QUANTITATIVE ANALYSIS OF PHASE TRANSFORMATIONS IN NANOCRYSTALLINE MATERIALS VIA RIETVELD REFINEMENT

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1 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol QUANTITATIVE ANALYSIS OF PHASE TRANSFORMATIONS IN NANOCRYSTALLINE MATERIALS VIA RIETVELD REFINEMENT X. Bokhimi, A. Morales, 0. Novaro, T. L6pez2, R. G6mez2, A. Garcia-Ruiz3 1. Institute of Physics, The National University of Mexico (UNAM), A. P , MBxico D. F., Mexico 2. Department of Chemistry, Universidad Autbnoma Metropolitana-I, A. P , 0949 MBxico D. F., Mexico 3. UICSA, COOFA, The National Polytechnic Institute, TB No. 950, Esq. Resina, Mexico D. F., Mexico ABSTRACT Crystalline structures of nanophases can be refined with the Rietveld method by using the codes developed for microcrystalline materials. The software, however, must be corrected to incorporate the angle dependence of atomic scattering and polarization factors for each diffraction peak, and to model the amorphous phases that frequently coexist with the nanophases. To show the usefulness of the present non-modified software, the phase transformations of nanocrystalline yttria-doped and non-doped zirconia were analyzed. Amorphous zirconia atomic distributions were modeled with a tetragonal phase having an average crystallite size of In yttria-doped samples annealed at 4OO C, amorphous and crystalline structures coexisted with concentrations that depended on yttria content. In non-doped samples, the tetragonal phase was stabilized by the carboxyls involved in the synthesis. INTRODUCTION Nanostructured materials have phases with crystallite sizes between 1 and 100 nm that give them novel properties (l-5). For example, the free electrons of nanostructured conductors or semiconductors in an insulating matrix emit fluorescence with a wavelength that depends on crystallite size (1). The large number of crystal boundaries in nanophases stops dislocations easily, enhancing the mechanical properties of the material (2). Because in these materials the area to volume ratio is high, they are also very attractive as catalysts (3). When nanostructures are prepared by using chemical routes, frequently some of the ions involved in the synthesis are incorporated as impurities into the nanocrystals, expanding the lattice (4-6). This gives rise to changes in the macroscopic physical properties of the material, which are only understood after a detailed atomic distribution analysis. Crystallites smaller than 10 mn are normally analyzed by using high-resolution electron microscopy (7), which provides crystal morphology, size, and unit cell symmetry. This information, however, comes from only a few crystals that could not be representative of the sample. In contrast, x-ray and neutron powder diffraction are alternative techniques to obtain the same information, but averaged from about lo9 crystallites, which are more sample representative. X-ray and neutron diffraction also provide information about phase concentrations, and the atom positions, occupancies and temperature displacements in unit cell. This information is obtained by refining the crystalline structure of the phases (8).

2 This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website ICDD Website -

3 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Because nanocrystalline materials are mainly produced from amorphous atomic distributions, the samples in the initial step of crystallization are a mixture of crystalline and amorphous phases. For a quantitative analysis, the amorphous phase must be also modeled and refined. In the present work, we show that the crystalline structure of nanophases can be refined with the Rietveld method by using the software developed for microcrystalline materials. Amorphous phases were modeled with a crystalline phase having a crystallite size of 1.2 nm. The refinement was applied to study the phase transformations of zirconia and yttria-doped zirconia. Nanocrystalline zirconia is an important material, because it has extraordinary mechanical, electrical and corrosion-resistance properties. The martensitic transformation from tetragonal to monoclinic zirconia produces high toughness (9). At high temperatures, it has a huge ionic conductivity that is employed to detect oxygen (10). It is also used in thermal barrier coatings of advanced engines working at extremely high temperatures (11). EXPERIMENTAL Zirconia samples were prepared by using the sol-gel method, with zirconium n-butoxide as zirconium precursor, ter-butyl alcohol as solvent, and acetic acid as hydrolysis catalyst. The gel dried at 70 C was annealed in air at various temperatures between 100 and 800 C. Yttria-doped zirconia samples, with 2.5 and 5.0 wt %, were synthesized by ultrasonically spraying an aqueous solution of zirconyl chloride, yttrium chloride, and ammonium hydroxide, into a diluted solution of NH40H in deionized water. The reaction product was ultrasonicated dried and then annealed in air at various temperatures between 100 and 800 C. X-ray diffraction measurements were performed in a Siemens D5000 diffractometer with CuK, radiation. Sample powders were packed in a glass holder. Diffraction intensity was measured at room temperature in the 28 interval between 20 and 1 lo, with a 20 step of 0.02 for 2 s per point. Crystalline structures were refined with the Rietveld technique by using DBWS (12) and WYRIET (13) programs; peak profiles were modeled with a pseudo-voigt function that contains average crystallite size as a refining parameter (14). Standard deviations are given in parentheses. When they correspond to Rietveld refined parameters, their values are not estimates of the probable error in the analysis as a whole, but only of minimum possible probable errors based on their normal distribution (15). RESULTS AND DISCUSSION The zirconia samples annealed below 300 C were amorphous with the local order of tetragonal zirconia. Amorphous phases partially crystallized into nanocrystalline tetragonal zirconia when samples were annealed at 400 C. Because amorphous phases had a tetragonal local order, they were modeled with a tetragonal phase with an average crystallite size of 1.2 run, which is the characteristic radius where atomic local order exists. After refining the tetragonal and amorphous phases, the calculated concentrations of the crystalline tetragonal and amorphous zirconia phases were 38(l) and 62(3) wt % respectively (Fig.1 and Tablel). These concentrations depended on annealing time and previous sample history.

