Neutron Absorber Materials Research Articles

COOLING OF CONTROL RODS AND SPECIFICATION OF CRITICAL TEMPERATURES TO JUSTIFY SAFE OPERATION

The paper analyzes the cooling conditions of the control rods in the mixed core of the WWER-1000 reactor containing fuel assemblies of different vendors (TVSA, WFA/RWFA). The coolant heat-up in the guide thimbles due to own energy release in control rod materials and control rod temperatures required to justify safe operation were calculated for the most conservative case, when the core consists only of TVSAs with a standardized guide thimble inlet plug of NCCP. The energy release was obtained using the calculation method for the boron carbide absorber (B4C), dysprosium titanate (Dy2O3·TiO2), control rod cladding (42CrNiMo), water gap between the cladding and the guide thimble and in the guide thimble (zirconium alloy), fully immersed and 70% immersed RCCA 10th control group. The highest calculated energy release will be observed in fully immersed control rods with boron carbide material at the height position corresponding to the zone of maximum neutron fluence and will be 43.8 W/cm3. The maximum energy release of the 70% immersed (from the bottom of the core) 10th control group is 29.4 W/cm3 for fresh B4C. For the condition of the reactor facility at which the temperatures in FA guide thimbles are maximum, for a "fresh" control rod characterized by maximum energy release in the neutron-absorbing material, the maximum coolant heat-up in the guide thimbles does not exceed 28.9 °C, with the maximum coolant heat-up in FAs being 44 °C, and the maximum control rod cladding temperature not exceeding 335.6 °C at a coolant saturation temperature of 345.8 °C, which indicates that there will be no coolant boiling in the guide thimbles under operation. The maximum temperature typical for the central part of the control rod absorber and for the most conservative calculation for a "fresh" absorber is 529.6 °C, which is significantly lower the melting point of boron carbide, which is ~2350 °C. The maximum calculated temperature in the contact zone of the B4C absorber with control rod cladding is 348 °C. The performed calculations and further analysis of the results confirm that during operation of the RCCA control rods with both “fresh” and “burned-up” B4C, there will be no boiling of the coolant and melting of the absorber in the central part of the control rod. This means that the VVER-1000 core with TVSAs and WFAs/RWFAs and the RCCA rods are reliably cooled.

SYNTHESIS OF MATERIALS BASED ON COMPOUNDS OF RARE EARTH ELEMENTS WITH TITANIUM, HAFNIUM AND ZIRCONIUM AS PROMISING NEUTRON ABSORBERS FOR NUCLEAR REACTORS

A review of the methods for the synthesis of titanates, hafnates, and zirconates of rare earth elements, primarily dysprosium, which have been applied as neutron-absorbing materials for nuclear reactors or are promising due to their high radiation resistance, phase stability, compatibility with structural materials, and corrosion resistance is presented. The characteristics of titanates, hafnates, and zirconates of dysprosium obtained by these methods are presented: high-temperature solid-phase synthesis in compacted mixtures of initial oxides; induction melting of oxides in a “cold” container; chemical methods based on co-precipitation and heat treatment of aqueous solutions; mechanochemical activation of oxide powders in planetary mills followed by heat treatment; plasma-chemical syn-thesis.

Neutron shielding performance of Cd/316L composite fabricated by arc plasma sintering

Ensuring subcriticality over storage duration, even in accident condition, is one of the important requirements for dry cask designed to store spent fuel from nuclear reactor. To comply this requirement, neutron absorbers are incorporated in the spent fuel basket to decrease the neutron multiplication factor and reactivity. The objectives of this study are to prepare Cd/316L composite for neutron absorber material by powder metallurgy and determine the neutron shielding performance of the obtained composite. Powder mixtures of SS316L with various Cd contents were milled using high energy milling, followed by pressing and sintering at 450 °C and 700 °C. The analyses of the samples were carried out using XRD, SEM-EDS, XRF, and neutron transmittance test. Additionally, the neutron transmittance was also calculated using MCNP5. The results show that transformation of austenite to α-ferrite occurred during powder milling process which remained in the sample after sintering at 450 °C. Transformation of α-ferrite in the milled sample to austenite occurred after sintering at 700 °C. Cd in the samples were predominantly oxidized to form CdO phase during sintering process at both temperature conditions. The loss of Cd content in the Cd/SS316L samples after milling process was approximately 10 %. The Cd content further decreased by approximately 10 and 50 % after sintering at 450 and 700 °C, respectively. Neutron transmittance test shows that the transmittance value for thermal neutron decreased with the increased of Cd in the Cd/316 sample. A good agreement has been obtained between the results from experiment and MCNP calculation.

