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The problem of thermal stability of a cylindrical sample with nonlinear heat generation placed in a medium with the ambient temperature random walk was studied. The behavior of this system was examined depending on the parameters of the problem (heat generation intensity, random walk variance). A numerical algorithm based on averaging multiple random trajectories of the ambient temperature was proposed. A numerical method was developed for solving the heat transfer problem with the heat source and stochastic boundary which combines both explicit and implicit schemes for linearized transfer equations and the Euler–Maruyama method. The distributions of ignition characteristics and their moments were obtained. Their dependencies on the parameters of the problem were investigated.

Objectives: Coating treatment on the surface of diamond particles is an important technique to effectively overcome the problem of difficult bonding between diamond and substrate, and the thermal explosion reaction is a common surface coating technique for diamond particles. However, this technology has disadvantages such as difficulty in separating diamonds from the product and a low proportion of diamonds, which increases its complexity and production costs, greatly limiting the promotion and application of this technology. This article aims to introduce polytetrafluoroethylene (PTFE) into thermal explosion reaction technology to form a coating mainly composed of TiC on the surface of diamond particles. It is expected to optimize the coating preparation process and promote the popularization and application of thermal explosion reaction technology in the field of diamond plating, so as to improve the wear resistance and service life of the diamond tools. Methods: Using two raw material systems, Ti/carbon black/diamond and Ti/carbon black/PTFE/diamond powders, the thermal explosion reaction of Ti/carbon black/diamond is induced by the chemical furnace method, and the intense chemical reaction between PTFE and titanium at low temperature ensures that the Ti/carbon black/PTFE/diamond system directly undergoes a thermal explosion reaction. At the same time, the TiC coating can be generated on the surface of diamond particles by adjusting the ratio of raw materials and triggering the thermal explosion reaction under high temperature conditions. The macroscopic morphology of diamond particles before and after coating is observed and compared by optical microscope to roughly infer the plating condition, and the phase compositions of the coating were analyzed by X-ray diffraction. Then the scanning electron microscope and the energy dispersive spectroscopy are used to observe the surface morphology of diamond particles, determine the elemental compositions, and infer the surface reaction state. Results: The thermal explosion reaction of both raw material systems can form a TiC coating on the surface of diamond. The main phase of the binder reaction product is TiC, and the main phases of the coating on the surface of diamond particles are TiC and Ti. But for the Ti/carbon black/diamond system, the chemical furnace method is needed to induce a thermal explosion reaction. When the diamond mass fraction in the raw material is 30% or lower, the TiC coating on the surface of the diamond particles is good. When a small amount of PTFE is introduced into the Ti/carbon black/diamond system, the reaction between Ti and PTFE releases a large amount of heat, which induces the thermal explosion reaction between Ti and carbon black and synthesizes TiC, and finally forms a TiC coating on the surface of diamond particles. In addition, the system does not need the chemical furnace method to detonate. When the diamond mass fraction in the raw material is less than or equal to 60%, the diamond particle surface coated with TiC coating is good. At the same time, appropriately reducing the content of carbon black in the raw materials can enable diamond to obtain a good TiC coating on its surface even when the mass fraction of diamond is 90% or higher. Conclusions: TiC coatings are prepared on the surface of diamond particles using thermal explosion reaction technology, and the important effects of raw material compositions and PTFE additives on the formation of diamond particles' surface coating are revealed. Adding an appropriate amount of PTFE can directly induce the thermal explosion reaction, which greatly promotes the increase of the proportion of diamond in the raw material, and effectively improves the formation quality of the coating. This can greatly save binder powder, thereby reducing production costs, while obtaining loose powder products that are easy to separate from diamonds. In addition, drawing on the work of this study, other carbide materials (such as SiC) can be analogously extended for coating on the surface of diamond particles, thereby promoting the promotion and the application of thermal explosion reactions in diamond coating.

Porous NiAl intermetallics were synthesized from Ni-50at.%Al powder compact using an energy-saving and facile method of thermal explosion (TE). The effect of preheating treatment at 470 °C for 2 h on exothermic behavior, macroscopic appearance, phase composition and microstructures are investigated. Results shown that the combustion temperature decreases from 1645 to 1516 °C and the synthesized porous NiAl compounds possess a complete cylindrical shape. Some Ni2Al3 and NiAl3 phases preferentially generate in the preheating process through the solid-phase diffusion reaction. Afterward, the eutectic reaction of Al-NiAl3 and the melting of Al promote the occurrence of an obvious exothermic reaction even at a low temperature. After TE reaction, three-dimensional interconnected pore channels are formed among the product skeletons with a high porosity of 60%, indicating the pore structures of porous NiAl sintered compact can be well controlled. The oxidation kinetics curve suggests that porous NiAl compounds exhibit excellent oxidation resistance at high temperature. [ABSTRACT FROM AUTHOR]

Co-Al porous materials were fabricated by thermal explosion (TE) reactions from Co and Al powders in a 1:1 ratio using NaCl as a space retainer. The effects of the NaCl content on the temperature profiles, phase structure, volume change, density, pore distribution and antioxidation behavior were investigated. The results showed that the sintered product of Co and Al powders was solely Co-Al intermetallic, while the final product was Co4Al13 with an abundant Co phase and minor Co2Al5 and Co-Al phases after added NaCl dissolved out, due to the high Tig and low Tc. The open porosity of sintered Co-Al compound was sensibly improved to 79.5% after 80 wt.% of the added NaCl dissolved out. Moreover, porous Co-Al intermetallic exhibited an inherited pore structure, including large pores originating from the dissolution of NaCl and small pores in the matrix caused by volume expansion due to TE reaction. The interconnected large and small pores make the open cellular Co-Al intermetallic suitable for broad application prospects in liquid–gas separation and filtration. [ABSTRACT FROM AUTHOR]

