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As a result, the metal precursors are the volatile components, and the carbon source remains solid during the reaction. In this case, metal precursor vapors react with the carbon to form the metal carbides, which we define as the inverse gas-solid reaction interface Fig. In contrast, in the traditional carburization process 12 , a gaseous hydrocarbon such as methane CH 4 is introduced to the solid metal precursors.

The carbon diffusion through the solid-gas interface is usually fast and results in a coked carbide surface due to the excessive supply of carbon sources Fig.

We first tried to synthesize molybdenum carbides that are attractive for catalysts 11 , 19 , 29 , The phases of molybdenum carbide are complex due to their temperature-, composition-, and vacancy-dependent stability MoCl 3 was chosen as the precursor because of its high vapor pressure Fig.

We found that three pure phases of molybdenum carbides could be selectively synthesized by adjusting FJH voltages Fig. The 0. The purple hexagon depicts the shape of the nanocrystal.

To investigate the electronic structures, X-ray photoelectron spectroscopy XPS spectra of the Mo 3 d core level was collected Fig. The morphology characterization by scanning electron microscopy SEM shows the fine powder feature of all three carbide phases Supplementary Fig.

Transmission electron microscopy TEM and XRD were used to characterize the size and crystallinity of the molybdenum carbides. The particle sizes of the molybdenum carbide phases are determined by the FJH voltages Supplementary Fig. The smaller particle size obtained under higher voltage could be attributed to the faster nucleation kinetics at higher temperature The particle size values measured by TEM match well with the crystal size values determined by XRD using the Halder-Wagner method Supplementary Table 2 , indicating the single-crystal feature of the synthesized carbide particles.

Nevertheless, no preferred orientation is observed for these carbide nanocrystals according to XRD results Fig. To explain the voltage-dependent phase formation, we first recorded the current passing through the samples and the temperature under different FJH voltages Supplementary Fig.

A higher voltage leads to higher temperatures and energy inputs Supplementary Fig. The red line denotes the projected phase transformation pathway. The dashed circles denote the carbon vacancies. This explicitly demonstrates the critical role of the ultrafast cooling rate of the FJH process in kinetically accessing the metastable phases.

The side-by-side electrochemical comparison of the three phases of molybdenum carbide reveals the effect of the phase control on their individual intrinsic characteristics and catalytic behaviors. To demonstrate their catalytic properties, the HER performances of the three molybdenum carbide phases were measured in 0. The phase-dependent HER activity of molybdenum carbides was observed. The durability of the three molybdenum carbides phases was evaluated by sweeping the electrocatalysts for cycles using the cyclic voltammetry method.

The LSV curves of the 1st and th cycle for the three phases of molybdenum carbides are shown in Fig. The performances were normalized to the same mass loading of molybdenum carbides. Inset is the ratio of overpotentials at 1st cycle and th cycle for three phases of molybdenum carbide. The blue dashed line denotes the position of the Fermi level. In addition, the flash graphene support provides a conductive pathway and prevents the carbide nanocrystals aggregating, which is beneficial for improving the HER performance 7 , Because of the ultrahigh available temperature by the FJH process, various TMCs are readily synthesized regardless of the availability of metal precursors with high vapor pressure.

The uniform temperature distribution permits the phase-pure synthesis throughout the entire sample Supplementary Fig. According to the Ellingham diagram, the reduction temperatures of the metal oxides were calculated, which serve as reference values to evaluate carbide formation since the reaction of metal with carbon is exothermic Fig.

Nearly all the low-cost metal or metal compounds, including oxides, hydroxides, and chlorides, could be used as precursors, making FJH a promising low-cost production method when compared to previous methods that rely on the availability of volatile compounds 18 , 22 , These values matched well with the crystalline sizes determined by XRD Supplementary Table 2 , demonstrating that the as-synthesized carbide nanoparticles are mostly single-crystal.

The successful synthesis of the metastable W 2 C is attributed to the high energy input and ultrafast cooling rate of the ultrafast electrical thermal reaction, once again demonstrating the excellent phase engineering ability of the FJH process.

The as-synthesized carbide nanocrystals are supported on flash graphene. The necessity of the separation of graphene and carbides depends on the further application. For the application of nanocrystalline carbides in electrocatalysts, the graphene support is beneficial for improving the performance by providing conduction and preventing particle aggregation Fig.

For another major application of nanocrystalline carbides as precursors for ultra-strong ceramics, the removal of excess carbon is necessary. Here, we realized the efficient purification of the carbides by post-synthesis processes Supplementary Note 2 , including the simple calcination in air 42 for SiC Supplementary Fig.

In addition, we also demonstrated the greatly improved purity of B 4 C by using controlled feeding during the synthesis Supplementary Fig. The carbide nanocrystals are synthesized at only 2. We demonstrated the synthesis of carbide nanocrystals up to gram scale by increasing the FJH voltage Supplementary Fig.

