**2. Laser induced plasmas on memory shape alloys**

When investigating the ejected cloud of particle, the *ideal* investigation technique should be non-invasive and offer global and local information about the plasma components. Such a technique can be considered the combination of ICCD fast camera imaging and space and time resolved optical emission spectroscopy, which is used consistently by our group [7, 13, 14] and it was also validated by a significant number of papers [15, 16]. Our approach was a global - local one, meaning that the initial step was to collect the global emission (in the 300–700 nm regime) of the LPP at consecutive time-delays with respect to the laser beam. The result for a Fe-Mn-Si laser produced plasma is shown in **Figure 1**, where we present selected images during the LPP expansion in a 2 *μ*s time lapse.

We observe that the plasma has a quasi-spherical shape and increases its volume as plasma evolves. The expansion velocity was estimated using the technique presented other previous papers [1], where it is discussed the effect of multielement composition of the ablation process. When performing cross-section on the recorded images in axial and transversal directions, we notice different behaviors across the two directions. We also performed cross section across the main expansion axis (axial cross-section) reveals a splitting of the plasma cloud in multiple

*Dynamics of Transient Plasmas Generated by ns Laser Ablation of Memory Shape Alloys DOI: http://dx.doi.org/10.5772/intechopen.94748*

**Figure 1.** *Global evolution of the Fe-Mn-Si LPP.*

feedback and accurate predictions on the behavior of physical processes. The dual approach of experimental investigations and theoretical modeling has proven to be a successful method for understanding the dynamics of multi-element fluids [5, 6] or as it was showcased recently by our group for complex laser produced plasmas (LPP) [7]. The study presented in this chapter expands our previous attempts for stoichiometric transfer and plasma chemistry in the case of laser ablation of complex alloys. We discuss here the ablation of metallic particles as a result of short laser ablation interaction with ternary alloys from both an experimental and theo-

retical point of view. To comprehend the ablated particle dynamics we

*Practical Applications of Laser Ablation*

**2. Laser induced plasmas on memory shape alloys**

selected images during the LPP expansion in a 2 *μ*s time lapse.

When investigating the ejected cloud of particle, the *ideal* investigation technique should be non-invasive and offer global and local information about the plasma components. Such a technique can be considered the combination of ICCD fast camera imaging and space and time resolved optical emission spectroscopy, which is used consistently by our group [7, 13, 14] and it was also validated by a significant number of papers [15, 16]. Our approach was a global - local one, meaning that the initial step was to collect the global emission (in the 300–700 nm regime) of the LPP at consecutive time-delays with respect to the laser beam. The result for a Fe-Mn-Si laser produced plasma is shown in **Figure 1**, where we present

We observe that the plasma has a quasi-spherical shape and increases its volume

as plasma evolves. The expansion velocity was estimated using the technique presented other previous papers [1], where it is discussed the effect of multielement composition of the ablation process. When performing cross-section on the recorded images in axial and transversal directions, we notice different behaviors across the two directions. We also performed cross section across the main expansion axis (axial cross-section) reveals a splitting of the plasma cloud in multiple

functions).

**122**

implemented optical emission spectroscopy in conjecture with ICCD fast camera imaging to record global and local information about their spatial distribution within the ablated cloud and their individual kinetic and thermal energy. From a theoretical perspective we built on our model from [7] and focused on exploring under, a fractal paradigm of motion, the effect of the plasma thermal energy (temperature) and ion physical properties (mass) on the spatial distribution of complex alloy plasmas. Usual models used to simulate the dynamics of complex systems are based on an assumption of the physical variable differentiability (e.g. density, momentum, energy, etc. [8–12] and the processes which they define. The practicality of such methods can be accepted sequentially, on space–time domains for which the differentiability still respected. However, the differential approach often fails when confronted by the reality of complex physical system (i.e. plasma plume expansion in PLD). To better represent most of the interactions at both local and global scales, it is required to introduce explicitly the scale resolution dependence. This breathes a new physical system where the variable dynamic that previously were dependent only on space and time, will now contain explicitly the dependence on the scale resolution. This can be even more abstracted and instead of using non-differential function, admittedly rather difficult to implement, just utilize different approximations of these multifractal mathematical functions derived by means of averaging at various scale resolution. A paramount consequence of this approximation is that any dynamic variable will behave as a limit of specific function families, which are non-differentiable for a null scale resolution (multifractal

