Increasing Laser Power Research Articles

The Effect of Process Parameters on the Temperature and Stress Fields in Directed Energy Deposition Inconel 690 Alloy.

Additive manufacturing (AM) technology has the advantages of designability, short process times, high flexibility, etc., making it especially suitable for manufacturing complex high-performance components for high-end industrial systems. However, the intensive temperature gradients caused by the rapid heating and cooling processes of AM can generate high levels of residual stresses, which directly affect the precision and serviceability of the components. Taking Inconel 690 alloy, which is widely used in nuclear power plants, as the research object, a thermo-coupled mechanical model of temperature field and residual stress field of directed energy deposition (DED) of Inconel 690 was established based on ABAQUS 2019 finite element software to study the influence of process parameters on the temperature history and the distribution of residual stresses in the DED process. The experimental results show that the peak temperature of each layer in the fabrication process increases with the increase in laser power and preheating temperature, and decreases with the increase in scanning speed and interlayer dwell time. Substrate preheating only has a large effect on the peak temperature of the first four layers. Residual stresses are mainly concentrated in the upper and middle parts, the bottom of the substrate, and the sides combined with the substrate, and the residual stresses increase with the increasing laser power and decrease with the increasing interlayer dwell time. Decreasing laser power, longer dwell time, higher preheating temperature, and appropriate scanning speed are beneficial for the reduction in residual stresses in Inconel 690 components. This research has important significance for the process design and residual stress modulation in the additive manufacturing of Inconel 690 alloy.

An experimental study on the effect of CO2 laser powers on melting characteristics of clear ice – Part II: Vertical irradiation

Icing phenomenon widely exists and plays negative effects in aviation and electricity fields. Laser deicing technology is a typical non-contact and high-efficiency deicing method. To accurately predict and control the laser-induced ice melting process, an experimental study on melting characteristics of clear ice under vertical CO2-laser irradiation and natural convection is carried out, with the laser power varied at a range of 20–60 W. As resulted, the axial melting rate tends to increase and then decrease with the increase of laser power. The maximum of average and instantaneous axial melting rate at 40 W are 5.85 mm/s and 13.95 mm/s, respectively. The higher the laser power, the larger the peaks of maximum melting length. At 20 W and 60 W, the peaks of maximum melting length are 10.51 mm and 12.19 mm, respectively. There is little correlation between the deflection of angle and laser power. At 30 W and 50 W, the maximum angles of melting length are 0.77° and 2.52°, respectively. When the melting depth is smaller than 81.5 mm, the maximum energy efficiency at 20 W is 64.8 %, while when it is greater than 81.5 mm, the maximum energy efficiency at 60 W is 63.6 %. Results of this study are meaningful for the optimization of laser deicing technology.

Evolution mechanism of scratch removal based on the implementation of magnetorheological finishing.

Scratches on optical components induce laser damage and limit the increase in laser power. Magnetorheological finishing (MRF) is a highly deterministic optical manufacturing technology that can improve the surface roughness of optical components. Although MRF has exhibited significant potential for reducing subsurface damage and removing scratches, the principle and mechanism behind the scratch removal are not sufficiently understood. In this study, the theory of fluid mechanics is used to analyze the pressure, velocity, and particle trajectory distribution near a scratch. A physical model was developed for the differential removal of scratches at the bottom and surface of the optical components. The morphological evolution of the scratch was predicted during removal, and detailed experiments were performed to verify the effectiveness of the proposed model. The results indicate that scratches expand laterally rather than being completely removed. Furthermore, scratch removal efficiency is greater when the removal direction is perpendicular to the scratch rather than being parallel. This study offers an intrinsic perspective for a comprehensive understanding of the MRF technique used for scratch removal, which can be beneficial for removing scratches from aspherical optical systems.

