Brittle Alloy Research Articles

Improving strength-ductility balance of a brittle Al-doped FeCrNi multi-principal element alloy by introducing a heterostructure with hard phase enveloping soft phase

In the present work, a heterostructure was created in a brittle Al-doped FeCrNi multi-principal element alloy via thermomechanical treatment. This heterostructure consists of a hard phase surrounding a soft phase, with the soft defect-free face-centered cubic (FCC) phase formed through phase transformation evenly distributed within the hard body-centered cubic (BCC) matrix. This unique heterostructure promotes more uniform deformation, thereby enhancing the deformability of the original hard BCC matrix. As a result, the elongation was increased from 2.4 % to 17 %, while the ultimate tensile strength was just decreased from 1076 MPa to 1021 MPa. The maintenance of strength is primarily attributed to the hetero-deformation-induced (HDI) strengthening effect provided by this distinctive heterostructure. Overall, this special heterostructure formed through phase transformation opens up new possibilities for developing alloys with both high strength and ductility.

Grain Size Dependent Plastic Behaviour in Bulk Nanocrystalline FeAl

While the deformation behavior of nanocrystalline ductile metals and alloys is extensively studied, there is little understanding for brittle intermetallic alloys with very small grain sizes. In the present work B2 ordered FeAl with different grain sizes is produced and deformed by high pressure torsion. At a grain size of 120 nm conventional dislocation processes remain dominant resulting in a disordered saturation structure with highly defected grains of around 100 nm. The situation is different for an initial grain size of 30 nm; grain‐boundary mediated processes appear along with dislocation processes and deformation shows a tendency towards extreme localization in the form of thin bands. Interestingly, the saturation structure is not reached after severe plastic deformation. The nanocrystals remain ordered with a grain size of 30 nm; only within the deformation bands, some degree of disordering and an increase of the dislocation density is revealed by profile analysis using selected electron diffraction. This results demonstrates an extreme stability of ordered FeAl at very small grain sizes, and indicates that the deformation behaviour in brittle intermetallics can strongly depend on the grain sizeThis article is protected by copyright. All rights reserved.

The Microstructure and Magnetic Properties of a Soft Magnetic Fe-12Al Alloy Additively Manufactured via Laser Powder Bed Fusion (L-PBF)

Soft magnetic Fe-Al alloys have been a subject of research in the past. However, they never saw the same reception in technical applications as the Fe-Si or Fe-Ni alloys, which is, to some extent, due to a low ductility level and difficulties in manufacturing. Additive manufacturing (AM) technology could be a way to avoid issues in conventional manufacturing and produce soft magnetic components from these alloys, as has already been shown with similarly brittle Fe-Si alloys. While AM has already been applied to certain Fe-Al alloys, no magnetic properties of AM Fe-Al alloys have been reported in the literature so far. Therefore, in this work, a Fe-12Al alloy was additively manufactured through laser powder bed fusion (L-PBF) and characterized regarding its microstructure and magnetic properties. A comparison was made with the materials produced by casting and rolling, prepared from melts with an identical chemical composition. In order to improve the magnetic properties, a heat treatment at a higher temperature (1300 °C) than typically applied for conventionally manufactured materials (850–1150 °C) is proposed for the AM material. The specially heat-treated AM material reached values (HC: 11.3 A/m; µmax: 13.1 × 103) that were close to the heat-treated cast material (HC: 12.4 A/m; µmax: 20.3 × 103). While the DC magnetic values of hot- and cold-rolled materials (HC: 3.2 to 4.1 A/m; µmax: 36.6 to 40.4 × 103) were not met, the AM material actually showed fewer losses than the rolled material under AC conditions. One explanation for this effect can be domain refinement effects. This study shows that it is possible to additively manufacture Fe-Al alloys with good soft magnetic behavior. With optimized manufacturing and post-processing, further improvements of the magnetic properties of AM L-PBF Fe-12Al may still be possible.

