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P Scardi - One of the best experts on this subject based on the ideXlab platform.
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whole Powder Pattern modelling macros for topas
Journal of Applied Crystallography, 2018Co-Authors: P Scardi, C Azanza L Ricardo, C Perezdemydenko, A A CoelhoAbstract:Macros implementing the main concepts of the whole Powder Pattern modelling approach have been written for TOPAS. Size and strain broadening components of the diffraction line profiles can be convolved with the instrumental profile already available among the standard commands of TOPAS. Specific macros are presented with examples of applications including plastically deformed Powders and atomistic simulations. A macro is presented for the modelling of surface relaxation effects in spherical nanocrystals.
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debye equation versus whole Powder Pattern modelling real versus reciprocal space modelling of nanomaterials
Zeitschrift für Kristallographie Supplements, 2009Co-Authors: Kenneth R Beyerlein, Matteo Leoni, Antonio Cervellino, Robert L Snyder, P ScardiAbstract:Real space methods like the Debye equation are increasingly being employed as an alternative to traditional Line Profile Analysis (LPA) techniques for the study of size and strain effects in nanomaterials. Until recently, the use of this technique in modelling was hindered by the time necessary to complete a calculation. This limitation encouraged development of the alternative, reciprocal-space Whole Powder Pattern Modelling, which on the other hand lacks physical validation when applied to the study of very small atomic clusters ( V) of 2.7 nm and 4.0 nm, respectively; while the standard deviations of the natural logarithm (σ) used were 0.15 and 0.40, resulting in a narrow and wide distribution for each set. (See ref. 6, and references therein, for a precise definition of V and σ.) In order to perform the Debye function simulation [3,7], a series of increasingly large spherical Au clusters with fcc structure were created. The diameter that related to less than .1 percent of the assumed volume weighted size distribution defined the maximum sphere size used in the simulations. Since in these constructions the diameter was not a continuous variable, two rules to govern the step size have been assumed: i) that the radius difference Δr between consecutive clusters is constant, ii) that the volume increment between consecutive clusters is an integer multiple of the Wigner-Seitz unit cell volume. Using these two assumptions it is simple to see that Δr = a(3/2π)/2=0.39a. This discrete spacing is arbitrary but also sensible, as confirmed by our results. Clusters have been processed in order to obtain sets of interatomic pair distances and multiplicities. If we imagine that each unique distance is a Dirac delta weighted by its multiplicity, we can see that the pair distance density distribution is a Dirac comb. Immediately, though, the generated set of unique distances is fed into the sampling routine, which convolutes the distance Dirac comb with a suitable Gaussian profile [7], sampling the resulting continuous distance density. As the sampling step is inversely related to the maximum diffraction vector length Qmax, the sampling is performed simultaneously with different steps ranging from 0.03 to 0.96 A, covering quite all possible experimental conditions. The sampled pseudodistance sets were then used to calculate diffraction Patterns via a suitably adapted Debye formula, which is amenable to a fast transZ. Kristallogr. Suppl. 30 (2009) 87 form. More details on the fast Debye simulation algorithms can be found elsewhere [3,7]. Three levels of Poisson noise were then added to the simulated intensity to obtain Patterns with signal-to-noise ratios (SNR=√Imax) of 316.2, 100, and 31.6 (max noise added). Then simulated Patterns were modelled with the WPPM approach [4,5,8], refining the parameters of the fcc lattice, size distribution, small angle scattering contribution and a Chebyshev polynomial background. A range of trial size distribution forms was assumed including: continuous and discrete lognormal distributions, and a continuous gamma distribution. The results of these analyses for each distribution are given in the following sections. Continuous lognormal distribution The Patterns calculated by the Debye approach were first modelled assuming a continuous lognormal distribution of spheres in the WPPM framework. The obtained size distributions matched exactly the expected Debye distribution for all studied Patterns. Even at the small particle size range of 1-10 nm, the WPPM method was able to accurately distinguish the different lognormal parameters of two size distributions with the same Scherrer size (integral breadth). The exact match between the discrete distribution used in the Debye simulations and the continuous curve employed in WPPM was beyond expectations (cf. figure 2). The lower residual and weighted sum of squares (wss ≡∑[(IDebye-IWPPM)/IDebye]) for the distributions with a larger Scherrer size of 4.0nm was an expected result (cf. figure 1). As the size increases the differences between the discrete Debye crystal, and the spatially averaged reciprocal space method, become less influential. Furthermore, at larger sizes the shape of the particle created in the Debye approach is increasingly well represented by a sphere. 20 40 60 80 100 120 140 0.0 5.0x10 1.0x10 20 40 60 80 100 120 140 0.0 5.0x10 1.0x10 20 40 60 80 100 120 140 0.0 5.0x10 1.0x10 -1500
