Chlorine-containing gases including HCl or Cl2 severely attack many metals. Table 16 shows the applicable temperatures for various materials in dry HCl and Cl2 gases.7,8,10,30,31 Nickel can be used in hydrofluoric acid provided there is no condition of flowing in which its protective fluoride film would be removed. Nickel also can be used at temperatures higher than 500 °C, similar to Alloy 600. Nickel — chromium-iron is better as a structural alloy in this application due to its high strength compared to pure nickel. However, nickel and Alloy 600 severely cor­rode in HCl and Cl2 gas in the presence of water vapor. Aeration or the presence of oxidizing chemi­cals will also increase corrosion rate of nickel in hydrofluoric acid.

2.12.2.2.1 Thermal conductivity

It is reasonable to assume that the single-crystal form of SiC, compared to the other varieties, exhibits the highest thermal conductivity. However, high-purity and dense polycrystalline CVD SiC exhibits practi­cally the same conductivity as the single-crystal material. It is worth noting that the impurity content of the very high thermal conductivity CVD SiC mate­rials is negligibly small, and this material has near theoretical density (~3.21 gcm—3). The curve-fitting to the single-crystal SiC data above 300 K yields an upper limit of the thermal conductivity of SiC (in Wm—3K—3):

Kp = (-0.0003 + 1.05 x 10—5T)—1 [7]

2.12.2.2.2 Specific heat

The temperature dependence of the specific heat can be treated in two temperature regions: a rapid increase at low temperatures (below 200 K), and a gradual increase at higher temperatures. No system­atic difference can be distinguished between the struc­tural types. The specific heat, Cp (in J kg-1 K), over the temperature range 200-2400 K can be approximately expressed as

Cp = 925.65 + 0.3772T — 7.9259 x 10—5T2

— 3.1946 x 107/T2 [8]

The specific heat of SiC at room temperature is taken as 671 ± 47Jkg~1K.

2.12.2.2.3 Thermal expansion

The coefficient of thermal expansion for p-SiC has been reported over a wide temperature range. The average value in the interval from room temperature to 1700 K is a = 4.4 x 10~6K~

At higher temperatures (T> 1273 K), a = 5 x 10~6K_1

At lower temperatures (550 < T< 1273 K), a = 2.08 + 4.51 x 10~3T

A great uncertainty still exists in the critical tem­peratures, pressures, and densities of the LM of interest. These parameters are very important for the development of EOS and the extension of the

Temperature (K)

Figure 3 Saturated vapor pressure of Na, Pb, and Pb-Bi(e) (p < patm).

properties’ recommendations to higher temperatures and pressures.

With satisfactory precision they were determined only for sodium. The available experimental data and theoretical estimations for the critical parameters of Na were reviewed in 1985 by Ohse et at., who recommended Tc(Na) = 2497 ± 18 K, pc(Na) = 25.22 ± 0.60 MPa, and pc(Na) = 211 ± 2kgm-3.

Later, Fink and Leibowitz22 extended this review by including the results ofnew studies and analyses from Thurnay53 and Petiot and Seiler54 and suggested to use Tc(Na) = 2503.7 ± 12 K, pc(Na) = 25.64 ± 0.40 MPa, and pc(Na) = 219 ± 20 kgm-3. In the recent com­pilation of IAEA,26 the Na critical parameters are reproduced from the earlier review.30 The rounded within uncertainty values from the review of Fink and Leibowitz22 are recommended in the present compilation (see Table 6).

A lot of studies were performed to determine the critical point of lead, but the obtained results show a large variation. In 1990, Pottlacher and Jager55 published a summary of experimentally determined and theoretically estimated parameters for the criti­cal point of lead available in the literature as of that date. They considered 16 sets of data as well as their
own estimations based on the experimental results obtained using the pulse-heating technique. Their summary shows that the experimental and theoretical data on the critical temperature of lead lie within the range of 3584-6000 K, while their own estimation yields T((Pb) = 5400 ± 400 K. For the Pb critical pres­sure and density, they recommend pc(Pb) = 250 ± 30 MPa and p = 3200 ± 300 kgm-3. Morita et a/.56 analyzed the previous and later publications using different methods to estimate the critical parame­ters of lead. The IAEA compilation26 suggests to use Tqpb) = 5000 ± 200 K, pc(Pb) = 180 і 30 MPa, and Pc(Pb) = 3250 ± 100 kgm-3 with the reference to the handbook of Babichev et a/.57 These values give good compromise and they were selected in the present compilation (see Table 6).

