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.

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.

Effect of cryogenic milling on Al7075 prepared by spark plasma sintering method

2017 ◽  
Vol 32 (S1) ◽  
pp. S221-S224 ◽  
Author(s):  
Frantisek Lukac ◽  
Tomas Chraska ◽  
Orsolya Molnarova ◽  
Premysl Malek ◽  
Jakub Cinert
Keyword(s):  
Spark Plasma Sintering ◽  
Rietveld Analysis ◽  
Deformation Energy ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cryogenic Milling ◽  
Plasma Sintering ◽  
Crystallite Sizes ◽  
Spark Plasma ◽  
Sintering Method

Precipitation of secondary intermetallic phases in aluminium alloy Al7075 sintered by spark plasma sintering method from powders milled at room and cryogenic temperature was studied by X-ray powder diffraction. Deformation energy stored during cryogenic milling influences the precipitation in Al7075 alloy. High temperature X-ray diffraction experiment revealed the potential for further precipitation strengthening of samples prepared by spark plasma sintering of milled powders. It was established that the correction of absorption edge of metal Kβ-line filter used for laboratory sources greatly enhances the precision of quantitative Rietveld analysis as well as the determination of precipitates’ crystallite sizes.

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.

scholarly journals Characterization of Mixed-Metal Oxides Using Synchrotron-Based Time-Resolved x-ray Diffraction and x-ray Absorption Spectroscopy

1999 ◽  
Vol 590 ◽  
Author(s):  
José A. Rodriguez ◽  
Jonathan C. Hanson ◽  
Joaquín L. Brito ◽  
Amitesh Maiti
Keyword(s):  
Metal Oxides ◽  
Density Functional ◽  
Chemical Properties ◽  
Local Symmetry ◽  
Mixed Metal Oxides ◽  
X Ray Diffraction ◽  
Time Resolved ◽  
X Ray ◽  
Mixed Metal ◽  
X Ray Absorption

ABSTRACTExperiments are described showing the utility of synchrotron-based time-resolved x-ray diffraction (TR-XRD) and x-ray absorption near-edge spectroscopy (XANES) for characterizing the physical and chemical properties of mixed-metal oxides that contain Mo and a second transition metal (Fe, Co or Ni). TR-XRD was used to study the transformations that occur during the heating of a FeMoO4/Fe2(MoO4)3 mixture and the α⇒β phase transitions in CoMoO4 and NiMoO4. The Mo LII- and O K-edges in XANES are very useful for probing the local symmetry of Mo atoms in mixed-metal oxides. The results of XANES and density-functional calculations (DMo13, DFT-GGA) show large changes in the splitting of the empty Mo 4d levels when going from tetrahedral to octahedral coordinations. XANES is very useful for studying the reaction of H2, H2S and SO2 with the mixed-metal oxides. Measurements at the S K-edge allow a clear identification of S, SO2, SO3 or SO4 on the oxide surfaces. Changes in the oxidation state of molybdenum produce substantial shifts in the position of the Mo LII- and MIII-edges.

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 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.

Routine Crystallite-Size Determination by X-Ray Diffraction Line Broadening

1961 ◽  
Vol 5 ◽  
pp. 104-116 ◽  
Author(s):  
R. C. Rau
Keyword(s):  
Crystallite Size ◽  
Ceramic Materials ◽  
Diffraction Line ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Routine Basis ◽  
Crystallite Sizes ◽  
Standard Set ◽  
Sintering Characteristics

AbstractIncreasing interest in the sintering characteristics of various ceramic materials has resulted in the need for a knowledge of the crystallite sizes of many constituent ceramic powders. Standard X-ray diffraction line-broadening techniques have been utilized to determine these crystallite sizes. This paper presents a general review of the theory of line broadening as a means of measuring crystallite size and gives the methods and modifications used to perform this type of analysis rapidly and on a routine basis.Four modifications have been used in the determination of crystallite size routinely by X-ray line broadening. These methods are (1) a graded set of powder photographs, (2) a computer program to calculate sizes from diffractometer data, (3) a set of crystallite-size curves for a given material for use with diffractometer data, and (4) a standard set of curves to use with diffractometer data for any strain-free materials. The preparation, use, and limitations of each of these methods is presented.

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.

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