X-ray diffraction spectra, field-effect scanning electron microscopy, focused ion beam milling , and photoluminescence (PL) spectrometry were used to analyze the effects that different synthesis times and different thicknesses of Al sacrificial layer had on the properties of ZnO nanoflower arrays. These effects included an increased diameter, and a decreased height, density , total surface area, total volume, and maximum emission intensity of PL spectrum. We showed that when the synthesis time and the thickness of the Al sacrificial layer were increased, the emission intensities of the ultraviolet light and visible light had different variations.A novel method to synthesize large-scale ZnO nanoflower arrays using a protrusion patterned ZnO seed layer was investigated. Different thicknesses of aluminum (Al) film were deposited on the concave patterned sapphire substrate as a sacrificial layer. ZnO gel was layered onto the Al film as a seed layer and OE-6370HF AB optical glue was used as the adhesive material. A lift-off technique was used to transfer the protrusion patterned ZnO/AB glue seed layer to a P-type Si <100> wafer. The hydrothermal method using Zn(CH Zinc oxide (ZnO) is used in a variety of materials with many different applications, including nano-ZnO/Ag in antimicrobial applications , and Co-Nanomaterials with high surface areas have a better ability to absorb scattered light or to emit excited light; thus, the light harvesting efficiency or light emission efficiency of these materials are improved. There is interest in increasing the surface area of ZnO nanomaterials with one-dimensional (1D) morphologies, such as ZnO nanorods and ZnO nanowires, which would be advantageous in terms of light harvesting and emission , which c6H12N4 (hexamethylenetetramine (HMT)) and Zn(CH3COO)2 (zinc acetate) solutions as precursors. The synthesized ZnO nanorods grew perpendicular to the protrusions in the ZnO seed layer in a radial direction, such that they formed a hierarchical structure. Therefore, this method was successfully used to synthesize ZnO nanoflowers.Although there are many methods that have been used to synthesize 1D ZnO nanostructured materials, the hydrothermal method is the most commonly used technology. The hydrothermal method is a simple, useful, and economical way to synthesize 1D ZnO nanostructured materials at low temperatures . ZnO nan2 substrate; then they used a laser to write the holes in the matrix. Then they used the hydrothermal method to synthesize the nanoflowers on the prepared substrate [2 substrate and a laser to prepare that substrate. Katiyar et al. used the ultrasonic-assisted hydrothermal method to grow the ZnO nanoflowers at a low temperature with no substrate [−2), total surface area per unit area , total volume per unit area , and photoluminescence (PL) spectrum. Changes in the characteristic emissions in the PL spectra of the ZnO nanoflower arrays under different synthesis times were also investigated.The important novel technology presented in this study was that of a protrusion patterned ZnO seed layer used to fabricate ZnO nanoflowers that possessed a remarkable repeatability to form ZnO nanoflower arrays. In the past, Guo et al. used the spinning method to layer PMMA 1 μm thick onto a GaN/LiAlOubstrate . A shortubstrate . A shortubstrate . HoweverIn this study, a lift-off technique was used to transfer a ZnO seed layer with periodic arrays and a protrusion patterned structure to a P-type Si <100> wafer. The hydrothermal method was then used to synthesize ZnO nanorods on the ZnO seed layer to construct ZnO nanoflower arrays. In order to synthesize the ZnO nanoflower arrays, we used a sapphire substrate as a template, which had a patterned concave structure and was provided by Shun Haw Technology Ltd. , to prepare the ZnO seed layer with a patterned convex structure . The cro−6 torr and no gas was introduced during the deposition process. Sample A, which was abbreviated as SC-A, had an Al thickness of 120 nm; sample B (SC-B) and sample C (SC-C) had Al thicknesses of 420 and 720 nm, respectively. Heat-resistant tape  was used as an adhesive on the Al-coated sapphire substrate to create an access for sacrificial removal of the Al film from underneath the ZnO seed layer. The area that was used to prepare the ZnO seed layer was 10 mm × 10 mm, as shown in 3Fe(CN)6:KOH:H2O (10 g:1 g:100 mL) was used with an etching speed of the process that varied at 10 min/s. After the Al film was etched, the protrusion patterned ZnO/AB glue seed layers were obtained; then they were lifted off the sapphire substrate and transferred to the P-type Si <100> wafer. The OE-6370HF AB glue was used to attach the ZnO/AB glue seed layers to the Si <100> wafer. Finally, the hydrothermal method was used to synthesize the ZnO nanoflower arrays, because the sapphire substrate had the structure of concave pattern arrays, as First, a thermal evaporation coating machine  was used to deposit Al sacrificial layers of different thicknesses on the sapphire substrate . The dep6H12N4 and Zn(CH3COO)2 were maintained at 0.02 M, while the duration of the process was increased from 10 min to 60 min. After the ZnO nanoflower arrays were synthesized on the protrusion patterned ZnO seed layer, their X-ray diffraction spectra  were measured to analyze the crystalline phases. Field emission scanning electron microscopy  was used to observe the surface morphologies of the arrays. The prepared protrusion patterned ZnO seed layer and the ZnO nanoflower arrays were cut using a focused ion beam  system so that the cross-sectional morphologies could be observed. FESEM equipped with energy-dispersive X-ray spectroscopy  was used to analyze the undefined residual particles on the surface of the prepared protrusion patterned ZnO seed layer. An iHR550 fluorescence spectrophotometer  with a single laser at a wavelength of 325 nm was used as the excitation light source. The PL properties of the ZnO nanoflower arrays in the wavelength range of 350~650 nm at room temperature were measured.During the synthesis process, the concentrations of CThe XRD spectra were used to analyze the crystal characteristics of the ZnO seed layers. The XRD spectra for the SC-A, SC-B, and SC-C substrates are shown in 3), which deposited on the surfaces of the protrusions and in the gaps. When EDS was used to analyze the white particles, the Al element was indeed readily detected.3+ ions or Al2O3; when the concentration of Al increased from 1 at% to 2 at%, the crystal grain size of Al-doped ZnO also increased [3, that is deposited on the surface of a ZnO seed layer increases with the thickness of the Al sacrificial layer. Therefore, we believe that, as the etching time increases with the thickness of the Al sacrificial layer, the amount of the Al-based impurity also increases, which causes an increase in the particle sizes.These images show that the diameters of the top part of the ZnO seed layer were about 365, 380, and 390 nm, respectively. Apparently, as the thickness of the Al sacrificial layer etching time increased, the etching took longer, which increased the particle sizes and the diameters of the ZnO seed layer. These observations could be related to the presence of the Al element. Zhang and Que found that the crystal grain size of Al-doped ZnO changed with the concentration of Alncreased . In the 3, which formed during the etching process.To prove that Al element was residual in the ZnO seed layer, EDS analyses were performed on the surfaces of the ZnO seed layer. 3COO)2 and 0.2 M C6H12N4 solutions were used. The XRD spectra of the ZnO nanoflower arrays that were synthesized on the SC-B substrate are shown in Various conditions were changed in order to investigate the effect of the synthesis time on the crystalline and optical properties of the synthesized ZnO nanoflower arrays. First, the synthesis time was changed from 10 min to 60 min, the synthesis temperature was set at 90 °C, and 0.2 M Zn2 and C6H12N4 solutions to deposit ZnO on; thus, more ZnO nanorods could be formed at the same time. In addition, when ZnO nanorods were synthesized on large seed particles, they had a greater chance to merge with each other, which increased the growth rates in the vertical direction  and in the radial direction. Therefore, the diameter increased, and the height decreased, with the thickness of the Al sacrificial layer.Correspondingly, the calculated aspect ratios (H/D) of the ZnO nanoflower arrays decreased from 16.77, to 10.9, and to 8.48 when the SC-A, SC-B, and SC-C substrates were used. Thus, the aspect ratio of the ZnO nanoflower arrays was influenced by the substrates, which affected the relative synthesis rates in the vertical and radial directions. A comparison with 2, the image of the ZnO nanoflower arrays was segmented into squares, each with an area of 1 μm2, as shown in −2, 20 μm−2, and 18 μm−2, respectively  in nm2, and the S/V ratio. The results are given in To estimate the density  of the ZnO nanoflower arrays in a unit area of 1 μmectively . The estUV). This band was mainly caused by the near-band-edge electron transition between the valence band and the conduction band [G). The emission intensities of the ZnO nanoflower arrays at the broad emission band of 420~600 nm were lower than those of the ZnO seed layer. The full width at half maximum (FWHM) values for the spectra shown in dE1 and dE2), which indicate that the hollow ZnO nanoflower arrays were n-type semiconductors, and the electron transitions from the dE1 and dE2 to the valence band were related to the energies 3.08 and 2.92 eV, and they would release blue light emissions [UV peaks was the decrease of the intensities in the two donor states.ion band , and a lmissions . We beliZn; bandgap energy (Eg) = 3.06 eV; and emission light ~405 nm), interstitial zinc , antisite defect , interstitial oxygen , and oxygen vacancy  [G is believed to be caused by combinations of different defects at local levels, including an interstitial oxygen defect (~544 nm) and an antisite defect (~521 nm) in the ZnO seed layer and ZnO nanoflower arrays.The broad visible emission band corresponds to the transitions between the near-band-edge and the local levels, which are caused by intrinsic defects that exist in the synthesized ZnO nanomaterials , or corr~765 nm) . TherefoUV increased, while the emission intensity of IG decreased with the synthesis time of the ZnO nanoflower arrays. In addition, the IUV values of the ZnO nanoflower arrays were greater than those of the ZnO seed layer; correspondingly, the IG values of the ZnO nanoflower arrays were smaller than those of the ZnO seed layer. When the synthesis time increased from 10 min to 60 min, the intensity of IG decreased from 170 to 83 (a.u.), and the intensity of IUV increased from 594 to 2068; the IG/IUV ratio decreased from 0.285 to 0.040. UV values, IG values, and IG/IUV ratios of the ZnO nanoflower arrays with different substrates and synthesis times. When the images of the ZnO nanoflower arrays shown in It is well known that the crystal quality of ZnO nanoflower arrays is closely associated with the intensity of the near-band-edge emission . Both thG in the