**2. Results**

We studied the self-organized phenomena of micro- and nanostructure formation on metal surfaces under action of series of laser radiation pulses (λ = 1064 μm, τ = 10, 100 ns) at nearnormal incidence upon the mechanically polished titanium surface (VT—1-0). Formation of three types of structures versus the laser power density (q) and pulse number (N) was observed. At q values corresponding to partial metal melting during the pulse, the creation of resonant periodic grating with period

$$\mathbf{d}\_0 = \lambda / \eta \approx 1.04 \,\upmu\text{m} \tag{1}$$

and orientation **g0 || E** written as surface relief modulation was observed. Here η is the real part of the refractive index for titanium-air boundary for surface plasmon polaritons. Their formation was due to the interference of the incident laser radiation and surface plasmon polaritons excited by it (universal polariton model (UPM) [11]).

The second type of the structures (abnormal one) was also observed in the regime of partial metal melting; it was observed predominantly on the ridges of the main resonant relief (of the first-type gratings) and had the period [5]:

of universal polariton model (UPM) of laser-induced condensed matter damage [1]. The UPM well describes the spatial periods for normally oriented (**g || E**) [2] and abnormally oriented (**g** ⊥ **E**) gratings (**g**) as for long pulse durations [3] as for ultrashort laser pulses [4, 5]. Here **E** is the electric field strength vector of incident laser radiation. In the later case, the effect exists for condensed media with different physical properties: metals, semiconductors, and dielectrics. So the peculiar directions arise due to the vector nature of light, surface plasmon polaritons [6] and channel (wedge) surface plasmon polariton [4] excitation, and participation in the interference process. The produced spatial gratings have some distribution in directions and periods for ultrashort pulse durations, but for long pulses depending on laser wavelength and optical properties of boundary materials, the periods have well-defined values. In our experiments with the incident laser radiation of nanosecond duration, the field-oriented grating is formed with periods defined not so strictly as the universal polariton model dictated.

The contemporary theory of condensed media describes the spatially hierarchical synergetic behavior of structures in solids, including under conditions of relaxation from nonequilibrium state [7]. One example is the metal recrystallization [8], including laser-induced recrystallization [9]. It is known that the process of collecting recrystallization on metal's surface caused by heating up to the melting point is followed by grain boundary movement and enlarging of their scales [10]. This is the isotropic process because of the lack of separated direction in considered system. There are known experiments on metal films deposited on dielectric substrate recrystallization under cyclic heating by laser radiation up to the melting point followed by lateral spatial grain-scale enlargement [9]. The grain-scale growth in average is isotropic due to the absence of separated direction in considered system *metal-dielectric-laser*

We studied the self-organized phenomena of micro- and nanostructure formation on metal surfaces under action of series of laser radiation pulses (λ = 1064 μm, τ = 10, 100 ns) at nearnormal incidence upon the mechanically polished titanium surface (VT—1-0). Formation of three types of structures versus the laser power density (q) and pulse number (N) was observed. At q values corresponding to partial metal melting during the pulse, the creation of

and orientation **g0 || E** written as surface relief modulation was observed. Here η is the real part of the refractive index for titanium-air boundary for surface plasmon polaritons. Their formation was due to the interference of the incident laser radiation and surface plasmon

polaritons excited by it (universal polariton model (UPM) [11]).

<sup>0</sup> d / 1.04 m =l h» m (1)

So, the problem is the physical mechanism of the observed effect.

*radiation*.

162 Study of Grain Boundary Character

**2. Results**

resonant periodic grating with period

$$\mathbf{d} = \lambda \, / \, 4\xi \approx 0.2 \, 1 \, \text{μm} \tag{2}$$

and anomalous orientation **g** ⊥ **E**. Their formation was caused by participation of the wedge surface plasmon polaritons (WSPPs) guided by ridges of the main resonant relief (structures of the first type) explained by the nonlinear mathematical model of spatial period formation [12]. Here ξ is the real part of the refractive index for wedge surface plasmon polaritons of the considered boundary.

The third type of structures was observed only for laser pulse duration τ ≈ 10 ns at q values not exceeding the material melting threshold. The produced microrelief was the quasi-grating **G**, the period of which varied by laser radiation power density and orientation was **G** ⊥ **E**. Note that in contrast to the resonant micro- and nanostructures (of first and second types), the quasi-gratings had no precise value of the period according to formula (1) or (2). So, the third type of structures could not be explained in the framework of the universal polariton model. To explain their occurrence, the original model was developed.

