Fission Reactor Systems Research Articles

Raw Material Effect on the Characteristics of the Fission and Fusion Reactor System

Raw Material Effect on the Characteristics of the Fission and Fusion Reactor System

Thermal hydraulic design and mass optimization of a 100-kWe S-CO2 cooled Mars-surface fission reactor system

Fission reactor with electrical power of 100 kW to megawatt is a promising power option for upcoming deep space exploration. To reduce the number of space launches and the costs, it is necessary to design an energy supply system coupling fission reactor with energy conversion system of high efficiency and compactness. The combination of gas-cooled fast reactor and supercritical carbon dioxide (S-CO2) Brayton cycle has the advantages of simple system layout, compact structure and high thermal efficiency.This paper aims to carry out researches on the thermal hydraulic design and mass optimization of 100kWe reactor system for Mars-surface application.An analysis code which includes thermodynamic models for different components in the system, as well as mass evaluation models for radiator, recuperator and reactor, is developed and validated to provide an analysis tool. An S-CO2 Brayton cycle directly cooled reactor system is proposed, which applies Tube-In-Duct fuel assembly to make up the core and heat pipe radiator as heat rejection system. The thermal hydraulic evaluation of the reactor core, thermodynamic performance evaluation as well as overall mass evaluation of the whole system are carried out to achieve an optimized 100kWe fission reactor system for Mars surface with minimum mass. The optimal design has an operating pressure of 16 MPa, core outlet temperature of 600 °C, radiator panel area of 120 m2 and an overall mass of 1862.98 kg considering the reactor and key components of Brayton cycle. S-CO2 Brayton cycle directly cooled reactor system has a comparable specific mass as He-Xe cooled reactor with lower operating temperature, which is beneficial for material selection and provides another option for space reactor development.

Effect of a Hybrid Fusion Plant Operating in a Fission and Fusion Reactor System on the Fuel Cycle

Effect of a Hybrid Fusion Plant Operating in a Fission and Fusion Reactor System on the Fuel Cycle

Numerical simulation of micro-crack leakage on steam generator heat transfer tube

The pressure relief rate and loss rate of coolant, which affect largely safety of fission reactor systems, are determined by the flashing process inside cracked passages. Information about flashing phenomenon is of great significance for the leakage online monitoring system of SG (Steam Generator), which ensures the normal operation of SG and safety of the reactor system during early stage of tube rupture accidents. In this research, flashing flow inside a thin micro-crack in heat transfer tube of SG has been studied using ANSYS-FLUENT. The classic cavitation model and evaporation–condensation model, in combination with both the mixture two-phase flow model and Eulerian two-fluid model, are adopted to simulate flashing phenomenon. The real geometry and operation conditions of AP1000 nuclear system are adopted to reflect the reality leakage process in SG. Two types of micro-cracks including axial crack and circumferential crack, which both could happen in the reality operations, are considered. The CFD (Computational Fluid Dynamic) results gained from this research have been compared with test data, and good agreement is demonstrated. The results show that the evaporation–condensation model under Eulerian two-fluid model framework behaves superior to the classic cavitation models in simulating the flashing phenomenon after evaluating accuracy of leakage rate and rationality of thermal hydraulic parameters distribution. In addition, two-phase choking flow phenomenon is obtained by decreasing backpressure of cracked tubes. The simulation in this research reveals the flashing process in short and micro-crack and the results could be good reference for leakage prediction of SG under LBB (Leak Before Break) operations to improve operation performance of SG and safety of the whole nuclear power system.

Producing Useful Chemicals Using a Nuclear Reactor

In this paper, the irradiation of glycerol and ethylene glycol by either mixed (neutron-γ) or γ-only (γ) fields at the TRIGA reactor of the Jožef Stefan Institute is described. This is highly relevant to future applications of fission reactor systems to produce useful feedstock derivatives from organic waste, beyond the production of heat and power. Samples of glycerol and ethyl glycol have been exposed to neutron-gamma radiation with fast neutron fluxes ranging from 7.7×1010 to 3×1012 cm−2s−1 and gamma-only irradiation at maximum dose-rates of 492 and 10 kGy hr−1, respectively. A study of the dependence of product yield versus absorbed dose has been conducted, for total dose ranges of 1 to 100 kGy. The products of these exposures have been identified through Gas Chromatography – Mass Spectrometry (GC-MS) techniques. Analysis comparing neutron-gamma irradiated samples of ethylene glycol and glycerol with gamma-irradiated samples shows no detectable qualitative difference between either irradiation type. Although, additional radiolysis products were detected when compared with available literature; ethyl acetate from ethylene glycol and solketal from glycerol. Quantitatively, neutron-gamma irradiation seems to be less effective at producing acetaldehyde from ethylene glycol, compared with gamma-only which can be explained through neutron moderation and consequent heating effects due to the borosilicate vials.