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recent advancements in whole Powder Pattern modelling
Zeitschrift für Kristallographie Supplements, 2008Co-Authors: P ScardiAbstract:Abstract. Advantages of Whole Powder Pattern Modelling against conventional Line Profile Analysis methods are briefly reviewed, and a specific example is discussed on the possible ambiguity in the interpretation of the Williamson-Hall plot for polydisperse systems. Ad-vancements in WPPM concerning dislocation line broadening are illustrated with examples taken from the recent literature. Reliability and limits in the application of WPPM to nanocrystalline systems are also discussed. 1. Introduction In recent years, the growing interest in nanomaterials gave considerable momentum to dif-fraction Line Profile Analysis (LPA), recognised as one of the most used techniques to study crystalline domain shape and size distribution, as well as nature and amount of lattice defects [1]. As a consequence, LPA methods developed considerably: traditional methods based on diffraction peak integral breadths (e.g., Scherrer formula and Williamson-Hall (WH) plot [2,3]) or on the Fourier analysis of isolated peak profiles (e.g., the Warren-Averbach method [2,4]) have been paralleled by several new approaches with increasing tendency to deal with the full diffraction Pattern [5,6]. It is useful to introduce a distinction between methods based on the use of some flexible but arbitrary profile function (e.g., Voigt, pseudo-Voigt, Pearson VII functions [7]), and methods that exclusively rely on physical models of the microstruc-ture (e.g., describing coherent scattering effects from dispersed systems of crystalline do-mains, strain fields of lattice defects, etc.): we will refer to Whole Powder Pattern Fitting (WPPF) for the former and Whole Powder Pattern Modelling (WPPM) for the latter [8-10]. Profile fitting is almost invariably a need when dealing with X-ray Diffraction (XRD) pat-terns from finely dispersed and/or highly deformed systems – most cases of interest to LPA – to separate overlapping peak profiles and background. However, despite the simplicity in developing WPPF software [11] and the flexibility of this approach, WPPF is biased by the choice of the profile function which replaces, at some stage of the analysis, the experimental dataset, so that LPA is actually performed on the fitting parameters more than on the data. This can give results that do not match the original data [12].
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analytical expression for the dislocation contrast factor of the 001 100 cubic slip system application to cu 2 o
Physical Review B, 2007Co-Authors: Jorge Martinezgarcia, Matteo Leoni, P ScardiAbstract:An analytical solution was obtained for the average contrast factor C{sub hkl} of dislocations with (100) slip-system in anisotropic cubic crystals. The expression provides the dislocation contrast factor as an explicit function of the Miller indices (hkl), the elastic anisotropy factor A{sub z}, and the Poisson ratio {nu}, thus avoiding lengthy numerical calculations or approximate parametrizations. The expression was incorporated in the whole Powder Pattern modelling algorithm and used to study dislocations in ball milled nanocrystalline Cu{sub 2}O.
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whole Powder Pattern modelling of cubic metal Powders deformed by high energy milling
Zeitschrift Fur Kristallographie, 2007Co-Authors: P Scardi, Matteo Leoni, Mirco DincauAbstract:A Whole Powder Pattern Modelling of the dif- fraction Pattern has been used to study the effect of grind- ing on some cubic metal Powders: crystalline domain size distribution, unit cell parameter average dislocation den- sity, effective outer cut-off radius, effective (screw-edge) dislocation character and faulting probabilities provide a detailed picture of the microstructure of heavily deformed metals. Besides proving the effectiveness of the analytical ap- proach, the present study also suggests some generaliza- tion in the behaviour of pure Powders of cubic metals sub- jected to an extensive high-energy milling.