Production of spherical TiAl alloy powder by copper-assisted spheroidization

A copper-assisted spheroidization method was developed for preparing spherical intermetallic compound TiAl powder. By introducing copper into TiAl alloy, the brittle L21 Heusler structure TiAlCu2 alloy with low melting point (1050 °C) was produced. After preparing the spherical TiAlCu2 powder through solid–liquid interface de-wetting method, the porous TiAl alloy sphere with atomic ratio about 1:1 was prepared by dealloying the Cu element. Finally, the spherical TiAl alloy powder was prepared by sintering and deoxygenation. Compared with the current mature technology for preparing the spherical TiAl alloy powder, the size distribution of spherical particles can be easily regulated, which can meet the requirements for high-quality additive manufacturing technology. We believe that this method provides a new idea for preparing the spherical TiAl alloy powder and other spherical porous alloys.

Room-temperature polymer-assisted additive manufacturing of microchanneled magnetocaloric structures

Magnetic refrigeration is an energy-efficient, sustainable, environmentally-friendly alternative to the conventional vapor-compression cooling technology. There are several magnetic refrigerator device designs in existence today that are predicted to be highly energy-efficient, on condition that suitable working materials can be developed. This challenge in manufacturing magnetocaloric devices is unresolved, mainly due to issues related to shaping the mostly brittle magnetocaloric alloys into thin-walled channeled regenerator structures to facilitate efficient heat transfer between the solid refrigerant and the heat exchange fluid in an active magnetic regenerator (AMR) cooling device. To address this challenge, a novel extrusion-based additive manufacturing (AM) method has been developed to 3D print microchanneled magnetocaloric structures. The printing ink consists of magnetocaloric powders, a polymer binder, and multiple solvents to achieve desirable shear-thinning property, which is critical for a robust printing process. Acting as a sacrificial binding agent for the magnetic powders, the polymer binder holds the 3D printed structures in place and is removed subsequently using a two-step heat-treatment process. To demonstrate the effectiveness of the fabrication process, spatially designed microchannels with minimum dimensions of 150 µm were achieved using nanoscaled La 0.6 Ca 0.4 MnO 3 powders (diameter~10 nm). Results indicate that the crystallographic properties and magnetofunctional response of the sintered 3D printed samples are comparable to that of the precursor powders. Overall, this study provides a promising route for realizing low-cost magnetic regenerators, thus potentially eliminating one of the main barriers to the commercialization of magnetic cooling technology. • Room temperature extrusion-based method for 3D printing magnetocaloric structures. • Significant magnetocaloric response in 3D printed LCMO scaffolds (ΔS=4.9 J/kg-K at 5 T). • Microchanneled magnetocaloric structures with record spatial resolution (dia∼150 µm). • Overcoming a crucial barrier to the commercialization of magnetic cooling technology.

Investigation of interfacial thermal stabilities of Nbf/TiAl composites with and without Al2O3 coating in interface

Continuous Nb fiber-reinforced TiAl-matrix composites have tremendous potential for replacing brittle TiAl alloy. However, at elevated temperature, interfacial reaction between fiber and matrix is aggravated, causing instability of the interfacial microstructure and mechanical property of Nbf/TiAl composite. Fortunately, the problem could be solved by introducing fiber coating. Consequently, in this study, Al2O3 coating was prepared on Nb fiber by cathodic plasma electrolytic deposition (CPED) technique. Concurrently, interfacial microstructure changes of the composites were explored during thermal treatment at 1100 and 1200 °C. The results show that, during heat treatment at 1100 °C for up to 100 h, for the composite without Al2O3 coating, the interfacial microstructure changes are as follows: Nb/σ/α2/TiAl→Nb/σ/B2/α2/TiAl→Nb/σ/TiAl, which leads to serious thermal residual stress and cracks in interface. Inversely, the introduction of Al2O3 coating can prevent the formation of brittle σ phase during preparation and the 1100 °C heat treatment. However, under 1200 °C heat treatment, the Al2O3 coating gradually fads away and be replaced by α2-Ti3Al phase. Finally, the interfacial phases including σ and α2 are formed. The existence of the Al2O3 coating can delay the formations of the brittle phases and avoid cracks for a long time, which greatly improves interfacial thermal stability of the Nbf/TiAl composite.

