Atomic Size Effect in the X-Ray Scattering by Alloys

Warren, Β. E.; Averbach, B.L.; Roberts, B. W.

doi:10.1063/1.1699898

Cited by 318 publications

(92 citation statements)

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“…This level of strain is no greater than those predicted and measured in both dilute and concentrated binary alloys. 189,190,[196][197][198][199][200][201] Indeed, the displacements are of similar size to those expected from thermal vibrations around room temperature 185,190,196 and, therefore, cannot be described assevere.…”

Section: Pickering and Jones High-entropy Alloysmentioning

confidence: 99%

“…It is true that diffraction peak intensity should decrease with increasing lattice strain around solute atoms, and that these localised static displacements have a similar effect on intensity as thermal vibrations. [188][189][190][191][192][193] Typical lattice strains from solute atoms are not thought to generate significant levels of peak broadening, 190,191 as is observed in alloys with high dislocation densities or small crystallite sizes. However, it should be noted that a number of effects can influence the peak intensity and diffuse scattering observed in a diffraction pattern, including crystallographic texture, thermal vibrations and fluorescence.…”

Section: Severely Distorted Latticesmentioning

confidence: 99%

“…Hence, attentive assessment of high-quality experimental data is needed before any comment can be made on the magnitude of lattice distortions. [189][190][191][192][193][194] In addition, the levels of strain considered historically have been small, allowing for particular estimations to be made, and the effects of severe lattice distortions may be different.…”

Section: Severely Distorted Latticesmentioning

confidence: 99%

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High-entropy alloys: a critical assessment of their founding principles and future prospects

Pickering

Jones

2016

International Materials Reviews

736

299

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High-entropy alloys (HEAs) are a relatively new class of materials that have gained considerable attention from the metallurgical research community over recent years. They are characterised by their unconventional compositions, in that they are not based around a single major component, but rather comprise multiple principal alloying elements. Four core effects have been proposed in HEAs: (1) the entropic stabilisation of solid solutions, (2) the severe distortion of their lattices, (3) sluggish diffusion kinetics and (4) that properties are derived from a cocktail effect. By assessing these claims on the basis of existing experimental evidence in the literature, as well as classical metallurgical understanding, it is concluded that the significance of these effects may not be as great as initially believed. The effect of entropic stabilisation does not appear to be overarching, insufficient evidence exists to establish the strain in the lattices of HEAs, and rapid precipitation observed in some HEAs suggests their diffusion kinetics are not necessarily anomalously slow in comparison to conventional alloys. The meaning and influence of the cocktail effect is also a matter for debate. Nevertheless, it is clear that HEAs represent a stimulating opportunity for the metallurgical research community. The complex nature of their compositions means that the discovery of alloys with unusual and attractive properties is inevitable. It is suggested that future activity regarding these alloys seeks to establish the nature of their physical metallurgy, and develop them for practical applications. Their use as structural materials is one of the most promising and exciting opportunities. To realise this ambition, methods to rapidly predict phase equilibria and select suitable HEA compositions are needed, and this constitutes a significant challenge. However, while this obstacle might be considerable, the rewards associated with its conquest are even more substantial. Similarly, the challenges associated with comprehending the behaviour of alloys with complex compositions are great, but the potential to enhance our fundamental metallurgical understanding is more remarkable. Consequently, HEAs represent one of the most stimulating and promising research fields in materials science at present.

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Section: Pickering and Jones High-entropy Alloysmentioning

confidence: 99%

Section: Severely Distorted Latticesmentioning

confidence: 99%

Section: Severely Distorted Latticesmentioning

confidence: 99%

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High-entropy alloys: a critical assessment of their founding principles and future prospects

Pickering

Jones

2016

International Materials Reviews

736

299

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“…Equation 28 is a result given by Borie and Sparks (1964) that avoids an earlier assumption of radial displacements first given by Warren et al (1951). Shown in Figure 23 is …”

Section: Appendix A: Derivation Of the Diffuse Intensitymentioning

confidence: 99%

“…Our use of the double sum requires that the pairs of atoms be counted in both directions, that is, a p, q pair will become a q , p pair such that i (δ p -δ q ) = −i(δ q − δ q ) as shown in Figure From the definition of an average lattice, the weighted average of the displacements for all the kinds of pairs formed for any coordination shell is zero (Warren et al, 1951),…”

Section: Appendix A: Derivation Of the Diffuse Intensitymentioning

confidence: 99%

X‐ray and Neutron Diffuse Scattering Measurements

Ice

Robertson

Sparks

2012

Characterization of Materials

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Diffuse scattering from crystalline solid solutions is used to measure local compositional order among the atoms, dynamic displacements (phonons), and mean species‐dependent static displacements. It can also provide information on defects including vacancies, interstitials, dislocations and truncated sample dimensions. In locally ordered alloys, fluctuations of composition and interatomic distances break the long‐range symmetry of the crystal within local regions and contribute to the total energy of the alloy. Local ordering can be a precursor to a lower temperature equilibrium structure that may be unattainable because of slow atomic diffusion. In addition to local atomic correlations, neutron diffuse scattering methods can be used to study the local short‐range correlations of the magnetic moments. Interstitial defects, as opposed to the substitutional disorder defects described above, also disrupt the long‐range periodicity of a crystalline material and give rise to diffusely scattered x‐rays, neutrons, and electrons. This article will concentrate on the use of diffuse x‐ray and neutron scattering from single crystals to measure local chemical correlations and chemically specific static displacements. Particular emphasis is placed on the use of resonant (anomalous) x‐ray techniques to extract information on atomic size from binary solid solutions with short‐range order. By separating this diffuse intensity into its component parts we are able to recover pair correlation probabilities for the three kinds of pairs in a binary alloy. The interpretation of diffuse scattering associated with dynamic displacements of atoms from their average crystal sites are discussed briefly in this article.

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