distinct structures (two or three). Some studies report on a specific terminology for these structures, the *first one* also named the *fast one* is created by electrostatic mechanism (Cloulomb Explosion), the *second one* or *slower* structure is generated by thermal mechanisms (Explosive boiling), while the third consists of mainly clusters or nanoparticles. Their presence has beforehand been reported and extensively discussed in conjecture with the multiple ejection mechanism and their correlation with the fractality of the LPP [7, 14, 15, 17] by our group. However, our focus will not be on this third structure as the main optical signatures, seen through our experimental methods, are given by the dynamics of simpler plasma entities like atoms or ions. The velocities of the main structures were determined as follows: for the case of Cu-Mn-Al plasma – 15 km/s for the first structure and 7.4 km/s and for the second structure for the case of Fe-Mn-Si plasma - 20 km/s for the first one and 11 km/s for the second structure. The values are in good agreement with the other reports from literature [1, 18, 19]. The obtained values strongly are related to the differences of the melting points for each material and the overall mass of the cloud, with significant variance in the properties of the component directly affecting the ablation process and the subsequent evolution.

We notice a significant difference in the overall emission and shape of the LPP generated on the two alloys. The global emission is noticeably larger for the Fe-Mn-Si plasma and with less inner structuring, while for the Cu-Mn-Al the global emission is reduced and presents more pronounced structuring. These differences are induced by the energetic distribution uniformity on the excitation process as opposed to other types of interactions (i.e. ionization). Fe-Mn-Si plasma has an uniform aspect which is attributed similarities in the melting points of the composing elements, which leads to a uniform and homogeneous ablation. For the Cu-Mn-Al plasma there are significant differences between the physical properties of Al and Mn or Cu, could lead to a more heterogenous ablation process. These statements will further be verified with the space and time resolved OES. We would like to also note that, the fractality of the laser produced plasmas will also be affected by the inner energy of the plasma and its distribution on the composing entities [7, 13]. We anticipate here another type of analysis (fractal analysis) which we will further use in this study, that could offer valuable information about the laser produced plasmas.

In **Figure 2** we plotted the spatial distribution of atoms (Fe and Mn) from the Fe-Mn-Si plasma highlighting the discrepancies amongst the two elements. We would like to note that Si was not considered as the emission line intensity for its species insignificant (lower) than those of the other elements. The Fe atoms have a dual peak distribution, while the Mn one presents only a single peak distribution. This reads as Fe atoms can be excited throughout the whole plasma volume, especially at longer distance where the electron density is significantly lower. This assessment can also explain the elevated *Tex* reported earlier and it is in line with the multi-structure scenario seen by fast camera photography (ICCD fast camera

heavier ones are described by a lower fractality degree (lower collision rate). This difference in the fractality of the plasma entities will give us different spatial

*Dynamics of Transient Plasmas Generated by ns Laser Ablation of Memory Shape Alloys*

However, given our set-up optical configuration, lighter elements strongly scattered during expansion will appear to have a narrower distribution at relative short distances, while heavier particles will have a broader distribution most likely covering the whole plasma plume. Translating these results into the expansion of a three-dimensional plasma, low-mass elements are scattered towards the edge of the plasma plume while the high-mass ones are the building blocks the plasma core. For industrial applications like PLD, the result is of paramount importance interest as the particular volumes of the plasma plumes lack stoichiometry or uniformity. These properties could induce a non-congruent transfer of multielement material and affect the physical properties of the subsequent thin film. Furthermore, the diagnostic system used here allowed to capture the complex nature of the plasma and present some meaning behind it. We will further attempt to unravel more information about the relation between the fractality of specific elements and their

spatial distribution within the plasma volume in the following section.

