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Grazing incidence diffraction geometry. The angle of incidence, α, is close to the critical angle for the sample. The beam is diffracted in the plane of the surface of the sample by the angle 2θ.

High Resolution X-Ray Diffraction (HRXRD) Training. HRXRD is used to analyze epitaxial thin films – Can determine composition, strain/relaxation, lattice parameters (in- plane and out-of-plane), thickness, and defect concentration. X-Ray Reflectivity (XRR) is used to analyze thin films, including amorphous and non-textured films. It turns out (unlike many other crystals) that the reciprocal lattice of a cubic crystal is again a cubic crystal with a reciprocal lattice constant 2 /a. The reciprocal lattice vector 𝐾⃗ ℎ is now very useful to define the XRD scan around the (h,k,l) reflection, which is equivalent to a XRD scan at the (h,k,l) net plane. X-ray diffraction (XRD) is a powerful analytical tool for industry professionals and material scientists. A source (typically copper) produces x-rays which are directed at a flat sample. These x-rays are diffracted at certain angles by the crystal planes in the material and are detected at those angles.


Grazing incidence X-ray and neutron diffraction (GID, GIXD, GIND), typically from a crystalline structure uses small incident angles for the incoming X-ray or neutron beam, so that diffraction can be made surface sensitive. It is used to study surfaces and layers because wave penetration is limited. Distances are in the order of nanometres. Below (typically 80%) the critical angle of the surface material studied an evanescent wave is established for a short distance and is exponentially damped. Therefore, Bragg reflections are only coming from the surface structure.

Figure 1 shows a set of in-plane and out-of-plane scans from ZnO film on a c-axis sapphire substrate collected on the SmartLab X-ray diffractometer with the in-plane arm. The phi scan which is sample in-plane rotation at ZnO (100) is also shown in Figure 2. The lamellar spacing was determined to be 3.25 nm from the out-of-plane XRD measurement. Compared with the calculated value, the actual value is 0.33 nm shorter. This suggests that not all of the dodecyl side chains have an all- trans conformation and the gauche conformer is present in the lamellar structure.


An advantage of GIXD is that the electric field at the critical angle is amplified locally by a factor of four, making the signal stronger. A disadvantage is the limited in-plane spatial resolution (beam footprint).

When very small scattering angles are being studied, the technique is called grazing-incidence small-angle scattering (GISAS, GISAXS, GISANS), and requires special methodology.


Before synchrotron-based X-ray sources became strong enough very little research was possible. The first paper published was by Marra and Eisenberger[1] who used both a rotating anode x-ray source and the Stanford Synchrotron Radiation Laboratory (SSRL). Soon dedicated ultra-high-vacuum diffractometers were developed for preparing and studying surfaces in-situ,[2][3] the first at SSRL and the second at the National Synchrotron Light Source (NSLS).

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See also[edit]

Further reading[edit]


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  • Als-Nielsen, J. & McMorrow, D. (2011). Elements of Modern X-ray Physics (2 ed.). Wiley. ISBN978-0470973950.
  • Dietrich, S. & Haase, A. (1995). 'Scattering of X-rays and neutrons at interfaces'. Physics Reports. 260: 1–138. doi:10.1016/0370-1573(95)00006-3.


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  1. ^Eisenberger P, Marra WC (April 1981). 'X-Ray Diffraction Study of the Ge(001) Reconstructed Surface'. Physical Review Letters. 46: 1081–4.
  2. ^Brennan S, Eisenberger P (1984). 'A Novel X-Ray Scattering Diffractometer for Studying Surface Structures under UHV Conditions'. Nuclear Instruments and Methods. 222: 164–7.
  3. ^Fuoss PH, Robinson IK (1984). 'Apparatus for X-Ray Diffraction in Ultra-High Vacuum'. Nuclear Instruments and Methods. 222: 171–6.
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