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The structural changes inside rock-salt crystals after femtosecond (fs) laser irradiation are investigated using a microscopic pump-probe technique and an elastic simulation. The pump-probe imaging shows that a squircle-shaped stress wave is generated after the fs laser irradiation as a result of the relaxation of thermal stress in the photoexcited region. Pump-probe crossed-Nicols imaging and elastic simulation elucidate that shear stresses and tensile stresses are concentrated in specific regions during the propagation of the stress wave. The shear stresses and tensile stresses observed in this study can explain the characteristic laser-induced structural changes inside rock-salt crystals.
©2011 Optical Society of America
1. Introduction
Understanding the tendency and mechanism of deformation is very important for the improvement of machining techniques of crystalline materials, because the characteristic deformations that appear in these materials during machining are dependent on their atomic arrangements [1]. The two most important types of deformation inside crystals are dislocation and cleavage (formation of a crack) [2–8]. Dislocation is important for understanding the deformation process of crystals, because plastic deformation is always accompanied by the formation of dislocations [4], and the crystal’s elastic properties change as the dislocation density increases [6, 8]. For instance, a slip deformation is facilitated by the formation of a dislocation [2], and the strength of a crystal changes with the density of the dislocations during deformation [6]. The process of cleavage has been recognized since ancient times, and has been utilized to make a smooth plane in a crystal, split a crystal sharply, and so on [7].
Laser machining inside transparent crystalline materials is also often accompanied by characteristic deformations [9–11]. For example, when a focused femtosecond (fs) laser pulse is incident inside a MgO crystal, which has a rock-salt structure [12], the volume around the focus is photoexcited due to nonlinear photoionization, and a characteristic structural change occurs due to the photoexcitation. When the incident direction is normal to the (001) plane, the structural change is often accompanied by the formation of highly concentrated dislocation bands and cleavage in the <110> and <100> directions from the photoexcited region [11]. These characteristic structural changes should be determined by the crystal structure, because they have also been observed in a LiF crystal, which belongs to the same class of crystal structure as the MgO [2, 3].
However, from a dynamical viewpoint, the mechanism of the structural changes inside these crystals during a fs laser machining is not yet understood. From a static perspective, the slip and cleavage systems can be understood from the atom arrangement and bond strengths [2, 3]. For example, in fcc crystals, a slip occurs in the <110> direction, and a cleavage occurs along the (001) plane [2–4]. Only these systems, though, cannot explain the direction-dependent deformation induced by fs laser irradiation inside crystals, because the external forces that induces the slip and cleavage in the specific directions have not been elucidated. Therefore, it is essential to observe the dynamics of the deformation in order to understand the origin of the structural changes. A number of researchers have observed the generation of a stress wave as a result of the relaxation of thermal energy, which is localized around the photoexcited region after fs laser irradiation inside transparent materials [13–16]. Although it is possible that the localized thermal stress and the stress wave play important roles in the formation of dislocation and cracks, there has not been any clear explanation on the mechanism of the formation of the dislocation bands and cleavage after the laser irradiation. In this study, we observe the transient stress distribution inside MgO and LiF rock-salt crystals, using pump-probe microscopic imaging after focusing a fs laser pulse, and investigate the relation between the laser-induced stress wave and the structural changes.
2. Methods
2.1 Pump-probe transmission imaging
Figure 1 (a) shows a schematic illustration of a pump-probe microscopic imaging system with a fs laser pulse. Fs laser pulses came from a Ti-sapphire laser with a regenerative amplifier (the central wavelength was 800 nm, the pulse duration was 120 fs, and the repetition rate was 50 Hz; Mira-Legend, Coherent Inc.). The laser pulse was divided by a beam splitter. One beam was used as a pump pulse; it was focused inside a sample using an objective lens (Nikon, LU Plan 50×, N.A. = 0.9). The other beam was passed through a BBO (β-BaB2O4) crystal and the second harmonic was generated. The second harmonic was used as a probe pulse, which was delayed by an optical delay line and then passed through the sample from the opposite direction to that of the pump pulse. The transmitted probe pulse was collected by the objective lens, and the image of the transient structural change around the photoexcited region was focused on a charge coupled device (CCD) camera (HAMAMATSU; C10054-03).
Fig. 1 (a) Schematic illustration of the pump-probe microscopic imaging with a fs laser machining system. (b) Schematic illustration of the incident of the focused pump pulse inside a sample (left), and the crystal structure of MgO or LiF (right).