Matteo Leoni - One of the best experts on this subject based on the ideXlab platform.
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evolution of the lattice defects and crystalline domain size in carbon nanotube metal matrix composites processed by severe plastic deformation
Materials Characterization, 2019Co-Authors: Katherine Aristizabal, Matteo Leoni, Andreas Katzensteiner, Frank Mucklich, Sebastian SuarezAbstract:Abstract Nickel (Ni) and carbon nanotube (CNT)-reinforced Ni-matrix composites were processed by high-pressure torsion (HPT). The evolution of dislocation densities and crystalline domain sizes were analyzed by means of X-ray diffraction (XRD) using Whole Powder Pattern Modelling (WPPM). The composites showed an evident gradient in the microstructural refinement and in hardness with increasing applied strain. This effect was found to be more pronounced in the presence of higher amounts of CNT. In particular, a higher amount of screw dislocations was measured by WPPM after HPT. It was concluded that the strengthening of CNT-MMC processed by HPT is mainly due to work hardening and grain refinement, both mechanisms being assisted by the presence of CNT, with marginal contribution of particle strengthening.
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debye equation versus whole Powder Pattern modelling real versus reciprocal space modelling of nanomaterials
Zeitschrift für Kristallographie Supplements, 2009Co-Authors: Kenneth R Beyerlein, Matteo Leoni, Antonio Cervellino, Robert L Snyder, P ScardiAbstract:Real space methods like the Debye equation are increasingly being employed as an alternative to traditional Line Profile Analysis (LPA) techniques for the study of size and strain effects in nanomaterials. Until recently, the use of this technique in modelling was hindered by the time necessary to complete a calculation. This limitation encouraged development of the alternative, reciprocal-space Whole Powder Pattern Modelling, which on the other hand lacks physical validation when applied to the study of very small atomic clusters ( V) of 2.7 nm and 4.0 nm, respectively; while the standard deviations of the natural logarithm (σ) used were 0.15 and 0.40, resulting in a narrow and wide distribution for each set. (See ref. 6, and references therein, for a precise definition of V and σ.) In order to perform the Debye function simulation [3,7], a series of increasingly large spherical Au clusters with fcc structure were created. The diameter that related to less than .1 percent of the assumed volume weighted size distribution defined the maximum sphere size used in the simulations. Since in these constructions the diameter was not a continuous variable, two rules to govern the step size have been assumed: i) that the radius difference Δr between consecutive clusters is constant, ii) that the volume increment between consecutive clusters is an integer multiple of the Wigner-Seitz unit cell volume. Using these two assumptions it is simple to see that Δr = a(3/2π)/2=0.39a. This discrete spacing is arbitrary but also sensible, as confirmed by our results. Clusters have been processed in order to obtain sets of interatomic pair distances and multiplicities. If we imagine that each unique distance is a Dirac delta weighted by its multiplicity, we can see that the pair distance density distribution is a Dirac comb. Immediately, though, the generated set of unique distances is fed into the sampling routine, which convolutes the distance Dirac comb with a suitable Gaussian profile [7], sampling the resulting continuous distance density. As the sampling step is inversely related to the maximum diffraction vector length Qmax, the sampling is performed simultaneously with different steps ranging from 0.03 to 0.96 A, covering quite all possible experimental conditions. The sampled pseudodistance sets were then used to calculate diffraction Patterns via a suitably adapted Debye formula, which is amenable to a fast transZ. Kristallogr. Suppl. 