No systematic study of the Np-C phase diagram has yet been performed. Neptunium monocarbide NpC1-x and neptunium sesquicarbide Np2C3 are the only two phases definitely observed. The struc­ture of Np monocarbide was extensively investigated in the early studies performed at ANL.4,9 Composi­tions between NpC082 and NpC10 were identified to have fcc rock-salt structure (Fm 3m), with the lattice parameter increasing slightly with the carbon content, from 499.1 ± 0.1 pm for NpC0.82 to 501.0 ± 0.1pm for NpC10. Some data dispersion was attributed to oxygen impurities.

Np2C3 crystallizes in a bcc Pu2C3-like lattice (I 43d). The lattice parameter was measured with precision by Mitchell and Lam,199 who found a = 810.30 ± 0.01pm. The stoichiometry range of this compound is believed to be narrow because Lorenzelli found nearly the same lattice parameter for the phase in equilibrium with the monocarbide and with pure carbon.

The structure of NpC2 was reported to be iso­structural with tetragonal CaC2 (same as a-UC2), but data are uncertain.

The heat capacity of NpC0.91 determined by Sandenaw et a/.197 showed a l-type anomaly with a peak at 228.4 ± 0.2 K. This feature was attributed to ferromagnetic ordering, in agreement with the ferro­magnetic Curie temperature reported by Lam eta/.20 and by Lander and Mueller.201 The latter authors also report that NpC orders antiferromagnetically around 300 K, and attribute the difficulties in having reproducible results for T > TCurie to the strong dependence of magnetic properties on the carbon content. This lack of reproducibility introduces some uncertainty into the room-temperature thermo­dynamic parameters (Table 7). Only the enthalpy of formation of NpC091±002 and NpC15 was directly

measured by oxygen bomb combustion. The other values and the temperature dependence were esti­mated by assuming neptunium carbides to have inter­mediate behavior between uranium and plutonium carbides.4

Molecular geometry has not been measured. Quantum chemical calculations for the uranium (III) fluoride indicate a pyramidal structure104 but with a bond angle close to the planar 120°.

The thermodynamic data on solid uranium tri­fluoride recommended by Grenthe et at.24 are presented in Table 12.

Values for the heat capacity and entropy ofUF3(g) are calculated from estimated molecular parameters given by Glushko et at.91

2.06.4.4.1 Vapor pressure

On heating, solid UF3 does not vaporize congruently but disproportionately into solid UF4 and uranium by the following reaction:

4UF3 ! 3UF4 + U

The vapor pressure measurements, which are diffi­cult, can explain the scattered results (Figure 20). Roy et at.105 determined the vapor pressure of UF3(s) by the transpiration technique using hydrogen as the carrier gas in the 1229-1367 K temperature range, and Gorokhov et at.106 deduced it from their mass spectrometry determinations. The temperature depen­dence of the vapor pressure is described, respectively, by the following equations105,106

logPUF3 = (13.26±0.23)-(15666±302)^1^) (pinPa)
logPUF3 = (13.39±0.46)-(20040±0.62)т(Ку (pinPa)

The discrepancy is very large, about three orders magnitude.

2.06.4.4.2 Enthalpy of formation

Enthalpy of formation of gaseous UF3 has been eval­uated from experimental studies by Grenthe et at.24 It has been deduced from

• the enthalpy of sublimation obtained by third — law analysis of the vapor pressure data

measurements,106

107,108

• mass spectrometric measurements.

The Th-O and Np-O phase diagrams, according to the experimental studies by Benz34 and Richter and Sari35 are given, respectively, in Figure 3(a) and 3(b).

In the Th-O phase diagram (Figure 3(a)), only the dioxide ThO2 exists. At low temperature, accord­ing to Benz,34 the oxygen solubility limit in solid Th is low (O/Th < 0.003). A eutectic reaction occurs at 2008 ± 20 K with a liquid composition very close to pure thorium. The existence of a miscibility gap has been found to occur above 3013 ± 100 K that leads to the formation of two liquid phases with O/Th ratios equal to 0.4 and 1.5 ± 0.2, respectively. The phase boundary of ThO2 _ x in equilibrium with liquid tho­rium was measured. The lower oxygen composition for ThO2 _ x at the monotectic reaction corresponds to O/Th = 1.87 ± 0.04. The melting point of ThO2 recommended by Konings et at.36 is Tm = 3651 ± 17 K. This value corresponds to the measurement by Ronchi and Hiernaut,37 which is in good agreement with the one reported on the phase diagram proposed by Benz34 in Figure 3(a).