As the samples in experiments the VT1-0 titanium plates mechanically polished with optical quality were used (geometrical sizes: 7 mm diameter and 1 mm thickness). The Q-switched linear polarized radiation of Nd3+:Yttrium Aluminum Garnet (YAG) laser (λ = 1064 nm, τ = 10 ns, 100 ns, f ≤ 12.5 Hz) with power density q ≤ 0.5 MW/cm2 was used for sample irradiation. Laser radiation was focused by lens with focal length f = 18 cm into the typical diameter of irradiated spot (0.6 ÷ 1) mm. The sample surface reflectivity dynamics from pulse to pulse at λ = 632.8 nm was measured with the help of integrated sphere. The residual surface relief was studied by optical microscopy (preferentially in dark field) and atomic force microscopy. The main experiments were made with normal incidence of laser radiation or for p-polarized radiation and not high angles of incidence.

In experiments, the following evolution of the micro- and nanorelief was observed, which can be by convention divided by three consecutive stages. The *first stage* was the fine-scale formation of quasi-isotropic nanorelief, the typical size of which was less than the optical microscope resolution value in mode of fine-scale deformation grain boundary network. The *second stage* was the rise of mean grain-size dimension with the grain anisotropy appearance. The grain boundaries were observable with optical microscopy. This is the typical stage of collective recrystallization. At the *third stage*, the grain boundary was gradually converted into quasi-linear relief having typical size *s* ~ (4 ÷ 6) μm. The relief was formed in mode of thermal grooves (see **Figure 1**). Its quasi-grating vector **G** was near perpendicular to **E**<sup>t</sup> : Here **E**<sup>t</sup> is the tangential projection of electric field strength vector of the incident radiation. Especially note that the *s* value was power density dependent and rising with *q*. The *s* value also was varied from the center to periphery of irradiated spot (see **Figures 2** and **3**). This dependence was the indicator of that the structure appearance is not in the framework of UPM. After the action of approximately N ≥ 300 pulses at the periphery of irradiated zone, the low contrast resonant surface relief with period *d− = λ∕(η − sinθ)* (**g**<sup>−</sup> ∣∣ **E**<sup>t</sup> ) was observed for <30°. Here *θ* is the angle of incidence of laser radiation. For >30° the quasi-grating **G** disappears, and only the grating **g**− appears at the central part of spot expanding toward periphery frequently in mode of separated tracks which fill much more area with angle *θ*. Note here that the effective sources of SPP's scattering and incident laser radiation transformation into SPPs are grain boundaries (see, for instance, Ref. [13]).

**Figure 1.** Topography of titanium surface produced under the interaction of 60 pulses of linear polarized laser radiation with power density ≈0.8 MW/cm2 : (a) the initial stage of anisotropic grain growth dark-field optical microtopography, (b) the enlarged view of atomic force topography, and (c) typical profilogram of irradiated surface made along the white line indicated in (b).

Control the Metal Grain Boundary Recrystallization Evolution by the Laser Radiation Electric Field Strength... http://dx.doi.org/10.5772/66248 165

approximately N ≥ 300 pulses at the periphery of irradiated zone, the low contrast resonant

of incidence of laser radiation. For >30° the quasi-grating **G** disappears, and only the grating

**Figure 1.** Topography of titanium surface produced under the interaction of 60 pulses of linear polarized laser radia-

phy, (b) the enlarged view of atomic force topography, and (c) typical profilogram of irradiated surface made along the

: (a) the initial stage of anisotropic grain growth dark-field optical microtopogra-

 appears at the central part of spot expanding toward periphery frequently in mode of separated tracks which fill much more area with angle *θ*. Note here that the effective sources of SPP's scattering and incident laser radiation transformation into SPPs are grain boundaries

) was observed for <30°. Here *θ* is the angle

surface relief with period *d− = λ∕(η − sinθ)* (**g**<sup>−</sup> ∣∣ **E**<sup>t</sup>

(see, for instance, Ref. [13]).

164 Study of Grain Boundary Character

tion with power density ≈0.8 MW/cm2

white line indicated in (b).