The sample was a MgO or LiF single crystal, in which the (001) surface had been cleaved and optically polished (denoted by MgO(001) and LiF(001), respectively). The sample volume was 10×10×0.5 mm. As shown in Fig. 1(b), the incident direction of the pump pulse was normal to the (001) plane, and the depth of the photoexcited region from the surface was about 200 μm. During observation, the sample was translated normal to the pump beam at a speed of 10 mm/s to avoid multiple photoexcitations at the same position. The polarized direction of the probe pulse was controlled by a half wave plate and a polarizer. A linearly polarized probe pulse was used in both the transmission and crossed-Nicols imaging, although the polarization direction was not important in the transmission imaging. An analyzer was used to select the polarization of the transmitted probe pulse in the crossed-Nicols imaging, but this was removed from the optical setup in the transmission imaging.
2.2 Simulation of stress relaxation dynamics
After irradiation by a strong laser pulse inside transparent materials, stress is generated as a result of temperature elevation and material property change [15, 16]. The origin of the material deformation around the photoexcited region is the relaxation of the stress in this region. Therefore, we simulated the stress relaxation dynamics based on the elastic dynamics. We assumed that the stress would come from the temperature elevation, and that the temperature elevation would occur much faster than the stress relaxation. For simplicity, the temporal evolution of the temperature distribution change was expressed by:
where t is the time after the temperature increase due to photoexcitation, r ( = (x, y, z)) is the position, ΔT is the temperature increase at the center, wth is the radius of the temperature distribution, and τth is the rise time of the temperature elevation. Based on elastic mechanical theory, the response to a temperature change in an anisotropic material can be calculated by the following wave equation [13, 16, 17]:where ρ is the density, u( t,r) is the displacement vector, ∇=(∂/∂x, ∂/∂y, ∂/∂z), P(t, r) is the stress tensor, and β is the thermal expansion coefficient. The stress tensor is expressed by the elastic tensor of the crystal C and the strain tensor E(t, r) as follows: C is material-dependent. In the case of a rock-salt crystal [3, 17], the explicit expression of C can be simplified as:The elements in the elastic tensor of MgO and LiF, and other properties, are shown in Table 1 [18–21]. Using these elastic parameters, we obtained the temporal evolution of u(t, r) by calculating Eq. (2) numerically with the following initial and boundary conditions:
Table 1. Densities, Thermal and Elastic Properties of MgO and LiF Crystals.
In fact, the choice of the boundary conditions is unimportant, because the calculation was stopped when the deformation induced by the temperature change reached the boundary. Using the calculated u(t, r), we obtained the temporal evolution of the density and strain distributions.
3. Results and discussion
3.1 Fs laser-induced deformation inside MgO(001) and LiF(001)
Figure 2(a) is a transmission optical microscope image of the modification inside a MgO crystal after focusing a single fs laser pulse of 10 μJ from the (001) direction. The morphology of the modification did not depend on the polarization of the laser pulse. The modification consists of a circular void at the center and a dark cross pattern in the <110> direction from the center. According to a study by Kanehira et al. [11], it has been found that the void-like structure at the center consists of nanocracks and a dislocation. The dark cross-shaped pattern was attributed to highly-concentrated dislocation bands, in which the slip direction is <110>, based on observations with a transmission electron microscope. The dislocation in the region of the dark cross can also be confirmed by the crossed-Nicols image from a polarization microscope (Fig. 2(b)), in which the polarization plane of the illumination light was parallel to the (100) plane and the analyzer selected a (010) polarized light. The crossed-Nicols image of the modification shows that light transmission is greater in the cross-shaped region. This image shows that the stress in the <100> direction appeared in the cross-shaped region. Because stress is generated around a dislocation, the bright cross-shaped pattern in the crossed-Nicols image confirms the formation of dislocations in this region. With a much larger excitation energy (>30 μJ/pulse), cracks appeared along the <100> direction from the center.
Fig. 2 (a), (b) Optical microscope images (transmission and crossed-Nicols images, respectively) of MgO after irradiation with a single focused fs laser pulse. The red arrow in (b) indicates the polarization direction of the illumination light. (c), (d) Those of LiF.
Figure 2(c) is a transmission optical microscope image of the modification inside a LiF crystal after focusing a single fs laser pulse of 5 μJ. A void appeared in the photoexcited region and cleavages occurred in the <100> direction from the center. Although we could not determine the specific threshold of the cleavage, we found that the threshold of cleavage in a LiF crystal was lower than 1 μJ/pulse, which is much lower than that in a MgO crystal (higher than 30 μJ/pulse). The much lower threshold is consistent with a report on nanosecond laser-induced cracks in MgO and LiF crystals [10]. However, modifications along the <110> lines, which correspond to the dark cross pattern of dislocation bands inside a MgO crystal (Fig. 2(a)), were too weak to observe in the transmission image. They could only be observed in a crossed-Nicols image (Fig. 2(d)). The smaller modifications in the <110> direction inside a LiF crystal suggest that the energy given by the photoexcitation was used both for cleavages in the <100> direction and the formation of dislocations in the <110> direction.