broad emission band of 420~575 nm was. In general, the maximum emission intensity of IG can be used to judge the crystal quality of ZnO nanomaterials, because it indicates defects. UV were successfully obtained when the synthesis time was extended.The greater the amount of antisite defects and interstitial oxygen defects that existed in the ZnO seed layer and ZnO nanoflower arrays, the stronger the emission intensity of IG, in the ZnO nanoflower arrays than in the ZnO seed layer; the emission intensities of IUV from the ZnO nanoflower arrays were also weaker than those from the ZnO seed layer. UV and IG increased with synthesis time. UV of the ZnO nanoflower arrays as a function of the synthesis time and thickness of the Al sacrificial layer. This figure shows that, for the same synthesis time, the emission intensity of IUV decreased with a decrease in thickness of the Al sacrificial layer. These results match the results shown in The results of this study prove that when different synthesis times were used, there were fewer defects, shown as IThe drawings of the UV-visible absorption spectroscopy of the ZnO nanoflower arrays for samples with the synthesis time of 60 min and Al sacrificial layers of 120, 240, and 720 nm are shown in 1s peak of the ZnO nanoflower arrays are of samples with a synthesis time of 60 min and Al sacrificial layers of 120 and 720 nm. The typical surface O1s peaks of the ZnO nanoflower arrays were centered at 530.1 ± 0.1 eV and fitted by three Gaussian components of OI, OII, and OIII peaks, as 1s peak was divided into three peaks, OI, OII, and OIII, which were centered at 529.8 ± 0.1 eV, 530.3 ± 0.1 eV, and 532.1 ± 0.1 eV, respectively. For the ZnO nanoflower arrays, the bond energy for the component of the OI peak was caused by the Zn2+-O2− bond, the bond energy for the component of the OII peak was caused by the oxygen vacancies, and the bond energy for the component of the OIII peak was caused by the chemical absorption of oxygen on the surfaces [For further discussing the effect of the thickness of the Al sacrificial layer, we used an X-ray photoelectron spectroscopy (XPS) technique to measure the chemical-bonding state of oxygen. These measured results were used to find the relationship between the defects caused by the different substrates and the optical properties of the ZnO nanoflower arrays. The drawings of the Osurfaces .1s peaks measured according to the XPS spectra of the ZnO nanoflower arrays are compared in I peak increased from 45.26% to 48.54%, the area of the OII peak decreased from 43.06% to 40.93%, and the area of the OIII peak decreased from 11.68% to 10.54%. Apparently, the area of the OII peak of the ZnO nanoflower arrays decreased with the increase in the thickness of the Al sacrificial layer, which proves that the oxygen vacancies of the ZnO nanoflower arrays decrease with the increase in the thickness of the Al sacrificial layer. These results also suggest that the defects in ZnO nanoflower arrays decrease with the increase in the thickness of the Al sacrificial layer. Because the oxygen vacancies decreased with the thickness of the Al sacrificial layer, these results indirectly prove that the intensity of the IG value of ZnO nanoflower arrays decreases with the thickness of the Al sacrificial layer, which matches the measured results shown in The areas of the OUV, IG, and IG/IUV ratio of the ZnO nanoflower arrays decreased with the thicknesses of the Al sacrificial layer.In this study, ZnO seed layers that had a protrusion patterned array structure were prepared on Al sacrificial layers of different thicknesses. For Al sacrificial layers that were 120, 420, and 720 nm thick, the particle sizes of the ZnO seed layers were about 35, 65, and 80 nm, the diameters of the top parts of the ZnO seed layers were about 365, 380, and 390 nm, and the ZnO seed layers were 206, 184, and 180 nm thick, respectively. The SEM and EDS analyses indicated that when a thick Al sacrificial layer was deposited, a longer etching time was needed and more Al-based impurity was residual. The heights of the ZnO nanoflower arrays decreased and the diameters increased with the thicknesses of the sacrificial Al layer. The results also indicated that the diameter increased and the height, aspect ratio, density, total surface area (S), total volume (V), S/V ratio, I


While the conventionally laser cladded layers show tendency for decomposition of carbide particles and resolidifying dendritic complex carbides mainly M2C, M3C and M7C3 containing iron, nickel, and tungsten, and with Ni/Ni3B matrix. The quantitative relationship between heat input, cooling conditions and the carbides grain size distribution as well as carbides share in relation to the matrix was determined.The purpose of this study was to demonstrate the effect of forced and localized cooling by nitrogen vapours stream under cryogenic conditions during laser deposition of WC-Ni powder on the geometry, microstructure of clad layers and dry sliding wear resistance of the coatings. For this purpose, comparative tests were performed by conventional laser cladding at free cooling conditions in ambient air and by the developed novel process of laser deposition with additional localized cooling of the solidifying deposit by nitrogen vapours stream. Due to presence of gaseous nitrogen in the region of the melt pool and solidifying deposit, the process was considered as combining laser cladding and laser gas nitriding (performed simultaneously), thus the hybrid process. The influence of the heat input and cooling conditions on the geometrical features, dilution rate, share of carbides relative to the matrix, and the fraction share of carbides, as well as hardness profiles on cross sections of single stringer beads was analysed and presented. The XRD, EDS analysis and the sieve test of the experimental powder were used to characterize the composite WC-Ni type powder. The OM, SEM, EDS and XRD test methods were used to study the microstructure, chemical and phase composition of clad layers. Additionally, ball-on-disc tests were performed to determine the wear resistance of representative coatings under dry sliding conditions. The results indicate that the novel demonstrated technique of localized forced cooling of the solidifying deposit has advantageous effect, because it provides approximately 20% lower penetration depth and dilution, decreases tendency for tungsten carbides decomposition, provides more uniform distribution and higher share of massive eutectic W Laser cladding offers some advantages over the other methods of cladding or coatings ,7,8,9,10Another technique that allows to reduce the effect of the heat on the material and to control the solidification rate is a forced cooling. An original technique of micro-jet cooling by compressed gas streams of the deposit during arc cladding was elaborated and demonstrated by Węgrzyn et al. . They prLiquid nitrogen bath providing cryogenic conditions of cooling was also tested by some researchers during laser surface melting or heat treatment, mainly for nonferrous alloys ,21,22,23The preliminary tests of laser cladding of composite WC-Ni coatings, conducted by the authors, have shown that the forced cooling of the substrate by liquid nitrogen bath can provide some beneficial effects. The most significant are limited penetration depth, limited dilution, limited tendency for tungsten carbide melting, uniform and dense distribution of carbides, favourable hardness distribution and high values of hardness. However, some disadvantages and limitations of the liquid nitrogen bath (volume cooling) applied for laser powder deposition were identified. Due to high extent of supercooling the substrate and intensive dissipation of the heat during laser heating, the tendency for incomplete or lack of penetration of the clad was observed, especially at the lowest heat input range. Therefore, another technique of forced cooling by means of liquid nitrogen based on stream local cooling of the deposition region, that allows controlled and less intensive cooling of the substrate was developed and investigated by the authors.According to the authors’ knowledge and experience, the presented results are fully original and unique, and the results of similar studies have not been available nor published so far.2.The non-alloy structural steel S235JR (according to EN 10025-2) was chosen as the substrate for technological tests. This grade of steel with a low content of alloying elements, good plasticity and excellent weldability was chosen to minimize the influence of the substrate material on the cladded layer, especially minimize the internal stresses and tendency for cracking of clad layers, In turn, the powder for cladding was experimentally composed in such a way as to ensure high abrasion resistance, and corrosion resistance of deposit even at elevated temperatures. Therefore, tungsten carbides, as the reinforcing phase, were mixed with nickel-based powder providing the ductile metal matrix characterized by high resistance for corrosion and high temperature. The nickel-based metal powder was gas atomized in argon atmosphere and the spherical particles size range was 63 ÷ 160 µm. While the tungsten carbide irregular shaped (crushed) particles size range was 100 ÷ 160 µm. The sieve test of the mixed experimental powder was performed for statistical analysis according to the standard PN-EN 24497/ISO 4497. Sieve shaker LPzE-2e  and the moisture analyser with the laboratory scales BTS110  were applied in the sieve test. The sieve test was repeated three times for different batches of powder weighing approx. 