The effect of the dislocation distribution on the electrical resistivity in deformed metals

Abstract

s 70th birthdayThe effective resistivity is calculated for a simple cell structure by means of the Boltzmann equation. I n less heavily deformed metals the cell structure has only a negligible effect on the residual resistivity. In heavily deformed metals the observed DMR is in the same order of magnitude as that arising from the presence of the cell structure. Oleo decreases with increasing amount of cold work and this experimental result suggests that the DMR arising from the anisotropic dislocation scattering is larger than the DMR due to the cell structure.Wt Hilfe der Boltzmann-Gleichung wird der spezifische Widerstand einer einfachen Zellstruktur bestimmt. I n maRig verformten Metallen ist der EinfluR der Zellstruktur auf den Restwiderstand zu vernachlassigen. I n stark verformten Metallen liegt die Abweichung von der M E in derselben GroBenordnung, wie sie der inhomogenen Versetzungsverteilung entspricht. A/@, nimmt mit zunehmender Verformung ab, woraus geschlulfolgert wird, daR die Abweichung, die von der Anisotropie der Versetzungsstreuung stammt, groBer ist als die, die von der Zellstruktur hervorgerufen wird.

Three dimensional line profile analysis

“…The categorization of lattice defect types indicates that the most important source of strain broadening is dislocations. The effect of the strain field of dislocations was discussed in detail by Krivoglaz and Ryaboshapka [1963], Wilkens [1970], Krivoglaz et al [1983], Gaál [1984], Groma et al [1988] and Groma [1998]. Wilkens [1970] has shown that the higher order terms in the series expansion can be approximated by a second order expression by rescaling the length dependence of the deformation field of dislocations.…”

Grain Size, Size‐Distribution and Dislocation Structure from Diffraction Peak Profile Analysis

“…(22) and (23) in [29]. For small values of K the Wilkens function can be approximated by a logarithmic function [6,11,12]:…”

“…The following five or six fitting parameters are used: (i) m and (ii) V, the median and the variance of the log-normal size distribution density function in the size profile, (iii) U and (iv) M, the density and the arrangement parameter of dislocations in the strain profile and (v) q or q 1 and q 2 for the average dislocation contrast factors as in eqs. (6) or (7) for cubic or hexagonal crystals, respectively. The values of C h00 or C hk0 are not fitting parameters since they are only multiplicative factors in the Fourier coefficients of the strain profiles.…”

“…These observations provide details on the micron or submicron scales. Average properties of the microstructure, especially on the hundreds of microns up to millimeters scale like crystallite size-distributions [1][2][3] or specific properties of dislocations as long range internal stresses [4][5][6][7], dislocation densities [8][9][10], arrangement parameters [11,12] or statistical fluctuations [13][14][15] are better obtained by diffraction peak profile analysis [16].…”

“…Strain anisotropy means that neither the breadth nor the Fourier coefficients of the diffraction profiles are monotonous functions of the diffraction angle or g where g is the absolute value of the diffraction vector [18][19][20][21][22][23][24][25][26][27]. Further difficulty is encountered by the fact that the mean square strain, <H L,g 2 >, is never a constant, neither as a function of L nor g, where L is the Fourier length [2,[5][6][7][8][9][10][11][12][13][14][15][16]18,[21][22][23][24]. In order to separate strain and size broadening correctly strain anisotropy has to be treated properly.…”