Waller Factor Research Articles

Incoherent ultrarelativistic channeling particle scattering by electrons

The problem of high-energy charged particle motion in the field of atomic strings and planes of oriented crystals, widely applied to control large accelerator beams and generate intense gamma radiation, is addressed. Following the previously developed theory of channeled particles incoherent scattering by crystal atom nuclei, we consider here the same by crystal atom electrons. The theory developed takes into consideration all the effects of momentum transfer between fast particles and electrons of atoms in a crystal in the range from the nuclear radius up to the many inter-atomic distances. The theory also includes the temperature-dependent Debye – Waller factor, as well as both the atomic form factors and scattering function, evaluated with the detail consideration of atomic structure. All the modifications of electron scattering in crystals are reduced to the value of the effective minimum momentum transfer, which by an order of value exceeds that one, related with the Bethe – Bloch mean atomic energy. Substituting this quantity to the expression for the mean square of the scattering angle of a classically moving particle makes it possible to compare the scattering by electrons and nuclei, while its joint use with the Rutherford cross section allows for the correct simulations of the planar channeling of positively charged particles in the thickest crystals, supposed to be used for the beam extraction from high energy accelerators, measurement of electromagnetic characteristics of short-living particles and development of intense narrow-band X-ray and gamma radiation sources based on crystal undulators.

Application of the Debye model to study anharmonic correlation effects for the CuAgX (X = 72; 50) intermetallic alloy

Based on the Debye - Waller factor in extended x-ray absorption fine structure spectra, the correlated displacement function, mean square displacement (MSD) and mean square relative displacement (MSRD) were determined. Analytical expressions of MSD and MSRD were considered using Debye models. Challenging problems due to many-particles effects were replaced by a calculation based on the anharmonic effective potential, including the interaction of absorbing and scattering atoms with their nearest neighbours atoms. The difference between MSRD and MRD was analyzed. The methods were applied to face-centred-cubic crystals and their alloys, and have discovered irregularities in the structure of CuAg (at a 50:50 rate) alloy at low temperatures. Numerical results for copper (Cu) crystal and copper–silver alloys (CuAgX (X = 72; 50)) agreed with experimental values and calculations conducted in other studies.

High precision electronic charge density determination for L10-ordered γ-TiAl by quantitative convergent beam electron diffraction

Low order structure and Debye–Waller (DW) factors for tetragonal L10-ordered γ-TiAl were measured simultaneously using quantitative convergent beam electron diffraction. The high precision and accuracy (largest error <0.5%) measurements allowed the construction of charge density difference maps from full sets of structure and DW factors, suitable for validation of first principles density functional theory (DFT) calculation results. Comparison of the experimentally determined charge density distribution with theoretical DFT predictions shows excellent qualitative agreement in this study. The three-dimensional charge density representations indicate a large electron charge localisation centred about the tetrahedral site at ¼, ¼, ¼, which is coordinated by two Ti atoms at 0, 0, 0 and ½, ½, 0 and two Al atoms at ½, 0, ½ and 0, ½, ½, respectively. Compared to experimental data, the DFT calculations based on full-potential linearised augmented plane wave (LAPW) method (implemented in WIEN2K) were found to quantitatively overestimate charge density between Ti–Ti second nearest neighbour atoms. Moreover, the results from the DFT method based on the projector-augmented wave (PAW) method and a plane wave basis set (implemented in VASP) were found to differ appreciably from both the experimental and LAPW-DFT results, implying that the PAW approach may not accurately describe the bonding in the intermetallic systems with 3 d electrons, such as γ-TiAl.

The Chemical Information Contained in the EXAFS Debye−Waller Factor: Covalency in Iron(III) Bis-diketonato Complexes

A new procedure to extract chemical information from EXAFS spectroscopy beyond the classic parameters, such as coordinating atoms, coordination numbers, and bond distances, by thorough analysis of the Debye-Waller-like factor is presented. In a comparative study of different iron(III) bis-diketonato complexes, which are highly relevant for the iron-catalyzed Michael addition reaction, the degree of covalency of the Fe-O bond between the iron center and the ligand is determined by a combined EXFAS, Raman, and UV/vis spectroscopic approach. A detailed description of the methodology is presented, and it will demonstrated that the comparative degree of covalency is correlated to the pK(a) value of the coordinating diketone. Moreover, it is shown that the distinct catalytic activity of the diketones can not be explained by differences of the covalency of the iron-ligand Fe-O bond.