The Effect of Laser Power on the Microstructure and Wear Resistance of a Ni3Al-Based Alloy Cladding Layer Deposited via Laser Cladding

A coating prepared via laser cladding has the advantages of a high-density reinforced layer, a low matrix dilution rate, and combination with matrix metallurgy. In this study, Ni3Al-based alloy cladding layers with Cr7C3 were prepared via laser cladding, and the corresponding microstructures and wear resistance were studied in detail. The results show that the Ni3Al-based cladding layer prepared using laser cladding technology had good metallurgical bonding with the matrix, and there were no pores, cracks, or other defects on the surface. The microstructures of the laser cladding layer were mainly γ′-Ni3Al, β′-NiAl, and in situ C7C3. As the laser power increased, the heat input increased, resulting in an increase in the dilution rate. Simultaneously, the carbide size in the laser cladding layer increased. With the increase in laser power, the hardness of the laser cladding layer of the Ni3Al-based alloy decreased, and the wear resistance of the laser cladding layer first strengthened and then weakened. When the laser power increased to 2.0 kW, the wear rate of the laser cladding layer decreased to 0.480 × 10−5 mm3/N·m. When the laser power increased to 2.4 kW, the wear rate of the laser cladding layer increased to 0.961 × 10−5 mm3/N·m, which was twice the rate at 2.0 kW. This could be attributed to small Cr7C3 particles, which could not effectively separate the wear pairs, resulting in more serious adhesive wear. Large Cr7C3 particles caused the surface of cast iron material with lower hardness to be damaged, which suffered more serious particle wear. The generation of short rod-shaped carbides should be avoided because, in the process of friction and wear, carbides with these shapes are easy to break, thus leading to crack initiation.

Nonlinear optical effects in polycrystalline transparent Al2O3 ceramics using femtosecond laser pulses—supercontinuum generation and laser damage

Nonlinear optical properties play a key role in technologies such as broadband laser light sources and ultrafast laser machining. With the emergence of transparent nanocrystalline Al2O3 ceramics as an alternative to single crystal alumina (sapphire), it is critical to understand their nonlinear optical behavior. Here, we report the demonstration of supercontinuum generation in polycrystalline alumina ceramics. Substantial broadening was observed when a focused 515 nm pulsed (260 fs) laser propagated through the ceramic sample. The broadening increased with increasing laser power and displayed stokes/anti-stokes asymmetries. At higher incident power, permanent damage was observed. Our results show that transparent nanocrystalline Al2O3 ceramics have a higher material removal rate than single crystal alumina. These results have interesting implications for laser machining as well as integrated photonics.

Laser-induced changes on the upconversion luminescence properties of BiF3:Yb,Er nanoparticles

BiF3 nanoparticles doped with Yb3+ and Er3+ ions in varying ratios were prepared by co-precipitation method and its upconversion luminescence (UCL) properties were investigated in detail before and after high-intensity laser treatment. Green-to-red ratio (GRR) of luminescence from cubic-BiF3:Yb,Er nanoparticles is found to increase with an increase in laser power for as prepared sample. Unlike this, for conventional Yb,Er doped upconversion nanoparticles (UCNPs) such as cubic NaYF4:Yb,Er and hexagonal-NaYF4:Yb,Er, a decrease in GRR values is observed with an increase in laser power. This has been explained based on the reduced extent of Er3+-Er3+ interaction in BiF3:Yb,Er nanoparticles compared to that existing in cubic and hexagonal forms of NaYF4:Yb,Er, nanoparticles. Reduced interaction is brought about by higher lattice parameter of BiF3 host compared to the NaYF4 host which leads to a lesser extent of cross-relaxation in the former host thereby favoring the population of 4S3/2 and 2H11/2 levels of Er3+. Effect of high-intensity laser (180W/cm2) irradiation on BiF3:Yb,Er nanoparticles resulted in an irreversible five-fold increase in upconversion luminescence intensity and this is attributed to combined effect of partial conversion of BiF3 to cubic Bi2O3 and removal of adsorbed water molecules. These inferences are confirmed by XRD and TEM measurements carried out on laser-treated sample. Improved luminescence intensity from the laser-treated sample is also confirmed by the high-contrast clear images obtained from impressions made using high-intensity laser irradiation on BiF3:Yb,Er nanoparticles. BiF3:Yb,Er nanoparticles showed an excellent thermal sensitivity of 0.3% K−1 at room temperature and the value is comparable with that of conventional β-NaYF4:Yb,Er nanoparticles.

