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What is XRPD - X-Ray Powder Diffraction?

At DANNALAB, we are sometimes confronted with the question: could you tell what is XRPD? The answer, "X-ray Powder Diffraction analysis", is not very illuminating... This page is an attempt to present a compact summary in answer to the the question above - what is XRPD?

About terminology: XRPD (X-ray Powder Diffraction) is a method for measuring the X-rays scattered by a polycrystalline sample as function of scattering angle.

In practice the term XRPD is often substituted by XRD - "X-ray Diffraction" - thus dropping the P for "Powder" which denotes the polycrystalline character of the sample type. Without the P, the acronym XRD is broader term describing all fields of X-ray diffraction such as monocrystal diffraction, fiber X-ray diffraction, the aforementioned X-ray powder diffraction XRPD, X-ray diffraction on thin films and epitaxial layers, and more. These different methods are distingushed by differences in geometry, instrumentation, mathematical treatment of the data, and sample types.

An XRPD sample is a "polycrystalline" sample consisting of many small randomly oriented crystallites. This makes it different from a sample used for monocrystal (single-crystal) X-ray diffraction. Polycrystalline samples may exist in solid form (metals,ceramics) or as a loose powder (figure above).

Major questions answerable with XRPD

Below is list of questions often typically asked by industrial and sometimes research users of XRPD:

  • What are the crystalline phases present in the material? In which amount? Is there an amorphous phase also present?
  • Did the chemical synthesis, deposition or processing proceed correctly through examination of the material produced ?
  • Can the reason for deviation from normal propery parameters or failure be identified?
  • What is the size, shape and orientation of the particles? Do these parameters influence the mechanical and physical properties?
  • What is the amount of residual stress and is it close to a failure limit?
  • Are there any material differences within the volume of one product, within a production batch, between the products from different vendors?
  • How will material (microstructure) perform when being incorporated in the real product? How will they perform in a heavy duty, aggressive environment, subject to mechanical or thermal shocks?
  • When should XRPD be included into a patent application for new material? Could the patent infringement be confirmed or avoided by means of XRPD?
  • And many more....

  • Understanding XRPD patterns

    When reading a scientific paper or report you may come across an XRPD pattern, and it may be useful to understand what kind of information may be extracted from the data representing such a pattern. The analysis of XRPD patterns is normally done with help of analytical software. A typical XRPD pattern is shown in Figure 1. Along the abscissa (horizontal axis) the so-called 2Theta values are shown - the series of angles between the incident and diffracted beams. The ordinate (vertical axis) records the intensity of the scattered X-ray registered by detector.

    Figure 1. XRPD pattern of Calcium Hydroxylapatite - a coating material used for artificial bone implants

    An important property of the XRPD pattern is the set of peaks acting as a unique fingerprint of the crystallogaphic unit cell within a crystalline substance. The crystallographic unit cell is the smallest atomic-scale 3D fragment that is repeated periodically in three dimensions throughout the entire crystal (see Figure 2). All crystalline substances are distinguished by their crystallographic unit cells (and therefore peak positions). By comparing measured peak positions with those held in a database, the crystalline substance may be identified uniquely. For pure substances, the positions of all peaks are generally a function of three parameters a,b,c and three angles alpha,beta,gamma defining the elementary parallelepiped that constitutes the crystallographic unit cell (the parallelepiped is shown blue in Figure 2).

    Figure 2. Crystallographic unit cell (blue) within the crystalline space of Tiotropiumbromid monohydrate.

    The intensities of the XRPD peaks are related to actual atomic arrangment inside the crystallographic unit cell. Using special mathematical methods, the actual positions of atoms in the unit cell may be recovered. Measured peak intensities must be considered with care because intensities in powder diffraction are easily affected by so-called "texture" effects - resulting in non-isotropic (non-random) distribution of crystallites in the sample. If special care is taken to bring about the full randomization of crystallites in a sample, the intensities of the resulting peaks may be used to determine or refine the atomic structure of the material, that is, to obtain the exact location of each atom within the unit cell. Crystalline structure determination by XRPD for obtaining exact information about atomic positions is an alternative (or can be complementary to) the relatively more common method of structure determination by monocrystal diffraction. The latter requires a monocrystal sample and different instrumentation.

    Other information obtainable from the measured pattern is encoded in the widths of the peaks themselves. Peak broadening increases with an increasing level of microdeformations (in the so-called 2nd order) inside the crystallites and with a decrease in crystallite dimensions. The resulting peak shape is a convolution of "physical" broadening, spectral width, and broadening coming from instrumental aberrations (discussed below). The physical parameters can be determined by mathematical deconvolution procedures..

    The peaks in the diffraction pattern may have a specific structure related to the presence of double wavelength components (so called Ka1 and Ka2) in the spectrum, if the measurements have been performed without a "Ka1" monochromator. The peaks may also exhibit asymmetry coming from instrumental aberrations. The instrumental aberrations manifest themselves as different trajectories in the system. The diffraction angle of each trajectory is therefore slightly different from the "ideal" angle of detector and this leads to a visible deformation of the diffraction peaks.

    Other possible types of measuremens are: texture measurements (of the anisotropy of the crystallies orientation versus that of the sample surface) and stress-strain measurements (anisotropy of cell parameters versus that of the sample surface) - both described below. These measurements do not produce the pattern as shown at Figure 1.