Search for a structural response to the intermediate phase inGexSe1−xglasses

Atomic pair distribution functions (PDFs) obtained from high energy x-ray synchrotron radiation and x-ray absorption fine structure measurements were performed on 18 closely spaced compositions of chalcogenide glasses (${\mathrm{Ge}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}$ with $0.15\ensuremath{\le}x\ensuremath{\le}0.40$), which span the range of the floppy to rigid phase transition in these glasses. Structural parameters such as PDF peak widths, Debye--Waller factors from extended x-ray absorption fine structure, and the first sharp diffraction peak in $S(Q)$ were extracted as a function of composition. These parameters smoothly evolve with composition, but there are no clear discontinuities or breaks in the slope associated with the appearance of the intermediate phase (IP). Therefore, these measurements do not confirm a structural origin for the IP.

Local Structural Evolution of Co-Doped ZnO Nanoparticles upon Calcination Studied by in Situ Quick-Scan XAFS

Co-doped ZnO is a good dilute ferromagnetic semiconductor candidate with high Curie temperature. In this work, Zn0.93Co0.07O nanoparticles of about 5 nm in size were synthesized by the coprecipitation method. X-ray absorption fine structure spectra at both Co and Zn K-edges were acquired at an in situ and quick-scan mode while the sample was heated to 730 °C in air. The results show a good incorporation of cobalt ions into substitutional zinc sites in zinc oxide. Upon calcination, a systematic structural variation can be monitored, from removal of hydroxyl groups to cobalt oxide precipitation. The Einstein temperature, estimated from the Debye−Waller factor−temperature plot, indicates a stronger Co−ligand bond strength in the lattice compared to that of the ZnO matrix.

In-Situ X-ray Absorption Spectroscopic Study on Variation of Electronic Transitions and Local Structure of LiNi1/3Co1/3Mn1/3O2 Cathode Material during Electrochemical Cycling

In-situ X-ray absorption spectroscopic investigations have been carried out to examine the changes of the electronic transitions and local structure at the Mn, Co, and Ni K-edge for the LiNi1/3Co1/3Mn1/3O2 electrode during charging and discharging process in this study. It was found that only Ni atom in Li1-xNi1/3Co1/3Mn1/3O2 is electroactive from the evolution of the XANES spectra and the bond length variation of Ni−O. It was found that the redox pairs of Ni2+/Ni3+ and Ni3+/Ni4+ exist and the oxidation states of Mn and Co remain as MnIV and CoIII, respectively, in Li1-xNi1/3Co1/3Mn1/3O2 upon charge and discharge. The oxygen, rather than the transition-metal ions (Ni, Co, and Mn), functions as electron donor at the end of charge. In addition, the irreversible capacity at the first cycle derives mainly from the appearance of inactive Ni, which is evidenced by the energy shift E − E0 of the absorption edge for the Ni absorber and the bond length change of the Ni−O. A decrease/increase of Debye−Waller factor...

X-ray Diffraction Study of MgB2 at Low Temperatures

We have performed powder X-ray diffraction of MgB2 superconductor between 10 and 300 K. Temperature dependence of integrated intensities of both (002) and (110) X-ray reflections shows a peak at around TC, superconducting transition temperature. The integrated intensity of the X-ray reflection is related to the phonon frequency through a Debye--Waller factor. Lattice parameters a and c show negative thermal expansions at low temperatures. The negative thermal expansion might be due to an electronic origin and not directly related to the superconducting transition.

Double-Electron Excitation Channels at the Ca2+ K-Edge of Hydrated Calcium Ion

To investigate the effect of multielectron transitions on the EXAFS data analysis at the Ca K-edge, we collected spectra of Ca2+ in aqueous solution. The anomalous peaks detected in the experimental data have been assigned to the simultaneous excitations of the [1s3p] and [1s3s] electrons. An accurate determination of the hydration geometry of the Ca2+ ion has been performed. The hydrogen atoms have also been included in the EXAFS data analysis, and a Ca−H distance of 3.10 Å has been obtained. The influence of multielectron excitations on the quantitative extraction of the structural parameters from the EXAFS spectrum has been investigated. Omission of double-electron excitation edges from the atomic background significantly worsens the quality of the EXAFS fits and results in unreliable values of the Ca−O coordination number and Debye−Waller factor. A proper determination of the coordination geometry of calcium compounds can be obtained only if multiexcitations effects are accounted for.

