Bragg Peak Profiles Research Articles

Effect of Normalization Algorithms on the Analysis of Bragg Peak Profiles

A study has been performed to evaluate the effect of normalization criteria applied to the comparison of depth dose profiles relevant to proton therapy applications. The results suggest that the widely used criterion of rescaling dose profiles based on the Bragg peak height (or on the dose value at any specific depth) affects the outcome of the goodness-of-fit tests. A normalization procedure consisting of rescaling dose profiles according to the respective integral is demonstrated to be a more robust method.

The Deformation Mechanisms of TWIP Steels (Fe-Mn-C) Viewed by X-Ray Diffraction

Fully austenitic steels of the Fe-Mn-C system can show extensive deformation twinning (TWIP effect). The deformed microstructure of such steels has been analysed using X-ray diffraction at the European Synchrotron Radiation Facility (ESRF). The experimental diffractograms, recorded using a 2D CCD camera, are analysed in terms of Bragg peak profiles (broadening and asymmetry) and position (shift from the reference [undeformed state] position) leading to an estimation of dislocation and stacking faults densities.

SU-FF-T-388: Study of Dose Distribution in Passively Scattered Proton Beams for Small Field Sizes

Purpose: To investigate the characteristics of the dose distribution of passively scatteredproton beams for field sizes smaller than 5 × 5 cm2 through measurement and comparison with the results of calculation by the Eclipse treatment planning system (TPS). Method and Materials: The spread out Bragg peak (SOBP) curves and profiles of the passively scatteredproton beams were measured using PTW Markus and PinPoint ion chambers in a PTW MP3 water tank for field sizes of 10 × 10 cm2, 5 × 5 cm2, 2 × 2 cm2 and other small fields used in patient treatments. The profiles of small fields were also measured by film dosimetry to assess the detector size effect. The field size factors (FSF) were measured using the ionization chambers. Measured SOBPS and profiles were compared with the results of Eclipse TPS calculation. SOBPs of different field sizes were compared to asses any significant change in the dose distribution with field size.Results: Both measured and Eclipse TPS calculated small field SOBPs show significant dose non‐uniformity between the distal 90% to proximal 95% as compared to those of the larger fields. The penumbra widths did not change significantly in reducing the field size from 10 × 10 to 2 × 2 cm2. Profiles calculated by Eclipse TPS agree very well with the measured data validating the accuracy of the TPS for small field dose calculation. FSF were found to be insensitive to the decrease in field size up to 5 × 5 cm2, but is reduced significantly in going from 5 × 5 to 2 × 2 cm2. FSF for small fields has a complex dependence on energy and snout position. Conclusion: Small field proton dose distributions were found to have certain unique features that require special attention while using them for treatment planning.

Vacancies in plastically deformed copper

In discussing hardening characteristics in terms of crystalline lattice defects, in most cases the properties and kinetics of dislocations and their arrangement have been considered. However, during plastic deformation also vacancies and/or vacancy-type defects are produced in very high densities which are typically close to those of vacancies in thermal equilibrium at the melting point. This paper presents measurements of deformation-induced vacancies in deformed copper which have been achieved by combined evaluation of resistometry, calorimetry and X-ray diffraction. The density of vacancies during and after severe plastic deformation (SPD) deformation is found to be markedly higher than in cases of conventional deformation and/or coarse-grained material, which is attributed to the particular conditions of SPD, i. e., the enhanced hydrostatic pressure as well as the- changes in the deformation path. The use of synchrotron radiation allows to apply the XPA method for in-situ deformation monitoring of intrinsic structural parameters. This also includes deformation-induced vacancies, evaluated by the diffuse background of Bragg peak profiles.