The goal of this research is to design the Gudermannian neural networks (GNNs) to solve a type of two-point nonlinear singular boundary value problems (TPN-SBVPs) that arise within thermal-explosion theory. The results of these investigation are provided for different neurons (4, 12 and 20), as well as absolute error along with the time complexity. For solving the TPN-SBVPs, a genetic algorithm (GA) and sequential quadratic programming (SQP) are used to optimize the error function. The accuracy of designed GNNs is provided by using a hybrid GA–SQP combination, which is based on a comparison of obtained and actual solutions. Furthermore, statistical analysis of the data is proposed in order to establish the competence as well as effectiveness of designed and the efficacy of the designed computing framework for solving the TPN-SBVPs. [ABSTRACT FROM AUTHOR]

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The paper proposes a two-dimensional thermokinetic model of the composite synthesis process in the mode of dynamic thermal explosion taking into account the structurization of the synthesis product. Structurization in the model is understood as a transition from amorphous to crystalline state. The model takes into account the heating of the reactor walls by thermal radiation from the device, the temperature of which can vary at different rates. Chemical reactions are described by a summary scheme that corresponds to the synthesis of Ni3Al composite. The kinetic law takes into account a possible strong inhibition of the rate of the reaction with the accumulation of the synthesis product, which is typical for reactions controlled by diffusion at the particle level. The effective thermophysical properties of the components of mixture and reaction products in the reactor depend on the properties of the constituents of the initial mixture and the fraction of reaction product. The properties of the latter also depend on the degree of structurization. The structurization process is described by a special additional parameter whose evolution is modeled by a reversible reaction. It is assumed that the structurization process starts from the moment of product appearance and continues during the cooling of the system. It is shown that synthesis results in the formation of a composite containing the initial components and the reaction product with the matrix partly in the amorphous state and partly in the structured state. The dynamics of synthesis and structurization are influenced by heating conditions and reactor size. [ABSTRACT FROM AUTHOR]

The combustion in thermal explosion mode of reactive mixtures of Ti–Ni–graphite(carbides, borides, oxides), under load, was used to produce complex composite materials, densified and joined to a C55 carbon steel support. The ignition of the exothermic reaction, carried out thanks to the rapid high-frequency heating of a green compact up to 1573 K, was followed by an isothermal holding at 1373 K for 360 s. This procedure ensured a perfect mechanical assembly between the composite material and the steel substrate. SEM analysis and concentration profiles carried out at the interface testified to the interdiffusion of iron and titanium atoms between the two materials. The maximum combustion temperature (Tmax.) exceeding 2200 K induced the appearance of a liquid phase that assisted densification and joining, and in which a part of the additions was dissolved before cooling. The starting chemical composition of reactive mixtures largely determined the microstructure, hardness and tribological behavior of the composites after the process. Thereby, the maximum hardness (1235 HV0.15) and the lowest wear rate (1.824 × 10−6 mm3.N−1.m−1) were obtained in the sample containing TiC, Al2O3 and TiB2 hard phases. The manufactured samples exhibit no deterioration of the composite by spalling, regardless of the starting composition. [ABSTRACT FROM AUTHOR]

A TiC coating was rapidly formed on the surface of diamond particles by thermal explosion reaction using Ti/Carbon black/PTFE/Diamond powders as raw material. XRD and SEM were used to analyze and observe the phase composition and microstructure of the coating. Results show that the phase composition of bonders was TiC, Ti, and TiF3 after thermal explosion reaction. The diamond surface obtained after the reaction can achieve good coating. Changing the diamond content in the raw material can regulate the phase composition of the coating. The coating on the diamond surface was mainly composed of TiC. When the diamond content in the raw materials was 20–40%, the coating was composed of TiC and TiF3. When the diamond content in the raw material was 60–80%, the coating was composed of TiC and Ti. [ABSTRACT FROM AUTHOR]

This work focused on the production of the MoAlB MAB phase through self-propagating, high-temperature synthesis in the thermal explosion mode. The influence of the method of a Mo-Al-B-powder reaction mixture preparation on the combustion temperature, mechanism, and stages of the MAB phase formation in the combustion process was investigated. The combustion temperatures of the mixtures obtained in the rotary ball mill and high-speed planetary ball mill were 1234 and 992 °C, respectively. The formation of intermediate compounds Mo3Al8 and α-MoB in the combustion front, along with MoAlB, was established using the time-resolved X-ray diffraction method. In the case of the mixture prepared in a ball mill, the primary interaction in the combustion front occurred through the Al melt, and in the case of using a planetary mill, solid-phase reactions played an important role. The mechanical activation of the mixture in a planetary mill also accelerated the processes of phase formation. The method of a reaction mixture preparation has virtually no effect on the MoAlB MAB phase content in combustion products (92–94%), but it does affect their structure. The synthesis products have a lamellar structure composed of MAB grains with a thickness of ~0.4 μm and a length of ~2–10 μm. [ABSTRACT FROM AUTHOR]

This paper describes the effect of preliminary low-energy mechanical activation of nickel powder on the thermal explosion of a Ni3Al intermetallic compound. Two synthesis methods are considered. The first method requires that a mixture is continuously heated by an external energy source. The second method requires that an external source is turned off upon reaching a certain temperature. It is revealed that low-energy mechanical activation of nickel intensifies the Ni3Al synthesis. With continuous heating, the ignition temperature does not depend on activation time and is equal to the melting point of aluminum. In the case of heating with an external source turned off, preliminary activation of nickel reduces the solid-phase ignition temperature. It is established that nickel activation in a laboratory mill allows one to eliminate its passivation factors. [ABSTRACT FROM AUTHOR]