Temperature-Dependent Signatures of Coherent Vibrational Openings in DNA

We report numerical simulations of the contribution of the transverse hydrogen bond stretching vibrations in the dynamic structure factor of a DNA sequence. We apply a simple nonlinear dynamical model to a finite segment of the bacteriophage T7 core promoter DNA. The temperature dependence of the dynamic structure factor is investigated. A distinct feature is identified and attributed to coherent localized thermal openings (hot-spots) due to nonlinearity combined with sequence specificity. We present the variation of the position and the width of the corresponding dynamic structure factor feature with temperature. Finally, a strong deviation of the Debye−Waller factor from the usual harmonic form is evaluated.

Hydration of Sr2 + in Hydrothermal Solutions from ab Initio Molecular Dynamics

Ab initio molecular dynamics calculations have been used to study the dynamical properties of the strontium hydration shell as a function of temperature. At 25 °C, we obtained Sr−O bond lengths of 2.6 A and a coordination number of 7.5. These are in good agreement with available experimental data. Increasing the temperature to 350 °C led to a decrease in the coordination number to 6.7 and a contraction of the first shell by about 0.1 A. This is in agreement with the data which predict octahedral coordination of Sr in water at high temperatures. Our calculated Debye−Waller factors also agree well with the experimental values. At higher temperatures (600 °C), we predict that the Sr ion remains in 6-fold coordination.

Structure of Cathodically Deposited Nickel Hexacyanoferrate Thin Films Using XRD and EXAFS

X-ray diffraction (XRD) and extended X-ray absorption fine structure (EXAFS) data were used to explore the structure of cathodically deposited thin films of nickel hexacyanoferrate (NiHCF). Thin films were electrodeposited on Pt substrates and analyzed in both the reduced and oxidized states and when intercalated with Cs+, K+, and mixtures of Cs+/K+. All experiments were performed at room temperature. XRD data provided lattice parameters and confirmed the cubic nature of this polycrystalline material, but it could not establish the exact space group from the many known to exist for this class of materials. The lattice parameter monotonically increased from ca. 10.15 to 10.21 Å as the fraction of intercalated cation went from 100% K+ to 100% Cs+. EXAFS data permitted the determination of average nickel coordination, a property directly related to the material's refined structure. Fe and Ni K-edge data were fit using feffit2.32 and FEFF7; the data were fit simultaneously in order to break the correlation between coordination number and the Debye−Waller factor. This resulted in mean nickel coordination values between 4.4 and 5.1 and estimated lattice parameters which are ca. 0.1 Å greater than those found from XRD, a trend indicative of local disorder within the sample.

Structure and Chemical Transformation in Cerium Oxide Nanoparticles Coated by Surfactant Cetyltrimethylammonium Bromide (CTAB): An X-ray Absorption Spectroscopic Study

Cerium oxide nanoparticles coated by cetyltrimethylammonium bromide (CTAB) were prepared using reverse micelles and microemulsion method. The as-prepared nanoparticles (25 °C) were annealed at 200, 350, 500, and 700 °C for 2 h. Their particle sizes are, respectively, 230, 50, 2, 6, and 10 nm as identified by transmission electron microscopy and X-ray diffraction patterns. A chemical transformation from amorphous Ce3+ component to crystalline Ce4+ component was found in the temperature range of 200 °C to 400 °C. X-ray absorption spectroscopy was used to reveal the electronic and atomic structures. The intermediate spectroscopic valence of formally tetravalent compounds and four features A, B, C, and D were detected from the X-ray absorption near edge structure (XANES) spectra of Ce-LIII absorption for samples annealing at 350, 500, and 700 °C. As in trivalent bulk Ce(NO3)3·6H2O, the Ce3+ characteristic was also found for samples annealing at 25, 200, and 350 °C. Multielectron excitation effect on the EXAFS spectra was eliminated. Local atomic structures of these nanoparticles were probed by using extended X-ray absorption fine structure (EXAFS) technique. The obtained structural parameters for bulk Ce(NO3)3·6H2O were in excellent agreement with its crystallographic data. For nanoparticles annealed at 500 °C and 700 °C, similar atomic structures with bulk CeO2 were found. For the as-prepared nanoparticles without annealing (25 °C), a single shell (10 × 2.59 Å) is sufficient to describe its local structures, while two shells had to be used for the nanoparticles annealed at 200 °C and 350 °C. One shell is corresponding to the Ce3+ component. Another is corresponding to the Ce4+ component. All Ce4+ components have the same structural parameters except different Debye−Waller factors or atom-pair distribution functions. A core−shell model was used to explain the structural parameters around cerium for the two samples annealed at 200 °C and 350 °C. The core part is the Ce4+ component with crystalline CaF2-type cubic structures (eight oxygens at 2.343 Å around Ce); the shell part is an amorphous Ce3+ component with different structures. The mechanism of chemical transformation was discussed in this paper.