100 g each, for statistical reasons. The mass fraction share and cumulative particle size distribution curve determined for the experimentally composed powder are presented in The tests of laser deposition were performed by means of a prototype robotized stand. The stand was equipped with a six-axis robot Panasonic GII TL-190  with maximum load capacity 6.0 kg, high power fiber laser (HPFL) IPG YLS-3000-CT-Y15  with maximum output power 3.0 kW, emitting at a wavelength 1.07 µm, and characterized by a single mode energy distribution across the spot (Gaussian intensity distribution), custom made powder delivery system, and a specially designed system for localized delivery of liquid nitrogen or nitrogen vapours stream. The laser beam was transmitted from the laser generator to the focussing head IPG FLW by 20 m long HLC-8 fiber with a core diameter 200 µm. The focal length of the applied FLW head was 200 mm, while the collimator focal length was 100 mm. The beam parameter product (BPP) of the laser beam determined for the applied optics configuration was 5.8 mm⋅mrad. The BPP was measured by Primes Focus Monitor FM-120 .The stream localized cooling system was designed based on the experiences of previous preliminary study of laser cladding the steel substrate immersed partially in liquid nitrogen bath, to overcome the encountered limitations of such technique of volume cryogenic cooling . During Prior to the laser cladding tests, the specimens were sandblasted (surface roughness Ra 25 ÷ 60 μm) and degreased with acetone to remove surface contamination and provide stable and repeatable surface conditions for absorption of laser radiation. Surface roughness was determined by a portable surface roughness tester SJ-210 Surftest . The test cladded layers were produced as single stringer beads by laser deposition of the experimentally composed powder at different heat input and different conditions of cooling. The length of the individual bead was 80 mm, while the shift between beads was 20 mm, The scanning speed was kept constant at 500 mm/min, while the laser output power was varied from 500 W, 1000 W, 1500 W, and 2000 W. The feeding rate of the composite WC-Ni powder was maintained constant at 8.5 g/min. The powder was fed into the melt pool by three coaxial nozzles with a diameter of 0.8 mm each. The nozzles were attached to head body providing the ability to change the angle of inclination and vertical shift, as can be seen in The laser beam was set perpendicularly to the surface of the substrate, and it was transmitted through a 10.0 mm diameter cylindrical nozzle in argon atmosphere, at the flow rate 20.0 L/min. The argon flow was used mainly for protection the optics inside the laser head against spatter. While the task of shielding the melt pool was negligible due to long distance (160 mm) between the nozzle and the substrate surface, as a result of defocusing the laser beam spot, Nitrogen vapours from a pressurized container (cryogenic dewar) were transported via a flexible hose into the jet nozzle. The nozzle tip was designed to be replaceable. Thanks to that different diameter tip nozzles could be applied. In this study a nozzle tip with a diameter of 5.0 mm was used, providing localized cooling of the clad area just behind the melt pool. The jet nozzle was fixed on the laser processing head, and the distance between the nozzle tip and the target surface was maintained constant at 40.0 mm, 3 + 3HCL reagent to disclose the microstructure.The specimens with test clad layers produced both by conventional laser cladding at free cooling conditions in ambient air, and the clad layers produced at forced cooling under cryogenic conditions were examined by visual inspection first. All the clad layers fulfilled the main criterion of complete penetration of the substrate. Therefore, all the test layers were cut perpendicularly and samples for metallographic study were prepared. Three sliced sections were taken from each test clad layer. One was taken from the middle region, and next two at a distance 15 mm from the beginning and the end of the clad layer, Observations of macrostructure at low magnifications (up to 25×) were carried out by means of a stereoscopic microscope OLYMPUS SZX9 , while the microstructure observations were done by the inverted metallographic microscope NIKON Eclipse MA100 . The microstructure was additionally examined by scanning electron microscopy SEM , equipped with the Energy Dispersive Spectrometer EDS  and Phenom Pro-X SEM equipped with EDS and BSD detectors . The phase composition was determined by X-Ray diffraction  with CuKα source of radiation, with the scanning range of the diffraction angle 2θ from 0 to 140°.The hardness was measured on the cross-section of the test clad layers after microstructural studies by Vickers test, at the load 5 N and the dwell time 10 s. The hardness tester WILSON WOLPERT 401 MVD  was applied in the study. Measurements were taken along the vertical axis of symmetry, starting from the under surface region of the clad layer (face of the clad). The first measuring point was 0.15 mm under the top surface, while the distance between the subsequent points was constant at 0.2 mm. In such a way, the hardness distribution from the under surface region, through the clad, fusion zone, heat affected zone, till to the base metal was determined.n—normal load (30 N), T—tangential force of friction.FThe tribological tests of coatings produced by laser deposition of experimental composite powder at free cooling and under cryogenic conditions were conducted by a ball-on-disc tribometer T-01M under room temperature of 22 °C, according to the ASTM G99 standard. The relative humidity was about 45% ± 5%. The specimens were prepared in a form of discs with diameter of 45.0 mm balls made of bearing steel  with a diameter of 10.0 mm were used as the counter face material. The normal load was set as 20 N. The number of revolutions was 1500, while radius of the track was 15 mm. Therefore, the sliding distance was 141.3 m, while the sliding speed was 0.157 m/s. The tangential force of friction and displacement value were continuously measured and recorded during tests using a data acquisition system with PC computer. While the coefficient of friction µ was calculated by dividing the value of tangential force of friction by the value of normal load used:At the first stage of the study the cross-sections of the clad layers produced as single stringer beads by conventional laser cladding at free cooling conditions were compared with the single stringer beads produced by the novel technique considered as a hybrid laser deposition under cryogenic conditions, It is worth to note, when the heat transfer efficiency into the material is known and considered in the calculation, this parameter is called heat input. In laser processing the heat transfer efficiency is related with the absorption of laser energy, and under certain conditions it can take the value 1. Therefore, for simplicity the term “heat input” will be used in the remainder of the manuscript text. As seen in D” was calculated by the following formula:FZA is the cross-section area of the fusion zone, and the CLA is the cross-section area of the clad layer  and different cooling conditions (LC4 and HC4) are presented on optical micrographs in The clad layer LC4 was produced by conventional laser cladding at free cooling in ambient and at relatively high heat input 240 J/mm, 2C/WC carbides, The carbide particles dissolved in the melt pool first enrich the liquid solution with carbon and tungsten and then recrystalize as secondary carbides in the form of dendrites, needle-like or block-like precipitations. So, the optical micrographs of the clad layer LC4 are typical for the clad produced at excessive energy and heat input, characterized by unfavourable microstructure with low share of massive tungsten carbides and high amount of secondary precipitations, Beside comparison of microstructure, the optical micrographs revealed a cluster of pores on the cross section of the clad LC4 produced by conventional laser cladding. The pores are placed in the upper part of the clad layer and the average diameter is approx. 20 ÷ 30 µm.In turn, the optical micrographs of the comparative clad layers produced at minimum heat input of 60 J/mm and different cooling conditions (LC1 and HC1) also show differences in microstructure, In contrast to the clad layer produced at maximum heat input and free cooling, the microstructure of the clad LC1 in the regions between the massive carbides is characterized by a low number of individual precipitations not exceeding 10 µm in length, as can be clearly seen in 23C6, M7C3, and M6C, which distribute in the matrix to form needle-like or block-like. However, a detailed analysis of this boundary and an attempt to explain this phenomenon is provided in the further part of the discussion.Close observation of the massive carbide’s morphology on the optical micrographs in To quantify the relationship between of laser output power of deposition process  and the cooling conditions and the morphology of the clad layer, the share of carbides relative to the matrix was determined on the cross sections, and the carbides size distribution for different clad layers was determined. The calculations were made by digitalising the micrographs images and using the NIS-Elements software  for determining the area share of carbides, and the results are presented in As can be seen, the calculated percentage share of carbides on cross section of the clad layer produced at maximum heat input of 240 J/mm and free cooling conditions is below 7%, while the share of carbides in the case of clad layer produced at the same heat input but with additional forced cooling is significantly higher, approx. over 22%, The relationship indicates generally the lower heat input the higher the share of carbides in the matrix. However, as can be seen, the effect of the forced localized cooling is advantageous, because it provides significantly higher share of carbides for every clad layer produced in the range of investigated parameters. In turn, the carbides size distribution determined for the comparative clad layers produced at minimum heat input of 60 J/mm show that the dominant size for the clad layer LC1 produce under free cooling conditions is approx. 150 ÷ 200 µm. While in the case of the clad layer HC1 produce under forced cooling conditions the carbides distribution is different and the share of carbides sized in the range 50 up to 150 µm is even and proportional, 2C manufactured as a result of melting and crushing. As can be seen from In turn the size distribution of carbides determined on the surface of the specimen indicates that the proportion of fine carbides is significant, higher than it would appear from the fraction share for the powder. The first reason for this phenomenon is the presence of secondary carbides precipitated in the liquid because of crystallization. However, these are carbides mainly in dendritic form. The share of such dendritic carbides is greater in the range of higher heat inputs (laser power), due to the conditions conducive to the dissolve of carbides in the liquid solution because of diffusion, decomposition due to direct heating with a laser beam, and then precipitation from the liquid solution. However, the presence of a large amount of very small carbide particles is also evident. The explanation for the presence of such many fine carbides is the primary form and morphology of WC-type carbides, which are in fact the eutectic of WC + WHowever, in the conditions of laser cladding the particles are exposed to direct action of the laser beam, and thus separation or even decomposition. If the carbide gets directly to the melt pool with a temperature below the carbides melting point, its decomposition will be slight, mainly due to the mutual diffusion of carbide and the liquid. When the carbide is exposed to direct laser beam radiation with high power density, it can directly lead to its partial or complete decomposition. In such a case, the carbide decomposes into fine carbides of needle-like or block-like form, as can be seen in 2C/WC carbides with feather structure are composed of needle-like and trapezoidal blocks of carbides which are light grey and white, The representative and comparative SEM micrographs were presented for the clad layers produced at the minimum heat input and different cooling conditions in 2C (β phase) and 20% of stoichiometric WC (δ phase), it can be assumed that the remaining phases on boundary are WC carbides. According to a W-C phase diagram, the melting point of tungsten monocarbide WC is at least 