As this review has illustrated, ZrC possesses a combi­nation of thermodynamic, thermal, and mechanical properties that are promising for nuclear fuel appli­cations requiring high-temperature resistance and structural integrity. However, it is also clear that more data are needed. The body of mechanical prop­erty data is limited. The degree of scatter in experi­mental data indicates that methods for fabricating dense, pure, homogeneous, stoichiometric ZrC are not mature. Properties of ZrC are known to be affected by oxygen and nitrogen impurities, but the thermodynamics of the Zr-C-O-N system has not been elaborated. The effects of irradiation on prop­erties and performance must be more thoroughly characterized. ZrC is stable over a large range of nonstoichiometry, which is promising for irradiation damage tolerance, but carbon vacancies are shown to cause a decrease in bond strength, reflected in decreased heat capacity and hardness and increased CTE. The introduction of lattice defects also reduces thermal and electrical conductivity. With the renewed interest in ZrC for advanced composite nuclear fuels, much work lies ahead in building the required knowl­edge base in both processing and performance that will enable the nuclear community to take full advan­tage of ZrC as a high-temperature structural ceramic. Chapter 1.02, Fundamental Point Defect Proper­ties in Ceramics; Chapter 1.05, Radiation-Induced Effects on Material Properties of Ceramics (Mechanical and Dimensional); and Chapter 3.08, Advanced Concepts in TRISO Fuel.

2.14.1 Introduction

Liquid metals (LM), such as sodium (Na), lead (Pb), and lead-bismuth (Pb-Bi) eutectic (e), are considered as potential coolants for the fast spectrum nuclear reactors of the next generation.1 In the period 1960­1980, a lot of studies were performed for the creation of adequate databases of thermophysical properties of Na in the frameworks of development, construc­tion, and operation of liquid metal (cooled) fast breeder reactors LMFBR in the United States, European Union, and in the former USSR.2 Most of these results were collected later and published in review reports and handbooks.3- 1 Since that time, the interest for fast reactors with Na coolant increased significantly worldwide, especially after the launch of the Generation IV International Forum (GIF) initia­tive,1 where the sodium fast reactor (SFR) is considered as the main candidate for future nuclear power plants, which can be used for both electricity production and transuranium elements (TRU) incineration — a way for closing the nuclear fuel cycle. In the GIF documents, the lead-cooled fast reactor (LFR — cooled by Pb or Pb-Bi) is considered as the second candidate.1 An interest to use Pb and Pb-Bi(e) in the civil power reactors appeared mainly after communications in open literature about the preliminary design studies on BREST12 and SVBR13 reactors in the Russian

Federation. LFR systems are now considered in few other countries: PBWFR, 14 SLPLFR,15 and CAN­DLE16 in Japan, PEACER17 and BORIS18 in Korea, SSTAR19 in the United States, and ELSY20,21 in the European Union. At present, the available data on thermophysical properties of Pb and Pb-Bi(e) in the temperature range of interest are still incomplete and often contradictory. This complicates the design calcu­lations and the prediction of the normal and abnormal behavior of nuclear installations where they will be used. Intensive studies have been performed in differ­ent countries aiming at better understanding of their properties needed for design and safety analysis of the nuclear installations. Recently, a review of the Na properties was performed in Argonne National Labo — ratory22; compilations with the recommendations for the properties ofPb and Pb-Bi(e) were prepared by the WPFC (OECD) Expert Group on Heavy Liquid Metals Technology23,24 and for all three LM ofinterest by expert groups of the IAEA.25,26

This chapter gives a brief review of the compila­tions and recommendations developed for the main thermophysical properties of Na, Pb, and Pb-Bi(e), which include melting temperature, boiling temper­ature, critical point parameters, saturated vapor pres­sure, melting and boiling enthalpies, surface tension, density, thermal expansion, adiabatic and isothermal compressibility, speed of sound, heat capacity at con­stant pressure and at constant volume, enthalpy, elec­trical resistivity, viscosity, and thermal conductivity. The properties of these coolants were measured in many laboratories but mainly at normal atmospheric pressure and at relatively low temperatures (except for Na). In general, the reliability of the data is satisfactory; however, a large uncertainty still exists in some properties of Pb and Pb-Bi(e). A set of correlations for the estimation of the main properties of Na, Pb, and Pb-Bi(e), as a function of tempera­ture and pressure, is proposed based on the previous reviews and new results that appeared in open litera­ture. For the prediction of the missing properties at high temperatures and pressures, relevant equations of state (EOS), based on the proven physical models and available experimental data, were indicated. Taking into account that the critical parameters for the considered metals are not yet well defined with adequate precision, the EOS validation at high tem­peratures and pressures is still a problem.

In Section 2.14.2, general properties of liquid Na, Pb, and Pb-Bi(e) at a temperature of 400 °C, which is within the typical temperature range of coolant in SFR and LFR, are compared.

Characteristic temperatures (melting, boiling, and critical), and the enthalpies of melting and boiling are given in Section 2.14.3. Thermodynamic proper­ties are reviewed in five subsections of Section 2.14.4. Section 2.14.5 is devoted to transport prop­erties. Conclusions are formulated in Section 2.14.6. Compatibility of structure materials with liquid sodium and lead alloys is considered in Chapter 5.13, Material Performance in Sodium and Chapter 5.09, Material Performance in Lead and Lead-bismuth Alloy, respectively.