Al–B4C-(Gd, Gd2O3) composite materials: Synthesis and characterization for neutron shielding applications

In this study, Al–20%B4C-x%Gd and Al–20%B4C-x%Gd2O3 (x = 1, 3, 5) composite powders were prepared using a high-energy planetary ball milling method to enhance the physical properties of Al–B4C neutron shielding composites. The prepared powders were subjected to uniaxial cold compaction at 500 MPa, resulting in cylindrical specimens. Subsequently, the specimens were sintered in a tube furnace at 600 °C for 1 h under an Ar atmosphere to prevent oxidation. The microstructure of the resulting composites was characterized using X-ray diffraction (XRD) and scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM/EDX). Archimedes density, hardness, and corrosion tests were performed on the compacted samples. Moreover, the composite's thermal and fast neutron absorption rates were calculated using the MCNP6.2 simulation code. The neutron equivalent dose rate was experimentally determined using the Am–Be neutron source. The simulation results demonstrated that the composite materials containing Gd exhibited the highest thermal neutron absorption rate, while those containing Gd2O3 demonstrated the highest fast neutron absorption rate. This research contributes valuable insights into the design and utilization of neutron-absorbing materials with suitable mechanical properties.

Effect of Al2O3 on the Mechanical Properties of (B4C + Al2O3)/Al Neutron Absorbing Materials

Effect of Al2O3 on the Mechanical Properties of (B4C + Al2O3)/Al Neutron Absorbing Materials

Materials Science Analysis of RCCA Structural Materials and Calculations for Lifetime Extension

The paper considers the possibility of lifetime extending of the rod control cluster assemblies in operation by determining their residual lifetime using an approach that takes into account the actual position of the rod control cluster assembly in the core. Excessive conservatism was introduced by assuming that the immersion of the 10th working group in the core during all fuel campaigns is 70 %, while the actual position is 85-90 %. Taking into account the actual position of the rod control cluster assemblies indicates much less irradiation of the lower, most loaded part of control rod cladding and much less burnup of the 10B compared to 70 % immersion of the rod control cluster assemblies, since they are in the area of lower neutron flux density.
 The results of a comprehensive analysis of available studies and test results to determine the phenomena that can potentially approach the achievement of the boundary state of the structural components or limit the lifetime of control rods and rod control cluster assemblies in general are presented. Such phenomena include general corrosion of structural materials (42CrNiMo, Cr18Ni10Ti) (decrease in wall thickness, increased transfer of radioactive corrosion products the coolant); radiation resistance (degradation of mechanical characteristics) of control rod cladding materials (42CrNiMo) and other structural components of the rod control cluster assemblies (42CrNiMo, CrKh18Ni10Ti); radiation resistance of neutron-absorbing materials (B4C, Dy2O3∙TiO2); compatibility of absorbing materials with the control rod cladding.
 Based on the results of post-irradiation examinations of control rods tested in research reactors as dummy rods or rod control cluster assembly rods operated in the VVER-1000 core, the following boundary values were established that can be used as criteria for maintaining the integrity of the control rod cladding: maximum fast neutron fluence in the lower, most loaded part of the control rod cladding (in the weld area of the lower end plug and the cladding) should not exceed 34×1021 n/cm2; maximum burnup of the 10B isotope should not exceed 45 %. If these two criteria are met, the possibility of other potentially damaging phenomena is too low.
 According to the calculations that use the schedule of changes in the position of the rod control cluster assemblies of the control group and the power of one of the power units during one fuel cycle, one can preliminary conclude that the proposed approach will extend the lifetime of almost all rod control cluster assemblies from 25500 to 38000 hours in the automatic control group and from 75600 to 113500 hours in the shutdown group. The residual lifetime should be assessed for a particular power unit and each rod control cluster assembly separately, since each rod control cluster assembly has its own operating history.