50÷60 degree higher if compared to melting point of W2C [2C is often reported at 2730 °C, while for δ-WC at 2870 °C. Moreover, the δ-WC phase is metastable almost up to melting point. However, it should be noted that the conditions of phases transformation during laser deposition are far from the conditions of thermodynamic equilibrium, due to high rates of heating, cooling and high maximum temperature and also high temperature gradients.Another evidence that the light grey particles on the boundaries of massive eutectic carbides were not recrystalized are the very fine crystals growing epitaxially on the tips of some of needles and tops of trapezoidal blocks, as shown in t of W2C ,33. AccoIn the case of chemical composition analysis with an EDS spectrometer, the quantitative content of elements such as nitrogen and carbon are usually not given due to the high uncertainty and measurement error. However, in the case of the presented results of the study on chemical composition, a satisfactory and sufficient convergence of the results of carbon and nitrogen content was obtained, allowing for the identification and confirmation of the presence of the expected constituents. For this reason, it was decided to include the results of the quantitative measurements of carbon and nitrogen content to ensure greater clarity of the results.2C/WC, 3B eutectic, and possible share of M2C type carbides, 7C3 type, The EDS analysis conducted on the cross-section of the clad layer HC1 produced at the lowest heat input and forced cooling, confirmed that the composition of the massive carbides is typical for eutectic WAlthough the quantitative results of the measurement of nitrogen content should be considered with a great uncertainty, it is evident that the nitrogen was detected in the clad layer produced under cryogenic conditions, mainly in regions of matrix dendrites and interdendritic regions, On the other hand, the morphology of the clad layer LC1 produced at minimum heat input but at free cooling conditions observed on the SEM micrographs is completely different that the morphology of the clad layer produced under forced cooling conditions, 2C (β phase) which is less stable than the stoichiometric monocarbide WC (δ phase). In 2C/WC carbides. Since the particles are small and have low heat capacity, thus they heat up intensively and next completely dissolve in the liquid malt pool. However, it must be emphasised that the observations and findings are valid just for the specific conditions of the experiment, determined technological conditions such as the laser beam characteristic , processing parameters, the way of powder delivery, thermal conditions.Just little traces of local dissolution and subsequent resolidification can be found on the carbides’ boundary. However, it should be noted that these are just few massive eutectic carbides that have not completely dissolved. The explanation is that the liquid solution has reached the solubility limit of carbon and tungsten, at least locally, which inhibited the further dissolution of remaining massive carbides in the melt pool. The resolidified regions of boundaries show fine light grey dendritic precipitation smaller than 10 µm, 2C/WC, confirmed presence of M2C type carbides as dendritic precipitations, 3C carbides in eutectic, The EDS analysis conducted on the cross-section of the clad layer LC1 produced at the lowest heat input and free cooling, beside the massive eutectic W3B eutectic, possibly with some amount of M2C type carbides, The composition of dark grey matrix indicates presence of Ni/Ni2C, as well as the γ-Ni. Additionally, clear picks for Ni3B and complex carbides M7C3 type were identified, Although the quantitative results of the measurement of nitrogen content should be considered with a great uncertainty, it is evident that in this case the nitrogen content is significantly lower, on the limit of the measurement error of EDS spectrometer, In turn, the X-ray diffraction patterns for two comparative samples are presented in 23C6 and M7C3 type. Moreover, slight peaks for δ-WC and Ni3B were identified. The obtained results are consistent with the previous observations of SEM micrographs and EDS analysis. The phase composition of the clad layer produced under free cooling LC1 is also affected by the higher dilution by the substrate material, mainly iron Fe, as shown the chemical composition analysis. In turn, the X-ray diffraction patterns indicate that the share of eutectic W2C/WC is significantly higher in the coating produced under cryogenic conditions. The dominant γ-Ni phase in the coating produced at free cooling is a result of different thermal conditions of the deposition process, higher impact of the heat, and thus higher degree of carbides decomposition and dissolution, as well as higher dilution by the Fe from the substrate of non-alloy steel. Therefore, the carbides precipitated from the liquid solution are more complex, as shown in The initial and general comparison of the two X-ray diffraction patterns show a clear difference in the phase composition. The sample coated at forced cooling under cryogenic conditions (parameters for HC1) shows simply more peaks compared to the sample coated at free cooling (parameters for LC1), It should be noted that the detection level of the applied XRD method is approx. 3% for the individual phase, therefore, it does not allow for precise identification of the fine precipitations at a low share. However, due to the conjunction with chemical composition analysis in the micro regions and individual constituents, precise detection of the phase composition was provided.The profiles of hardness were determined on cross-section of the clad layers produced at minimum and maximum heat input at free cooling and under cryogenic conditions. For the Vickers tests of the composite clad layers the applied load was set at 5N. The large load was chosen to avoid large scatter of results  providing mean hardness value for the subsequent regions. However, the profiles of Vickers HV0.5 hardness presented in On the other hand, despite the difference in the chemical and phase composition of the clad layers, the maximum values of hardness and the scattering of results are very similar. It should be noted that the presented results of hardness measurement for each point on the graphs are a mean value taken from three different sections for every tested clad layer. The values of standard deviation indicate small dispersion of results. This is due to relatively large size of Vickers’s indenter imprint at the load of 5N. The clad layers HC1 produced al lowest heat input and under cryogenic conditions showed the highest value of hardness 520HV0.5 directly under the top surface (face) of the clad. In turn, the highest measured hardness approx. 600HV0.5 was detected for the clad layer produced at maximum het input and cryogenic conditions. For every tested clad layer, starting from a certain depth the hardness decreases gradually till the value of the base metal of non-alloy steel (S235JR) approx. 120 ÷ 15HV0.5. This finding contrasts with the phenomenon described in the previous manuscript on “Laser Deposition of Fe-based metallic powder under cryogenic conditions” [It must be noted that the task of the study is not a comprehensive analysis of the mechanisms of wear and tribological characteristics. Therefore, just basic results of tribological ball-on-disc tests were presented for the final comparison of the characteristics and wear resistance of the comparative coatings produced under different technological conditions and different thermal conditions. The values presented at the graphs are mean values taken from at least three individual measurements. The volume loss of the coatings was calculated by determining the wear track profile in four places around the circumference of the wear track. Comparison of the wear tracks for representative samples produced at the lowest heat input but different cooling conditions (coating produced at parameters for HC1 and LC1) is shown in 2C/WC) in the matrix of every clad layer produced under cryogenic conditions is higher than for the clad layers produced at free cooling. Even in the case of the clad layer produced at the maximum heat input HC4 (laser output power 2000 W) but with simultaneous localized cooling the share of massive carbides is 22.4%, while in the case of the clad layer produced at the lowest heat input LC1 (500 W) but free cooling the share of carbides is less than 15%. Thus, the results show that under the test conditions, the wear resistance of the composite coatings is proportional to the massive carbides (eutectic W2C/WC) content in the matrix. On the other hand, the volume loos of the counter face material of steel ball is directly proportional to the volume loos of the discs samples. This phenomenon may be explained by the values of the coefficient of friction determined during individual tests. The values of coefficient of friction presented at the graph in The wear track of the sample HC1 produced under cryogenic conditions and the lowest heat input has the smallest width, as shown in The novel technique of laser deposition of composite WC-Ni powder with forced localized cooling of the deposit by nitrogen vapours stream under cryogenic conditions was successfully demonstrated and its potential for shaping the geometry and the microstructure was presented. The results of the study confirmed the advantageous effect of the forced cooling in terms of chemical and phase composition, microstructure, and wear resistance under dry sliding conditions. The use of the forced cooling technique significantly reduces the tendency to decomposition and to dissolve carbides in the melt pool during laser deposition of composite WC/Ni powder. The share of carbides on cross section of the clad layer produced at minimum heat input (laser output power 500 W and scanning speed 500 mm/min) at conventional conditions of free cooling was less than 15%, while thanks to the application of forced localized cooling of the deposit the share of carbides was maintained over 51%. Moreover, the degree of dilution was significantly reduced thanks to the forced localized cooling. The chemical composition of clad layer produced at minimum heat input and with forced cooling under cryogenic conditions was very similar to that of experimental composite WC-Ni powder, except for the increased nitrogen content in the dendritic matrix and interdendritic regions. The increased content of nitrogen detected in the matrix of the clad layer is resulted by presence of high amount of gaseous nitrogen in deposition region if the nitrogen vapours stream is applied. Therefore, during the laser deposition of composite powder (laser cladding) the alloying process takes place additionally. The material of the clad layer (the deposit) is simultaneously enriched by nitrogen from the gaseous atmosphere, so the demonstrated process of laser deposition of composite powder with simultaneous localized cooling by the nitrogen vapor stream can be considered as hybrid process, combining the conventional laser cladding (LC) and also laser gas nitriding (LGN).