Design and Development of High-Strength and Ductile Ternary and Multicomponent Eutectoid Cu-Based Shape Memory Alloys: Problems and Perspectives

An overview is presented on the structural and phase transformations and physical and mechanical properties of those multicomponent copper-based shape memory alloys which demonstrate attractive commercial potential due to their low cost, good shape memory characteristics, ease of fabrication, and excellent heat and electrical conductivity. However, their applications are very limited due to brittleness, reduced thermal stability, and mechanical strength—properties which are closely related to the microstructural features of these alloys. The efforts of the authors of this article were aimed at obtaining a favorable microstructure of alloys using new alternative methods of thermal and thermomechanical treatments. For the first time, the cyclic martensitic transformations during repeated quenching, methods of uniaxial megaplastic compression, or torsion under high pressure were successfully applied for radical size refinement of the grain structure of polycrystalline Cu-Al-Ni-based alloys with shape memory. The design of the ultra- and fine-grained structure by different methods determined (i) an unusual combination of strength and plasticity of these initially brittle alloys, both under controlled heat or hot compression or stretching, and during subsequent tensile tests at room temperature, and, as a consequence, (ii) highly reversible shape memory effects.

Mechanical Behavior and Structural Characterization of a Cu-Al-Ni-Based Shape-Memory Alloy Subjected to Isothermal Uniaxial Megaplastic Compression.

For the first time, uniaxial megaplastic compression was successfully applied to a polycrystalline shape-memory Cu-Al-Ni-based alloy. The samples before and after uniaxial megaplastic compression were examined by methods of X-ray diffraction, optical, electron transmission, and scanning microscopy. The temperature dependences of electrical resistance and the mechanical properties of the alloys under uniaxial tension were also measured. The mechanical behavior under uniaxial megaplastic compression in isothermal conditions in the range of 300–1073 K was studied using the Instron 8862 electric testing machine. The microstructure, phase composition, and martensitic transformations in the eutectoid alloy (Cu-14wt.%Al–4 wt.%Ni) were studied. The radical refinement of the grain structure of the initial hardened D03 austenite was found under controlled isothermal compression, due to dynamic recrystallization in the temperature range 673–1073 K and velocities of 0.5–5 mm/min. Compression at 873–1073 K was accompanied by simultaneous partial pro-eutectoid decomposition with the precipitation of the γ2 phase. Compression at temperatures of 673 and 773 K—that is, below the eutectoid decomposition temperature (840 K)—was accompanied by the precipitation of disperse γ2 and α phases, and ultradisperse B2’ particles. Cooling of the deformed alloy to room temperature after performing each regime of compression led to thermoelastic martensitic transformation, together with the precipitation of the β′ and γ′ phases. The formation of a fine-grained structure produced an unusual combination of strength and plasticity of the initially brittle alloy both under controlled uniaxial compression, and during subsequent tensile tests at room temperature.

Ferroelastic oligocrystalline microwire with unprecedented high-temperature superelastic and shape memory effects

A compelling demand exists for high-performance high-temperature shape memory alloys (HTSMAs) that can be applied as intelligent components in the rapidly developing aerospace, robotics, manufacturing, and energy exploration industries. However, existing HTSMAs are handicapped by their high cost and unsatisfactory functional properties, which impede their practical application. Here, by using the strategy of creating an oligocrystalline structure, we have developed a high-performance, cost-effective high-temperature shape memory microwire exhibiting an exceptional combination of superb superelasticity with a large recoverable strain of up to 15%, an outstanding one-way shape memory effect with a maximum recoverable strain as high as 13% and a remarkable two-way shape memory effect with a large recoverable strain of 6.3%. These unparalleled comprehensive properties provide this microwire with a high potential for use in high-temperature actuation, sensing, and energy conversion applications, especially in miniature intelligent devices, such as high-temperature microelectromechanical systems. The present strategy may be universally applicable to other brittle phase-transforming alloys for achieving outstanding functional properties at high temperatures.

Pure shear plastic flow and failure of titanium alloys under quasi-static and dynamic torsional loading

The pure shear responses of Ti6Al4V alloy and Ti3Al2.5V alloy, conceived for unique applications in jet engine components, are compared using Digital Image Correlation technique from quasi-static (10−3/s), medium strain rate (101/s) and high strain rates (103/s). A series of bespoke torsion tests have been performed on a screw driven mechanical system, a fast hydraulic Instron machine and a Campbell split Hopkinson torsion bar, equipped with high speed photographic equipment. Observations have provided the strain rate dependence and the relation of pure shear failure at quasi-static and high strain rates. The quasi-static shear constitutive relationships including shear modulus, yield stress and failure strain of both alloys are compared at the location of failure initiation, using a bespoke four camera system. The Ti3Al2.5V alloy presents lower shear flow stress and strain rate sensitivity with higher ductility, as opposed to the Ti6Al4V alloy with limited plastic deformation capacity. Associated with modest estimated overall temperature rise until final collapse of the specimen, both ductile Ti3Al2.5V alloy and brittle Ti6Al4V alloy fail by adiabatic shear banding at high strain rates. This is different from the void growth induced failure at medium strain rate with mild temperature rise and at quasi-isothermal condition. The present results show a general description of brittle and ductile alloys in engineering design. Likewise, this study will guide the characterization of pure shear flow and failure for current and future developed impact resistant alloys.

