In order to make a piezoelectric vibration energy harvester collect more energy on a broader frequency range, nonlinearity is introduced into the system, allowing the harvester to produce multiple steady states and deflecting the frequency response curve. However, the harvester can easily maintain intra-well motion rather than inter-well motion, which seriously affects its efficiency. The aim of this paper is to analyze how to take full advantage of the nonlinear characteristics to widen the bandwidth of the piezoelectric vibration energy harvester and obtain more energy. The influence of the inter-permanent magnet torque on the bending of the piezoelectric cantilever beam is considered in the theoretical modeling. The approximate analytical solutions of the primary and 1/3 subharmonic resonance of the harvester are obtained by using the complex dynamic frequency (CDF) method so as to compare the energy acquisition effect of the primary resonance and subharmonic resonance, determine the generation conditions of subharmonic resonance, and analyze the effect of primary resonance and subharmonic resonance on broadening the bandwidth of the harvester under different external excitations. The results show that the torque significantly affects the equilibrium point and piezoelectric output of the harvester. The effective frequency band of the bistable nonlinear energy harvester is 270% wider than that of the linear harvester, and the 1/3 subharmonic resonance broadens the band another 92% so that the energy harvester can obtain more than 0.1 mW in the frequency range of 18 Hz. Therefore, it is necessary to consider the influence of torque when modeling. The introduction of nonlinearity can broaden the frequency band of the harvester when it is in primary resonance, and the subharmonic resonance can make the harvester obtain more energy in the global frequency range. The battery is a traditional energy storage device. Many devices  rely on batteries for energy supply. However, the battery cannot achieve long-term energy supply due to limited life, energy storage, and power efficiency and often needs frequent replacement or maintenance. An increasing number of researchers have paid attention to topics such as collecting energy from the environment to eliminate the demand for batteries or extend batteries’ life. Vibration energy is typical mechanical energy in the environment. There are many ways to produce it, such as the surrounding environment, wind flow, fluid movement, mechanical work, and human behavior. Piezoelectric vibration energy harvesters are widely used in research for low power electronic devices such as embedded electronic devices, implantable biomedical devices, wireless sensor nodes, and portable electronic devices due to their simple structure, long life, high power density, and no need for an initial voltage source.The piezoelectric cantilever beam is the most commonly studied and discussed structure in a piezoelectric vibration energy harvester because of its simple structure and convenient modeling. In the linear piezoelectric cantilever beam structure, the mass is usually added to the free end of the cantilever beam , which cThe realization of the multi-steady state of the piezoelectric vibration energy harvester mainly uses the magnetic field force provided by permanent magnets. A different number of steady states can be obtained by using different arrangement modes of permanent magnets. Erturk et al.  propose For the nonlinear piezoelectric energy harvester, the forward sweep can obtain a wider effective bandwidth than the reverse sweep when the sweep is conducted. Therefore, the nonlinear harvester cannot always obtain a higher amplitude as the external excitation frequency varies. Qing et al.  propose The frequency sweep of a nonlinear piezoelectric energy harvester cannot reveal all the steady-state behaviors it can achieve, and frequency sweep does not reveal the subharmonic motion. Syta et al.  studied The theoretical method for solving strongly nonlinear vibration has always been a difficulty. In order to solve this problem, Wang et al.  proposedIn modeling the piezoelectric cantilever beam harvester, the magnetic repulsion between permanent magnets is generally considered ,20. The In this paper, the energy harvester of the piezoelectric cantilever beam structure is studied. The permanent magnets provided nonlinearity for the harvester, and the magnetic repulsion and torque between them are considered. In order to achieve a bistable state, the distance between the free-end permanent magnet of the cantilever beam and the fixed permanent magnet is determined according to the static analysis. The approximate analytical solution and amplitude–frequency relationship of the strongly nonlinear harvester’s steady-state motion are obtained using the CDF method. The broadening effect of primary resonance and subharmonic resonance on the bandwidth of the harvester is compared and analyzed.The rest of this paper is organized as follows. The piezoelectric material as an energy transfer device directly affects the collection efficiency of the harvester. Currently, commonly used piezoelectric materials ,23,24 inL is the length of the composite beam, which consists of a substrate beam and two piezoelectric plates. The materials of the substrate and piezoelectric plate are beryllium bronze QBe1.9 and FMC M2807 P2. A layer of the piezoelectric plate is pasted on the substrate’s top and bottom surfaces, and the substrate is rigidly connected to the piezoelectric plates without considering the influence of the multilayer beam. One end of the composite beam is fixed on base C, and the other is free. Permanent magnet A is fixed to the free end of the composite beam, and permanent magnet B is fixed to another side of base C. The two permanent magnets are mutually exclusive and horizontally aligned. When the system is in equilibrium, the gravity of the composite beam and permanent magnet A has no effect on the deformation of the piezoelectric cantilever beam. P(t) is the basic motion; x is the axial spatial coordinate; t is the time coordinate; z is the transverse deformation of the position on the cantilever beam at any time; and xF, zF, and cM are the magnetic force in the x-direction, the magnetic force in the z-direction, and the torque in the y-direction of the permanent magnet A under the action of the permanent magnet B, respectively. The physical parameters and material properties of the piezoelectric cantilever beam vibration system are shown in The mechanical model of the piezoelectric cantilever beam is shown in Due to the sizeable length/thickness ratio of the beam, this paper only considers the bending deformation of the piezoelectric cantilever beam; regardless of the shear deformation and the influence of the rotational inertia of the section around the neutral axis, the piezoelectric cantilever beam is regarded as an Euler–Bernoulli beam. The nonlinear magnetic force at the free-end boundary is regarded as a concentrated load, as shown in T is the system’s kinetic energy, U is the system’s potential energy, W is the energy of the magnetic repulsion and torque, and δ is the variational symbol. According to b is the width of the substrate, The influence of temperature and residual stress on the piezoelectric cantilever beam is not considered in the modeling. According to the Hamilton principle, the governing equation of the harvester can be written asBy considering the first-order vibration mode of the piezoelectric cantilever beam, we can setLet the virtual work of moment In order to obtain the natural frequency and mode of the system, the Euler–Bernoulli beam transverse vibration equation without damping free vibration  is used,ω = 154 rad/s. By using the above normalization conditions, all the unknown variables By combining the eight Equations in (19)~(21), we can obtain the linear homogeneous equations for In the study of nonlinear vibration energy harvesters, many researchers ,27,28 prThe structure of the piezoelectric cantilever beam is shown in z. The magnetic force in the z-direction and the torque in the y-direction can be obtained as followsBy analyzing the equilibrium point and stability of the autonomous system corresponding to Equations (11) and (12), the static bifurcation characteristics of the piezoelectric cantilever beam system are obtained. Fourier expansion omits higher-order terms for magnetic force and torque applied to the free end of a piezoelectric cantilever beamLetting d < 25 mm, the system produces bistable motion.The system has three fixed points: , If the term containing damping does not appear in Equation (32), the energy function of the system isThe contour diagram of the energy function d is small, there is almost no difference in the equilibrium position in both cases. When d > 20 mm, the effect of torque on the equilibrium position is greater as d increases. In order to study the influence of torque on the energy output of the harvester, the effect of torque on the RMS voltage and power is analyzed below when d > 20 mm.d = 24 mm.Since the system is a strongly nonlinear vibration system, the approximate analytical solution of the system is obtained using the complex dynamic frequency (CDF) method and compared with the multiscale method and the numerical solution.For convenience, we rewrite Equations (11) and (12) asa is the amplitude; The complex dynamic frequency (CDF) method is used to solve the primary resonance solution of the system Equations (34) and (35). It can clearly be seen from Equation (35) that Rewriting Equation (39) asf,Substituting Equation (44) into (41), and considering t, we can obtainThe complex dynamic frequency (CDF) method is used to solve the 1/3 subharmonic resonance solutions of the system Equations (34) and (35). The solution of the system is set toSolving Equation (48) we can obtainBy solving Equations (34), (46) and (49) simultaneously, and considering Letting the coefficients corresponding to Balancing the other harmonic terms of the Equation (50), the dynamic frequency of the system is obtainedSubstituting Equations (46) and (47) into Equation (35), balancing corresponding harmonic terms, we obtainWhen 1/3 subharmonic resonance occurs in systems Equations (34) and (35), the approximate analytical solution isCombined with Equation (7), the actual response of the harvester when 1/3 subharmonic resonance occurs can be obtained.a increases and the 1/3 subharmonic coefficient b decreases as the excitation frequency increases in Equation (55).f = 14 Hz and f = 17.5 Hz, respectively. When the system undergoes 1/3 subharmonic resonance, the response contains the primary harmonic and 1/3 harmonic. The conditions for 1/3 subharmonic resonance of the system are discussed below. Equation (51) is rewritten top < 1.5 m/s2, the 1/3 subharmonic resonance does not occur at any excitation frequency; when f < 5.5 Hz, the 1/3 subharmonic resonance does not occur at any excitation amplitude. In the region where the 1/3 subharmonic resonance can occur in the system, the corresponding excitation frequency range increases with excitation amplitude. Similarly, as the excitation frequency increases, the corresponding excitation amplitude range increases. Therefore, for a piezoelectric energy harvester whose parameters have been determined, the method can be used to grasp the external excitation conditions for its generation of the 1/3 subharmonic resonance; if a piezoelectric energy harvester is to be designed to broaden the bandwidth using the 1/3 harmonic resonance under specific environmental conditions, the method can be used to invert the parameters of the harvester and provide theoretical guidance for the design of the harvester.It can be seen from Equation (57) that the conditions for the 1/3 subharmonic resonance of the nonlinear system are related to excitation frequency, excitation amplitude, linear stiffness coefficient, and nonlinear stiffness coefficient. 