Profile Fitting Procedure Research Articles

The Certification of Standard Reference Material 1979: Powder Diffraction Line Profile Standard for Crystallite Size Analysis.

This rather long-standing project has resulted in a National Institute of Standards and Technology (NIST) Standard Reference Material (SRM) for the analysis of crystallite size from a consideration of powder diffraction line profile broadening. It consists of two zinc oxide powders, one with a crystallite size distribution centered at approximately 15 nm, and a second centered at about 60 nm. These materials display the effects of stacking faults that broaden specific hkl reflections and a slight amount of microstrain broadening. Certification data were collected on the high-resolution powder diffractometer located at beamline 11-BM of the Advanced Photon Source, and on a NIST-built laboratory diffractometer equipped with a Johansson incident beam monochromator and position sensitive detector. Fourier transforms were extracted from the raw data using a modified, two-step profile fitting procedure that addressed the issue of accurate background determination. The mean column lengths, 〈L〉area and 〈L〉vol, were then computed from the Fourier transforms of the specimen contribution for each reflection. Data were also analyzed with fundamental parameters approach refinements using broadening models to yield 〈L〉area and 〈L〉vol values. These values were consistent with the model-independent Fourier transform results; however, small discrepancies were noted for the 〈L〉area values from both machines and both crystallite size ranges. The fundamental parameters approach fits to the laboratory data yielded the certified lattice parameters.

Probing the thermal state of the intergalactic medium at z > 5 with the transmission spikes in high-resolution Ly α forest spectra

ABSTRACT We compare a sample of five high-resolution, high S/N Ly α forest spectra of bright 6 < z < ∼6.5 QSOs aimed at spectrally resolving the last remaining transmission spikes at z > 5 with those obtained from mock absorption spectra from the Sherwoodand Sherwood–Relics simulation suites of hydrodynamical simulations of the intergalactic medium (IGM). We use a profile-fitting procedure for the inverted transmitted flux, 1 − F, similar to the widely used Voigt profile fitting of the transmitted flux F at lower redshifts, to characterize the transmission spikes that probe predominately underdense regions of the IGM. We are able to reproduce the width and height distributions of the transmission spikes, both with optically thin simulations of the post-reionization Universe using a homogeneous UV background and full radiative transfer simulations of a late reionization model. We find that the width of the fitted components of the simulated transmission spikes is very sensitive to the instantaneous temperature of the reionized IGM. The internal structures of the spikes are more prominent in low temperature models of the IGM. The width distribution of the observed transmission spikes, which require high spectral resolution (≤ 8 km s−1) to be resolved, is reproduced for optically thin simulations with a temperature at mean density of T0 = (11 000 ± 1600, 10 500 ± 2100, 12 000 ± 2200) K at z = (5.4, 5.6, 5.8). This is weakly dependent on the slope of the temperature-density relation, which is favoured to be moderately steeper than isothermal. In the inhomogeneous, late reionization, full radiative transfer simulations where islands of neutral hydrogen persist to z ∼ 5.3, the width distribution of the observed transmission spikes is consistent with the range of T0 caused by spatial fluctuations in the temperature–density relation.

Evolution of microstructures, dislocation density and arrangement during deformation of low carbon lath martensitic steels

In this paper, the role of solute carbon on the strengthening and work hardening behavior of lath martensite was studied by analyzing the microstructures and dislocation density in the undeformed and deformed conditions. An increase in carbon content from 0.18% to 0.30% decreases the martensite start (Ms) temperature, leading to refinement of both the block and lath widths. Although reduction of the “effective grain size” is observed via Electron Backscatter Diffraction (EBSD) and Electron Channeling Contrast Imaging (ECCI) techniques, this effect is considered secondary in increasing the strength of lath martensite with increased carbon content. The higher strength is attributed mainly to the phase transformation-induced dislocation density in the high-carbon martensite. Comparing this total dislocation density calculated using a Convolutional Multiple Whole Profile (CMWP) fitting procedure with the estimated geometrically necessary dislocations (GND) from the misorientation distribution of EBSD analysis, it appears that a high fraction of the dislocations in lath martensitic steel is GND. Furthermore, the analysis of the samples strained to a different level suggests that the dislocation density shows minimal change during deformation, whereas the dislocation arrangement rapidly decreases at the beginning of the plastic deformation. Finally, the strain hardening behavior of the lath martensitic steel is quantitatively described by considering lath width, dislocation density, and dislocation arrangement parameters through the α coefficient in Taylor's equation.

