Resonant X-ray diffraction: `forbidden' Bragg reflections induced by thermal vibrations and point defects

Дмитриенко, В. Е.; Овчинникова, Е. Н.

doi:10.1107/s0108767300003421

Cited by 74 publications

(45 citation statements)

References 18 publications

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“…We need to consider an additional contribution to the resonant atomic factor, which is provided by transient proton configurations 20,33 : protons occupy only half of their crystallographic positions and, in the paraelectric phase, each of them tunnels back and forth between both sites of a double-well potential at a jump rate of the order of 10 . Because the waiting time between jumps is larger by several orders of magnitude than the typical time of x-ray resonant scattering (∼ 10 −15 s), x-rays "see" the crystal as a series of snapshots, producing an effect similar to thermal motion and static disorder 32 . Each transient proton configuration violates the crystal symmetry, but the space symmetry restores after averaging over all possible proton configurations.…”

Section: T MI αβmentioning

confidence: 99%

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Proton configurations in the hydrogen bonds ofKH2PO4as seen by resonant x-ray diffraction

et al. 2015

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KH2PO4 (KDP) belongs to the class of hydrogen-bonded ferroelectrics, whose paraelectric to ferroelectric phase transition is driven by the ordering of the protons in the hydrogen bonds. We demonstrate that forbidden reflections of KDP, when measured at an x-ray absorption edge, are highly sensitive to the asymmetry of proton configurations. The change of average symmetry caused by the 'freezing' of the protons during the phase transition is clearly evidenced. In the paraelectric phase, we identify in the resonant spectra of the forbidden reflections a contribution related to the transient proton configurations in the hydrogen bonds, which violates the high average symmetry of the sites of the resonant atoms. The analysis of the temperature dependence reveals a change of relative probabilities of the different proton configurations. They follow the Arrhenius law and the activation energies of polar and Slater configurations are 18.6 and 7.3 meV respectively.

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Section: T MI αβmentioning

confidence: 99%

“…The latter was ascribed to thermal-motion induced (TMI) scattering 32 . This mechanism is also expected in KDP.…”

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Proton configurations in the hydrogen bonds ofKH2PO4as seen by resonant x-ray diffraction

et al. 2015

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“…Its main feature is the growth of the integrated intensity with temperature in contrast to conventional Bragg reflections, whose intensity decreases with temperature according to the Debye-Waller factor. An additional contribution to the resonant scattering factor caused by point defects has been predicted [33], but not yet observed experimentally.…”

Section: Introductionmentioning

confidence: 99%

“…When the conventional part of x-ray scattering is absent, reflections still can appear at incident radiation energies close to absorption edges due to the anisotropy in resonant scattering [25][26][27][28]. These "forbidden" reflections provide the possibility to study small contributions to the atomic scattering factor caused by various multipole transitions or displacements of the atoms from their average sites [29][30][31][32][33]. Even slight atomic displacements due to thermal vibrations influence the resonant atomic scattering factor resulting in the so-called thermal motion induced (TMI) scattering contribution, which was successfully observed in Ge [34,35], ZnO, and GaN [36,37].…”

Section: Introductionmentioning

confidence: 99%

Mechanisms of the paraelectric to ferroelectric phase transition in RbH2PO4probed by purely resonant x-ray diffraction

et al. 2014

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Resonant x-ray diffraction was used to study the proton jumps in hydrogen-bonded rubidium dihydrogen phosphate (RDP) crystals. In the paraelectric RDP phase, hydrogen is delocalized between two crystallographically equivalent positions. At lower temperatures, this symmetry can be broken, which defines the processes that lead to the para-to ferroelectric phase transition. We have measured the energy spectra of the forbidden reflections 006 and 550 at incident radiation energies close to the Rb K edge in a wide temperature range, down to the temperature of the ferroelectric phase transition. In the paraelectric phase, we observed a growth of integrated intensity for both forbidden reflections with temperature. This behavior is opposite to conventional nonresonant Bragg reflections, where intensity decreases in accordance with the Debye-Waller factor. The developed theoretical model explains this effect with the thermal motion induced (TMI) scattering mechanism and also confirms the adiabatic approximation stating that electrons instantly follow the nuclei movements. In the 550 energy spectra, we have observed an additional contribution to the resonant structure factor, which could be associated with the presence of transient Slater-type proton configurations (PC) in the half-filled hydrogen position.