2, the system has only a small vibration; when the excitation amplitude is 5.9~36.7 m/s2, the system has a single excitation amplitude corresponding to multiple response amplitudes, one unstable solution, and two stable solutions; and when the excitation amplitude is greater than 36.7 m/s2, the system can maintain large vibration. The trajectories of response amplitudes during forward and reverse sweep are shown by arrows ③ and ④, respectively. When sweeping, the steady-state response under the previous excitation amplitude is the initial condition for the vibration at the next excitation amplitude. It can be easily seen that the steady-state motion of the system depends on the initial condition in the multi-value excitation amplitude region. This is similar to 2 and the excitation frequency is 4, 10, and 16 Hz, the excitation amplitude range of the system with large vibration is 0.7~10, 3.2~10, and 7.7~10 m/s2, respectively; the range of excitation amplitude that can ensure the system vibrates greatly is 1.5~10 m/s2, 0, and 0 respectively. High-frequency excitation can obtain a large amplitude response, thus obtaining a higher output power. However, the excitation amplitude range of multi-values is wide, and only small vibration in the multi-values may be obtained, so as to obtain the smaller output. At this time, the low-frequency excitation can obtain a larger response amplitude, but this limits the bandwidth of the system. If the 1/3 subharmonic motion is considered, when the excitation frequencies are 4, 10, and 16 Hz, the excitation amplitude ranges of 1/3 subharmonic motion in the system are 0, 3.2~8.7, and 7.2~32.7 m/s2. The excitation amplitude range of 1/3 subharmonic motion is basically in the range of multi-valued excitation amplitude generated by primary resonance, and it enlarges with the increase in excitation frequency. Although the amplitude of 1/3 subharmonic resonance is smaller than that of the large amplitude motion of the primary resonance, it is larger than that of the small amplitude of the primary resonance. If 1/3 subharmonic motion is considered instead of the small amplitude motion of the primary resonance, the harvester can obtain more energy. For f = 4 Hz, the system has no 1/3 harmonic resonance, consistent with p > 1.5 m/s2, f > 5.5 Hz, 1/3 subharmonic resonance occurs in the system, and when p is larger, the frequency range of 1/3 subharmonic resonance is wider. At this point, the 1/3 subharmonic resonance can replace intra-well motion, so that the harvester can obtain higher energy output in the broader frequency range. In practical application, the CDF method can provide theoretical guidance for the parameter design of the harvester to obtain higher power output in the environment of low-frequency excitation and small excitation amplitude.In this paper, the influence of nonlinear characteristics on the bandwidth of a piezoelectric vibration energy harvester is studied using the CDF method. Firstly, we modified the model, considered the influence of torque on the bending of the cantilever beam when modeling with the Hamiltonian principle, and compared it with the situation without considering the torque. It is found that torque greatly influences the equilibrium point and piezoelectric output of the harvester. In the range of bistable parameters, with the increase in permanent magnet spacing, the influence of torque also increases. Therefore, the influence of torque should be considered in the theoretical modeling. Secondly, the static analysis of the system is carried out to obtain the static bifurcation behavior and determine the parameter conditions for the bistable state of the harvester. Then, the approximate analytical solution and amplitude–frequency relationship of the primary resonance and 1/3 subharmonic resonance of the system are obtained using the CDF method. Finally, the CDF method is used to analyze the dynamic behavior of the energy harvester. The introduction of nonlinearity makes the harvester produce a bistable state and increases the bandwidth of primary resonance. When the 1/3 subharmonic vibration occurs in the harvester, it mainly contains the primary harmonic and the 1/3 subharmonic, and with the increase in the excitation frequency, the larger the proportion of the subharmonic. At the same time, it is found that the frequency range of 1/3 subharmonic vibration is within the frequency range of multi-values generated by the primary resonance, and the subharmonic motion’s amplitude is greater than that of the intra-well motion. Similarly, 1/3 subharmonic resonance also increases the excitation amplitude’s bandwidth of the harvester at a specific excitation frequency. Therefore, to a certain extent, the subharmonic motion can compensate for the low energy collection efficiency caused by the low robustness of inter-well motion. Making full use of the nonlinear characteristics of a system can effectively broaden the bandwidth of the piezoelectric vibration energy harvester and improve the efficiency of obtaining environmental energy. The theoretical method (CDF) can accurately predict the dynamic behavior of this kind of strongly nonlinear vibration energy harvester and provide guidance for its theoretical research.In the next step, the parameters of the harvester model are optimized by considering the effects of residual stress, temperature, damping, and the dimensions of the multilayer beam. On this basis, the following studies will be carried out.① An optimal load resistance exists in the system. A more significant power can be output under the same conditions when the optimal load resistance is obtained. However, the variation of the load resistance may affect the dynamic behavior of the system. Determining the optimal load by integrating the mechanical system and the circuit system remains to be studied.② Subharmonic resonance occurs only within a specific range related to the excitation frequency, excitation amplitude, linear stiffness coefficient, and nonlinear stiffness coefficient. By adjusting these parameters, the subharmonic resonance can maximize the bandwidth of the harvester.


Due to the large amount of old hardened cement mortar attached to the surface of aggregate and the internal micro-cracks formed by the crushing process, the water absorption, apparent density, and crushing index of recycled coarse aggregate are still far behind those of natural coarse aggregate. Based on the performance requirements of different qualities of recycled coarse aggregate, the performance differences of recycled coarse aggregate before and after physical strengthening were observed. The results showed that the physical strengthening technique can remove old hardened mortar and micro powder attached to the surface of recycled coarse aggregate by mechanical action, which can effectively improve the quality of recycled coarse aggregate. The optimum calcination temperature of the recycled coarse aggregate was 400 °C and the grinding time was 20 min. The contents of the attached mortar in recycled coarse aggregates of Class I, II, and III were 7.9%, 22.8%, and 39.7%, respectively. The quality of recycled coarse aggregate was closely related to the amount of mortar attached to the surface. The higher the mortar content, the higher the water absorption, lower apparent density, and higher crushing index of the recycled coarse aggregate. Construction waste treatment and recycling is an important part of the circular economy, and its significance is beyond doubt. Recycled coarse aggregate prepared by crushing and screening construction waste and applied to recycled concrete  can cons2 concentration, CaCO3 is formed by the reaction of the cement slurry with CO2, and CaCO3 is deposited in the pores or cracks to improve the performance of recycled coarse aggregate or strengthen recycled coarse aggregate by microbial induced mineralization deposition of calcium carbonate [(1) Physical technology ,12,13,14arbonate . (4) Nanarbonate ,28,29 isThere is a great difference in the thermal expansion coefficient between the aggregate and mortar . AttacheTherefore, based on the performance requirements of the recycled coarse aggregate of different qualities, the performance differences of recycled coarse aggregate before and after physical strengthening, and separated the attached mortar on the surface of recycled coarse aggregate from the old aggregate by using the collision principle of high-speed rotating ball grinding beads were investigated to determine the content of recycled coarse aggregate attached mortar.The recycled coarse aggregate was obtained from the waste concrete with a strength grade of C40. The physical strengthening method of particle shaping can effectively improve the quality of recycled coarse aggregate. The basic principle is to strip the attached mortar on the surface of the recycled coarse aggregate by high-speed impact and grinding between the aggregate and equipment and between the aggregate and aggregate. In this way, high-quality recycled coarse aggregate with a low content of attached mortar and good shape morphology can be obtained. The production principle of particle shaping equipment is shown in After jaw crusher crushing screening, a 5–25 mm simple crushing of class I recycled coarse aggregate can be obtained using a physical reinforced plastic device to a part of the class I recycled coarse aggregate physical strengthening treatment after screening, a 5–25 mm physically strengthened class II recycled coarse aggregate can be collected, again when recycled coarse aggregate physically reinforces a class II, one can obtain a high quality of class III recycled coarse aggregate. Recycled coarse aggregate comes from discarded concrete with a strength grade of C40, which uses physical strengthening technology  to obtaiAccording to the national standard method (GB/T25177-2010), the performance indexes of recycled coarse aggregate were measured. The influence of physical strengthening technology on the quality and properties of recycled coarse aggregate was analyzed, and the grade of different recycled coarse aggregates was evaluated. The obtained test results are shown in 3, fully meeting the standard for Class I recycled coarse aggregate.After the physical strengthening process, the mortar and micropowder attached to the surface of the recycled coarse aggregate were removed mechanically, and the grain shape and basic properties of the aggregate were significantly improved, which effectively improved the quality of the recycled coarse aggregate. Among them, the content of micropowder was reduced by 68.4%, the water absorption was reduced by 69.8%, the content of needle flakes was reduced by 80.3%, and the crushing index was reduced to 9.5%, and the apparent density reached 2474 kg/mHigh temperature calcination produces the difference in linear expansion between the aggregate and attached mortar. The large stress difference caused by thermal expansion makes the thermal compatibility of the granite in the recycled coarse aggregate and the old mortar worse, which results in greater damage in the interface transition zone, and the overall structural performance of recycled coarse aggregate is destroyed.The old interface in the recycled coarse aggregate will produce tiny cracks after calcination at high temperature. The separation efficiency of waste