Influence of Nd or Ca addition on the dislocation activity and texture changes of Mg–Zn alloy sheets under uniaxial tensile loading

In situ hard X-ray diffraction experiments were carried out to investigate the dislocation slip activity of Mg-1 wt.% Zn-based alloys containing Nd or Ca during tensile loading. Diffraction patterns collected during tensile loading at 3 temperatures were analyzed using a convolutional multiple whole profile fitting procedure. High activation of nonbasal <a> and pyramidal <c+a> dislocations was found in the Nd- and Ca-containing alloys. The microstructure evolution after 10% deformation was examined by complementary EBSD measurements. The microstructure evolution was related to the differences in the initial texture and active deformation modes, according to the alloying and temperature. In-grain misorientation axes analysis obtained from the EBSD measurements confirms that the addition of Nd or Ca contributes to the higher activity of prismatic <a> slip. The high activity of prismatic <a> slip leads to a broadening of the basal poles perpendicular to the loading direction and a strengthening of the <101‾0> pole along the loading direction. The overall dislocation density evolution at elevated temperatures is controlled by dynamic recovery and dynamic recrystallization. These thermally activated mechanisms are retarded in the Nd- or Ca-containing alloys.

Electron density measurement in atmospheric pressure plasma jets: Stark broadening of hydrogenated and non-hydrogenated lines

Electron density is one of the key parameters in the physics of a gas discharge. In this contribution the application of the Stark broadening method to determine the electron density in low temperature atmospheric pressure plasma jets is discussed. An overview of the available theoretical Stark broadening calculations of hydrogenated and non-hydrogenated atomic lines is presented. The difficulty in the evaluation of the fine structure splitting of lines, which is important at low electron density, is analysed and recommendations on the applicability of the method for low ionization degree plasmas are given. Different emission line broadening mechanisms under atmospheric pressure conditions are discussed and an experimental line profile fitting procedure for the determination of the Stark broadening contribution is suggested. Available experimental data is carefully analysed for the Stark broadening of lines in plasma jets excited over a wide range of frequencies from dc to MW and pulsed mode. Finally, recommendations are given concerning the application of the Stark broadening technique for the estimation of the electron density under typical conditions of plasma jets.

Impact of Absorber Ring Position and Cavity Length on Acoustic Damping

The influence of axial position and cavity length of an absorber ring with grazing flow on damping of acoustic amplitudes in a rocket combustion chamber is experimentally investigated under nonreactive ambient temperature conditions. At the perforated inlet, high-bias flow velocities are present, providing strong damping. On the basis of power spectral densities gained from flow noise excitation, damping rates for the first transverse mode are derived using a Lorentzian profile fitting procedure. Results show that an absorber ring located in close proximity to the nozzle leads to enhanced damping, whereas in the case of a ring placed closely to the inlet, damping rates are reduced. Absorption coefficients show that an isolated absorber ring is not capable of acoustic amplification. It is concluded that reduced damping originates from weaker impact of the perforated inlet on the acoustics, resulting from a shielding effect by the absorber ring. The highest damping rate is found for a cavity length below the theoretically predicted optimum length for an absorber ring located close to the nozzle.

Quantitative study of particle size distribution in an in-situ grown Al–TiB2 composite by synchrotron X-ray diffraction and electron microscopy

Synchrotron X-ray diffraction and transmission electron microscopy (TEM) were applied to quantitatively characterize the average particle size and size distribution of free-standing TiB2 particles and TiB2 particles in an in-situ grown Al–TiB2 composite. The detailed evaluations were carried out by X-ray line profile analysis using the restricted moment method and multiple whole profile fitting procedure (MWP). Both numerical methods indicate that the formed TiB2 particles are well crystallized and free of crystal defects. The average particle size determined from different Bragg reflections by the restricted moment method ranges between 25 and 55nm, where the smallest particle size is determined using the 110 reflection suggesting the highest lateral-growth velocity of (110) facets. The MWP method has shown that the in-situ grown TiB2 particles have a very low dislocation density (~1011m−2) and their size distribution can be described by a log-normal distribution. Good agreement was found between the results obtained from the restricted moment and MWP methods, which was further confirmed by TEM.