**g**−

**Figure 2.** Dark-field optical microscopy image of the titanium surface spot area irradiated by linear polarized laser radiation (λ = 1064 nm, τ = 20 ns) shows the quasi-grating formation of grooves of thermal grooving.

**Figure 3.** Image of titanium surface irradiated by series of N = 62 pulses of linear polarized laser radiation with q < qmelt obtained by atomic force microscopy.

The experiments also were conducted in atmosphere of active and inert gases at atmosphere pressure. The number of laser pulses needed to produce relief of given height in inert gases was higher by (1.5 ÷ 2) times in comparison with air and was lower by (2 ÷ 2.5) times in oxygen atmosphere. As is known the formation of resonant gratings by circular polarized laser radiation is difficult because the gratings of all possible orientations (but discrete) must be produced. For this case, the degree of positive feedback via grating height occurs to be insufficient. So, in our experiments for circular polarization, neither resonant gratings nor quasi-grating formation was observed. The experiments were made at laser power density in the range (0.3 ÷ 0.8) MW/cm2 to be sure that the melting point of titanium surface will not be achieved.

To study pulse-to-pulse reflectivity dynamics of irradiated area, the integrated sphere and probe radiation (λ = 632.8 nm) were used. The time dependence of surface absorptivity has shown the shallow minima for N ≈ 40 followed by gradual rise. The absorptivity change at minima was ΔA = A0 − Amin ≤ 0.14, where A0 is the initial absorptivity value and the Amin value corresponds to surface absorptivity minima; the initial value is A0 = 0.5 (see, for instance, Ref. [14]). In our experiments, the final value of A was near 1.2 A0.

The dynamics of surface relief changes was caused by grain boundary displacement in the surface layer of the order of the depth of surface layer pulsed heating. The local minima existence in the function A = A(N) is the consequence of two following process competitions, namely, the collective recrystallization which enhances the optical properties and causes the metal absorptivity falling and oxygen dissolution in metal skin layer and surface oxide film growth cause the absorptivity rising. The experimentally observed evolution of the surface relief on the initial stage is the consequence of technique of its polishing. Really, in the process of mechanical polishing, the metastable highly cold-hardening layer of titanium is formed having properties approaching to ones of amorphous metal. The action of repetitive pulses of laser radiation leads to more equilibrium metal state through the recrystallization process [10]. So in a whole, the process is followed by sufficient grain-size growth of surface layer.

Next discuss the quasi-grating vector **G** orientation correlated with the laser radiation polarization origin. The propagation directions of excited SPPs are mainly along the *E<sup>t</sup>* vector. That is why SPPs most efficiently interact with grain boundaries which have orthogonal to **E**<sup>t</sup> orientation. The directional SPP's propagation causes the appearance of current of electrons in metal skin layer [15, 16]. The current appears due to the tangential component of the Lorentz force *Ft* ~ [*v* x *H* ] where *v* is the electron velocity and *H* is SPP's magnetic field strength vector. The action of the SPP's vertical component of electric field strength vector (*Ez*) accelerates the skin-layer electrons in vertical direction (*vz*) which produces the Lorentz force component along SPP's propagation direction, **F***<sup>t</sup>* ||(*ks*/*ks*). The sign of vertical component of the electric field strength (*Ez*) is changing simultaneously with the sign of magnetic field strength (*H* ) that is why the direction of the Lorentz force component **F***<sup>t</sup>* always remains along the SPP propagation direction *ks*/*ks*.

The directed flux of electrons interacts with grain boundaries as with a wall, thus supplying an additional force action and directed grain displacement. Obviously, maximal momentum will transfer to the deformation boundary, which is orthogonal to the SPP's propagation direction. In such a way, the anisotropy of grain growth is rising.

**Figure 4.** Scheme illustrated the subsequent grain boundary evolution under their interaction with directed flux of skin-layer electrons dragged by laser-excited surface plasmon polaritons. The progressive stages of the grain growth are shown in (a), (b), and (c). The vector orientation of quasi-grating formed at the final stage is *G* ⊥ *Et*.