The Np-O phase diagram looks very similar to the Th-O system but the experimental information is very limited. In the Np-NpO2 region, a miscibility gap in the liquid system is expected but no experi­mental data exist on the oxygen solubility limit in liquid neptunium and on the extent of this miscibility gap. The dioxide exhibits a narrow hypostoichio — metric homogeneity range (NpO2 _ x) for tempera­tures above 1300 K. The phase boundary ofNpO2 _ x in equilibrium with the liquid metal is not well known. The minimum O/Np ratio is estimated to be about 1.9 at approximately 2300 K according to Figure 3(b). The recommended melting point for NpO2 is Tm = 2836 ± 50 K.36,38 Only the part richer in oxygen differs from Th-O with the presence ofthe

decomposes into gas and intermediate oxides (Cm0183 and Cm0171). Cm02 _ x exhibits a small range of com­position with a minimum O/Cm ratio of 1.97.

During irradiation in reactors, the fuel pellets are deformed by various processes, including densifica — tion, thermal expansion, swelling by fission products, and creep. This deformation may eventually lead to an interaction with the cladding, which has resulted in reactor failure. The elastic and plastic properties of fuel pellets, as well as creep rate, are very important,
given the above interaction. The swelling behavior is also important and is described in another chapter. Thermal expansion is discussed in this chapter.

2.03.4.1 Mechanical Properties of UN

The mechanical properties of UN have been sum­marized by Hayes et a/94 A summary of the different measurements of creep rate is plotted in Figure 29. As the creep rate depends on many parameters such as stress level, stoichiometry, density, and impurity, as well as temperature, there is no systematic trend at each specific temperature. High temperature, steady state creep is generally expressed by the following

94

equation,

є = Ad-man exp{-Q/RT} [24]

where e is creep rate, A is a constant, d is grain size, a is stress, m is the grain size exponent, n is the stress exponent, Q is the activation energy, R is the gas constant, and T is the temperature. n and m are involved in the creep mechanism, and the value of n is especially important in determining the mecha­nism that controls the creep. Hayes et a/. have tried to estimate the n values using several creep data sets reported in individual studies, and they have found that almost all n values were in the range of 4.0-5.9, suggesting a dislocation climb mechanism in UN. Assuming a dislocation climb mechanism, where creep rate does not depend on grain size, with an average n value of 4.5, and an m value of zero, the following correlation94 is suggested;

e’ = 2.054 x 10-3a4 5exp{—39369.5/T} [25]

This equation is valid only for the creep of theoreti­cally dense UN in the temperature range of 1770— 2083 K and under stress ranging from 20 to 34 MPa. It has been reported that if the density of UN is below the TD, the creep rate can be obtained by multi­plying it with the following factor,95

z 4 0.987

f (p) = 276exp{-8-65P} N

(1 — p)

where p is the porosity.

Various measurements of Young’s modulus at room temperature are summarized in Figure 30. Young’s modulus depends not only on temperature but also on porosity. The variation in Young’s modulus, as a function of porosity, has been measured by two different methods, velocity measurement and fre­quency measurement; but no clear difference between the results of these two methods has been found. A power law relation was fitted to these experimental data at room temperature and was combined with the linear temperature dependence data reported by Padel and deNovion96 and the following correlation was obtained94:

E = 0.258D3-002 [1 — 2.375 x 10-5 T] [27]

where E is the Young’s modulus and D is the ratio of density with TD in percent. This equation is valid where the ratio of TD is from 75% to 100% and the temperature ranges from 298 to 1473 K. As this equa­tion fits well with all the experimental data obtained
from samples with uncontrolled pore shape and ori­entation, porosity distribution, average grain size, grain shape, orientation, and impurities, as shown in Figure 30, the dependence of Young’s modulus on these parameters is small.

The following correlation94 of the shear modulus with density and temperature was obtained by a method similar to that used for determining the Young’s modulus:

G = 1.44 x 10-2D3-446[1 — 2.375 x 10-5 T] [28]

where G is the shear modulus. This relation is valid under the same density and temperature conditions as the Young’s modulus.

As the data for the bulk modulus could not be measured directly and was calculated from measure­ments of Young’s and shear modulus in the various studies, the degree of data scatter is larger here, com­pared to the other properties. The following correla — tion94 with density and temperature was obtained in a method similar to that used for Young’s modulus and shear modulus:

K = 1.33 x 10-3D4-074[1 — 2.375 x 10-5 T] [29]

where K is the bulk modulus.

Poisson’s ratio for UN was assumed to be indepen­dent of temperature. Similar to the bulk modulus, Poisson’s ratio can be estimated from measurements of Young’s modulus and shear modulus, and small errors in measurements of Young’s and shear

modulus have resulted in the large scatter of these calculations. Under the assumption that Poisson’s ratio is independent of temperature, the following correlation94 with porosity is obtained:

n = 1.26 x 10~3D1,174 [30]

where n is Poisson’s ratio and D is the density ranging 70-100%.