Failure investigation of a Ag sinter-joining SiC power device under harsh cycling conditions

Silicon-Carbide (SiC) power devices have become the prime candidates for future high-performance energy conversion on account of their superior performance over traditional silicon power devices. The superior electro-thermal properties of SiC power devices permit higher temperature of operation and enable higher power density. Nevertheless, the high operation temperature has introduced new changes in die attachment packaging of the SiC power device, which is one of the most vulnerable places due to a direct connection to the SiC chip. Traditional Pb-free solder-joining is hardly to withstand high temperatures because of the low melting point of solder materials. Besides, severe temperature swings of the SiC chip can introduce severe deterioration in the solder layer due to brittle alloy compounds. Currently, Ag sinter-joining is an ideal connection technique for high reliable power electronics packaging. Due to excellent thermal stability and chemical resistance, the Ag sinter-joining is applicable to various harsh conditions, such as extreme temperatures, high humidity, high heavy current, etc., showing promising application scenarios in die attachment packaging. In this work, we applied Ag sinter-joining to die attachment of a molded SiC device and focused reliability of Ag sinter joining under harsh thermal cycling and power cycling conditions. The SiC device was assembled by a SiC diode and direct bonding copper (DBC) substrate via the Ag sinter-joining. Ribbon bonding was used for the topside connection of the SiC device. An imide resin was applied to mold the SiC device. The thermal cycling test was conducted at a temperature range from -50 °C to 200 °C and the power cycling test was conducted at an initial junction of 200 °C. The structures inspection, thermal resistance variations, and voltage-current curve were investigated to understand failures in the SiC device. The thermal cycling can introduce crazing cracks in the sintered layer due to drastic thermal stress caused by a huge temperature swing. However, the thermal resistance, of the SiC device measured by T3ster, was not significantly affected by the crazing pattern. The Ag sinter-joining also shows an excellent resistance during the power cycling test, while the ribbon lift-off will introduce a final failure of the SiC device. Figure 1 shows a cross section of the structure of the SiC power device with and without a power cycling test. Obvious cracks can be differentiated at the ribbon bonding interface after cycling, while there is no deterioration happened in the sintered Ag layer. Base on the present results, it can be concluded that the Ag sinter-joining can withstand a harsh cycling condition either in huge temperature swings or heavy currents. Figure 1

Tribological Properties of High-Entropy Alloys under Dry Conditions for a Wide Temperature Range-A Review.

High-entropy alloys (HEAs) are composed of multiple elements with equimolar or near equimolar composition that have superior mechanical and tribological properties. In this article, we present a review on the tribological performance of HEAs. The tribological properties of different HEAs systems have been evaluated, and it has been found that the wear rate strongly depends on the crystal structure of the phases. The most common structures are face-centered cubic (FCC), body-centered cubic (BCC), and dual-phase (FCC + BCC) alloys due to the high entropy of mixing instead of forming intermetallic phases. In general, HEAs with a BCC structure showed superior hardness and wear properties compared to FCC and FCC + BCC alloys. The lesser wear rate of HEAs with a BCC structure is attributed to the reductions in ductility, resulting in strong but brittle alloys. In addition to the crystal structure, the effect of temperature on the tribological performance of the HEAs is also discussed, which highlights their potential applications for high temperatures. Moreover, various other factors such as grain size, formation of an oxide layer, and wear mechanisms are discussed.