    Summary of XRPD methods

  • Crystallography - the indexing and determination of crystallographic unit cell. The 6 parameters of the crystallographic unit cell (a,b,c,alpha,beta,gamma as mentioned earlier) may be determined from the analysis of XRPD peak positions. There are databases available holding peak positions, cell parameters, and full patterns with which one can identify different substances.

  • Qualitative and quantitative phase analysis - Important methods to identify the presence and to determine the concentration of different phases in a mixture. Different methods are avialable to determine the quantitative content including the determination of the amount of amorphous phase if any. An example is shown in Figure 3.

  • Figure 3. XRPD patterns of pharmaceutical formulations with different amounts of amorphous (non-crystalline) phase.

  • Atomic structure determination and structure refinement. The "Rietveld analysis" allows the refinenement of the actual atomic positions versus the known reference structure based on the criteria of best fit between experimental and simulated patterns. An example of this is shown in Figure 4. There are currently more advanced methods (as for example "Charge flipping") enabling the use of "ab-initio" structure determination based on XRPD data.

  • Figure 4. Rietveld analysis of D-Mannitol.

  • Determination of grain size and micro-deformations: "Line Profile Analysis"
  • Determination of residual stresses. This method determines the so-called 1st order strain resulting in the dependence of the crystallographic cell parameters on the orientation relative to the sample surface.
  • Texture analysis - measurement of the anisotropy of the crystallies orientation versus that of the sample surface resulted in reconstruction of Orientation Distribution Function (ODF)
  • Microdiffraction - determination of spatially resolved constitutents of the sample by scanning the sample with a very small X-ray beam.

  • Instrumentation for X-ray Powder Diffraction experiments

    Experiments in X-ray Powder Diffraction are conducted with an X-ray Diffractometer.

    A Laboratory-based X-ray powder diffractometer consists of the following:

  • X-ray generator delivering high tension current to X-ray source
  • X-ray source: a vacuum-sealed X-ray tube (could be with a roating anode or microfocus or standard, oriented in "line-focus" or "point-focus" configuration in the equatorial plane).
  • Sample holder to carry the sample to be investigated. Possible sample types are decribed below.
  • X-ray detector capable of measuring X-ray photons scattered by the sample; it may contain multiple channels in 1D or 2D arrangement;
  • X-ray optics assembled at the primary beam site and on secondary (diffracted) beam site for collimation, conditioning, or focusing of X-rays. These may consist of simple apertures (slits), a set of parallel plate apertures (Soller slits), crystal-monochromators, multilayer mirrors (parabolic, elliptical or flat), capillary optics (monocapillary or X-ray lens).
  • Goniometer providing precise relative angular positioning of X-ray source, sample and detector in "equatorial" plane with the axis of rotation perpendicular to the equatorial plane "axial" direction.

  • Figure 5. The main components of modern X-ray powder diffractometer shown together with the goniometer (courtusy PANalytical B.V.)

    The XRPD pattern is obtained by recording the intensities of X-rays scattered by the sample at different angles between the beam incident on the sample and beam scattered by the sample. The series of rotational displacements of the detector and sample (or of the X-ray source) together with the recording of scattered X-ray intensity at each displacement is refered to as a "scan".

    Geometries of X-ray Powder Diffraction experiments

    There following lists the possible geometries for X-ray Powder Diffraction experiments:

  • 2D detection scheme. A narrow pencil-like incident beam illuminates a small spot on the sample and a broad cone of scattered radiation is intercepted by relatively large detector with pixels arranged two-dimensionally.
  • 1D detection with focusing (commonly known as the Bragg-Brentano geometry). A divergent incident beam in the equatorial plane illuminates a flat sample and the scattered radiation is intercepted by a relatively small detector with pixels arranged one-dimensionally. The sample surface is oriented along the focusing circle.
  • 1D detection without focusing (parallel beam geometry). A parallel incident beam in the equatorial plane illuminates the sample and the scattered radiation is intercepted by an optical setup accepting beams coming from a given direction before entering the single detector. The sample surface orientation and flatness are irrelevant.

  • These geometries may be implemented for the sample in both the reflection or the transmission positions (see figure 6).

    Figure 6. Different geometries of 1D detection.

    Types of samples and sample preparation

    Ideal diffraction experiments should provide clean low-background patterns with high resolution. A range of special experimental techniques exists to achieve this and each requires different methods of sample preparation. This is the non-trivial part of the process, because most polycrystalline substances may be altered during preparations. Texture (the preferred orientation of crystallites), amorphisation, defects, and even phase transformations may be introduced during the sample preparation. Nevertheless, methods exist to minimise the influence on the actual sample preparation. Notable among these are methods employing non-destructive XRPD which dispense with sample preparation altogether (figure 6). For characterisation of pharmaceuticals, the following types of samples may, by way of example, be prepared and submitted for analysis:

  • Solid dosage form - tablets of different shapes, possibly with a protective layer.
  • Powder pressed to the flat surface for surface analysis. Drawbacks include possible strong texture effects, possible influence from the milling process, and exposure of the sample to the atmosphere
  • Powder or slurry in thin capillary for volume analysis. The sample is protected, texture is nearly absent, and quantity below 1mg is sufficient. The milling of aggregates may be required. Samples may be sealed at the customer site.
  • Powder deposited as thin layer on a surface (can also be achieved through drying). Exhibits reduced texture and a small quantity is sufficient but the sample is unprotected
  • Powder deposited as a loose layer of low density (20%-40% from bulk) . Exhibits reduced texture, but sample is unprotected
  • Solid form split in a controlled manner to access the interior - very low sample influence. Drawbacks - possible texture, sample is unprotected