Theoretically and under very special applied conditions a nuclear fission reactor may explode as nuclear bomb

This article/presentation describes a theoretical and applied research in nuclear fission reactor systems. It concerns with theoretical approaches and in very special applied cases consideration where a common nuclear fission reactor system may be considered to explode as nuclear bomb. This research gives critical impacts to the design, operation, management and philosophy of nuclear fission reactors systems. It also includes a sensitivity analysis of a particular applied problem concerning the core melting of a nuclear reactor and its deposit to the bottom of reactor vessel. Specifically, in a typical nuclear fission power reactor system of about 1000 MWe, the nuclear core material (corium) in certain cases can be melted and it may deposited in the bottom of nuclear reactor vessel. So, the nuclear criticality conditions are evaluated for a particular example case(s). Assuming an example composition of melted corium of 98 tones of U238 , 1 tone of U235 , 1 tone Pu239 and 25 tones Fe56 (supporting material) in a 5 m diameter of a finite cylindrical nuclear reactor vessel it is found that it may result in nuclear criticality above the unit. This condition corresponds to Supercritical Fast Nuclear Fission Reactor case, which may under certain very special applied conditions to nuclear explode as nuclear bomb.

Preliminary analysis of reactivity reconstruction capability based on inverse kinetics method under different initial reactivity states

Online reactivity monitoring plays an important role in operation and safety analyses of fission reactor systems. The inverse kinetics method, which is based on a point kinetics model, is the most widely used method for reactivity reconstruction of critical water reactors. However, this method is seldom applied to the reactivity reconstruction of subcritical reactors. In this study, an inverse kinetics method was employed for the reactivity reconstruction of a lead-based reactor under different initial reactivity states (ρ0 = 0, − 2786, − 5486, − 8367, and − 12,371 pcm). The results showed that the deviation in the reactivity of the lead-based subcritical reactor was greater when ρ0 became smaller. The reactivity reconstructed using the inverse kinetics method was globally underestimated. At a given reactivity perturbation, the relative and absolute errors increased with the decrease in the initial reactivity. At a given initial reactivity, with the increase in the reactivity perturbation, the absolute error increased, whereas the relative error remained the same. This deviation is due to the variation in the external neutron source, spatial-spectral effects, and sub-diffusive effects, which require further study.

Helium Interaction with Y2Ti2O7: A First Principles Study

ABSTRACTHelium embrittlement poses a great threat to materials used in both fusion and fissionreactor systems due to (n,α) transmutation reactions. Because of this, materials capable of moderating the helium content reaching grain boundaries and voids must be developed and improved to prevent catastrophic failure of reactor materials. Nanostructured ferritic alloys (NFAs) have shown great promise in preventing helium embrittlement due to the large number density of nanoscale precipitates acting as trapping sites for helium clusters and helium bubbles. In this study, we present density functional theory calculations on the interaction of helium with nanoscale precipitates found in NFAs as a preliminary study to furthering our understanding of the energetic mechanisms causing the precipitates to act as trapping sites for helium.

Effect of thermal cycling of SiCf/SiC composites on their mechanical properties

SiCf/SiC composites are class of high temperature structural materials being developed for use in nuclear fusion and fission reactor systems because of their superior high temperature mechanical properties, low radiation damage and low induced radioactivity. Two types of 2D SiCf/SiC composites were made through isothermal and isobaric chemical vapor infiltration process using eight harness satin-woven ceramic-grades Nicalon™ fibers with boron nitride (BN) interface, namely: one with lower interface thickness and a second type with higher interface thickness. The BN interface was applied to the fiber prior to SiC matrix addition to modify the interfacial bond strength leading to better toughness and improved oxidation resistance. The density achieved was around 2.6g/cc. The composite specimens were subjected to thermal cycling treatment using an in-house furnace. The mechanical properties such as tensile strength, fracture toughness and interfacial bond strength were also studied for all the composites before and after thermal cycling. It is seen from the results that both composites withstood thermal shocks and thermal cycling treatment. It was also concluded from the present work that good balance between load transfer and crack arresting was established.