The modifications caused by a fs laser focusing inside MgO and LiF crystals are summarized as follows:
- (i) A circular void appears in the photoexcited region.
- (ii) Dislocation bands appear in the <110> direction from the photoexcited region.
- (iii) Cleavages occur in the <100> direction.
- (iv) The threshold of cleavage in a LiF crystal is much lower than that in a MgO crystal.
3.2 Pump-probe imaging of MgO
Figure 3 shows transmitted light distributions of a probe beam at various time delays after photoexcitation inside a MgO(001) crystal by a 20 μJ pump pulse. Under this irradiation condition, no crack is formed inside the MgO crystal. The photoexcited region became dark at 0 ps, and after 1 ps the center became darker and the surrounding region became brighter. The change around 0 ps can be attributed to an optical Kerr effect of the pump pulse, because it disappeared over the duration of the pump pulse. The dark region surrounded by a bright ring at 1 ps remained unchanged until 20 ps. After 20 ps, the shape of the central region changed gradually, and a squircle-shaped wave was generated and propagated away from the surrounding region. The velocity of the wave in the <100> and <110> directions was 9.4 μm/ns and 10.6 μm/ns, respectively. The direction-dependent velocity comes from the anisotropy of the elastic properties of a MgO crystal. The sound velocity can be calculated as v <100> = 9.11 μm/ns and v <110> = 9.92 μm/ns, using the theoretical equations for the sound velocity of plane waves [17]:
Fig. 3 Transmission images of a probe beam through a MgO crystal at various time delays after photoexcitation by a focused 20 μJ fs laser pulse (Media 1).
As these sound velocities are similar to those of the observed wave, the squircle-shaped wave must be a stress wave, generated by the relaxation of thermoelastic stress in the photoexcited region. The small difference between the calculated and observed values is due to the difference in shape between the observed stress wave and those for Eqs. (6) and (7), which give the velocities of plane waves.
To obtain the transient stress distribution clearly, crossed-Nicols images were taken under the same irradiation condition. The crossed-Nicols images of the (100) and (110) polarized probe beams at various time-delays are shown in Figs. 4 (a) and (b) , respectively. In the following discussion, we call them the (100) crossed-Nicols image and the (110) crossed-Nicols image. In the (100) crossed-Nicols images, a bright wave propagated in the <110> directions from the photoexcited region, and a bright cross-pattern appeared around the photoexcited region. The bright regions in the (100) crossed-Nicols images imply that stresses in the <110> directions have appeared in these regions. On the other hand, in the (110) crossed-Nicols images, the wider bright wave propagated in the <100> direction, which means that the stresses in the <100> direction appeared in the bright region. Comparing them with the transmission images, we conclude that these propagating bright regions are identical to the stress wave.
Fig. 4 Crossed-Nicols images at various time-delays after photoexcitation by a focused 20 μJ fs laser pulse inside a (001) MgO crystal (Media 1). (a) (100) crossed-Nicols images, in which the direction of the polarization plane of the probe beam was (100) and that of the analyzer was (010). (b) (110) crossed-Nicols images.
In the (110) crossed-Nicols images, we observed other bright regions propagating in the <100> direction inside the squircle-shaped stress wave. We call this propagating bright region an “inner stress wave”, and the squircle-shaped wave is a “primary stress wave”. While the inner stress wave was visible in the (110) crossed-Nicols images, it was hardly observed in the (100) ones. This means that the direction of the stress in the inner stress wave is parallel or perpendicular to the (100) plane. The effect of the inner stress wave on the structural change will be discussed later.
While a cross pattern along the <110> lines was clearly observed in the transmission optical microscope image after photoexcitation, this feature was not visible in the pump-probe transmission images. Although there is no clear explanation for this, we tentatively interpret it that the density of the dislocations along the <110> lines was too small to be observed several nanoseconds after the photoexcitation. It has been known for the multiplication and diffusion of dislocations to occur under stress loading [2, 3]. The pump-probe crossed-Nicols images (Fig. 4) show that the thermal stress remained around the photoexcited region at 4 ns. This thermal stress could induce the multiplication and diffusion of dislocations over much longer time periods (~microseconds), and, as a result, the cross pattern of the dislocation may become visible after a long time, as shown in Fig. 2(a).