hardened mortar can be improved by using these cracks and loose interfacial transition zone. The heated aggregate was put into the planetary ball mill for ball grinding, and the waste hardened mortar was stripped from the surface of the recycled coarse aggregate through the collision and grinding between materials and materials, and between ball grinding beads and materials. While removing the waste mortar, it also reduces the prominent edges and corners on the surface of the recycled coarse aggregate, so that the aggregate particles tend to be smooth to achieve the effect of ball grinding on the recycled aggregate.Due to the irregular shape of the recycled coarse aggregate Natural coarse aggregates with the size of 5–25 mm and recycled coarse aggregates of class I, class II, and class III were calcined at different temperatures , placed in a planetary ball mill after cooling. Twenty batches of various coarse aggregates were randomly selected, and the average value was taken after each batch was ground three times;(2)The grinding time was sequentially controlled at 5 min, 10 min, 15 min, 20 min, 25 min, and 30 min. After reaching the specified grinding time, we sieved and weighed the remaining amount M of the aggregate at different grinding times, and calculated the mass loss rate of two adjacent grinding time points;(3)In order to eliminate the loss and influence of the original natural aggregate during the grinding process, the natural aggregate was taken as a control group. Grinding can be terminated when the quality loss rate of various recycled coarse aggregates approaches the same as that of natural aggregates, and the amount of attached mortar removed A is:RCA refers to the mass of recycled coarse aggregate after ball milling, g; Mnatural refers to the mass of natural coarse aggregate after ball milling, g; and Msample refers to the mass of sample before ball milling, g.In the formula, A refers to the amount of attached mortar removed, %; MThe morphology of the recycled coarse aggregate after high temperature calcination is shown in 2 led to large crystal particles [It can be seen from articles  and highThe natural coarse aggregates were calcined at 100 °C, 200 °C, 300 °C, 400 °C, 500 °C, 600 °C, and normal temperature, respectively. Three samples for each temperature level was selected, and the testing samples were cut into 10 mm slices. These were then subjected to grinding and polishing treatment to meet the requirements of the microhardness test specimens . Six meaCalculation of the loss rate of natural aggregate microhardness at different temperatures:V(T0) is the normal environmental hardness value, MPa; and HV(T1) is the hardness value after T1 high temperature calcination, MPa.In the formula, S is the microhardness loss rate, %; HDue to the different calcination temperature, the grinding time of the attached mortar on the surface of the recycled coarse aggregate was different. After the calcination temperature exceeded 400 °C, the damage to the old aggregate in the recycled coarse aggregate was more serious. Therefore, in order to research the content of the attached mortar on the surface of the aggregate, the temperature was controlled in the range of 100–400 °C, and by adjusting the grinding time, testing, and analyzing the content of the attached mortar, the calcination temperature and grinding time can eventually be determined.It can be seen from After the low-quality recycled coarse aggregate underwent particle shaping and strengthening treatment, the attached amount of waste mortar was effectively removed under the action of external force. In particular, the high-quality recycled coarse aggregate after the shaping and strengthening treatment contained less waste mortar on the surface, its surface had no edges and corners and the grain shape was relatively smooth, and the content of the mortar obtained after calcination and grinding was only 7.5%. Therefore, it was also proven that the use of the particle shaping physical strengthening method can effectively reduce the waste mortar attached to the surface of the recycled coarse aggregate, and improve the basic performance and quality of the recycled coarse aggregate. With the increase in the calcination temperature, the removal rate of the recycled aggregate gradually increased. This was mainly due to the difference in thermal expansion between the aggregate and mortar under the action of the high temperature of recycled coarse aggregate, which produced an obvious thermal stress concentration at the interface transition zone and produced a large number of microcracks and damage at the interface transition zone and the mortar matrix, which weakened the interface structure performance of the recycled aggregate . Under t3. The content of II type RCA attached mortar was 22.8%, the water absorption rate and crushing index increased 65.2% and 57.4%, respectively after high temperature calcination-grinding, and the apparent density decreased 177 kg/m3. The basic properties of the II and III type aggregates were obviously lower than that of the high-quality recycled coarse aggregate (I type). This is because the attached mortar on the surface of class II and class III RCA formed internal damage such as micro voids and cracks in the attached mortar and the transition zone of the old interface in the crushing process, which led to the degradation of its performance.By fitting the measured test data, the relationship between the attached amount of recycled aggregate mortar and water absorption, apparent density, and crushing index was obtained. It can be seen from After calcination and grinding, the water absorption, apparent density, and crushing index of class I recycled coarse aggregate showed relatively little change, and was similar to the natural aggregate. This was because after two-time physical strengthening, the content of attached mortar on the surface of class I recycled coarse aggregate decreased obviously, but there was still a small amount of hardened cement mortar. In contrast, the properties of recycled coarse aggregate of class II and class III were significantly affected by the content of the attached mortar. 2 was 0.9724, 0.9567, and 0.9889, respectively, which is very consistent with the measured value. After high temperature calcining and high-speed grinding, the water absorption, apparent density, and crushing indexes of the recycled coarse aggregate were basically the same as those of the natural aggregate, which indicates that the high-temperature calcination-grinding method can effectively remove the attached mortar on the surface of the recycled coarse aggregate. For the recycled coarse aggregate used in practical application engineering, only the water absorption rate, apparent density, and crushing index of the recycled coarse aggregate can be detected. Using the established linear relationship, the content of waste mortar attached to the surface of different recycled coarse aggregates can be accurately measured, and the internal defects of recycled coarse aggregate can also be quantitatively reflected.It can be concluded from In this study, based on the performance requirements of different recycled coarse aggregates, the performance of recycled coarse aggregates through the process of physical strengthening methods were comprehensively compared and analyzed, and the content of attached mortar of the recycled coarse aggregate was quantitatively analyzed by the calcination-grinding method, where the following results were obtained.(1)The physical strengthening method can effectively reduce the content of attached mortar to the surface of the recycled coarse aggregate, improving the performance of recycled aggregate. Through the secondary physical strengthening process, the water absorption rate of recycled coarse aggregate was reduced to 2.2% from 7.3%, the needle flake content was only 1.2%, and the crushing index was only 3.1% higher than that of the natural coarse aggregate, which fully meets the standard of the class I recycled aggregate.(2)The calcining-grinding method can effectively separate the recycled aggregate and attached old cement mortar. The calcination temperature below 100 °C had no great influence on the aggregate. When the temperature was 400 °C, the microhardness decreased to 245 MPa, and the hardness loss rate was 14.6%. The hardness of the aggregate had been damaged. Combined with the quality change of different-class recycled coarse aggregate and the microhardness loss of the aggregate under high temperature, the appropriate calcination temperature for the class I, II, and III recycled coarse aggregate was determined as 400 °C and the optimum grinding time was 20 min.(3)The measured attached mortar contents of classs I, II, and III recycled coarse aggregates were 7.9%, 22.8%, and 39.7%, respectively, by calcining-grinding technology. Meanwhile, the water absorption, apparent density, and crush index had a good linear relationship, and the established linear relationship could accurate measure the content of the RCA adhesive mortar on the surface, which can directly reflect the internal defects of RCA.


Nanocomposites were deposited by ion-beam sputtering onto glass and glass-ceramic substrate. By studying the spectral and field dependences of the transversal Kerr effect (TKE), it was found that the transition of nanocomposites from superparamagnetic to the ferromagnetic state occurs in the region of fmx~30 at%, that corresponds to the onset the formation of ferromagnetic nanocrystals CoFeZr with hexagonal syngony in amorphous dielectric matrix of MgF2. With an increase of concentrations of the metal alloy for fmx > x, the features associated with structural transitions in magnetic granules are revealed in the TKE spectra. Comparison of the spectral and concentration dependences of TKE for nanocomposites on the glass and glass-ceramics substrates showed that the strongest differences occur in the region of the phase structural transition of CoFeZr nanocrystals from a hexagonal to a body-centered cubic structure at x = 38 at.% on the glass substrates and at x = 46 at.% on glass-ceramics substrates, due to different diffusion rates and different size of metal nanocrystals on amorphous glass substrates and more rough polycrystalline glass-ceramics substrates.The results of complex studies of structural-phase transformations and magneto-optical properties of nanocomposites (CoFeZr) The continuing interest in nanocomposite (NC) materials is due to the modification of the known metals and alloys properties during their transition to the nanocrystalline state. Magnetic nanocomposites of metal-dielectric type have a number of unique physical properties that are promising for their use in spintronics, in the technologies for recording and storing information, in the creation of shielding coatings, sensitive magnetic sensors and other devices ,2,3. TheAll these properties of nanocomposites appreciably depend on their composition and microstructure, especially on the shape and size of metal granules, on their distribution over the sample volume, and primarily on the concentration of the magnetic metal phase. In this regard, magneto-optical (MO) studies are of a considerable interest, since they are sensitive to the changes in the magnetic and electronic structures caused by the characteristic sizes, shapes, and topology of metal particles ,7,8,9,10xper, i.e., at such value of the concentration of metal component at which a finite conducting network of contacting metal particles is formed in the entire volume of the sample. It can be stated that the threshold of percolation is an intermediate state during the transition of the nanocomposite from an electrically nonconducting to an electrically conductive state, where the metal granules begin to come into contact with each other. In this area, all the unique physical properties that are inherent to granular composites are more pronounced [Concentration dependences of the electromagnetic properties of nanocomposites show dramatic nonlinear changes at the threshold of percolations onounced .x, from x = 100 at.