2.14.2 General Properties

Almost all main thermophysical properties of liquid Na, Pb, and Pb-Bi(e) (such as density, thermal expan­sion, compressibility, heat capacity, surface tension, sound velocity, and compressibility) are measured with satisfactory precision in the region close to normal melting temperature. An exception is the saturated vapor pressure, which is rather small at these temperatures to be measured with high preci­sion. The aforementioned parameters of liquid Na, Pb, and Pb-Bi(e), calculated with the recommended correlations given below for normal atmospheric pressure and at the typical mean temperature 400 °C (673 K) of the normal operation of the considered LM coolants in a Gen IVreactor, are compared in Table 1.

The main advantages of Na coolant in comparison with Pb and Pb-Bi(e) are the lower density and viscosity and the higher other transport coefficients (electrical conductivity and thermal conductivity); its disadvantages are higher compressibility, high satura­tion vapor pressure, and lower surface tension. More detailed information about the thermophysical prop­erties of liquid Na, Pb, and Pb-Bi(e) is given in the following sections.

The pressure diapason of the normal operation of the LM coolants in nuclear installations usually ranges from 0.1 to 1-1.5 MPa and the temperature diapason is between 300 °C (573 K) and 600 °C (873 K). Under accidental conditions, the coolant temperature can locally increase up to the fuel melting temperature, and the local coolant pressure can increase up to the cladding failure limit. Therefore, coolant properties have to be known within larger temperature and pressure ranges. For the development of an EOS of the LM coolants needed for the correct extension of the properties’ recommendations to higher tempera­tures and pressures, their critical parameters (temper­ature, pressure, and density) should be known.

2.14.3 Characteristic Temperatures, Pressures, and Heats

A temperature range of the normal operation of a liquid metal coolant is usually determined by its melting and boiling temperatures. Under accidental conditions, it can even be close to the critical point region. The melting temperature increases very weakly with pressure, but the boiling temperature increases rapidly, so the temperature range is larger at the higher pressures.

The melting temperatures of the chemically pure Na, Pb-Bi(e), and Pb were measured with high pre­cision at normal atmospheric pressure.3-30 However, the difference between the values coming from dif­ferent sources sometimes reaches a few tenths of degree of Celsius (a few tenths of Kelvin) for Na and Pb, and a few degrees for Pb-Bi(e). This disper­sion is mainly explained by the presence ofimpurities in the samples.30 Moreover, for Pb-Bi(e), supplemen­tary uncertainties exist due to a possible deviation from the eutectic composition (currently, most of the

researches fix it at 45.5 wt% Pb + 55.5 wt% Bi24’31; see Figure 1) and due to a possible presence of metastable phases.24’32 For the technically pure metals, the best estimated values of the melting temperature (TM 0) for the considered metals at the standard atmospheric pressure are 371.0 ± 0.1 K for Na, 600.6 ± 0.1 K for Pb, and 398 ± 1K for Pb — Bi(e).9’24-34

In 1999, Stolen and Gronvold35 performed the critical assessment of the available data on the enthalpy of melting (AHM0) of pure metals, used as enthalpy standards, at the standard atmospheric pres­sure. The values recommended by them for Na and Pb are 2.60 ± 0.03 and 4.78 ± 0.03 kJ mol-1, respec­tively. For the Pb-Bi(e) melting enthalpy, the analysis of the available data was performed in Sobolev and Benamati24 and Sobolev,34 where the mean value of

8.4 ± 0.06 kJ mol-1 of three more reliable sources Bogoslovskaia et a/.,25 Kirillov et a/.,26 Cevolani36 was recommended, which is adopted in this work.

The boiling temperatures of these LM were measured with a lower precision than their melting temperatures. The uncertainty ranges from 10 to 20 K for Pb and Pb-Bi(e)24 and about 1-2 K for Na.22,27,30 The selected ‘best estimate’ values of the normal boiling temperatures (TB0) of Na, Pb, and Pb-Bi(e) are 1155 ± 2 K, 2021 ± 3 K, and 1927 ± 16 K, respectively.

The available data on the enthalpy of boiling of Na were analyzed in Fink and Leibowitz22 and Kirillov et a/.,26 and the selected recommended value
of AHB 0(Na) = 97.4 ± 0.1 kJ mol-1 is recommended for the standard atmospheric pressure. The literature values on the boiling latent heat of Pb at normal atmospheric pressure were reviewed in Sobolev and Benamati.24 The difference <3% was found be­tween the maximum and minimum reported values: AHB 0(Pb) = 177.9 ± 0.4 kJ mol-1. In the same compi­lation,24 the mean value of 178 ± 1 kJ mol-1 of only three available sources25,26,36 was recommended for the latent heat of boiling of LBE at normal pressure.

The most probable values of the melting and boiling temperatures, together with the latent enthal­pies of the melting and boiling of Na, Pb-Bi(e), and Pb at normal atmospheric pressure, recommended earlier, and the operation temperature ranges of these liquid metal coolants, are presented in Table 2.