Let's Do Experiment Using XRD: How to Interpret the Diffractogram

      Basically, XRD (X-Ray Powder Diffraction), as a nondestructive technique has some functions for identifying crystalline phases and orientation, determining structural properties (lattice parameters, strain, grain size, phase composition, thermal expansion, etc), measuring thickness of thin films and multi layers, determining atomic arrangement. Thus, XRD 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.

       In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals. Informally, two crystals tend to be in the same crystal system if they have similar symmetries, though there are many exceptions to this. Space groups and crystals are divided into 7 crystal systems according to their point groups, and into 7 lattice systems according to their Bravais lattices. Five of the crystal systems are essentially the same as five of the lattice systems, but the hexagonal and trigonal crystal systems differ from the hexagonal and rhombohedral lattice systems.

        Doing experiment using XRD takes some procedural activities to achieve the objectives. Collecting, analyzing, and interpreting activities should be done by the researchers.

Data Collection

       The intensity of diffracted X-rays is continuously recorded as the sample and detector rotate through their respective angles. A peak in intensity occurs when the mineral contains lattice planes with d-spacings appropriate to diffract X-rays at that value of θ. Although each peak consists of two separate reflections (Kα1 and Kα2), at small values of 2θ the peak locations overlap with Kα2 appearing as a hump on the side of Kα1. Greater separation occurs at higher values of θ. Typically these combined peaks are treated as one. The 2λ position of the diffraction peak is typically measured as the center of the peak at 80% peak height.

Data Reduction

       Results are commonly presented as peak positions at 2θ and X-ray counts (intensity) in the form of a table or an x-y plot (shown above). Intensity (I) is either reported as peak height intensity, that intensity above background, or as integrated intensity, the area under the peak. The relative intensity is recorded as the ratio of the peak intensity to that of the most intense peak (relative intensity = I/I1 x 100).

Determination of an Unknown

       The d-spacing of each peak is then obtained by solution of the Bragg equation for the appropriate value of λ. Once all d-spacings have been determined, automated search/match routines compare the ds of the unknown to those of known materials. Because each mineral has a unique set of d-spacings, matching these d-spacings provides an identification of the unknown sample. A systematic procedure is used by ordering the d-spacings in terms of their intensity beginning with the most intense peak. Files of d-spacings for hundreds of thousands of inorganic compounds are available from the International Centre for Diffraction Data as the Powder Diffraction File (PDF). Many other sites contain d-spacings of minerals such as the American Mineralogist Crystal Structure Database.

Determination of Unit Cell Dimensions

        For determination of unit cell parameters, each reflection must be indexed to a specific hkl known as Miller indices. Miller indices is a notation system in crystallographic for planes and direction in crystal (Bravais) lattices. They are written (hkl), and each index denotes a plane orthogonal to a direction (h, k, l) in the basis of the reciprocal lattice vectors. By convention, negative integers are written with a bar, as in 3 for −3. The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. Miller index 100 represents a plane orthogonal to direction ℓ; index 010 represents a plane orthogonal to direction m, and index 001 represents a plane orthogonal to n.

         The crystallographic directions are fictitious lines linking nodes (atoms, ions or molecules) of a crystal. Similarly, the crystallographic planes are fictitious planes linking nodes. Some directions and planes have a higher density of nodes; these dense planes have an influence on the behavior of the crystal such as optical properties, absorption and reactivity, surface tension, and dislocations (plastic deformation). For all these reasons, it is important to determine the planes and thus to have a notation system.

      
         As summary, in order to do phase identification, one of the most important uses of XRD, there are several steps. We can conclude as obtaining XRD pattern, measuring d-spacings, obtaining integrated intensities, and comparing data with known standards in the ICDD file formerly known as JCPDS. In the last step, we can use JCPDS Card. The card contain file number (1), three strongest lines (2), lowest angle line (3), chemical formula (4), data on diffraction method used (5), crystallographic data (6), optical and other data (7), data on specimen (8), and data on diffraction pattern (9). Commonly this information is an integral portion of the software that comes with the instrumentation.