The hardness values, which are easily obtained experimentally, decreased with porosity and tem­perature. The hardness decrease with porosity linearly and decrease with temperature exponentially. In the porosity range of 0-0.26 and the temperature range of 298-1673 K, the following correlation94 is valid:

HD = 951.8{1 — 2.1p}exp{-1.882 x 10-3T} [31]

where HD is the diamond point hardness.

HCP Hexagonal close-packed structure

IM Phase diagram type introduced in the

present article for convenience. IM means all phases are immiscible in the phase diagram.

LS Phase diagram type introduced in the

present article for convenience. LS means liquid and solid are miscible in the wide composition region of the phase diagram.

MG Phase diagram type introduced in the

present article for convenience. MG

means several there is a limited miscibility gap in the phase diagram. SEM Scanning electron microscope

WDX Wave length dispersive X-ray

spectrometry

Symbols

f/ Activity coefficient of /’-component

R Gas constant T Temperature (K)

Gmix Gibbs energy of mixing for j-phase OG/p Standard Gibbs energy for pure substance, /, for j-phase

x/ Mole fraction of /-component

Chemical potential of /-component for j-phase

Interaction parameter for j-phase

2.05.1 Introduction

In this chapter, comprehensive features of and recent progress on the phase diagrams of actinide alloys are introduced. Phase Diagrams of Binary Actinide Alloys edited by Kassner and Peterson in 19951 summarized 384 binary phase diagrams involving actinide ele­ments from Ac to Lr. Some phase diagrams were evaluated through the effort of the Alloy Phase Dia­gram (APD) program initiated by ASM International and the National Institute of Standards and Technol­ogy, while the remainder largely taken from Binary Alloy Phase Diagrams2 and Molybdenum.3 The assess­ment by the APD program has been continued, and a handbook was published in 20004 The main part of the present compilation is based on these data books.

Regarding the phase relation among actinide ele­ments, a composite phase diagram from Ac to Cm was suggested originally by Smith and Kmetko,5 and then a color version was given by Moore and van der Laan,6 as shown in Figure 1. The body-centered cubic (bcc) phase is formed prior to melting for the actinides below Cm, and the bcc phase is completely soluble between neighboring actinides as well as the liquid phase. The increase in complex­ity of the crystal structure of the low-temperature allotropes and the reduction in melting point are observed from Ac toward Pu. Many low-symmetry allotropes as well as the lowest melting temperatures are seen in the region between Np and Pu. In the early part between Ac and Th, the structure of the low-temperature allotropes is close-packed face — centered cubic (fcc) and somewhat similar to the transition metals, while beyond Am the typical struc­ture seen for light lanthanides is observed, that is, double hexagonal close-packed (DHCP). These sug­gest that the alloying behavior of those actinide metals, such as Ac and Th, and beyond Am, with other series metals becomes similar to that of transi­tion metals and light lanthanides, respectively. A wide

monophase region is seen even for the low — temperature allotropes in the case of neighboring actinides. However, several additional features can be pointed out. The solubilities of Pa and U into Th and Pa, respectively, are very limited in the low — temperature region, although those of Th and Pa in Pa and U, respectively, are very good. The mutual solubilities of Pu and Am for the low-temperature allotropes are very limited, with the only exception of the fcc phase. When observing the phase relation between actinides alternately in the periodic table, the miscibility becomes poorer. For instance, a mis­cibility gap appears for the liquid phase in the Th-U and Np-Am binary systems. Those features originate from the difference in the 5f electron characteristics. The details are discussed in other chapters. Simply put, the features on alloying of U, Np, and Pu with other elements are different from the other actinides. In general, the degree of the decrease in the Gibbs energy of mixing between U or Np and the other elements is smaller than that related to Ac through Th or beyond Am with several exceptions. Plutonium has intermediate characteristics.

As for the comprehensive observation of APD between actinides and other metals, it is still conve­nient and useful to take a semiempirical thermody­namic model into account for a brief understanding to the phase relations between various metals. The details of the semiempirical method, the so-called CALPHAD approach, are given in another chapter. In the present review, some phase diagrams are assessed in a semiempirical manner. The equation treated in the CALPHAD approach is given for the solution phases as follows:

GlxiT; xb) =(1 — XB)OGj + xBOGj

+ RT [(1 — xb ) ln (1 — xb)

+ ХвіПХв] + OjXB (1 — xb) [1]

Here, is the Gibbs energy of mixing for the j-phase; °Gj, °Gj are the standard Gibbs energy of A and B for the j-phase, Oj is the interaction parameter of regular solution model for the j-phase; xb is the mole fraction of B; R is the gas constant; and T is the temperature (K) which indicates the Gibbs energy of mixing between the A and B components in the A-B binary system. It is useful to introduce the interaction parameter, Oj, as an index to show the tendency of mixing between A and B. When the O j = 0, A and B can form an ideal solution. When O j > 0 or O j < 0, Gmjix shifts to the positive and negative directions, respectively, and the degree of Oj shows how large the tendency of ‘mixing’ or ‘demixing’ is in the A—B alloy system. Usually, Oj is indicated as a simple function of temperature and composition.