The process of quasi-grating formation occurs with positive feedback. Qualitatively, the directed flux of electrons action is mostly effective for the grain boundary orientation *n* || *ks*, where *n* is normal to the grain boundary laying in the plane of irradiated surface and *ks* is the wave vector of SPP's. Taking in mind the grain boundary continuity, the neighbor boundary areas' curvature reduces. This enhance the efficiency of SPP's excitation (in given direction). This brings about the rise of Lorentz force Ft acting on grain boundaries of neighbor grains for which the direction of normal n is nearly parallel to *E<sup>t</sup>* , (**Figure 4**) This process takes place with the positive feedback and spreads over the irradiated zone. Finally, the self-consistent situation arises in which effective SPP's excitation is realized mainly on almost linear grain boundaries with *n* || *ks*. The process is stabilized when SPP's intensity is insufficient to move the grain boundary and their energy is dissipated into the metal. Such situation occurs for the optimal values of typical distances between the neighborhood grooves of formed quasi-gratings of the order of SPP's propagation length *L = 1/α*, where α is the attenuation coefficient of the metalair boundary for SPPs. The spatial areas of irradiated spot with higher laser radiation intensity are awaited to have the quasi-grating periods higher than for lower power density areas due to nearly linear dependence of excited SPP's intensities on the intensity of incident radiation. This conclusion is supported by our experimental results.

corresponds to surface absorptivity minima; the initial value is A0 = 0.5 (see, for instance, Ref.

The dynamics of surface relief changes was caused by grain boundary displacement in the surface layer of the order of the depth of surface layer pulsed heating. The local minima existence in the function A = A(N) is the consequence of two following process competitions, namely, the collective recrystallization which enhances the optical properties and causes the metal absorptivity falling and oxygen dissolution in metal skin layer and surface oxide film growth cause the absorptivity rising. The experimentally observed evolution of the surface relief on the initial stage is the consequence of technique of its polishing. Really, in the process of mechanical polishing, the metastable highly cold-hardening layer of titanium is formed having properties approaching to ones of amorphous metal. The action of repetitive pulses of laser radiation leads to more equilibrium metal state through the recrystallization process [10].

So in a whole, the process is followed by sufficient grain-size growth of surface layer.

polarization origin. The propagation directions of excited SPPs are mainly along the *E<sup>t</sup>*

Next discuss the quasi-grating vector **G** orientation correlated with the laser radiation

That is why SPPs most efficiently interact with grain boundaries which have orthogonal to **E**<sup>t</sup> orientation. The directional SPP's propagation causes the appearance of current of electrons in metal skin layer [15, 16]. The current appears due to the tangential component of the Lorentz force *Ft* ~ [*v* x *H* ] where *v* is the electron velocity and *H* is SPP's magnetic field strength vector. The action of the SPP's vertical component of electric field strength vector (*Ez*) accelerates the skin-layer electrons in vertical direction (*vz*) which produces the Lorentz force component

field strength (*Ez*) is changing simultaneously with the sign of magnetic field strength (*H* ) that

The directed flux of electrons interacts with grain boundaries as with a wall, thus supplying an additional force action and directed grain displacement. Obviously, maximal momentum will transfer to the deformation boundary, which is orthogonal to the SPP's propagation

**Figure 4.** Scheme illustrated the subsequent grain boundary evolution under their interaction with directed flux of skin-layer electrons dragged by laser-excited surface plasmon polaritons. The progressive stages of the grain growth

are shown in (a), (b), and (c). The vector orientation of quasi-grating formed at the final stage is *G* ⊥ *Et*.


always remains along the SPP propa-

vector.

[14]). In our experiments, the final value of A was near 1.2 A0.

along SPP's propagation direction, **F***<sup>t</sup>*

gation direction *ks*/*ks*.

166 Study of Grain Boundary Character

is why the direction of the Lorentz force component **F***<sup>t</sup>*

direction. In such a way, the anisotropy of grain growth is rising.

Let us estimate the value of SPP's attenuation coefficient α using the tabulated optical constants for *λ* = 1064 nm [14]:

$$\alpha = 2\operatorname{Im} k\_s = 2k\_o \left(\frac{\varepsilon\_m}{\varepsilon\_m + 1}\right)^{1/2}.\tag{3}$$

Here *ks* is the SPP's wave vector's module, *εm* is titanium metal complex dielectric permittivity, k0 = ω/c is the wave number of laser radiation in vacuum, ω is the circular frequency of laser radiation, and *c* is the velocity of light in vacuum. The estimate based on expression (3) and optical constants of titanium for *λ* = 1064 nm shows that the SPP's propagation length *L = α*−1 *≈* 4*λ* for *λ* = 1064 nm and this value well coincides with experimentally measured value *s* ≈ 5 μm. For surface areas with higher power density, the *s* value may reach (6 ÷ 6.5) μm (see **Figure 2**).