The process of creating a porous metal-ceramic material based on Ni-Al alloy and gadolinium-doped cerium oxide (CGO) using the thermal explosion method has been investigated. This study aims to analyze the effect of CGO on the thermal explosion parameters and the architecture of the resulting Ni-Al-CGO materials. In this regard, the influence of adding CGO powder to the Ni-Al system on the synthesis process and structure formation during controlled heat loss thermal explosion has been studied. Dependencies of temperature and time characteristics of the thermal explosion on initial parameters have been measured. It has been demonstrated that the concentration of CGO in the initial mixture and heat dissipation from the sample significantly affect the rate of the exothermic reaction. The phase composition of the obtained porous materials, depending on the CGO content and the temperature of subsequent vacuum annealing, was analyzed using X-ray diffraction. The chemical composition and microstructure of the synthesis products were examined through electron microscopy and energy-dispersive X-ray spectroscopy. The possibility of forming metal-ceramic composites with a porosity of 60–65 % for use as supporting substrates for solid oxide fuel cells with a NiO/CGO anode has been shown. An anodic layer of NiO/CGO was applied to a metal-ceramic base of the composition (Ni+25 %Al)+5 %CGO using screen printing, which was then annealed in an air atmosphere at 1300 °C and reduced at 900 °C in a hydrogen atmosphere. The dilatometric method determined that adding 40 wt.% Cr to a mixture of Ni-Al powders reduces the average coefficient of thermal expansion of the new material.

High-entropy carbides are a new class of inorganic compounds promising for a wide range of applications. A new concept was proposed for the synthesis of powders of high-entropy carbides by self-propagating high-temperature synthesis (SHS) in the gasless thermal explosion mode from previously mechanically synthesized and structured reaction mixtures. For the first time, high-entropy carbides TaTiNbVWC5 and TaNbVMoWC5 were produced by this method, and their crystal structure was determined and compared with those of similar compounds synthesized by sintering. [ABSTRACT FROM AUTHOR]

The basic principles of a thermal explosion had been studied and published by 1980. It seemed that the research was completed, but later it was discovered that Zeldovich's "ignition condition" does not correlate with the experimental data. "The theory of ignition by a heated surface" is the basis of ignition theory, but, although the calculations are correct, the results obtained are mistakenly attributed to ignition—in reality they describe the spontaneous ignition of an infinite combustible. Our work shows that a thermal explosion of a combustible from a heated body can develop as ignition and self-ignition. The conditions for self-ignition of an infinite combustible by a flat surface and a cylinder are given, as is the likely condition for the ignition of a combustible between parallel walls of different temperatures. [ABSTRACT FROM AUTHOR]

The processes occurring during the induction of a thermal explosion in titanium and aluminum powder mixtures are analyzed. The role of the oxide film on aluminum particles and the heating rate of samples during interaction between titanium and aluminum is considered, and various mechanisms of the oxide film destruction at temperatures near the melting point are proposed. It is shown that, depending on the heating rate of the samples, there are three possible mechanisms of formation of direct contact between titanium and aluminum: mechanical destruction of the oxide film on aluminum, the reaction of aluminum oxide with titanium, and the reaction of aluminum oxide with aluminum. Mechanical activation of the powder mixture lowers the ignition temperature by 20–30°C. As the average titanium particle size reduces from 90 to 10 m, the ignition temperature is lowered by 100°C. It is shown that a two-stage ignition mechanism is observed in a number of cases. The isothermal section of aluminum melting is followed by the stage of a slow temperature rise up to 700–800°C, after which the temperature rise rate increases tenfold. [ABSTRACT FROM AUTHOR]

Porous TiAl3 materials were prepared by a time- and energy-saving thermal explosion (TE) method with Ti-75 at% Al mixture powders. Cyclic oxidation tests were performed in air at 650 °C, 800 °C, and 900 °C. Only a weak peak of the oxide phase was detected by X-ray diffraction when the oxidation temperature was below 800 °C. The pore structures remained stable without pore blockage or collapse due to the thin protective oxide layer formed on the surface of the product skeleton at 650 °C, which was confirmed to be Al2O3. The thickness of the oxide scale increased with increasing the oxidation temperature from 800 °C to 900 °C. The compressive strength of the oxidized sample was inversely proportional to its corresponding porosity. Additionally, the antioxidant mechanism at high temperature was further investigated, indicating excellent oxidation resistance. Therefore, porous TiAl3 intermetallic can be considered as promising materials for applications such as filtration, separation, and catalysis at a high temperatures up to 800 °C.

In this study, the approximate and exact solutions for the stationary-state of the solids model with neglecting reactant consumption for both non-uniform and uniform temperature systems were applied on gas ignition under a constant pressure condition. The criticality conditions for a slab, an infinite cylinder, and a sphere are determined and discussed using dimensionless temperatures under constant ambient and surface temperatures for a non-uniform temperature system. Exact solution for a Semenov model with convection heat loss was also presented. The solution of the Semenov problem for constant volume or density as a solid and constant pressure were compared. The critical parameter δ is calculated and compared with those of Frank-Kamenetskii solution values. The validation of the calculated ignition temperatures with other exact solution and experimental results were offered. The relation between critical parameters form Semenov and F.K. models solution was introduced.

Phase composition of thermal explosion products in compacts made of Ti–C–Al powder mixtures with an equiatomic ratio of titanium and black carbon (soot) and with an aluminum content of 10–40% (wt.) is studied. The compacts are heated at a rate of °C/min in an argon atmosphere. Self-ignition temperature of all compositions was close to the melting point of aluminum (660°C). Peak temperatures and the maximum rate at which temperature increment becomes larger as the aluminum powder content in the mixtures increases. Synthesis products contain titanium carbide and Al3Ti titanium trialuminide, whose ratio depends on the aluminum content in the mixture. Pretreatment of reaction mixtures in a planetary mill flattens aluminum particles, thereby preventing the formation of a melt. The spreading of a melt over the titanium surface with subsequent reaction diffusion and the formation of Al3Ti increases the synthesis temperature in compacts made of nonactivated mixtures. [ABSTRACT FROM AUTHOR]

MoAlB ceramics containing a small amount of Al2O3 and MoB as impurities were synthesized by thermal explosion technique using Mo, Al, and B2O3 as the raw materials. The effect of Al content on the reaction synthesis of MoAlB materials was investigated. Results showed that adding excess Al could compensate for the Al volatilized during the thermal explosion reaction Moreover, it could remarkably promote the formation of gaseous AlO and inhibit the synthesis of solid-phase Al2O3. Thus, it substantially promoted the synthesis of MoAlB. High-content MoAlB ceramics were prepared at 800 °C for 1 min by using 2Mo/4.6Al/B2O3 as the raw materials. The MoAlB grains were flaky and had a thickness of 500 nm and a length of 1–5 μm.

