Thermal motion induced (TMI) scattering is a unique probe of changes in electronic states with atomic displacements in crystals. We show that it provides a novel approach to extract atomic correlation functions. Using numerical calculations, we are able to reproduce the temperature-dependent energy spectrum of the 115 'forbidden' Bragg reflection in ZnO. Our previous experimental studies showed that the intensity growth of such reflections over a wide range of temperatures is accompanied by a dramatic change in the resonant spectral lineshape. This is the result of the interplay between the temperature-independent (TI) and temperature-dependent TMI contributions. Here, we confirm that the TI part of the resonant structure factor can be associated with the dipole-quadrupole contribution to the structure factor and show that the temperature-dependent part arises from the zinc and oxygen vibrations, which provide additional temperature-dependent dipole-dipole tensor components to the structure factor. By fitting the experimental data at various temperatures we have determined the temperature dependences of autocorrelation and correlation functions.
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.
The influence of atomic vibrations on the "forbidden" Bragg reflections, excited near absorption edges owing to anisotropic resonant X-ray scattering, is discussed. It is shown that in spite of the difference of Xrays and phonons energies the "forbidden" reflections can be extremely sensitive to the atomic vibrations and their correlations. The numerical calculations are performed taking into account the correlations of atomic thermal displacements, which give an adequate description of the thermal growth of the 600 forbidden reflection in Ge and describe drastic changes of the "forbidden" reflections spectra in ZnO.1 Introduction In view of the very different x-ray and phonon energies, it is rather surprising that phonons can drastically affect both the intensity and the spectrum of resonant x-ray scattering in crystals. The reason is that resonant scattering is extremely sensitive even to very small atomic displacements distorting the electronic states. Moreover, phonon vibrations permanently change the symmetry of atomic sites, induce an additional anisotropy of the atomic scattering factors (ASF) and therefore give rise to extra Bragg reflections, otherwise forbidden (see [1][2][3][4][5] and references therein). It was shown that this effect is sensitive mainly to optical phonon modes (even at zero temperature). It allows to observe vibrations of selected resonant atoms because the anisotropy of ASF is significant only near the X-ray absorption edges where ASF becomes a tensor.In the beginning of this studies, the phenomenological expressions describing a scattering amplitude of thermal motion induced (TMI) forbidden reflections in Ge were obtained supposing independent atomic motion [1], and the microscopic calculations, using such a model, gave a satisfactory description of the phenomenon [3,6,7]. Later it was shown for Ge [4] that the description becomes better, if one takes into account the correlation of atomic displacements, i.e. a cooperative type of atomic movements. Recently the spectral intensity of "forbidden" reflections in ZnO was calculated [8] supposing a special character of the phonon modes, which contributed to atomic displacements. In the present paper we discuss what information about phonons in crystals could be obtained from the energy spectra and simulate the contribution of different phonon modes into the "forbidden" reflections.
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