Thermodynamic equilibrium state calculations for oxidation and corrosion reactions of B4C and oxide-based neutron absorber compounds in reactor control rods

The challenges associated with conventional boron carbide (B4C) control rod materials, including helium gas accumulation and susceptibility to oxidation and corrosion in various environments, have been thoroughly explored. To address these issues, a comprehensive investigation into the potential of oxide-based neutron absorber compounds for control rods has been undertaken. Thermodynamic equilibrium state calculations have been conducted to assess the oxidation and corrosion reactions of various neutron absorber materials (Gd, Hf, Sm, Er, Eu, Dy-based oxide), including B4C, in various environments such as oxygen, steam, air, and air–steam mixtures. The results have unveiled vulnerabilities of B4C in these environments, notably the generation of gases such as H2, CO, and boron compounds. Furthermore, neutron absorber oxide materials have exhibited potential susceptibility to oxidation and corrosion in steam environments. Consequently, the potential of oxide-based neutron absorber compounds, formed by combining neutron absorber oxide materials with highly oxidation-resistant substances (ZrO2, TiO2), has been explored. Thermodynamic equilibrium state calculations indicate that these compounds maintain robust resistance to oxidation and corrosion across various environments. This paper demonstrates the superiority of oxide-based neutron absorber compounds as alternatives to existing boron carbide neutron absorber materials. Additionally, the oxide-based neutron absorber compounds are expected to extend the lifetime of the LWR control rod as well as improve stability and resistance to oxidation and corrosion.

I-LAMP: Global, Industrywide Learning Aging Management Program for Neutron-Absorber Materials in Spent Fuel Pools

Neutron-absorber materials are used in spent fuel pool (SFP) storage racks to increase storage capacity while maintaining criticality safety margins. Previously, the Electric Power Research Institute (EPRI) proposed a global, industrywide learning aging management program (i-LAMP) as an alternative monitoring program as part of an aging management program. This proposal, along with other EPRI work, was accepted as a concept to close the issued generic letter by the regulator. Since then, EPRI has been working with EPRI-member utilities around the world on data collection. Furthermore, recently, a utility removed two neutron-absorber panels from an operating SFP to meet a regulatory commitment made prior to the i-LAMP proposal. Because of their age and unique history, these panels provided a unique opportunity not only to analyze the conditions of the panels, but also to potentially bound i-LAMP. This paper presents i-LAMP development to date with a focus on BORAL analysis results for these two unique panels, pilot pools as case studies to demonstrate the i-LAMP implementation, and a proposal for a path forward.

Characterization of Various Stainless Steels Containing Gadolinium as Thermal Neutron Absorbing and Shielding Materials

Developing next-generation thermal-neutron-shielding and -absorbing materials for the safe storage and transportation of spent nuclear fuel is a topic of active research in academia. Gadolinium (Gd) boasts superior neutron absorption capacity compared with other nuclei. Consequently, it has garnered significant attention as a potential replacement for boron in spent nuclear fuel (SNF) applications. In this study, the austenitic stainless steels 304 and 316 and the duplex stainless steel 5A were reinforced with 2 wt.% of gadolinium to explore their thermal-neutron-absorbing efficiency. Their properties were then compared with commercial-grade borated stainless steel, as per ASTM standard A887. After the inclusion of Gd, both the yield strength and ultimate tensile strength of the alloys slightly increased, which was attributed to the evenly distributed Gd intermetallics within the matrix. However, the elongation rate was reduced. The Charpy impact absorption energy also decreased. The influence of the Gd intermetallic was further explored by examining the fractography. While the corrosion resistance of the alloy slightly diminished after the addition of Gd, its neutron absorption capacity demonstrated superior performance, especially when the Gd content was equivalent to that of boron. Although most properties of the experimental alloy deteriorated after the Gd addition, they still outperformed commercial borated stainless steel, suggesting that this alloy might be a promising candidate for SNF applications.