Effects of Bragg peak profiles and nanoparticle sizes on the real-space pair distribution function

A study of the effects of Bragg peak profiles and nanoparticle size broadening on the real-space pair distribution function (PDF) is presented, using `synthetic' powder diffraction data. Bragg peak profiles from both asymmetric time-of-flight (TOF) spallation neutron data and symmetric synchrotron X-ray data are considered. Due to their asymmetric peak profiles, the TOF data cause artificial shifts of the PDF peak positions towards higher pair distances. Coupled with this effect is a broadening of the PDF peak widths due to aQ-dependent spectrometer resolution, making reliable refinement of thermal parameters difficult. These effects become more pronounced as theQresolution becomes worse. By contrast, the symmetric X-ray powder diffraction data do not cause a systematic shift of the PDF peak positions, and the broadening of the PDF peak widths has a relatively minor effect on the extraction of the thermal parameters. Finally, nanoparticle size broadening of the asymmetric neutron TOF powder diffraction data causes a shift of the PDF peak positions towards lowerrvalues and smears the PDF intensities from one atomic shell to another.

Structure determination of forms I and II of phenobarbital from X-ray powder diffraction

From pure powders of forms I and II of phenobarbital, X-ray diffraction patterns were recorded at room temperature. The starting crystal structural models were found by a Monte-Carlo simulated annealing method. The structures of the two forms were obtained through Rietveld refinements. Soft restraints were applied on bond lengths and bond angles, all H-atom positions were calculated. The cell of form I is monoclinic with the space group P2(1)/n, Z=12, Z'=3. Form II has a triclinic cell, with the space group P1 , Z=6, Z'=3. For both forms, the crystal cohesion is achieved by networks of N-H...O hydrogen bonds along [101]. The broadening of the Bragg peak profiles is interpreted in terms of isotropic strain effects and anisotropic size effects.

Plastic deformation of nickel under high hydrostatic pressure

Samples of nickel were deformed in torsion under very high hydrostatic pressures (up to 8 GPa) up to strains being much larger than those reached under normal pressure conditions. The obtained stress–strain curves were fitted by the model of Zehetbauer and Kohout which has been developed from the work hardening model of Zehetbauer designed for conventional large strain deformation. The configuration parameters of dislocations were determined from strain dependent dislocation densities which were measured by Multiple Whole X-ray Bragg Peak Profile Analysis (MXPA). Using actual materials and physical constants of Ni, the obtained values of fitting parameters could be related to realistic numbers of physical quantities hidden in those. The main part of the deformation stress increase observed with increasing hydrostatic pressure can be ascribed to the increase of dislocation density which arises from the restriction of diffusion controlled annihilation mechanisms. This restriction is related to the pressure-induced decrease of diffusion, i.e. to the increase of vacancy migration enthalpy which is due to the shrinking of interatomic spacing when the hydrostatic pressure is enhanced. However, the calculated concentrations of deformation induced vacancies for pressures 5 GPa and beyond are unacceptably high. Data from measurements of microhardness and MXPA after unloading show that beyond a pressure of 4 GPa both the strength and the dislocation density is not being increased anymore which suggests the onset of spontaneous vacancy and dislocation annihilation due to the high overall concentration of vacancies reached. This failure of the model is not surprising since it has not considered so far any limits in the vacancy concentration.

Neutron diffraction study of field-cooling effects on the relaxor ferroelectricPb[(Zn1/3Nb2/3)0.92Ti0.08]O3

High-temperature (T) and high-electric-field (E) effects on Pb[(Zn_{1/3} Nb_{2/3})_{0.92} Ti_{0.08}]O_3 (PZN-8%PT) were studied comprehensively by neutron diffraction in the ranges 300 <= T <= 550 K and 0 <= E <= 15 kV/cm. We have focused on how phase transitions depend on preceding thermal and electrical sequences. In the field cooling process (FC, E parallel [001] >= 0.5 kV/cm), a successive cubic (C) --> tetragonal (T) --> monoclinic (M_C) transition was observed. In the zero field cooling process (ZFC), however, we have found that the system does not transform to the rhombohedral (R) phase as widely believed, but to a new, unidentified phase, which we call X. X gives a Bragg peak profile similar to that expected for R, but the c-axis is always slightly shorter than the a-axis. As for field effects on the X phase, we found an irreversible X --> M_C transition via another monoclinic phase (M_A) as expected from a previous report [Noheda et al. Phys. Rev. Lett. 86, 3891 (2001)]. At a higher electric field, we confirmed a c-axis jump associated with the field-induced M_C --> T transition, which was observed by strain and x-ray diffraction measurements.