Assessing crack susceptibility in blended copper-stainless steel compositions during laser directed energy deposition-based additive manufacturing

This study investigates the effect of composition and process parameters on the crack susceptibility of the Cu -SS304L system during laser directed energy deposition (LDED). The microstructure of LDED deposits is analysed aiming at elemental distribution and crack susceptibility. The trapping behaviour of Cu changes with Cu concentration. The crack susceptibility reduces with Cu concentration and escalates with an increase in laser power and scan speed, irrespective of composition. The mode of solidification cracking varied from the rupture of Cu film to crack-assisted porosity. Furthermore, the critical solidification cooling rate is estimated for LDED of different blended Cu -SS for crack-free deposition. The above findings offer insights into cracking behaviour and provide processing guidelines for LDED of Cu -SS.

Optimization of structure and properties of WC-reinforced FeCoNiCr high-entropy alloy composite coating by laser melting

High entropy alloys have the potential to be used as coating materials in many fields due to their excellent mechanical properties, corrosion resistance and high-temperature stability. Based on the application requirements of high-entropy alloys, this study aims to explore how tungsten carbide can optimize the properties of high-entropy alloys. Through theoretical research and experimental validation, the effects of the organizational structure of high-entropy alloy coatings on their properties and the effects of tungsten carbide content on the properties of high-entropy alloy coatings were investigated. The micro hardness of the coatings is relatively high at low power laser melting, while it decreases with the increase of laser power. After laser melting of different materials, the average impact toughness of the studied materials exceeded 70 J/cm2, and the average values of microhardness of the optimized coatings prepared at laser powers of 1400 W and 1600 W were more than 160 HV0.2. In addition, the properties of the high-entropy alloys were significantly improved when the content of tungsten carbide reached a certain percentage. The composite coatings have excellent wear resistance, corrosion resistance and thermal stability. Overall, the optimized tungsten carbide on high entropy alloys in this study has good performance, which is of great theoretical and practical significance for understanding the performance regulation and optimal design of high entropy alloy coatings.

Effect of laser remelting on internal defects and properties of Ni-based coatings reinforced by multi-channel WC in situ

In order to investigate the effect of laser remelting on the properties of hot work die steel, WC reinforced Ni base remelting layer was prepared on H13 steel surface. Optical metallography microscope, X-ray diffractometer and scanning electron microscope were used to analyze the macroscopic defects, phase evolution and microstructure of the coating before and after laser remelting. Microhardness tester and friction and wear tester were used to test the microhardness and wear resistance of the remelted layer, and compared with the coating without remelting. The results show that the inner porosity of the coating decreases with the increase of laser power. With the dissolution of WC/W2C ceramic particles and the uniform distribution of W element, the distribution of reinforcement particles in the coating becomes more and more uniform. When the laser power reaches 1500 W, the WC/W2C ceramic particles inside the coating basically disappear, the porosity is reduced to the lowest, the coating uniformity is the best, and the microhardness and wear resistance are the highest.

Effect of Spatter Behavior on Mechanical Properties and Surface Roughness of Printed Parts during PBF-LM of 316L.

The spatter generated by the interaction between laser and powder during Powder Bed Fusion-Laser Melting (PBF-LM) can significantly affect the quality of printed parts. A high-speed camera is used to observe the dynamic process of spatter's behavior under different layer thickness and laser powers during the printing process, and to analyze the printed samples' surface roughness, microstructure, and mechanical properties. In terms of spatter image processing, employing an optical flow approach to track and quantify the number of spatters efficiently eliminates statistical redundancy and improves statistical correctness. It is found that under the same laser power, the number of spatters produced by the laser scan direction with the gas flow (LSD-W) is more than that by the laser scan direction against the gas flow (LSD-A), and the number of spatters produced increases with the increase of laser power. Analyzing the mechanical properties and surface roughness of the printed samples under different process parameters quantitatively reveals that differences in the spatter amount generated under different process parameters in the PBF-LM process is not the determining factor affecting the difference in tensile strength of printed parts. During LSD-W, the number of spatters generated at laser power of 170 W and layer thickness of 0.03 mm is 87, and the tensile strength of the printed sample is 618 MPa. During LSD-W, the number of spatters generated at laser power of 320 W and layer thickness of 0.05 mm is 211, and the tensile strength of the printed sample is 680 MPa. Instead, spatter generation has a more direct impact on the surface roughness of printed parts. The layer thickness is 0.03 mm, the laser power is 170 W, and (Ra = 2.372 μm) is the surface roughness of the sample. The layer thickness is 0.05 mm, the laser power is 320 W, and (Ra = 8.163 μm) is the surface roughness of the sample.

