X-Ray Powder Diffraction
   This handout provides background on          Theory and Methodology
 the use and theory of X-ray powder               The three-dimensional structure of
 diffraction. Examples of applications of       nonamorphous materials, such as
 this method to geologic studies are            minerals, is defined by regular, repeating
 provided.                                      planes of atoms that form a crystal
 Introduction                                   lattice. When a focused X-ray beam
                                                interacts with these planes of atoms, part
    Rocks, sediments, and precipitates are      of the beam is transmitted, part is
 examples of geologic materials that are        absorbed by the sample, part is refracted
 composed of minerals. Numerous                 and scattered, and part is diffracted.
 analytical techniques are used to              Diffraction of an X-ray beam by a
 characterize these materials. One of           crystalline solid is analogous to                Figure 1. Simplified sketch of one
 these methods, X-ray powder diffraction        diffraction of light by droplets of water,       possible configuration of the X-ray
 (XRD), is an instrumental technique that       producing the familiar rainbow. X-rays           source (X-ray tube), the X-ray detector,
 is used to identify minerals, as well as        are diffracted by each mineral                  and the sample during an X-ray scan. In
 other crystalline materials. In many            differently, depending on what atoms            this configuration, the X-ray tube and the
 geologic investigations, XRD                    make up the crystal lattice and how these       detector both move through the angle
 complements other mineralogical                                                                 theta (θ), and the sample remains
 methods, including optical light                atoms are arranged.                             stationary.
 microscopy, electron microprobe                   In X-ray powder diffractometry, X-rays
 microscopy, and scanning electron               are generated within a sealed tube that is
 microscopy. XRD provides the                    under vacuum. A current is applied that        n λ = 2 d  sin θ, where the integer n is the
 researcher with a fast and reliable tool for    heats a filament within the tube, the          order of the diffracted beam, 1 is the
 routine mineral identification. XRD is          higher the current the greater the number      wavelength of the incident X-ray beam, d
 particularly useful for identifying fine-       of electrons emitted from the filament.        is the distance between adjacent planes
 grained minerals and mixtures or                This generation of electrons is analogous      of atoms (the d-spacings), and θ is the
  intergrowths of minerals that may not          to the production of electrons in a            angle of incidence of the X-ray beam.
  lend themselves to analysis by other           television picture tube. A high voltage,       Since we know λ and we can measure θ,
  techniques. XRD can provide additional         typically 15-60 kilovolts, is applied          we can calculate the d-spacings. The
  information beyond basic identification.       within the tube. This high voltage             geometry of an XRD unit is designed to
  If the sample is a mixture, XRD data can       accelerates the electrons, which then hit a    accommodate this measurement (fig. 1).
  be analyzed to determine the proportion        target, commonly made of copper. When          The characteristic set of d-spacings
 of the different minerals present. Other        these electrons hit the target, X-rays are     generated in a typical X-ray scan
  information obtained can include the           produced. The wavelength of these X-           provides a unique "fingerprint" of the
  degree of crystallinity of the mineral(s)      rays is characteristic of that target. These   mineral or minerals present in the
  present, possible deviations of the            X-rays are collimated and directed onto        sample. When properly interpreted, by
  minerals from their ideal compositions         the sample, which has been ground to a         comparison with standard reference
  (presence of element substitutions and         fine powder (typically to produce particle     patterns and measurements, this
  solid solutions), the structural state of the  sizes of less than 10 microns). A              "fingerprint" allows for identification of
  minerals (which can be used to deduce          detector detects the X-ray signal; the         the material.
  temperatures and (or) pressures of             signal is then processed either by a
  formation), and the degree of hydration        microprocessor or electronically,              Applications
  for minerals that contain water in their       converting the signal to a count rate.
  structure. Some mineralogical samples          Changing the angle between the X-ray              XRD has a wide range of applications
  analyzed by XRD are too fine grained to        source, the sample, and the detector at a      in geology, material science,
  be identified by optical light microscopy.     controlled rate between preset limits is an    environmental science, chemistry,
  XRD does not, however, provide the             X-ray scan (figs. 1 and 2).                    forensic science, and the pharmaceutical
  quantitative compositional data obtained         When an X-ray beam hits a sample and         industry, among others. At the U.S.
  by the electron microprobe or me textural      is diffracted, we can measure the              Geological Survey, researchers use XRD
  and qualitative compositional data             distances between the planes of the            to characterize geologic materials from a
  obtained by the scanning electron              atoms mat constitute the sample by             wide variety of settings; a few examples
  microscope.                                    applying Bragg's Law. Bragg's Law is           follow.
