Hello,
I have prepared 3%, 5%, 10% gadolinium doped CeO2 (GDC) and have heat treated it at 400 C, 500 C, and 1200 C.
See attached figure for peak shift.
I have calculated lattice parameter for all the doped samples. I observed that for 400 C samples the lattice parameters were 0.5412 nm, 0.5418 nm, and 0.5422 nm.
While when heat treated at 500 C the lattice parameter decreased. i.e., 0.5392, 0.5400, 0.5405.
For 1200 C they are 0. 5360, 0.5362, and 0.5368.
That is the 2theta values shifts towards right side on increasing the temperature. The strain values are positive for 400 while negative for rest two temperature.
What can be the possible mechanism behind such observation ?
@Elie Assaf: Thanks for your feedback. The sample follows Vegard rule (lattice parameter increases linearly with dopant concentration.
But my question is why is lattice parameter decreasing with increase in temperature.
Did you heat treat in air? There could be conversion of Ce3+ to Ce4+ (smaller ionic radius), hence the decrease in lattice parameter.
Dear Bhasker
I agree with answer of Mr.Hais, also i think the structure tend to compress when temperature increase because changing in some phases of structure which cause changing in bonds strength for the compound, hence the decrease in lattice parameters may obtain.
The reason for such a behavior is the size effect, It is known that with the decrease of particle size lattice tends to expand [1-3]. Since heat treatment induces particle growth the lattice parameter drops. Considering the width of X-ray lines provided the particles are nano-sized ones, so one can estimate their size by Scherrer formula [4].
In terms of lattice expansion usually the effect of particle size is higher than the effect of cation substitution, which seems to be the case here. However, in general one should look at the particle size, strain and lattice anisotropy altogether to have an idea of what is happening upon doping. Of course lattice anisotropy is important if the lattice is not cubic.
Solubility of the doping element in the host lattice is also of major importance since one have to make an assumption that all of the doping cations have been embedded into the host lattice to establish the relationship between doping and lattice parameter change.
Coming to the data provided there’s definitely the lack of the “control group” with no substitutional cations, and of course it’s better to have at least four points simply because one can fit any function to three points. So, increasing the number of points and introducing reference sample along with estimation of particle size and potential insight into composition via XPS/EDA analysis will give more information about the relationships between lattice parameter, strain and concentration of dopant.
Potential explanation of the effect on the qualitative level might be that interaction potential changes proportionally to the number of atoms in the system (particle) in order to reach minimum energy. However, such interpretation obviously involves the size of the particle and hence the change in surface energy with particle size. There are some models which address such problems for example [5] but one fits all solution seems not to exist due to complexity and distinct character of each case.
1. Naughton, B. T. and Clarke, D. R. (2007), Lattice Expansion and Saturation Magnetization of Nickel–Zinc Ferrite Nanoparticles Prepared by Aqueous Precipitation. Journal of the American Ceramic Society, 90: 3541–3546. doi:10.1111/j.1551-2916.2007.01980.x
2. Growth Behavior, Lattice Expansion, Strain, and Surface Morphology of Nanocrystalline, Monoclinic HfO2 Thin Films, C. V. Ramana, K. Kamala Bharathi, A. Garcia, and A. L. Campbell The Journal of Physical Chemistry C 2012 116 (18), 9955-9960 DOI: 10.1021/jp211109h
3. Sui, M.L. and Lu, K., Variation in lattice parameters with grain size of a nanophase Ni3P compound, Materials Science and Engineering: A, 179 (1994) pp. 541-544
4. https://en.wikipedia.org/wiki/Scherrer_equation
5. J.S. Vermaak ∗, C.W. Mays ∗∗, D. Kuhlmann-Wilsdorf, On surface stress and surface tension: I. Theoretical considerations, Surface Science, 12 (2), 1968, pp 128-133.
@Igor A. Iashchishyn: thanks for your descriptive detailed explanation. Its very supportive to me.
Regards,
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