# Influence of Sulphur Content on Structuring Dynamics during Nanosecond Pulsed Direct Laser Interference Patterning

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{2}pieces and polished with diamond suspension (Masterprep, Buehler, Lake Bluff, IL, USA) of 0.05 µm size to an average surface roughness (Sa) of 0.008 µm. The root mean square roughness (Sq) of the same samples was 0.020 µm, with a maximum height of the assessed profile (Sz) at 0.450 µm. Before structuring, the surfaces were cleaned in an ultrasonic bath with ethanol (99.99% purity) for 25 min at room temperature to remove all preprocess contamination and were dried with compressed air.

#### 2.2. Nanosecond Direct Laser Interference Patterning

^{2}< 1.2. This main beam is then split into two sub-beams by passing through a diffractive optical element (DOE) and the beams are subsequently parallelised by a prism. A schematic representation of the main DLIP components is shown in Figure 2a. A lens is overlapping the beams on the surface with a focal distance of 40 mm and produces an interference spot of 160 µm in diameter. Varying the angle of incidence of the partial beams by changing the distance between DOE and prism, the spatial period determined by Equation (1) is specified in the range between 1.29 µm and 7.20 µm. The latter period was chosen for the structuring on the steel samples to keep the single line-like melt pools separated from each other and to prevent thermal influence among themselves.

^{2}and 1.1 J/cm

^{2}, which correspond to 58% to 91% of laser power, respectively. The samples were positioned under the laser spot with an x-y-axis system (Pro115 linear stages, Aerotech Inc., Pittsburgh, PA, USA), and the focus position was controlled by vertically moving the DLIP optical head on a z-axis. Laser microprocessing experiments were carried out in ambient environment without posttreatments. In all cases, the structuring process was made without overlapping pulse.

#### 2.3. Surface Characterisation

^{2}in the x-y-plane. The recorded measurements were processed using the software MountainsMap 7.3 (Digital Surf, Besançon, France), utilising profile extraction including the step height measurement function for analysis of the peak formation and the image tools for three-dimensional images of the structured surfaces. In addition, the laser treated substrates were also evaluated using a scanning electron microscope (SEM) (Supra 40 VP, Zeiss, Jena, Germany) at an operating voltage of 5.0 kV.

#### 2.4. Mathematical Model

^{2}is the surface excess at saturation, ${k}_{1}=3.18\times {10}^{-3}$ is a constant related to the entropy of segregation, and $\Delta {H}_{0}=-1.88\times {10}^{5}$ J/mol is the standard enthalpy of adsorption [38,45]. The values of the temperature coefficient of surface tension, which is required for the melt pool convection in the boundary condition (A9) (see Appendix A) resulting for the binary system Fe–S can be used for the simulation of stainless steel melt pools [46]. Further considering the values ${\gamma}_{\mathrm{m}}^{0}=1.943$ N/m, ${\left(\right)}_{}\mathrm{pure}\mathrm{metal}$ N/(mK) and ${T}_{\mathrm{m}}=1723$ K [38,45,47] in Equation (8), the surface tension is evaluated and presented in Figure 3a for liquid steel with different concentrations of the surfactant sulphur. Differentiating Equation (8) with respect to T, the relation for the temperature coefficient of surface tension is obtained as follows [38,45]:

#### 2.5. Numerical Simulation

^{2}and 0.375 J/cm

^{2}were used in the numerical simulations. Considering an interference spot radius ${r}_{\mathrm{spot}}=$ 80 µm and a Gaussian beam radius ${r}_{0}=$ 100 µm, the average fluence in the central period of the interference pattern results from Equation (7) as $2{\Phi}_{0}=$ 0.532 J/cm

^{2}and 0.665 J/cm

^{2}, respectively. Furthermore, simulations were performed for sulphur contents of 30 ppm, 100 ppm, 300 ppm, and 1500 ppm.