3.3 Pump-probe imaging of LiF
Figure 5(a) shows pump-probe transmission images following photoexcitation inside a LiF(001) crystal by a 10 μJ pump pulse. Generation of the squircle-shaped stress wave, as well as the formation of cracks along the <100> direction, was observed in the LiF crystal. The temporal evolution of the position of the stress wave on the <100> line and the edge of the crack is shown in Fig. 5(b). The evolution suggests that the crack propagation should be accompanied by the propagation of the stress wave. The cracks elongated at about 3.2 μm/ns, which was about half the speed of the stress wave in <100>. Considering that the velocity of the inner stress wave in a MgO crystal was also about half that of the primary stress wave, the inner stress wave appears to be responsible for the elongation of the crack. The role of the inner stress wave on the elongation of cracks will be described by an elastic simulation in the following section.
Fig. 5 (a) Transmission images of a probe beam inside a LiF(001) crystal after photoexcitation by a focused 10 μJ fs laser pulse. (Media 2) (b) Temporal evolution of the position of the stress wave on the <100> line (blue open squares), those of the edge of the crack (red filled circles) and the inner stress wave in the simulation.
The pump-probe crossed-Nicols images inside the LiF crystal are shown in Fig. 6 . The (100) crossed-Nicols images were similar to those of a MgO crystal, i.e., the bright regions propagated in the <110> directions and a bright cross-shaped pattern appeared in the <110> direction around the photoexcited region. In contrast, the (110) crossed-Nicols images were completely different from those of a MgO crystal. The (110) crossed-Nicols images of MgO and LiF crystals at 3000 ps are compared in Fig. 6(c); in a MgO crystal, the bright regions inside a primary stress wave are separated from the primary stress wave. As described in section 3.2, the bright regions correspond to the inner stress wave. On the other hand, in a LiF crystal, four fan-shaped bright regions spread from the edge of the cracks to the primary stress wave. The difference in these (110) crossed-Nicols images corresponds to the difference in the distribution of the stress in the <100> directions. Because the main difference between the modifications inside MgO and LiF crystals is the occurrence of cleavage (Fig. 2 and Fig. 6(c)), the distribution of the <100> stress could be modified by the crack formation. The main region of different stress distribution is located around the inner stress wave. As elucidated by the elastic simulation in the following section, a tensile stress is generated in the inner stress wave. When there is no crack formation, the material which is expanded by the tensile stress can return to its original position after the inner stress wave passes away (red arrows in Fig. 6(c)). On the other hand, when there is a crack formation, the material that is expanded by the tensile stress cannot return to its original position and the tensile stress remains (light blue arrows in Fig. 6(c)). The difference in material dynamics with and without crack formation is thus responsible for the different stress distributions.
Fig. 6 (a), (b) Pump-probe crossed-Nicols images after fs laser irradiation inside a LiF crystal (Media 2). (c) Comparison of pump-probe images at a time-delay of 3000 ps; the transmission and (110) crossed-Nicols images of a MgO (left) and LiF crystal (right). The red and light blue arrows indicate the stress directions.
3.4 Simulation of stress relaxation dynamics
The stress relaxation dynamics following sudden heating inside a MgO crystal were simulated using parameter values of ΔT = 1,000 K, wth = 2.0 μm, and τth = 1 ps. In practice, τth does not influence the simulated stress relaxation dynamics when it is smaller than 10 ps, because the stress relaxation occurs much more slowly than the heating [13]. Therefore, we chose the simple value of τth = 1 ps for the simulation. In addition, the amplitude of the stress is nearly proportional to ΔT, because Eq. (2) is almost a linear differential equation, and hence we chose the value ΔT = 1,000 K. The radius of the temperature distribution, wth = 2.0 μm, was based on an estimate of the radius of the photoexcited volume.
Figure 7(a) shows the simulated density distributions at various times after the sudden heating inside a MgO crystal. Thermal expansion occurred in the heated region over several hundred ps, and, at the same time, the materials around the heated region were gradually compressed. After that, the compressed regions propagated away from the heated region. The propagation rate depended on the direction, which resulted in the generation of the squircle-shaped stress wave. The propagation rates were 9.24 μm/ns in <100> and 10.1 μm/ns in <110>, which were the same as those determined from the pump-probe observation within the width of the stress wave. The calculation results for a LiF crystal were qualitatively similar to those of MgO. The propagation rates in a LiF crystal were 6.7 μm/ns in <100> and 7.2 μm/ns in <110>. There was no crack formation in the simulation, because the disruption of chemical bonds, which is the seed of a crack, was not taken into consideration. As molecular dynamics must be considered in the simulation in order to model bond disruption, the simulation of cleavage will be a future subject of research.