Uniformity of neutron absorber distribution in Gd-containing neutron absorber materials

For neutron absorber materials (NAMs), it is important to evaluate their neutron-absorption capability and quantitatively evaluate the uniformity of the distribution of neutron-absorbing elements within the materials. In this study, neutron attenuation testing with cold neutrons was conducted on Ti-based model alloys with Gd concentrations ranging from 1 to 10 wt%. The neutron attenuation coefficients (μ) of the Ti-Gd alloys were determined and compared with the total macroscopic cross sections (Σt), which were computed using the latest ENDF/B library. Although the measured μ increases with the Gd-content, the coefficients were not linearly proportional to the absorber amount, and the ratio of μ to Σt gradually decreased. This was caused by beam hardening, which is more significant for higher-absorbing and thicker NAMs. To examine the uniformity of the neutron absorbers (NAs) in plates, we propose a method for characterizing the degree of homogeneity by introducing a radial distribution function (RDF). After the optical microscopic images of the Ti-Gd alloys were converted to grayscale, the RDF of the Gd particles in the alloys was calculated under the assumption that a large particle is composed of many adjacent unit particles. A unit particle was regarded as one pixel in the digital image. For all Ti-Gd alloys, the RDF had a value of > 1 at short interparticle distances, which indicated a dense population of particles in a small area due to cluster formation. The method of using the RDF as a uniformity parameter was validated through a case study involving a fixed NA content with different distributions.

A neutron source for the study of biological objects formed from superficially touching cones made of borated spheroplastics

At the Prometheus medical accelerator with a proton beam energy of 225 MeV, a source of fast and epithermal neutrons was constructed and measurements of neutron dose profiles at the output of the neutron channel were carried out using the BDMN-100 detector. A heavy NaI target was used to produce fast neutrons. Together with the research laboratory of the Central Laboratory of Avangard JSC, a new protective material against neutrons called wikineutron was developed, with a different percentage of 10B. This new material has been studied many times at the Prometheus proton accelerator and the Pakhra electron accelerator. Based on the developed new protective materials against neutrons, a shadow protection was formed, made in the form of surface contacting cones, forming a channel of fast and epithermal neutrons. Fast neutrons can be used for remote therapy. Also, a neutron beam can be used to study biological objects and cells. It is also possible to use a neutron source from the Prometheus accelerator for the treatment of superficial tumors. The developed neutron channel can be used for medical work on the creation of new radiopharmaceuticals containing boron and other highly absorbing elements. The developed neutron source is a compact low-power source of therapeutic neutrons, which can be used for the treatment of superficial types of cancer. The main goal of the work was: the formation, based on the developed neutron-absorbing materials, of a neutron channel, which has a simple design and can be used for boron-neutron capture therapy and nadepithermal therapy; creation on the neutron channel of a beam of epithermal neutrons and supra-epithermal neutrons to assess the effectiveness of the use of radiopharmaceuticals.The developed neutron-absorbing materials made it possible to create a neutron channel of epithermal neutrons and supra-epithermal neutrons for therapy and the development of gold-based radiosensitizers.

Comparing the effects of various (p,xn) radionuclide production routes on induced radioactivity in the concrete walls of a cyclotron vault.

In sum, 11 (p,xn) related nuclear reactions with 9 target materials, namely 18O(p,n)18F, 15N(p,n)15O, 68Zn(p,n)68Ga, 68Zn(p,2n)67Ga, 69Ga(p,2n)68Ge, 89Y(p,n)89Zr, 100Mo(p,pn)99Mo, 100Mo(p,2n)99mTc, 112Cd(p,2n)111In, 124Xe(p,2n)123Cs and 203Tl(p,3n)201Pb, are involved in the operation of 13 radionuclide-production cyclotrons in Taiwan. The secondary neutrons accompanying these production routes could induce varying degrees of material activation in the cyclotron facility. Accordingly, this study compared the effects of various (p,xn) production routes on the neutron-induced long-lived radioactivity in the concrete walls of a hypothetical cyclotron vault. In addition, an activation-reduction approach involving the addition of a layer of neutron-absorbing material to the surface of inner concrete walls was evaluated.

Development of a conceptual scheme for the creation of environmentally friendly Gd-containing neutron-absorbing nanocomposites

The nature and properties of neutron radiation impose specific requirements on the creation and operation of such materials. The presence of accompanying and induced radiation, weather conditions, as well as the peculiarities of the location of functional layers require a hierarchical approach to the development of such neutron-absorbing materials. It was shown that the conceptual scheme of creating Gd-containing protective materials consists in taking into account all factors of their operation. In particular, it is shown that the presence of neutron-absorbing components is a necessary but not sufficient condition for their successful application in environmental conditions. In this work, Gd-containing chitosan films were prepared as an example of the proposed conceptual scheme for the creation of environmentally friendly neutron-absorbing nanocomposites. The prepared Gd films were characterized and their neutron permeability was estimated. The approach presented in this work contributes to the development of sustainable and responsible production practices, supporting SDGs 9 and 12.