Crystal Chemistry of the Antibiotic Doripenem

Doripenem, an ultrabroad spectrum-injectable antibiotic belonging to the wide class of carbapenem beta-lactams, is commonly marketed as powders of a pure monohydrate phase. Here, we have selectively prepared another hydrated phase (a dihydrate) and determined the crystal structure of both forms by state-of-the art powder diffraction methods. Both phases crystallize in the monoclinic P21 space group, and, to some extent, are structurally related. Moreover, by using variable temperature diffractometric analyses, we also discovered a crystalline anhydrous form of doripenem, the structure of which (with two crystallographically independent molecules in the monoclinic P21 space group) remains so far unknown. The thermal interconversion among these phases was further studied by thermogravimetry, differential scanning calorimetry, and thermodiffractometric analyses, and their (metric or stereochemical) mutual relations fully analyzed. The complete structural characterization of the two hydrated phases allows the use of accurate whole pattern profile-fitting procedures for quantitative analyses of these drugs in polycrystalline, or even amorphous, matrices, opening the way to industrial process control and legal protection. © 2014 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci 103:3641-3647, 2014.

Characterization of crystallite size, dislocation characteristics and stacking faults in nanostructured mechanically alloyed Cu–Fe system using an advanced X-ray diffraction analysis method

Developments in the synthesis of nanostructured materials have expanded the need for appropriate characterization methods. The aim of this work is to apply new X-ray diffraction analysis methods for simultaneous investigation of various microstructural characteristics. For this purpose, the structure of mechanically alloyed Cu–Fe system with three compositions of 30wt%, 50% and 70% of iron was studied. By applying the modified Williamson-Hall method, the type of dislocations in the FCC phase is distinguished. Afterwards by modification of previous XRD analysis methods, the proportion of edge/screw dislocations was characterized. Moreover, the outer cut-off radius, the density and energy of dislocations were calculated as a function of the composition and the milling time. On the other hand, using the extended convolutional multiple whole profile fitting procedure, the variations in the crystallite size and size distribution of FCC and BCC phases were studied. Finally, the stacking fault probability was calculated in different milled samples. It is revealed that smaller steady state crystallite size of samples with higher Fe content, is relevant to reduction of the outer cut-off radius of dislocation. On the other hand, the density of dislocations and stacking faults increased continuously up to 96h of milling.

Observations of the atmospheric boundary layer height under marine upstream flow conditions at a coastal site

AbstractWe investigate several lidar‐type instruments and methodologies for boundary layer height (BLH) estimation during 2 days at a coastal site for winds that experience marine upstream flow conditions. Wavelet and profile fitting procedures on the aerosol backscatter signals from a ceilometer and an aerosol lidar reveal similar BLHs, but their agreement depends on the presence of clouds and the instrument signal, among others. BLHs derived by a threshold on the carrier‐to‐noise profiles of a wind lidar agree well with those derived by using a threshold on the backscatter profile of the ceilometer and are used as reference for a 10 day BLH intercomparison. Furthermore, the BLHs from the aerosol analysis are comparable to those derived from wind speed and direction profiles from combined mast/wind lidar measurements. The BLH derived from simulations performed with the Weather Research and Forecasting (WRF) model shows similar behavior compared to the lidar observations. The seasonal diurnal variation of the BLH for 2010, derived from the wind lidar and ceilometer thresholds, shows similar BLHs but generally higher values compared to that from WRF. No clear BLH diurnal variation is observed neither from the observations nor from the WRF model outputs, except in summer for the latter. Both observations and WRF model simulations reveal higher BLHs during autumn compared to spring time. These BLHs are used to evaluate the intra‐annual variation and show high peaks in September, November, and February.

The influence of annealing temperature on the slip plane activity and optical properties of nanostructured ZnO films

The zinc oxide films were prepared by the sol–gel method on the ordinary glass substrates. The activity of slip systems were evaluated by X-ray diffraction line broadening analysis using convolution multiple whole profile (CMWP) fitting procedures. It was found that in all temperatures the 〈a〉 type dislocations is dominating and its fraction increases with the rise of annealing temperature in the range of 350–600°C. The investigation on the optical properties of films showed that the optical band gap energy increases linearly with the annealing temperature and crystallite size but decreases with the lattice strain.