30 (2009) 87 form. More details on the fast Debye simulation algorithms can be found elsewhere [3,7]. Three levels of Poisson noise were then added to the simulated intensity to obtain Patterns with signal-to-noise ratios (SNR=√Imax) of 316.2, 100, and 31.6 (max noise added). Then simulated Patterns were modelled with the WPPM approach [4,5,8], refining the parameters of the fcc lattice, size distribution, small angle scattering contribution and a Chebyshev polynomial background. A range of trial size distribution forms was assumed including: continuous and discrete lognormal distributions, and a continuous gamma distribution. The results of these analyses for each distribution are given in the following sections. Continuous lognormal distribution The Patterns calculated by the Debye approach were first modelled assuming a continuous lognormal distribution of spheres in the WPPM framework. The obtained size distributions matched exactly the expected Debye distribution for all studied Patterns. Even at the small particle size range of 1-10 nm, the WPPM method was able to accurately distinguish the different lognormal parameters of two size distributions with the same Scherrer size (integral breadth). The exact match between the discrete distribution used in the Debye simulations and the continuous curve employed in WPPM was beyond expectations (cf. figure 2). The lower residual and weighted sum of squares (wss ≡∑[(IDebye-IWPPM)/IDebye]) for the distributions with a larger Scherrer size of 4.0nm was an expected result (cf. figure 1). As the size increases the differences between the discrete Debye crystal, and the spatially averaged reciprocal space method, become less influential. Furthermore, at larger sizes the shape of the particle created in the Debye approach is increasingly well represented by a sphere. 20 40 60 80 100 120 140 0.0 5.0x10 1.0x10 20 40 60 80 100 120 140 0.0 5.0x10 1.0x10 20 40 60 80 100 120 140 0.0 5.0x10 1.0x10 -1500
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analytical expression for the dislocation contrast factor of the 001 100 cubic slip system application to cu 2 o
Physical Review B, 2007Co-Authors: Jorge Martinezgarcia, Matteo Leoni, P ScardiAbstract:An analytical solution was obtained for the average contrast factor C{sub hkl} of dislocations with (100) slip-system in anisotropic cubic crystals. The expression provides the dislocation contrast factor as an explicit function of the Miller indices (hkl), the elastic anisotropy factor A{sub z}, and the Poisson ratio {nu}, thus avoiding lengthy numerical calculations or approximate parametrizations. The expression was incorporated in the whole Powder Pattern modelling algorithm and used to study dislocations in ball milled nanocrystalline Cu{sub 2}O.
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whole Powder Pattern modelling of cubic metal Powders deformed by high energy milling
Zeitschrift Fur Kristallographie, 2007Co-Authors: P Scardi, Matteo Leoni, Mirco DincauAbstract:A Whole Powder Pattern Modelling of the dif- fraction Pattern has been used to study the effect of grind- ing on some cubic metal Powders: crystalline domain size distribution, unit cell parameter average dislocation den- sity, effective outer cut-off radius, effective (screw-edge) dislocation character and faulting probabilities provide a detailed picture of the microstructure of heavily deformed metals. Besides proving the effectiveness of the analytical ap- proach, the present study also suggests some generaliza- tion in the behaviour of pure Powders of cubic metals sub- jected to an extensive high-energy milling.
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line profile analysis Pattern modelling versus profile fitting
Journal of Applied Crystallography, 2006Co-Authors: P Scardi, Matteo LeoniAbstract:Powder diffraction data collected on a nanocrystalline ceria sample within a round robin conducted by the IUCr Commission on Powder Diffraction were analysed by two alternative approaches: (i) whole-Powder-Pattern modelling based upon a fundamental microstructural parameters approach, and (ii) a traditional whole-Powder-Pattern fitting followed by Williamson-Hall and Warren-Averbach analysis. While the former gives results in close agreement with those of transmission electron microscopy, the latter tends to overestimate the domain size effect, providing size values about 20% smaller. The origin of the discrepancy can be traced back to a substantial inadequacy of profile fitting with Voigt profiles, which leads to systematic errors in the following line profile analysis by traditional methods. However, independently of the model, those systematic errors seem to have little effect on the volume-weighted mean size.
Melinda J Duer - One of the best experts on this subject based on the ideXlab platform.