% down to the percolation threshold xper, the resistivity of nanocomposites increases, as physical contact between most of the granules continuously disappears. There is still the tunneling conductivity for the concentrations down to xc (per > x > xcx), where metal–insulator transition occurs. In this concentration range, novel transport properties, such as tunnel anomalous Hall effect and logarithmic temperature dependence of conductivity, have been found [xc [With decreasing metal concentration en found . Hoppingound [xc ,13,14.x << xper) or large (x > xper) NC exhibits superparamagnetic or ferromagnetic (FM) properties, respectively. The magnetic percolation threshold fmx does not coincide with the transport threshold [xper, since the ferromagnetic order (FM) can occur without physical contact between the granules. Therefore, it is possible to define fmx as the concentration at which the magnetization and the coercive force dramatically increase. Depending on the relative intensity of the dipole-dipole and exchange interactions, complex magnetic states can occur in the vicinity fmx of superferromagnetic (SFM) state, superspin glass state, superparamagnetism (SPM), and mixed SFM–FM–SPM state [The character of magnetic properties in NC is even more complex. In the region of very low concentrations of the metal component 100−x with a multi-element ferromagnetic alloy in oxygen-free dielectric matrix of MgF2 on the glass and glass-ceramics substrates and to identify the influence of the composition and phase transformations on their magneto-optical properties and self-organization processes.The aim of this work is to study magneto-optical properties of nanocomposites (CoFeZr)2 and the MO percolation threshold will be determined. Thus, for the first time, new data will be presented on the magneto-optical properties and the effect of phase transitions on them when changing the composition of a composite obtained of a three-element alloy CoFeZr and an oxygen-free matrix MgFThe main known methods for producing thin composite films are thermal, cathode, and ion-plasma sputtering. Each of these methods has its own advantages and disadvantages, depending on the sputtered material and the goal of the work. In , the anax (MgF2)100−x with metal granules of the CoFeZr alloy in the MgF2 dielectric matrix on glass and glass-ceramics substrates within the range of changes in the nominal values of x calculated from the geometry of the composites deposition, x = 9–51 at.%, including the percolation threshold [This paper presents the results of the study for two series of nanocomposite films (CoFeZr)hreshold .45Fe45Zr10 and the dielectric component MgF2 were obtained at the original ion-beam sputtering facility [Nanogranulated composite films with different content of the initial metal alloy Cofacility . The optfacility .45Fe45Zr10 with inserts made of dielectric MgF2 material was carried out in an argon atmosphere at the operating pressure of ~5 × 10−4 Torr. Sputtering of a composite target made from a plate of an amorphous metal alloy Co45Fe45Zr10 was used to precipitate the amorphous ferromagnetic metal component of the composites. It was made by vacuum melting from metals of the appropriate composition using an induction furnace. Preparation of attachments for the alloy was carried out from carbonyl high-purity iron (99.9%), high-purity cobalt (99.98%) and zirconium (99.8%) with a weight content of components in accordance with the composition of the alloy Co45Fe45Zr10. The melt of the corresponding composition was poured into a specially prepared ceramic mold in a vacuum. The target had sizes of 270 mm × 70 mm × 14 mm. The target were ground on both sides, soldered to a water-cooled base, and placed in the spray position in the ion-beam sputtering facility. MgF2 insets with a thickness of ~2 mm and a width of ~9 mm were fixed on the surface of the alloy target perpendicular to its longitudinal axis, not equidistant, in order to obtain a continuous set of concentrations of the components of the composite target along its length in one technological deposition cycle  with a molecular weight of 62.30 atomic mass units was used. The mass fraction of calcium (Ca) was about 0.1–0.3%.For the production of dielectric inserts, magnesium fluoride MgFFR and DR-coefficients spraying metal alloy and dielectric, respectively; FS and DS sputtering target area occupied by the alloy and dielectric, respectively; S is the area of the entire target (270 mm × 70 mm); n-the number of dielectric inserts in composite target; s-area of a single insert (9 mm × 70 mm); L-length of the target compound (270 mm); b-width of the dielectric insert. Deposition was performed on glass-ceramics and glass substrates with a size of 60 mm × 48 mm. The use of non-uniform arrangement of dielectric inserts allowed us to obtain a continuous spectrum of changes in the compositions of alloy and dielectric components of the composite from 20 to 70 at.% of the metal phase in one technological cycle of deposition. The approximate ratio of the volume fraction of an alloy to the volume fraction of a dielectric with a uniform distribution of attachments can be estimated by the formula:x in the alloy composition [The layer thicknesses of the film samples of granular composites with different compositions varied smoothly in the range of 2–4 μm while increasing position .x (MgF2)100−x, expressed in atomic percentages. In this case, the variable x of the value of metal component in the composite is the sum of the atomic concentrations of the three metals of the alloy Co, Fe, and Zr.The concentrations of the chemical elements that make up the composites were measured by electron-probe X-ray spectral microanalysis with JEOL JSM-6380LV scanning microscope (Japan) attachment, equipped with three crystal diffraction spectrometers and an energy-dispersion analysis system, with an error less than 1.0 at.% of the content of the measured element. The determined composition of the samples represented the content of each chemical element in the composite layer (CoFeZr)The phase composition of nanocomposites and nanocrystals formed as a result of self-organization of two components, metallic and dielectric in different ratios, were studied by X-ray diffraction (XRD) with DRON-4 diffractometer  using Co Kα radiation. X-ray diffraction patterns were obtained in the step-by-step scanning model ,22.p-polarized light reflected by a sample when magnetized in a magnetic field parallel to the sample surface and perpendicular to the plane of light incidence. The TKE value,I(H) and I(0) are the intensities of reflected light in the presence and absence of a magnetic field, respectively, has been measured by the dynamic method at the magnetic field modulation. This method allows the use of a differential measurement scheme, providing the accuracy measuring the relative changes in the reflex light intensity of ~10−5 [The magneto-optical (MO) properties of nanocomposites were studied in the geometry of the transversal Kerr effect (TKE), which consists in changing the intensity of of ~10−5 ,24.E = 0.5–4.0 eV at the applied magnetic field up to 3.0 kOe and room temperature. Magnetic field TKE(H) dependences were measured at some fixed energies to analyze the magnetic structure of the nanocomposites.The TKE spectra were recorded in the energy range The magnetic properties of the samples were studied on a LakeShore Vibrating Sample Magnetometer (VSM) 7407 in fields up to 16 kOe.x (MgF2)100−x obtained on the glass substrates.x in at.% for the samples is indicated to the right of each diffraction pattern. The lower diffraction patterns in 2 powder, are given for comparison.Nominal content of the metal component x ≤ 25 at.%) the metal alloy CoFeZr is in the X-ray amorphous state in the form of metal clusters distributed in MgF2 nanocrystalline matrix, represented in diffraction patterns for the values x = 9–30 at.% by two wide reflections (110) and (220) at 2θ = 32° and 2θ = 67° from MgF2 nanocrystals.From the analysis of XRD data, it follows that in the range of low concentrations , that is especially clearly visible at x = 38 at.%.But just at x = 43 at.%, the crystal structure of CoFeZr nanocrystals is rearranged into a cubic volume-centered phase based on α-Fe with a predominant orientation of (110), like that of α-Fe. And already at x = 47–50 at.% in the amorphous MgF2 matrix (its reflections (110) and (220) disappeared at x = 38 at.%), only one nanocrystalline BCC phase of the CoFeZr alloy is present in the composites.However, with a further increase in the metal alloy content, starting from 45Fe45Zr10 on the glass-ceramics substrate without MgF2, which provides an intense reflection in the form of halo in the range of angles 2θ = 45–60° with a small peak at the top position close to the position of the most intense lines (110) of α-Fe and the second by intensity of the line (002) α-Co, and with the most intense lines of nanocrystals CoFeZr in the composites with x = 41–51 at.%.45Fe45Zr10 on the glass-ceramics, along with the amorphous phase of CoFeZr, can possibly contain nuclei of clusters of both cubic and hexagonal symmetry. The remaining weak lines on this diffraction pattern are attributed to glass-ceramics substrate.Hence it follows that the film of the pure alloy Co2 and the glass-ceramics substrate, one can see that all of the main lines of MgF2 coincide with the lines of the glass-ceramics having a larger number of reflections. And since glass-ceramics, unlike glass, is not X-ray amorphous, it provides additional weak reflections in all of the diffraction patterns of nanocomposites with different composition.When comparing the diffraction patterns of the dielectric component MgFx ≤ 28 at.%) the metal alloy CoFeZr is in the X-ray amorphous state in the form of metal clusters distributed in the MgF2 nanocrystalline matrix, represented in the diffraction patterns of However, from x = 35 at.%, the first reflection (100) from the group of three ones appears in the diffraction pattern in the halo region, corresponding to the beginning of the formation of hexagonal nanocrystals of the CoFeZr alloy, with the most intense line (100), in contrast to the metal cobalt with the most intense line (101).For the composition of the NC with x = 46 at.% the most intense lines from the group of three ones becomes the middle line, which at x = 51 at.% remains the dominant one in this range of Bragg angles, like α-Fe, as a result of the rearrangement of the hexagonal crystal structure of the alloy into a BCC one.But at x ≈ 30 at.%, then the compositions for the beginning of the second phase transition of the CoFeZr alloy from the hexagonal to the BCC structure differ significantly: x = 38 at.% in nanocomposites on the glass substrates and x = 46 at.% in nanocomposites on glass-ceramics substrates. At the same time, in the latter, the phase transition process is not completed within the observed limits of concentrations, and at x = 51 at.