Shock-wave synthesis of nanoparticles during ion sputtering. Page: 4 of 7
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Fig. 2. First, the displayed power-law fits to the data from the four individual irradiations all
have the same slope despite large differences in the total sputtering yield (e.g., ~5 for the Ne and
>100 for the Au). Second, the magnitude of this slope is -2 within remarkably tight error limits;
the average standard deviation determined for the four runs was < 0.05.
Early after their discovery, it was recognized [2] that a mechanism involving the
cooperative motion of atoms was probably responsible for the emission of intact clusters during
ion bombardment. Expanding on this concept, and noting that clusters were formed with the
greatest probability under energetic heavy-ion bombardment, Bitensky and Parilis [7] formulated
an analytical model for cluster emission based upon the formation and emergence of shock
waves that originate from energetic subsurface collision cascades. Essentially, the arrival and
reflection of a shock wave at a sample surface places the latter under tension. If this tension
exceeds a critical value, known as the fracture strength, the surface fractures and fragments are
ejected. The Bitensky and Parilis model predictions are in excellent agreement with the results
displayed in Fig. 2. Their shock-wave model predicts a power-law decrease for the cluster size
distribution with an exponent of -2. The inverse-square dependence arises because the critical
parameter in the fracture process is the energy required to create new surface area, which for a
three-dimensional particle increases as its characteristic dimension squared.
The experimental verification that relatively large atom clusters, ones up to
approximately 10,000 atoms, are generated during high-energy ion bombardment also offers a
possible explanation for why many previously reported investigations [3-5] yielded power-law
size distributions with considerably higher exponents. Very simply, a higher exponent means
that smaller clusters are present with disproportionately higher probabilities in the mass
spectrometry studies. Such an excess of smaller clusters is of course what would occur if all the
larger clusters do not remain completely intact. As alluded to in the introduction, the very fact
that the inter-atomic bond energy is so small in comparison to the energies involved in the
displacement events implies that some clusters can be expected to fragment after being ablated.
We also note from the data displayed in Fig. 2 that the size of the largest nanoparticle that
is ablated from the target surface increases systematically, and substantially, with increasing ion
mass. Although the smallest observable particle size will depend strongly on TEM imaging
conditions, and therefore can vary considerably from sample to sample, the largest particles are
the easiest to observe, and the easiest to characterize. With this fact in mind, we see that some
particles containing in excess of 8000 atoms were generated by the Au irradiation, while the
largest for the Kr irradiation contained approximately 5000 atoms, and it decreased even further,
to only approximately 3000 atoms, for the Ar and Ne bombardments. This increase in the largest
observed nanoparticle size can be readily understood in terms of the maximum energy available
in the displacement-cascade-induced shock wave, which also increases with increasing ion mass.
It might appear surprising at first that an element as ductile as Au actually fractures in the
manner described by the shock-wave model of Bitensky and Parilis. To understand this, it is
important to note the exceedingly fast time scale on which the shock wave develops and impacts
the surface. The pressure pulse generated by a highly energetic displacement cascade is fully
developed within a time less than approximately one picosecond. Traveling at the speed of
sound, a criterion which can actually be exceeded by a strong shock wave, the shock wave would
reach the surface from a depth of approximately 100 A also in a time of approximately one
picosecond. This extremely short time scale of less than a few picoseconds is not sufficient for
dislocations to either develop or move. Hence even normally highly ductile materials will
become brittle at such high strain rates.
This latter observation implies that the ion-ablation technique described above should be
useful for synthesizing nanoparticles of a wide variety of alloy compositions and phases, i.e.,
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Rehn, L. E.; Birtcher, R. C.; Donnelly, S. E.; Bado, P. M. & Funk, L. Shock-wave synthesis of nanoparticles during ion sputtering., article, December 11, 2001; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc724133/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.