The partial molar Gibbs energies of the compo­nents A or B, that is, the chemical potentials ofA or B, corresponding to the Gibbs energy expression given above, are obtained with eqns [2] and [3].

, XB)=°Gj + RTln( 1 — xB)+OjxB [2]

mj(T, xb) =OGj + RTlnxb + Oj(1 — xb)2 [3]

By introducing an activity coefficient, these equa­tions are given alternatively by

mj(T, XB) = OGj + RT ln fA(1 — xb) [4]

mj(T, XB)=OGj + RT ln fB xb [5]

The Gibbs energy of formation of intermetallic compounds can be defined in a similar manner. A rough estimation of the order of the various Gibbs energies can be attempted by observing the feature of the actinide phase diagrams. The precision of parameters treated in the CALPHAD approach, that is, the interaction parameters in the regular solution model, is lower than those in the nonempir­ical approach such as an ab initio method. Sometimes, the interaction parameters must be treated as just simple fitting parameters. However, the Gibbs ener­gies themselves estimated from the CALPHAD approach have quite good accuracy and are sufficient to reconstruct the actinide phase diagrams or to estimate the thermodynamic functions. Due to the lack of experimental data, this method may be often practically useful when taking actinide-containing systems into considerations.

HTGR High-temperature gas-cooled reactor

2.08.1 Introduction

Nickel was first used as an alloying element for steels in the mid-eighteenth century. The development of corrosion-resistant steels was started in the nineteenth century. , These studies led to the development of various kinds of stainless steels, particularly in the early 1900s. Particularly, the 300 series austenitic stain­less steels were developed and became the ‘most widely used tonnage’ materials in the twentieth century.

The nickel-copper Alloy 400 (Monel 400, UNS N04400) was developed as the first nickel-based alloy at the beginning of the twentieth century.3 This alloy was developed as an alternative chloride-corrosion — resistant material to austenitic stainless steel.

Nickel is a less noble element than copper; how­ever, it is more noble than iron and zinc. It exhibits higher corrosion resistance than iron in most envir­onments due to the formation of denser and more protective corrosion films with superior passivation characteristics compared to iron.

Nickel has superior corrosion resistance in caustic or nonoxidizing acidic solutions, and in gaseous halo­gens. It can be relatively easily alloyed with various elements such as chromium, molybdenum, iron, and copper. Many nickel-based alloys have been devel­oped and applied as corrosion-resistant alloys in var­ious environments, as well as creep-resistant alloys in high-temperature applications.4

Based on their excellent properties, nickel-based alloys have been widely applied in a number of fields, for example, the aerospace industry, chemical indus­tries, and electricity generation plants. In the nuclear power industry, nickel-based alloys have been used in pressurized water reactors (PWRs) and boiling water reactors (BWRs) since their initial development in the early 1950s. In particular, Alloys X-750 (UNS N07750) and X-718 (UNS N07718) have been widely applied, for example, for jet-engine blades, due to their excellent creep strength. A high-creep-strength material is one that is highly resistant to stress relax­ation at high temperatures. Alloys X-750 and 718 have therefore been applied as bolting and spring materials for PWRs and BWRs.

Alloy 600 (UNS N06600) has superior resistance to stress corrosion cracking (SCC) in boiling 42% MgCl2 solution as high-chloride solutions.5 In the Shipping — port and Yankee Rowe reactors, 347 stainless steel was used as a steam generator (SG) tube material. (The Shippingport reactor was the first full-scale nuclear powered electricity generation plant (proto­type reactor), and the Yankee Rowe reactor was the first commercial PWR.) Beginning with the Connecticut Yankee PWR, the next electricity generation plant, Alloy 600 was used as the SG tube material, and then subsequently applied in PWRs worldwide, due to its superior SCC resistance in high-chloride solutions.

Among the other superior properties of Alloy 600, its thermal expansion coefficient is noted to be between that of ferritic steels and austenitic steels. Based on this, the residual stress and strain for dissimilar weld joints of ferritic steels and austenitic steels can be minimized by the use of Alloy 600 and its compatible weld metals. In nuclear power plants, ferritic steels and austenitic steels are widely used as the main component materi­als, especially for the pressure boundary. Numerous dissimilar metal weld joints are therefore found in nuclear power plants. Alloy 600 and its weld metals such as Alloys 82, 132, and 182 have also found wide­spread application in such plants.