However, this measurement is invasive , time consuming, expensive, uncomfortable for the patients, and as such not ideal for serial measurements. Recent advances in the technology now provide for portable and rapidly responding measurement of the PO2 and PCO2 in expired gas, which combined with the well-established measurement of arterial oxygen saturation via pulse oximetry (SpO2) make practical a non-invasive surrogate measurement of the A-aDO2, the oxygen deficit. The oxygen deficit is the difference between the end-tidal PO2 and the calculated arterial PO2 derived from the SpO2 and taking into account the PCO2, also measured from end-tidal gas. The oxygen deficit shares the underlying basis of the measurement of gas exchange efficiency that the A-aDO2 uses, and thus the two measurements are well-correlated (r2~0.72). Studies have shown that the new approach is sensitive and can detect the age-related decline in gas exchange efficiency associated with healthy aging. In patients with lung disease the oxygen deficit is greatly elevated compared to normal subjects. The portable and non-invasive nature of the approach suggests potential uses in first responders, in military applications, and in underserved areas. Further, the completely non-invasive and rapid nature of the measurement makes it ideally suited to serial measurements of acutely ill patients including those with COVID-19, allowing patients to be closely monitored if required.The efficiency of pulmonary gas exchange has long been assessed using the alveolar-arterial difference in PO Any degree of spatial mismatch between ventilation and perfusion [ventilation-perfusion (VA/Q) inequality] will lower the efficiency of the exchange of any gas, resulting in a difference between the partial pressure of a gas in the arterial blood leaving the lung, and gas in the exhaled breath  cannot add more oxygen to blood exiting regions of high VA/Q. In contrast, the quasi-linear CO2 dissociation curve means that low and high VA/Q regions can compensate for each other. Thus, it is common to see patients with pulmonary disease with arterial hypoxemia, while having a normal arterial PCO2  has long been a mainstay in assessing the disruption to pulmonary gas exchange caused by disease . The final term in this equation is often ignored as it typically has a magnitude of only a few mmHg. A more detailed description of Riley’s innovative approach can be found in 2, and it does so without actually measuring alveolar gas.The ideal alveolar POequation :idealPA2 and PCO2. The Riley construct utilizes the ideal alveolar PO2 to obviate the need to make a “technically difficult” measurement to calculate the A-aDO2. The oxygen deficit (OD) comes from a direct measurement of expired gas partial pressures and uses a non-invasive means to determine what would otherwise be an invasive measurement, the arterial PO2.Compact, rapidly responding gas analysis devices are now readily available, allowing direct measurement of expired PO2 and CO2 while the patient breathes quietly on a mouthpiece while wearing a noseclip. The final concentrations measured just before the abrupt transition to inspired gas are taken as the end-tidal values of PO2 and PCO2. An example of the expired gas record is shown in 2 and ~0.7mmHg for PCO2 , the A-aDO2 could be measured directly by taking an arterial blood sample to measure arterial PO2. However, to make the process both rapid and non-invasive, arterial PO2 is estimated from the arterial oxygen saturation (SaO2) as measured by pulse oximetry (SpO2) as determined simultaneously using a fingertip pulse oximeter. This is then used to determine the corresponding arterial PO2 from the Hill equation:50 is the PO2 at a saturation of 50%, and the SaO2 is expressed as the fractional saturation; range . PO2 is determined by taking the logarithm of the equation and solving algebraically.Having directly measured the alveolar partial pressure for O2-Hb dissociation curve, and a value of 2.7 is commonly used (2 over the entire range of saturation (The term n (commonly referred to as the “Hill-n”) is that required to match the sigmoidal shape of the Only used . While aturation , in practuration .50 of blood is normally ~27mmHg, however this varies with alterations in PCO2, body temperature, base excess, and levels of 2,3-diphosphoglycerate  can be accounted for. Using the Kelman routines  PO2 is termed the OD. This can be thought of as a surrogate measurement of the A-aDO2. In the latter case the arterial value is measured, and the alveolar value estimated as described by Riley (above), while in the case of the OD, the alveolar value is measured, and the arterial value estimated. This should not be confused with the “oxygen deficit” that provides a measure of the anaerobic contribution during exercise , the naturally occurring volume for end expiration at rest, the effect of ongoing gas exchange is minimal. Thus, the end tidal PO2 is a direct and useful measurement of the alveolar PO2  can be directly accounted for. This effect is the principal cause of shifts in the O2-Hb dissociation curve, and so the ability to correct for this is critical. Failure to do so would result in errors in the OD of >5mmHg for SpO2 values of 94%  are not taken into account with the non-invasive approach. These however, are much smaller, and produce only minor errors in the calculated OD  and typical variability of ~5mmHg at an SpO2 of 94%, with both of these values decreasing as SpO2 fell, showing the viability of the approach  to ensure that the SpO2 fell into the range in which OD could be reliably measured (SpO2<95%). A study of 20 young subjects (19–31years) and 11 older subjects (47–88years) showed a very small OD in the young cohort (~2mmHg), which was increased in the older  up to and including breathing air  was performed in 25 normal subjects during hypoxic exercise, showing a correlation between OD and A-aDOn A-aDO2 . The nonn A-aDO2 ,b. The s2 measured by the collection of an ABG in 23 patients with an SpO2 of 95% or less, there was a high correlation , suggesting that the measurement was a potentially useful means of assessing severity. Similarly, the oxygen deficit was significantly higher in the patients requiring supplemental O2 than in those who did not  again suggesting that the non-invasive measurement of gas exchange impairment provided useful clinical insight in a rapid non-invasive manner.In the context of the ongoing SARS-CoV-2 pandemic, a small preliminary study investigated the usefulness of the non-invasive approach to measuring the impairment of pulmonary gas exchange in patients with suspected COVID-19 considered to be at risk of deterioration before obvious respiratory failure had ensued . Patient2 first developed by Riley, and there is considerable physiological overlap in the measurements. This is shown in 2-CO2 diagram and highlights the aspects of the VA/Q inequality that the two methods encompass.The studies performed to date show that a non-invasive approach can be used to quantitatively assess the gas exchange deficit in patients with pulmonary disease. The approach taken is in many respects comparable to the traditional measurement of the A-aDO2 to the arterial blood , the result being arterial hypoxemia and an increased A-aDO2. The measurement of oxygen deficit encompasses the effects of low VA/Q and high VA/Q, although the effect of high VA/Q regions on arterial PO2 is small because of the shape of the O2-Hb dissociation curve. The large overlap in the areas of influence of the two methods  and increase OD, so too will hypoventilation. Because the alveolar PCO2 is also measured, hypoventilation can readily be detected which may provide an important clinical distinction of the cause of hypoxemia in some patients. Further, the OD takes into account the effect of changes in PCO2 on the O2-Hb dissociation curve. Thus, the oxygen deficit directly addresses the efficiency of gas exchange, in the same way that the A-aDO2 does.It is reasonable to question what additional information is gained by measuring the OD as opposed to simply measuring SpO2 has been performed using an invasive approach for ~70years. However, its use has become less common in recent years, likely due to the cost, time required for the measurement, and the uncomfortable and invasive nature of the procedure. In contrast, the OD is a rapid, non-invasive measurement that can be readily performed on patients ranging from ambulatory to those on mechanical ventilation. The measurement takes only a few minutes, requiring only that the patient breathe quietly on a mouthpiece while wearing a noseclip for ~2min, while wearing a fingertip pulse oximeter. The equipment is portable, making it suitable for use not only in the hospital, but in the field, and in underserved areas.The important clinical measurement of the A-aDOGP wrote, edited, and approved the article. JW edited and approved the article. All authors contributed to the article and approved the submitted version.Support for some was provided by MediPines Corporation which provided AGM100TM units for use in some of the studies referenced. Support was provided by MediPines Corporation to cover publication costs.The University of California, San Diego, has exclusively licensed technology to MediPines Corporation, Orange County, CA, to develop a device (the AGM100TM) used in some studies referenced in this work. JW declares a financial interest with MediPines Corporation.The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


A Brillouin distributed acoustic sensor (DAS) based on optical time-domain refractometry exhibiting a maximum detectible strain of 8.7 m High sensitivity and long sensing range of Distributed Acoustic Sensors (DASs) have made them ideal devices for sensing vibrations of elongated structures such as pipelines, railways, and subsea cables ,3,4,5,6.of pε/Hz ,12,13,14ng fiber ,16  systems have been developed capable of measuring large dynamic strains ,24,25,26BOTDA interrogation technique is based on the interaction of two counter propagating optical signals, i.e., a pulsed pump signal and Continuous Wave (CW) probe signal, separated in frequency by the BFS of the fiber. Conventional BOTDA interrogators form the BGS by stepping the frequency of the CW probe over a certain frequency range, a time-consuming process which limits the sampling rate of the sensor ,28. To o of 85 m . Several 85 m [ε  at typic 85 m [ε  with spa 85 m [ε  and a ma 85 m [ε ,32.BOCDA is another Brillouin-based interrogation technique that has been used to map dynamic strains along sensing fibers. The operation of BOCDA-based systems is based on generating stimulated Brillouin scattering (SBS) at a single point on the sensing fiber by sinusoidally modulating the frequency of two Brillouin-frequency-shifted CW signals and launching them from two opposite ends of the sensing fiber ,33. In tsolution . Brillousolution ,35. Sensng fiber . DespiteBOTDR is the simplest interrogation technique which is based on direct detection of the spontaneous Brillouin Scattering ,26,36,37er range . This meer range  demonstrn signal . Using treported , by emplThe rest of the paper is organized as follows. In n denote the wavelength of the probe pulse and effective refractive index of the fiber, respectively. For such DAS systems relying on optical interferometry, the maximum detectible vibration at each point along the fiber depends on both the repetition rate of the probe pulse, I is the intensity at the output of the MZI, A and B are constant values, and t. For any given section of a fiber, the value of L. For a sinusoidal strain wave with frequency f, the value of In this section, the theoretical limit of e points . Each selevel, ε . This regiven by (2)Δφt=0f may not necessarily translate to an intensity modulation with the same frequency at the detector. As an example, This equation shows that a sinusoidal vibration with frequency N is an integer. This equation shows that the detector experiences a maximum excursion rate at t = 0. Using Maclaurin expansion for In order to determine the maximum intensity excursion rate at the interferometer output, the derivative of Equation (4) needs to be calculated: f and According to this Equation, the intensity modulation frequency of the detector for a sinusoidal strain wave with frequency and amplitude of Therefore, to avoid temporal aliasing, DAS interrogator should have a minimum pulse repetition rate ofD, the maximum repetition rate isc is the speed of light in vacuum. By combining Equations (8) and (9), the relationship between the length of the sensing fiber and the maximum detectible strain rate would beAnalysis of Equation (8) demonstrates a trade-off between the strain rate experienced by the fiber and the repetition rate of the probe pulse. For an OTDR system, the maximum pulse repetition rate is determined by the round-trip time of light in the sensing fiber. For a fiber with length L = 1 m) can detect as a function of the strain amplitude is plotted in For a fiber with a given length, this equation puts an upper limit on the strain rate that a A is the intensity of the light at the input of the MZI. Any changes in the wavelength of the input signal translates into optical intensity variation at the photodetectors. Thus, the strain-induced BFS results in an intensity variation of the light at the three output arms of the MZI. This variation is illustrated in The frequency transfer function of the imbalanced MZI at the output of the B-DAS system determines the response of the sensor to BFS. A schematic of the MZI used for demodulation of the BFS is shown in itten as (11)I1=AΔL and λ (12)Φ=fIThe backscattered light was collected via an optical circulator and amplified by an optical pre-amplifier (EDFA2). A band-pass Dense Wavelength Division Multiplexing (DWDM) filter with 100 GHz bandwidth and a Fiber Bragg Grating (FBG) with 59% reflectivity and 0.03 nm bandwidth were employed to suppress the ASE and Rayleigh backscattered lights, respectively. The wavelength of the seed laser was tuned to align the frequency of the backscattered Brillouin anti-stokes signal with the central frequency of the FBG filter. The filtered light was then passed through a polarization scrambler to reduce the effect of the polarization dependent components in the MZI on the Brillouin signal. The path imbalance of the MZI was set to  MHz FSR . The outFor the tests with 8.5 km fiber, the repetition rate of the probe pulse was set to 1.2 kHz. The Brillouin backscattered light from the fiber under test was filtered by the MZI after pre-amplification. The MZI filter was used to convert the changes in BFS into intensity variations. The short path imbalance of the MZI relative to the duration of the probe pulse guaranteed mixing the backscattered light from the same section of the fiber. For low frequency vibrations , to reduce the noise level, the BOTDR traces obtained at the PDs were averaged 100 times to reduce the noise level and then analyzed using differentiate and cross-multiply demodulation scheme to extract the dynamic strain information. This method provides a large dynamic range detection through fringe counting algorithm . A recipf = 21, 76, 103 and 120 Hz are plotted in The frequency response of the sensor to higher frequency vibrations at Due to the different group velocities of signal and pump modes , the amplification was limited to the fiber location where pump and signal pulses spatially overlap. The amplification length can be approximately given by −ns=10−3 , a pump A comparison of the output of the B-DAS system, operating under various Raman amplification conditions, is shown in In order to compare the noise level of the three amplification configurations, the FFT of the measured signals are plotted in shown in . Althougshown in . Hence, A long-range B-DAS system capable of measuring vibrations with high strain rate was demonstrated. The proposed method provides a sensing system based on interferometric demodulation which does not suffer from intensity fading and does not require any locking mechanism associated with other types of B-DASs ,30,31. T


LiH, TiC and 2I diatomic molecules is considered. The Schrodinger equation in cosmic string spacetime is solved with the generalized Morse potential using the well-known (NU) method. The energy spectra and eigenfunction are obtained respectively. The energy spectra is used to obtain the partition function which is then used to evaluate the thermal properties of the system is evaluated accordingly. We find that the energy spectra in the presence of the TD differ from their flat Minkowski spacetime analogue. The effects of the deformation parameter and TD on the thermal properties of the system is also analysed in detail. We observe that the specific heat capacity of the system tends to exhibit quasi-saturation as the deformation parameter and topological defect approaches unity. The results of our study can be applied in the astrophysical situation where these modifications exist in the understanding of spectroscopical data and it may be used as a probe of the presence of a cosmic string or a global monopole in the Universe.In this study, the impacts of TD on the energy spectra and thermal properties of  The deficiency of the harmonic oscillator in the description of interatomic interactions in diatomic molecules brought about the Morse potential in 1929 , Frost–MIn respect to what has been observed in previous studies of molecular potential, Ikot et al.  modifiedFurthermore, for many years, the study of quantum dynamics of a single particle interacting in a given potential with a topological defect has been a subject of great interest to researchers. The formation of a topological defect is thought to have occurred during a phase transition in the early universe ,18,19,20Topological defects play an important role in modifying the physical properties of many quantum systems, and they have long been a popular topic in fields such as condensed matter and gravitational physics. In gravitation, topological defects appear as monopoles, strings, and walls ,26. In cA global monopole is an exotic object that may have been formed during the phase transition in the very early universe. When the corresponding vacuum is non-contractible, M≅S2 . Such anid angle ,27. LiH, TiC and 2I diatomic molecules. These molecules were considered for diatomic molecules because of their wide industrial applications. Lately, another area of research that has gained unparalleled attention is the study of thermal properties of quantum systems ,34,35. IThe major goal of this paper is two-fold: first, we studied the energy shift related with a non-relativistic quantum particle interacting with the GMP in the spacetimes generated by a cosmic string for selected diatomic molecules. Further, we analyzed the effects of the topological defect on the thermal these diatomic molecules.LiH, TiC and 2I diatomic molecules placed in the gravitational field of a cosmic string. Finally, in This paper is organized as follows. In The NU approach reduces a second-order linear differential equation to a generalized hypergeometric form equation ,51,52,53In order to find the solution to Equation (2), a wave function of the form :(3)ψ(s)=equation  is obtaiThe wave function is given as:The hyper-geometric-type function ation as (6)yn(s)For bound solutions, it is required thatTherefore, the function The values of By equating Equations (11) and (12), the energy eigenvalue is obtained.For spacetime with a point-like global monopole (PGM), the line element that explains it is given by ,55: (13)In this way, the Schrödinger equation (SE) is given as follows:In what follows, let us consider a particular solution to Equation (16) given in terms of the eigenvalues of the angular momentum operator Over the years, it has been known that equations of the form of (18) cannot be solved in the presence of the centrifugal term,  Pekeris  proposed Pekeris  to solve Pekeris  to bypasBy using approximation in Equation (19) and using the change of coordinate Comparing (21) with the hypergeometric equation of Equation (2), we obtain the following polynomials:The polynomial To find the expression for The substituting Taking the negative value of To obtain the polynomial The derivative of The parameter The eigenvalue expression holds ifSubstituting Equation (22a) into (32) and evaluating it, we obtain the energy as follows:To find the eigenfunction, the weight function is first evaluated. From Equation (7), we obtainIntegrating Equation (5), we obtainRecalling The polynomial solution of Combining the Laguerre polynomials All thermodynamic properties can be obtained from the system’s partition function, according to the extensive literature and basic text ,34,35. Tactor as ,34,35:(3Substituting Equation (33) in (39), we have:If we set LiH, TiC and 2I [Using Mathematica 9.0 to integrate the integral in Equation (43) yields the following vibrational partition function of the generalized Morse potential with topological defects:C and I2 ,34,35: electronic state of the LiH, TiC and 2I diatomic molecules are taken from the literature [In this section, the results obtained in the previous sections are used to study i et al.  studied i et al.  obtainedo et al.  studied thors of ,58,59 stterature  and showLiH, TiC and 2I molecules for different quantum states with various values of the topological and deformation parameter. It is observed that for a given quantum state, the energy decreases as the deformation parameter increases. However, if one pays close attention to the behavior of the energy spectra as it varies with the We used the following conversions: utations . Table 2 Bezerra . LiH, followed by TiC and then 2I. In LiH but was quasi-constant for TiC and 2I In LiH diatomic molecule, but increases with rising temperature for TiC and 2I. In LiH was found to be highest, followed by TiC and then 2I. In LiH first peaks in the interval TiC and 2I, the free energy decreases with increasing 2I. In In In LiH first peaks in the interval TiC and 2I, the average energy decreases with increasing In LiH reveals a sinusoidal behavior as the deformation parameter varies. The specific heat capacity of TiC decreases with increasing 2I increases with increasing In LiH, TiC and 2I diatomic molecules. We see here that the presence of the defect and deformation can be used to alter the behavior of the system and its thermal properties. We also found that to create an upward shift in the energy spectra, the topological defect is required, whereas the deformation parameter can be used as a controller or an enhancer. The effects of the topological defect and deformation parameter on the thermal properties of the system is duly analyzed. We observe that the specific heat capacity of the system tends to exhibit quasi-saturation at large as the deformation parameter and topological defect approaches unity. Conclusively, we note here that our study of the generalized Morse potential in non-trivial gravitational background, such as what we treated in this study, will aid in the understanding of the problems of combining quantum mechanics and general relativity. The present model (GMP) could be applied for calculating the mass spectra of heavy mesons such as charmonium and bottomonium [In this research article, we have scrutinized the effects of topological defect on the energy spectra and thermal properties of the generalized Morse potential for tomonium ,62,63.