Fig. 7 (a) Simulated temporal evolution of density distributions after a temperature increase at the center of a MgO crystal in 1 ps. (b)–(d) The lattice deformations in the (001) plane at 2000 ps in three regions: (b) Around the primary stress wave around the <110> line, (c) around that around the <100> line, and (d) around the inner stress wave.
This simulation provides us with the transient strain distributions. To elucidate the mechanism of the observed characteristic structural changes, we focused the strain distributions along the <100> and <110> lines in the primary stress wave and the strain distributions around the inner stress wave. The simulated strain distributions at 2000 ps are shown in Figs. 7(b)–(d) by the lattice deformation in the (001) plane, which includes the center of the heated region. Comparing the strain distributions in the stress wave (Figs. 7(b) and 7(c)), the compression of the lattice is larger in the stress wave along the <110> line. In addition, the shear strain between the adjacent lattices is larger around the <110> line, which is consistent with the pump-probe (100) crossed-Nicols images. On the other hand, the shear strain is much smaller in the stress wave around the <100> line, because the lattices in this region are compressed almost exclusively in the <100> direction. In the region around the inner stress wave (Fig. 7(d)), the lattice is expanded in the direction normal to the propagation direction. This expansion corresponds to the tensile stress normal to the <110> line. In Fig. 5(b), the positions of the inner stress wave are plotted against time. This plot shows that the inner stress wave, i.e., the tensile stress, is located at nearly the same position as the edge of the crack observed in a LiF crystal. Therefore, we conclude that the tensile stresses in the [010] and [0ī0] directions could facilitate the propagation of the crack in the [100] direction.
3.5 Mechanism of dislocation generation along <110>
Based on the pump-probe imaging and elastic simulation of MgO(001) and LiF(001) crystals following fs laser focusing, we found that the anisotropic elastic properties of the crystals resulted in the generation of squircle-shaped stress waves and the concentration of stresses at specific directions from the photoexcited region. The pump-probe (100) crossed-Nicols images (Figs. 4(a) and 6(a)) show that the stress in the <110> direction is concentrated in the stress wave around the <110> lines from the photoexcited region. The simulated lattice deformation in this region shows that this stress concentration induces the largest lattice compression and shear strain between adjacent lattices. Therefore, the origin of the dislocation bands along <110> inside MgO and LiF crystals can be attributed to the large compression and shear strain in this region induced by the primary stress wave. We speculated that the densification and shear strain in the stress wave could facilitate the dissociation of Mg–O bonds and the slip in the MgO crystal, which could be the seed of dislocations.
The optical microscope images after fs laser irradiation inside the crystals showed that there was no dislocation around the <100> lines, although the stress wave had also propagated in the region. Based on the pump-probe (110) crossed-Nicols images and elastic simulation, the stress wave propagating in the <100> direction compresses the material almost exclusively in the <100> direction, and generates little shear strain between adjacent lattices. Because <100> is parallel to the direction of the Mg–O bond, it is difficult for the stress to dissociate this bond. Therefore, the stress wave around the <100> lines cannot initiate the generation of dislocations.
3.6 Mechanism of crack generation along <100>
When a fs laser pulse is focused inside a LiF crystal, cleavages occur in the <100> direction from the photoexcited region [10]. The pump-probe imaging showed that the cracks were generated and elongated during the elastic relaxation. Comparison of the positions of the primary stress wave and the edge of the crack suggests that the driving force of the crack elongation could not come from the primary stress wave, because their propagation rates differed by a factor of two. On the other hand, the propagation velocities of the inner stress wave and the edge of the crack are almost the same. In addition, according to the elastic simulation, there are tensile stresses normal to the (010) plane in the inner stress wave (Fig. 7(d)). Because the tensile stress at the edge of the crack can rapture the crack, we can conclude that the tensile stress in the inner stress wave must be responsible for the propagation of the crack in a rock-salt crystal following fs laser irradiation.
4. Conclusion
Pump-probe microscopic imaging and an elastic simulation elucidated that photoexcitation by a fs laser pulse inside a rock-salt crystal caused a sudden stress in the photoexcited region, and the relaxation of this stress resulted in the generation of a squircle-shaped primary stress wave and an inner stress wave. The primary stress wave concentrated a compressive stress and shear stress along the <110> line from the photoexcited region, which could be the origin of the dislocation bands around the <110> line. In contrast, the inner stress wave generated tensile stresses normal to the <100> line. The positions of the edge of the crack and the inner stress wave were almost the same, and therefore the inner stress wave must be responsible for the cleavage in <100> following fs laser irradiation.
Acknowledgments
This work was supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), 2010, No. 22750187 and Amada foundation for metal work technology.
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