Preparation and properties of Gd2O3–Eu2O3–ZrO2 ceramics as promising control rod material

Gray control rods enable the safe operation of nuclear reactors by controlling and adjusting nuclear reactivity, in which neutron-absorbing materials with low reactive worth loss play an important role. In this work, new types of Gd2O3–Eu2O3–ZrO2 ceramics used as neutron absorbers are successfully prepared by simple thermal decomposition following the air sintering method. The cross-sectional SEM images and density curves of ceramics are analyzed, and the ceramic with a content of 85 wt% Eu2O3 sintered at 1500 °C presents a higher density (7.193 g/cm3) than other samples. When the content of Eu2O3 is 70 wt%, the Vickers hardness of the sintered ceramic is 4.89 GPa, which is higher than 4.01 GPa of Eu2O3 (sintered at 1500 °C). This material, which is easy to prepare and has good properties, is regarded as a potential reactor control rod material.

Thermomechanical Properties of Neutron Irradiated Al3Hf-Al Thermal Neutron Absorber Materials.

A thermal neutron absorber material composed of Al3Hf particles in an aluminum matrix is under development for the Advanced Test Reactor. This metal matrix composite was fabricated via hot pressing of high-purity aluminum and micrometer-size Al3Hf powders at volume fractions of 20.0, 28.4, and 36.5%. Room temperature tensile and hardness testing of unirradiated specimens revealed a linear relationship between volume fraction and strength, while the tensile data showed a strong decrease in elongation between the 20 and 36.5% volume fraction materials. Tensile tests conducted at 200 °C on unirradiated material revealed similar trends. Evaluations were then conducted on specimens irradiated at 66 to 75 °C to four dose levels ranging from approximately 1 to 4 dpa. Tensile properties exhibited the typical increase in strength and decrease in ductility with dose that are common for metallic materials irradiated at ≤0.4Tm. Hardness also increased with neutron dose. The difference in strength between the three different volume fraction materials was roughly constant as the dose increased. Nanoindentation measurements of Al3Hf particles in the 28.4 vol% material showed the expected trend of increased hardness with irradiation dose. Transmission electron microscopy revealed oxygen at the interface between the Al3Hf particles and aluminum matrix in the irradiated material. Scanning electron microscopy of the exterior surface of tensile tested specimens revealed that deformation of the material occurs via plastic deformation of the Al matrix, cracking of the Al3Hf particles, and to a lesser extent, tearing of the matrix away from the particles. The fracture surface of an irradiated 28.4 vol% specimen showed failure by brittle fracture in the particles and ductile tearing of the aluminum matrix with no loss of cohesion between the particles and matrix. The coefficient of thermal expansion decreased upon irradiation, with a maximum change of -6.3% for the annealed irradiated 36.5 vol% specimen.

Application of data assimilation in searching better lattice-physics parameters of fuel assembly

This study aims to apply the data assimilation technique to adjust the fuel enrichment to find a better performance of the fuel assembly lattice-physics parameters. In this study, the STARU data assimilation, which can deal with the highly non-linear system behaviors and many parameters, was implemented; and MCNP6 was used to evaluate the lattice-physics parameters of the fuel assembly. Furthermore, restriction and non-restriction sampling algorithms were employed to efficiently find the enhanced candidates for the NuScale fuel assembly. We found that the improvements were up to 0.1 w/o, and the fuel depletion of the optimal candidate was compared well with the equivalenced enrichment of the typical fuel assembly. Eventually, the conceptual design configuration was proposed using the alpha and theta requirements for adjusting the fuel rod dimensions and enrichments, methodically. Consequently, the proposed conceptual design illustrated an excellent performance of the lattice-physics parameters such as high k∞-value and low PPPF. Nevertheless, the burn-up performance of the proposed conceptual design was slightly poor compared with the NFAC-01. Future studies should examine the application of neutron absorber materials to overcome this limitation.