Evolution of texture and dislocation distributions in high-ductile austenitic steel during deformation

The microstructural evolution of Fe–Mn–C austenitic steels, which exhibit outstanding high-ductile deformation in their plastic regions, was characterized by line-profile and texture analyses. The convolutional multiple whole profile fitting procedure was used for a line-profile analysis of 2θ−θ diffraction data to evaluate variations of crystallite size, dislocation density, and dislocation arrangement. A substantial refinement of the crystallite size proceeded at an early deformation stage. In addition, the dislocation density increased with an increase in the tensile strain. Texture evolution was characterized by the analysis of orientation distribution functions. Three texture components grew with an increase in the tensile strain. According to the pole figure describing the full width at half maximum (FWHM) distribution of the 220 reflection, the nontextured grains had more microstructural defects than the textured grains. To evaluate the microstructural defects in detail, the 220 reflection observed at each texture orientation was analyzed by the single-line-profile method. The crystallite size and dislocation density were almost comparable, irrespective of the kind of texture component. The crystallite size of the nontextured grains was also comparable to that of the textured grains, whereas the nontextured grains had a dislocation density several times that of the textured grains.

Microstructural evolution of ball-milled MgH 2 during a complete dehydrogenation–hydrogenation cycle

Repeated dehydriding–hydriding cycles of ball-milled nanocrystalline MgH 2 was carried out in a Sieverts’-type apparatus. In order to characterize the microstructural changes during a complete MgH 2 → Mg → MgH 2 transformation, the fourth desorption and subsequent absorption were interrupted at different hydrogenation stages. Convolutional multiple whole profile fitting procedure of the corresponding X-ray diffractograms was applied to reveal the evolution of microstructural parameters during the sorption cycle, such as average coherent domain size and crystallite size distribution. Complementary analysis of lattice parameters was also carried out. In this paper we demonstrate that analysing solely the evolution of microstructural parameters during cycling leads to similar rate-controlling mechanisms obtained by sorption kinetic measurements.

Stacking faults and microstructural parameters in non-mulberry silk fibres

We have analysed the broadening of X-ray reflections observed in nonmulberry silk fibres in terms of stacking faults and microstructural parameters using a single-order method and have, with these parameters, developed, for the first time, a procedure to compute the whole pattern of these silk fibres. The essential deviations in the values of microstructural parameters obtained from line profile and whole pattern fitting procedures are discussed in this paper.

Hydriding kinetics of ball-milled nanocrystalline MgH2 powders

The kinetics of hydride formation and decomposition described by semiempirical models generally do not involve particle and grain-size dependence. However, ball-milled nanocrystalline powders usually exhibit log-normal grain-size and particle-size distribution. Considering size dependence, a total reacted function for a multiparticle system has been developed. We show that the shape of the measured reaction fraction curves do not determine unambiguously the rate-controlling mechanism of hydrogen sorption, since the kinetics are strongly affected by the microstructure. With the application the convolutional multiple whole profile fitting procedure for nanocrystalline MgH2, the parameters, e.g., the median and variance of the log-normal grain-size distribution have been determined. Taking these values into account, the reaction constants corresponding to different sorption states are considerably modified compared with values obtained from classical single-particle models.

Improving the quality of diamond anvil cell data collected on an area detector by shading individual diamond overlaps

Crystallographic data collected on a CCD using a diamond anvil cell may present overlapping diamond and sample reflections. These false intensities may not be rejected by common data processing programs and may affect the finalhkllist. A utility was developed that shades these reflections during the integration, enabling their elimination before the solution or refinement. Moreover, this procedure avoids the error propagation to other reflections, caused by overlapping spots, through the profile fitting procedure of an integration run.

Microstructural development in nanocrystalline [formula omitted] during H-absorption/desorption cycling

Repeated dehydriding/hydriding cycles of ball-milled nanocrystalline MgH 2 powders were carried out in a Sievert's-type apparatus. The microstructural changes during cycling were characterized by X-ray diffraction. Using the convolutional multiple whole profile fitting procedure, several microstructural parameters, i.e. the average grain size and the grain-size distribution of the as-milled and treated samples were determined. Based on the shrinking core model, the significant difference between the microstructures obtained after the first and repeated cyclings was explained.

Microstructure of crystalline materials determined by whole powder pattern X-ray line profile analysis