%, the traces of two lines (100) and (101) of the hexagonal phase are still observed by both sides of the main line (110) of the BCC phase of CoFeZr nanocrystals. A careful comparison of the XRD results for the composites of two series  obtainedIn addition, the sizes of the alloy nanocrystals (according to Scherrer) also differ, and they are about 15–20 nm on a glass substrate and about 25–30 nm on a glass-ceramics one, with their same orientation relative to the substrates ,23.X-ray diffraction and magneto-optical investigations were performed with the same samples.When studying magneto-optical properties, the spectral, field, and concentration dependences of the transverse Kerr effect were obtained.x ≤ 30 at.%.cx = 30 at.% at the energy of approximately ~1.75 eV.In this concentration range, the behavior of the TKE spectra is similar to those ones of nanocomposites with metal granules CoFeZr in oxide matrices . With anx ≤ 20 at.% a linear dependence of the TKE on the magnetic field is observed. With an increase of the concentration up to x = 30 at.% there is a nonlinear dependence of TKE on the magnetic field, but the value of TKE does not reach saturation in the fields up to 3kOe.For the samples with c on the concentration of the metal component for nanocomposites (CoFeZr)x (MgF2)100−x on the glass substrates.For a more complete understanding of the magnetic structure of our films, we also carried out magnetostatic studies on a vibration magnetometer in fields up to 16 kOe. c in all of the composites at x ≤ 30 at.% is equal zero. Therefore, the main contribution to the coercive force is made by single superparamagnetic particles, and after that, a nonlinear increase in the coercive force is observed, which is explained by the formation of FM clusters in the sample.Analysis of the hysteresis loops showed that the value of the coercive force Hx ≤ 30 at.%, the samples are superparamagnets, and the critical magnetic percolation threshold for this system is fmx = 30 at.%.Thus, in the concentration range fmx = 30 at.%, some features in the behavior of magneto-optical properties are observed that correlate with the features of the structural properties of nanocomposites, namely, with the beginning of the nucleation of CoFeZr nanocrystals of hexagonal syngony.When the concentration increases above magnetic percolation threshold x ≥ 30 at.%. According to the given curves it follows that at x = 34 at.%, the type of the TKE spectra changes. The effect begins to decrease in the energy range E > 1.57 eV, and the peak is shifted to E~1.65 eV. The shift of the TKE maximum coincides with the appearance of hexagonal CoFeZr nanocrystals in the amorphous dielectric matrix. TKE field dependencies become more magnetically hard.x = 38 at.% leads to a sharp decrease in the magnitude of the MO effect and a further shift of TKE maximum towards lower energies. This behavior can be attributed to the nucleation of BCC nanocrystals based on α-Fe. In the same concentration region, a reflection corresponding to α-Fe (110) begins to appear in the diffraction pattern. In the sample with x = 43 at.%, the effect in TKE spectra begins to increase once again, and a maximum appears in the region of 1.25 eV, which is manifested in the diffraction pattern as the growth of intensity of one of the most intense lines (110), as in the alloy of CoFe and α-Fe.Further increase of the metal concentration at With increasing x to 47–51 at.%, a further transformation of the shape of the MO spectra occurs: the modulus of the TKE value decreases, and the maximum of the spectrum shifts towards lower energies.x (MgF2)100−x at the energy values of 1.14 eV, 1.97 eV, and 3.17 eV. Unlike of NCs with amorphous metallic granules in oxide matrices, where the maximum on the concentration dependences of TKE corresponding to the threshold of magnetic percolation was observed in the near-IR region of the spectrum [2 matrix, this maximum at fmx = 30 at.% is most pronounced in the visible region of the spectrum at the energy values of 1.97 eV and 3.17 eV.A more complex behavior of the concentration dependences of the TKE is observed in the near-IR region of the spectrum.fmx region and two maxima corresponding to the structural-phase transition from the amorphous phase to the nanocrystalline hexagonal phase (x = 34 at.%) and a feature in the concentration range of 38 ≤ x ≤ 47 at.%, at which the crystal structure of CoFeZr is rearranged from a hexagonal to a body-centered cubic lattice.At the energy of 1.14 eV, we can distinguish an inflection in the x (MgF2)100−x, on the glass substrates.Thus, the concentration dependences of the TKE correlate well with the results of X-ray diffraction studies of structural-phase transitions in nanocomposites (CoFeZr)x (MgF2)100−x on the glass-ceramics substrates at different concentrations of the metallic phase.fmx = 31.4 at.%.As well as for NC on the glass substrates, the modulus of the TKE value in the samples on glass-ceramics substrates increases with an increase of the concentration up to values of x = 31.4 at.% coercive force of Hc is zero, and non-zero values of Hc appear at x > 31at.%. Comparison of the dependences of coercive forces for the systems on glass and glass-ceramics substrates, shown in Magnetic measurements  also shoComparison of the spectral dependences of the TKE for nanocomposites on different substrates also shows their significant differences .x~21at.% in the nanocomposites on the glass-ceramics substrates, TKE values in the energy range E > 1.5 eV are approximately by 1.5–2 times less than in nanocomposites on the glass substrates, and the maxima are shifted to the low energy region. This may be connected with the different size of metal clusters due to different diffusion rates of the atoms on amorphous glass and more rough polycrystalline glass-ceramics substrates.At the concentration of fmx are also different. For NC on the glass substrates, a wide maximum in the range of 1.5–2 eV (x = 20 at.%) gradually shifts to the region of 1.25 eV (at x = 47 at.%) with an increase of x. For NC on the glass-ceramics substrates for x = 21 at.% a maximum in the region of ~1.5 eV is observed, which gradually shifts to 2.0 eV (at x = 43 at.%) and at x= 47 at.% we can once again observe a maximum in the region of ~1.65 eV.Position of the maximum values of MO effects and the trends of their change with an increase in alloy concentration greater than x = 31 at.% for the energies of 1.97 and 3.17 eV, associated with the formation of hexagonal nanocrystals of the CoFeZr alloy. For the energy of 1.14 eV, a maximum is observed at the same concentration of x = 31 at.% and the beginning of the effect enhancement associated with the transition to a cubic BCC structure.Comparison of the concentration dependences of TKE for nanocomposites on different substrates, made of glass and glass-ceramics, is shown in x (MgF2)100−x on the glass and glass-ceramics substrates indicates that self-organization processes in nanocomposites on different substrates are different. The material and structure of the substrate  affect the formation of CoFeZr nanocrystals with an increase in the concentration of the metal component x in the composites. The absence of the formation of a large negative maximum in the TKE spectra within the energy range of ~1.25 eV at the increase of x up to 46.4 at.% indicates that the transformation of CoFeZr nanocrystals from a hexagonal structure to BCC structure proceeds slower with x growth than in the nanocomposites on glass substrates.The difference in the spectral dependences of TKE for nanocomposites (CoFeZr)x (MgF2)100−x, depending on the content of the metal component in the oxygen-free dielectric matrix, are associated with the substrate material and they affect magneto-optical properties of these nanocomposites.The obtained results show that the processes of formation of CoFeZr alloy nanocrystals in the film composites of (CoFeZr)x (MgF2)100−x with a polyelement metal component in an oxygen-free dielectric matrix of magnesium fluoride on glass and glass-ceramics substrates have established the influence of the composition, substructure and phase transformations of nanocomposites on their magneto-optical properties.Thus, for the first time, new complex investigations of the structural-phase transformations and magneto-optical properties of nanocomposites (CoFeZr)MO spectroscopy revealed the features corresponding to phase structural transitions in magnetic granules during the transition from an amorphous CoFeZr alloy to a nanocrystalline CoFeZr alloy based on a hexagonal α-Co lattice and during the rearrangement of CoFeZr nanocrystals from a hexagonal to a cubic body-centered structure.x(MgF2)100−x corresponds to the nominal value of fmx~30 at.%, corresponding to the onset the formation of ferromagnetic nanocrystals of hexagonal syngony.It was found that magnetic percolation threshold in nanocomposites (CoFeZr)x = 38 at.% on the glass substrates and x = 46 at.% on glass-ceramics substrates.A comparison of the spectral and concentration dependences of TKE for NC on glass and glass-ceramics substrates showed that self-organization processes in nanocomposites on different substrates are different and the strongest differences occur in the region of the phase structural transition of CoFeZr nanocrystals from a hexagonal to a body-centered cubic structure at


One of the ways to increase the efficiency of the desalination process in membrane systems is to use intensive current modes. Recently, the phenomenon of space-charge breakdown was theoretically described for desalination under intensive current modes. The space-charge breakdown is a decrease in the magnitude and size of the extended space charge regions (SCRs) of opposite signs, formed at the cation- and anion-exchange membranes in the desalination channel, when they approach each other. Therefore, this phenomenon negatively affects the intensity of electroconvection and the efficiency of mass transfer in membrane systems. We report the results of the first theoretical analysis of the space-charge breakdown in the galvanostatic electric mode, which is generally used in the research and operation of membrane systems. For this purpose, a one-dimensional model of the ion transfer of the electrolyte solution in the section of the desalination channel at the direct current is developed. The regularities of changes in the extended SCRs in the galvanostatic mode are determined. A relation is obtained for the onset time of the space-charge breakdown, which makes it possible to determine the parameters of the effective operation of the membrane system. Membrane systems form the basis of electrodialysis, nano- and microfluidic devices, which are used in water purification, agricultural processing , chemical analysis and many other human activities ,2,3,4. TRubinstein and Shtilman  theoretiThe emergence of the SCR at the membrane surface explained the nonlinear shape of the current-voltage characteristic (CVC) of the CEM, in which the following regions can be distinguished: the initial linear region, the region of slow current change (plateau), followed by the region of accelerated growth with increasing potential (overlimiting currents) ,8. The fTo simulate desalination with intensive currents, it is necessary to consider the entire desalination channel formed by the AEM and CEM. Liu et al.  numericaNumerical modeling of the mass transfer process in the membrane system until complete desalination of the electrolyte solution was carried out in the article . For thiThe above-mentioned studies ,15,16 wex, varies from 0 (the solution/AEM interface) to h (the solution/CEM interface).Consider a quiescent layer of the binary electrolyte solution located between two ion-exchange membranes: AEM and CEM. The normal to the surface membrane coordinate, n, respectively; 0ε is the dielectric permittivity of vacuum; rε is the