Indexing Electron Diffraction Patterns

In this post, I want to include something I have been working on since a long time- electron diffraction. Electron diffraction patters are those which are generated by scattering of electrons by certain lattice planes in a crystal, causing a pattern of spots or rings to form. This pattern represents the reciprocal lattice vector (k) in reciprocal space. Anyways, the point here is that if the electron diffraction pattern is a ring-like pattern, then the diameter of each ring is equal to 2/d where, d is the inter-atomic spacing in a crystal lattice, which is characteristic of the material. Below are two transmission electron microscope (TEM) images of TiO2 (titania) nanofibers which have been differently heat-treated. In the inset are the electron diffraction patterns which have been indexed up to the first 5 rings. Those rings correspond to the two structurally distinct phases of titania- anatase (represented by A) and rutile (R). The diameters of the rings obtained and the corresponding indexing order is listed below:

Sample: aHT07a

2/d (1/nm)   d (nm)        Plane                  
5.84            0.34           A(101)
8.80            0.23           R (200)
11.011        0.18           A (200)
12.29          0.16           R (220) /A (211)
14.13          0.14           R (221)            
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[TEM image of TiO2/Ag nanofiber aHT07a; inset: electron diffraction from the same sample.]

 

[TEM image of TiO2/Ag nanofiber aHT07b; inset: electron diffraction from the same sample.] 

Similarly, for electron diffraction patterns which are more of a spot-like appearance, the distance between the two corresponding spots from the same k vector will be 2/d. This information about the d-spacings can also be obtained from high-resolution TEM (HR-TEM) imaging. As an example, the d-spacing in the TEM image below corresponds to the distance between two parallel lattice fringes. The parallel lines that you see in the image below are distinct planes of atoms of Ag (silver) arranged in a specific manner to form a single crystal. The Ag nanoparticle in the image below seems to be comprised of about 3 such crystals, called twins. 

The types of characterization techniques possible with electron microscopy are many. All these different techniques give us material scientists information about physical structure, chemical composition, crystallinity, phases, distribution, and even 3D reconstruction of nanoscale models.

[This article is also published in the blog, Nano Pulse, here: link.]