Use of Reciprocal Lattice Layer Spacing in Convergent Beam Electron Diffraction Analysis
- PDF / 858,976 Bytes
- 4 Pages / 594 x 774 pts Page_size
- 4 Downloads / 205 Views
I.
INTRODUCTION
CONVERGENT Beam Electron Diffraction (CBD) analysis in the modern probe forming instruments has received increasing attention in the analysis of the crystal structures of complex phases. The CBD analysis provides three dimensional structure and symmetry information and can be used to determine point and space groups of crystalline phases. The theory and technique of the analysis are discussed in several recent articles.~'2 One of the many advantages of CBD is that it provides information about the crystal dimension parallel to the electron beam and this information can be utilized to uniquely identify crystal structure and orientation. As described by Steeds, 1 the radius of the First Order Laue Zone (FOLZ) can be used to measure the reciprocal lattice layer spacing, H, in reciprocal units, using the expression H,, = A G2/2
[1]
where A is the wavelength of the electron beam, G is the radius of the FOLZ ring in reciprocal units, and the subscript m refers to the measured value of H. This measurement of the layer spacing from the FOLZ ring requires no prior knowledge of the crystal structure orientation or cell dimensions. However, if the crystal structure and the zone axis of the diffraction pattern are known, it is possible to calculate the layer spacing, He, from these parameters (subscript c stands for the calculated value of H). If the diffraction pattern is correctly indexed, then measured and calculated values of H should be identical, provided that the structure factor of the crystal allows reflections in all the Laue zones. If the structure factor permits reflections only in some of the Laue zones because of systematic extinctions, then these zones will be absent and the calculated and measured values will differ by integral values. This will be discussed in a later section. In a recent study,it was demonstrated that the zero-layer [1]-0] sigma and [102] P diffraction patterns were very simiM. RAGHAVAN, Research Associate, and J.C. SCANLON are with Corporate Research Science Laboratories, Exxon Research & Engineering Company, Route 22 East, Annandale, NJ 08801. J. W. STEEDS is with the Department of Physics, University of Bristol, Tyndal Avenue, Bristol, United Kingdom, Manuscript submitted October 17, 1983.
METALLURGICALTRANSACTIONS A
lar and could not be used to uniquely identify these phases.3 Similar situations often arise in distinguishing compounds which have closely related crystal structures. However, when the interlayer spacings measured from the CBD patterns were compared with the interlayer spacings calculated for these orientations, the values compared well for only the [102] P phase and not for the [11-0] sigma phase, thus uniquely identifying the crystal to be P phase. In this illustration, the interlayer spacings were calculated by constructing the reciprocal lattices for the respective phases. In cases of complicated crystal structures and/or low symmetry orientations, such constructions are impractical. Consequently, it would then be extremely useful to have analytical
Data Loading...
