Hi all,
I have prepared Pd nano particles using different reducing agents and the size of the particles varied from 10 to 16 nm. In the XRD pattern, there is a change in the 2 theta value of ~1 radian for each peak obtained (For eg: the 2 theta value for Pd(111) plane is 39.79 and 40.58 for particle size 16nm and 12 nm respectively) . What could be the reason for this change in 2 theta value? I will be grateful if anybody from platform could explain the reason.
Thanks in advance.
Regards
ANSARI P
Dear Ansari Palliyarayil It is evident that peak broadening occurs when the particle size falls in the nano range sizes. I guess this relationship may have any effect. I'm also following your question, to find the right solution.
Dear Dinesh,
I think the diffraction angle shift is related to a change in lattice constant. Such changes exist in nanoparticles and are linked to the effect of "Laplace pressure". See by way of illustration the effects of nanoscale on crystal structure or melting temperature in the enclosed papers.
Best regards.
Philippe.
In trivial cases, we can analyze the situation using Bragg's law: 2d.sinθ = nλ. As you prepare particles of smaller dimension in nano-regime, clearly there will be higher FWHM and smaller peak-height (keeping the area under the peaks nearly constant). But, the value of θ should not change ideally. However, smaller particles might bring up a few unintentional effects. Very often, tiny nanoparticles comprise vacancies and other kinds of defects. Presence of defects or impurities (dopants) can change the lattice constant and d. If d increases, XRD peaks should shift to smaller angles; and vice-versa. I think, you should test the composition of your sample using XPS/EDX, followed by Rietveld refinement of the XRD patterns. It can enlighten the situation precisely.
Dear Sir, Philippe Tailhades Good to learn from you ... Thank you!
The positions of XRD lines are controlled by symmetry and by the parameters of the unit cell. If the observed change of the lattice parameters does not affect the symmetry, a change of the line positions may be observed (with the same intensity ratio and with the positions of these lines defined by the same diffraction equation). Please remember that the theoretical positions of XRD lines are defined by equations specific to each symmetry of the unit cells. If the symmetry is changed, another equation, compatible with the new symmetry has to be used.
Complex modifications of the spectrum are expected if the distortions are affected the symmetries of the unit cell.
Please observe that line widths are governed by the size of CRSTALLITES (not of the unit cell) and are affected by both the size of crystallites and local stresses/strains.
A little bit more detail....
The positions of XRD lines are controlled by symmetry and by the parameters of the unit cell. If the observed change of the lattice parameters does not affect the symmetry, a change of the line positions may be observed (with the same intensity ratio and with the positions of these lines defined by the same diffraction equation). Please remember that the theoretical positions of XRD lines are defined by equations specific to each symmetry of the unit cells. If the symmetry is changed, another equation, compatible with the new symmetry has to be used. However, if the symmetry is preserved but the lattice parameters are modified the positions of the reflections are also modified.
Complex modifications of the spectrum are expected if the distortions are affecting both the symmetries of the unit cell and its parameters.
Please observe that line widths are governed by the size of CRSTALLITES (not of the unit cell!) and are affected by both the size of crystallites and local stresses/strains. The change of the size of nanoparticles MAY imply a change in the size of crystallites (this is not always the case and is frequently observed if the size of confinement is smaller than the size of crystallites) and sometimes a change of the parameters of the unit cell.
Hi,
For many metals such as Pd, Pt, Ag, among others, there is a relation between the lattice parameter and the crystal size: as the size decreases, the lattice parameter also decreases. Several experimental and theoretical studies have shown this behavior. However, for Pd nanoparticles, most of the literature data shows the opposite behavior: lattice dilation! We have discussed this effect for the specific case of palladium in a recent publication (you can also see some interesting references therein):
E. G. Ciapina et al. On the lattice dilation of palladium nanoparticles and a new methodology for the quantification of interstitials. Journal of Alloys and Compounds 881:160628 (DOI:10.1016/j.jallcom.2021.160628).
Best regards,
Prof. Dr. Eduardo . Ciapina.
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