solution relative permittivity (assumed to be constant); F is the Faraday constant; R is the gas constant; T is the absolute temperature. t, and coordinate, x.In the 1D case, the mathematical model of the non-stationary ion transfer includes the Nernst–Planck equation, Equation (1); the matter conservation equation , Equation (2); the Poisson equation, Equation (3). Convective transfer is not considered. This equation system for a binary electrolyte is as follows:i, is equal to the sum of the faradaic (or conduction) current, The current density in the system, e charge ,19:(4)i=aN (cN) times greater than the initial concentration of the electrolyte c0 [The boundary conditions for the concentrations of counterion set constant values that are olyte c0 :(5)c1–(4) includes the electric field potential only in the form of spatial derivatives; therefore, only the potential drop, x = h, we use the condition that determines the derivative of the electric potential through the current density [On the other boundary,  density :(10)∂ϕ∂xt = 0, the electroneutrality condition is satisfied at all points of the channel section, and the concentrations of cation and anion are equal to the initial concentration of the electrolyte, At the initial moment, c0, significantly increases the computational complexity of the boundary value problem of the model. To obtain an acceptable accuracy of the results, the calculations in this section are performed for a low input concentration of the NaCl electrolyte solution, c0 = 0.001 mol/m3. c0 = 2 mol/m3).The described above model in  is a comradients , which ivalue c0 ; therefoh = 10−3 m; the system temperature T = 298 K; the diffusion coefficients of cations D1 = 1.33·10−9 m2/s and anions D2 = 2.04·10−9 m2/s; the charge numbers of ions z1 = 1, z2 = −1; cN = Na = 1; water dielectric permittivity rε = 81. The calculations are performed for two types of membranes: (a) perfectly selective membranes, that is TC2 = 0 and TA1 = 0; (b) membranes, the transport numbers of which correspond to the values of MK-40 [TC2 = 0.03 and TA1 = 0.03.Values of other system parameters: the channel width of MK-40 , T2C = 0t1 is the cation transport number in the electrolyte solution.In the analysis of the study data of processes in membrane systems, it is accepted to normalize the current density by the value of the diffusion limiting current density. The value of the limiting current density can be determined by the Peerce formula :(12)iFDci/ilim. The current density normalization facilitates the study of the similarity of transport processes at different electrolyte concentrations –(11) was found by the finite element method on the non-uniform computational grid (the density of grid elements was increased near the solution/membrane interfaces). The implementation of the equation system is described in .i, is less than 3%.The error in the calculations performed for these parameter values, estimated as the difference between the average total current density in the channel, i = 2ilim). t = 0, 4, …, 24, 25.65 s, calculated for the perfectly selective membranes . As the current flows in the quiescent electrolyte layer, the concentrations of ions of both types decrease over time  it follows that the time derivatives of the charging and conduction currents have opposite signs, that is, the decrease in the conduction current is accompanied by an increase in the charging current. The electric field strength, Consider the changes in the SCRs in the section of the desalination channel when the constant current density flows , while the conduction current, i  and AEM (xA) and the absolute values of their movement velocity, that is, the velocities of the SCRs extension, vC, vA. Once the SCRs are formed, the speed of movement of their local extrema increases slowly and at t > 25 s, when the distance between them becomes small : the higher values of the effective transfer numbers of coions in membranes correspond to the lower velocity of the local extrema of the SCRs, since a certain additional number of coions enter the channel through the membranes.Ci, is small, as in the calculation shown in Ci < 0.05ilim at t < 25 s. Therefore, it can be assumed that the electric current in the electrolyte solution of the system under consideration is determined by the cation and anion fluxes formed during the complete electrolytic dissociation of the NaCl salt with the concentration c0, which was present in the channel section at the initial time (Equations (11)), x = h, the current density is equal to:In the galvanostatic mode, the space-charge breakdown time can be estimated from the current density set in the system. Before the start of the process of space-charge discharging, the value of the charging current density, In Equation (13), the first term is the current density of the solution cations. If we define the time of the space-charge breakdown, From Equation (13), it is easy to obtain a formula for the time of the space-charge breakdown, taking into account the selective properties of the membrane:A similar expression can be written for the AEM/solution interface.T2C = T1A = 0.5, the complete desalination of the solution will never occur, Equation (14) shows that, in the galvanostatic mode, the time of the space-charge breakdown  is directly proportional to the electrolyte concentration at the initial time and the channel width, and is inversely proportional to the current density. Thus, the space-charge breakdown is a limitation of the possibility of increasing the mass transfer efficiency in electromembrane systems by reducing the intermembrane distance (the channel width) or increasing the current density. Equation (14) also reflects the fact that an increase in the transport numbers of coions in the membrane increases the breakdown time. In the limiting case, when membranes are equally permeable to ions of both types (cations and anions), ilim to 2ilim does not exceed 1%.At, decreases faster than at the CEM, Ct,  and (6) and with Equations (15) and (16) are close to each other everywhere except for the quasi-equilibrium parts of the SCR . The usec0 = 2 mol/m3 with sufficient accuracy . The results of this calculation are shown by triangular markers in c0, does not affect the time, c0 = 0.001 mol/m3 and 2 mol/m3 is less than 1% and in calculations of i/ilim ) is introduced into Equation (14), the breakdown time, c0.Conditions (15) and (16) made it possible to calculate the model for the electrolyte concentration Thus, calculations with Equations (15) and (16) have an acceptable accuracy and allow calculations for electrolyte concentration values corresponding to those used in actual experiments and in practice.The desalination of the electrolyte solution by intense currents in the section of the membrane channel in the galvanostatic mode are investigated through the developed numerical model. The model describes the SCRs changes from formation at the surfaces of the ion-exchange membranes to complete discharge. The simplification of the model by excluding a quasi-equilibrium part of the SCR from the consideration made it possible to obtain the numerical solution for the values of the electrolyte concentration used in experiments. Numerical results have shown that the ratio of the ion diffusion coefficients determines the ratio of the SCR extension velocities of different signs and the location of the space-charge breakdown, but does not affect the breakdown time. An approximate formula is derived to estimate the space-charge breakdown time for the galvanostatic mode, taking into account the selective properties of the membrane. The difference between the breakdown time calculated by using the approximate formula and the proposed model does not exceed 1%. It is shown that the deviation of the selective properties of the membrane from the perfect values leads to the slowdown in the processes of desalination and the delay in the onset of the space-charge breakdown.The development of the proposed model for the 2D case will make it possible to study the phenomenon of space-charge breakdown in the desalination channel at a direct current, taking into account the forced flow and the development of electroconvection. Dissociation/recombination reactions of water molecules are another aspect of further investigation of the space-charge breakdown.


Bietti crystalline dystrophy (BCD) is an autosomal recessive genetic disorder that causes progressive vision loss. Here, 12 patients were followed up for 1–5 years with fundus fluorescein angiography (FFA) to observe BCD disease progression.FFA images were collected for 12 patients with BCD who visited our clinic twice or more over a 5-year period. Peripheral venous blood was collected to identify the pathogenic gene related to the clinical phenotype.We observed two types in FFA images of patients with BCD. Type 1 showed retinal pigment epithelium (RPE) atrophy in the macular area, followed by choriocapillaris atrophy and the subsequent appearance of RPE atrophy appeared at the peripheral retina. Type 2 showed RPE atrophy at the posterior pole and peripheral retina, followed by choriocapillaris atrophy around the macula and along the superior and inferior vascular arcades and the nasal side of the optic disc. The posterior and peripheral lesions of both type 1 and type 2 BCD subsequently extended to the mid-periphery; finally, all the RPEs and choriocapillaris atrophied, exposing the choroid great vessels, but type 2 macular RPE atrophy could last longer.The characterization of two different types of BCD development provides a better understanding of the phenotype and the progression of the disease for a precise prognosis and prediction of pathogenesis. Bietti crystalline dystrophy (BCD) is an autosomal recessive retinal dystrophy characterized by numerous tiny sparkling yellow-white spots at the posterior pole of the fundus. The causative gene has been identified as CYP4V2 , 2. In 1The aim of the present study was to outline the phenotype of BCD more clearly and to obtain a better understanding of the natural course of the disease. Here, we present 12 cases of BCD focusing on its progression via FFA images with the goal of identifying the features of BCD development. The implementation of all research methods in this study followed the provisions of the Declaration of Helsinki, the Ethics Committee of Beijing Tongren Hospital, Capital Medical University, and the Ethics Committee of Hebei Provincial Eye Hospital. This study included 12 unrelated Chinese patients who were followed up at our hospital clinic over a 5-year period. The clinical characteristics and images of these patients were retrospectively analysed. For convenience, patients 1–12 were designated P1-12.This was a retrospective analysis of 24 eyes of 12 unrelated Chinese patients who had visited our hospital clinic twice or more between January 2013 and December 2018. All patients consented for mutation screening in our laboratory. Written informed consent was obtained from each patient before peripheral venous blood was drawn for genomic DNA extraction and mutation screening of the CYP4V2 gene by direct sequencing, as previously described .All patients underwent complete ophthalmic examinations, including best corrected visual acuity (BCVA), slit-lamp microscopy, Goldman tonometry, indirect dilatation fundus examination, and fundus photography . The BCVA measurements were converted to logarithm of the minimum angle of resolution (logMAR) values . The FFAThe general conditions and genetic diagnoses for P1–12 are shown in Tables The severity of the fundus appearance was graded at each patient’s first visit according to the system