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Zirconium (Zr) alloy fuel cladding is exposed to harsh environments such as high temperature and high pressure for a long time. Surface modification technology can effectively improve its high-temperature oxidation resistance. In this work, pulse laser nitriding technology was used to perform laser nitriding treatment on Zr alloys at different laser energies. The effect of different energy levels of laser nitriding treatments on the superheated steam corrosion resistance of Zr alloys was studied. First-principles was used to reveal the mechanism of how the diffusion layer improves the performance of Zr alloys in resisting superheated steam corrosion after nitriding treatment. Results indicate that the surface of Zr alloys treated with laser nitriding exhibits a molten feature. When the laser energy is 100 mJ, N mainly exists in the form of a diffusion layer in the Zr alloy substrate. As the laser energy rises to 200 mJ and above, the ZrN phase is generated. After 1000 h of superheated steam corrosion, the corrosion weight gain of the 100 mJ sample was reduced by approximately 50 % compared to the Zr alloy. The corrosion weight gain of the 400 mJ sample increased by approximately 12 %. The presence of the ZrN phase accelerates the oxidation degradation rate of Zr alloy. When N atoms exist as a diffusion layer, the transition from tetragonal zirconia to monoclinic zirconia can be suppressed. First-principles calculations showed that when O and N atoms coexist in the Zr alloy substrate, their binding performance with surface O is significantly decreases, thus further improving the 100 mJ sample's resistance to superheated steam corrosion. [ABSTRACT FROM AUTHOR]

Maximum distance separable (MDS) matrices play a crucial role not only in coding theory but also in the design of block ciphers and hash functions. Of particular interest are involutory MDS matrices, which facilitate the use of a single circuit for both encryption and decryption in hardware implementations. In this article, we present several characterizations of involutory MDS matrices of even order. Additionally, we introduce a new matrix form for obtaining all involutory MDS matrices of even order and compare it with other matrix forms available in the literature. We then propose a technique to systematically construct all 4 × 4 involutory MDS matrices over a finite field F 2 m . This method significantly reduces the search space by focusing on involutory MDS class representative matrices, leading to the generation of all such matrices within a substantially smaller set compared to considering all 4 × 4 involutory matrices. Specifically, our approach involves searching for these representative matrices within a set of cardinality (2 m - 1) 5 . Through this method, we provide an explicit enumeration of the total number of 4 × 4 involutory MDS matrices over F 2 m for m = 3 , 4 , ... , 8 . [ABSTRACT FROM AUTHOR]

Diffusion layer dispersed electrodes were presented for application in electrochemical immunoassays. The diffusion layer refers to the region on the electrode surface where concentration gradients occur during the redox reactions of the target analytes. To control the diffusion layer, electrodes of the same area and size were fabricated, and the shape of the diffusion layer was controlled by adjusting each electrode distance. To estimate the properties of the electrodes, cyclic voltammetry (CV) analysis was performed using ferricyanide ([Fe(CN)6–3]) and 3,3′5,5′-tetramethylbenzidine (TMB) as a model redox couple. Changes in the diffusion layer shape according to electrode distance were compared through simulation. The redox currents for the target analytes increased as electrode distance increased. These results indicate that even if the electrode shape and area are the same, dispersing the diffusion layer by adjusting the distance between the electrodes can affect the microelectrode characteristics. Finally, the diffusion layer dispersed electrode was applied for the medical diagnosis of the human hepatitis B virus (hHBV) antigen, and the human hepatitis C virus (hHCV) antibody was compared with conventional assay methods, such as TMB-based chromogenic detection. [ABSTRACT FROM AUTHOR]