Engineering of combined valve flow for power conversion system

A computational and experimental study is presented on the combined control and stop valve for power plant turbine system. Combined Airflow Regulation Analysis (CARA) and Combined Airflow Regulation Operation (CARO) are performed to check on hydrodynamic characteristic, which is represented by flow coefficient characteristic, of the control valve in the combined configuration. Air is selected as working fluid in the CARO test. Based on CARA and CARO results, a computational analysis on typical steam turbine system was performed to show the benefit of combined valve compared to the conventional separated stop valve and control valve configuration. The results show that the combined valve turbine system performance is observed to improve over the conventional one. The combined valve is found to not only reduce the pressure loss but also shrink the footprint of the turbine system. The CARA and CARO results can be utilized in the fusion reactor system as well as fission reactor system plus any other power conversion systems.

Recent applications of small-angle neutron scattering in the characterization of irradiated steels for nuclear technologies

Small-angle neutron scattering (SANS) is a powerful experimental tool to investigate the microstructural evolution under irradiation in steels for fission and future fusion reactor systems. We present recent SANS results concerning the modelling of helium bubble growth in F82H-mod. steel implanted with α-particles and the dose dependence of microstructural radiation damage in Eurofer-97 steel for fusion reactors irradiated at 250 °C. The discussion of these results is focussed on the quality of the metallurgical information obtained by such SANS measurements and consequently on their usefulness also for engineering and design purposes.

Analysis of temperature distribution, burn-up and breeding parameters in nuclear fuel rod in fusion-fission reactor system fueled with mixed ThO2-UO2 fuel

Temperature distribution in nuclear fuel rod, burn-up (BU), possibility of nuclear fuel rejuvenation and breeding parameters are investigated for different coolants under various first wall loads (Pw=2, 5 and 7 MW m−2) in a deuterium–tritium driven fusion–fission reactor system, fueled with mixed UO2-ThO2 fuel. The fuel mixture is considered to be mixed with various mixture fractions. A (D-T) fusion reactor acts as an external high energetic (14.1 MeV) neutron source. The plasma chamber dimension, DR, with a line fusion neutron source is 300 cm. In the tritium breeding zone of the blanket Li2O is used and blanket is reflected by graphite for neutron economy. The fissile fuel zone is considered to be cooled with three different coolants [gas (He, CO2), Flibe (Li2BeF4) and natural lithium (Li)] with the volumetric ratio of coolant-to-fuel [e=(Vcoolant/Vfuel)=1:1 (45.515% coolant, 45.515% fuel and 8.971% clad)] for nuclear heat transfer. The behavior of the blankets fueled with mixed fuel mentioned above are observed for 48 months for discrete time intervals of Δt=15 days and by a plant factor of 75%. The fissile fuel zone, containing 10 fuel rod rows in the radial direction, covers the cylindrical fusion plasma chamber. The fissile fuel breeding occurs through the neutron capture reaction in the 232Th (ThO2), in the 238U (UO2) isotopes. As a result of the calculations, fuel mixtures having the best performance parameters have been obtained as follows for different coolants and under the 7 MW m−2 first wall load during operation period without reaching the melting point: • The blanket fueled with 70 wt% UO2−30 wt% ThO2 for Flibe (Li2BeF4) coolant • The blanket fueled with 80 wt% UO2−20 wt% ThO2 for Gas (He, CO2) coolant • The blanket fueled with 90 wt% UO2−10 wt% ThO2 for natural lithium (Li) coolant Clad surface temperature Tc controlled by coolant velocity is taken between certain operation temperatures (Tc=200, 300, 400, 500 and 600°C). The best Cumulative Fissile Fuel Enrichment (CFFE) grade of the nuclear fuel calculated as the sum of the isotopic ratios of all fissile materials (233U, 235U, 239Pu, and 241Pu) is obtained in Flibe (Li2BeF4) coolant blankets, followed by Gas (He, CO2), whereas natural lithium (Li) coolant shows a poor rejuvenation performance in all fuels. CFFE reaches the maximum value (CFFE=10.6200%) in blanket cooled with Li2BeF4 coolant, followed by gas coolant with 9.0319% and natural lithium coolant with 7.9863% without reaching the melting point (Tmax=Tm>2830°C) of the fuel materials. At this point, the maximum temperature in centerline of the fuel rod (Tm) reach to 2727.57°C in blanket cooled with Li2BeF4 coolant. However, in the blanket fueled with pure UO2 fuel and cooled with Flibe, CFFE and Centerline Temperature of the fuel rods (Tm) are reached to 9.7277% and 2811.13°C respectively at the end of 39 months. In the blanket fueled with pure UO2 and cooled with gas, CFFE and Centerline Temperature of the fuel rods (Tm) are reached to 7.8115% and 2814.57°C at the end of 38 months and 7.2777% and 2724.34°C at the end of the 43 months in the blanket cooled with natural Li. In the blanket fueled with pure ThO2, CFFE reaches the maximum value with 9.2843% in the blanket cooled with Flibe. The enrichment is sufficient for LWR reactor. The temporal change of the fuel composition during the hybrid reactor plant operation and the most pertinent nuclear reactions been considered in the course of BU. The BU reaches the maximum value (72 749.1 MWd t−1 (tone)) in the gas coolant blanket, followed by Flibe coolant blanket with 67 641.0 MWd t−1 natural lithium coolant blanket with 63 897.5 MWd t−1 during the operation period without reaching the melting point. Copyright © 2010 John Wiley & Sons, Ltd.

