Hostname: page-component-89b8bd64d-72crv Total loading time: 0 Render date: 2026-05-07T12:59:18.740Z Has data issue: false hasContentIssue false
  • English
  • Français

X-Ray Dynamical Diffraction in Powder Samples with Time-Dependent Particle Size Distributions

Published online by Cambridge University Press:  02 December 2019

Adriana Valério ,
Sérgio L. Morelhão ,
Alex J. Freitas Cabral ,
Márcio M. Soares  and
Cláudio M. R. Remédios
Adriana Valério*
Affiliation:
Institute of Physics, University of São Paulo, São Paulo 05508-090, Brazil
Sérgio L. Morelhão
Affiliation:
Institute of Physics, University of São Paulo, São Paulo 05508-090, Brazil
Alex J. Freitas Cabral
Affiliation:
Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará, Belém, PA, Brazil Universidade Federal do Oeste do Pará, Santarém, PA, Brazil
Márcio M. Soares
Affiliation:
Laboratório Nacional de Luz Síncrotron - LNLS/CNPEM, Campinas, SP, Brazil
Cláudio M. R. Remédios
Affiliation:
Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará, Belém, PA, Brazil
*
*(Email: avalerio@if.usp.br)
Get access

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.

Keywords

in situnucleation & growthx-ray diffraction (XRD)crystallization

Information

Type
Articles
Information
MRS Advances , Volume 5 , Issue 29-30: Materials Theory, Computation and Characterization , 2020 , pp. 1585 - 1591
Check for updates
Copyright
Copyright © Materials Research Society 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Vamvakeros, A., Jacques, S. D. M., Di Michiel, M., et al. Nat Commun. 9, 4751 (2018).10.1038/s41467-018-07046-8CrossRefGoogle Scholar
Gu, Ying-Qiu, Fu, Xin-Pu, Du, Pei-Pei, et al. J. Phys. Chem. C 119, 17102-17110 (2015).CrossRefGoogle Scholar
Bak, S.-M., Shadike, Z., Lin, R., Yu, X., Yang, X.-Q.. NPG Asia Materials 10, 563–580 (2018).CrossRefGoogle Scholar
Mi, J.-L., Jensen, T. N., Christensen, M., Tyrsted, C., Jørgensen, J. E., Iversen, B. B.. Chem. Mater. 23, 1158–1165 (2011).CrossRefGoogle Scholar
Clarke, G., Rogov, A., McCarthy, S. et al. Scientific Reports 8, 10473 (2018).CrossRefGoogle Scholar
Zhang, Z., Wang, Z., He, S., Wang, C., Jin, M., and Yin, Y., Chem. Sci. 6, 5197 (2015).CrossRefGoogle Scholar
Morelhão, S. L., Computer Simulation Tools for X-ray Analysis. (Graduate Texts in Physics Springer, Cham, 2016).CrossRefGoogle Scholar
Dina, G., Gonzalez, A. G., Morelhão, S. L., Kycia, S.. MRS Advances 3, 2347-2352 (2018).10.1557/adv.2018.511CrossRefGoogle Scholar
Freitas Cabral, A. J., Valerio, A., Morelhão, S. L., Soares, M. M., Remedios, C. M. R.. To appear in Cryst. Growth & Design (2019).Google Scholar
Scherrer, P.. Nachr. Ges. Wiss. Göettingen, Math.-Phys. Kl, 98 (1918).Google Scholar
Morelhão, S. L., Remédios, C. M. R., Freitas, R. O., dos Santos, A. O.. J. Appl. Cryst. 44, 93-101 (2011).10.1107/S0021889810042391CrossRefGoogle Scholar
Morelhão, S. L., Avanci, L. H.. Acta Cryst. A 57, 192-196 (2001).CrossRefGoogle Scholar
Avanci, L. H., Hayashi, M. A., Cardoso, L. P., Morelhão, S. L., Riesz, F., Rakennus, K., Hakkarainen, T.. J. Cryst. Growth 188, 220-224 (1998).CrossRefGoogle Scholar
Integrated reflectivities in semi-infinite crystals (infinite thickness) have maximum values smaller than the intrinsic width W of each Bragg reflection. It follows from the fact that reflectivity curves are always limited to values smaller than 1 hence their area A < 1 × W.Google Scholar
$W = {\rm{r}}_{\rm{e}} {\rm{\lambda }}^2 \left| {{\rm{F}}_{{\rm{hkl}}} {\rm{F}}_{{\rm{\bar h\bar k\bar l}}} } \right|^{1/2} /{\rm{V}}_{{\rm{cell}}} \sin 2{\rm{\theta }}_{\rm{B}} $ for σ-polarized x-rays where re = 2.818 × 10−5Å is theclassic electron radius, Fhkl is the structure factor of the hkl reflection with Bragg angle θB for the wavelength λ, and Vcell is the unit cell volume [7].Google Scholar
Kiss, L. B., Söderlund, J., Niklasson, G. A., Granqvist, C. G.. Nanotechnology 10, 25-28 (1999)CrossRefGoogle Scholar
Cervellino, A., Giannini, C., Guagliardi, A., Ladisa, M.. Phys. Rev. B 72, 035412 (2005).10.1103/PhysRevB.72.035412CrossRefGoogle Scholar
Bruno, M.. CrystEngComm 21, 4918-4924 (2019).CrossRefGoogle Scholar
Palewicz, A., Przeniosło, R., Sosnowska, I., Hewat, A. W.. Acta Cryst. B 63, 537-544 (2007).CrossRefGoogle Scholar