proposed by Yuzawa and coauthors  for con.The total number of crystalline deposits decreased over time in all eyes. At the first visit, the posterior pole retina showed a dirty bluish grey colour. At the last visit, the dirty bluish grey colour of the retina had diminished gradually, and the choroidal great vessels were clearer than before. More pigment clumps were apparent P1-5) (Fig. -5 (Fig. The fluorescence of both eyes in all patients was similar, except the left eye of P5 had branch retinal vein occlusion and the left eye of P6 had CNV. In this study, the FFA images at the early phases revealed hypo-fluorescence due to a filling defect of the choriocapillaris. The hypo-fluorescent lesions showed filling of the choroidal great vessels. The FFA images at the late stage indicated hyper-fluorescence staining of the hypo-fluorescent lesion margins. The mottled fluorescence in this study indicated RPE atrophy, which Mataftsi et al [At their first visits, P1–P4 showed patchy hypo-fluorescence at the macular region and mottled fluorescence around it. The peripheral retina also showed mottled fluorescence, while the mid-peripheral retina showed normal retinal fluorescence Fig. b and 4c.At the first visit by P5, patchy hypo-fluorescence was observed at the macular region, with mottled fluorescence around it, whereas the mid-peripheral and peripheral retinal regions showed normal fluorescence. The left eye of P5 had branched retinal vein occlusion Fig. c. At theAt the first visit of P6, the posterior pole and the peripheral and optic disc nasal side retina showed mottled fluorescence, and a few patchy areas of hypo-fluorescence were observed at the nasal and superior nasal areas of the optic disc. The mid-periphery, except for the nasal side, showed normal retinal fluorescence Fig. a, c. CNVAt the first visits of P7 and P8, only a few areas of mottled fluorescence remained in the peripheral retina and the superior temporal retina of the optic disc. Most of the fundus was hypo-fluorescent, and the fluorescence of the choroidal great vessels was exposed Fig. d. At theAt the first visits of P9 and P10, large areas of hypo-fluorescence were seen in the posterior poles of both eyes, with the rest of the area showing mottled fluorescence Fig. e. PatchyAt the first visits of P11 and P12, the macular region showed mottled fluorescence, with patchy hypo-fluorescence observed around the macular area Fig. e. The hyThe natural progression of P6, 11, and 12 was different from that of the others. For convenience of description, we call the natural progression mode of P1-5 and P7-10 type 1: retinal pigment epithelium atrophy at the macular area, followed by choriocapillaris atrophy, then RPE atrophy at the peripheral retina. Similarly, we call the natural progression mode of P6, 11, 12 type 2: RPE atrophy at the posterior pole and peripheral retina, followed by choriocapillaris atrophy around the macula and along the superior and inferior vascular arcades and the nasal side of the optic disc. Subsequently, the posterior and peripheral lesions of both patients with type 1 and patients with type 2 extended to the mid-periphery; finally, all the RPEs and choriocapillars atrophied, exposing the choroid great vessels, but the macular RPE atrophy of type 2 patients could persist for a longer period of time.The disease progressed more rapidly on the nasal side of the retina of the optic disc, whereas the retina in the mid-peripheral part of the temporal side of the macular area was involved last.The natural progression of BCD remains poorly understood, with few reports of follow-up appearing in the published literature. The previous staging methods for BCD have included the Yuzawa staging , fundus We found that the expansion of the RPE-choriocapillaris complex atrophy was not centrifugal. This result is different from that of the previous studies. The Yuzawa staging was based on the finding of three patients . Its desSome reports have suggested centrifugal expansion of the visual defect based on the central scotoma seen with the 30° visual field test , 19, 27.In the same retinal area, our FFA results showed that RPE atrophy occurs first, followed by choroidal vessel atrophy, in agreement with previous research, including that by Yuzawa and coauthors . ImmunohWe re-examined the FFA images in the previous literature, and we found that those images can also be divided into the two atrophy types we have mentioned before. Type 1 shows choriocapillaris atrophy first appearing at the macula , 32, 33, The reason for these two different atrophy patterns is unknown. We looked at the gene mutation sites of P6, P11, and P12 and found that P6 and P11 had homozygous c.802-8_810del17insGC mutations, while P12 was heterozygous for the c.802-8_810del17insGC and c.332T > C; p. l111T mutations. In this study, P1 and P7 also had homozygous c.802-8_810del17insGC mutations, but their phenotypes differed from those of P6 and P11 (Table In this study, we also used the Yuzawa staging as a cross-sectional staging method according to the width and depth of the BCD lesions. Since the Yuzawa staging has been used widely for many years, its application in this study was intended as a convenience for the readers to understand the condition of the eyes of our patients. It was not meant to indicate the natural progression of the disease.In the early stage of BCD, is difficult to distinguish the type of progression in eyes with disordered pigment epithelium and no choriocapillaris atrophy. Only patients with choriocapillaris atrophy can be typed. The type of progression also cannot be determined in patients at the end stage of the disease because the choriocapillaris and RPE are atrophied and no longer visible; only the image of the choroidal great vessels is left.This study had several limitations. First, there was a small number of included eyes and a lack of primary patient observations. However, considering the rarity of the disease and our review of the previous literature, our study on the progression of BCD using FFA picture jigsaws provides one of the largest collections of images and the largest number of patients. Second, the present study lacked multimodal imaging comparisons, but we performed cross-sectional research on multimodal patient imaging. We hope to perform multimodal imaging comparisons in the near future. Third, our study lacked patients transitioning from stage 1 to stage 2, but it is difficult to locate BCD patients with early-stage disease because the visual acuity of patients at this stage is not substantially damaged, so they seldom come to the hospital. This needs further research in the future.The natural progression of BCD in our study shows two patterns. The reasons for these different types of development need further study. However, this study provides a better understanding of the phenotype and the development of the disease. The findings presented here will be helpful for future pathogenesis research and for prognostic assessment of patients with BCD.


The study investigated the dependence of the indentation load on nanomechanical properties for a gas-borided layer produced on Inconel 600-alloy. During the measurements, the indentation load range from 10 mN to 500 mN was used. Three types of tested areas, differing in the concentration of chromium, were examined. The increase in chromium concentration was accompanied by an increase in indentation hardness and Young’s modulus. Simultaneously, the increase in the indentation load resulted in a decrease in the indentation hardness and Young’s modulus, for each type of the tested area. The presence of the indentation size effect was analyzed using four models: Meyer’s law, Hays and Kendall model, Li and Bradt model, Nix and Gao model. For all tested areas, good agreement with the Meyer’s law was obtained. However, areas with a higher chromium concentration were more susceptible to indentation size effect (ISE). The proportional specimen resistance (PSR) model was used to describe the plastic-elastic behavior of the tested materials, as well as to detect the presence of ISE. It was found that the increase in chromium concentration in the tested area was accompanied by a greater tendency to elastic deformation during nanoindentation. Simultaneously, the increase in the percentage of nickel borides in the tested area resulted in a decrease in hardness and elastic modulus [Boriding of nickel-based alloys causes the formation of a multiphase layer which differs in phase composition depending on the chemical composition of the substrate material. The most popular group of nickel alloys are superalloys containing chromium, cobalt, molybdenum or iron as the main alloying elements. As a result of boriding of nickel-chromium alloys, a layer composed of various types of nickel borides and chromium borides is formed. The gas-borided layers formed on the Inconel 600-alloy and Nimonic 80A-alloy contained a mixture of NiB, Niand Cr2B ,2,3. Thiand Cr2B ,2,3. In  modulus ,6, nicke modulus  or nitri modulus . The occ modulus . The pos modulus . Titaniu modulus . Such co2-H2-BCl3 atmosphere. The continuous process was carried out at the temperature of 1193 K. The gas source of boron used in this process was boron trichloride with a concentration of 1.36 vol.% in relation to the entire atmosphere used (N2-H2-BCl3). After 2 h of boriding, the specimens were cooled under a protective nitrogen atmosphere.The multiphase boride layer was produced on a nickel-chromium alloy (Inconel 600). This material contained 15.72% Cr, 0.16% Mn, 0.04% Cu, 8.63% Fe, 0.18% Si, 0.078% C, 0.06% Al, and 75.132% Ni. The boriding method selected to produce the thick layer was gas boriding in Nα radiation. The samples for microstructure analysis and nanoindentation required metallographic preparation including mounting in a conductive resin, grinding, polishing and etching with Marble’s reagent. The microscopic observations and EDS microanalysis were performed using a Vega 5135 Scanning Electron Microscope . After the nanoindentation measurements finished, the tested areas were examined in a respect of their chemical composition. The content of the main elements  occurring in the borided layer, were measured using an Avalon X-ray microanalyzer  equipped with an energy dispersive spectrometer (EDS).The first investigation carried out immediately after gas boriding was the phase analysis. An EMPYREAN X-ray diffractometer  was used for this study. X-ray diffraction patterns (XRD) were measured using Cu K3 nanoindenter  equipped with a Berkovich diamond tip. The measurements were carried out on the cross-section of the borided layer in areas with different amounts of chromium borides. Due to the characteristic fine-grained microstructure of the gas-borided layer formed on the Inconel 600-alloy, it was necessary to analyze the chemical composition of the tested areas. It was impossible to determine the amount of chromium borides (CrB and Cr2B mixture) and nickel borides . However, it is obvious that the increase in chromium concentration in the examined area, accompanied by an increased boron content, indicated the presence of chromium borides. For this reason, the increase in chromium content (measured by EDS method) was related to the increase in the amount of chromium borides mixture in the examined areas. Based on the results of EDS microanalysis, the testing areas were classified into three groups according to their chromium content: 10 wt.%, 20 wt.% and 30 wt.