## 3. Results and Discussion

#### 3.1. Experimental Results

^{2}, 0.63 J/cm

^{2}, 0.82 J/cm

^{2}, and 0.99 J/cm

^{2}). The grey highlighted area represents the region of maximum laser intensity (interference maximum) during structuring. For instance, the steel with 30 ppm sulphur treated with a laser fluence of ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.46 J/cm

^{2}exhibits a line-like pattern with a central peak (∼40 nm height) surrounded by two valleys (∼15 nm depth) below the initial surface level. Increasing the laser fluence to ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.82 J/cm

^{2}leads to a transformation stage, where the central single peak splits into two peaks with a structure height of approximately 50 nm, forming a well-defined valley between them. By further increasing the laser fluence, both the height of the peaks and the depth of the valley increases, determined by a significant flow of the molten material during the DLIP process; see Figure 5 for 30 ppm S content and ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.99 J/cm

^{2}.

^{2}, with similar peak heights and valley depths; see Figure 5. However, the central peak, with a maximum structure height of 50 nm as well, starts to split only at laser fluences above ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.63 J/cm

^{2}. By fluence increase to ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.99 J/cm

^{2}, both peak height and valley depth constantly increase further and reach a similar magnitude as that for the geometries on 30 ppm S steels irradiated with ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.99 J/cm

^{2}.

^{2}. As the laser fluence is increased, the split peaks become larger, reaching up to 50 nm absolute structure height at ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.82 J/cm

^{2}. At ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.99 J/cm

^{2}, the height of the split peaks is further increased, similar to the 30 ppm and 100 ppm samples.

^{2}–0.99 J/cm

^{2}are further illustrated by the scanning electron micrographs shown in Figure 6. The small graphs inserted into the SEM images in Figure 6 indicate the areas of maximum laser intensity on each surface.

^{2}in Figure 6 depict structures with a single central peak. With an increase in laser fluence, the structure width grows, where a smaller central peak and two neighbouring subpeaks evolve instead of the single peak structure. On the other hand, microstructures fabricated using the highest laser fluence of 0.99 J/cm

^{2}display a split peak formation, induced by the dominant recoil pressure during the patterning process. In contrast, the SEM images of structures made on steel substrates with 300 ppm S in Figure 6 show a split peak formation for all laser fluences applied, where the structure width increases with the laser fluence up to 0.99 J/cm

^{2}.

^{2}are shown in Figure 7a. The topography shown in Figure 7b on steel with 300 ppm S after DLIP treatment at ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.82 J/cm

^{2}is characterised by split peaks and an enclosed valley below the initial surface level. The structure heights are decreasing from the DLIP spot centre towards the spot edge, following the Gaussian intensity distribution of the laser beam. Even at the spot edge, no structures in transformation stage or single peaks are visible in Figure 7b.

^{2}in Figure 5. For an augmented sulphur content of 100 ppm, the magnitude and temperature range of the positive temperature coefficient of surface tension is enlarged, resulting in a stronger inward convection and more marked single peak structures at moderate fluences, as presented in Figure 5 for ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.46 J/cm

^{2}and 0.63 J/cm

^{2}.

^{2}and 0.82 J/cm

^{2}and for 100 ppm S at ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.82 J/cm

^{2}in Figure 5. On the contrary, it is evident from the split peak structures observed in Figure 5 for steel with 300 ppm S at fluences up to ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.82 J/cm

^{2}that the conception of an even stronger inward convection at higher sulphur contents is not confirmed by the experiments. This deviation suggests that, in the presence of higher impurity levels, the expression for the temperature-dependent surface tension in Equation (8) is no longer appropriate or that effects other than thermocapillary convection are responsible for the microstructure evolution. For a high fluence of ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.99 J/cm

^{2}, split peak structures of similar height are produced on all steel samples, independent of the sulphur content; see Figure 5. This observation may be attributed to the dominance of the recoil pressure induced by vapourisation of molten metal at high laser intensity, which causes a lateral ejection of melt during the patterning process [56].

^{2}or at the edges of the DLIP spots. In these cases, single peaks are observed without the surrounding valleys, as compared to the centre peaks of the 30 ppm and 100 ppm S samples treated with ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.46 J/cm

^{2}. In other words, this structure has been produced without the flow of molten metal and thus can only be explained by the transformation of the crystalline structure of the used steel. When an austenitic steel is heated, depending on the temperature reached and the cooling rate, the structure can transform to martensite, which has a lower density (austenite: 7.9 g/cm

^{3}; martensite: 6.5 g/cm

^{3}[57]). Taking into consideration that the measured height of the peak was 15 nm, it is estimated that the austenitic steel was affected up to a depth of 69 nm.

