The Experimental Value of f(220) for Copper

Abstract

Aust. J. Phys., 1984,37, 651-6 The value of the atomic form factor, /(220), for copper has been determined in recent years by a variety of methods. All the dynamical methods agree on a value in the region of 16'70-16·75. These methods include two X-ray methods, one involving measurement of intensity profiles and the other of Pendellosung beats, and also an electron diffraction measurement using a critical voltage procedure. By contrast, two recent kinematical measurements using y rays both report a distinctly different value of about 16·45. One of these determinations has already been re-examined by the present authors and the discrepancy removed by an appropriate extrapolation to zero extinction. The present paper shows that the published experimental data for the other y-ray determination should lead to a value of about 16·69. This value confirms the linearity of our extrapolation and the importance of this extrapolation in deriving experimentally based extinction-free values of structure factors.

A study of charge density in copper

“…The absolute scale and even the extinction correction of the -ray data has therefore been questioned, and several different corrections have been proposed. By applying an improved extinction correction scheme to the 220 structure factor, Mackenzie & Mathieson (1984) obtained a value closer to that of other experiments. On the other hand, Tabbernor et al (1990) pointed out that good agreement can also be achieved by rescaling the data set to fit the 111 reflection of Fox & Fisher (1988).…”

Adsorption of line segments on a square lattice

“…In order to extrapolate to k → ∞, we must guess the large k behaviour. Analogous analyses have been performed previously in one dimension [14] and in two dimensions for the deposition of squares [2,6]. In both cases the large k limit corresponds to the continuum limit and is approached up to a 1/k corrective term.…”

“…Among the distinct solutions that we have obtained, namely (G 1 (∞), α) = {(0.956, 0.887), (0.713, 1.165), (1.889, 0.333)} and (G 2 (∞), α) = {(−1.377, 0.694), (−0.791, 1.368)}, the prefered solution, which corresponds to a larger number of intersecting central approximants, has been quoted first. These values of G 1 (∞) and G 2 (∞) and the known asmptotic behaviour of θ 1 (k, ∞) [14] allows us to finally give our prefered estimates for A 1 and A 2…”

“…Finite size effects are exactly known in one dimension [14,15]. MacKenzie has shown that, for RSA of k-mers at jamming, the number of vacant sites on a lattice of L sites with open boundary conditions is given by…”

On the Contribution of A McL Mathieson to Crystallography

“…Guided by the general philosophy of extrapolation to extinction-free limits, Mathieson and Mackenzie l05 ) [see also ref. 121)] were able to show that )I-ray data 134) for Cu, which had been claimed to be extinctionfree, gave an anomalously low value for the 220 structure factor because of residual extinction effects.…”