X-Ray Dynamical Diffraction in Powder Samples with Time-Dependent Particle Size Distributions
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MRS Advances © 2019 Materials Research Society DOI: 10.1557/adv.2019.445
X-Ray Dynamical Diffraction in Powder Samples with Time-Dependent Particle Size Distributions Adriana Valério1, Sérgio L. Morelhão1, Alex J. Freitas Cabral2;3, Márcio M. Soares4, and Cláudio M. R. Remédios2 1
Institute of Physics, University of São Paulo, São Paulo 05508-090, Brazil
2
Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará, Belém, PA, Brazil
3
Universidade Federal do Oeste do Pará, Santarém, PA, Brazil
4
Laboratório Nacional de Luz Síncrotron - LNLS/CNPEM, Campinas, SP, Brazil
ABSTRACT
In situ X-ray diffraction is one of the most useful tools for studying a variety of processes, among which crystallization of nanoparticles where phase purity and size control are desired. Growth kinetics of a single phase can be completely resolved by proper analysis of the diffraction peaks as a function of time. The peak width provides a parameter for monitoring the time evolution of the particle size distribution (PSD), while the peak area (integrated intensity) is directly related to the whole diffracting volume of crystallized material in the sample. However, to precisely describe the growth kinetics in terms of nucleation and coarsening, the correlation between PSD parameters and diffraction peak widths has to be established in each particular study. Corrections in integrated intensity values for physical phenomena such as variation in atomic thermal vibrations and dynamical diffraction effects have also to be considered in certain cases. In this work, a general correlation between PSD median value and diffraction peak width is deduced, and a systematic procedure to resolve time-dependent lognormal PSDs from in situ XRD experiments is described in details. A procedure to correct the integrated intensities for dynamical diffraction effects is proposed. As a practical demonstration, this analytical procedure has been applied to the single-phase crystallization process of bismuth ferrite nanoparticles.
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INTRODUCTION Advanced synchrotron sources of high flux combined with detector systems capable of collecting, in just a few seconds, full X-ray diffraction (XRD) patterns of powder samples create opportunities for in situ studies of a variety of processes such as catalysis [1,2], energy storage and conversion [3], and crystallization of nanoparticles from amorphous precursors [4,5]. Fast in situ data acquisition may result in thousands of XRD patterns containing information on structural changes along the processes. Particularly in crystallization studies, there will be information on crystalline phases, lattice strain, and particle size distribution (PSD) as a function of time and temperature, covering the whole process from amorphous to fully crystalline phases. Besides p
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