An evaluation of diffraction peak profile analysis (DPPA) methods to study plastically deformed metals

Simm, Thomas H.; Withers, Philip J.; Fonseca, João Quinta da

doi:10.1016/j.matdes.2016.08.091

Cited by 23 publications

(21 citation statements)

References 62 publications

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“…The Williamson-Hall method [19] is a common method to define the broadening of a diffraction peak; here the full-width at half maximum intensity (full-width, or FW) of a diffraction peak is defined as being due to micro-strain and size components. In terms of broadening by dislocations this equation can be written as [4,20]: Schematic of an edge dislocation in a face-centred cubic crystal. The dislocation will cause maximum broadening when the diffraction vector is paralell to [110] and a minimum when it is parallel to [11 2].For the dislocation shown b is [110], n is [1 11], and s is [ 11 2].…”

Section: The Contrast Factormentioning

confidence: 99%

“…The Williamson-Hall method [19] is a common method to define the broadening of a diffraction peak; here the fullwidth at half maximum intensity (full-width, or FW) of a diffraction peak is defined as being due to micro-strain and size components. In terms of broadening by dislocations this equation can be written as [4,20]:…”

Section: The Contrast Factormentioning

confidence: 99%

“…In the work of Simm et al [4] two face-centred cubic (FCC) alloys, stainless steel and a commercially pure nickel, were deformed by compression to a range of applied strains. The samples were then measured using a laboratory X-ray diffractometer and subsequently analysed using different DPPA methods (more details are provided in [4]). The changes in the q values from three different modified Williamson-Hall analyses is shown in Figure 4.…”

Section: Homogeneous Approachmentioning

confidence: 99%

“…Following the traditional method of using peaks of the same reflection can be problematic because of the relatively low intensity of the 222 peak, as well as the use of less diffraction peaks. An example of the difference between using the traditional and modified (with the contrast factor) approaches is shown in Figure 5, which shows the change in dislocation density using the Warren-Averbach method [4]. The figure shows that using the modified approach reduces the scatter, as given by the deviation from the best fit line.…”

Section: Homogeneous Approachmentioning

confidence: 99%

“…The technique can be used to quantify the dislocation density, crystal/dislocation-cell size, planar fault percentage and the dislocation slip systems present in samples in a statistically significant manner that is either practically very difficult or not possible using other techniques. However, its more widespread use is limited due to practical and mathematical limitations of the technique [4,5]. One of the main limitations of the technique is due to peak broadening anisotropy, which has implications on the results of the broadening methods and its use with other techniques.…”

Section: Introductionmentioning

confidence: 99%

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Peak Broadening Anisotropy and the Contrast Factor in Metal Alloys

Simm

2018

Crystals

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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]).

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