Phase Identification           Quantitative XRD            Semi-Quantitative XRD (RIR)            Percent Crystallinity/Crystallite Size

Phase Identification

Phases are identified by taking an unknown sample's diffraction pattern and search/matching it against an XRD database. Phases are matched one by one until all the diffraction peaks in a sample have been identified.

Conditions/Assumptions

  1. Crystallites are randomly orientated
  2. Sample has been sufficiently ground
  3. Sample has been properly mounted
  4. The sub sample given to the technician is representative of the whole sample

Limitations

  1. The limit of detection on the XRD is between 1 - 5 wt% depending on the quality of sample preparation and sample type
  2. You cannot tell the elemental composition quantitatively with powder XRD, other analytical techniques are needed for this i.e. XRF, EPMA, SEM
  3. You cannot resolve phases with identical structures and similar atomic sizes, additional information about the elemental composition are needed to resolve this
  4. Preferred Orientation - can minimize this with proper sample preparation and mounting, but can still be a factor distorting intensity ratios
  5. The more phases there are, the more difficult it is to properly identify
  6. The lower the abundance of a phase the more difficult it is to identify

Quantitative XRD - Rietveld Refinement

The sample's diffraction pattern is modeled using a least squares refinement to determine the amount of each phase contributing to the diffraction pattern, giving a semi-quantitative estimate of the phase abundances. Clays are particularly tricky to model due to the fact that their structure changes with varying conditions (i.e. humidity) and require extra care.

Conditions/Assumptions

  1. That you have an ideal diffraction pattern of that sample (No preferred orientation, crystallites are randomly orientated, 1 μm particle size, perfect sample mounting, high quality scan conditions)
  2. That all the phases in the sample have been identified and identified correctly
  3. Detailed structure information is available for all the phases identified

Limitations

  1. The more phases present in the sample, the more difficult the refinement becomes
  2. Phases below the limit of detection are not included in the analysis
  3. There is 2 wt% error associated with any of the estimates provided


Semi-Quantitative XRD - Reference Intensity Ratios

Uses the ratio between intensity of the strongest peak of your identified phase compared and the strongest peak of a standard (corundum is internationally used) in a 50 - 50 mixture (I/Ic) to determine the abundance of that phase in a sample. The ratio I/Ic can be either experimentally derived or calculated theoretically. The ICDD has published the I/Ic ratios for over 10000 materials. Therefore the abundances of phases within a sample can be determined without an internal standard or with extensive modelling i.e. Rietveld Refinement.

Conditions/Assumptions

  1. That there is minimal to no preferred orientation
  2. That the crystallite size is the same for all the phases within the sample
  3. That there is a constant diffraction volume

Limitations

  1. Cannot resolve overlapping peaks as well as a Rietveld Refinement
  2. Cannot model preferred orientation or instrumental parameters, a Rietveld Refinement can
  3. Larger error associated with RIR compared to a Rietveld Refinement

Percent Crystallinity

The relative amount of amorphous versus crystalline material within a sample is determined by performing a profile fitting and comparing the area attributed to the amorphous material to that of the crystalline material.

Conditions/Assumptions

  1. That the amorphous and crystalline material reflect x-rays with equal efficiency

Limitations

  1. Amorphous materials do not always reflect x-rays as efficiently as crystalline material
  2. The less amorphous material there is, the larger the error on the amorphous content estimation

Crystallite Size

The width of the peaks in a diffraction pattern are controlled by the crystallite size for that phase. The smaller the crystallites the broader the peaks become. Crystallite sizes for phases within a sample can be estimated by using the Sherrer Equation:

Conditions/Assumptions

  1. Assumes spherical crystallites
  2. Assumes a normal crystallite distribution

Limitations

  1. Does not provide accurate dimensions of a non spherical crystallite