^{2}produce slight surface elevations related to phase changes austenite–martensite in the steel. A fluence increase from ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.46 J/cm

^{2}to ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.9 J/cm

^{2}results in a gain in structure heights, up to 49 nm for single peaks with surrounding valleys for <100 ppm S steels. A further rise in fluence only results in a decrease in structure height due to a transformation stage from single peak to split peaks. Structures on steel with higher sulphur content (>100 ppm S) show negative structure heights, that is, valleys at the centre, for fluences above ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.46 J/cm

^{2}due to the split peak formation. With increasing fluence to ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.99 J/cm

^{2}, the valley enclosed by the split peaks becomes slightly deeper and increases further for fluences above ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.99 J/cm

^{2}. Maximum peak heights of 150 nm are found for ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 1.1 J/cm

^{2}on all steel samples, irrespective of the sulphur content.

^{2}. Starting from ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.46 J/cm

^{2}, a separation distance (half distance between both peaks) increasing with the laser fluence up to a maximum of 2 µm is measured for high sulphur content steels.

#### 3.2. Simulation Results

^{2}or $2{\Phi}_{0}=$ 0.665 J/cm

^{2}, corresponding to a laser number of $\phantom{\rule{-0.166667em}{0ex}}\mathit{La}=18.0241$ or $\phantom{\rule{-0.166667em}{0ex}}\mathit{La}=22.5301$.

^{2}is presented in Figure 9 along with the temporal variation of the laser pulse intensity. The maximum surface temperature trend in Figure 9 is in line with earlier simulation results in [44], although ${T}_{max}\sim 2570$ K is lower here, for DLIP of stainless steel at a laser wavelength of $\lambda =355$ nm and a lower fluence of $2{\Phi}_{0}=$ 0.4 J/cm

^{2}, which is attributed to the higher reflectivity at the present wavelength. It is evident from Figure 9 that the substrate surface is heated up to a temperature significantly above the liquidus point at the interference maximum due to the action of the laser pulse. Accordingly, a melt layer with the dimensions computed by the SPH model and presented in Figure 10 develops near the interference maximum after the onset of the laser pulse. Concerning the trends in Figure 10, the discrete values of the melt pool dimensions are employed only once at a central point in time to avoid a stair-step appearance of the graphs. The melt pool depth and the duration of the melt presence are compatible with the aforementioned numerical results in [44], whereas the melt pool width in Figure 10 exceeds the earlier calculations owing to the larger periodicity $\Lambda $ of the interference pattern considered here.

^{2}to investigate the influence of the laser fluence on the material behaviour, in particular the nonlinear effect on the melt pool dimensions and the velocity field, and the structure formation reported in Section 3.1. Consequently, the evolution of the maximum surface temperature computed by the SPH model is also shown in Figure 9. The temporal maximum of the surface temperature ${T}_{max}\sim 3150$ K at the interference maximum is below the vapourisation point, unlike the simulation results in [44] for the comparable fluence 2${\Phi}_{0}=0.5$ J/cm

^{2}and the laser wavelength $\lambda =355$ nm with a lower reflectivity of the stainless steel substrate. These differences from the earlier results are attributed to the slightly larger width of the laser pulse considered in the present investigation. The computed dimensions of the melt layer developing after the beginning of the laser pulse are shown in Figure 10 for the elevated fluence 2${\Phi}_{0}=0.665$ J/cm

^{2}as well. In accordance with the numerical results in [44], the maximum melt pool dimensions are roughly 20% wider and even 50% deeper than the calculations for the moderate fluence, i.e., 2${\Phi}_{0}=0.532$ J/cm

^{2}here. Again, the duration of the melt presence and the determined melt pool depth conform with the previous results in [44] unlike the increased melt pool width due to the larger periodicity $\Lambda $ employed.

^{2}. If the surface of the melt pool is heated to higher temperatures, the temperature coefficient of surface tension is negative in the proximity of the interference maximum and an additional outward flow from the centre of the melt pool surface towards regions of maximum surface tension develops. The predicted velocity magnitude of this outward convection is indicated by the dashed lines in Figure 11a for different sulphur contents.

^{2}, Figure 12a illustrates the strong outward convection for a low sulphur content of 30 ppm, which gradually decreases and is dominated by the inward convection for higher sulphur concentrations of 100 ppm and 300 ppm. Compared with the results in [44], lower horizontal velocity magnitudes are obtained in this work, which is attributed to the generally smaller magnitude of the surface tension temperature coefficient in the presence of a surfactant and the lower surface temperature gradients due to the larger periodicity $\Lambda $ and longer pulse duration ${\tau}_{\mathrm{p}}$.