Powder diffraction patterns consisting of broadened line profiles are used to evaluate microstructure parameters. The microstructure is modelled in terms of crystallite size and microstrain, where microstrain is assumed to be caused by dislocations, triple junctions corresponding to sinter stresses, and to some extent, by planar defects, especially stacking faults and twin boundaries. Crystallite size needs special interpretation, in the case of ceramic powders it is often identical to the particle or grain size, whereas in the case of bulk materials, especially bulk metals or alloys it is equal to the subgrain size. Electron microscopy strongly facilitates the appropriate interpretation of X-ray crystallite size. The diffraction patterns are evaluated by the method of convolutional multiple whole profile (CMWP) fitting procedure [1,2]. In this procedure strain and size is modelled by dislocations and spherical or ellipsoidal crystallites with log-normal size distributions, respectively. The model generated and the measured diffraction patterns are compared by a nonlinear least squares method, in a similar way as in the whole powder pattern modelling (WPPM) method [3]. The effect of stacking faults and twins on X-ray diffraction patterns has been calculated numerically by using the DIFFaX [4] software for the first 15 Bragg reflections in fcc crystals up to 20 % fault densities [5]. It is found that the Bragg reflections consist of 5 types of sub-reflections which are of Lorentzian type. About 15.000 sub-reflections are evaluated and parametrized according to their FWHM and positions relative to the exact Bragg angles. These parameter files are incorporated into the CMWP software for evaluating planar faults together with dislocations and crystallite and/or sub-grain size distributions [5]. In nanocrystalline Cu and Cu-Zn alloys it has been found that twinning becomes a substantial mode of deformation when the grain size is smaller than about 40 and 60 nm, respectively. An unusual behaviour of line broadening in ball milled fluorides has been observed [6]. About twenty diffraction patterns corresponding to different ball milled states of the CaF 2, SrF2, BaF2 and CdF2 fluorides have been analysed in terms of dislocation densities and types, and crystallite size and size distributions by X-ray line profile analysis [6]. The diffraction patterns have been evaluated by the method of convolutional multiple whole profile (CMWP) fitting procedure [2,3]. In about 10 of the 20 patterns the calculated and measured diffraction patterns are in perfect agreement throughout the entire angular range of measurement. However, in the cases of the rest of the patterns the first few measured line profiles appear to be narrower than the calculated profiles based on the model. Nevertheless, also in these latter cases the measured and calculated patterns are in perfect agreement for the higher angular parts of the patterns consisting of 10 to 13 profiles. In the cases where this discrepancy is present, it is interpreted as an X-ray optical interference effect [6] similar to what has been observed by Rafaja et al. [7] in nanocrystalline thin layers. The interference effect has been corrected successfully, either by (i) excluding the affected profiles from the evaluation procedure or by (ii) assuming a diffraction angle dependent apparent bimodal size distribution of crystallites [6].

Stacking faults and twin boundaries in fcc crystals determined by x-ray diffraction profile analysis

A systematic procedure is developed to evaluate the density of planar defects together with dislocations and crystallite or subgrain size by x-ray line profile analysis in fcc crystals. Powder diffraction patterns are numerically calculated by using the DIFFAX software for intrinsic and extrinsic stacking faults, and twin boundaries for the first 15 Bragg reflections up to 20% fault density. It is found that the Bragg reflections consist of five subreflection types categorized by specific selection rules for the hkl indices in accordance with the theory of Warren [Prog. Met. Phys. 8, 147 (1959)]. It is shown that the profiles of the subreflections are Lorentzian-type functions. About 15 000 subreflections are evaluated for their full widths of half maxima and their positions relative to the exact Bragg angle. These values are parametrized as a function of the density and type of planar faults. A whole profile fitting procedure, previously worked out for determining the dislocation structure and crystallite size distributions, is extended for planar fault by including these data into the software. The method is applied to evaluate twin densities in nanocrystalline and submicron grain-size copper specimens. It is found that twinning becomes substantial under a critical crystallite or subgrain size of about 40nm, in accordance with other observations.

Rapid shear viscosity calculation by momentum impulse relaxation molecular dynamics

Recently, Arya et al. [J. Chem. Phys. 113, 2079 (2000)] introduced a new molecular dynamics method to rapidly compute the viscosity of fluids. The technique, termed momentum impulse relaxation (MIR), involves the imposition of a Gaussian velocity profile on an equilibrated system, after which the decay in the profile is monitored as a function of time. The shear viscosity is computed by matching the rate of decay of the velocity profile to the corresponding solution of the Navier-Stokes equation. The method was originally applied to simple systems (argon and n-butane) and found to give a comparable accuracy to conventional equilibrium and nonequilibrium methods with more than an order of magnitude reduction in computing time. In this work, we extend and generalize the method to examine larger molecules with higher viscosities than have been examined previously. A detailed analysis of the method is given, including the effect the velocity boundary conditions have on the viscosity, the sensitivity of the results to the velocity profile fitting procedure, the effect of preequilibration of the Gaussian profile, and the effect the system size and box shape have on the accuracy and speed of the method. It is shown that the MIR method can be extended to treat multiatom systems without loss of accuracy or computational efficiency.