Nickel-based alloys were developed not only as corrosion-resistant materials but also as heat — resistant materials. These alloys are suitable for various components and parts in light water reactors, heavy water reactors, gas reactors, etc.

The detailed features and various physical proper­ties of these nickel-based alloys are described in the following sections.

There are essentially three primary energy sources for the billions of people living on the earth’s surface: the sun, radioactivity, and gravitation. The sun, an enormous nuclear fusion reactor, has transmitted energy to the earth for billions of years, sustaining photosynthesis, which in turn produces wood and other combustible resources (biomass), and the fossil fuels like coal, oil, and natural gas. The sun also provides the energy that steers the climate, the atmospheric circulations, and thus ‘fuelling’ wind mills, and it is at the origin of photovoltaic processes used to produce electricity. Radioactive decay of primarily uranium and thorium heats the earth underneath us and is the origin of geothermal energy. Hot springs have been used as a source of energy from the early days of humanity, although it took until the twentieth century for the potential of radioactivity by fission to be discovered. Gravitation, a non-nuclear source, has been long used to generate energy, primarily in hydropower and tidal power applications.

Although nuclear processes are thus omnipresent, nuclear technology is relatively young. But from the moment scientists unraveled the secrets of the atom and its nucleus during the twentieth century, aided by developments in quantum mechanics, and obtained a fundamental understanding of nuclear fission and fusion, humanity has considered these nuclear processes as sources of almost unlimited (peaceful) energy. The first fission reactor was designed and constructed by Enrico Fermi in 1942 in Chicago, the CP1, based on the fission of uranium by neutron capture. After World War II, a rapid exploration of fission technology took place in the United States and the Union of Soviet Socialist Republics, and after the Atoms for Peace speech by Eisenhower at the United Nations Congress in 1954, also in Europe andJapan. Avariety of nuclear fission reactors were explored for electricity generation and with them the fuel cycle. Moreover, the possibility of controlled fusion reactions has gained interest as a technology for producing energy from one of the most abundant elements on earth, hydrogen.

The environment to which materials in nuclear reactors are exposed is one of extremes with respect to temperature and radiation. Fuel pins for nuclear reactors operate at temperatures above 1000 °C in the center of the pellets, in fast reactor oxide fuels even above 2000 °C, whereas the effects of the radiation (neutrons, alpha particles, recoil atoms, fission fragments) continuously damage the material. The cladding of the fuel and the structural and functional materials in the fission reactor core also operate in a strong radiation field, often in a dynamic corrosive environment of the coolant at elevated temperatures. Materials in fusion reactors are exposed to the fusion plasma and the highly energetic particles escaping from it. Furthermore, in this technology, the reactor core structures operate at high temperatures. Materials science for nuclear systems has, therefore, been strongly focussed on the development of radiation tolerant materials that can operate in a wide range of temperatures and in different chemical environments such as aqueous solutions, liquid metals, molten salts, or gases.

The lifetime of the plant components is critical in many respects and thus strongly affects the safety as well as the economics of the technologies. With the need for efficiency and competitiveness in modern society, there is a strong incentive to improve reactor components or to deploy advanced materials that are continuously developed for improved performance. There are many examples of excellent achievements in this respect. For example, with the increase of the burnup of the fuel for fission reactors, motivated by improved economics and a more efficient use of resources, the Zircaloy cladding (a Zr-Sn alloy) of the fuel pins showed increased susceptibility to coolant corrosion, but within a relatively short period, a different zirconium-based alloy was developed, tested, qualified, and employed, which allowed reliable operation in the high burnup range.

Nuclear technologies also produce waste. It is the moral obligation of the generations consuming the energy to implement an acceptable waste treatment and disposal strategy. The inherent complication of radioactivity, the decay that can span hundreds of thousands of years, amplifies the importance of extreme time periods in the issue of corrosion and radiation stability. The search for storage concepts that can guarantee the safe storage and isolation of radioactive waste is, therefore, another challenging task for materials science, requiring a close examination of natural (geological) materials and processes.

The more than 50 years of research and development of fission and fusion reactors have undoubtedly demonstrated that the statement ‘technologies are enabled by materials’ is particularly true for nuclear technology. Although the nuclear field is typically known for its incremental progress, the challenges posed by the next generation of fission reactors (Generation IV) as well as the demonstration of fusion reactors will need breakthroughs to achieve their ambitious goals. This is being accompanied by an important change in materials science, with a shift of discovery through experiments to discovery through simulation. The progress in numerical simulation of the material evolution on a scientific and engineering scale is growing rapidly. Simulation techniques at the atomistic or meso scale (e. g., electronic structure calculations, molecular dynam­ics, kinetic Monte Carlo) are increasingly helping to unravel the complex processes occurring in materials under extreme conditions and to provide an insight into the causes and thus helping to design remedies.