Fe2AlB2 material was prepared through spark plasma sintering (SPS) by using Fe/Al/B mixed powder as the raw material. The effects of sintering temperature, holding time, and Al content on the phase composition and microstructure of the product were studied to obtain materials with high Fe2AlB2 content. Results showed that when the sintering temperature was increased to approximately 1000°C, SPS induced a thermal explosion reaction, resulting in the formation of a dense sintered sample with high Fe2AlB2 content. The sample contained a small amount of FeB and FeAl3 impurities. The synthesis of Fe2AlB2 could be promoted by optimizing holding time and increasing Al content in the raw materials. The most suitable process parameters for the synthesis of materials with high Fe2AlB2 content were 1000°C, no holding, and 2Fe/1.1Al/2B raw material. The Fe2AlB2 sample had good mechanical properties. Its Vickers hardness and bending strength were 10.5 GPa and 352 MPa, respectively. Given that the synthesized Fe2AlB2 material was unstable, continuously increasing the temperature or extending the holding time would cause it to decompose.

Heat generation as a result of the exothermic reaction reaches the environment mainly due to the conduction through the walls of the vessel. The balance between the heat generated and the heat conducted away, resulting in the explosion is described by the Frank-Kamenetzkii (FK) parameter ρ. The critical value of FK for which the explosion occurs depends upon the shape of the vessel, which requires the solution of governing singular nonlinear Poisson-Boltzmann equation. Owing to the exponential nonlinearity and singularity the analytical exact solution for the non-integer k values does not exist. This work focuses on implementing the polynomial collocation by exploiting the global optimization features of the genetic algorithm to solve the Poisson-Boltzmann equation for integer and non-integer shape factors (k). The governing equation was converted into coupled nonlinear algebraic equations and an objective function was formulated. The method was examined for six different configurations of the control parameters of GA to find the best set of parameters. The solution for temperature distribution is obtained for cylindrical (k = 1), parallelepiped (k = 0.438, 0.694), and an arbitrary shape (k = 0.5) respectively. The solution obtained from Polynomial Collocation Genetic Algorithm (PCGA) remained in good agreement with the corresponding analytical results for k = 1, with the minimum absolute error of 10−10. The critical values of the FK are obtained as 1.5,1.4,and1.7 for shape factor k=0.438,0.5,and0.694 respectively with the convergence of the order of 10−6to10−5. The obtained solution is fairly stable over appropriate independent runs with the variation in the fitness value ranging from 10−05to10−03. Further simulations were performed to validate the results through statistical error indices. The diminutive errors of the order of 10−6 confirm reliable optimum solution, accuracy, and stability.

With the new discovery of layered boride compounds M 2 AB (M = Zr, Hf, Nb; A = S, Se) with the typical Cr 2 AlC-type structure, MAX phases have been successfully expanded from carbides and nitrides to borides. However, only five MAX phase borides have been synthesized at present, which means that the research on MAX phase borides is still in its infancy. Therefore, the exploration of new MAX phase borides is necessary and can provide a solid basis for future research. In this paper, we describe the discovery of the first tellurium (Te)-containing layered ternary compound Hf 2 TeB using combinatorial methods of thermal explosion synthesis, XRD, SEM, and HRTEM analyses. This new MAX phase crystallizes with a Cr 2 AlC-type structure with the space group of P6 3 / mmc, and the lattice parameters are a = 3.60475 Å, c = 13.12663 Å, respectively, and atomic positions are Hf at (1/3, 2/3, 0.57505), Te at (1/3, 2/3, 1/4), and B at (0, 0, 0). [ABSTRACT FROM AUTHOR]

Synthesis products in mechanically activated powder mixtures of titanium and nickel of three compositions corresponding to double intermetallic compounds are studied. The mixtures are mechanically activated in a planetary mill at a rate of 40 g and a processing duration of 20 min. Synthesis is carried out by a thermal explosion: the mechanically activated mixtures are heated in a sealed reactor in an argon atmosphere at an average heating rate of 70°C /min. The phase composition of the powder products after synthesis and additional annealing is studied by X-ray diffraction analysis, and the results are discussed using the reference data on the temperature dependences of the Gibbs energy of intermetallic compounds. It is revealed that, regardless of the elemental composition of the mixtures, the TiNi3 intermetallic compound, which has the highest negative Gibbs energy, is predominantly formed during synthesis. Therefore, a single-phase target product can be obtained only from a TiNi3 mixture. Thermal explosion products in mixtures of the other two compositions are multiphase. Annealing causes no qualitative changes in the phase composition, and the quantitative changes in the phase content are negligible. [ABSTRACT FROM AUTHOR]

The effect of various conditions of mechanical activation of Ti + Zr + Hf + Nb + Ta + 5C mixtures on the microstructure of composite particles, regularities of their ignition, and phase composition of final products was studied. The activation of mixtures was found to decrease the ignition temperature by 600–900°C. It was shown that the intense mechanical activation reduces the activity of the mixture and the subsequent ignition in the thermal explosion mode transforms the mixture into high-entropy compound. Such transformation is not observed in conditions of long-term low-intensity activation. [ABSTRACT FROM AUTHOR]