4 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol x 3 I I Y,O,IZrO, o- I II I I III II III II I III 1111l ll I,111 I I II I1111,111 II 20 M Fig. 1 Rietveld refinement plot of non-doped zirconia (RWP = 0.08); sample was annealed at 400 C. Dots represent the experimental data; continuous line, the calculated data. Upper and lower tick marks correspond to tetragonal zirconia. Fig. 2 Rietveld refinement plot of yttria-doped zirconia with 2.5 mol % yttria (RW = 0.085); sample was annealed at 400 C. Dots represent the experimental data; continues line, the calculated data. Upper and lower tick marks correspond to tetragonal zirconia. A similar behavior was observed when nanocrystalline zirconia was stabilized with yttria (Fig. 2). Amorphous phase concentration, however, was lower and diminished even more when yttria concentration was increased. In the amorphous phase model, only lattice parameters and scaling factor were refined. Amorphous phases were also modeled with the local order of monoclinic zirconia; the fit to the experimental diffraction pattern, however, was not as good as for the tetragonal symmetry. TABLE 1 Non-doped zirconia: Phase compositions and average crystallite size as a function of sample annealing temperature The Rietveld refinement provided not only the concentrations of the phases but also the evolution of their crystallographic variables as a function of sample annealing temperature (Tables 1 and 2).

5 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol ZrO, ul. z a I- Ok II I I ii, 1, ,::,:,.,, :,I: I. :,.:,:,:~~,A.:,,,Al ~L,:: 20 ; Fig. 3 Rietveld refinement plot of non-doped zirconia (RWP = 0.084); sample was annealed at 600 C. Dots represent the experimental data; continuous line, the calculated data. Upper tick marks correspond to tetragonal zirconia; lower tick marks, to monoclinic zirconia. Fig. 4 Rietveld refinement plot of non-doped zirconia (RV = 0.086); sample was annealed at 800 C. Dots represent the experimental data; continuous line, the calculated data. Upper tick marks correspond to monoclinic zirconia; lower tick marks, to tetragonal zirconia. Phase stability with temperature depended on doping. When samples were annealed at high temperature, yttria-doped phases were stable, but the tetragonal phase of non-doped samples was partially transformed into nanocrystalline monoclinic zirconia (Figs. 3 and 4). In the non-doped samples annealed at 600 C the tetragonal phase concentration was large, indicating a high stability caused by the ions involved in the synthesis. Because hydroxyls left the sample at lower temperatures (6), they are discarded as stabilizers. The carboxyls from acetic acid, however, are stable at this temperature, and could stabilize the phase. This is possible because the parallelepiped of oxygen atoms in the tetragonal structure of zirconia have an interstitial site at its center, which can be occupied by the carbon atoms of carboxyl group. Since x-ray diffraction from carbon is very weak, the best way to test the above assumption is with neutron diffraction, where all atoms scatter similarly. TABLE 2 Non-doped zirconia: Lattice parameters as a function of sample annealing temperature

6 Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol Copyright(C)JCPDS-International Centre for Diffraction Data 2000, Advances in X-ray Analysis, Vol The models of the nanophases fitted experimental data well (Figs. 1 through 4), although the used software was developed for refining microcrystalline phases that produce sharp diffraction peaks, for which atomic scattering and polarization factors are considered constant (12-13). Nanocrystalline materials, however, produce very broad diffraction peaks, in which atomic scattering and polarization factors notoriously depend on scattering angle. Therefore, this dependence should be introduced in the software used for modeling the crystalline structure of nanophases. This software correction would probably increase the time required for the refinement calculation. CONCLUSIONS Although the software used for refining crystalline structures was developed for microcrystals, it worked well when applied to nanophases. The software assumes constant atomic scattering and polarization factors for each diffraction peak. This choice is valid for microcrystalline materials, which produce sharp peaks; but, for nanocrystalline phases, which produce very broad diffraction peaks, the dependence of these factors on diffraction angle should be considered. We also modeled amorphous atom distributions starting from a tetragonal crystalline structure of only 1.2 m-n. A more realistic model, however, would provide better results; for example, one model based on atomic radial distribution. Via Rietveld refinement, the evolution with temperature of non-doped and yttria-doped zirconia nanophases was analyzed quantitatively, which included phase concentrations, average crystallite size and lattice parameters. When samples were annealed at 400 C nanocrystalline and amorphous phases coexisted. In yttria-doped samples the amorphous phase content diminished as yttria content was increased. ACKNOWLEDGEMENTS We would like to thank Mr. Manuel Aguilar for technical assistance. REFERENCES VI I?1 171 [91 M. Benaissa, M. Jose-Yacaman, J. M. Hernandez, Bokhimi, K. E. Gonsalves and G. Carlson, Phys. Rev. B, 54 (1996) E. Bonetti, L. Pasquini and E. Sampaolesi, Nanostructured Materials, 9 (1997) 61 l-614 D. D. Beck and R. W. Siegel, J. Mater. Rex, 7 (1992) Bokhimi, A. Morales, T. Lopez and R. Gomez, J. Solid State Chem., 115 (1995) Bokhimi, A. Morales, 0. Novaro, T. Lopez, E. Sanchez y R. Gomez, J. Mater. Rex, 10 (1995) X. Bokhimi, A. Morales, 0. Novaro, M. Portilla, T. Lopez, F. Tzompanzi and R. Gomez, J. Solid State Chem., 135 (1998) D. E. Newbury, Nanostructured Materials, 9 (1995) 25 l-256 R. A. Young, The Rietveld Method, Oxford University Press: New York (1993) Q.-M. Yuan, J.-Q. Tan, and Z.-G. Jin, J Am. Ceram. Sot., 69 (1986)

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