In this context, Comprehensive Nuclear Materials aims to provide fundamental information on the vast variety of materials employed in the broad field of nuclear technology. But to do justice to the comprehensiveness of the work, fundamental issues are also addressed in detail, as well as the basics of the emerging numerical simulation techniques.

R. J.M. Konings European Commission, Joint Research Centre, Institute for Transuranium Elements, Karlsruhe, Germany

T. R. Allen

Department ofEngineering Physics, Wisconsin University, Madison, WI, USA

R. Stoller

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

S. Yamanaka

Division of Sustainable Energy and Environmental Engineering, Graduate School of Engineering, Osaka University, Osaka, Japan

Owing to the large range of nonstoichiometry with temperature in UO2 ± x, different types of defects (metal and oxygen vacancies and interstitials) and clusters are expected to form. In slightly hypostoi- chiometric UO2 _ x for example, oxygen vacancies are expected to be the dominant defects. In that simple case, one knows from point defect model (see See — Bauer and Kratzer14 ) that the concentration of oxy­gen vacancies [Lg*] is a function of the oxygen pressure pO2 (see also Figure 18):

[VO*] / pO_1/6 [11]

Such a simple description can be applied to slightly hyperstoichiometric dioxides too (see Figure 18). This means that — in principle — one can extract the nature of defects and the concentration of, for exam­ple, oxygen vacancies VO** (or oxygen interstitials [Ig]), which depends upon the slope of the curve, here 1/6, from SeeBauer and Kratzer14 and

Ling,146 and the formation energy of those defects in hypostoichiometric urania, from the measure­ments of oxygen potential (eqn [12]) as a function of temperature and stoichiometry. This simple model was developed in the 1980s by Matzke147 on the basis of the experimental oxygen potential data.

Unfortunately, nonstoichiometric urania cannot be rationalized using simple point defects — such as oxy­gen interstitials or vacancies — within the large non­stoichiometric composition range (see phase diagrams in Figure 1). For large deviations from stoichiometry, the defects become nonisolated and start to interact with each other. The oxygen ions are known to aggre­gate and form Willis clusters according to Willis102 and cuboctahedral clusters. According to electrical

conductivity measurements by Ruello et a/.,148 these clusters have a net charge of -1. Park and Olander149 derived in the 1990s a point defect model that takes into account the Willis defect (2:2:2). Their model also included the oxygen interstitials (I"), oxygen vacancies [VO], polarons (U3+), holes (U5+), and vacancy dimers (V. U:V)". In this model, the structural defect in UO2 is the oxygen Frenkel pair. The cation Frenkel defect and the anion and cation Schottky defects can be neglected (unless cation diffusion is considered). In hyperstoichiometric urania (x > 0.01), the oxygen interstitials form Willis clusters. No clus­ters were found experimentally in UO2 _ x. However, vacancy dimers were assumed to form.

For highly concentrated point defects in oxides (such as ceria), Ling146 added Coulombic interactions as well as generalized exclusion effects to improve the description depicted by simple point defect models. Stan and Cristea implemented such defect model in plutonia and urania.1 0-1 4 Stan and Cristea150 con­sidered in PuO2 _ x small polarons (Pu3+), singly charged vacancies (VO)", doubly charged vacancies (Vo)"", neutral pairs (PuVo)x, and singly charged pairs (PuVo)x as defect species. The model predicts that the small polarons and doubly charged oxygen vacancies are the dominant defects in the very low nonstoichiometric region. The intermediate region is controlled by singly charged vacancies and the deep nonstoichiometric region by neutral pairs. For UO2 + x, Stan eta/.153 developed a simple model with four major defects: oxygen Frenkel pairs, doubly negatively charged oxygen interstitials (//’), positively charged (UU or U5+) uranium ions, and positively doubly charged oxygen vacancies [VO].

Recently, Kato eta/.155 analyzed oxygen potential data for (U0.7Pu0.3P2 ± x and (U0.4Pu0.2P2 ± x versus oxygen stoichiometry and temperature using a point defect model. It showed that intrinsic ionization is the dominant defect in stoichiometric mixed oxide. The defect model reproduces quite well the experimental oxygen potential data as a function of stoichiometry.

The reverse approach consists in calculating the formation energy of well-chosen defects using atom­istic simulations (ab initio and/or MD). One can then estimate the oxygen pressure as a function of stoichi­ometry. This was done in the 1980s by means of empirical potentials MD by Catlow and Tasker,156 and later by Jackson eta/.157 More recently Yakub158 used the same method to investigate the formation of different types of clusters (Willis’s 2:2:2 intersti­tial dimers, and cuboctahedral tetra — and pentamers) in UOy + x.