Variational formulations are proposed for equations describing the stationary states of nonisothermal one-dimensional reactors, including those under convective transfer. Several versions of a numerical solution are considered for the proposed variational formulations on the basis of the method of local variations and the Rayleigh–Ritz method. The special features of using numerical methods to solve the problems under consideration are discussed: convergence and ratio of a spatial grid step to the degree of an approximating polynomial. Modifications of the thermal ignition problem with account for convective transfer and heat losses are considered. A variational principle is proposed that determines the structure of a combustion front at a given propagation velocity. It is shown that this variational principle can be used along with the principle of minimum entropy production for a complete solution to the problem of stationary propagation of an exothermic reaction wave. [ABSTRACT FROM AUTHOR]

In this study, the approximate and exact solutions for the stationary-state of the solids model with neglecting reactant consumption for both non-uniform and uniform temperature systems were applied on gas ignition under a constant pressure condition. The criticality conditions for a slab, an infinite cylinder, and a sphere are determined and discussed using dimensionless temperatures under constant ambient and surface temperatures for a non-uniform temperature system. Exact solution for a Semenov model with convection heat loss was also presented. The solution of the Semenov problem for constant volume or density as a solid and constant pressure were compared. The critical parameter d is calculated and compared with those of Frank-Kamenetskii solution values. The validation of the calculated ignition temperatures with other exact solution and experimental results were offered. The relation between critical parameters form Semenov and F.K. models solution was introduced. [ABSTRACT FROM AUTHOR]

This paper investigated the critical ignition conditions of combustible gas containing liquid fuel droplets. The analysis is done based on the criteria of the thermal explosion theory. It includes analytical and numerical solutions of modeling equations of fuel droplets heating and evaporation by convection and radiation from the surrounding reactive hot gas. The exothermic reaction is usually modeled as a single-step reaction obeying an Arrhenius temperature dependence. The thermal conductivity of the fuel droplet is dependent on temperature. The analytical solution produced relations between the main critical characteristic parameters in all planes of the solution. The results obtained from investigating the effect of the characteristic parameters on the explosion behavior of gas and fuel droplets and the thermal radiation proved that both of them are significant. The study proved that the criticality definitions of the thermal explosion of a single-phase system can be used effectively and efficiently to determine the critical conditions of a multi-phase system. Finally, the application of the numerical solutions of the modeling equations was used to analyze the explosion characteristics of a diesel fuel spray system. [ABSTRACT FROM AUTHOR]

Transition metal sulfides and their corresponding derivatives, such as MAX phases, have been widely studied because of their unique physical properties. However, due to the low melting/boiling point and volatile characteristics of sulfur, it is difficult to control the element ratio in their in-situ synthesis, and some impurities are introduced. Based on this, we first studied the reaction mechanism of sulfur-containing MAX phase Hf 2 SB. Previous studies generally believed that the mechanism of MAX phase synthesis is that elements M and X first form compounds and then react with elements A. Interestingly, Hf reacts with sulfur to form Hf 2 S firstly, and then boron enters the octahedral gap between the two layers of hafnium to form Hf 2 SB. Based on the reaction mechanism, Hf 2 SB with a purity of 91.99 wt% and its corresponding sulfide Hf 2 S with a purity of 96.75 wt% were successfully and rapidly synthesized by thermal explosion synthesis using a spark plasma sintering furnace. The microstructure of the sample fractured surface was observed by scanning electron microscopy, which confirmed that the Hf 2 SB grains were in lath shape, that is, the typical grain shape of MAX phases. The crystal structure and atomic positions of Hf 2 SB and Hf 2 S were obtained accurately, and the similar structure between them confirms our conclusion on the reaction mechanism. [ABSTRACT FROM AUTHOR]

Mn/Al/B mixed powders were used as raw material for the thermal explosion reaction in a tubular furnace to rapidly prepare Mn2AlB2 ceramics with high content at low temperature. The effects of raw material ratio, raw material particle size, and NaCl additives on the synthesis of Mn2AlB2 were studied systematically. The formation mechanism of Mn2AlB2 was proposed. The thermal explosion reaction was induced when the preheating temperature was approximately 686.9°C. The materials with MnB, Al, and Mn2AlB2 were synthesized as main phases. Mn2B and AlMnx were obtained in small amounts. Increasing the content of Al or refining the Mn and B size in the raw material reduced the content of MnB and other impurities in the product significantly, thereby promoting the synthesis of Mn2AlB2. The thermal explosion products were porous, and the sintering degree was weak. Many lathed Mn2AlB2 grains with an approximate size of 4 μm were obtained. A mechanism for the thermal explosion synthesis of Mn2AlB2 was proposed. [ABSTRACT FROM AUTHOR]

Ceramics with high MoAlB content were rapidly synthesized via thermal explosion by using Mo/Al/B mixed powders as the raw materials. The effects of raw material ratio and heating mode on the phase composition of the products were studied through DSC, X-ray polycrystalline diffractometer, and SEM. Results showed that ceramics with high MoAlB contents could be prepared from 1.1Mo/1.2Al/1.05B powders by using a tubular furnace at 800 °C for 1 min. They could also be obtained from 1.1Mo/1.1Al/1B powders through spark plasma sintering at 1000 °C without holding. Finally, the reaction mechanism of MoAlB material synthesis via thermal explosion was proposed on the basis of thermodynamics analysis.

