## 3 Formation of Cobalt Nanoparticles by Ion Implantation
### Results
Figure 6: \(Cont.\)  
Experimental data comparing the vibrational properties of bulk HCP and FCC Co is appreciably scant. Our measurements suggest they are subtly different, with \(\Theta_{E}\) values of 295 \(\pm\) 1 and 286 \(\pm\) 2 K, respectively. If one considers the \(\Theta_{E}\) as a measure of effective bond strength [42], the data presented herein is indicative of slightly stronger metallic bonds in the HCP phase compared to the FCC phase. The validity of such a difference is supported by our findings for 5.2 nm diameter HCP and 13.2 nm diameter FCC NPs which yield \(\Theta_{E}\) values of 291 \(\pm\) 3 and 285 \(\pm\) 3 K, respectively. Recall from Table 2 that the structural properties of these NPs were nearly bulk-like. Clearly their vibrational properties are also near bulk-like including the subtle phase-specific difference in \(\Theta_{E}\). Finite-size effects are more apparent in the vibrational (and structural) properties of smaller NPs. The 2.8 nm diameter HCP NPs exhibit a \(\Theta_{E}\) value of 280 \(\pm\) 3 K. Relative to bulk HCP material, the reduction in \(\Theta_{E}\) reflects a lower mean vibrational frequency and softening of the metallic bonds in the NP sample. Simulations for elemental metallic NPs show capillary pressure and disordered surface atoms shift the vibrational density of states (VDOS) in opposite directions--to higher and lower frequencies, respectively [55]. Our results thus indicate that surface/interfacial disorder is the dominant influence on the vibrational properties of Co NPs. A similar size-dependent trend in the \(\Theta_{E}\) values was reported for small FCC Cu and (recently) Ni NPs embedded in SiO\({}_{2}\)[49,56]. The temperature dependence of the \(C_{3}\) values is shown in Figure 6(b). At temperatures below 100 K the \(C_{3}\) values are very small, though non-zero due to low temperature quantum effects and zero point motion [57]. From \(\sim\)150 K onwards \(C_{3}\) increases in value. Similar trends can be observed across all bulk and NP data sets, each with a different constant offset due to different static contributions (\(C_{3S}\)). Fitting results from the temperature dependence of \(C_{3}\) with Equation (2) are tabulated in Table 3. In general, the magnitude of both \(\beta\) and \(C_{3S}\) is greater for the NP samples relative to the bulk standards and, furthermore, increases as the NP size decreases. Again, these trends are attributed to the increase in SBR or equivalently the increase in relative fraction of surface/interfacial atoms with a distorted environment different to that from the (contracted) FCC or HCP NP core. Figure 6(c) shows the evolution of the BL as a function of measurement temperature for all bulk standards and NP samples. The NPs are offset from the bulk standards due to the \(BL\) contraction discussed above. Figure 6 shows that the NPs exhibit less thermal expansion compared to the bulk Co standards and the effect is more pronounced for NPs of smaller sizes. Similar results have been observed for Pt [58] and Ge [45] NPs embedded in SiO\({}_{2}\), where both studies demonstrated that the thermal expansion of the interatomic distances was lowest for small NPs and increased with increasing NP size. It was suggested that the SiO\({}_{2}\) matrix restricts the thermal expansion of the embedded NPs. The thermal expansion coefficient of SiO\({}_{2}\) is negative below 180 K and above this temperature becomes positive but low in value [59,60]. Like the aforementioned studies, the reduced thermal expansion of the Co NPs is attributed to the restriction imposed by the surrounding SiO\({}_{2}\) matrix.