Investigation of precision, accuracy and confidence of X-ray diffraction for determining crystallite size in nanopowders

2021 ◽  
Vol 54 (3) ◽  
Author(s):  
Alexander P. Moore ◽  
Martin B. Nemer ◽  
Mark A. Rodriguez ◽  
Christine C. Roberts ◽  
Patrick F. Fleig ◽  
...  
Keyword(s):  
Crystallite Size ◽  
Weighted Least Squares ◽  
Bulk Sample ◽  
Quantitative Information ◽  
Particle Identification ◽  
Inversion Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Peak Broadening ◽  
Crystallite Sizes

X-ray diffraction (XRD) is often utilized as a method of determining bulk sample crystallite size in powder characterization. While it is generally accepted that XRD peak broadening allows for qualitative crystallite size comparisons, its use for quantitative information is still debated. This study investigates the quantitative capability of XRD for determining the crystallite sizes of magnesium oxide nanocrystals by examining the precision, accuracy and uncertainty using the whole pattern (WP) weighted least-squares and Williamson–Hall (WH) methods. The precision of the methods was investigated by re-preparing, re-running and re-analysing identical samples. Both methods were found to be precise within 2 nm. The accuracy of the methods was investigated by comparing them against independent crystallite size analyses using visual particle identification from scanning electron microscopy micrographs and from indirect calculations using Brunauer–Emmett–Teller (BET) adsorption-determined surface areas. The WP method was found to be more accurate than the WH method, which consistently underpredicted the crystallite size. Finally, the confidence of the methods was investigated using a Bayesian inference statistical inversion method. The WP method was found to have a narrower confidence distribution in its crystallite size determination than the WH method. The broad WH confidence indicates that reliable quantitative single-measurement crystallite size determinations are not feasible using the WH technique. However, the WP method demonstrated precision, accuracy and confidence, allowing quantitative crystallite size determinations to be made.

Crystallite size and lattice strain of lithiated spinel material for rechargeable battery by X-ray diffraction peak-broadening analysis

2019 ◽  
Vol 43 (5) ◽  
pp. 1903-1911 ◽  
Author(s):  
Ahmed A. Al-Tabbakh ◽  
Nilgun Karatepe ◽  
Aseel B. Al-Zubaidi ◽  
Aida Benchaabane ◽  
Natheer B. Mahmood
Keyword(s):  
Crystallite Size ◽  
Lattice Strain ◽  
Diffraction Peak ◽  
Rechargeable Battery ◽  
X Ray Diffraction ◽  
X Ray ◽  
Peak Broadening

X-ray diffraction Warren–Averbach mullite analysis in whiteware porcelains: influence of kaolin raw material

Clay Minerals ◽  
2018 ◽  
Vol 53 (3) ◽  
pp. 471-485 ◽  
Author(s):  
Angel Sanz ◽  
Joaquín Bastida ◽  
Angel Caballero ◽  
Marek Kojdecki
Keyword(s):  
Crystallite Size ◽  
Firing Temperature ◽  
Microstructural Analysis ◽  
Stoichiometric Composition ◽  
Raw Material ◽  
Size Distributions ◽  
X Ray Diffraction ◽  
X Ray ◽  
Different Temperatures ◽  
Crystallite Sizes

ABSTRACTCompositional and microstructural analysis of mullites in porcelain whitewares obtained by the firing of two blends of identical triaxial composition using a kaolin B consisting of ‘higher-crystallinity’ kaolinite or a finer halloysitic kaolin M of lower crystal order was performed. No significant changes in the average Al2O3 contents (near the stoichiometric composition 3:2) of the mullites were observed. Fast and slow firing at the same temperature using B or M kaolin yielded different mullite contents. The Warren–Averbach method showed increase of the D110 mullite crystallite size and crystallite size distributions with small shifts to greater values with increasing firing temperature for the same type of firing (slow or fast) using the same kaolin, as well as significant differences between fast and slow firing of the same blend at different temperatures for each kaolin. The higher maximum frequency distribution of crystallite size observed at the same firing temperature using blends with M kaolin suggests a clearer crystallite growth of mullite in this blend. The agreement between thickening perpendicular to prism faces and mean crystallite sizes <D110> of mullite were not always observed because the direction perpendicular to 110 planes is not preferred for growth.