^{2}are presented in Figure 11b. It is noted in Figure 11b that the velocity magnitude of the inward flow from the melt pool edges is consistently higher than the results in Figure 11a for the moderate laser fluence. As the surface temperature largely exceeds the point of maximum surface tension in the central region due to the elevated fluence $2{\Phi}_{0}=0.665$ J/cm

^{2}, the outward flow from the centre of the melt pool surface is significantly enhanced; see Figure 11b. Considering a low sulphur content of 30 ppm, Figure 11b shows that the outward flow clearly dominates the melt pool convection. For a concentration of 100 ppm sulphur in liquid steel, outward and inward convection both contribute considerably to the melt pool flow pattern. On the contrary, the graphs in Figure 11b suggest that the inward flow still dominates the melt pool convection for a higher sulphur content of 300 ppm in spite of the augmented outward flow. The foregoing statements are further illustrated in Figure 12b, which depicts the temperature and velocity fields computed for DLIP of stainless steel employing the elevated fluence in a section comprising the melt pool half width. In particular, a comparison of the results for 100 ppm sulphur presented in the central columns of Figure 12a,b reveals that a slight increase in the laser fluence changes the melt pool convection from a predominant inward flow to competing outward and inward flow. This changed melt flow character may explain the transition from a single peak microstructure to split peaks in Figure 5 when augmenting the laser fluence.

## 4. Conclusions

^{2}, low peak heights were produced independently of the sulphur content. An explanation can be found in the phase change in the steel microstructure from austenite to martensite, which involves a volume expansion due to the lower density of martensite. A slight enhancement of the laser fluence resulted in an increase in height of the single peak structures formed on low sulphur steels, which can be related to the inverse Marangoni convection in the melt pool. With a further increase in laser fluence, the structures on low sulphur steels change from single peak to split peaks. In contrast, for steels with high sulphur content, structures with split peaks were produced also at low laser fluences. Structures generated employing laser fluences above ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.90 J/cm

^{2}exhibited split peaks, irrespective of the sulphur content, due to the dominance of the recoil pressure during the DLIP process. The difference in the surface topography observed as a function of the laser parameters and sulphur content can be used in the future to create pattern geometries different from the yet achievable with two-beam or three-beam DLIP and thus to produce surfaces with novel functions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AISI | American Iron and Steel Institute |

DLIP | direct laser interference patterning |

DOE | diffractive optical element |

FOV | field of view |

FWHM | full width at half maximum |

LASER | light amplification by stimulated emission of radiation |

Nd:YLF | neodymium-doped yttrium lithium fluoride |

ppm | parts per million |

SEM | scanning electron microscope |

SPH | smoothed particle hydrodynamics |

TEM${}_{00}$ | fundamental transverse electromagnetic mode |

## Appendix A. Governing Equations and Boundary Conditions

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**Figure 1.**Surface evolution during laser processing due to temperature gradients and thermocapillary flow for (

**a**) negative and (

**b**) positive temperature coefficients of surface tension $\phantom{\rule{-0.166667em}{0ex}}\mathrm{d}\gamma /\phantom{\rule{-0.166667em}{0ex}}\mathrm{d}T$, outlines adopted from [32,43].

**Figure 2.**Setup employed for direct laser interference patterning (DLIP) experiments on steel substrates: (

**a**) nanosecond pulsed infrared laser, optical head for DLIP on a z-stage, and sample mounted on an x-y positioning stage and (

**b**) laser fluence distribution of interference pattern due to two coherent partial beams with a Gaussian intensity profile.

**Figure 3.**Temperature-dependent (

**a**) surface tension and (

**b**) its temperature derivative for liquid steel with different sulphur contents.

**Figure 4.**Particle discretisation of computational domain, dummy particles less opaque, details: (

**a**) 7.5 µm × 4.4 µm, coarse particles start at the bottom, (

**b**) 440 nm × 440 nm, near-surface equidistant initial array and coarsening.

**Figure 5.**Overview of peak transformation of DLIP structures made on steels with varying sulphur contents. The columns show profiles of produced patterns in steels with sulphur contents of 30 ppm, 100 ppm, and 300 ppm at different laser fluences (${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.46 J/cm

^{2}, 0.63 J/cm

^{2}, 0.82 J/cm

^{2}, and 0.99 J/cm

^{2}). The grey highlighted areas represent the regions of maximum laser intensity during patterning.

