Peak Broadening Anisotropy and the Contrast Factor in Metal Alloys

Abstract

Diffraction peak profile analysis (DPPA) is a valuable method to understand the microstructure and defects present in a crystalline material. Peak broadening anisotropy, where broadening of a diffraction peak doesn't change smoothly with 2θ or d-spacing, is an important aspect of these methods. There are numerous approaches to take to deal with this anisotropy in metal alloys, which can be used to gain information about the dislocation types present in a sample and the amount of planar faults. However, there are problems in determining which method to use and the potential errors that can result. This is particularly the case for hexagonal close packed (HCP) alloys. There is though a distinct advantage of broadening anisotropy in that it provides a unique and potentially valuable way to develop crystal plasticity and work-hardening models. In this work we use several practical examples of the use of DPPA to highlight the issues of broadening anisotropy. of 31where, D is the crystal size, K Sch is the Scherrer constant (often taken as 0.9 for spherical crystals), g is the reciprocal of the d-spacing of a peak, f m is a function related to the arrangement of dislocations (and represents how the arrangement of groups of dislocations influence their total strain), ρ is the dislocation density and C hkl is the average contrast factor of dislocations in grains that contribute to the hkl diffraction peak. In Equation 1 and other DPPA approaches, C hkl is assumed to be the only term that accounts for broadening anisotropy and its value is required to be able to obtain the dislocation density.TEM to be able to identify details of dislocations [15,16], especially in cases when g.b=0 does not lead to vanishing contrast or due to practicalities of rotating a sample. In the same manner, the diffraction broadening caused by a dislocation varies depending on the diffraction vector, and can be calculated by modelling the dislocation's displacement field. The contribution of a dislocation's displacement field to the broadening of different diffraction profiles is through what is known as the contrast (or orientation) factor of dislocations. The contrast factor of an individual dislocation is dependent on the angles between the diffraction vector and the vectors that define the dislocation: it's Burgers vector (b), slip plane normal (n), and dislocation line (s). The contrast factor of an individual dislocation can be calculated using the computer program ANIZC [17]. For example, the edge dislocation in Figure 2 has a contrast factor of 0.46 when g is [110] and parallel to the dislocations Burgers vector. The value is 0.00 when g is parallel to the slip line ([11 2]) and 0.05 when g is parallel to the slip plane normal ([1 11]).

The τ-plot, a multicomponent 1-D pole figure plot, to quantify the heterogeneity of plastic deformation

“…The use of polycrystal plasticity models to predict diffraction peak broadening [4,14,28,29] is a less developed modelling route than for texture or lattice strains. In this method a polycrystal plasticity model is used to predict the activity of different slip systems in different grains, this is converted to broadening by an assumption on the relationship between slip activity and dislocation density.…”

“…There are two main approaches that are generally followed: powder diffraction method and crystallographic texture measurements. In the former, plastic deformation can be quantified by measuring the changes in phase fraction [1], lattice strain [2], and the quantity and arrangement of dislocations [3][4][5]; whereas the latter gives information about changes in texture [6] of the alloy and orientations of individual phases. The two approaches provide complementary information about plastic deformation but require separate experimental set-ups.…”

Microstructural Control of Pyrolytic Carbon Layer Deposited from Methane by Isotropic Chemical Vapor Infiltration

“…22) The measured full-widths at half maximum (FWHMs), asymmetric factors, and crystallite sizes of the PyC layers are listed Table 1. The asymmetric factors, which increase with the generation of stacking faults, 23) of P5 and P100 were calculated to be 1.27 and 1.4, respec-tively. With a decrease in FWHM values and asymmetric factors, defects like stacking faults also decrease.…”

Characterization of Dislocation Rearrangement in FCC Metals during Work Hardening Using X-ray Diffraction Line-Profile Analysis

“…Simm et al, have applied the line-profile analysis methods to investigate the dislocation character in FCC and hexagonal closed-packed alloys [26][27][28]. The results showed that heterogeneous microstructures were formed during plastic deformation in FCC nickel and stainless steel.…”