Tensor X-ray optical properties of the bromate ion

Templeton, David H.; Templeton, L. K.

doi:10.1107/s0108767385000277

Cited by 157 publications

(87 citation statements)

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“…There is quite a close similarity between this effect and the anisotropy-induced re¯ections which were predicted by Templeton & Templeton (1980), theoretically developed by Dmitrienko (1983Dmitrienko ( , 1984, and experimentally observed for the ®rst time by Templeton & Templeton (1985) for the dipole± dipole transition in NaBrO 3 . They are usually called forbidden re¯ections' or ATS (anisotropy of the tensor of the susceptibility) re¯ections, because in the absence of the anisotropy they are strictly forbidden by the glide-plane and/ or screw-axis selection rules.…”

Section: Introductionsupporting

confidence: 85%

Chirality-induced `forbidden' reflections in X-ray resonant scattering

Дмитриенко

Овчинникова

2001

Acta Cryst Sect A

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It is shown that additional Bragg re¯ections can appear exclusively owing to the local chirality associated with the left±right asymmetric environment of scattering atoms in non-magnetic crystals. The structure amplitude of these re¯ections depends on the antisymmetric part of a third-rank tensor describing the spatial dispersion effects. It enhances for resonant near-edge scattering through a mixed multipole transition, which includes a dipole±quadrupole contribution. It is shown that this mechanism works even for centrosymmetric crystals, and some realistic examples are considered in detail ( -Fe 2 O 3 , LiNbO 3 etc.). For instance, the interference between the dipole±quadrupole and quadrupole±quadrupole terms may be responsible for the threefold symmetry of the azimuthal dependence of the hhh, h = 2n + 1, re¯ections observed recently in hematite.

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Section: Introductionsupporting

confidence: 85%

Chirality-induced `forbidden' reflections in X-ray resonant scattering

Дмитриенко

Овчинникова

2001

Acta Cryst Sect A

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“…New general extinction rules and structure factors of the ATS re¯ections were found in the dipole approximation (Dmitrienko, 1983). For the ®rst time, these`forbidden' re¯ections were observed by Templeton & Templeton (1985, 1986 in NaBrO 3 near the bromine K-absorption edge. Later, the ATS re¯ections were observed in many crystals; they demonstrate very unusual polarization properties [see Belyakov & Dmitrienko (1989) and Kirfel & Petcov (1991) for reviews].…”

Section: Introductionmentioning

confidence: 97%

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

Дмитриенко

Овчинникова

2000

Acta Cryst Sect A

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In general, the local atomic environment becomes less symmetric owing to point defects and thermal vibrations of atoms in crystals. It is shown that, as a result of this phenomenon, an additional anisotropy of the resonant scattering factors can occur and the forbidden Bragg re¯ections can be excited near absorption edges. Examples of crystals are presented (Ge, K 2 CrO 4 , C-15 type) where such thermal-motion-induced (TMI) and point-defect-induced (PDI) re¯ections can be observed. The tensor structure factors of both types of re¯ection are computed. Owing to their resonant character, the PDI re¯ections allow both impurity atoms and host atoms of different types to be studied separately. The considered phenomena can provide a very sensitive method to study point defects because only the atoms distorted by defects produce contributions to the PDI re¯ections.

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“…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 .…”

mentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

“…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 .…”

mentioning

confidence: 99%

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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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Tensor X-ray optical properties of the bromate ion

Cited by 157 publications

References 14 publications

Chirality-induced `forbidden' reflections in X-ray resonant scattering

Chirality-induced `forbidden' reflections in X-ray resonant scattering

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

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

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