Theoretical cross sections of 209Bi, 232Th, 235U and 238U on deuteron-induced reactions

There are many application fields for fast neutrons. The main application fields of the fast neutrons are accelerator-driven sub-critical systems (ADS) and fusion–fission (hybrid) reactor systems for fission energy production. Thorium (Th) and uranium (U) are nuclear fuels in fusion–fission (hybrid) reactor systems and bismuth (Bi) is also the target nucleus in the ADS reactor systems. In this study, neutron production cross sections produced by (d, xn) reactions for spallation targets such as 209Bi, 232Th, 235U and 238U have been investigated. New evaluated hybrid model and geometry dependent hybrid model have been used to calculate the pre-equilibrium neutron production cross sections. For the reaction equilibrium component, Weisskopf–Ewing model calculations have been preferred. The obtained results have been discussed and compared with the available experimental data and found in agreement with each other.

Innovative materials for energy technology

Abstract High performance materials are indispensable for economical and environmentally acceptable operation of fusion power and innovative fission reactor systems. In order to provide materials design data for short term needs of the ITER Test Blanket Modules and for a Fusion Demonstration Reactor, the international fusion materials community is concentrating their R&D work mainly on the four reduced-activation structural materials 8 – 9 CrWTa ferritic/martensitic steels, V – Ti – Cr alloys, W alloys and SiCf/SiC composites as well as on functional materials such as CVD diamond windows. Besides the development of the European reduced activation reference steel EUROFER, emphasis will be placed on synergies between fusion and fission materials R&D, namely the development of ductile oxide dispersion strengthened ferritic/martensitic steels with nano-scaled Y2O3 or Y2Ti2O7 particles that increase not only high temperature strength but also substantially the microstructural stability against irradiation embrittlement and high temperature ageing. Finally, the corrosion behaviour of zirconium-1.5 wt.% tin alloy, a well established cladding material for nuclear fuel rods, will be shown in different environments.

Synergies in the design and development of fusion and generation IV fission reactors

Future fusion reactor and Generation IV fission reactor systems are designed and developed in worldwide programmes to investigate and assess their potential for realisation and contribution to the future energy needs beyond 2030 mostly involving the same partners. Huge scientific and financial effort is necessary to meet these objectives. First programmes have been launched in Generation IV International Forum (GIF) for fission and in the Broader Approach for fusion reactor system development. Except for the physics basis for the energy source, future fusion and fission reactors, in particular those with fast neutron core, face similar design issues and development needs. Therefore, the call for the identification of synergies became evident. Beyond ITER cooled by water, future fusion reactor systems will be designed for high-temperature helium and liquid metal cooling but also water including supercritical water and molten salt similar to those proposed for some of the six fission reactor concepts in GIF with their diverse coolants. Beside materials developments which are not discussed in this paper, design and performance of components and systems related to the diverse coolants including lifetime and maintenance aspects might offer significant potentials for synergies. Furthermore, the use of process heat for applications in addition to electricity production as well as their safety approaches can create synergistic design and development programmes. Therefore, an early identification of possible synergies in the relevant programmes should be endorsed to minimise the effort for future power plants in terms of investments and resources. In addition to a general overview of a possible synergistic work programme which promotes the interaction between fusion and fission programmes towards an integrated organisation of their design and R&D programmes, some specific remarks will be given for joint design tools, numerical code systems and joint experiments in support of common technologies.