The driving force to displace the grain boundaries is the result of the flux of moving electrons dragged by SPP's interaction with grain boundaries, is limited in depth by titanium skin layer, and is of the order lower than the thermal heating depth. The skin-layer size spatial localization of driving force makes the boundaries displacement process easier. At the final stage of evolution, the *G* quasi-grating relief performs the nearly parallel and equidistant grooves of thermal etching (see **Figures 5a**, **5b**, and **1c**), having the inverse knife structure shapes with the depth up to 500 nm. The cross section of groove has radius of tip curvature of the order 50 nm or less, and dihedral angle at the tip is of the order 120°.

**Figure 5.** (a) Enlarged fragment of surface area of produced thermal grooves and (b) cross-sectional profile of surface obtained along white horizontal line of **Figure 4a**.

From **Figure 3**, it follows that as a result of multipulsed irradiation, the titanium surface locally becomes sufficiently more smooth than the initial one (surface roughness after surface mechanical polishing, stretching, and so on is smoothing; see **Figure 1b**). This is a well-known result of material redistribution caused by surface atom diffusion [17].

The inverse knife-shaped metal groove can support the channel surface plasmon polariton (CSPP) propagation [3, 5, 18]. In considered geometry of experiment, the direction of quasigrating vector is orthogonal to laser radiation polarization *Et*. For efficient excitation of CSPP, the electric field strength component of incident radiation must be maximal. So, the metal surface covered with quasi-grating has anisotropic absorptivity due to CSPP excitation and dissipation of their energy into heat. It is known that micro- and nanostructured metal surface also has anisotropy of electrical properties [19].

Note that the effect of the electrons drag by surface plasmon polaritons becomes apparent in the surface current in metal skin layer [12, 15] and in the *lateral* flux of relativistic electrons in vacuum under the metal surface irradiation by exawatt laser power density (pulse duration less than 1 ps) [20].

One may wait that the discovered effect may be well observable for powerful ultrashort laser pulse interaction with metals. Really, the experimental data for the multipulsed laser interaction with metals and alloys have been published for femtosecond pulse durations followed by quasi-grating **G** ⊥ **E** formation for titanium metal [21, 22] and Ti-based alloy Ti-Zr-Cu-Pd [23] without any suggestions about the origin of their appearance (see **Figure 6**). From our opinion the production mechanism of quasi-grating **G** superimposed on the **g** ∣∣ **E** resonant grating is analogous for one suggested for nanosecond irradiation regime. Note that the thermal etching groove formation is inherent to (poly)crystalline materials, but the alloy Ti-Zr-Cu-Pd is the amorphous one. In fact under the alloy heating up to high temperature, the alloy transfers from its metastable state to the crystalline one, and the suggested model works further.

Control the Metal Grain Boundary Recrystallization Evolution by the Laser Radiation Electric Field Strength... http://dx.doi.org/10.5772/66248 169

**Figure 6.** The quasi-periodic microrelief obtained on a titanium surface under the action of ultrashort pulses (τ = 150 fs, λ = 800 nm, pulse-repetition rate 1 kHz, N =10) for energy densities Q = 0.25 J/cm2 (a) and (d), 0.75 J/cm2 (b) and (e), and 1.5 J/cm2 (c) and (f) at low (upper row) and high magnification (lower row), **g** ⊥ **E**<sup>t</sup> [21].

In one of the previous models proposed for explanation of spatial periodic relief on metal surfaces under ultrashort laser illumination [24], the process was considered with nucleation in a distended metal and the ensemble of cavitating bubble self-ordering [24]. According to authors [24] and physics of the process, the orientation and periods of produced nanostructures are independent on laser radiation polarization and wavelength, accordingly. The typical power densities of laser radiation must be higher than in our consideration. In this model, the predicted spatial periods are of the laser heating depth (10 ÷ 100) nm order. Hence, the model [24] is not applicable for our case.