Numerous studies were performed using the density functional theory (DFT) by Petit et a/.,159 Crocombette et a/.,160 Freyss et a/.,161 Gupta et a/.,162 Nerikar eta/.,163 and Yu eta/.164 The energy of forma­tion of clusters were determined by Geng eta/.,165-167 and by Andersson et a/.5,168 Recently a Brouwer dia­gram of urania was drawn by Crocombette et a/.169 based on charged point defect formation energies. The hypostoichiometric part is in agreement with the oxygen potential data from Baichi et a/.9 and evidenced the existence of both (Vo)° and (V0)°°. All these works using DFT are subjects of contro­versy in relation to the problems to be encountered when using ab initio for actinides (see Chapter 1.08, Ab Initio Electronic Structure Calculations for Nuclear Materials).

Konashi et a/.170 used first principle MD simula­tion to investigate the point defects in PuO2. They show that in PuO2 _ x, the oxygen vacancy is bound by two neighboring Pu ions which lead to the change of plutonium valency from 4 to 3. The most favorable position of the two Pu3+ cations is nearby the oxygen vacancy.

Martin et a/.17 characterized (U1 _ JPuy)O2 solid solutions using X-ray powder diffraction, X-ray absorp­tion spectroscopy (XAS), and extended X-ray absorption fine structure measurements (EXAFS). The EXAFS results suggested that for Pu content lower than 30at.%, the mixed oxide has a disordered hyperstoi­chiometric structure (U1 _ JPuy)O2 + x with cuboctahe — dral defects that are located around uranium atoms and not in the Pu environment.

A number of multielement thorium carbides have been studied. They occur as mixed phases of binary thorium carbides with other elements by the forma­tion of either continuous solid solutions, like ternary carbides, or immiscible compounds. The most inter­esting are certainly the carbide-oxides and-nitrides. They form relatively easily during the ThCx prepa­ration and on exposure to air. It is therefore useful to explore some of their properties, at least for the Th-rich compositions.

2.04.2.2.6.1 Thorium carbide oxides

The Th-C-O ternary system6 was extensively studied by Potter.66 It is characterized by a hypostoi — chiometric Th monocarbide oxide fcc solid solution Th(C, O)i_x with x> 0, stable around 1800 K. It was experimentally observed that the maximum solubil­ity of oxygen in ThC in equilibrium with ThC2 and ThO2 corresponds to the composition ThC08O0.2 (1.3 wt% oxygen). Heiss and Djemal91 observed that the maximum solubility of oxygen in ThC1.94 corre­sponds to the composition ThC194O004 (0.25 wt% oxygen), at 2273 K. The room-temperature lattice parameter of oxygen-saturated ThC0.8O0.2 is esti­mated to be between 532.6 and 532.9 pm.

2.04.2.2.6.2 Thorium carbide nitrides

The Th-C-N system has been investigated more than the Th-C-O system, thanks in particular to Benz eta/.,92 Pialoux,93 and Benz and Troxel.94

For low nitrogen contents, the addition of nitrogen has been observed to raise the a! p transition tempera­ture of Th-rich ThC2_x. The effect on the same transi­tion in C-saturated ThC2_x and on the transition

temperature seems negligible, indicating that N is prob­ably more soluble in a-ThC2_x than it is in g-ThC2_x. Similar to oxygen, the addition of nitrogen to the fcc ThC1_x phase reduces its lattice parameter.

For N contents >0.05 at.%, literature data are few and scattered. The Th-Th(C, N) region is char­acterized by a continuous fcc NaCl-type solid solu­tion between ThN, stoichiometric ThC, and slightly hypostoichiometric ThC1_x. Hyperstoichiometric

Th(C, N)1+x exists as a solid solution on the ThC side above 2073 K. ThN and very hypostoichiometric ThC1_x are separated by a two-phase field. No eutectic has been observed in the Th-ThC-ThN region, but a peritectic four-phase equilibrium between a-Th, p-Th, Th(C, N), and liquid is postu­lated at 1993 ± 30 K. Alloys with C/Th « 1 were observed to melt at 2473 K under 2 bar of N2, and a ternary eutectic exists just below 2500 K with compo­sition Th0.38C0 35N0.27. The lattice parameter of the Th(C, N) solid solution between ThC and ThN fol­lows Vegard’s law almost exactly, from approximately 534 pm for ThC to 516 pm for ThN. The lattice parameter of Th(C, N) in equilibrium with Th3N4 and ThCN, a = 522.4 ± 0.6 pm, corresponds to the composition ThC0.35N0.65 and is almost independent of temperature. ThC0.35N0.65 is also the congruently melting composition of the Th(C, N) solid solution, with Tm = 3183 ± 35 K. The solidus temperature was observed to increase with nitrogen pressure.