Microstructure, Hardness and Corrosion Resistance of Al-TiC MMC Prepared by Laser Cladding on AZ31B Magnesium Alloy

Magnesium alloy is extensively used in aircraft, automobiles, and electronic industries due to its low density, high specific strength, and enhanced machinability. However, low hardness and poor corrosion resistance limit its application. In this work, an Al-TiC metal matrix composite (MMC) was prepared on AZ31B magnesium alloy via laser cladding. The effects of laser power and TiC content on the microstructure, hardness, and corrosion resistance of the MMC were investigated. The results showed that the MMC with 10% TiC had a hardness of 184 HV0.1, which was 3.5 times higher than 52 HV0.1 of the substrate. The current density of MMC with 10% TiC was 3.90 × 10−7 A/cm2, which was three orders of magnitude lower than 5.45 × 10−4 A/cm2 of the substrate. Due to more intermetallic compounds (IMCs) and TiC particles, the MMC with 30% TiC had higher hardness. The increased laser power would not change the phase composition, but it contributed to the formation of a concave crescent shape, promoted the diffusion of Mg, and induced the formation of a thicker Al3Mg2 transition layer. Modifications in the TiC concentration markedly influenced the coating’s microstructural characteristics.

Study on the Effect of Electrolytes on Processing Efficiency and Accuracy of Titanium Alloy Utilizing Laser and Shaped Tube Electrochemical Machining.

Electrochemical machining (ECM) has become more prevalent in titanium alloy processing. However, the presence of the passivation layer on the titanium alloys significantly impacts the performance of ECM. In an attempt to overcome the passivation effects, a high-temperature electrolyte or the addition of halogen ions to the electrolyte has been used. Still, it often results in compromised machining accuracy and surface roughness. This study applied laser and shaped tube electrolytic machining (Laser-STEM) for titanium alloy drilling, where the laser was guided to the machining zone via total internal reflection. The performance of Laser-STEM using different types of electrolytes was compared. Further, the effects of laser power and pulse voltage on the machining side gap, material removal rate (MRR), and surface roughness were experimentally studied while drilling small holes in titanium alloy. The results indicated that the use of passivating electrolytes improved the machining precision, while the MRR decreased with an increase in laser power during Laser-STEM. The MRR showed an increase while using aggressive electrolytes; however, at the same time, the machining precision deteriorated with the increase in laser power. Particularly, the maximum feeding rate of 6.0 mm/min for the tool electrode was achieved using NaCl solution as the electrolyte during Laser-STEM, marking a 100% increase compared to the rate without the use of a laser. Moreover, the model and equivalent circuits were also established to illustrate the material removal mechanisms of Laser-STEM in different electrolytes. Lastly, the processing of deep small holes with a diameter of 1.5 mm, a depth of 38 mm, and a surface roughness of Ra 2 µm was achieved via Laser-STEM without the presence of a recast layer and heat-affected zones. In addition, the cross-inner flow channels in the titanium alloys were effectively processed.

Experimental study and mechanism analysis of a pulsed laser cleaning aluminum alloy process.

A pulse laser with a wavelength of 1064nm and a pulse width of 1µs was used to experiment on the coating of a 2024 aluminum alloy surface. The removal performance of the pulse laser cleaning coating was explored by a single factor analysis and orthogonally conditions, and the effects of the laser power, scanning speed, and pulse frequency on the quality of laser coating removal were summarized. The mechanisms of pulse laser cleaning the coating were studied. The results show that the three parameters of the laser power, scanning speed, and pulse frequency have different effects on the quality of laser coating removal. Among them, with the increase of the scanning speed and pulse frequency, the quality of laser cleaning first increases and then decreases, respectively. With the increase in laser power, the quality of laser cleaning increases. A good laser cleaning quality can be achieved at the laser power of 16.5W, a scanning speed of 600mm/s, and a pulse frequency of 30kHz. The laser cleaning coating involves a variety of mechanisms such as combustion, explosion, gasification, thermal vibration stripping, and laser plasma impact. The result can provide practical references for a better searching of the paint removal.