                                                 Predictive Stratigraphic                    Analysis of airborne imaging
    Mineral-Environmental Studies
      In studies of areas affected by acid       Analysis                                    spectrometer data can directly map
    mine drainage, the identification of           Mineralogical characteristics of          mineral occurrences by detecting
    secondary minerals and fine-grained         paleosols(ancient buried soil horizons)      diagnostic spectral absorption bands, the
    precipitates is a critical element. Acid is and underclays (the fine-grained detrital    shape and position of which are
    generated when iron sulfide minerals,       material lying immediately beneath a         determined by individual mineral
    such as pyrite, weather. Elements           coal bed) have been instrumental in          structures. A detailed knowledge of
    derived from the alteration of the sulfide  correlating coal zones from the              sample mineralogy, provided at least in
    minerals can form secondary minerals or     Appalachian basin into the Western           part by XRD, is required to understand
    go into solution. Elements that go into      Interior basin. They have been the key to   the observed spectral absorption features.
    solution may form mineral precipitates as   quantifying the paleolatitudinal climate
    conditions (temperature, acidity, solution   gradient in North America during the late    Genesis of Coal Beds
    composition) change. Accurate                Middle Pennsylvanian.                          XRD is one of the primary tools used
    mineralogical characterization of the                                                    to evaluate the lateral and vertical
    precipitates and secondary minerals,         Remote-Sensing Studies                      variations in mineral matter and major,
    together with hydrogeochemical data,           Mineralogical analysis by XRD is used     minor, and trace elements in coal beds.
    helps us to better understand the            in conjunction with remotely sensed data    These data are used to help determine the
    solubility, transport, and storage of        in several research investigations.XRD       impact of geologic and geochemical
    metals.                                      is used to identify the minerals             processes on coal bed formation in order
    Ore Genesis Studies                          composing clay-rich, hydrothermally          to understand and predict both inorganic
                                                 altered rocks that occur on several          and organic variability within and among
      Minerals form under specific ranges of     Cascade volcanoes. Such rocks are            mineable coal beds.
    temperature and pressure. Mineralogical      believed to play an important role in the
    identification of ore minerals and           generation of large landslides and           Mineral-Resource
    associated minerals, including fine-         mudflows. XRD is used to analyze             Assessments
    grained hydrothermal alteration minerals,    saline minerals, including borates.            Mineralogical characterization
    provides evidence used to deduce the         Many saline hydrate minerals produce         provides part of the data required to
    conditions under which ore deposits          diagnostic spectral bands, and spectral      determine the particular kind of mineral
    formed and the conditions under which,       data provide a basis for mineral             deposits encountered in mineral-resource
     in many cases, they were subsequently       exploration using remote-sensing data.       assessment studies. XRD allows us to
    altered.                                                                                  identify fine-grained mixtures of
                                                                                              minerals found in associated gangue and
                                                                                              alteration assemblages, which cannot be
                                                                                              resolved by other methods.
                                                                                              -Prepared by Marta J.K. Flohr
                                                                                              For more information, please contact:
                                                                                              Frank T. Dulong
                                                                                              U.S. Geological Survey, MS 956
                                                                                              Reston, VA 20192
                                                                                              Telephone: (703) 648-6416
                                                                                              E-mail: fdulong@usgs.gov
                                                                                              John C. Jackson
                                                                                              U.S. Geological Survey, MS 954
                                                                                              Reston, VA 20192
    Figure 2.Example of an X-ray powder diffractogram produced during an X-ray scan.          Telephone: (703) 648-6321
    The peaks represent positions where the X-ray beam has been diffracted by the             E-mail: jjackson@usgs.gov
    crystal lattice. The set of d-spacings (the distance between adjacent planes of atoms),
    which represent the unique “fingerprint” of the mineral, can easily be calculated from
    the 2-theta (2θ) values shown. The use of degrees 2-theta in depicting X-ray powder
    diffraction scans is a matter of convention and can easily be related back to the
    geometry of the instrument, shown in figure 1. The angle and the d-spacings are
    related by Bragg’s Law, as described in the text.
    U.S. Department of the Interior                                                                                            May  1997
    U.S. Geological Survey