Co–Al porous intermetallics were fabricated by an efficient and energy-saving method of thermal explosion (TE) reactions. The effects of Co/Al molar ratios on the temperature profiles, phase compositions, expansion behaviors, density, pore characteristics, and oxidation resistance were investigated. When the target furnace temperature was set at 700°C, there was an obvious exothermic peak in the temperature profiles. The ignition temperatures were in the range of 600–645°C, and the combustion temperatures were in the range of 984–1,421°C. Co–Al porous intermetallics had the open porosity of 27–43%, and the pores were from nonfully dense green compacts and explosion behaviors of TE. The specimen with Co:Al = 2:9 possessed a higher open porosity of 42.8%, the lowest density of 1.86 g cm−3, and the largest volume expansion of 76.7%. The porous specimens with Co:Al = 1:1 possessed the highest open porosity of 43.2%, the lowest volume expansion of 12.3%, and the highest density of 3.42 g cm−3. All Co–Al porous intermetallics showed excellent oxidation resistance at 650°C in air, especially the specimen with Co:Al = 1:1 had the highest oxidation resistance.

• The thermal effects occurring during the heating of the levextrel TBP are studied. • The kinetics parameters describing the exothermic processes are estimated. • The gaseous products of the complete decomposition of the levextrel TBP are studied. • The safety limits of the sorption-type column are estimated by modeling. Solid extractants based on tributyl phosphate (levextrel TBP) are of interest for the additional extraction of uranium and plutonium from high level waste during the processing of spent nuclear fuel. To assess the possibility of application of the levextrel TBP, considering its potential fire and explosion hazard, the method of differential scanning calorimetry was used to determine the exothermic effects occurring during the heating of the levextrel TBP saturated with nitric acid solutions. It was found that at 37 % concentration of nitric acid solution containing a number of metal nitrates, the heating is accompanied by the exothermic thermal effect of 1034 ± 178 J/g, which is the average value for the heating rates from 1 to 5 K/min. The value of the heat release makes it possible to potentially classify the levextrel TBP as a class of self-decomposing substances and mixtures. The kinetic parameters of the multistage reaction describing the thermal decomposition of the levextrel TBP are estimated by mathematical optimization. Using computer modeling, the critical conditions for the occurrence of a thermal explosion in the sorption-type column for the additional extraction of radionuclides from high level waste are estimated, namely, the maximum permissible values of: the temperature of the core of the material inside the column; the radius of the column; additional heat generation of non-reactive origin inside the column. [ABSTRACT FROM AUTHOR]

High-energy ball milling (HEBM) of powders is a complex process involving mixing, morphology changes, generation and evolution of defects of the crystalline lattice, and formation of new phases. This review is dedicated to the memory of our colleague, Prof. Michail A. Korchagin (1946–2021), and aims to highlight his works on the synthesis of materials by self-propagating high-temperature synthesis (SHS) and thermal explosion (TE) in HEBM mixtures as important contributions to the development of powder technology. We review results obtained by our group, including those obtained in collaboration with other researchers. We show the applicability of the HEBM mixtures for the synthesis of powder products and the fabrication of bulk materials and coatings. HEBM influences the parameters of synthesis as well as the structure, phase composition, phase distribution (in composites), and grain size of the products. The microstructural features of the products of synthesis conducted using the HEBM precursors are dramatically different from those of the products formed from non-milled mixtures. HEBM powders are also suitable as feedstock materials for depositing coatings by thermal spraying. The emerging applications of HEBM powders and future research directions in this area are discussed. [ABSTRACT FROM AUTHOR]

Results of receiving a diborid of magnesium are given in work by magniathermal oxidation of boron composite compounds at different argon pressures and temperatures. The relevance of a research is proved by superconducting properties of magnesium diboride. Synthesis of magnesium diboride itself accelerates, due to wall burning and thermal explosion of exothermic mixture of the reaction products of magniathermal. It is shown that the use of SHS method at high argon pressure and temperature allows to obtain magnesium diboride of high purity.

Fe2AlB2 material was prepared through spark plasma sintering (SPS) by using Fe/Al/B mixed powder as the raw material. The effects of sintering temperature, holding time, and Al content on the phase composition and microstructure of the product were studied to obtain materials with high Fe2AlB2 content. Results showed that when the sintering temperature was increased to approximately 1000°C, SPS induced a thermal explosion reaction, resulting in the formation of a dense sintered sample with high Fe2AlB2 content. The sample contained a small amount of FeB and FeAl3 impurities. The synthesis of Fe2AlB2 could be promoted by optimizing holding time and increasing Al content in the raw materials. The most suitable process parameters for the synthesis of materials with high Fe2AlB2 content were 1000°C, no holding, and 2Fe/1.1Al/2B raw material. The Fe2AlB2 sample had good mechanical properties. Its Vickers hardness and bending strength were 10.5 GPa and 352 MPa, respectively. Given that the synthesized Fe2AlB2 material was unstable, continuously increasing the temperature or extending the holding time would cause it to decompose. [ABSTRACT FROM AUTHOR]

The volume filling degree (VFD) is a universal property of materials whose influence is often overlooked in the assessment of their property and performance. The present work exemplifies its significance by evaluating its influence on the thermal explosion of a typical 1,3,5-trinitro-1,3,5-triazinane (RDX) energetic material (EM) and the related underlying mechanism, with experimental measurements of the critical temperature for an explosion delay of 5 ​s (T5s), and reactive molecular dynamics (MD) simulations. Three samples with different VFDs are accounted for in the T5s measurements, whereas seven RDX-containing models are established for our MD simulations, considering two kinds of surfaces, four VFDs of 1, 0.5, 0.1, and 0.05, and three heating styles. The experimental measurements show that a higher VFD leads to a lower T5s, or readier thermal decay. The origin of the VFD influence on T5s is that a smaller VFD favors dissociation reactions such as the NO2 partition, and disfavors the combination ones such as NO2 consumption in rapid complete decay to obtain final stable products and enhance heat release. Particularly, the reduced VFD increases the energy required to complete decay, lowers the decay rate and heat release, and results in reduced temperature, pressure elevation and explosion power, in agreement with the experimental observation that a higher VFD causes a lower T5s. Moreover, the origin of the VFD influence is principally from the pressure effect. Therefore, the VFD is crucial in the thermal decomposition of EMs because various VFDs can cause a significant difference in power. Moreover, the difference in the surface effect on the thermal decay of RDX between the (021) and (210) faces is clearly discriminated under adiabatic heating, because more activated molecules are found around the (021) face owing to the higher internal energy. In summary, the influence of VFD is significant when dealing with issues related to the surfaces of EMs.