Scattering Patterns of Self-Assembled Cubic Phases. 1. The Model

Bragg reflection amplitudes are examined for the structures P, D, G, C(P), C(D), I-WP, and F-RD in amphiphilic systems. For these ordered phases, a very simple analytical formula for the scattering amplitudes is given. The formula allows determination of the scattering amplitudes for any cross-sectional density profile of the membrane decorating the minimal surface. Within this approximation an analytical solution for the Debye−Waller factor is presented. Finally we propose a simplified model that can greatly facilitate examination of the experimental scattering patterns.

On the Determination of the Location of Metal Clusters Supported on Molecular Sieves by X-ray Absorption Spectroscopy

Typically, smaller metal−metal contributions are found in the EXAFS of zeolite supported metals compared to metals on nonporous supports. Two factors may account for this, i.e., (i) a smaller average coordination number, which is related to smaller metal particles, and (ii) an increase in the Debye−Waller factor indicating less ordered metal clusters. Based on experimental results as well as on theoretical calculations we compare both effects and assign the decrease in the metal−metal contributions to an exponential dampening of the EXAFS oscillations resulting from contributions of the zeolite lattice atoms. This leads to an increase in the Debye−Waller factor, which is not related to a decrease in the statistical order of the metal clusters supported on the zeolite. The model discussed can be used as an indication for the location of small metal clusters on porous supports. It is shown that a large value of Δσ2, in addition to the particle size, can be used to determine the location of metal particles o...

A Transition in the Ni2+Complex Structure from Six- to Four-Coordinate upon Formation of Ion Pair Species in Supercritical Water: An X-ray Absorption Fine Structure, Near-Infrared, and Molecular Dynamics Study

The coordination structure about Ni2+ in water at temperatures up to 525 °C was measured by the X-ray absorption fine structure (XAFS) technique. Solutions containing 0.2 m NiBr2 and 0.2 m NiBr2/0.8 m NaBr were explored at pressures up to 720 bar. For certain systems, both Ni and Br XAFS data were acquired and a global model was used to fit the two independent sets of XAFS data. These two independent measurements gave excellent agreement on the coordination structure of the Ni2+/Br- contact-ion pairing. The result is a complete picture of the coordination structure of the contact-ion pairing including the coordination numbers, distances for the water−ion and ion−ion associations, and also a high-quality measurement of the binding strength and amount of disorder (Debye−Waller factor and the anharmonicity) of the Ni2+/Br- association. The XAFS measurements strongly indicate a transitional change in the coordination of Ni2+ from the octahedral Ni2+(H2O)6 species at room temperature to the 4-coordinate struct...

Spectroscopy and Photochemistry of meso-Diphenyltribenzonaphthoporphyrin at Low Temperatures: A Novel System for Hole-Burning Applications

We present a custom-tailored material for the application of spectral hole-burning in optical storage and imaging spectroscopy. The photoactive molecule meso-diphenyltribenzonaphthoporphyrin (P2TriBNP) combines the advantages of chlorins and simple porphyrins used so far, namely, the spectral separation between photoeduct and photoproduct states and a high photochemical hole-burning yield. Basic characteristics of the material were measured. We obtained the values of 3.2 ± 1.5% for the hole-burning yield, of ∼0.6 for the Debye−Waller factor in poly(vinyl butyral) (PVB), and a spectral separation between the educt and product absorption of 120 cm-1. The difference in the dipole moment between the ground and the excited state shows two contributions. The permanent dipole moment difference has a value of 0.29 ± 0.03 D. A root mean square value of 0.15 ± 0.02 D for a distributed, matrix-induced component was measured. Because of their high photochemical yields and the large absorption cross sections, P2TriBNP and similar compounds open the way for a new class of experiments dealing with lower light intensities and shorter exposure times than before. However, we observed the lifetime of narrow spectral holes to be limited to several hours. Nevertheless, the material exhibits a high potential for the application in imaging spectroscopy, e.g., the simultaneous recording of spatial and spectral information of astronomical objects.