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“…A different explanation for the origin of resonant scattering in Ge, termed Thermal Motion Induced (TMI) scattering, was recently proposed by Dmitrienko and Ovchinnikova 25 .…”

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Polarization analysis of K-edge resonant X-ray scattering of germanium

Detlefs

2004

Physica B: Condensed Matter

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The polarization of K-edge resonant scattering at the space group "forbidden" (0 0 6) reflection of Ge was measured as function of the azimuthal angle, ψ. The experimental results are compared to model calculations based on symmetry analysis of the resonant scattering tensors.PACS numbers: 61.10. Dp, 61.10.Eq, 78.70.Ck In the last few years the investigation of resonant scattering phenomena has allowed novel studies of antiferromagnetism (through resonant magnetic xray scattering 1 ) and, more recently, of orbital 2,3,4,5 and quadrupolar order 6 . Although much progress has been made in the theory and interpretation of these effects, a large number of open questions concerning the origin of the scattering remains.A characteristic feature of resonant scattering is its polarization dependence, which differs markedly from that of normal Thompson scattering. Indeed, polarization analysis (PA) has now been developed into a standard tool for the study of the aforementioned effects. In this communication I present a study of resonant x-ray scattering at the Ge K-edge with emphasis on the analysis of polarization effects. Anisotropic tensor susceptibility (ATS) scattering 7,8,9 and orbital/quadrupolar order resonances are intimately related as the scattering arises from the same transitions between core level and valence band electronic states 10 . Therefore systematic studies of a well-known reference system may lead to better understanding of the complex situation in compounds exhibiting orbital order.One may distinguish three different classes of ATS scattering, depending on the rank of the scattering tensor: The original experiment on NaBrO 3 may be described by second rank tensors corresponding to electric dipole (E1) transitions 7,8,9 . A later experiment on α−Fe 2 O 3 evidenced electric quadrupole (E2) transitions, which give rise to fourth rank tensors 11 . Finally, ATS scattering in Ge was attributed to rank three tensors. Two different origins of this tensor were proposed: An E1-E2 mixed resonance 12,13,14 , and an E1-E1 process combined with a displacement of the scattering atom due to thermal motion 15,16 . The subject is still under discussion 17,18 .The azimuthal dependence of the scattered beam intensity was calculated and experimentally verified by Templeton and Templeton 12 , but without polarization analysis. For some selected photon energies, the phase of the (0 0 6) and (2 2 2) resonant scattering was determined by Lee et al. 19 through the interference with Umweg reflections. Finally, Kokubun et al. 15 and Kirfel et al. 16 studied the temperature dependence of the (0 0 2) and (0 0 6) resonant scattering. They observed a strong increase of the intensity with increasing temperature, but only minor variations in the line shape of the resonance.They concluded that the dominant origin of resonant scattering lies in anisotropic thermal motion of the Ge atoms.The aim of the present experiment was to complement the existing body of experimental data to further study resonant x-ray scattering of odd-rank...

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Resonant X-ray diffraction: `forbidden' Bragg reflections induced by thermal vibrations and point defects

Cited by 74 publications

References 18 publications

Proton configurations in the hydrogen bonds ofKH2PO4as seen by resonant x-ray diffraction

Proton configurations in the hydrogen bonds ofKH2PO4as seen by resonant x-ray diffraction

Mechanisms of the paraelectric to ferroelectric phase transition in RbH2PO4probed by purely resonant x-ray diffraction

Polarization analysis of K-edge resonant X-ray scattering of germanium

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