This work investigates possible factors that lead to acetone-water explosion in a hydrothermal extraction reactor that happened in our laboratory. To begin with, acetone-water reactivity was checked in CAMEO. Next, pressure build-up curves at varying operating conditions were simulated in Aspen Batch Modeler. Analysis of variance (ANOVA) was conducted in IBM SPSS Statistical Software to determine the most significant factors causing the explosion. Results from CAMEO showed that the explosion was a boiling liquid expanding vapour explosion (BLEVE). Outputs from Aspen simulation indicated that the reactor pressure rise increased with the increment of acetone ratio, heating temperature and reactant total volume. The reactor wall ruptured as the pressure exceeded the maximum allowable working pressure. IBM SPSS showed that the heating temperature was the most significant factor causing the pressure to build-up within the reactor, followed by the acetone-water ratio and total reactant volume. Among all three factors, the heating temperature added to largest pressure build-up, especially when the temperature was increased near to 360 °C. The time required to trigger explosion was predicted to be within 13.8–15 min of heating.

The personal awareness of explosion protection increases consequently with the terrorist threat throughout the world in recent years, so explosion protection becomes a worldwide problem. People pay more and more attentions to the explosion-proof of building. Glass window is the weakest component of a building. Therefore, it is very important to study the explosion-proof performance of glass windows for improving the building protection capability. The experiment is the most intuitive method to detect the explosion-proof performance of glass windows. The critical safety distance of the glass window under small explosion load was measured by experiment in this paper. However, due to the high risk and cost of explosion experiments, so the experiment data were rather rare. For comprehensive understanding the explosion-proof performance of laminated glass windows, the critical charge for double laminated toughened glass under explosion was simulated. According to the fitting curve of critical charge, the empirical formulas for calculating the critical charge for laminated glass windows with three panel sizes, three glass thicknesses and four interlayer thicknesses are obtained at different distances. The error analysis shows that the empirical formulas are accurate and available, which can provide some reference for the anti-explosion design of laminated tempered glass.

This paper is concerned with the development of a collocation method based on the Bessel polynomials for numerical solution of a general class of nonlinear singular boundary value problems (SBVPs). Due to the existence of singularity at the point x = 0 , we first modify the problem at the singular point. The proposed method is then developed for solving the resulting regular boundary value problem. To demonstrate the effectiveness and accuracy of the method, we apply it on several numerical examples. The numerical results obtained confirm that the present method has an advantage in terms of numerical accuracy over the uniform mesh cubic B-spline collocation (UCS) method (Roul and Goura in Appl Math Comput 341:428–450, 2019), non-standard finite difference (NSFD) method (Verma and Kayenat in J Math Chem 56:1667–1706, 2018), three-point finite difference methods (FDMs) (Pandey and Singh in Int J Comput Math 80:1323–1331, 2003; Pandey and Singh in J Comput Appl Math 205:469–478, 2007) and the cubic B-spline collocation (CBSC) method (Caglar et al. in Chaos Solitons Fractals 39:1232–1237, 2009) [ABSTRACT FROM AUTHOR]

Due to the high exothermic characteristic of NiAl during the reaction synthesis process from Ni–Al elemental powders, the NiAl intermetallic melts frequently, and the specimens are difficult to maintain their original shape, which leads to the inhomogeneity of the pore size and morphology. To tackle this problem, porous NiAl intermetallic monolith with controllable shape and pore structure was prepared through thermal explosion (TE) using NaCl as space holder. The TE behavior was recorded, and the effect of the volume fraction of NaCl on the phase composition, macroscopic feature, pore morphology and open porosity were investigated. The results showed that NiAl was the main phase in the products, and the specimen was free from cracking or deforming when NaCl content reached 30 vol%. The interconnected channel and pore windows were formed, and the open porosity was improved greatly to 63% by adding 50 vol% NaCl. The leachable space holder route provides a simple way to control the shape, pore structure and open porosity of the synthesized porous NiAl intermetallic. The use of NaCl as space holder reduced the combustion temperature of NiAl porous intermetallic compounds and kept the macroscopic shape intact. [ABSTRACT FROM AUTHOR]

This paper investigated the critical ignition conditions of combustible gas containing liquid fuel droplets. The analysis is done based on the criteria of the thermal explosion theory. It includes analytical and numerical solutions of modeling equations of fuel droplets heating and evaporation by convection and radiation from the surrounding reactive hot gas. The exothermic reaction is usually modeled as a single-step reaction obeying an Arrhenius temperature dependence. The thermal conductivity of the fuel droplet is dependent on temperature. The analytical solution produced relations between the main critical characteristic parameters in all planes of the solution. The results obtained from investigating the effect of the characteristic parameters on the explosion behavior of gas and fuel droplets and the thermal radiation proved that both of them are significant. The study proved that the criticality definitions of the thermal explosion of a single-phase system can be used effectively and efficiently to determine the critical conditions of a multi-phase system. Finally, the application of the numerical solutions of the modeling equations was used to analyze the explosion characteristics of a diesel fuel spray system. [ABSTRACT FROM AUTHOR]