Local structure around cations in the Nd(Ce) based superconducting system: an EXAFS study

EXAFS measurements on all the cations in (NCCO) and (NACCO), A=Sr, Ca or Ba, x = 0.06 or 0.18, have been made using synchrotron radiation. Bond lengths (R), coordination numbers (N) and Debye - Waller factors have been obtained from the EXAFS analysis. The curved wave theory in the single-scattering approximation and the small-atom multiple-scattering theory have been applied to experimental EXAFS data and it is found that the latter gives a better fit. The plane contains a strong multiple-scattering contribution. Further, all the dopants (Ce, Sr, Ca and Ba) occupy the Nd site without affecting the basic structure. Doping affects the local structure around the substituents as reflected by the changes in R and values. The observed layer distortion (or large Cu - O - Cu angle deviation from linearity, ) is found to have an adverse effect on as observed in Ca or Ba doped NACCO samples. Further, it is realized that critical levels of charge carriers, oxygen vacancies and planar effects have a strong influence on the SC behaviour of the electron doped cuprates.

The structure of solid in porous Vycor glass

The structure of solid confined in porous Vycor glass has been studied as a function of temperature via x-ray diffraction. The confined solid has the same structure as the bulk solid but with a slightly larger lattice constant of 5.644 Å at 150 K compared to the bulk lattice constant of 5.624 Å at the same temperature. Broad diffraction peaks are observed indicating that the solid phase of the in the pores forms in small crystallites approximately 160 Å in diameter. This is comparable to the pore dimensions in the Vycor indicating that solidification occurs separately in each of the pores. A large temperature-independent static disorder, analogous to the Debye - Waller factor, was observed in the form of strong damping of the Bragg peaks with increasing Q.

Phthalonaphthalocyanines: New Far-Red Dyes for Spectral Hole Burning

Mixed phthalocyanines carrying one anthracene (Pc3An) or substituted naphthalene nucleus (Pc3NcR2, R = H, OCH3, or SC12H25) are proposed as low-temperature photochroms for spectral hole burning. Solubility of these compounds in polymers was greatly enhanced by introducing the 2,4-dimethyl-3-pentoxy substituent to the remaining three benzopyrrolic fragments. The wavelengths and intensities of the Q transitions (S1 and S2) were measured for two prototropic tautomers having different position of the pair of inner protons. The average energy of the two lowest transitions is very similar in both tautomers, although the S1−S2 splitting is much smaller in the less stable form. The relative equilibrium concentration of the tautomers at room temperature depends on the electron releasing properties of the substituents. This allows one to predict the positions of protons in each form. Absorption dichroism of stretched polyethylene films was used in order to establish the direction of the S1 and S2 transition dipole moments in the molecular framework. The tautomers can be completely converted into each other at 10 K by light with quantum yields of (1−2) × 10-3 and (5−8) × 10-3, respectively, depending on the direction of the process. Most probably the phototransformation occurs in the vibrationally relaxed triplet state via the tunneling of a single proton which results in an intermediate state with cis-configuration of protons. The photochemically accumulated less stable form decays at higher temperatures (T) as a result of a thermally activated tunneling process at characteristic T of 115 and 153 K for protonated and deuterated Pc3Nc, respectively. The strength of linear electron−photon coupling (EPC), which is crucial from the point of view of spectral hole burning, is characterized by Debye−Waller factors (DWFs) about 0.6−0.75, depending on the compound and the polymer matrix. The T dependence of quasihomogeneous hole width (Γqh) obeys a power law with coefficients 2.5 ± 0.5 (between 6 and 30−45 K). In different polymer hosts, the DWF increases and the hole width decreases in the following order: polystyrene > poly(vinyl butyral) > polyethylene. The strength of EPC for the lowest transitions is similar in both tautomeric forms. A slight enhancement of the EPC strength in the series of dyes Pc3Nc(OCH3)2 ∼ Pc3Nc < Pc3Nc(SC12H25)2 < Pc3An is correlated with the increase of electron-withdrawing power of substituents, plausibly, as a result of the increase of dipole moment change upon electronic excitation. Spectroscopic properties, phototautomerization quantum yields, and the EPC strength of mixed phthalocyanines were compared with those of chlorin and porphyrins.