Microstructural Analysis of Hexagonal Close-Packed Metals Using X-Ray Diffraction and Transmission Electron Microscopy
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MICROSTRUCTURAL ANALYSIS OF HEXAGONAL CLOSE-PACKED METALS USING X-RAY DIFFRACTION AND TRANSMISSION ELECTRON MICROSCOPY
M. GRIFFITHS AND J.E. WINEGAR AECL Research, Chalk River Laboratories,
ijo.
Chalk River,
Ontario,
Canada,
KOJ
ABSTRACT The techniques employed for X-ray diffraction analysis of dislocation substructures in hexagonal close-packed metals are descibed and assessed by comparison with direct observations using transmission electron microscopy. INTRODUCTION Many of the core components in BWR, PWR and PHWR reactors are made from zirconium alloys and a considerable amount of materials research is directed at assessing how the alloys perform in service conditions. As their properties depend largely on microstructure, it is necessary to have adequate techniques for measuring microstructural variables. Some of the techniques developed for cubic materials (for example, grain size and texture determination using X-ray diffraction analysis) are applicable to zirconium based alloys even though they have hexagonal close-packed (hcp) crystal structures. However, because of the marked anisotropy of the hexagonal structure, analysis of microstructural variables such as dislocation densities from X-ray diffraction line-broadening measurements cannot be performed by assuming a cubic structure. In addition, lattice parameters are subject to modifications due to intergranular stresses that can be significant in hcp and body-centred cubic (bcc) materials but not in face-centred cubic (fcc) materials. A distribution of intergranular stresses can introduce errors into the determination of dislocation densities by contributing to the broadening of X-ray diffraction lines. This paper describes methods developed for improved analysis of dislocation densities in zirconium alloys using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The techniques described can be equally applied to other hexagonal close-packed metals. LINE-BROADENING THEORY General The method adopted by most researchers for dislocation density measurements is that developed by Williamson and Smallman [1]. They originally used the breadth of the strain distribution (e - 8 coteB, where P is the angular breadth of the diffraction line) for their calculations. This was related to the average strain in the lattice by a constant determined by the shape of the distribution (somewhere between a Cauchy (elasticity) and Gaussian (probability) distribution). For cubic materials, they assumed that the dislocations were all screw type and distributed equally along the three directions. They then related the energy of the lattice, calculated from the measured average strain, to the energy of a dislocation:
Mat. Res. Soc. Symp. Proc. Vol. 209. 01991 Materials Research Society
84
Energy stored inthe lattice V - 3 E (Ac2)/2 where E isYoung's modulus, e isthe average strain measured from the diffraction line and A isa constant. The factor 3 comes from the fact that the diffracting planes are distorted by only 1/3 of the available dislocations. Self
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