Investigation of the properties of the nuclei used on the new generation reactor technology systems

The main application fields of the fast neutrons are accelerator-driven subcritical systems (ADS) and fusion–fission (hybrid) reactor systems for fission energy production. Thorium (Th) and uranium (U) are nuclear fuels in these reactor systems. Lead (Pb), bismuth (Bi) and tungsten (W) are the target nuclei in the ADS reactor systems. The technical design of ADS and hybrid reactor systems require much effort and data. The Hartree–Fock (H–F) method with an effective interaction with Skyrme forces is widely used for studying the properties of nuclei such as binding energy, root mean square (RMS) charge radii, mass radii, neutron density, proton density, electromagnetic multipole moments, etc. In this study, by using H–F method with interaction Skyrme RMS charge radii, RMS mass radii, neutron density and proton density were calculated for the 232Th, 238U, 207Pb, 209Bi and 184W isotopes. The calculation results of charge radii were compared with experimental data. Obtained RMS mass radii, neutron density and proton density results were discussed for ADS and hybrid reactor systems.

Materials degradation in fission reactors: Lessons learned of relevance to fusion reactor systems

The management of materials in power reactor systems has become a critically important activity in assuring the safe, reliable and economical operation of these facilities. Over the years, the commercial nuclear power reactor industry has faced numerous ‘surprises’ and unexpected occurrences in materials. Mitigation strategies have sometimes solved one problem at the expense of creating another. Other problems have been solved successfully and have motivated the development of techniques to foresee problems before they occur. This paper focuses on three aspects of fission reactor experience that may benefit future fusion systems. The first is identification of parameters and processes that have had a large impact on the behavior of materials in fission systems such as temperature, dose rate, surface condition, gradients, metallurgical variability and effects of the environment. The second is the development of materials performance and failure models to provide a basis for assuring component integrity. Last is the development of proactive materials management programs that identify and pre-empt degradation processes before they can become problems. These aspects of LWR experience along with the growing experience with materials in the more demanding advanced fission reactor systems form the basis for a set of ‘lessons learned’ to aid in the successful management of materials in fusion reactor systems.

Synergies Between Generation-IV and Advanced Fusion Power Plant Research Programs

For the first time since the early 1990’s, the U.S. Department of Energy has long term research and development programs in both nuclear fission and nuclear fusion, the Generation IV program and the ARIES program, respectively. The Generation IV program has introduced a safety goal for future fission reactor systems that has long been reflected in the ARIES mission: no off-site emergency response to any design basis accident. This change, in concert with the overall departure from light water reactor technology, will drive a change in the regulatory framework for both Generation IV reactors and fusion power plants of the future. Further, both fission and fusion power plants will have to compete in similar future energy markets with uncertainties in energy prices and the development of alternative energy products. Enabling the success of nuclear energy, advanced materials will be a cornerstone to both programs, driven both by higher temperatures and heat fluxes and by a desire for longer lifetimes in high radiation environments. The synergies created by these increasingly parallel programs open the door for renewed collaborations that will increase the total effectiveness of research needed in both.

The implication of high-flux fusion neutron source for the self-consistency in multi-component nuclear energy system

Among fission products (FP) discharged from a fission reactor, long-lived fission products are considered as of primary concern. Their transmutation has been of high priority to reduce the long-term consequences of nuclear energy generation. A self-consistent nuclear energy system (SCNES) in which we center fast breeder reactor may not have enough degree of excess neutron sources to transmute the fission products that potentially would poses environmental hazards in long-term period if they are buried in geologic disposal. Here we propose a so-called multi-component SCNES in which fission reactor systems can be combined with fusion reactor systems mainly for compensating the loss of enough capability for the transmutation. Amongst long-lived fission products, major concern has been paid for iodine and technetium and little attention was given to radioactive 93Zr, although its hazard appears to be rather substantial. The importance of 93Zr transmutation is emphasized and the transmutation capability was examined with fusion neutron sources by incorporating adequate moderation structures. As a result, we have demonstrated that the fusion neutron sources with high-flux blanket can be applied to transmute 93Zr sufficiently and resolve the problem of its accumulation within the time period of several decades.