The lattice parameter of Th(C, N) in equi­librium with ThC2 and ThCN, a = 519.7 ± 0.5 pm, corresponds to the composition ThC0.20N080. The Th(C, N)-C region is characterized by the ternary compound ThCN, which exists in two modifications. a-ThCN crystallizes in the prototype C-centered monoclinic structure, with space group C2/m (No. 12) and lattice parameters a = 702.5 ± 0.5 pm, b = 394.6 ± 0.1pm, c = 727.7 ± 0.2 pm, and b = 95.60 ± 0.1°. At 1398 K, this phase transforms into p-ThCN, having a hexagonal structure with the space group P 31m (No. 162) and lattice parameters a = 703.5 pm and c = 732.4 pm. p-ThCN decomposes into Th3N4 and C at sufficiently high nitrogen pressure.

The metallic electrical resistivity of the Th(C, N) solid solution decreases from 1.8 to <0.05 p. Q m with increasing nitrogen content and decreasing tempera­ture. The electrical properties of this phase depend primarily on the conduction electrons and the vacancy concentration in the fcc lattice.95 Th(C, N) becomes superconducting at low temperature, with a maximum transition temperature of 5.8 K for the composition ThC0.78N0.22, sharply decreasing with increasing car­bon content. The decrease is more gradual at higher nitrogen content, up to 3.2 K for pure ThN.

Among the numerous compounds in the U-F system (UF3, UF4, U4F17, U2F9, UF5, and UF6 as condensed phases, and UF, UF2, UF3, UF4, UF5, U2F10, and UF6 as gaseous species), UF6 is certainly the most known because of the wide use of this gas to enrich the 235U fraction in uranium. Indeed UF6 has a vapor pressure of 1500 mbar (1.5 x 105Pa) at 337 K that appears as a striking contrast with the refractory UO2, which melts at 3120 K.1,2 This difference is typical of fluoride/ oxide difference, and also VI/IV oxidation state.

UF6 was first prepared by Ruff in 19113 through reaction of F2 on U metal or carbide. The chemistry of UF6 was then more completely investigated in the 1940s due to the development of nuclear technology. By the end of 1950, Agron had published a phase diagram including the intermediate fluorides U4F17, U2F9, and UF5. Further research continued at a slower pace in the 1960s on these intermediate fluor­ides. The scientific interest later decreased with the rise of AVLIS laser-based enrichment technology of U metal that did not need UF6 to enrich in 235U. In this period, some R&D was also performed on UF6 to define a dry reprocessing route using the fluoride volatility technique, such as the Fluorex process, to extract U from less-volatile fluorides such as fission products.

On the other end, UF4 had been known for a long time as a green solid used for the preparation of UF6 and uranium metal. It was first prepared by the reac­tion of aqueous HF on U3O8 by Hermann in 1861. More recently UF4 is now considered for molten salt reactor technology.

Finally, the UF3-UF4 system was then studied more recently from an academic point of view, but UF3 today does not present any industrial application.

Except for UF4 that only yields a hydrate when exposed to air, all these compounds are unstable when exposed to the humidity of air yielding UO2F2 and/or UF4. UF6 is also very corrosive and can act as a strong fluorinating reagent. Hence, the characterization of these intermediate fluorides has always been quite limited. For example, the descrip­tion of the UF5 liquid phase is not well known. UF5 may melt congruently at 621 K or undergo decompo­sition. The eutectic compositions between UF4-UF5 and UF5-UF6 are unknown.

2.06.2 Phase Diagram

Agron has published a phase diagram (Figure 1) for the intermediate fluorides4 based on the three following reactions:

2U4F17 (s)^7UF4(s)+UF6(g)
2u2F9(s)^3/2U4F17 (s) + UF6 (g)

3UF5(s)^U2F9(s) + UF6(g)

From the equilibrium constant of these reactions K = K0e—AG|j/rt = P(UF6), the experimental results can be expressed as log P(UF6) = log K0 — (AG0/RT), where K0 and AG0/R are constants.

Plotting log P(UF6) versus 1/T gives the stability domain of these compounds.

The UF3-UF4 system has been studied by Khripin et al.5 and Slovianskikh et al6 by differential thermal analysis; UF3 being obtained through the reduction of UF4 with H2. In the two cases, they found a eutectic transition at, respectively, (1152 ± 7) K and 1143 K, which is slightly lower than that at the temperature found by Thoma et al.7 and selected by Knacke et al.8 The eutectic composition is quite different between the two authors with 0.7835 at. F (atomic fraction of F) found by Khripin et al.5 (value extrapolated from

the liquidus and solidus data) and 0.788 at. F by Slovianskikh et al6 In 1969 Knacke et al. published the most complete phase diagram (Figure 2) to date8 with three eutectics at 1165, 621, and 328 K and three con­gruently melting compounds UF3, UF4, and UF6 at, respectively, 1700, 1309, and 337 K.