A novel fabrication method of surface-porous Mg-Al alloy and its corrosion property

The specific stiffness, strength and damping capacity of a Mg alloy may be further enhanced if the Mg alloy has a specifically porous surface layer. However, it is not practical to use a faveolated brittle alloy precursor to generate such a porous microstructure. Hence, in this study, surface alloying was employed for the first time to fabricate the precursor of Mg-Al alloys with porous surfaces. The porous surface could be obtained via chemical etching of the precursor. The corrosion performance of the precursor alloy before and after the etching was measured and the corrosion mechanism was analyzed. It was found that in the alloyed surface layer of the precursor, the α-Mg was Al-supersaturated and potential difference of the α-Mg from the secondary phase was relatively small, which was helpful to form a uniform surface film to suppress micro galvanic corrosion. The porous surface had a high ratio of cathodic-to-anodic area and thus showed poor corrosion resistance compared with the surface of the precursor Mg-Al alloy.

Suppression and Recovery of Martensitic Transformation and Magnetism in Mechanically and Thermally Treated Magnetic Shape‐Memory Ni−Mn−Ga Melt‐Spun Ribbons

As‐melt‐spun Ni50.2Mn28.3Ga21.5 ribbons are subjected to milling and subsequent annealing for various times. With progressing milling time, the martensitic transformation is gradually suppressed, magnetic moment deteriorates, whereas the crystal structure undergoes a body centered tetragonal (bct) into face centered cubic (fcc) change. High‐resolution transmission electron microscopy demonstrates a twin‐deformed zone in fcc powder particles, which works to improve circularity of as‐produced powders. Subsequent annealing of as‐milled powders restores martensitic transformation and magnetism, as well as it reverts the fcc into the original 5M structure. It is hence showcased that due to an allotropic transformation, brittle Heusler alloys are mechanically optimized for 3D printing without loss of their functional properties.

Comparison of powder bed fusion and directed energy deposition for tailoring mechanical properties of traditionally brittle alloys

The mechanical performance of an Fe-Co intermetallic alloy processed by laser powder bed fusion (L-PBF) and laser directed energy deposition (L-DED) additive manufacturing is compared. L-PBF material was characterized by high strength (500–550 MPa) and high ductility (35%) in tension, corresponding to a ~250% increase in strength and an order-of-magnitude improvement in ductility relative to conventional material. Conversely, L-DED material exhibited similarly poor tensile properties to the conventional wrought alloy, with low strength (200–300 MPa) and low ductility (0–2.7%). The disparity in properties between L-PBF and L-DED material is discussed in the context of the fundamental differences between manufacturing methods.

Performance assessment of TiNbf/TiAl composites with different fiber structural characteristics

Continuous TiNb fiber reinforced TiAl composites (TiNbf/TiAl) have tremendous potential for substituting brittle TiAl alloy to service on advanced aerospace equipment. This study has clarified microstructure evolution of TiNbf/TiAl composites and successfully achieved the structure modification of TiNb fiber by aging process where strengthening phase α-Ti could precipitate homogeneously in basket shape at the core of fiber meanwhile the formation and growth of brittle O phase could be effectively inhibited. Through aging process, both strength and toughness of composites have achieved a remarkable enhancement. Tensile fracture strength and strain of composites were significantly improved by 87% and 74% respectively compared with TiAl matrix. The K1C reflecting the toughness was enhanced nearly doubled benefit from multiple interaction mechanisms. The compressive strength of composites at 700 °C can reach 1078 MPa which still reached up to 847 MPa at 800 °C. The micromechanical properties of each phase were investigated systematically to reveal the strengthening and toughening mechanism. The growth behavior and the stability of interface structure were also involved with first-principles method.

Achieving an exceptional ductility at room temperature in a low SFE copper alloy fabricated by severe plastic deformation

Abstract Low stacking fault energy alloys often exhibit low ductility. However, sometimes these alloys show unusual mechanical behavior following specific processing parameters. In this study, a low stacking fault energy α+β brass was processed by equal channel angular pressing (ECAP) at 350 °C in ‘route C’ through three passes. Room temperature tensile testing showed that ductility, surprisingly, reached ~80%, whilst good tensile strength was maintained. Investigation of alloy microstructure revealed a combination of deformation mechanisms, including slip and twinning, accompanied by grain boundary serration and grain fragmentation. It is suggested that these deformation modes triggered these unexpected mechanical properties in this intrinsically brittle alloy. The required energy for discontinuous recrystallization was supplied after only one pass in the α phase, and three passes in the β phase, which then prompted good ductility. In order to study texture evolution, the macro-texture was measured. A high fraction of recrystallized grains and change in strain path fostered the development of Goss, Rotated Goss and Rotated Cube components in the α phase. While in the β phase {011} and Goss components were dominant. Despite the high Schmid factor, Hall-Petch effects and work hardening led to increase of strength and hardness after the final pass.