Block circulant MDS matrices are used in the design of linear diffusion layers for lightweight cryptographic applications. Most of the work on construction of block circulant MDS matrices focused either on finite fields or $ GL(m, \mathbb{F}_2) $. The main objective of this paper is to extend the above study of block circulant MDS matrices to finite commutative rings. Additionally, we examine the behavior of the XOR count distribution under different reducible polynomials of equal degree over $ \mathbb{F}_2 $. We show that the determinant of a block circulant matrix over a ring can be expressed in a simple form. We construct $ 4 \times 4 $ and $ 8 \times 8 $ block circulant matrices over a ring. Furthermore, for non-negative integer $ l $, we identify the conditions under which a ring $ \mathfrak{R}_l = \frac{\mathbb{F}_2[x]}{\langle (f(x))^{2^l} \rangle} $, contains a finite field of order $ 2^m $, where $ f(x) $ is an irreducible polynomial of degree $ m $. To facilitate efficient implementation, we analyze XOR distributions within specific rings, such as $ R_1 = \frac{\mathbb{F}_2[x]}{\langle (1+x^2+x^6) \rangle} $ and $ R_2 = \frac{\mathbb{F}_2[x]}{\langle (1+x^4+x^6) \rangle} $. Our calculations reveal distinct XOR distributions when utilizing two reducible polynomials of equal degree, with XOR count distributions 776 and 764, respectively. However, when using irreducible polynomials of the same degree, the XOR count distributions remain the same. This difference is advantageous for applications in lightweight cryptography.

The use of MgB2 superconducting material in liquid hydrogen level sensors has problems with significant differences in critical transition temperature and liquid hydrogen liquefaction temperature and interface reactions between the original powder and metal sheath. These problems make it difficult to measure and control the liquid hydrogen level sensors. We studied the Al doping modification technology to reduce the critical transition temperature of MgB2. And we studied the effects of the interface reaction between the original powder and the metal sheath Fe, Monel and annealing temperature on its superconducting transition width. The results show that when the doping amount x=0.15, the critical transition temperature of Mg1-x Alx B2 polycrystalline sample is about 30 K, which meets the requirements for the use of liquid hydrogen level sensors. There is a diffusion interface between the metal sheath Fe, Monel and the precursor powder Mg, Al. The diffusion layer thickness of the Fe metal sheath sample is relatively small, approximately 25 µm. So, the Fe metal sheath is more suitable for preparing sheath materials for Al doped MgB2 superconducting wires. Fe and Monel modified MgB2 samples with metal sheaths at different annealing temperatures still exhibit significant superconducting transitions. and the superconducting transition temperature meets the operating environment of liquid hydrogen level sensors. [ABSTRACT FROM AUTHOR]

The article presents the results of a study on the generation of electricity using porous Ca6H2O19Si6 structures as an example during moisture adsorption. It has been determined that the potential difference at the contacts of a single‐layer structure of compacted Ca6H2O19Si6 particles depends on the time of formation of the potential‐determining and diffusion layers and processes that destroy the diffusion layer or prevent its formation can increase the efficiency of moisture electric generator. The concept for creating the moisture electric generators based on multilayer structures, which may allow the use of such structures as moisture electric generators for continuous operation under constant external conditions, has been proposed. [ABSTRACT FROM AUTHOR]

The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. However, in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch numbers offer a better balance between security and efficiency as a diffusion layer, compared to MDS matrices. In this paper, we study NMDS matrices, exploring their construction in both recursive and nonrecursive settings. We provide several theoretical results and explore the hardware efficiency of the construction of NMDS matrices. Additionally, we make comparisons between the results of NMDS and MDS matrices whenever possible. For the recursive approach, we study the DLS matrices and provide some theoretical results on their use. Some of the results are used to restrict the search space of the DLS matrices. We also show that over a field of characteristic 2, any sparse matrix of order n ≥ 4 with fixed XOR value of 1 cannot be an NMDS when raised to a power of k ≤ n . Following that, we use the generalized DLS (GDLS) matrices to provide some lightweight recursive NMDS matrices of several orders that perform better than the existing matrices in terms of hardware cost or the number of iterations. For the nonrecursive construction of NMDS matrices, we study various structures, such as circulant and left-circulant matrices, and their generalizations: Toeplitz and Hankel matrices. In addition, we prove that Toeplitz matrices of order n > 4 cannot be simultaneously NMDS and involutory over a field of characteristic 2. Finally, we use GDLS matrices to provide some lightweight NMDS matrices that can be computed in one clock cycle. The proposed nonrecursive NMDS matrices of orders 4, 5, 6, 7, and 8 can be implemented with 24, 50, 65, 96, and 108 XORs over F 2 4 , respectively. [ABSTRACT FROM AUTHOR]

