Analysis of data
Qualitative powder diffraction
Qualitative powder diffraction involves the identification of a phase or phases in a specimen by comparison with single-phase X-ray powder diffraction patterns compiled in a database called the Powder Diffraction File (PDF-2). Information obtained from this database include: interplanar spacings (d), relative intensities (I/Io), Miller indices, cell data, physical properties and references to sources of information. The latest version contains 163,835 entries of inorganic and organic phases. It is maintained and continually upgraded by the International Centre for Diffraction Data (ICDD).
PDF-2 is incorporated with XRD processing software such as Evaluation (DIFFRACplus EVA V. 9.0). To process a trace a Peak Search is undertaken initially to assign d-values for each reflection. A Search Match routine is then carried out which gives the user a list of possible minerals or phases in a specimen. For each phase a good match is one where relative intensites and positions of 3 strongest lines and minor lines (the greater the number of lines that match the better) of unknown and standard pattern from database coincide. Logical choices of possible phases in the specimen are made by the user based on information he has about the sample (results from other analyses, environment of formation eg., geological specimen, and information from previous works/ literature).
Some steps for performing qualitative analysis of an XRD sample are as follows:
Peak identification. The first part of data evaluation is to identify diffraction peaks. This involves several steps:
- Kα2-stripping: most diffractometers use bichromatic radiation that corresponds to the Kα1/Kα2-doublett of the anode material. This is reflected by a splitting of peaks. To prevent an accidental counting of α2-peaks, these contributions are automatically stripped off.
- Background subtraction: powder diffractograms contain a significant amount of background due to air scattering and the presence of amorphous phases. The background is fitted with a mathematical polynomial and then subtracted. This way it does not interfere with the data evaluation.
- Smoothing: most diffraction patterns contain a considerable amount of noise. This may hamper the discrimination of peaks from random noise. A step of smoothing is often employed to reduce the random noise.
- Peak search: smoothing is followed by the actual identification of peaks. With good patterns (high signal to noise ratio, narrow peaks) this can be done automatically. Otherwise it is necessary to insert peaks by hand and refine them.
- Profile fit: whether found automatically or by hand, peak positions and intensities are not well determined by the previous step. A profile fit refines peak positions and intensities.
Phase identification. In powder diffraction the term phase is often used as a synonym for substance.
- Using the powder diffraction file: Every single substance has a characteristic powder pattern at a given wavelength in terms of peak position and peak intensity. This pattern can be used as a fingerprint to identify this substance in a powder pattern. For this purpose, the International Centre of Diffraction Data has collected known powder patterns found in the Powder Diffraction File (PDF) to help identify various substances. As of 2006 the PDF contains 186,107 entries.
- Identification of peaks: the next step is to assign the peaks in the experimental pattern to the correct phase. Once all peaks have been identified with the correct phase, the powder pattern can be considered solved.
Limit the database: it is useful to limit the database in a reasonable way. The first thing to examine is the preparation method. Let’s say the present sample was made from calcium fluoride, phosphoric acid and calcium carbonate. After precipitation, the raw product was filtered off and calcined in an alumina crucible. The following elements can possibly be found in your sample: Calcium, phosphorus, oxygen, fluorine, carbon, hydrogen and aluminium (don’t dismiss the crucible material in a high temperature reaction!). Oxygen will have to be present at any rate, due to the reaction conditions. Calcium, phosphorus and fluorine are at least present in one phase each, and carbon, aluminium and hydrogen are optional.
- The powder diffraction file contains deleted and doubtful entries. These are also to be dismissed. After dismissing these two entries, the database is to reduce to only 702 choices.
- Automatic search: an automated search procedure can be performed. The best matches will be displayed first and the database patterns can be overlaid into the experimental one. In the case of the example pattern, all peaks can be explained with substance only. If unexplained peaks remain, these residual peaks should be saved separately and the procedure repeated with the residual peaks until all are explained. Thus a qualitative analysis of the powder pattern is obtained.
Quantitative powder diffraction
Quantitative powder diffraction leads to determination of the lattice parameters and can also identify the fraction of each phase in a sample. Reitveld methods of analysis of powder diffraction patterns enables structure refinement. Reciprocal space methods and real space methods can be used to obtain structure solutions from powder diffraction data. Peak analysis gives us information on crystallite size distribution, microstrain analysis and extended defect concentration.
Some simple steps for performing quantitative analysis of an XRD sample are as follows, but note that quantitative analysis is largely beyond the scope of this online module:
- Using sophisticated Rietveld software such as Fullprof or Topas, there can be further analysis of powder diffraction data.
- A quantitative analysis of all crystalline components can be obtained from the integrated intensities. This can also include a refinement of the crystal structure.
- The exact lattice parameters of each crystalline component are refined from the peak positions. The profile shape can be used to extract micro-structural information on the phases present such as crystallite size and strain for each phase.
Summary of analysis cues
Peak positions show:
- Crystal system
- Space group symmetry
- Translational symmetry
- Unit cell dimensions
- Qualitative phase information
- Unit cell contents
- Point symmetry
- Quantitative phase fractions
- Crystallite size
- Non-uniform microstrain
- Extended defects (stacking faults, antiphase boundaries etc)