scholarly journals X-RAY DIFFRACTION ANALYSIS OF NANOPARTICLES: RECENT DEVELOPMENTS, POTENTIAL PROBLEMS AND SOME SOLUTIONS

2004 ◽  
Vol 03 (06) ◽  
pp. 757-763 ◽  
Author(s):  
PAMELA WHITFIELD ◽  
LYNDON MITCHELL
Keyword(s):  
Simple Technique ◽  
Size Analysis ◽  
X Ray Diffraction ◽  
X Ray ◽  
Peak Broadening ◽  
Potential Problems ◽  
Recent Developments ◽  
Crystallite Sizes ◽  
Crystallite Shape ◽  
Nanocrystalline Oxides

Powder X-ray diffraction has become a cornerstone technique for deriving crystallite size in nanoscience due to speed and "simplicity". Unfortunately, this apparently simple technique commonly has unexpected problems. Anisotropic peak broadening related to crystallite shape, defects, and microstrain occurs frequently in nanomaterials and can significantly complicate the analysis. In some instances, the usage of the conventional single peak approach would give erroneous results, and in others, this type of analysis is not even possible. A number of different nanocrystalline oxides have been examined to determine their crystallite sizes by different techniques. They differ in terms of crystal symmetry, crystallinity, density, and present different challenges with regard to size analysis.

Applicability of Routine Methods of Crystallite Size Analysis*

1962 ◽  
Vol 6 ◽  
pp. 191-201
Author(s):  
Robert C. Rau
Keyword(s):  
Crystallite Size ◽  
Beryllium Oxide ◽  
Testing Procedure ◽  
Individual Performance ◽  
Size Analysis ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Geometry ◽  
Crystallite Sizes ◽  
Performance Results

AbstractSeveral methods for the routine determination of crystallite size by means of X-ray diffraction line-broadening have previously been reported. Although these techniques have proven useful and reliable when utilized with the single X-ray diffractometer and instrumental geometry used to originally develop the methods, it was not known whether other instruments would provide similar reliability. Therefore a study was performed to evaluate the applicability of routine methods of crystallite size analysis to other X-ray diffraction units. A series of six beryllium oxide powder specimens, whose average crystallite sizes ranged stepwise from about 35 to nearly 3000 Å, were used to test a number of X-ray diffractometers. By using a predetermined diffraction geometry for each instrument tested, measured crystallite sizes were found to be quite reproducible and well within the limits of experimental error. The testing procedure, instrumental conditions, and individual performance results are presented in this paper.

A structural study of size-dependent lattice variation: In situ X-ray diffraction of the growth of goethite nanoparticles from 2-line ferrihydrite

2020 ◽  
Vol 105 (5) ◽  
pp. 652-663
Author(s):  
Peter J. Heaney ◽  
Matthew J. Oxman ◽  
Si Athena Chen
Keyword(s):  
Metal Oxides ◽  
Crystallite Size ◽  
Coefficient Of Thermal Expansion ◽  
Particle Growth ◽  
Rietveld Analysis ◽  
Order Kinetic ◽  
X Ray Diffraction ◽  
Time Resolved ◽  
X Ray ◽  
Crystallite Sizes