Evaluation of BORAL Panels from an Operating Spent Fuel Pool

Neutron absorber materials are used in spent fuel pool (SFP) storage racks to increase storage capacity while maintaining criticality safety margins. BORAL is the most commonly used neutron absorber material in SFPs in the United States and is used in many countries, including England, Mexico, Korea, and Taiwan. This paper presents the results from an analysis of neutron absorber panels that were removed from an operating SFP. These panels provide very valuable data points due to their age and unique history since they represent rack modules that were placed in two separate SFPs. Given their history and service time, these neutron absorber panels mostly bound the absorber panels within the industry.

Neutron calorimeter development at fission and fusion pulsed neutron sources

A neutron calorimeter fielded in pulsed neutron irradiation experiments at the National Ignition Facility (NIF) and White Sands Missile Range Fast Burst Reactor (WSMR FBR) is described, and results are provided and discussed. The calorimeter is modular in design to allow fielding of various neutron absorber materials and thicknesses, as well as use at both fission and fusion sources, all of which has been done. Neutron calorimeters designed for fission sources have been fielded at fusion sources as well, but these instances are not documented in available literature—making this work novel. The functional calorimeter consists of a neutron absorber and two sheathed, grounded thermocouples secured within a subassembly made of thermally insulating materials. This subassembly is placed into a sealed vessel for material and facility safety considerations. The device was fielded at NIF in four polar-direct-drive exploding pusher shots and eleven WSMR FBR pulses. Calorimeter data from NIF experiments show a discernable thermal response accredited to neutron heating within the first 10 s, but the data are dominated by noise from ambient X-ray heating after time = 10 s post-pulse. This response is highly consistent between shots and linearly related to incident neutron fluence and neutron absorber thickness. A temperature rise of 1.1E−2 K/(1013 neutrons/cm2) per millimeter of absorber thickness was determined for both 0.4 mm and 1 mm thick depleted uranium absorbers with linear best fit R2 of 0.97 and 0.98 for each thickness and y-axis offsets of 8.8E−3 and 1.3E−2, respectively. WSMR FBR experiment data show a temperature rise of 6.2E−2 K/(1013 neutrons/cm2) with linear best fit R2 of 0.14 and y-axis offset of 7.6E−3 for a calorimeter with a 1 mm thick enriched boron carbide (10B4C) absorber, though it must be noted that device-to-device variability is significant at both facilities. These data are also affected by noise on a similar timescale as at NIF, though the noise is significantly lesser in magnitude but oscillatory.

Fixed neutron absorbers for improved nuclear safety and better economics in nuclear fuel storage, transport and disposal

Current designs of both large reactor units and small modular reactors utilize a nuclear fuel with increasing enrichment. This increasing demand for better nuclear fuel utilization is a challenge for nuclear fuel handling facilities. The operation with higher enriched fuels leads to reduced reserves to legislative and safety criticality limits of spent fuel transport, storage and final disposal facilities. Design changes in these facilities are restricted due to a boron content in steel and aluminum alloys that are limited by rolling, extrusion, welding and other manufacturing processes. One possible solution for spent fuel pools and casks is the burnup credit method that allows decreasing very high safety margins associated with the fresh fuel assumption in spent fuel facilities. This solution can be supplemented or replaced by an alternative solution based on placing the neutron absorber material directly into the fuel assembly, where its efficiency is higher than between fuel assemblies. A neutron absorber permanently fixed in guide tubes decreases system reactivity more efficiently than absorber sheets between the fuel assemblies. The paper summarizes possibilities of fixed neutron absorbers for various nuclear fuel and fuel handling facilities. Moreover, an absorber material was optimized to propose alternative options to boron. Multiple effective absorbers that do not require steel or aluminum alloy compatibility are discussed because fixed absorbers are placed inside zirconium or steel cladding.

Discussion of options to increase the control drum worth in fast reactor

Abstract The control drum is usually placed in the periphery of the active zone of the reactor core, and the control drum worth is generally small. This paper discusses different schemes to improve the control drum worth by the combination of neutron reflectors and absorbers, and the design optimization of the drums under the condition that external dimensions of the drums and positions of the drums relative to the core are fixed. The results show that BeO as the reflector, B4C and Gadolinium as the neutron absorber can obtain relatively higher drum worth. In addition, the control drum worth can also be appropriately improved by using a double-layer combination of moderator material and neutron absorber material, but it cannot be effectively improved by enlarging the central angle of the neutron absorber sector.