Dislocations in Submicron Grain Size and Nanocrystalline Copper
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Dislocations in Submicron Grain Size and Nanocrystalline Copper T. Ungár1, G. Tichy2, P. G. Sanders3 and J. R. Weertman4 1 Dept. of General Phys. and 2Dept. of Solid State Phys., Eötvös University Budapest, H-1518, P.O.B. 32, Budapest, Hungary, 3 Harvard University, 402 Gordon McKay, 9 Oxford St, Cambridge, MA, 02138 U.S.A. 4 Dept. of Mater. Sci. and Eng., Northwestern University Evanston, IL, 60208 U.S.A. ABSTRACT Using the dislocation model of strain anisotropy in X-ray diffraction peak profile analysis it is shown that in nanocrystalline copper produced by inert gas condensation dislocations are present, at least, down to average grain sizes of the order of 20 nm. Based on the analysis of the dislocation contrast factors it is suggested that with decreasing grain size the proportion of Lomer-Cottrell type dislocations increases. INTRODUCTION The existence and type of dislocations in bulk nanocrystalline metals is still under debate [1-3]. High resolution electron microscopy indicates the presence of dislocations in the grain boundary regions, while the grain interior regions become clear of dislocations with decreasing grain size [4]. Using the method of X-ray diffracion peak profile analysis it was shown earlier that nanocrystalline copper produced by inert gas condensation does contain dislocations [5]. The previously used interpretation of X-ray data has been further developed and refined [6,7]. In the present work a series of copper specimens produced by inert gas condensation and deformed in some cases either by tension or compression will be analysed for the grain size, the grain sizedistribution, the dislocation densities and the type of dislocations. Instead of the earlier suggested screw type it is found that as the grain size decreases the proportion of Lomer-Cottrell dislocations increases. The evaluation of broadened X-ray diffraction peak profiles is based on the dislocation model of strain anisotropy [5]. This means that neither the FWHM (full width at half maximum) nor the integral breadth nor the Fourier coefficients of diffraction profiles are monotonous functions of the diffraction vector. A procedure has been developed to determine the crystallite size-distribution function and the dislocation structure in terms of the median and variance of a log-normal size-distribution and the density, the arrangement and the character (edge or screw type) of dislocations [6-8]. The FWHM, the integral breadths and the Fourier coefficients are analysed in terms of the modified Williamson-Hall and Warren-Averbach procedures. EVALUATION OF X-RAY DIFFRACTION EXPERIMENTS The Fourier transform of diffraction peak profiles can be written in the form of the WarrenAverbach equation [9]: ln A(L) ≅ ln ALS - 2π2L2g2 ,
(1)
B1.7.1
where A(L) are the absolute values of the Fourier coefficients of the physical profiles, ALS are the size Fourier coefficients, g is the absolute value of the diffraction vector and is the mean square strain in the g direction. L is the Fourier length, L=na3 [6], where a3=λ/2(sinθ2-sinθ1), n
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