The viscoelastic measurements, carried out on the as-prepared hydrogels, showed that the monomer concentration had the largest impact, its three-time enhancement causing a 30-fold increase in the storage modulus, as compared with only a fivefold increase in the case of the crosslinking agent and 1.5-fold increase for MMT in response to a similar threefold concentration increase. Swelling studies, performed at three pH values, revealed that the water absorption of the hydrogels decreased with increasing concentration of both the monomer and crosslinking agent, with the amplitude of the effect of concentration modification being similar at pH 5.4 and 7.4 in both cases, but very different at pH 1.2. Further, it was shown that the increased pH differently influenced the swelling degree in the case of the hydrogel series in which the concentrations of the monomer and crosslinking agent were varied. In contrast to the effect of the monomer and crosslinking agent concentrations, the increase in the MMT amount in the hydrogel resulted in an increased swelling degree at pH 5.4 and 7.4, while at pH 1.2, a slight decrease in the water absorption was noticed. The hydrogel crosslinking density determinations revealed that this parameter was most affected by the increase in the monomer concentration.The present work aims at comparatively studying the effects of the concentrations of a monomer (10–30 wt% based on the whole hydrogel composition), crosslinking agent (1–3 mol% based on the monomer), and reinforcing agent  on the swelling and viscoelastic properties of the crosslinked hydrogels prepared from methacrylic acid (MAA) and N,N′-methylenebisacrylamide (BIS) in the presence of K Hydrogels can be defined as hydrophilic polymeric networks formed from natural and/or synthetic polymers that are capable of absorbing and retaining a large amount of water or aqueous fluids without dissolving due to the crosslinked structure . Over tiPoly(methacrylic acid) (PMAA) hydrogels are pH-sensitive anionic materials with mucoadhesive properties. Because of this, they have found many applications in the drug-controlled release field, as they ensure protection to the drugs inside the stomach at acidic pH ,9. GarciThe literature also describes hydrogels based on PMAA that have been studied in combination with natural polymers 2 × yH2O. Its employment for the reinforcement of hydrogels is more advantageous economically because MMT is both readily available in nature and is environmentally friendly. Another important advantage of MMT is that it has a hydrophilic character and can be easily dispersed in the presence of hydrophilic polymers. Zhumagaliyeva et al. obtained bentonite-reinforced poly(acrylic acid)/PMAA composite hydrogels and studied the influence of several factors  on the swelling properties of hydrogels. They concluded that the swelling degree increased with pH and temperature and decreased with the concentration of the reinforcing agent [Mechanical properties are very important in the case of hydrogels used for controlled release, as well as for any other field. These properties can be improved by adding reinforcing agents such as clays . Montmorillonite (MMT) is a natural clay that belongs to the smectite category, displaying the empirical formula Alng agent . Furtherng agent  and studng agent , as wellng agent . It was Crosslinked hydrogels based on PMAA or PMAA and MMT have potential uses in the controlled release of drugs ,10,11,12The present work aimed to compare the effects of the monomer (MAA) and reinforcing agent (MMT) concentrations and crosslinking agent (BIS)/monomer (MAA) ratio on the viscoelastic properties and water absorption at various pH values of the crosslinked PMAA hydrogels. To the best of our knowledge, this is the first report of such a study. For a better comparison of the effect of the various components, the viscoelastic properties of hydrogels were investigated immediately after synthesis (“as-prepared hydrogels”), when their composition was identical to that of the precursor solution, while the water absorption/swelling degree was calculated in relation to the amount of polymer in the hydrogel only. We will show within this paper that, out of the three components mentioned which were employed within the usual concentration limits, the monomer concentration used in the synthesis process displhadayed the most pronounced influence on both the viscoelastic properties and crosslinking density of hydrogels. Further, the swelling degree of the PMAA hydrogels decreased with the concentration of the monomer and crosslinking agent and increased with the concentration of MMT; the resulting values depended on the pH of the medium, in agreement with the pH-sensitive nature of these types of hydrogels.Unmodified montmorillonite  provided by Southern Clay Products Inc.  was purified by magnetic stirring with distilled water (100 g/1 L distilled water) at room temperature for 24 h, followed by decantation for 24 h. The sedimented part was separated, and the supernatant was centrifuged at 900 rpm for 30 min; the collected sediment was dried by lyophilization and used in experiments. Methacrylic acid , N, N methylenebisacrylamide , and ammonium persulfate (APS 98% Sigma Aldrich) were used as received. The solvent used in the synthesis of hydrogels was deionized water . Swelling studies were performed in deionized water (pH 5.4), HCl solution (pH 1.2), and PBS  solution  obtained from tablets (Sigma) and deionized water according to the manufacturer’s instructions and adjusted as needed to obtain the desired pH.The clay was dispersed under magnetic stirring in the calculated amount of DI for 24 h, and the monomer and crosslinking agent were added, followed by the initiator. The polymerization mixture was then injected into a mold consisting of two glass plates separated by a 1-mm-thick Teflon gasket. The mold was sealed and placed in a thermostatted bath at 60 °C for 5 h. At the end of the polymerization process, the mold was cooled down, disassembled, and discs of 8 mm and 20 mm in diameter were cut from the hydrogel. The 8 mm discs were purified for seven days in DI, with the water being replaced every day, while the 20 mm discs were used immediately for rheological measurements. 2 to a constant mass and weighed (Wo). The dry xerogel was then immersed for purification in DI, which was changed daily for seven days, and then dried again (Wext). The monomer conversion (C%) was calculated according to Equation (1):MMT is the amount of MMT contained in the material used to determine the conversion.To determine the monomer conversion, part of the hydrogel was dried first in air and then over anhydrous CaClX) were immersed in 30 mL of swelling solution at 37 °C for 72 h or other various time intervals. The hydrogels were then removed from the solution, wiped superficially with filter paper, and weighed (WH). All the measurements were performed in duplicate. The swelling degree (SD) was calculated as the ratio of the amount of water absorbed to the mass of polymer in xerogel according to Equation (2):To determine the swelling degree, the pre-weighed xerogels (W1 represents the molar volume of the solvent (for water V1 = 18 cm3/mol), 3/g in the case of PMAA), while The average molecular weight between crosslinks (tion (3) ,22.(3)Mnization .3 for PMAA [3 in the case of water), while Wh and Wx represent the mass of the hydrogel at equilibrium swelling (The polymer volume fractions (tion (4) (4)ν2r/mfor PMAA  and solvThe crosslinking density of the hydrogels was calculated according to Equation (5) .(5)ρc=1The rheological measurements were carried out at 25 °C on a Kinexus Pro instrument  by using 20 mm parallel plates with roughened surface to avoid slippage. The normal force applied was 0.5 N. The amplitude sweep measurements were performed a 1 Hz constant frequency, while the frequency sweep experiments were carried out in the 0.1–10 Hz range, a deformation within the linear viscoelasticity range being applied.The FTIR spectra were recorded on a Tensor 37 Bruker equipment  equipped with a Golden Gate ATR unit, by using ground xerogels.X-ray diffraction (XRD) measurements were carried out on a Rigaku Ultima IV X-ray diffractometer  operated at 40 kV and 30 mA by employing xerogel powders.The thermogravimetric analysis (TGA) of the xerogels was performed on a TA Q5000 IR  in a nitrogen atmosphere (40 mL/min), the samples being heated from room temperature to 700 °C with a 10 °C/min heating rate.t-test was used for assessment of statistical significance. Values were considered significant at p < 0.05.The swelling experiments were performed in duplicate, and the results are presented as average values and standard deviation. Student’s The studied hydrogels were obtained by the radical copolymerization of MAA with BIS in aqueous solution, in the presence of APS as the initiator, by using different concentrations of the monomer, crosslinking agent, and MMT, within the usual concentration range employed for the synthesis of hydrogels. The standard hydrogel (SH), against which the concentration of the monomer and BIS was modified, while MMT was added in the case of composite hydrogels, contained 10 wt.% MAA and 2 mol% BIS. For a better comparison of the effect of the various components, the viscoelastic properties were measured on as-prepared hydrogels, whose composition was identical to the one of the precursor solution. Further, for a correct interpretation of the results, the water absorption/swelling degree was determined after the purification of the hydrogels and calculated in relation only to the amount of polymer in the hydrogel, excluding the amount of MMT incorporated in the case of composite hydrogels and taking into account the total monomer conversion. Because both the viscoelastic properties of hydrogels and their swelling degree depend on the monomer conversion, this was determined in each case, resulting very high conversions (90–98%), which allows the comparison of rheological and swelling measurements in all cases. To prove the incorporation of the reinforcing agent, the purified composite hydrogels were further characterized by FT-IR spectroscopy, XRD, and TGA analyses.The change in the monomer concentration in the initial mixture influences the crosslinking degree ,8,26 andThe effect of the monomer concentration was studied for three different values, namely, 10, 20, 30 wt% based on the whole reaction mass by keeping constant the crosslinking agent  and the initiator (KPS 1 mol% to MAA) concentrations.The obtained hydrogels in their as-prepared state were characterized by both amplitude sweep and frequency sweep measurements. The amplitude sweep measurements a showed In the case of environmentally sensitive hydrogels, the swelling degree may be influenced by the medium in which the swelling takes place. PMAA hydrogels belong to the pH sensitive hydrogel category due to the presence of acidic groups within their molecules. When the pH value of the swelling medium is higher than pKa, ionization of the acid groups in the hydrogel takes place, leading to the increase in the swelling degree . The equp < 0.05), namely, approximately four times in the case of the hydrogel synthesized at 10% MAA, 4.3 times for the one with 20 wt% MAA, and 4.6 times in the case of the 30 wt.% MAA hydrogel. Regardless of the pH value of the medium, the swelling degree increased with the decrease in the monomer concentration, in agreement with previous reports [As we expected based on the pH-sensitive character of the hydrogels, regardless of the monomer concentration in the synthesis step, ESD increased with increasing pH, with the highest swelling degree being obtained at pH 7.4 . The hig reports ,21,25,26 reports ,21,25. TThe crosslinking density, determined in the case of hydrogels that swelled at pH 1.2 , displayThe concentration of the crosslinking agent in the hydrogel network is an important parameter to investigate because it directly affects the swelling degree and therefore the viscoelastic properties of the hydrogel. In this study, the effect of three different concentrations of the crosslinking agent was investigated, namely, 1, 2 and 3 mol% relative to the monomer, with the concentration of the monomer being 10 wt% based on the whole hydrogel composition.The viscoelastic properties of hydrogels depend on their swelling degree  and therThe use of a higher concentration of crosslinking agent in the synthesis process leads to hydrogels with a higher density of crosslinking bridges, and therefore, more crosslinked structures are obtained that have higher mechanical properties. Indeed, the amplitude sweep and frequency sweep rheological measurements  showed tThe adjustment of the crosslinking agent concentration is one of the most important methods of controlling the crosslinking density of a hydrogel and, as a consequence, of the ability to swell in water . Indeed,p < 0.05). We do not have an explanation for this phenomenon at this time.Regarding the effect of the pH of the medium, in this case as well, the pH increase led to an increase in ESD as expected; the reason for this effect is explained above. It is worth noting, however, that the two series of hydrogels behaved differently from this of point view as well. Namely, while in the case of hydrogels obtained at different monomer concentrations, the ratio R = (ESD at pH 7.4)/(ESD at pH 1.2) practically did not depend on the monomer concentration at synthesis (R ≈ 4), in the case of the crosslinking agent concentration modification, R significantly decreased with the increase in the amount of BIS from about 6 for the hydrogel with 1 mol% BIS relative to the monomer, to 4 and about 3 in the case of hydrogels with 2 mol% BIS and 3 mol% BIS, respectively  obtained for the studied composites and the pure MMT are displayed in The thermogravimetric analysis revealed the presence of three decomposition stages in the case of the nanocomposite hydrogels . The fir2 elimination [2 decreased. This phenomenon may be explained by a lower degree of crystallinity of the polymer at higher MMT concentrations , leading to a smaller decomposition temperature of the PMAA chains.In the second stage (120–300 °C), xerogel dehydration occurred by inter- and intramolecular elimination of water between COOH groups with the formation of anhydride cycles, as well as decarboxylation of COOH groups and COmination . The lasmination . Total lmination . All MMT−5–10−1), and therefore no appreciable decrease in elasticity (narrowing of LVER) with increasing amount of MMT was noticed. The frequency sweep measurements , in agreement with the pH-sensitive character of these PMAA hydrogels  swollen at three different pH values revealed that the hydrogels present large interconnected pores which change their size depending on the swelling medium .The present paper comparatively discusses, for the first time, the influence of the monomer (MAA), crosslinking agent (BIS), and reinforcing agent (MMT) concentrations employed within the usual range, upon the viscoelastic properties determined on the as-prepared hydrogels, and the water absorption/swelling degree at various pH values of the PMAA hydrogels. It should be mentioned that the two properties investigated here are essential in establishing the applications of hydrogels. The results showed that the most important effect on the viscoelastic properties was displayed by monomer concentration, the tripling of which led to an approximate 30-fold increase in G′ as compared to an increase of only five times in the case of BIS and 1.5 times when the MMT concentration was raised from 1 wt% to 3 wt% .The swelling studies confirmed, as expected, the pH-sensitive character of the studied hydrogels, the ESD increasing with the pH of the medium in all cases. The increase in the concentrations of the monomer and crosslinking agent led to a decrease in water absorption due to the increase in the crosslinking density of the hydrogels in both cases.The amplitude of the effect of the monomer and BIS concentrations on water absorption was similar at pH 5.4 and 7.4, but they behaved very differently at acidic pH, when the effect of the monomer amount was much stronger. Further, the pH increase had different effects in the case of these two hydrogels series. Namely, while in the case of hydrogels obtained at different monomer concentrations, the (ESD at pH 7.4)/(ESD at pH 1.2) ratio practically did not depend on the amount of the monomer, the same ratio decreased with the crosslinking agent concentration.As opposed to the effects of the monomer and crosslinking agent concentrations, the increase in the MMT concentration in the hydrogel resulted in an increase in the swelling degree of the hydrogel at pH 5.4 and 7.4, due to the basic character of the clay, while at pH 1.2, a slight decrease in water absorption was noticed, ascribable to a slight crosslinking effect of the MMT, in agreement with the rheological measurements.This study is very important due to the use of such hydrogels (pH sensitive) in the medical field as devices for controlled-release drugs and also in the environmental protection and sustainable development field for wastewater purification.