Based on the fractal geometry science and the model of flow friction resistance when fluid flows through rough microcapillaries, the formula of diffusion layer thickness and the spatial charge density distribution of the pipe were derived. The relationship between the amount of space charge and the structural parameters of rough elements, relative roughness, liquid conductivity, pipeline diameter, and other physical quantities was discussed. It was found that the height of rough elements is directly proportional to the thickness of the diffusion layer, and also positively proportional to the amount of current. The predicted results of the model are in good agreement with existing models and various published experimental data, verifying the accuracy and reliability of the model. [ABSTRACT FROM AUTHOR]

The structure and properties of the surface and of the core of steel 08Kh18N10T-Sh subjected to radial forging and subsequent saturation by the method of ion-plasma nitriding are studied. It is shown that the complex deformation–ion-plasma treatment accelerates the nitriding process and provides a high level of strength of the surface and of the core of steel 08Kh18N10T-Sh. The lower the saturation temperature, the shorter the hold time and the higher the degree of the deformation of the steel, the more deformed α-phase capable to accelerate the saturation process is preserved in the structure. [ABSTRACT FROM AUTHOR]

The effects of five key processing parameters on the real and electroactive surface areas of porous nickel samples produced by the Lost Carbonate Sintering (LCS) process have been investigated systematically. The specific real and electroactive surface areas of the LCS porous Ni samples are 500–1600 cm−1 and 80–115 cm−1. Pore size, compacting pressure and sintering temperature have no significant effect on the surface areas. Porosity has no effect on the gravimetric real surface area, but a higher porosity leads to a lower volumetric real surface area and a higher electroactive surface area. Metal particle size has a huge effect on the surface areas of the LCS porous metal. An intermediate amount of fine Ni powder results in the highest real surface area, approximately 70% higher than the samples produced with coarse Ni powder. Samples produced with fine Ni powder can increase the electroactive surface area by up to 100%. [ABSTRACT FROM AUTHOR]

Using the AlCoCrFeNi high entropy alloy to enhance 2124 aluminum alloy composites is an effective way to solve its application limitations in friction and wear. In this study, the composites were prepared by mechanical alloying and spark plasma sintering. The results show that the diffusion layer was formed at the interface between high entropy particles and the matrix, and there were dislocations and significant lattice distortions near the interface. In addition, the friction coefficient (0.399) and wear rate (7.05∗10−4 mm3 N−1 m−1) of the composites were lower than the 2124 aluminum alloys. Moreover, the yield strength, tensile strength and compressive strength of composites were 396.2 MPa, 498.3 MPa, and 560.5 MPa, respectively. And the yield strength of the composite was almost 2 times more than that of AA2124. This work discussed the effect of interface on mechanical properties and explain the formation of diffusion layer. The present study provides a strategy to solve the lack of wear resistance and strength of composites.

Applying the maximum separable distance (MDS) matrices is one of the most common approaches to meet diffusion layer in modern block ciphers. Using Cauchy and extensions of Cauchy matrices are classical methods to generate MDS matrices. In this paper, using generalized Cauchy matrices, an approach to construct MDS matrices is proposed so that if A is an MDS matrix constructed with the proposed approach and B is a 3 × 3 sub-matrix of A , then interesting connections between the entries of B are introduced. More precisely, every element of the matrix B can be uniquely determined by eight other entries of B . Moreover, using generalized Cauchy matrices and also applying the proposed approach, some common forms of MDS matrices such as Hadamard, circulant and MDS matrices with maximum entries equal to the unit element, have been investigated. [ABSTRACT FROM AUTHOR]

The study of the microstructure and microhardness of borosiliconized diffusion layers on the 30KhGSA steel is presented. Diffusion coatings on cylindrical specimens of the 30KhGSA steel are obtained using simultaneous diffusion saturation with boron, chromium, titanium, and silicon. Metallographic analysis is carried out with the aid of a Carl Zeiss Axio Observer Z1m metallographic microscope and a ThixoMet PRO software. When silicon carbide SiC is introduced into the saturating mixture for borating at a concentration of 10 wt %, a diffusion layer (a solid solution of silicon in α-iron) is formed on the surface of the 30KhGSA steel, which is confirmed by the value of microhardness at a level of 180–186 HV0.1. During hardening of the diffusion-hardened 30KhGSA steel, the hardness of diffusion coatings also increases: the hardness of the borated layer increases by 25% due to hardening compared to the non-hardened layer, while the hardness of the borosiliconized layer increases by a factor of 2.7. At the same time, the borosiliconized layer, having a lower hardness, is more capable of running in under conditions for sliding friction and in the presence of aggressive salt solutions, in which the thrust bearings of drilling rigs operate. [ABSTRACT FROM AUTHOR]

This article presents a new hybrid method (combining search based methods and direct construction methods) to generate all 4×4 involutory maximum distance separable (MDS) matrices over F2m. The proposed method reduces the search space complexity at the level of ffiffiffinp, where n represents the number of all 4×4 invertible matrices over F2m to be searched for. Hence, this enables us to generate all 4×4 involutory MDS matrices over F23 and F24. After applying global optimization technique that supports higher Exclusive-OR (XOR) gates (e.g., XOR3, XOR4) to the generated matrices, to the best of our knowledge, we generate the lightest involutory/non-involutory MDS matrices known over F23, F24 and F28 in terms of XOR count. In this context, we present new 4×4 involutory MDS matrices over F23, F24 and F28, which can be implemented by 13 XOR operations with depth 5, 25 XOR operations with depth 5 and 42 XOR operations with depth 4, respectively. Finally, we denote a new property of Hadamard matrix, i.e., (involutory and MDS) Hadamard matrix form is, in fact, a representative matrix form that can be used to generate a small subset of all 2k×2k involutory MDS matrices, where k > 1. For k = 1, Hadamard matrix form can be used to generate all involutory MDS matrices. [ABSTRACT FROM AUTHOR]

Research data for diffusion layers obtained on ARMCO Pure Iron samples in boron- and copper-containing powder mixtures are reported. The aim of this study aim has been to reveal the influence of copper content in a saturating mixture on the structure and thickness of the diffusion layer. In experiments, from 120- to 220-µm-thick diffusion layers with different structures have been obtained on ARMCO Pure Iron samples. It has been found that the thickness of the diffusion layer grows and its structure changes with increasing copper content in the saturating mixture. [ABSTRACT FROM AUTHOR]

This article presents a new hybrid method (combining search based methods and direct construction methods) to generate all $4 \times 4$4×4 involutory maximum distance separable (MDS) matrices over $\mathbf{F}_{2^m}$F2m . The proposed method reduces the search space complexity at the level of $$\sqrt n $$ n, where n represents the number of all $4 \times 4$4×4 invertible matrices over $\mathbf{F}_{2^m}$F2m to be searched for. Hence, this enables us to generate all $4 \times 4$4×4 involutory MDS matrices over $\mathbf{F}_{2^3}$F23 and $\mathbf{F}_{2^4}$F24 . After applying global optimization technique that supports higher Exclusive-OR (XOR) gates (e.g., XOR3, XOR4) to the generated matrices, to the best of our knowledge, we generate the lightest involutory/non-involutory MDS matrices known over $\mathbf{F}_{2^3}$F23 , $\mathbf{F}_{2^4}$F24 and $\mathbf{F}_{2^8}$F28 in terms of XOR count. In this context, we present new $4 \times 4$4×4 involutory MDS matrices over $\mathbf{F}_{2^3}$F23 , $\mathbf{F}_{2^4}$F24 and $\mathbf{F}_{2^8}$F28 , which can be implemented by 13 XOR operations with depth 5, 25 XOR operations with depth 5 and 42 XOR operations with depth 4, respectively. Finally, we denote a new property of Hadamard matrix, i.e., (involutory and MDS) Hadamard matrix form is, in fact, a representative matrix form that can be used to generate a small subset of all $2^k\times 2^k$2k×2k involutory MDS matrices, where k > 1. For k = 1, Hadamard matrix form can be used to generate all involutory MDS matrices.

We demonstrate the conceptual feasibility of step-by-step calculation of the effective separation factor β in distillation and sublimation processes as a function of the evaporation temperature T and degree of distillation g. The variation of β with T and g is thought to stem from the influence of T and g on the impurity distribution over the vaporizing material. The β(T) and β(g) dependences can be found using the Burton–Prim–Slichter equation and calculated impurity distributions in the vaporizing material at particular parameters of the substance and material. We present examples of such calculations for a beryllium-based model material. [ABSTRACT FROM AUTHOR]

Due to its excellent diffusion avalanche performance, MDS linear transformation based on rotational-XOR shift operation is frequently employed in the construction of block cipher diffusion layer. In existing studies, the search for the best linear transformation on the small finite field (F2n)~4 is almost complete, however when the number of XOR terms is between 9 and 11, there is no best linear transformation on the huge finite field (F2n)~8. For the actual use of the 64-bit environment, it is crucial to investigate the most recent optimum linear transformation of the huge finite field (F2~8)~8. This work chooses a huge finite field (F2n)~8 as its research object based on the findings of earlier studies. The branch number test problem is converted into a Boolean Satisfiability problem (SAT) by examining the structural properties of the rotational-XOR diffusion layer. The issue is solved using the Satisfiability Modulo Theories (SMT) solver Boolector, and the final linear transformation group of the huge finite field (F2n)~8 is investigated. The experimental findings demonstrate the existence of a suboptimal linear transformation in the huge finite field (F2~8)~8 with up to 8 branches. Along with the test, a particular rotational-XOR form is provided, and a different approach is suggested for determining the true requirement for the ideal diffusion layer. Future research will focus on the theoretical properties and broadened applications of the suboptimal linear transformation of the huge finite field (F2n)~8. [ABSTRACT FROM AUTHOR]

Context: At the interface of W-Cu after direct jointing, diffusion layers with a thickness of approximately 22 nm are present but often overlooked in simulations of mechanical properties. In this study, an interface model with a W-Cu diffusion layer is developed using molecular dynamics (MD). The effects of the diffusion layers on the elastic–plastic behaviors, dissipation mechanisms, and fracture properties of the interface are analyzed under mode-I (perpendicular to the interface) and mode-II (parallel to the interface). The results demonstrate that the interface model with a diffusion layer exhibits superior mechanical properties under mode-I and mode-II loading compared to the model without a diffusion layer. Furthermore, a multi-scale method based on the classical Paris law is proposed, combining MD and finite element methods to investigate the fatigue crack propagation of W-Cu bimetallic composites under cyclic loading and predict their fatigue life. The findings of this study are meaningful for improving the mechanical properties of W-Cu interface materials, predicting the material's lifespan, and guiding related engineering applications. Methods: In this study, the molecular dynamics simulations have been carried out by using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The visualization of results is performed using the Open Visualization Tool (OVITO). Common neighbor analysis (CNA) and dislocation analysis (DXA) in OVITO have been employed to capture the structural evolution. Finite element method simulations are performed in Ansys Workbench. [ABSTRACT FROM AUTHOR]

The microstructure and microhardness of multicomponent diffusion boride coatings formed on the surface of prehardened 30KhGSA steel have been studied. Diffusion coatings on prehardened 30KhGSA steel have been obtained by simultaneous diffusion saturation with boron, chromium, titanium, and silicon. Metallographic analysis has been carried out on a Carl Zeiss Axio Observer Z1m metallographic microscope in the ThixoMet PRO software package. The efficiency of the multicomponent boriding process combined with the hardening has been demonstrated. The prehardening of 30KhGSA steel makes it possible to obtain higher microhardness indices as compared with the case of complex boron‒chromium‒titanosiliciding without prehardening. Under thermal treatment, the surface microhardness of the diffusion coating decreases from 1980 to 1160 HV0.1. This is accompanied by an increase in the diffusion-coating thickness by a factor of 3. [ABSTRACT FROM AUTHOR]

The possibility of producing blanks by combining the casting of iron elements and the plastic working of steel elements was tested. Manufacturing composite blanks by casting ensures sufficiently strong diffusion-bonded joint. The thermal conditions for the formation and microstructure of the transition diffusion zone were studied. It is proposed to use cast iron rather than steel to manufacture chaplets. The use of cast-iron chaplets allows maintaining the homogeneous structure of cast iron, which is important in manufacturing critical parts. [ABSTRACT FROM AUTHOR]

The possibility of acceleration of processes of thermal diffusion chromizing of steels by introducing additions (electron and oxygen anion emitters) into the saturating mixture is considered. A microscopic x-ray spectrum analysis of specimens chromized in powder mixtures with and without emitters is performed. The composition and the thickness of the diffusion layer are determined. It is shown experimentally that electric current emerges in the filler at the saturation temperature. The influence of the intrinsic thermionic field on the diffusion processes is explained. [ABSTRACT FROM AUTHOR]

Ultrasonic electroplating produces various effects, including refinement of the plating film structure, by generating localized agitation through cavitation bubbles. However, details of the agitation mechanism have not been clarified because ultrasonic cavitation is very small in scale and occurs rapidly, and its reproducibility is low. Therefore, using laser-induced cavitation, which can generate cavitation similar to ultrasonic waves with high reproducibility, the author attempted to elucidate the conditions and frequency of cavitation generation that affect the agitation phenomenon in ultrasonic electroplating. By controlling the laser irradiation position, three different cavitation conditions were established, and the microstructures of the plated films produced were compared. Microstructural refinement was the most advanced under the condition of microjet generation. The frequency of cavitation generation at any position in the ultrasonic electroplating was estimated to be

New variant of Background Oriented Schlieren (BOS) technique is proposed for the measurements of strongly refracting objects. The employed pattern presents a rectangular grid of color dots. Special color encoding makes every dot unique provided its nearest neighbors can be identified. This allows robust matching of the dot images for schlieren objects with arbitrary large apparent displacements. Also, possible formation of multiple images of the same dot due to strongly nonlinear variations of the refractive index can be used to improve the accuracy of the refractive index field measurement. Multi-frame approach is employed to improve the spatial resolution. Potential of the proposed technique is demonstrated by measurements of the diffusion layers in aqueous solutions of sodium chloride and ethanol.

(1) Background: Boriding is one of the most common methods of thermal-chemical treatment due to its excellent hardness and wear resistance of the produced diffusion layers. However, it has limited application compared to carburizing and nitriding because of fragility and chipping. Introducing another alloying element into the boron media helps avoid those drawbacks and improve other surface properties of the layer. The purpose of this work is to improve the surface mechanical properties of L6 and 5140 low alloy steels by two-component surface hardening with boron and copper. (2) Methods: The treatment was performed by means of a powder-pack method using boron, copper, and aluminum powders in the following proportions: 60% B4C + 20% Al2O3 + 16% CuO + 4% NaF. The time–temperature parameters of the treatment were four hours exposure at 950 °C. Microstructure, elemental, and phase composition were investigated as well as microhardness and wear resistance of the obtained layers. (3) Results: Layers of up to 180–200 μm thick are formed on both steels as a result of treatment. Needle-like structures similar to pure boriding was obtained. The maximum microhardness was 2000 HV on L6 steel and 1800 HV on 5140 steel. These values correspond to iron borides and were confirmed by XRD analysis revealing FeB, Fe2B, and Cr5B3. The wear resistance of both steels was about ten times higher after the treatment compared to non-treated samples. (4) Conclusions: Surface hardening with boron and copper significantly improves the mechanical properties of both alloy steels. The results obtained are beneficial for different tribo-pair systems or three-body wear with abrasion and minimum impact loads. [ABSTRACT FROM AUTHOR]

