Diffuse X-ray scattering from the displacement field of point defects and defect clusters

Peisl, H.

doi:10.1107/s0021889875009922

Cited by 45 publications

(13 citation statements)

References 2 publications

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“…Using the RG arguments of Weinrib and Halperin [25] for quenched long-range disorder, Altarelli et al [26] evaluated the exponent n in the skin layer in the presence of defects and dislocations and found n skin 2͞a independent of higher order corrections. In our case, we have effectively point defects, as stated earlier, and therefore a strain field asymptotically decaying~r 23 [26,29]. Thus a 3 and n 2 2͞a 2͞3 in agreement with our observation of n 2 0.69 6 0.09 above the crossover point.…”

supporting

confidence: 90%

“…Beyond this length scale the dressed interactions are screened. This may be thought of in direct analogy with the Stokes-Wilson radius that appears in the Huang diffuse scattering from point defects and defect clusters [29]. The behavior observed here is reminiscent of the results of Melnichenko et al [30] for a polymer solution near the critical demixing point, where their crossover is from intermolecular fluctuations at small t to intramolecular fluctuations at larger t. For related studies over a comparable range in t, the review of Cowley [9] covers the majority of the results where n 2 ranges from 0.5 to 1.3, depending on the defect type.…”

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confidence: 98%

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Two Length Scales and Crossover Behavior in the Critical Diffuse Scattering fromV2H

et al. 1998

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We have observed two length scales in a V 2 H crystal above the b 1 -b 2 phase transition. A sharp Lorentzian profile in the critical diffuse scattering was superimposed on a broader one for a low-energy x-ray experiment in reflection, while no sharp component appeared in transmission at high energy. For the sharp component, we extracted tricritical exponents n 1 and g 1 at small reduced temperatures t, where fluctuations are coherent over large distances. For larger t, where the correlation length is comparable to an effective defect size, there is a crossover to altered exponents. [S0031-9007(98)07111-7] PACS numbers: 64.60. Cn, 61.10.Nz, 61.72.Hh, 64.60.Fr The interstitial alloy V 2 H presents an excellent system to study the "two length-scale" issue first seen in SrTiO 3 by Andrews [1] who found, in a high resolution x-ray diffraction study, a narrow Lorentzian-squared peak in the critical diffuse scattering (CDS) on top of a broad Lorentzian in contradiction to theories of critical phenomena. Systematic studies of perovskites, e.g., SrTiO 3 , KMnF 3 , RbCaF 3 (see [2][3][4] and references in McMorrow et al. [5]), as well as magnetic scattering from Tb [6,7] and Ho [8] have led to the conclusion that the narrow component of the CDS (second length scale) arises from a skin layer of several mm extending below the surface, while the bulk material still shows normal critical behavior (see, e.g., references in Cowley [9] and Wang et al. [4]). Neumann et al. [10] observed that the sharp component in SrTiO 3disappears in a high-energy synchrotron x-ray experiment in transmission geometry which probed the "true" bulk behavior. However, the sharp component of the CDS still remained when the corner of the crystal was illuminated, thereby probing the behavior of a defective near-surface region, estimated by Rütt et al.[3] to be less than 100 mm. A transmission electron microscopy study of SrTiO 3 by Wang et al. [4] directly reveals structural defects in this skin layer, namely, dislocations, whose density decreased with increasing depth from the surface, which were thereby considered responsible for the second length scale. They also discuss the expected shift in the critical temperature due to defect strain (see also [9]). Two length scales have also been seen by Gehring et al. [11] in a neutron study of a 1 mm Ho film grown on a Y buffer, suggesting that the two may coexist within this small volume.In this Letter, we report on a second length scale and crossover behavior in the critical diffuse scattering from V 2 H above the order-disorder phase transition b 1 -b 2 . We first probed both the bulk and the skin layer, using lowenergy x-ray diffraction in reflection geometry and, in a separate experiment, the true bulk using high-energy diffraction in transmission geometry. In V 2 H, we find a transition on cooling from a regime in which the two length scales are observable at higher reduced temperatures, t T ͞T C 2 1, to one showing only the sharp component at lower t. This sharp component can best be fit with a sin...

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confidence: 90%

mentioning

confidence: 98%

Two Length Scales and Crossover Behavior in the Critical Diffuse Scattering fromV2H

et al. 1998

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“…That is, there is no measurable volume change due to the oxygen vacancies in the SrTiO 3 crystal, agreeing with previous reports 13,14 . Both of these experimental results are incompatible with the conventionally used diffuse scattering analysis [15][16][17][18] , which is based on the assumption that the point defects are randomly distributed.…”

Section: Resultsmentioning

confidence: 73%

Strain and oxygen vacancy ordering inSrTiO3: Diffuse x-ray scattering studies

et al. 2015

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We report systematic diffuse x-ray scattering measurements of the elastic strain fields generated by oxygen vacancies in strained bulk SrTiO3 crystals. Diffuse x-ray scattering has been used for decades to measure the elastic strain fields generated by point defects based on the assumptions that the defects are randomly distributed and uncorrelated. We find for SrTiO3 that (i) there are correlations between oxygen vacancies with different orientations, (ii) we can manipulate the relative concentrations of the three orientations via applied stress, and (iii) the oxygen vacancies cluster around the edge dislocations, creating a two-dimensional distribution.

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“…In addition the estimate of elastic intensities is then affected by the wavelength band-pass of the analyser crystal, and this can well introduce errors comparable to the TDS eliminated. Elastic diffuse scattering which is still detectable at some distance from a Bragg peak [such as, for example, Huang scattering (Peisl, 1975)] may in certain cases be discriminated from inelastic contributions by classical three-axis methods (Burkel, Von Guerard, Metzger, Peisl & Zeyen, 1979). However, in general such experiments require further improved energy resolution to eliminate inelastic scattering.…”

Section: A--nvp ~ J(q)'mentioning

confidence: 99%

On the use of neutron spin-echo to separate inelastic scattering from elastic scattering at high energy resolution

Hawter¹,

Lehmann²,

Mezei³

et al. 1979

Acta Cryst Sect A

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Generally the measured intensity of a Bragg peak or of elastic diffuse scattering contains an inelastic component (thermal diffuse scattering, low-lying phonon branches). Theoretical corrections for such effects are only possible in the limited number of cases where appropriate data are available. An experimental correction is difficult because the high energy resolution imposed reduces the beam intensity in a conventional experiment. In the case of neutron diffraction, the spinecho technique proposed by Mezei [Z. Phys. (1972), 255, 146-160] for neutron spectroscopy can be used as a filter for inelastic scattering without significant loss in elastic intensity. The application of the technique to an elastic neutron-scattering experiment is described, and it is shown that for a neutron wavelength of 1-5 A an energy resolution of better than 50 laeV can be obtained. With this energy band-pass, scattering even from very soft phonons or magnons can be avoided when studying critical scattering near phase transitions. Simple estimates also imply that more than 90% of the TDS contribution can be removed even for soft materials.

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Diffuse X-ray scattering from the displacement field of point defects and defect clusters

Cited by 45 publications

References 2 publications

Two Length Scales and Crossover Behavior in the Critical Diffuse Scattering fromV2H

Two Length Scales and Crossover Behavior in the Critical Diffuse Scattering fromV2H

Strain and oxygen vacancy ordering inSrTiO3: Diffuse x-ray scattering studies

On the use of neutron spin-echo to separate inelastic scattering from elastic scattering at high energy resolution

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