Abstract Unlike most native metals, the unit cells of metal oxides tend to expand when crystallite sizes approach the nanoscale. Here we review different models that account for this behavior, and we present structural analyses for goethite (α-FeOOH) crystallites from ~10 to ~30 nm. The goethite was investigated during continuous particle growth via the hydrothermal transformation of 2-line ferrihydrite at pH 13.6 at 80, 90, and 100 °C using time-resolved, angle-dispersive synchrotron X-ray diffraction. Ferrihydrite gels were injected into polyimide capillaries with low background scattering, increasing the sensitivity for detecting diffraction from goethite nanocrystals that nucleated upon heating. Rietveld analysis enabled high-resolution extraction of crystallographic and kinetic data. Crystallite sizes for goethite increased with time at similar rates for all temperatures. With increasing crystallite size, goethite unit-cell volumes decreased, primarily as a result of contraction along the c-axis, the direction of closest-packing (space group Pnma). We introduce the coefficient of nanoscale contraction (CNC) as an analog to the coefficient of thermal expansion (CTE) to compare the dependence of lattice strain on crystallite size for goethite and other metal oxides, and we argue that nanoscale-induced crystallographic expansion is quantitatively similar to that produced when goethite is heated. In addition, our first-order kinetic model based on the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation yielded an activation energy for the transformation of ferrihydrite to goethite of 72.74 ± 0.2 kJ/mol, below reported values for hematite nucleation and growth.

A Novel Route to Aluminum Nitride Ceramics Using a Polyaminoalane Precursor

1988 ◽  
Vol 121 ◽  
Author(s):  
M. Seibold ◽  
C. Rüssel
Keyword(s):  
Aluminum Nitride ◽  
Polymer Network ◽  
Polymerization Process ◽  
X Ray Diffraction ◽  
X Ray ◽  
Peak Broadening ◽  
Gas Atmosphere ◽  
Nitride Ceramics ◽  
Crystallite Sizes ◽  
Drying Up

ABSTRACTMetallic Aluminum is dissolved anodically in an electrolyte, containing a primary amine, an aprotic solvent and a tetraalkylammonium salt. Removal of the solvent and subsequent heating lead to a polymer network. Initial drying causes a more viscous liquid, further drying up to 150°C accelerates the polymerization process and a gel-like consistency is obtained. Pyrolysis is carried out under NH3 or inert gas atmosphere. X-ray diffraction data show amorphous products up to 800°C, treatment above 800°C leads to the desired ceramic product aluminum nitride. Peak broadening indicates extremely small crystallite sizes. Pressureless sintering without additives gives a compact product, having densities up to nearly 100% of the theoretical density.

Synthesis and Characterisation of Titania Nanotubes: Effect of Phase and Crystallite Size on Nanotube Formation

2007 ◽  
Vol 29-30 ◽  
pp. 211-214 ◽  
Author(s):  
D.L. Morgan ◽  
E.R. Waclawik ◽  
R.L Frost
Keyword(s):  
Raman Spectroscopy ◽  
Crystallite Size ◽  
Electron Spectroscopy ◽  
Driving Force ◽  
Titania Nanotubes ◽  
X Ray Diffraction ◽  
X Ray ◽  
Material Type ◽  
Transmission Electron ◽  
Crystallite Sizes

Nanotubes were produced from commercial and self-prepared anatase and rutile which were treated with 7.5 M NaOH over a temperature range of 100 – 200°C in 20°C increments. The formation of nanotubes was examined as a function of starting material type and size. Products were characterised by X-Ray Diffraction (XRD), Transmission Electron Spectroscopy (TEM), and Raman Spectroscopy. The results indicated that both phase and crystallite size affected the nanotube formation. Rutile was observed to require a greater driving force than anatase to form nanotubes, and increases in crystallite sizes appeared to impede formation slightly.