The FJH process is expected to be extended to the synthesis of carbide alloys 44 , heteroatom-decorated carbides 34 , and phase engineering of metastable carbides 45 , which provides a powerful technique for carbide production. The controlled synthesis of metastable phases is challenging in the synthesis of inorganic materials Hence, the FJH process could provide access to many non-equilibrium phases and subsequently retain it at room temperature, thus serving as a potential tool for engineering the metastable phases of various materials, such as metal nanomaterials 46 , layered oxides 47 , metal nitrides 48 , and two-dimensional materials A capacitor bank with a total capacitance of 60 mF was used as the power supply.

The metal precursors and carbon black with specific weight ratios Supplementary Table 2 were mixed by grinding using a mortar and pestle. Graphite rods were used as the electrodes in both ends of the quartz tube. The electrodes were loosely fitting in the quartz tube to permit outgassing.

The resistance was controlled by the compression force of the electrodes across the sample. The tube was then loaded on the reaction stage Supplementary Fig. The reaction stage was then connected to the FJH system. A relay with programmable ms-level delay time was used to control the discharge time.

After the FJH reaction, the apparatus rapidly cooled on its own to room temperature. Before removing the sample, make sure that the capacitor bank is fully discharged.

The detailed conditions for the synthesis of various carbides are listed in Supplementary Table 2. The recommended safety practices were listed in the Supplementary Information. The Halder-Wagner method was used for the crystal size determination. Elemental spectra were collected using a step size of 0. The temperature was measured by fitting the blackbody radiation of the sample during FJH using a homemade spectrometer Supplementary Fig.

The emission spectra were then fitted to the blackbody radiation by using the Eq. The temperature distribution was assessed based on the optical images of the sample during FJH taken using an ultrafast camera Chronos 1.

Electrochemical measurements were conducted using a CHI D electrochemical workstation in a 0. The standard three-electrode setup was applied, where a saturated calomel electrode SCE was used as the reference, the catalyst-loaded glassy carbon electrode was used as the working electrode, and a graphite rod was used as the counter electrode. Before measurement, the electrolyte was purged with Ar gas for Ar saturation.

Electrochemical impedance tests were carried out in the frequency range of to 0. Exchange-correlation was treated within the generalized gradient approximation GGA using the functional parameterized by Perdew, Burke, and Ernzerhof For calibration, we have calculated the three molybdenum carbides, graphite, and body-centered cubic BCC molybdenum metal bulk structures. Periodic boundary conditions were applied to the unit cell in all three dimensions. The Brillouin zone integrations were performed using Monkhorst-Pack type meshes 54 , with sufficient meshes of k -points chosen so that the energy and lattice constant were fully converged.

All structures were considered to be fully relaxed when the maximum force on each atom is smaller than 0. The calculated lattice constant of the BCC Mo metal is 3.

Therefore, such a cleavage results in asymmetric surfaces of one with a monolayer of C adatoms, and the other with no C adatoms.

The singularity-free adaptive controller is proposed to eliminate the singularity with parametric uncertainty. The proposed controller consists of four components: an adaptive linearizing controller, a deputy adaptive neural network controller, an auxiliary part designed for the controller to overcome the input constraint problem, and a smooth switching algorithm used to exchange the takeover rights of the two controllers.

Moreover, the controller is designed to obtain the stabilization of hysteretic state estimation for the vibration system. The adaptive algorithms are proposed to update the unknown system parameters and to observe the unmeasurable hysteretic state.

Meanwhile, closed-loop system stability is comprehensively assessed. Finally, the simulation performed on a quarter-car suspension with an MRE-based absorber shows the proposed controller's efficiency. Semiactive vibrating systems using magnetorheological materials have become well known.

In particular, the magnetorheological elastomers MREs used in semiactive controls have recently emerged as a new material for vibration control [ 1 , 2 ]. The system can change the natural frequency by varying the stiffness of the material. These properties are attractive for many engineering applications such as vibration isolators and vibration absorbers [ 3 — 5 ].

For example, Gao et al. The results showed that the natural frequency was adjustable by 3. This study introduces the MRE-based absorber to reduce the suspension system's vibration caused by road irregularities and onboard engines. Using the MREs, the system can adjust its own frequency to avoid resonances for different types of road and engine speeds.

There are many methods proposed to represent material properties in recent years [ 6 — 10 ]. Optimization algorithms are an effective method to determine model parameters. An innovative nonlinear model has been proposed for MRE, and an improved PSO algorithm has been designed to estimate the model's parameters [ 7 ].

An extreme machine learning method was proposed to predict the device's nonlinear shear force responses with applied current, displacement, and velocity level. The new swarm optimization method, called a binary coded discrete cat, was applied to select the optimal input and the number of neurons in the hidden layer for the network development [ 8 ].

The fruit fly optimization algorithm was used to determine the model parameters. A three-story standard building model under four standard earthquake excitations was tested to evaluate the model's effectiveness [ 9 ].

Artificial intelligence approaches, including linear and nonlinear regression analysis, adaptive neural fuzzy inference systems ANFIS , and artificial neural network ANN techniques, are highly reliable methods for predicting various nonlinear properties, which have been comprehensively analyzed in [ 10 ].