Investigation of the performance parameters and temperature distribution in fuel rod dependent on operation periods and first wall loads in fusion–fission reactor system fueled with ThO 2

The neutronic performance parameters, fissile breeding and temperature distribution in the fuel rod are investigated for different coolants (‘He, CO 2’, ‘Li 2BeF 4’, ‘Li’, and ‘Li 17Pb 83’) in the fissile fuel breeding zone with volume ratios of V coolant/ V fuel, ε, (0.5,1,2) under various first wall loads ( P w=2–10 MW m −2) in a fusion–fission reactor fueled with ThO 2. Depending on the type of coolant in the fission zone, first wall loads and volume ratios, fusion power plant operation periods between 1 and 4 years are evaluated to achieve a fissile fuel enrichment quality between 1.2274% and 13.7305% in the above mentioned situation for intervals of half month and by plant factor of 75%. A fusion reactor with (D,T) reaction acts as an external high energetic neutron source. The fissile fuel zone, containing 10 fuel rod rows in the radial direction, covers the cylindrical fusion plasma chamber with 300 cm chamber dimension. At the end of four years, the cumulative fissile fuel enrichment (CFFE) values, indicating rejuvenation performance, increased to 10.184%, 12.218%, 9.650% and 11.089% from 0% in gas, flibe, natural lithium and eutectic lithium coolant blankets with ε=0.5 for 10 MW m −2, respectively, without reaching the melting point of the fuel material. However, for ε=1, the CFFE values increased to 10.59% (the best CFFE value for gas coolant), 11.372%, 10.414% (the best CFFE value for natural lithium coolant) and 10.963% from 0% in the above mentioned coolants for 10 MW m −2, respectively. In the same way, for ε=2, the CFFE increased to 10.181%, 13.7305% (the best CFFE value for all coolants), 9.1369% and 11.4809% (the best CFFE value for eutectic lithium coolant) for 10 MW m −2, respectively. At the beginning of the operation period, for ε=0.5, the tritium breeding ratio (TBR) values, being about 0.9092, 0.7075, 0.7921 and 0.9512 for the above mentioned coolants, respectively, at the end of four years increased to 1.2924, 1.1475, 1.0724 and 1.441 (the highest TBR value for all blankets) for 10 MW m −2. For ε=1, these increments are 1.3067, 1.2303, 1.1653 and 1.4033 for 10 MW m −2. However, for ε=2, these values are 1.2256, 0.9993, 0.9341 and 1.4069 for 10 MW m −2 without reaching the melting point of the fuel material. For ε=0.5, the blanket energy multiplication ( M) increases to 2.7349, 2.8045, 2.5685 and 2.8183 (the highest M value for all blankets) for 10 MW m −2 from 2.1534, 2.0251, 2.0918 and 2.0793 in the blankets cooled with gas, flibe, natural lithium and eutectic lithium coolants, respectively, at the end of four years. These increments become 2.6707, 2.7301, 2.4332 and 2.7812 for 10 MW m −2 from 2.1037, 1.8985, 2.004 and 1.9874, respectively, for ε=1. However, the blanket energy multiplication ( M) increases to 2.4122, 2.4573, 2.1413 and 2.3800 for 10 MW m −2 from 2.0196, 1.7323, 1.8658 and 1.8303, respectively, for ε=2. The maximum temperatures in the centerline of the fuel rods have not exceeded the melting point of the fuel material for all coolants and ε under changing first wall loads between 2 and 10 MW m −2 during the operation periods. While the maximum CFFE values have been obtained in fuel rod row#10 in the gas, natural lithium and eutectic lithium coolant blankets, it has been obtained in fuel rod row#1 in the flibe coolant blanket for all ε and P w. Therefore, the investigated hybrid blankets are self-sufficient for all coolant and volume fractions and P w=10 MW m −2. The best neutron economy has been shown by flibe.