Powder x-ray diffraction of two-dimensional materials

An analytic solution for the normalized intensity for powder x-ray diffraction has been obtained for a simple two-dimensional lattice using a linear approximation for the interference function. The analytic solution, where the Bragg peaks are strongly asymmetric, is compared to computer simulations using the Debye formula, and is shown to be in closer agreement than earlier numerical solutions by Warren and others. For a two-dimensional structure consisting of more than one monolayer of atoms, the shape of the Bragg peaks is modulated by the structure factor. This structure factor modulation provides a continuous plot of the structure factor over the range of the diffraction tail and thus provides valuable information about the structure of the layer. It is demonstrated that because of structure factor modulation the Warren expression which relates the width of Bragg peaks to layer size cannot be used for a two-dimensional sheet with more than one layer of atoms, and it is proposed in such cases that measuring the low-angle side width of half-maximum intensity can be used for determination of the layer size. Single molecular layer MoS2 and WS2 suspensions, prepared by exfoliation, provide excellent randomly oriented two-dimensional systems for demonstrating the unique features of powder x-ray diffraction patterns of two-dimensional materials and for structure identification using Bragg peak profiles.

High resolution x-ray diffraction characterization of semiconductor structures

Abstract The high-resolution X-ray diffraction techniques, such as double-crystal rocking and triple-crystal diffraction, have become essential tools in the semiconductor materials and devices laboratory. Quick and non-destructive characterization is possible for basic layer parameters including layer composition, strain, mismatch and thickness. More sophisticated characterization of interface and quantum-well structures with submonolayer resolution is possible with the help of kinematical diffraction principles and diffraction profile simulation using the dynamical diffraction theory. These X-ray diffraction techniques are making it possible to correlate the structural properties to the epitaxial growth process, to the electrical,/optical properties and to the device performance. In this review article, I discuss some basic aspects of the instrument, simple determination of layer parameters, the dynamical and kinematical diffraction theories, and some recent results in the characterization of the heterostructure interfaces and strained quatum-well devices. I also discuss the diffuse scattering analysis of bulk semiconductors in the Bragg diffraction geometry. Interface analysis of the lattice-matched structures such as GaInAs/InP and AlGaAs/GaAs is discussed in terms of kinematical diffraction principles, namely the X-ray phase shift and the crystal truncation rod. Analysis of strained quantum wells is discussed using Bragg peak profile and Pendellosung fringe profile. Diffuse scattering in bulk semiconductors is discussed in the context of the analysis theory, namely the rocking-curve profile and the radial intensity profile around a reciprocal lattice point of the diffused scattered X-rays due to such defects as dislocation loops and spherical defect clusters.

Improved Kematical X-Ray Rocking Cjrve Analyses

ABSTRACTA new boundary condition is used in the kinematical x-ray diffraction model analysis of rocking curves. The boundary condition is the dynamical reflection amplitude instead of the previously used dynamical intensity for the substrate. It is shown that this boundary condition properly accounts for the angular shift effect in the Bragg peak profile of very thin epitaxial layers and in the 0th-order superlattice peak. We present experimental and simulated rocking curves for various samples. The simulation was performed by using the dynamical diffraction theory, the kinematical model with the new amplitude boundary condition, and the kinematical model with the old intensity boundary condition. We also analyzed the strained resonant tunneling device structure and single strained quantum well samples by x-ray interference technique. Our x-ray interference results showed a good agreement with the nominal values for both experimental and simulated rocking curves.

Low-temperature phase transitions in LiKSO 4: A neutron study

A single crystal neutron diffraction study of the low temperature structural phase transitions in LiKSO 4 has been carried out. Detailed temperature dependence of the Bragg peak profiles and integrated intensities for a group of about 20 reflections has been investigated upon cooling and heating in the temperature range 300 K to 96 K. The crystal undergoes three clear phase transitions at 205 K (from sp. gr. P6 3 to sp. gr. P31 c), at 189 K and at about 135 K on cooling. The corresponding temperatures are 250 K, 190 K and 138 K on the heating cycle. These transitions are extremely sluggish, the kinetics depending on the thermal treatment of the crystal.