The MRE-based device needs a suitable controller to achieve efficiency in the vibration system. The vibration system using an MRE-based absorber is as effective as an active system without the need for large energy. In [ 11 — 15 ], semiactive controllers have been widely used in vibration systems, such as the sky-hook, ground-hook, fuzzy clipped on-off, and LPV approaches.

These controllers do not consider the system's dynamics, so the controller does not guarantee stability in some cases. Many modern controllers have been proposed for the semiactive system, such as optimal control, adaptive control, and robust linear controller [ 16 — 18 ]. The adaptive control strategies ensure asymptotic stability with a small gain.

However, singularities can occur, which causes a tremendous control force in these controllers. A common remedy is to limit the estimated parameter to a compact set with no specified singularity. The system parameters were bounded by the maximum and minimum values to ensure that the singularity does not occur [ 19 , 20 ]. In recent years, adaptive intelligent control algorithms have achieved high efficiency in controlling complex, time-varying, and highly nonlinear civil structures [ 21 ].

These algorithms mainly work on the principles of soft computing methods and artificial intelligence. The adaptive neural network ANN controller has recently achieved high efficiency in controlling the system with unknown dynamics [ 22 ]. Optimization associated with multiple control devices is considered a difficult task. Rashid et al. However, the ANN controller often requires large amounts of computation.

The unknown dynamics have been approximated by the radial basis function where the weights are optimal. However, this method cannot identify the parameters of the system such as mass, stiffness, and damping coefficient. Therefore, control strategies encompassing all the aforementioned controller's advantages and eliminating drawbacks should be designed to yield high-quality performance. The major challenge with the semiactive device is the control force limitation and hysteresis state.

The force constraint is a complicated problem because the maximum force value depends on the displacement and velocity value. Consequently, the actuator is inadequate in the controller requirements. Actuator limitations need special attention in the controller design. Recent studies have also mentioned this problem in engineering systems [ 24 ]. Hysteresis is a fundamental phenomenon in engineering. The semiactive vibration system usually exhibits a stable hysteretic state.

The Bouc—Wen hysteresis model BWM is widely used to represent the properties of MR materials which have attracted researchers to develop intelligent vibration systems [ 25 , 26 ]. The model is flexible and can be adjusted for different hysteretic states. BWM, with its flexibility in shape control, has been used to describe asymmetric hysteresis loops.

The parametric modeling approach includes spring, damping, and Bouc—Wen models represented by a mathematical function. The coefficients of this function can be determined by using an optimization technique.

In contrast, nonparametric models are entirely based on the performance of a specific MR-based device, such as the neural network model and fuzzy model. These models are more flexible, but the physical relationship between modal parameters and hysteresis phenomena may not be explicitly maintained.

These methods need large amounts of data and are performed in advance. We introduce a hysteresis observer to approximate the hysteresis state. The developed observer is expected to estimate the hysteresis quickly. The observer supports the controller to improve robustness against unmeasurable hysteresis.

For practical applications, a novel controller is necessary to ensure the stability of a semiactive system.

In this study, we proposed an innovative control method to overcome the singularity in the traditional adaptive controller. The controller aims to exploit the advantages of adaptive controllers and neural network controllers and eliminate the disadvantages of these controllers with a smooth switching mechanism. Consequently, the denominator part of the adaptive control formula is absorbed near zero to eliminate the singularity problem.

The adaptive controller is temporarily disabled in the event of a singularity occurring. An adaptive neural network controller is introduced to take over the system to ensure system stability. The displacement response converges to zero using the proposed controller, and the output control value can be remarkably reduced near the singularity condition.

Firstly, a model was designed for the MRE-based isolator using the Bouc—Wen model, and an inverse model was developed to predict the desired current. Next, the ANN controller is used to estimate the uncertainty nonlinearity, and an adaptive controller e. A smooth switching algorithm is introduced to observe the singularity and determine the control authority between the ANN controller and a conventional adaptive controller.

The new strategy is expected to avoid singularities, small control force, and fast stability. The novel adaptive controller includes five components: i A robust adaptive controller is designed to ensure system stability. MRE samples' fabrication procedures like natural rubber synthesis consist of mixing, compressing, molding, and curing. Firstly, these components were mixed to form a homogeneous mixture for 12 minutes. The mixture was placed in a vacuum chamber to remove air bubbles inside the material for 30 minutes.

Finally, the mixture was vulcanized in a mold under a magnetic field or without a magnetic field for 24 hours at room temperature 26 degrees Celsius. Anisotropic MRE samples were vulcanized in a magnetic field, while isotropic MRE samples were vulcanized without a magnetic field.

The MRE-based absorber is used in this study, whose properties depend on displacement, amplitude, frequency, and magnetic field. In particular, its stiffness increases significantly when the applied current is increased.

Consequently, the absorber operates efficiently over a wide range of frequencies presented in the research. An MRE model is necessary for vibration system design; the hysteresis force-displacement loop is a major challenge under different applied currents.

The model consists of a Bouc—Wen component and a Maxwell component. In the Bouc—Wen model, the evolutionary variable z describes the hysteresis behavior. The force of the MRE-based absorber is given by where the linear stiffness force and purely hysteretic force are and , respectively.

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