**Figure 6.**Scanning electron micrographs of surfaces after DLIP ($\lambda $ = 1053 nm, $\Lambda $ = 7.2 µm, and ${\tau}_{\mathrm{p}}$ = 12 ns) on steel substrates with distinct sulphur contents using a single pulse and different laser fluences. Small graphs indicate areas of maximum laser intensity. The brightness and contrast of the SEM images were enhanced for better visualisation.

**Figure 7.**Three-dimensional confocal microscope images of DLIP laser spots on steel samples with different sulphur contents. (

**a**) Single peak structures generated on steel with 30 ppm S content and ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.46 J/cm

^{2}, (

**b**) split peak structures fabricated on steel with 300 ppm S content and ${\Phi}_{\mathrm{av},\mathrm{spot}}$ = 0.82 J/cm

^{2}.

**Figure 8.**Surface topography observed after single pulse DLIP ($\lambda $ = 1053 nm, $\Lambda $ = 7.2 µm, ${\tau}_{\mathrm{p}}$ = 12 ns) on steel with different sulphur contents as a function of fluence: (

**a**) structure height and (

**b**) distance of peak(s) from centre.

**Figure 9.**Maximum surface temperature during single pulse DLIP of stainless steel with Gaussian beams using the process parameters $\lambda $ = 1053 nm, $\Lambda $ = 7.2 µm, ${\tau}_{\mathrm{p}}$ = 12 ns and $2{\Phi}_{0}$ = 0.532 J/cm

^{2}or $2{\Phi}_{0}$ = 0.665 J/cm

^{2}.

**Figure 10.**Transient melt pool dimensions predicted by the smoothed particle hydrodynamics (SPH) model of DLIP ($\lambda $ = 1053 nm, $\Lambda $ = 7.2 µm, ${\tau}_{\mathrm{p}}$ = 12 ns) on stainless steel using a laser fluence of either $2{\Phi}_{0}$ = 0.532 J/cm

^{2}or $2{\Phi}_{0}$ = 0.665 J/cm

^{2}.

**Figure 11.**Horizontal velocity magnitudes at melt pool surface during DLIP with $\lambda $ = 1053 nm, $\Lambda $ = 7.2 µm, and ${\tau}_{\mathrm{p}}$ = 12 ns using a fluence of (

**a**) $2{\Phi}_{0}$ = 0.532 J/cm

^{2}or (

**b**) $2{\Phi}_{0}$ = 0.665 J/cm

^{2}on steel with sulphur content.

**Figure 12.**Simulation of melt pool flow during DLIP ($\lambda $ = 1053 nm, $\Lambda $ = 7.2 µm, and ${\tau}_{\mathrm{p}}$ = 12 ns) of steel with (l) 30 ppm, (c) 100 ppm, and (r) 300 ppm sulphur at a laser fluence of (

**a**) $2{\Phi}_{0}$ = 0.532 J/cm

^{2}and (

**b**) $2{\Phi}_{0}$ = 0.665 J/cm

^{2}with detail of 2 µm × 250 nm including isotherms, streamlines, and velocity vectors in melt pool half width at times (

**a**) t = 50 ns, 53 ns, 56 ns, 59 ns, and 62 ns, and (

**b**) t = 48 ns, 52 ns, 56 ns, 60 ns, 64 ns, and 68 ns.

Process Parameter | Symbol | Value |
---|---|---|

wavelength | $\lambda $ | 1053 nm |

intersection angle between beams | $\theta $ | 0.1464 rad |

periodicity of interference pattern | $\Lambda $ | 7.2 µm |

average fluence in interference spot | ${\Phi}_{\mathrm{av},\mathrm{spot}}$ | 0.300 J/cm^{2} |

fluence of interference pattern | $2{\Phi}_{0}$ | 0.532 J/cm^{2} |

pulse duration (FWHM) | ${\tau}_{\mathrm{p}}$ | 12 ns |

pulse time | ${t}_{\mathrm{p}}$ | 50 ns |

simulation duration | ${t}_{\mathrm{end}}$ | 200 ns |

initial substrate temperature | ${T}_{0}$ | 298.15 K |

gravitational acceleration | g | 9.81 m/s^{2} |

Fourier number | $\phantom{\rule{-0.166667em}{0ex}}\mathit{Fo}$ | $4.1\overline{6}$ |