The mean crystallite size within a hydrogenated nanocrystalline silicon based photovoltaic solar cell and its role in determining the corresponding crystalline volume fraction

2014 ◽  
Vol 92 (7/8) ◽  
pp. 857-861 ◽  
Author(s):  
K.J. Schmidt ◽  
Y. Lin ◽  
M. Beaudoin ◽  
G. Xia ◽  
S.K. O’Leary ◽  
...  
Keyword(s):  
Crystallite Size ◽  
Volume Fraction ◽  
Nanocrystalline Silicon ◽  
Crystalline Volume Fraction ◽  
X Ray Diffraction ◽  
X Ray ◽  
Photovoltaic Solar Cell ◽  
Crystallite Sizes ◽  
The Mean ◽  
Silicon Based

We examine the dependence of the crystalline volume fraction on the mean crystallite size for hydrogenated nanocrystalline silicon based photovoltaic solar cells; this work builds upon an earlier study by Schmidt et al. (Mater. Res. Soc. Symp. Proc. 1536 (2013)). For each photovoltaic solar cell considered, the X-ray diffraction and Raman spectra are measured. Through the application of Scherrer’s equation, the X-ray diffraction results are used to determine the corresponding mean crystallite sizes. Through peak decomposition, the Raman results are used to estimate the corresponding crystalline volume fraction. Plotting the crystalline volume fraction as a function of the mean crystallite size, it is found that larger mean crystallite sizes tend to favor reduced crystalline volume fractions. The ability to randomly pack smaller crystallites with a greater packing fraction than their larger counterparts was suggested as a possible explanation for this observation.

The Effect of Compression Force on Alteration of Desloratadine and its Multicomponent Crystal Crystallinities Using X-Ray Diffraction and ATR-FTIR Techniques

2018 ◽  
Vol 787 ◽  
pp. 43-51
Author(s):  
Ahmad Ainurofiq ◽  
Rachmat Mauludin ◽  
Diky Mudhakir ◽  
Arif Budi Setianto ◽  
Sundani Nurono Soewandhi
Keyword(s):  
Crystallite Size ◽  
Degree Of Crystallinity ◽  
Attenuated Total Reflectance ◽  
Compression Force ◽  
X Ray Diffraction ◽  
Crystallinity Degree ◽  
X Ray ◽  
Peak Broadening ◽  
The Degree Of Crystallinity ◽  
Better Than

This work studied the effect of compression force on the desloratadine (DES) and its multi-component crystal (MCC) formulation and focused on the molecular crystal behavior of DES and MCC after compression. Crystallinity behavior of drugs in a mechanical process is to be interesting manner. In this research, DES and MCC were compressed using hydraulic presser equipped with 13 mm flat-face punch under different compression pressures in a range of 25 – 350 MPa. The solid state of DES and its MCC was evaluated using powder X-ray diffraction (XRD) and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy. Single XRD was carried out to confirm the molecular structure of crystal lattice. Powder XRD diffractogram under different compression forces was compared to the crystallinity degree, crystallite size and peak broadening. Those parameters were processed using Origin software. Crystallinity degree was calculated using Ruland’s methods, meanwhile, the crystallinity size was calculated using Scherrer’s equation after corrected to the broadening (full width at half maximum; FWHM) and diffraction baseline. As increasing the compression force, degree and size of crystallinity and FWHM were altered. In addition, the degree of crystallinity and crystallite size of DES and MCC decreased, while the FWHM increased. Furthermore, alteration of PXRD in DES was higher than that of MCC which had no alteration as increase as the compression force. FTIR result showed that neither DES nor MCC had no significant alteration after compression. However, the tabletability of MCC was better than DES owing to the potential slip plane of MCC.

The Scherrer equation and the dynamical theory of X-ray diffraction

2016 ◽  
Vol 72 (3) ◽  
pp. 385-390 ◽  
Author(s):  
Francisco Tiago Leitão Muniz ◽  
Marcus Aurélio Ribeiro Miranda ◽  
Cássio Morilla dos Santos ◽  
José Marcos Sasaki
Keyword(s):  
Crystallite Size ◽  
Dynamical Theory ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
Linear Absorption ◽  
X Ray ◽  
Crystallite Sizes ◽  
Scherrer Equation ◽  
High Degree ◽  
Kinematical Theory

The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm−1the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.

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