The fractal analysis approach for understanding the dynamics of complex physical systems was shown over the years to provide with some of the most promising results towards understanding multiparticle flow in fluids [21, 22] or plasmas

This approach for describing LPP dynamics infers the building of novel geometric structures [23, 24] and probably new physical theories, in which the movement

For a laser ablation plasma, the nonlinearity and the chaoticity have a dual applicability being both structural and functional, with the interactions between the so-called plasma entities (structural components like electrons, ions, atoms, photons) determine reciprocal conditioning micro–macro, local–global, individualgroup, etc. In such a case, the universality of the laws describing the laser ablation plasma dynamics becomes obvious and it must be reflected by the mathematical procedures which are utilized. Basically, it makes use more and more often of the "holographic implementation" in the description of plasma dynamics. Usually, the theoretical models used to describe the ablation plasma dynamics are based on a differentiable variable assumption. Most of the notable results of the differentiable models must be understood sequentially, where the integrability and differentiability still apply. The differentiable mathematical procedures are limiting our understanding of more complex physical phenomena, such as the expansion of a laser produced plasma which implies various nonlinear behaviors, chaotic movement and self-structuring. In order to accurately describe the LPP dynamics and still remain tributary to differentiable and integral mathematics we must explicitly introduce the scale resolution. The scale resolution will be integrated in the expression of the physical variable, which describe the LPP, and implicitly in the fundamental equations, which govern these dynamics. This means that any physical variable becomes dependent on both spatial and temporal coordinates and the scale resolution. In other words, instead of using physical variables described by a nondifferentiable mathematical function, we will use different approximations of this mathematical function obtained through its averaging at various scale resolutions. As a consequence, the physical variables used to describe the LLP dynamics will act as a limit of functions family, which are non-differentiable for a null scale resolution and

distributions for each element.

*DOI: http://dx.doi.org/10.5772/intechopen.94748*

**3. Theoretical modeling**

differentiable for non-null scale resolution.

[7, 13–14, 17].

**125**

**Figure 2.** *Axial distribution of Fe (a) and Mn (b) atomic emission at various time-delays.*

imaging). By representing the intensity maximum for individual emission line as a function of time [20], we determined the expansion velocities for the individual elements, with 31 km/s for the first peak of Fe I and 10 km/s for the second one, while for the Mn I a velocity of 18 km/s. The expansion velocity estimated for the first peak of Fe I and the Mn atoms are similar with the values of the second plasma structure, while the velocities of the second group of Fe atoms are in line with the value determined for the first plasma structure. This concludes the fact that the two-plasma structure have uniformly distributed atoms and ions amongst them with the fast structure having a slight depletion of Mn.

We can take a broader view of the discussions made in the previous paragaphs for both investigated plasmas as the laser fluence and background pressure and are (expansion conditions) identical. The results are seen in **Figure 3**-right-hand side, where we can observe for a time-delay of 150 ns the spatial distribution of Fe and Mn in the Fe-Mn-Si plasma and Cu an Al in the Cu-Mn-Al plasma, respectively. We notice that for lighter elements we obtain a narrow spatial distribution, while the *heavier* ones (Cu and Fe) have a wider distribution. These differences can be seen as a separation of the composing elements based on their physical properties. The separation was previously discussed by our group in [7, 13] where the fractality of the components played a significant role, based on that the spatial distributions of different elements are reflecting the elevated degree of fractality. Lighter elements will have a higher collision rate and thus a higher fractality degree, whereas the

#### **Figure 3.**

*Axial distribution of the main elements in the alloys as seen through OES measurements at a time-delay of 150 ns (left) and a schematic representation of the particle distribution with the plasma volume (right).*

### *Dynamics of Transient Plasmas Generated by ns Laser Ablation of Memory Shape Alloys DOI: http://dx.doi.org/10.5772/intechopen.94748*

heavier ones are described by a lower fractality degree (lower collision rate). This difference in the fractality of the plasma entities will give us different spatial distributions for each element.

However, given our set-up optical configuration, lighter elements strongly scattered during expansion will appear to have a narrower distribution at relative short distances, while heavier particles will have a broader distribution most likely covering the whole plasma plume. Translating these results into the expansion of a three-dimensional plasma, low-mass elements are scattered towards the edge of the plasma plume while the high-mass ones are the building blocks the plasma core. For industrial applications like PLD, the result is of paramount importance interest as the particular volumes of the plasma plumes lack stoichiometry or uniformity. These properties could induce a non-congruent transfer of multielement material and affect the physical properties of the subsequent thin film. Furthermore, the diagnostic system used here allowed to capture the complex nature of the plasma and present some meaning behind it. We will further attempt to unravel more information about the relation between the fractality of specific elements and their spatial distribution within the plasma volume in the following section.