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recoupling of chemical shift anisotropy Powder Patterns in mas nmr
Journal of Magnetic Resonance, 2006Co-Authors: Melinda J DuerAbstract:Abstract A comparison of three different implementations of the chemical-shift recoupling experiment of Tycko et al. [R. Tycko, G. Dabbagh, P.A. Mirau, Determination of chemical-shift-anisotropy lineshapes in a two-dimensional magic-angle-spinning NMR experiment, J. Magn. Reson. 85 (1989) 265–274] is presented. The methods seek to reduce the effects of artefacts resulting from pulse imperfections and residual C-H dipolar coupling in organic solids. An optimised and constant time implementation are shown to give well-defined and artefact free Powder Pattern lineshapes in the indirectly observed dimension for both sp 2 and sp 3 carbon sites. Experimental setup is no more demanding than for the original experiment, and can be implemented using standard commercial hardware.
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recoupling of chemical shift anisotropy Powder Patterns in mas nmr
Journal of Magnetic Resonance, 2006Co-Authors: Melinda J DuerAbstract:Abstract A comparison of three different implementations of the chemical-shift recoupling experiment of Tycko et al. [R. Tycko, G. Dabbagh, P.A. Mirau, Determination of chemical-shift-anisotropy lineshapes in a two-dimensional magic-angle-spinning NMR experiment, J. Magn. Reson. 85 (1989) 265–274] is presented. The methods seek to reduce the effects of artefacts resulting from pulse imperfections and residual C-H dipolar coupling in organic solids. An optimised and constant time implementation are shown to give well-defined and artefact free Powder Pattern lineshapes in the indirectly observed dimension for both sp 2 and sp 3 carbon sites. Experimental setup is no more demanding than for the original experiment, and can be implemented using standard commercial hardware.
D Louer - One of the best experts on this subject based on the ideXlab platform.
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Powder Pattern indexing with the dichotomy method
Journal of Applied Crystallography, 2004Co-Authors: Ali Boultif, D LouerAbstract:The efficiency of the successive dichotomy method for Powder diffraction Pattern indexing [Louer & Louer (1972). J. Appl. Cryst. 5, 271–275] has been proved over more than 30 years of usage. Features implemented in the new version of the computer program DICVOL04 include (i) a tolerance to the presence of impurity (or inaccurately measured) diffraction lines, (ii) a refinement of the `zero-point' position, (iii) a reviewing of all input lines from the solution found from, generally, the first 20 lines, (iv) a cell analysis, based on the concept of the reduced cell, to identify equivalent monoclinic and triclinic solutions, and (v) an optional analysis of input Powder data to detect the presence of a significant `zero-point' offset. New search strategies have also been introduced, e.g. each crystal system is scanned separately, within the input volume limits, to limit the risk of missing a solution characterized by a metric lattice singularity. The default values in the input file have been extended to 25 A for the linear parameters and 2500 A3 for the cell volume. The search is carried out exhaustively within the input parameter limits and the absolute error on peak position measurements. Many tests with data from the literature and from Powder data of pharmaceutical materials, collected with the capillary technique and laboratory monochromatic X-rays, have been performed with a high success rate, covering all crystal symmetries from cubic to triclinic. Some examples reported as `difficult' cases are also discussed. Additionally, a few recommendations for the correct practice of Powder Pattern indexing are reported.
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effect of a crystallite size distribution on x ray diffraction line profiles and whole Powder Pattern fitting
Journal of Applied Crystallography, 2000Co-Authors: J I Langford, D Louer, P ScardiAbstract:A distribution of crystallite size reduces the width of a Powder diffraction line profile, relative to that for a single crystallite, and lengthens its tails. It is shown that estimates of size from the integral breadth or Fourier methods differ from the arithmetic mean of the distribution by an amount which depends on its dispersion. It is also shown that the form of `size' line profiles for a unimodal distribution is generally not Lorentzian. A Powder Pattern can be simulated for a given distribution of sizes, if it is assumed that on average the crystallites have a regular shape, and this can then be compared with experimental data to give refined parameters defining the distribution. Unlike `traditional' methods of line-profile analysis, this entirely physical approach can be applied to Powder Patterns with severe overlap of reflections, as is demonstrated by using data for nanocrystalline ceria. The procedure is compared with alternative Powder-Pattern fitting methods, by using pseudo-Voigt and Pearson VII functions to model individual line profiles, and with transmission electron microscopy (TEM) data.