Material Property | Symbol | AISI 304 Steel | Unit | References |
---|---|---|---|---|

solidus temperature | ${T}_{\mathrm{s}}$ | 1673 | K | [50] |

liquidus temperature | ${T}_{\mathrm{l}}$ | 1727 | K | [50] |

vapourisation temperature | ${T}_{\mathrm{v}}$ | 3273 | K | [51] |

density | ${\rho}_{0}$ | 7262 | kg/m^{3} | [50] |

specific heat | ${c}_{\mathrm{p}}$ | 704 | J/(kg K) | [50,52] |

thermal conductivity | $\kappa $ | 26.8 | W/(m K) | [50] |

thermal diffusivity | a | $5.24\times {10}^{-6}$ | m^{2}/s | |

enthalpy of fusion | ${L}_{\mathrm{f}}$ | 251 | kJ/kg | [50,51] |

enthalpy of vapourisation | ${L}_{\mathrm{v}}$ | 6500 | kJ/kg | [51] |

dynamic viscosity (at ${T}_{\mathrm{l}}$) | $\eta $ | $7.0\times {10}^{-3}$ | Pa s | [50] |

kinematic viscosity (at ${T}_{\mathrm{l}}$) | $\nu $ | $1.02\times {10}^{-6}$ | m^{2}/s | |

volumetric thermal expansion coefficient | $\beta $ | $8.5\times {10}^{-5}$ | 1/K | [53,54] |

temperature coefficient of surface tension | $\phantom{\rule{-0.166667em}{0ex}}\mathrm{d}\gamma \left(\right)open="/"\; close>\phantom{\rule{-0.166667em}{0ex}}\mathrm{d}T$ | $-4.3\times {10}^{-4}$ | N/(m K) | [45] |

absorption coefficient (at 1053 nm) | $\alpha $ | $5.15\times {10}^{7}$ | 1/m | [55] |

reflectivity (at 1053 nm) | R | $0.646$ | 1 | [55] |

Quantity | Symbol | AISI 304 Steel |
---|---|---|

thermal diffusion length | L | 501.5 nm |

laser number | $\phantom{\rule{-0.166667em}{0ex}}\mathit{La}$ | 18.0241 |

solid–liquid phase change number | $\phantom{\rule{-0.166667em}{0ex}}{\mathit{Ph}}_{\mathrm{s}/\mathrm{l}}$ | 0.119849 |

liquid–vapour phase change number | $\phantom{\rule{-0.166667em}{0ex}}{\mathit{Ph}}_{\mathrm{l}/\mathrm{v}}$ | 3.10367 |

Prandtl number | $\phantom{\rule{-0.166667em}{0ex}}\mathit{Pr}$ | 0.1947 |

Rayleigh number | $\phantom{\rule{-0.166667em}{0ex}}\mathit{Ra}$ | $3.04124\times {10}^{-8}$ |

Marangoni number | $\phantom{\rule{-0.166667em}{0ex}}\mathit{Ma}$ | 9.08939 |

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## Share and Cite

**MDPI and ACS Style**

Jähnig, T.; Demuth, C.; Lasagni, A.F.
Influence of Sulphur Content on Structuring Dynamics during Nanosecond Pulsed Direct Laser Interference Patterning. *Nanomaterials* **2021**, *11*, 855.
https://doi.org/10.3390/nano11040855

**AMA Style**

Jähnig T, Demuth C, Lasagni AF.
Influence of Sulphur Content on Structuring Dynamics during Nanosecond Pulsed Direct Laser Interference Patterning. *Nanomaterials*. 2021; 11(4):855.
https://doi.org/10.3390/nano11040855

**Chicago/Turabian Style**

Jähnig, Theresa, Cornelius Demuth, and Andrés Fabián Lasagni.
2021. "Influence of Sulphur Content on Structuring Dynamics during Nanosecond Pulsed Direct Laser Interference Patterning" *Nanomaterials* 11, no. 4: 855.
https://doi.org/10.3390/nano11040855