Microstructure and Electrochemical Performance Evaluation of Zn, Zn-5 wt.% Al and Zn-20 wt.% Al Alloy Coated Steels

A comparative study has been done on three coatings obtained on steel surface using pure Zn, two Zn-Al alloy baths. The coatings obtained using both Zn alloy baths are thinner than the same obtained using pure zinc bath as Al reacts with steel and forms very thin layer of Fe2Al5 phase which hinders iron-zinc reaction. Coating obtained using pure zinc bath predominantly consists of eta (~ 100 wt.% Zn) and zeta (FeZn13) phases in combination with less extent of delta (FeZn10) and gamma (Fe3Zn10) phases, whereas coatings obtained using Zn-Al alloy baths exhibit zinc-rich phase covered by aluminum rich phase with Al2O3 at the top. Al-rich phase content is higher for Zn-20 wt.% Al alloy coating. The coatings obtained on steel surfaces using both the Zn alloy baths show better ductility compared to pure zinc bath. This can be attributed to the presence of brittle Zn-Fe alloy phase in the coating obtained using pure zinc bath. The coatings obtained using both the Zn alloy baths were found to have a greater passivation characteristics compared to the coating obtained using pure zinc bath without compromising sacrificial characteristic of the coating. Electrochemical and salt spray tests results showed 3 and 6 times improved corrosion resistance properties of Zn-5 wt.% Al and Zn-20 wt.% Al alloy coatings than the pure zinc coating.

Microstructure Evolution and Mechanical Properties of Spark Plasma Sintered Manganese Addition on Ti-48Al-2Cr-2Nb Alloys

Titanium aluminide (TiAl) is one of the most promising materials for aerospace applications. It is a suitable replacement for nickel-based superalloys predominantly used in these applications. Titanium aluminide with superior processability is the main task in carrying out this work. A less brittle TiAl alloy was fabricated using spark plasma sintering by adding the nominal composition (2.5, 5, and 7.5 wt.%) of manganese (Mn) to Ti-48Al-2Cr-2Nb. The samples were sintered at 1150 °C using spark plasma sintering (SPS), which helped produce highly dense models with fine grain sizes at the high heating rate (here, 100 °C per minute). The effects produced by Mn additions on the densification, mechanical properties (yield strength, hardness, and % elongation), and microstructure of the Ti aluminide alloys are studied. Scanning electron microscopy (SEM) has been used to explore the sintered samples’ microstructures. The alloyed materials are entirely dissolved in the gamma matrix due to the manganese approaching its melting point. XRD and SEM analysis confirmed the new intermetallic related to Mn neither with titanium nor aluminum. The enhancement of % elongation at break is evident for the little improvement in the ductility of TiAl by the addition of Mn. The samples’ tensile fracture nature is also evidence for enhancement in the alloy’s % elongation.

Thermomechanical Processing of Cost-Affordable Powder Metallurgy Ti-5Fe Alloys from the Blended Elemental Approach: Microstructure, Tensile Deformation Behavior, and Failure

The development of cost-affordable Ti alloys is key for the application of Ti in other industries like the automobile sector. Therefore, a combination of powder metallurgy (PM) and low-cost compositions is an interesting approach. In this article, a cost-affordable PM Ti-5Fe alloy is processed following the blended elemental route and extruded at high temperature to remove porosity. Different extrusion temperatures and heat treatments (i.e., solution treatment and aging, STA) are performed to obtain ultrafine microstructures, and their effect on the mechanical behavior is studied. For extrusions in the β phase, microstructures consist of coarse lamellar colonies, resulting in alloys with improved properties compared to the as-sintered alloy but still lacking toughness due to the failure happening just after necking onset. Extruding in the α + β phase results in a bimodal microstructure of fine elongated primary α and coarse lamellar colonies, and the alloy becomes tougher. STA with aging below the eutectoid temperature of 590 °C leads to a hard but brittle alloy, whereas STA with aging above it results in alloys with strength comparable to the as-extruded conditions and enhanced ductility.