point, but does not provide all the required data.  This formation has different phases that exists based on the atmospheric conditions and exposure the starting material was exposed.

XRD provides a complimentary characterization tool to the chemical analysis to accurately identify the corrosion product.  Once the composition is known, the XRD analysis can easily determine the correct phase based on the spectra.  This provides the manufacturer key information to prevent future corrosion based on the actual phase that was formed during the corrosion process.

Typical examples of products that undergo this technique are:

  • Boiler tubes and pressure vessels
  • Flue stacks
  • Storage containers and vessels
  • Pipelines and valves
  • Mechanical components
  • Furnaces and surfaces exposed to high temperature

 

 Technical Specifications of Equipment

  • Signal Detected: Diffracted X-rays
  • Elements Detected: All elements, assuming they are present in a crystalline matrix
  • Detection Limits: Quantitative multiphase analysis: ~0.5% to 1%
  • External standard quantitative analysis: ~0.1%
  • Special quantitative analysis (quartz, polymorphs): ~0.02%
  • Depth Resolution: Sampling depth between ~20Å to ~30µm, depending on material properties and X-ray incidence angle
  • Imaging/Mapping: None
  • Lateral Resolution/Probe Size: Point focus: 0.1mm to 0.5mm; Line focus 2mm to 12 mm

Key Markets Served

  • Pharmaceuticals
  • Generic Drugs
  • Semiconductors
  • Mining & Metals
  • Ceramics
  • Life Sciences
  • Coatings and Adhesives
  • Lighting
  • Data Storage
  • Packaging
  • Personal Care Products
  • Raw materials Chemistry
  • Law and Litigation

Applications Notes

Precision Lattice Parameter Measurement

Quantitative Analysis by XRD

Analysis of Residual Stress

Particle Size and Strain Analysis by XRD

Retained Austenite Analysis