Hideo Toraya - One of the best experts on this subject based on the ideXlab platform.
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direct derivation dd of weight fractions of individual crystalline phases from observed intensities and chemical composition data incorporation of the dd method into the whole Powder Pattern fitting procedure
Journal of Applied Crystallography, 2018Co-Authors: Hideo TorayaAbstract:A formula for quantitative phase analysis (QPA), called the intensity–composition (IC) formula, can be used for deriving weight fractions of individual crystalline phases in a mixture from sets of observed integrated intensities, measured in a wide 2θ range, with chemical composition data [Toraya (2016). J. Appl. Cryst. 49, 1508–1516; Toraya (2017). J. Appl. Cryst. 50, 820–829]. In this study, the IC formula has been incorporated into the whole-Powder-Pattern fitting (WPPF) procedure to conduct QPA. The fitting function for calculating the profile intensity at each step of the scattering angle consists of three sub-functions that represent the individual component diffraction Patterns. The first sub-function calculates the diffraction Pattern using a set of integrated intensities, the parameter values of which are determined by the least-squares fitting of the whole-Powder Pattern as is usually done by the whole-Powder-Pattern decomposition (WPPD) method. The second sub-function uses a set of integrated intensity parameters, which are preliminarily prepared by WPPD or may be calculated from a crystal structure model. These intensity parameters, multiplied by a scale factor, are fixed at their original values while the scale factor is adjusted in WPPF. The third sub-function uses an observed or calculated diffraction Pattern multiplied by a scale factor. This diffraction Pattern can be fitted directly by adjusting the scale factor. Therefore, one can fit Patterns consisting of heavily broadened and degraded diffraction lines, like those of clay minerals, without being concerned with the problem of peak overlap in decomposing the diffraction Pattern. The IC formula uses the total sums of the intensities under the diffraction Patterns of individual phases as observed data sets; therefore, it can equally treat these intensity data sets irrespective of differences in the profile models used by the three sub-functions. The three sub-functions can arbitrarily be chosen and linearly combined, and then they can simultaneously be fitted to the observed diffraction Pattern of a target mixture. The capability of the above method has been demonstrated with QPA of mixtures consisting of α-quartz, albite and kaolinite. Theories of currently used QPA techniques are reviewed from a viewpoint of the present theory and they can be interpreted as being based on the same principle, whereby the total observed intensities of individual phases are divided by the standard reference intensity per unit weight.
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estimation of statistical uncertainties in quantitative phase analysis using the rietveld method and the whole Powder Pattern decomposition method
Journal of Applied Crystallography, 2000Co-Authors: Hideo TorayaAbstract:Formulae for estimating statistical uncertainties in quantitative phase analysis using the Rietveld method and the whole-Powder-Pattern decomposition method have been derived. The relative magnitude of statistical uncertainty for a derived weight fraction of a component in a mixture is given by σ(Wm)/Wm = (1/Wm − 1)1/2F(D\textstyle\sum_{i = 1}^NYoi)−1/2, where Wm is the weight fraction of the mth component, F is the goodness-of-fit index, D (≤1) is a factor depending on the degree of peak overlap, and ∑Yoi is the total sum of profile intensities in the 2θ range used for whole-Powder-Pattern fitting. If the step width Δ2θ in step scanning is halved, ∑Yoi is almost doubled; on the other hand, ∑Yoi is proportional to the fixed counting time T. Therefore, σ(Wm)/Wm ∝ (Δ2θ/T)1/2. Extension of the 2θ range for whole-Powder-Pattern fitting towards the high-angle region is not effective for improving the precision of the derived weight fractions if the profile intensities in that region are weak. The formulae provide guidelines for optimizing experimental parameters in order to obtain a required precision.