%. It was assumed that the increase in the concentration of chromium was accompanied by an increase in the amount of chromium borides in the microstructure. For each group, measurements were carried out using indentation loads ranging from 10 mN to 500 mN.Nanoindentation tests were performed using the NHTmax, maximum indentation depth hmax, permanent indentation depth hp, tangent indentation depth hr, contact depth of the indenter with the sample at maximum load hc, contact stiffness S. The dependence between the indentation load and the indentation depth can be expressed by the following Equation:max—maximum load, hmax—maximum indentation depth, hp—permanent indentation depth, m—empirically determined fitting parameter.Five measurements were performed for each indentation load. During the measurements, the load-displacement curves were automatically recorded and analyzed according to the Oliver-Pharr procedure . On the IT is defined as the ratio of the maximum indentation load Pmax, to the projected contact area Ap of the hardness impression, as follows:max—maximum load, Ap—projected contact area.The nanoindentation hardness HIT depended on the plane-strain modulus E* and the Poisson’s ratio νs, according to the Equation:s—Poisson’s ratio of tested material.The nanoindentation Young’s modulus EAfter the nanoindentation measurements, the tested areas were examined in a respect of their chemical composition. The content of the main elements  present in the tested areas was measured using the energy dispersive spectrometer (EDS)-equipped PGT Avalon X-ray microanalyzer.SEM micrographs of the cross-sections of the borided Inconel 600-alloy are presented in The presence of alloying elements  in the Inconel 600-alloy caused that the compact boride layer shows no needle-like morphology. The smooth morphology of the boundary between the compact boride layer and the material underneath them resulted from the presence of chromium atoms, which constituted a diffusion barrier that hindered the diffusion of boron atoms into the substrate material ,15,16,172-H2-BCl3 atmosphere consisted of two types of grains (4B3) and boron-poor nickel borides , as well as chromium borides . The identified phases differed in peak intensities. The peaks corresponding to nickel borides dominated in the XRD patterns.Borided layer formed on Inconel 600-alloy using gas boriding in Nf grains a. Howeve4B3, Ni2B, Ni3B) and chromium borides  in the produced layer. Hovewer, the distribution of each type of borides on the cross-secion of borided layer required the use of EDS microanalysis. The chemical composition of ten spots located in different areas of the layer was examined. The microstructure of the borided layer with marked test spots and areas were presented in 2B) in these grains. In the case of the results obtained from the light area (spots 6–10), an increased nickel concentration was observed, as well as a relatively low chromium content. Such a chemical composition indicated the presence of nickel borides  in these grains. Generally, it was impossible to determine the distribution of indicidual phase in the microstructure. Even at high magnification, it was impossible to identify a separate type of chromium borides  in the darker area. Taking into account the chemical formula of individual chromium borides, the EDS results obtained do not match the specific phase. The theoretical contents of chromium and boron in chromium borides differ from the results presented in 4B3, Ni2B, Ni3B) was also difficult. Based on the EDS microanalysis results, it was found that nickel borides  and chromium borides (two types) exist only in the form of a fine-grained mixture.Observation of the microstructure of the compact boride layer at higher magnifications  allows oIt was visible that the distribution of nickel borides and chromium borides on the cross-section of the compact boride layer was irregular, without clear zonation. In order to confirm the occurrence of this characteristic phase distribution in the microstructure, a linear EDS analysis and EDS maps were performed . The resBerkovich nanoindentation was used to determine the parameters necessary to analyze the presence of the indentation size effect in the borided layer. max , the average decrease in HIT and EIT was 23% and 20%, respectively, comparing the average values obtained for the indentation loads of 10 mN and 500 mN. The increase in the chromium concentration in the tested areas was the cause of the percentage decrease in the indentation hardness and the decrease in the elastic modulus obtained at the indentation loads of 10 mN and 500 mN, 21% and 18% for tested areas with 20 wt.% of Cr, 19% and 16% for tested areas with 30 wt.% of Cr. This situation suggested the presence of the indentation size effect.Three types of areas differing in chromium concentration were examined. The average values of HIn general, the indentation size effect (ISE) phenomenon determines the tendency to the increase in indentation hardness with decreasing indentation load. This situation is related to the nucleation of the dislocations in the plastic zone under the indenter pressure. The presence of dislocations in the plastic zone increases the effective yield strength of the tested material, and thus the increase in hardness is observed . Susceptmax—maximum indentation load, hc—contact depth of the indenter with the sample at maximum indentation load, A—constant derived from the curve fit of the plot on a bilogarithmic scale, n—Meyer’s index.The ISE phenomenon can be described by the Meyer’s law, as follows ,18:(4)Pmmax and the size of indent, represented by the contact depth of the indenter with the sample at maximum indentation load hc. The value of the Meyer’s index n indicates whether the tested material has a tendency to ISE. In the case where the value of the exponent n is less than 2, an indentation size effect occurs, especially in hard, brittle materials such as ceramic phases. The exponent n equal to 2 indicates the independents of the indentation hardness from the indentation load. When the Meyer’s index is greater than 2, the reverse of the ISE behavior appears [This equation shows the relationship between the applied indentation load P appears ,18.c) were presented in a bilogarithmic scale according to Meyer’s law. The ln(P)/ln(hc) dependence obtained for the tested areas containing 10 wt.% of Cr, 20 wt.% of Cr, and 30 wt.% of Cr is shown in The applied indentation loads from 10 mN to 500 mN and the average values of the contact depth of the indenter with the sample at maximum indentation load  model. In this model, it is assumed that the resistance of the tested materials to the permanent deformation is not constant, but increases linearly with the size of the indent ,19.eff can be calculated by plotting the experimental data for the indentation load P as a function of the square of the contact depth hc. As a consequence, the effective indentation load Peff can be expressed by the following equation:c—contact depth of the indenter with the sample at maximum indentation load.The basis of this model was taken from the concept developed by Hays and Kendall , which ac2 plots are presented in P vs. hIn the PSR model proposed by Li and Bradt  it was s1, a2— constants determined by the polynomial regression.Simultaneously, the effective indentation load can be expressed as:c, the following equation was obtained:When Equation (8) was modified by the linear regression in the form of c is shown in 1 and a2 are also presented. The positive values of the parameter a1 indicate that the PSR model is appropriate for describing the indentation size effect for the tested material. In the case of a negative value of a1, it is clear that the PSR model cannot provide a satisfactory explanation of the ISE observed for the tested material [1 parameter was higher than 0 . In the case of the gas-borided layer produced on Inconel 600-alloy, the following values of a1 parameter were obtained: 0.0494 for tested area containing 10 wt.% of chromium, 0.0631 for tested area containing 20 wt.% of chromium, 0.0794 for tested area containing 30 wt.% of chromium. This general tendency, showing that with the increasing chromium concentration in the tested area, the parameter a1 increased, was in good agreement with the information provided from the load-displacement curves. The position of the unloading curve on the load-displacement curve indicated that the increased concentration of chromium caused that the measured area was more prone to elastic deformation than plastic (permanent) deformation. In the case of the PSR model proposed by Li and Bradt, good agreement was achieved with the obtained nanoindentation results. Therefore, this model is suitable for describing the ISE phenomenon in the gas-borided layers produced on Inconel 600-alloy.In general, the parameters a0, which would be obtained without the presence of the geometrically necessary dislocations, according to the following formula:0—the indentation hardness at large indentation depths.From a microstructural point of view, indentation size effect phenomenon is attributed to the evolution of geometrically necessary dislocations (GNDs) beneath the Berkovich indenter. The presence of dislocations caused an increase in the strain gradients, and thus the formation of a plastically deformed zone ,23,24. N0 parameter is the hardness in the limit of infinite depth, which can be estimated by extrapolating the linear relations of H2 against 1/h [Hinst 1/h . Whereasinst 1/h :(11)h*=ζgiven by :(12)ζ=32 of GNDs .0 and h* parameters, graphs of the dependence H2 to 1/h, as well as (H/H0)2 to 1/h were plotted  . In the enomenon . It was enomenon ,26 that The nanomechanical properties of the multiphase gas-borided layer formed on Inconel 600-alloy were investigated using a Berkovich diamond tip. To determine the dependence of nanomechanical properties on the applied load, the indentation load range from 10 mN to 500 mN was used. The presence of the indentation size effect (ISE) was analyzed using four models: Meyer’s law, Hays and Kendall model, Li and Bradt model, Nix and Gao model. The tested areas were selected into three groups differing in the concentration of chromium. The increase in chromium concentration in the tested area was accompanied by an increase in indentation hardness and Young’s modulus. The analysis of the dependence of the load on nanomechanical properties showed that the increase in the indentation load resulted in a decrease in the indentation hardness and Young’s modulus.For all examined areas, the calculated Meyer’s index was lower than 2, therefore it can be concluded that the Meyer’s law can be used as a method of ISE detection in the gas-borided layer. Simultaneously, it can be seen that the increase in chromium concentration in the tested area was accompanied by a decreasing Meyer’s index. This indicates that a higher concentration of chromium, and thus an increased percentage of chromium borides in the microstructure, resulted in a greater tendency to the ISE phenomenon.Thd Hays and Kendall model was used to calculate the minimum indentation load (W) at which the material would exhibit permanent (plastic) deformation. The obtained experimental results were not consistent with the theory of Hays and Kendall. Simultaneously, the PSR model developed by Li and Bradt was used to describe the plastic-elastic behavior of the tested materials, as well as to detect the presence of ISE. It was found that the increase in chromium concentration in the tested area was accompanied by a greater tendency to elastic deformation during nanoindentation. Nix and Gao model applied to describe the role of dislocation in the occurrence of ISE confirmed that the tested areas with a higher chromium concentration were more susceptible to the ISE phenomenon.