According to the formulation of the nonlinear problem of stationary heat conduction in a homogeneous ellipsoid, when the intensity of volume energy release increases with temperature, a variational form of a mathematical model of a thermal explosion has been developed. This form contains a functional defined on a set of continuous and piecewise differentiable functions. These functions approximate the temperature distribution in the ellipsoid volume and accept a given temperature on its surface. The study of stationary points of the functional makes it possible to estimate a combination of defining parameters in which the temperature state in the ellipsoid precedes the thermal explosion. A quantitative analysis of the variational form of the model has been carried out with the exponential growth of the energy release intensity with temperature increase. The study introduces a relation for estimating an integral error arising when a specific approximating function is used. The comparison of such estimates for various approximating functions makes it possible to choose the function closest to the temperature distribution preceding the thermal explosion in the ellipsoid. [ABSTRACT FROM AUTHOR]

The goal of this work was to separate the reaction and spark plasma sintering (SPS) effects during the in-situ synthesis of TiC in mechanically milled Ti–C–3Cu powder mixtures. The powders were milled for 3–10 min in a high-energy planetary ball mill. Structural changes occurring in the reaction mixtures during thermal explosion (TE) in a furnace and SPS in a graphite die were compared. Although the maximum temperature of TE reached the melting point of copper in some samples, no evidence of extensive melting was observed in the microstructure of the products of TE. The ignition and maximum temperatures of TE were found to decrease with increasing milling time of the mixture. In the mixture milled for 10 min, the maximum temperature of TE was only 820 °C. Melting of copper at the inter-particle contacts during SPS was observed in samples milled for 5–10 min (SPS at 900–980 °C) and caused the formation of TiC-depleted regions in the microstructure. Those regions were the re-solidified melt partially filling the pores between the agglomerates. Based on the analysis of the TE parameters in the mixtures and microstructures of the products of TE and SPS, melting during SPS was attributed to the effect of electric current (a high electric current density at the inter-particle contacts) and not to the heat of reaction. The hardness, compressive strength and Young's modulus of the sintered composites are reported. A TiC–Cu composite (milling time 5 min, SPS at 980 °C, relative density 93%) shows a compressive yield strength of 890 MPa and an ultimate compressive strength of 920 MPa. [ABSTRACT FROM AUTHOR]

Gas evolution that resulted in the pressure elevation on LiNi1/3Mn1/3Co1/3O2 (NMC111) battery in case of a runaway reaction was discussed with the thermally explosive behaviors. The NMC111 cell and 2 series-connected (2S) NMC111 module both with 100% SoCs (state of charges) were examined the pressure rise rates in an open-circuit voltage (OCV) state using VSP2 adiabatic calorimetry. The charged NMC111 module underwent an extremely runaway reaction at elevated temperatures and caused a thermal explosion due to high potential energy inside the battery and interaction with the cell components. The surface temperature of the cell during the charge-discharge cycle was measured to compare with the difference in heat accumulation at 0.75, 1, 2 C-rates. Furthermore, the blasting pressure that propagated a thermal explosion for both single cell and 2S module were evaluated. The significant explosion potential increased with the electric potential. Moreover, the considerable quantities of gases eruption from the full-charged batteries can result in battery rupture and flames from a confined battery housing. [ABSTRACT FROM AUTHOR]

Silicon oxynitride nanopowders were successfully prepared by thermal explosion of the Si and SiO 2 mixed powders with the different particle sizes in various molar ratio (x / y = 2.0, 1.5) under N 2 , supplemented by the subsequent gravity separation strategy. The effects of Si/SiO 2 molar ratio, preheating temperature and insulation time on the phase composition of the as-oxynitrided products in the thermal explosion strategy were investigated. Meanwhile, the effects of sedimentation time on the phase composition and oxygen content of the as-obtained products in the gravity separation strategy were also discussed. It is shown that the by-products are absent in the as-oxynitrided products with a 1.5:1 M ratio. Prolonging the insulation time or preheating temperature is beneficial to improve the content of Si 2 N 2 O phase with a 2.0:1 M ratio. All the by-product phases are disappeared in the as-oxynitrided products with a 2.0:1 M ratio after sedimentation treatment of 120 s. The as-obtained silicon oxynitride nanopowders with 58% of recovery and 16.2% of oxygen content are close to the theoretical stoichiometric ratio of Si 2 N 2 O. The preparation mechanism of silicon oxynitride nanopowders was proposed. [ABSTRACT FROM AUTHOR]

Warmup of mechanically activated Ti–xC powder mixtures (x = 1.0, 2.1, 4.2, and 6.3 wt %) in a furnace preheated to 800°C was found to result in thermal explosion (volume reaction) in mixtures with x = 4.2 and 6.3 wt %. Activated powder mixtures and combustion products were characterized by XRD, optical metallography, and SEM/EDX. Combustion products represented metal-matrix Ti–TiC composites containing different amounts of strengthening agent. Our results may turn interesting to those engaged in deposition (cladding) of protective Ti–TiC coatings using reactive Ti–C mechanocomposites as a starting material. [ABSTRACT FROM AUTHOR]

In this paper, we develop a numerical scheme to approximate the solution of a general class of nonlinear singular boundary value problems (SBVPs) subject to Neumann and Robin boundary conditions. The original differential equation has a singularity at the point x=0, which is removed via L'Hospital's law with an assumption about the derivative of the solution at the point x=0. An exponential B‐spline collocation approach is then constructed to solve the resulting boundary value problem. Convergence analysis of the method is discussed. Numerical examples are provided to illustrate the applicability and efficiency of the method. Our results are compared with those obtained by other three numerical methods such as uniform mesh cubic B‐spline collocation (UCS) method, nonstandard finite difference method, and finite difference method based on Chawla's identity. [ABSTRACT FROM AUTHOR]

In this paper is presented a simple possible model which can explain the thermal explosion problem, the existence of an induction period and a sudden rapid temperature rise. As state variables used for modeling are: the pressure, the temperature and the concentration. The time evolutions of these state parameters are analogically modeled using ordinary differential equations. The numerical simulations of the obtained model are made in Matlab/SimulinkTM. The validation of the model is realized by comparison between experimental data and simulation results, presenting a good accuracy. [ABSTRACT FROM AUTHOR]