Multilayered and functionally graded coatings are extensively used for protection against wear of the working surfaces of mechanisms and machines subjected to sliding contact. The paper considers the problem of wear of a strip made of a functionally graded material, taking into account the heating of the sliding contact from friction. Wear is modeled by a moving strip along the surface of a hard abrasive in the form of a half-plane. With the help of the integral Laplace transform with respect to time, the solutions are constructed as convolutions from the law of the introduction of an abrasive into the strip and the original in the form of a contour integral of the inverse Laplace transform. The study of the integrands of contour quadratures in the complex plane allowed determination of the regions of stable solutions to the problem. Unstable solutions of the problem lead to the concept of thermoelastic instability of the contact with friction and formed regions of unstable solutions. The solutions obtained made it possible to determine a formula for the coefficient of functionally graded inhomogeneity of the coating material and to study its effect on the occurrence of thermoelastic instability of the contact taking friction into account, as well as on its main characteristics: temperature, displacement, stress and wear of the functionally graded material of the coating. The effects of the abrasive speed, contact stresses and temperature on wear of the coating with the functionally graded inhomogeneity of the material by the depth were investigated. Design of multilayered materials increased rapidly in the 1980–1990s, thus enabling the introduction of such materials with properties variable by depth in a number of industries such as construction, transport and other fields. Overall, their necessity in such fields was due to the increasing requirements for strength, wear and tear of details and parts. Recently, methods and technologies for the manufacturing of protective coatings from functionally graded materials (FGM) to micro- and nanometer technological levels have been developed: the centrifugal method ,4,5,6,7,FGM coatings are widely used to protect friction surfaces from wear. Generally, the tribological properties of FGM coatings are investigated by experimental methods, such as disc–pad ,5, ball–The need to optimize the design of FGM coatings, to predict wear of the working surfaces of mechanisms and machines, to diagnose and prevent abnormal situations necessitates mathematical modeling of the wear process. In modern microelectronics, semiconductor materials are used in the form of thin plates with a thickness not exceeding 20–30 µm down to 100 nm, and the presence of a functionally graded inhomogeneity of the material (FGIM) by depth. The process of thinning such plates in practice is carried out by grinding, polishing and washing. Mathematical modeling of the grinding process of the workpiece material is associated with the elucidation of the degree of influence of the properties of the FGIM of the workpiece material on the grinding process; on the nature of the workpiece heating; on the possibility of the occurrence of thermoelastic instability of the sliding contact; on acceleration/deceleration the grinding process, etc.A lot of research is devoted to mathematical modeling of the contact of bodies with FGM coatings ,24,25,26Today, when solving problems of material wear, Archard’s relations are most often used . Dow andIn the present paper, we consider a problem of wear of an elastic coating in the form of a strip made of FGM by a hard abrasive in the form of a half-plane, which slides along the strip at a constant speed, heating it due to friction. The influence of the FGIM of the strip on the process of wear (grinding), heating from friction, the conditions for the occurrence of thermoelastic instability of the sliding contact are investigated.IIIx) varies with depth I) sliding, the coating wear takes place, which can also be thought of as the abrasive grinding of the coating surface. The frictional heat generated at the contact interface flows into the coating. From the initial time moment, the abrasive  slides along the To investigate the effect of the FGIM of the coating on its wear we consider a quasi-static contact problem of sliding of a rigid heat-insulated abrasive, half-plane In the described problem formulation, the temperature, stresses and displacements distributions in the coating do not depend on the horizontal coordinate d time t ,39,40,41The heat equation has the formThe Duhamell–Neumann law takes place (3)σxx=2The differential equations of linear uncoupled elasticity are represented by the system of equilibrium Equation (1) and heat Equation (2), which together describe thermoelastic state of the coating. I) displacement due to the coating wear. To find the solution, we use the abrasive wear model [Boundary conditions for Equation (1) are as follows (ar model  in integThe boundary conditions for the heat Equation (2) are  by a certain depth with a hard abrasive in the form of a half-plane, taking into account heating from friction, is derived through the solution of the initial boundary value problem, including the system of the differential equations of elasticity (1) and heat conduction (2) with boundary (4)–(10) and initial (11) conditions. Note that vertical displacements We proceed to the solution of the formulated problem introducing the Laplace integral transform (12)TL, (14), (20), (21) into boundary conditions (16)–(19), we obtain the linear system for the determination of the constants For the image We apply the inverse Laplace transform to the Laplace images To obtain (35) from (26) we take into account that To find out the existence conditions of integrals in (32), (34), (36), (38) we analyze integrands for From (39) it follows that the integrands in (34), (36) do not decay at infinity (at ed sense . After rIntegrands in Equations (40) and (43) at These properties of integrands allow us to apply the methods of complex analysis for calculation of the integrals and stability analysis. In quadratures (32), (38), a regularization is carried out to obtain integrands decreasing at infinity, after which they are investigated by the same methods as in (40), (43).To investigate the stability of the solutions obtained in the previous subsection, we need to study effect of the problem parameters on the integrand poles in integrals (32), (38), (41), (44). The poles of the integrands are zeros of the equationThen, the parameter Locating zeros Equation (47) is solved using numerical methods and complex analysis methods . Analysimilar to ,53,54 anAnd do not depend on Asymptotic estimation of 1), 0.9 (2), 1.0 (3), 1.1 (4), 1.35 (5), 5.0 (6). Solid diamonds indicate locations of 4–6 on 1–3 on The numbers I, II denote regions , where One significant property of the poles from regions II, III is noted; they are complex conjugated, i.e., Wear causes a dramatic effect on the poles’ behavior. In quasi-static sliding contact problems with frictional heating but without wear, the poles V^∈[0,∞) ,53. In cWhen the poles By replacing symbolic index Calculating The horizontal displacements Analysis of Formulas (57)–(59) for Trajectories of the poles  axis V^ , shifts des with . The forameter η  on the bNote that the dimensionless parameter In Calculating integral (15) of the function in (64), we obtain the expression for Equation (65) allows one to determine other characteristics depending on Then, from (67), (68) we obtain an expression for the parameter I) into the coating is given by the formulaThe law The nature of the loss of thermoelastic stability of the main parameters of the contact (temperature I) of an elastic strip made from aluminum with a graded content of alumina (Al2O3) on the main characteristics of the contact: temperature −6 mm2/s, −6 1/K, t/(m·K), f = 0.47, V = 2.5 mm/s, Let us study the effect of the parameter Variation of the shear modulus −11 m2/N, we obtain the values of dimensionless parameters The wear of the coating surface at the depth V.1, 2, 3 are plotted for The effect of the parameter 3 indicates a greater stiffness of FGM than curve 1  will occur faster than the wear of the less stiff coating (curve 1), for the same reason according to (8), and also because the vertical movement of abrasive I carried out forcibly according to the law for  curve 1 , the val curve 1 . The weaFor the preparation of materials with grinding, the power supply of the abrasive is often used due to the contact pressure After inverting the previous formula, taking into account (27), we obtain the following formula for determining The temperature at the contact Similarly, it is possible to determine After inverting (78), we obtainWhen The present study was aimed at solving the problem of wear-grinding of a FGM coating with a depth-varying shear modulus. According to the results of the studies presented in the paper, it becomes feasible to solve the inverse problem of determining the law of distribution of the depth-varying shear modulus of the FGM l of the coating. It will be necessary to find out what the minimum set of information is for the unambiguous determination of the shear modulus varying by depth. The solution to this problem is important for the design of FGM coatings with special properties .−A dimensionless parameter −Boundaries of the regions of thermoelastic instability in the space of dimensionless parameters of the problem: −Features of the kinematic scheme of wear, which consists in setting an arbitrary law of upsetting of a hard abrasive on the surface of a strip made of FGM and leading to an uncontrolled increase in temperature and contact stresses;−A special grinding scheme, consisting in the development of such a law of displacement of a hard abrasive into the surface of a strip made of FGM, with the help of which the growth of both the temperature at the contact and the contact stresses is limited.The considered thermoelastic contact problem of sliding wear by a hard abrasive material at a constant speed over the surface of an elastic coating in the form of a strip made of FGM with an arbitrary shear modulus varying with the depth of the coating made it possible to establish: