Mechanical Properties Of Materials Research Articles

A nonlocal photoacoustic effect with variable thermal conductivity of semiconductor material subjected to laser heat source

This study explores the behavior of laser-exposed photo-excited carriers, investigating the propagation of photoacoustic waves in the thermoelastic domain. It also delves into the theoretical generation of surface acoustic waves in semiconductors through photo-thermoelastic processes. The research considers the interaction between thermomechanical and acoustic waves in a nonlocal medium with temperature-dependent thermal conductivity. Unlike relying on electron–phonon or electron-hole thermalization processes, photoacoustic waves here result from thermoelastic stress induced by the laser-induced temperature increase. The investigation accounts for the optical, mechanical, and thermoelastic properties of nanoscale semiconductor materials. Predictions of photoacoustic signals are derived by solving a combined thermal diffusion issue and a thermoelastic problem, using Laplace and Fourier transforms in the mathematical model. Numerical solutions encompass various physical fields within the time domain using the inversion technique of Laplace and Fourier transforms, such as thermal, acoustic, mechanical, and carrier density diffusion. The study evaluates and compares the influences of thermal memory and thermal conductivity presenting visual representations.

Investigating the grinding characteristics of vanadium-titanium iron ore tailings for sustainable utilization in cementitious material preparation

The study of the cementitious material activity of industrial solid wastes is a key issue in the comprehensive utilization of its green building materials. In this study, mechanical activation was used to prepare cementitious materials from vanadium-titanium iron ore tailings (VTIOT) as the main raw materials, and the effects of grinding time, the key parameter, on the grinding characteristics of VTIOT, the mechanical properties of the VTIOT cementitious material, and the hydration mechanism were investigated by means of surface area analysis, particle size analysis, X-ray diffraction (XRD), scanning electron microscopy (SEM), alkali leaching, mechanical testing, hydration heat analysis, and thermogravimetric analysis (TGA). The results show that: the grinding time and specific surface area of VTIOT exhibit a linear correlation. Prolonging the grinding time, the fractal dimension of the particles gradually increases. The activity of Si4+ and Al3+ elements increases rapidly, reaching a Si4+ and Al3+ content of 96 mg·L−1 at 90 min of grinding. With a VTIOT mixing amount of 30 %, a mortar paste ratio of 1:3, and a water cement ratio of 0.5, the 50 min ground VTIOT mortar demonstrates 7 d and 28 d compressive strengths of 29 MPa and 38.7 MPa, corresponding to the highest values of the activity index, measured at 71.4 % and 75.2 %, respectively. Under standard curing conditions, the hydration products of cementitious materials at 7 d are ettringite (AFt), calcium silicate hydrate (C-S-H), alumina, ferric oxide, monsulfate (AFm), calcium hydroxide (Ca(OH)2), and calcium silica (CS). In the hydration process of 7 d, the exothermic peak and exothermic amount of the 50 min VTIOT cementitious materials are greater than those observed for other grinding times, but lower than those of pure reference cement.

In-situ synchrotron diffraction analysis of deformation mechanisms in an AA5083 sheet metal processed by modified equal-channel angular pressing

Severe plastic deformation (SPD) is a process to significantly improve the mechanical properties of materials by grain refinement. For forming at room temperature (RT), higher strengths can thus be achieved; for increased temperatures (HT), greater elongations can be achieved. This great potential has been chiefly applied only on laboratory scale due to a lack of industrial process design. Equal-channel angular pressing (ECAP) offers the possibility to integrate these advantages in industrial processes. This paper investigates a modified ECAP process for aluminum AA5083 sheet metal. Two passes of ECAP for sheet metal and an additional heat treatment were used. To study the material deformation on a micro-scale, in-situ synchrotron measurements at DESY (Hamburg) were performed to analyze the evolution of lattice strains and dislocation densities during tensile testing. The mechanical properties of the ECAP-processed sheet material reveal an increase in yield strength and a decrease in elongation at RT. Higher strains can be measured for the processed material at elevated test temperatures. In-situ diffraction results show a changed behavior of the ECAP sheet material compared to the reference material for both temperature regimes. These changes are based on the increased defect density in the material, which leads to increased strength at RT. At HT, dynamic recrystallization occurs during tensile testing, and the prevailing deformation mechanisms reconfigure. Electron backscatter diffraction (EBSD) and micrographs are used to interpret and supplement the observations. The findings provide the basis for the in-depth understanding of the deformation behavior of the material and help to apply the ECAP process on an industrial scale.

Significantly improved mechanical properties of mullite ceramics by adding AlOOH with different sizes and morphologies

AbstractMullite ceramics with high purity and toughness were prepared by hot‐press sintering of pyrophyllite at 1300°C using AlOOH nanomaterials with different sizes and morphologies (nanoparticles, nanorods, nanoflakes, and micro‐sized sea urchin–like) as additives. Among the four types of AOOH additives, the incorporation of nanoflakes and sea urchins resulted in the formation of a relatively uniformly distributed and tightly packed microstructure within the ceramics, which significantly improved the density and mechanical properties of the ceramic materials. Compared to nano‐sized AlOOH, the addition of micron‐sized sea urchin–like AlOOH could produce mullite ceramics with best purity and flexural strength. The flexural strength and fracture toughness of ceramics prepared from micro‐sized sea urchin–like AlOOH and pyrophyllite reach 427.34 ± 1.99 MPa and 4.68 ± .31 MPa m1/2, respectively. During the ball milling process, the originally micron‐sized sea urchin–like AlOOH particles were broken down into micro‐ and nano‐sized AlOOH particles. The resulted micron and nanoscale AlOOH particles exhibited synergistic and multi‐scale effects with pyrophyllite, which contributed to the formation of uniformly sized and densely arranged mullite crystals within the ceramics. Additionally, the bridging between the mullite crystals further improved the mechanical properties of the mullite ceramic material.

Formation of Stable Vascular Networks by 3D Coaxial Printing and Schiff-Based Reaction

Vascularized organs hold potential for various applications, such as organ transplantation, drug screening, and pathological model establishment. Nevertheless, the in vitro construction of such organs encounters many challenges, including the incorporation of intricate vascular networks, the regulation of blood vessel connectivity, and the degree of endothelialization within the inner cavities. Natural polymeric hydrogels, such as gelatin and alginate, have been widely used in three-dimensional (3D) bioprinting since 2005. However, a significant disparity exists between the mechanical properties of the hydrogel materials and those of human soft tissues, necessitating the enhancement of their mechanical properties through modifications or crosslinking. In this study, we aim to enhance the structural stability of gelatin–alginate hydrogels by crosslinking gelatin molecules with oxidized pullulan (i.e., a polysaccharide) and alginate molecules with calcium chloride (CaCl2). A continuous small-diameter vascular network with an average outer diameter of 1 mm and an endothelialized inner surface is constructed by printing the cell-laden hydrogels as bioinks using a coaxial 3D bioprinter. The findings demonstrate that the single oxidized pullulan crosslinked gelatin and oxidized pullulan/CaCl2 double-crosslinked gelatin–alginate hydrogels both exhibit a superior structural stability compared to their origins and CaCl2 solely crosslinked gelatin–alginate hydrogels. Moreover, the innovative gelatin and gelatin–alginate hydrogels, which have excellent biocompatibilities and very low prices compared with other hydrogels, can be used directly for tissue/organ construction, tissue/organ repairment, and cell/drug transportation.

Promoting Cross-Link Reaction of Polymers by the Matrix-Filler Interface Effect: Role of Coupling Agents and Intermediate Linkers.

The matrix-filler interface effect plays an important role in determining the structural stability and mechanical properties of polymer composite materials, which remain ambiguous and need to be studied. The network-forming dynamics of poly(3,3-bis (azidomethyl) oxetane-tetrahydrofuran) (PBT) at the ammonium perchlorate (AP) surface was studied by using atomistic molecular dynamics simulation, considering the additives of curing agent toluene diisocyanate (TDI), cross-linker trimethylolpropane (TMP), and coupling agent triethanolamine (TEA). The presence of the AP surface promotes chain cross-link reaction, which is attributed to the increased production of intermediate linkers formed by TDI, TMP, and TEA. The intermediate linker has three reactive sites that can react with PBT main chains to form a cross-linked structure. Owing to the strong interaction with the AP surface, the coupling agent TEA plays a dominant role in forming the intermediate linker. At the early stage of network forming (reaction ratio r < 30%), the AP surface adsorbs TEA, which leads to a maximum contact density to PBT. As r increases to 60%, the density of intermediate linkers near the AP surface reaches a maximum value. Consequently, the chain cross-link reactions between the intermediate linker and PBT main chains are enhanced as r > 60%. This work explains the micromechanism of the promotion of chain cross-link reaction by the interface effect and provides important insights on designing polymer materials with high mechanical properties.

Progressive Damage Simulation of Wood Veneer Laminates and Their Uncertainty Using Finite Element Analysis Informed by Genetic Algorithms

Within the search for alternative sustainable materials for future transport applications, wood veneer laminates are promising, cost-effective candidates. Finite element simulations of progressive damage are needed to ensure the safe and reliable use of wood veneers while exploring their full potential. In this study, highly efficient finite element models simulate the mechanical response of quasi-isotropic [90/45/0/−45]s beech veneer laminates subjected to compact tension and a range of open-hole tension tests. Genetic algorithms (GA) were coupled with these simulations to calibrate the optimal input parameters and to account for the inherent uncertainties in the mechanical properties of wooden materials. The results show that the continuum damage mechanistic simulations can efficiently estimate progressive damage both qualitatively and quantitatively with errors of less than 4%.Variability can be assessedthrough the relatively limited number of 400 finite element simulations as compared to more data-intensive algorithms utilised for uncertainty quantification.

Theoretical Prediction of Strengthening in Nanocrystalline Cu with Multi-Element Grain Boundary Segregation Decoration

The composition of grain boundaries (GBs) determines their mechanical behavior, which in turn affects the mechanical properties of nanocrystalline materials. Inspired by GB segregation and the concept of high-entropy alloys (HEAs), we investigated, respectively, the mechanical responses of nanocrystalline Cu samples with and without multi-element GBs, as well as the grain size effects, aiming to explore the effects of GB composition decoration on mechanical properties. Our results show that introducing multi-element segregation GBs can significantly improve the mechanical properties of nanocrystalline Cu by effectively inhibiting GB migration and sliding. Additionally, we proposed an improved a theoretical model that can reasonably describe the strengths of the materials with multi-element or single-element segregation GBs. Notably, the introduction of multi-element segregation GBs inhibits both migration and sliding behavior, with migration being more effectively suppressed than sliding. These results present a novel approach for designing high-performance nanometallic materials and offer valuable insights into the role of GB composition decoration in enhancing mechanical properties.

An Assessment of Some Mechanical Properties of Harvested Potato Tubers cv. Spunta

Mechanical properties of vegetables or crop materials play a noteworthy part in designing new related implements. These properties can be extracted from force–deformation curves. Several factors, such as soil preparation, irrigation, and pre- and post-harvest treatments influence them. The core objective of this investigation work was to analyze force–deformation curves obtained from compression, penetration, and shear tests of potatoes (Spunta cv.) produced with three tillage implements. The potatoes cv. Spunta were cultivated in loamy sand soil under the center-pivot irrigation system. The tillage implements used were a disc harrow plow, chisel plow, and moldboard plow. The trials were performed at a constant planting depth (15 cm) below the soil and a single plowing speed of 5.4 km/h. All data were expressed as an average of five replicates ± standard deviation. The force–deformation curves analysis showed that the modulus of elasticity for potatoes cv. Spunta ranged from 4.32 to 5.8 N/mm, the bioyield force ranged from 84.25 to 114.12 N, and rupture forces ranged from 100.90 to 139.78 N. Furthermore, the results showed that the average values of the elastic and plastic ranges were 3.0 and 2.1 mm, respectively. The mean value of hardness was 1671.53 N·mm. No significant differences were observed with respect to the two planting seasons, but tillage implements had a significant impact on the characteristics extracted from the compression tests. The mean of the maximum forces required to penetrate the potato during the penetration stage were 41.24 N, 44.86 N, and 47.16 N for potatoes produced with the disc harrow plow, chisel plow, and moldboard plow, respectively. Similarly, the means of the maximum forces required to cut the potato in the shear stage were 724.38 N, 761 N, and 773.43 N for the disc harrow plow, chisel plow, and moldboard plow, respectively. The force–deformation curves showed that additional information might be required to obtain a complete description of the potato quality necessary to harvest potatoes cv. Spunta using harvesting and handling equipment with reduced economic loss. An extensive study of the soil characteristics and the above-mentioned properties is also recommended. The results obtained about the mechanical characteristics of potatoes cv. Spunta can be useful in providing information that aids in designing potato harvesting machines and in potato products factories.

Nanomechanical properties of ceramic materials from the SiO2–Al2O3-(Na2O)–K2O–MgO system with an addition of SrO

The ceramic materials studied in this paper consist of finely dispersed crystalline phases embedded in a glassy matrix, which is similar to glass-ceramic materials, porcelain, and VC products. The strength depends then not only on the properties of the individual crystalline phases but also on their interactions and the matrix. Differences in mechanical properties for materials with similar chemical compositions are most likely related to diverging microstructures. Crystal orientation, grain-size distribution and shape, the ratio of the glass matrix to the crystalline phase, and homogeneity control the flexural strength of glass-ceramic materials. The subject of the study is whiteware ceramic materials from the SiO2–Al2O3–Na2O–K2O–MgO–SrO system, fired similarly to the regime used for VC products. The effect of the type of alkali oxide and the share of SrO were tested. This paper presents the results of hot-stage microscopy, X-ray diffraction (XRD), scanning electron microscopy with a micro-analyzer (SEM-EDS) and biaxial flexural strength measurements. Additionally, nanoindentation technique was used to access local mechanical properties.

Effects of hydrotalcites with different laminate element composition on the properties of sulfoaluminate cement-based materials

Sulfoaluminate cement-based materials (SCBMs) are widely used for grout reinforcement. It is common to use a large water-to-binder ratio in the construction of sulfoaluminate cement-based materials (SAGMs) to obtain good workability and permeability, which results in poor early strength. Nanotechnology has been increasingly employed to enhance the mechanical properties of cementitious materials. Nano Zn-Mg-Al hydrotalcite-like (LDHs) and nano Mg-Al LDHs increased the early compressive strength, while nano Zn-Al LDHs had the opposite effect. However, the reason for this observation remains unclear. In this study, the influence of LDHs structures with different laminar element compositions on the hydration and hardening processes of SCBMs was analysed. The results showed that nano-ZnAl-LDHs, ZnAl-LDHs, and MgAl-LDHs could provide nucleation sites for ettringites. The three hydrotalcite-like materials slowly released different concentrations of zinc and/or magnesium ions and carbonate ions in the cement paste. Zinc ions entered the hydration product of ettringite and aluminum gel and promoted the transformation of amorphous aluminum gel to bayerite, which inhibited the hydration reaction of SCBMs. Magnesium ions could also enter the ettringite, and carbonate ions promoted the formation of calcium carbonate, which facilitated the hydration reaction of SCBMs. The nucleation effect and the release of zinc and/or magnesium ions and carbonate ions acted synergically to influence the hydration rate, pore size distribution, and compressive strength of SCBMs.

High mechanical properties of CNTs/Al composites achieved by second phase refinement and reinforcement dispersion via hot extrusion

The carbon nanotubes (CNTs) reinforced 2A70 alloy by the coating of ZrO2 (ZrO2@CNTs/2A70) are processed by a hot extrusion process. The microstructure and mechanical properties of ZrO2@CNTs/2A70 composites were investigated in this study. The results show that the second phase of the composites is broken and uniformly dispersed under the action of shear force and the second phase as well as the ZrO2@CNTs reinforcement is uniformly distributed along the extrusion direction. The hot extrusion process eliminates the cast defects and improves the reinforcing phase's dispersion and the material's mechanical properties are significantly improved. At the extrusion ratio of 25, the composites exhibited notable enhancements in their mechanical properties, as evidenced by a significant increase in hardness, yield strength (YS), ultimate tensile strength (UTS), and elongation (EL), with respective values of 141.7 HV, 237.4 MPa, 309.7 MPa and 13.9%. These values were higher than those obtained from cast composites by 17.5%, 20.0%, 20.9% and 152.7%, respectively. The fracture characteristics of the composite are mainly ductile fractures. Besides, the extruded composites are strengthened mainly by grain refinement and load transfer mechanism.

Recent Advancements in Material Waste Recycling: Conventional, Direct Conversion, and Additive Manufacturing Techniques

To improve the microstructure and mechanical properties of fundamental materials including aluminum, stainless steel, superalloys, and titanium alloys, traditional manufacturing techniques have for years been utilized in critical sectors including the aerospace and nuclear industries. However, additive manufacturing has become an efficient and effective means for fabricating these materials with superior mechanical attributes, making it easier to develop complex parts with relative ease compared to conventional processes. The waste generated in additive manufacturing processes are usually in the form of powders, while that of conventional processes come in the form of chips. The current study focuses on the features and uses of various typical recycling methods for traditional and additive manufacturing that are presently utilized to recycle material waste from both processes. Additionally, the main factors impacting the microstructural features and density of the chip-unified components are discussed. Moreover, it recommends a novel approach for recycling chips, while improving the process of development, bonding quality of the chips, microstructure, overall mechanical properties, and fostering sustainable and environmentally friendly engineering.

Study on the Alkali–Sulfur Co-Activation and Mechanical Properties of Low-Carbon Cementitious Composite Materials Based on Electrolytic Manganese Residue, Carbide Slag, and Granulated Blast-Furnace Slag

Study on the Alkali–Sulfur Co-Activation and Mechanical Properties of Low-Carbon Cementitious Composite Materials Based on Electrolytic Manganese Residue, Carbide Slag, and Granulated Blast-Furnace Slag

Comparative Study of the Mechanical Properties of a Novel Epoxy Composite Material Reinforced by Bidirectional Woven Carbon Fabric and Hybrid Kevlar/E-Glass

The objective of this work is to carry out a comparison of different materials in the form of a bidirectional carbon fabric and hybrid Kevlar and glass as reinforcements in an epoxy matrix with a loading rate of 30wt%. Two experimental tests have been carried out in order to determine the mechanical properties, such as tensile and Brinell hardness tests. In the case of tensile and Brinell hardness tests, the characterization was performed on two types of composite plates reinforced with Woven Carbon Fiber and Hybrid Woven Kevlar and E-Glass with Epoxy (WCF-HWKG/EPOXY) and Hybrid Woven Kevlar and E-Glass with Epoxy (HWKG/EPOXY). Consequently, it has been observed that the tensile and hardness properties of the hybrid composite material (HWKG/EPOXY) are respectively 36% and 46.43% lower compared to (WCF-HWKG/EPOXY). Based on these findings, the studied materials demonstrate potential applications across various fields, including aeronautics, aerospace, and high-performance automotive sectors.

Nanocomposites Derived from Construction and Demolition Waste for Cement: X-ray Diffraction, Spectroscopic and Mechanical Investigations

In the production of cement, raw materials can be partially substituted by regenerable waste provided from glasses, construction and demolition waste in order to reduce the environmental problem and burden of landfills. In this study, limestone–silicate composites were synthesized using starting materials such as glass waste and lime, brick, autoclaved aerated concrete (ACC), mortar or plaster waste. The structure and mechanical properties of the nano-composite materials have been studied. The mean CaCO3 crystallite sizes are higher for composites containing ACC and brick than for doping with lime, mortar and plaster. Cement-based materials are formed by replacing 2.5% of the Portland cement with limestone–silicate composites. The results indicate new possibilities for introducing 2.5%of composites in cement paste because they promote the formation of the C-S-H network, which provides strength and long stability for the cement paste. The influence of varied types of mix composites in the expired cement on the initial cracking strain and stress, tensile strength and compressive strength were investigated. The compressive strength values of composite-expired cement specimens are situated between 11.8 and 15.7 MPa, respectively, which reflect an increase from 22.9 up to 63.54% over the compressive strength of expired cement matrix.

Material strengths of shear-induced platelet aggregation clots and coagulation clots

Arterial occlusion by thrombosis is the immediate cause of some strokes, heart attacks, and peripheral artery disease. Most prior studies assume that coagulation creates the thrombus. However, a contradiction arises as whole blood (WB) clots from coagulation are too weak to stop arterial blood pressures (> 150 mmHg). We measure the material mechanical properties of elasticity and ultimate strength for Shear-Induced Platelet Aggregation (SIPA) type clots, that form under stenotic arterial hemodynamics in comparison with coagulation clots. The ultimate strength of SIPA clots averaged 4.6 ± 1.3 kPa, while WB coagulation clots had a strength of 0.63 ± 0.3 kPa (p < 0.05). The elastic modulus of SIPA clots was 3.8 ± 1.5 kPa at 1 Hz and 0.5 mm displacement, or 2.8 times higher than WB coagulation clots (1.3 ± 1.2 kPa, p < 0.0001). This study shows that the SIPA thrombi, formed quickly under high shear hemodynamics, is seven-fold stronger and three-fold stiffer compared to WB coagulation clots. A force balance calculation shows a SIPA clot has the strength to resist arterial pressure with a short length of less than 2 mm, consistent with coronary pathology.

Tensile and bond properties at elevated temperatures of a PBO-FRCM composite system for strengthening concrete elements: Experimental and analytical investigations

This paper presents experimental and analytical investigations on the tensile and bond behaviour at elevated temperature of a polypara-phenylene-benzo-bisthiazole (PBO) fabric reinforced cementitious matrix (FRCM) system for strengthening concrete elements. Direct tensile (DT) and single lap direct shear tests (DS) were performed under steady-state conditions at the following temperatures: 20 °C, 85 °C, 150 °C, 230 °C and 300 °C. The results obtained were evaluated in terms of strength, stiffness, ultimate strain, load vs. slip response at the interface PBO FRCM/concrete and failure modes. Overall, the tensile and bond properties were significantly affected by the temperature increase. These results are mainly associated with the reductions of mechanical properties of the FRCM constituent materials as well as the degradation of the interaction between the fibres and the inorganic matrix at elevated temperatures. The experimental results were then used (i) to evaluate the suitability of the Aveston–Cooper–Kelly (ACK) model in describing the tensile response of FRCM at elevated temperatures and (ii) to calibrate temperature-dependent local shear bond stress vs. slip laws for the FRCM-concrete interaction.

Microstructure and cyclic hardening/softening behavior of laser welded high strength steel joints under asymmetrical cyclic loading

The cyclic behavior of materials under load and its influence on the mechanical properties of materials have always been the focus of engineering research. In this study, high strength steel was successfully welded by laser welding. The microstructure of each region of the high strength steel DP590 post-welding was meticulously analyzed. Additionally, 500 cycles of low-cycle fatigue tests of laser welded high strength steel were carried out by using asymmetric stress control method. After fatigue test, tensile test shall be carried out on some samples. Under the specific combination of mean stress and stress amplitude, compare the specimens that have not been fatigue tested with those that have been fatigue tested, the change of properties of laser welded high strength steel joint under asymmetric cyclic load was analyzed. The results showed that, due to cyclic hardening, the tensile strength of the sample increased to 601 MPa and the yield strength to 325 MPa. Compared with the original sample, the tensile strength and yield strength of the sample after asymmetric cycling had increased by 8.65% and 31.3%, respectively.

Numerical simulation of concrete strength based on microstructure and mineral composition analysis using micro-CT and XRD technology

The investigation of mechanical properties in porous materials, such as concrete, has been a significant area of interest in the fields of civil engineering and architecture. Traditional macroscopic mechanical testing methods are limited due to destructive experimental conditions, time-consuming procedures, and the inability to characterize internal structures. To overcome these limitations, researchers have utilized microscopic factors with micro-CT and simulation models. Different simulation methods demand mechanical parameters to effectively model the constituent materials; however, there exists variability in the amount and standard values of these input parameters, which leads to a decrease in the reliability of the obtained results. In order to tackle this issue, a novel approach is proposed, which integrates mineral component analysis using X-ray diffraction (XRD) and establishes coefficients to minimize the number of necessary input parameters. Simulation results demonstrate excellent agreement with experimental measurements, accurately reproducing the stages of elastic deformation, failure, and fracture in the stress-strain curve of concrete. Our findings reveal that changes in the concrete skeletal structure, microstructure, and mineral composition significantly influence compressive strength. Coarse aggregates and high-mechanical-performance minerals, in particular, have a substantial impact. Additionally, the mechanical properties show a significant linear relationship with the strength reduction coefficient of aggregates and concrete cores. In conclusion, the proposed method, combining CT scanning and XRD with FDEM, proves to be a reliable and practical approach for accurately assessing the mechanical properties of concrete. This methodology simplifies the intricate processes associated with the time-intensive parameter calibration, leading to a more efficient parameter allocation procedure. As a result, this method enhances concrete design, promotes a better understanding of parameter impacts, and enables accurate prediction of concrete behavior across diverse scenarios.