Diffusion layers are crucial components for lightweight cryptographic schemes. Optimal binary matrices are widely used diffusion layers that can be easier to achieve the best security/performance trade-off. However, most of the constructions of binary matrices are concentrated in smaller dimensions. Besides, to maximize the number of branches, the performance is often neglected. In this paper, we investigate the diffusion of the Lai-Massey (L-M) structures and propose a series of binary diffusion layers with the best possible branch number and efficient software/hardware implementations as well for feasible parameters (up to 64). Firstly, we prove the lower bound of the circuit depth of a binary matrix with a fixed branch number. Then, we construct binary matrices by L-M structure with cyclic shift as round functions because of taking account of the improvement of software performance and demonstrate that this construction can not get the diffusion layers with branch number >4. Then, we get some 4 |$\times $| 4 and 6 |$\times $| 6 optimal binary matrices with branch number 4 by one-round L-M structure. Note that the depth of these results is optimal, i. e. they achieve the lowest hardware costs without loss of software efficiency. Secondly, we construct diffusion layers by extended L-M structures to obtain binary matrices with large sizes. We give a list of software/hardware friendly optimal binary matrices with large dimensions, especially for dimensions 48 and 64. In particular, some of the solutions are Maximum Distance Binary Linear matrices. Finally, we also present diffusion layers constructed by the extended generalized L-M structure to improve their applicabilities on other platforms. [ABSTRACT FROM AUTHOR]

In terms of security, MDS matrices are one of the best choices for the diffusion layer of block ciphers. However, as these matrices grow in size, their software implementation becomes a challenge. In this paper, to benefit from the properties of MDS matrices and avoid the mentioned challenge, we use 4 × 4 MDS matrices to build some 16 × 16 matrices with a low number of zero elements. We show that if these matrices are used as diffusion layers of software-based SPN structures, the resulting block ciphers have similar properties as AES in software implementation complexity (i.e. the number of required CPU instructions) and resistance against linear and differential attacks. Moreover, the best impossible differential and square distinguishers for the proposed 16 × 16 structures have a similar length as SPN structures with 16 × 16 MDS matrices. Thus, the new structures outperform AES concerning the impossible differential and square attacks. Additionally, we show that if the proposed SPN structure uses the AES key schedule, its results for the differential related-key attacks are better than those for AES. We also extend the idea and use 4×4 MDS matrices to design 24×24 and 32×32 matrices with acceptable properties for SPN structure design. Finally, we extend the idea to propose some matrices for Feistel structures with SP-type F-functions. We show that the resulting structures are more secure than the improved Type-II GFS. [ABSTRACT FROM AUTHOR]

In 2016, Chang et al. proposed a Format Preserving Encryption (FPE) scheme over a finite field and used an MDS matrix in the diffusion layer of the scheme for optimal diffusion. Later that year, Gupta et al. defined an algebraic structure named Format Preserving Set (FPS) is the diffusion layer of an FPE scheme. In 2018, Barua et al. showed that it is not possible to construct an FPS over a finite field in the diffusion layer of an FPE scheme if the cardinality of the set is not a power of prime. They extended the search of FPS over a finite commutative ring $\mathcal {R}$ and showed that if an FPS $S \subseteq \mathcal {R}$ is closed under addition then it gets module structure over some subring of $\mathcal {R}$. Moreover, in this case, the only possible cardinalities of FPS are some power of the cardinalities of subrings when the module is free. The purpose of this article is twofold. Firstly, we show that it is possible to construct format preserving sets over a finite commutative ring which are not closed under addition. Secondly, we search for format preserving sets and MDS matrices over torsion modules. We provide examples of format preserving sets of cardinalities 26 and 52 over torsion modules and rings. These cardinalities are interesting because they correspond to the set of English alphabets, without and with capitalization. By considering a finite Abelian group as a torsion module over a PID, we show that a matrix $M$ with entries from the PID is MDS if and only if $M$ is MDS under the projection map on the same Abelian group. [ABSTRACT FROM AUTHOR]

Explosive welding is a solid state welding process that is used for the metallurgical joining of two or more dissimilar metals. This paper presented a systematic study of microstructure and properties of copper/304 stainless steel fabricated by explosive welding. The microstructure and chemical composition were evaluated using Scanning Electron Microscope (SEM) and Transmission Electron Microscope (TEM). The properties were performed by the nanoindentation tests and bending experiments of the microcantilevers, and the microcantilevers were milled out using the Focused Ion Beam (FIB) system. The results showed that the interface between this couple metals presents a typical wavy structure. There are some vortex regions in front of the crest, which are strong intermixing of this couple metals. The diffusion layer and melting layer are two typical layers at the interface. The diffusion layers are formed by strongly collision points, while the melting layers only appear on the stainless steel side. The average nanohardnesses of diffusion layer and melting layer are between that of copper and 304 stainless steel. The nanohardness of this couple metals exhibits increasing trend from 0° to 60°, while decreasing trend from 60° to 90°. The nanohardness in Area 4 of the vortex region is highest, where is the highest temperature. The average flexural strength of micro-cantilevers shows the same change rules with the nanohardness.

The effect of the temperature of the ion‑plasma nitriding process on the enduring quality of the resulting hardened layers on titanium VT1‑0 and titanium alloys VT6 and OT4‑1 and the effect of ion‑plasma nitriding on the change in the Ra parameter of the surface roughness of titanium samples is investigated. It is defined that ion‑plasma nitriding leads to a significant increase in the enduring quality of the titanium alloys under study. The depth of the enduring quality groove in untreated samples of titanium VT1‑0, alloys VT6, OT4‑1 was 11, 7 and 10 microns, respectively, whereas in samples after ion‑plasma nitriding, the wear groove had a depth of 1.9, 0.9, 2.1 microns. It was revealed that when the initial roughness of the processed samples is more than Ra 0.1 microns after ion nitriding, the roughness index Ra, one of the key components of surface quality, decreases.

The Ti-6Al-7 Nb alloy and its carbide possess a wide range of engineering applications, therefore, it is utmost required to fabricate high-quality carburized layers on the alloy surface. In this study, the carburization of Ti-6Al-7 Nb alloy was conducted using molten salts (including Carbon Nano Tubes, LiCl, KCl, and KF) in a planetary ball mill, followed by placement in an alumina tube furnace under a nitrogen atmosphere at 1050 °C for various durations. Several characterization techniques were employed to analyze the results, including X-ray diffraction (XRD), field emission electron microscopy (FE-SEM), X-ray photoelectron spectroscopy (XPS), and atomic force microscopy (AFM). The XRD results reveal that as the carburization duration increased, the alloy achieved complete carburization, forming a 120 µm thick layer of TiC 0.3 N 0.7. After 24 h of carburization, the crystallite size of TiC 0.3 N 0.7 increased, and the micro-strain decreased, indicating improved structural quality. The morphology of the carburized layer at shorter durations exhibits micro-cracks and defects due to incomplete carburization, where carbon (C) and nitrogen (N) could not effectively occupy in the grain boundaries of alloy. After 24 h, an agglomerated, cauliflower-like layer of TiC 0.3 N 0.7 formed, enhancing the alloy's engineering properties. XPS confirmed the presence of carbon and nitrogen in the carburized sample, which contributed to the formation of the TiC 0.3 N 0.7 layer on the alloy surface. AFM analysis supported the SEM findings, revealing broad islands with microgrooves on the carburized layer. These features indicate a thick and well-formed carburized layer, confirming the successful carburization of Ti-6Al-7 Nb. Overall, the study demonstrates that a 24-h carburization process at 1050 °C in molten salts under a nitrogen atmosphere effectively produces a high-quality, thick, and adherent TiC 0.3 N 0.7 layer on Ti-6Al-7 Nb alloy, significantly enhancing its engineering properties. [Display omitted] • Carburization of Ti-6Al-7 Nb was successfully achieved after 24 h at 1050 °C. • Low duration of carburization leads to form cracks in the carburized layer. • C and N diffuse into grain boundary during carburization and form TiC 0.3 N 0.7 layer. • TiC 0.3 N 0.7 form a homogenous carburized layer after 12 and 24 h of carburization. [ABSTRACT FROM AUTHOR]