Influence of thermal loading parameters and microstructure on the formation of stratified surface layers on railway wheels

Due to an increasing trend towards environmentally friendly public transport, rail networks face higher speeds and wheel loads affecting the material degradation of the railway components. Within this study, influencing parameters on the formation of stratified surface layers, forming on railway wheels during service due to thermal loadings in the wheel-rail contact, are studied. These layers consist of white etching layer and underlying brown etching layer and are susceptible to fatigue crack initiation. By using laser surface treatments, its formation based on two consecutive thermal loadings is systematically demonstrated on ER7 wheel steel. Further, a decrease in layer thickness with decreasing laser power, and an increase in brown etching layer thickness with increasing laser power difference is shown. Moreover, the effect of finer grain size leading to an increased layer thickness, and the influence of the chemical composition by comparing the standard ER7 wheel steel to a micro-alloyed wheel steel are demonstrated.

Fabrication of Polymer Light Guide Plate (LGP) using Direct CO2 Laser Structuring

Light guide plates (LGPs) are an integral component that help distribute illumination from the light source in a variety of applications. Therefore, the design and quality of the microstructure pattern in LGPs play a significant role in achieving high luminous efficiency and light uniformity. This study investigates the relationship between laser power and laser scanning speed to the formation of micro-dots by using CO2 direct laser structuring on PMMA. Furthermore, the effect of different micro-dots pitch to the luminance was also evaluated using the luminance meter. Our finding shows that increase of laser power and decrease of laser scanning speed resulted in larger micro-dots diameter and deeper micro-dots. The results also showed that the smaller the pitch, the higher the luminance reading. Overall, the low-cost CO2 direct laser structuring demonstrated in the study able to produce consistent micro-dots pattern diameter and height which is suitable for fabrication of LGPs in the mass production.

Gradient-Pattern Micro-Grooved Wicks Fabricated by the Ultraviolet Nanosecond Laser Method and Their Enhanced Capillary Performance.

Capillary-gradient wicks can achieve fast or directional liquid transport, but they face fabrication challenges by traditional methods in terms of precise patterns. Laser processing is a potential solution due to its high pattern accuracy, but there are a few studies on laser-processed capillary-gradient wicks. In this paper, capillary step-gradient micro-grooved wicks (CSMWs) were fabricated by an ultraviolet nanosecond pulsed laser, and their capillary performance was studied experimentally. The CSMWs could be divided into three regions with a decreasing capillary radius. The equilibrium rising height of the CSMWs was enhanced by 124% compared to the non-gradient parallel wick. Different from the classical Lucas-Washburn model describing a uniform non-gradient wick, secondary capillary acceleration was observed in the negative gradient direction of the CSMWs. With the increase in laser power and the decrease in scanning speed, the capillary performance was promoted, and the optimal laser processing parameters were 4 W-10 mm/s. The laser-enhanced capillary performance was attributed to the improved hydrophilicity and reduced capillary radius, which resulted from the increased surface roughness, protrusion morphology, and deep-narrow V-shaped grooves induced by the high energy density of the laser. Our study demonstrates that ultraviolet pulsed laser processing is a highly efficient and low-cost method for fabricating high-performance capillary gradient wicks.

Influence of processing parameters on the corrosion resistance of additively manufactured nitinol parts for biomedical applications

The usefulness of additively manufactured (AM) nitinol and Ti6Al4V parts for the aerospace, automotive, machine and tooling, and biomedical industries depends on how well they withstand corrosion. AM is a manufacturing process that makes it possible to create intricate geometries at a reasonable price. Although significant progress has been made in decreasing metal corrosion, not much research has been done on optimizing input processing parameters to lower corrosion rates. Unique phase structures and preferential evaporation of alloying components might arise because of the melting and quick re-solidification that take place during additive manufacturing. This study looks at how processing parameter changes impact the metal parts made by laser-powder bed fusion (L-PBF) in terms of their ability to resist corrosion in a bodily environment. Electrochemical testing was used to conduct the research at a body temperature of 37 °C in both Hanks and Ringers solutions. The findings suggest that an increase in laser power during AM improves the passivation layer of the metal. Furthermore, compared to nitinol, Ti6AL4V exhibits a greater corrosion resistance. When a smaller hatch distance and lower laser beam strength were used, the nitinol sample's susceptibility to corrosion was reduced. This study demonstrates how the corrosion resistance of metal parts made by additive manufacturing can be increased by adjusting the laser powder bed fusion processing parameters in a bodily environment.

Exploring How LPBF process parameters impact the interface characteristics of LPBF Inconel 718 deposited on Inconel 718 wrought substrates

This work investigates the interface properties of LPBF Inconel 718 deposited on Inconel 718 wrought substrates fabricated using the laser powder bed fusion (LPBF) technique. The as-printed (S1, S2, S3, and S4) samples were characterized using optical microscopy (OM),scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) and micro-hardness techniques.The samples showed the development of a melted interface zone (MIZ) at the wrought substrate-deposition interface for all processing conditions. The developed interface showed a dendritic grain structure, signifying the remelting of the wrought substrate followed by rapid solidification. The MIZ thickness increased with an increase in laser power and scan speed (28.5 % increase in the MIZ thickness with a ∼ 12 % increase in normalized enthalpy). The assessment of the MIZ showed a high-quality interface. However, with an increase in scanning speed, the density of the MIZ decreases owing to increased porosity and lack-of-fusion (LOF) defects. The S1 condition (250 W and 850 mm/s) resulted in a highly dense part with no visible porosity, LOF defects, and a high relative density (∼99.9 %) in the MIZ region. The S4 condition showed the presence of large porosities and LOF defects at the deposition-MIZ interface, signifying an inferior bond between the deposition and substrate. The microstructural characterization of the LPBF-processed and MIZ region showed an increase in the primary dendritic arm spacing (PDAS) with increasing laser power due to a reduced cooling rate. The micro-hardness characterization of the sample shows a decrease in the hardness of the MIZ attributed to the dissolution of strengthening phases due to remelting. The present work outcome demonstrates the effectiveness of the proposed methodology for manufacturing high-quality parts using LPBF technology.

Grain refinement and anisotropy improvement of arc-directed energy deposited Ti–6Al–4V with oscillating laser

Ti–6Al–4V parts fabricated by wire plus arc additive manufacturing (WAAM) usually exhibit columnar grain shapes and serious anisotropy in mechanical properties. This study aims to solve these issues by proposing a laser-assisted WAAM technique in which a vertically oscillating laser beam acts on the molten pool in WAAM. The influences of oscillation laser power on the microstructure and mechanical properties of Ti–6Al–4V parts built in WAAM are revealed and discussed. The oscillation laser can refine prior-β grains in WAAM. As the laser power increases, the depths of laser fusion lines in deposited layers increase, the size of prior-β grains decreases first and then increases, and both the microhardness and ultimate tensile strength (UTS) increase first and then decrease. At a laser power of 1600 W, the columnar prior-β grains are completely transformed into equiaxed shapes. The UTS values in the vertical and horizontal directions reach 1322 and 1309 MPa, respectively, respectively 30.5% and 15.7% higher than those of the WAAM sample. Meanwhile, the indices of plane anisotropy of UTS and elongation decrease by 90.6% and 76.4%, respectively.

Microstructural and Hall–Petch Analysis of Additively Manufactured Ferritic Alloy Using 2507 Duplex Stainless Steel Powder

The powder bed fusion–laser beam (PBF-LB) process, a method of additive manufacturing (AM), was used to print duplex stainless steel (DSS) using commercial-grade 2507 powders. While conventionally processed DSS has a two-phase microstructure consisting of 50% austenite and 50% ferrite, the PBF-LB-printed 2507 alloy was nearly 100% ferrite. Optimal processing conditions that minimized porosity were determined to be 290 W laser power and 1000 mm/s scan speed, and grain size, texture, and phases were characterized as a function of laser power and scan speed. Grain size increased with increasing laser power but decreased with increasing scan speed. A <100> texture diminished with increasing scan speed from 1000 mm/s to 1400 mm/s. No austenite phase was detected. Transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) characterization revealed nanoscale chromium nitride precipitates in the ferritic matrix (incoherent hexagonal close-packed (HCP) precipitates at grain boundaries and coherent body-centered cubic (BCC) precipitates within the grains) and a high density of tangled dislocations. Tensile tests of as-printed alloys showed a yield strength of 570 MPa, an ultimate tensile strength of 756 MPa, and an elongation to failure of 10%. The tensile properties were analyzed based on the observed microstructure considering grain size, nanoscale precipitates, and the high density of dislocations.