Only theoretical estimations were found in the open literature for the critical parameters of

Pb-Bi(e).24,52,56,58 Based on these studies and on

the conclusions of the report,34 the following values and uncertainties are recommended for the critical temperature, pressure, and density of Pb-Bi(e): Tc(Pb-Bi) = 4800 і 500 K, Pc(Pb-Bi) = 160 і 70 MPa,

and pc(Pb-Bi) = 2200 і 200 kgm-3. The recommended values of the critical parameters of Na, Pb, and Pb-Bi(e) are summarized in Table 6.

As described in Section 2.15.3.2.7, two types of pin spacing for fuel assemblies, the grid type and the wire type, have been adopted for all FBRs. The wire type is more widely used except those for the Dounreay Fast Reactor in UK.34 Here, the rod fabrication and assembly are described taking a wire spacer type fuel assembly from the MONJU as an example.

The lower end plug is TIG-welded (tungsten inert gas-welded) to a cladding tube made of SUS 316 based alloy; this is done outside the PFPF. Clad­ding tubes with lower end plugs are then transferred to PFPF along with blanket pellets of depleted UO2 and the other cold components such as plenum sleeves and plenum springs. After adjusting the col­umn length of MOX pellets and measuring their weight, they are loaded into each cladding tube
with the other components; this is done in a glove box under a helium gas atmosphere. Then, an upper end plug is TIG-welded to the cladding tube. In this welding, the position ofthe weld electrode is adjusted automatically using image analysis. Figure 27 shows photographs of a welding torch installed in the glove box and an image display showing the position of the weld electrode.

Decontamination of the fuel rod surface is carried out prior to a contamination check. The fuel rods which pass the contamination check are brought from the glove box and are sent to the helium leak test to certify tightness of the welded part. An X-ray check of the welded part to confirm its soundness is also carried out prior to wrapping a spacer wire around the fuel rod. Finally, each fuel rod is checked for its weight, straightness, gap between spacer wire and fuel rod, g-ray spectrum from Am in the MOX pel­lets, and general surface appearance. Next, 169 fuel rods are transferred to the automated assembly sta­tion where 15 layers of fuel rods, consisting of 8-15 rods in each layer, are prepared at first. The layers of fuel rods are fixed to the entrance nozzle one by one to get a hexagonal cross-section. This bundle of 169

fuel rods is inserted into a wrapper tube, and then this wrapper tube is TIG-welded to the entrance nozzle.

Figure 28 shows a photograph of a bundle being inserted into a wrapper tube at the assembly station. The completed fuel assembly is then moved to an inspection station to confirm its straightness, twist, distance between opposite outer surfaces and appear­ance through automatic and remote operations.

Symbols

a Crystallographic a-direction (within the basal plane)

b Empirical constant c Crystallographic c-direction C Elastic moduli

C Specific heat

Cp Specific heat at constant pressure E Young’s modulus G Shear modulus h Plank’s constant k Boltzmann’s constant KIc Critical stress-intensity factor KT Thermal conductivity at temperature T la Mean graphite crystal dimensions in the

a-direction

lc Mean graphite crystal dimensions in the

c-direction

m Charge carrier effective mass N Charge carrier density

P Fractional porosity q Electric charge R Gas constant S Elastic compliance (1/C)

T Stress T Temperature

a Coefficient of thermal expansion a Thermal diffusivity

aa Crystal coefficient of thermal expansion in the a-direction

ac Crystal coefficient of thermal expansion in the c-direction

ay Synthetic graphite coefficient of thermal

expansion parallel to the molding or extrusion direction

a? Synthetic graphite coefficient of thermal expansion perpendicular to the molding or extrusion direction Dth Thermal shock figure of merit g Cosine of the angle of orientation with respect to the c-axis of the crystal во Debye temperature A Charge carrier mean-free path

m Charge carrier mobility

n Poisson’s ratio

nf Charge carrier velocity at the Fermi surface r Bulk density

s Electrical conductivity s Strength

sy Yield strength

t Relaxation time

v Frequency of vibrational oscillations

2.10.1 Introduction

Graphite occurs naturally as a black lustrous mineral and is mined in many places worldwide. This natural form is most commonly found as natural flake graphite and significant deposits have been found and mined in Sri Lanka, Germany, Ukraine, Russia, China, Africa, the United States of America, Central America, South America, and Canada. However, artificial or synthetic graphite is the subject of this chapter.

The electronic hybridization of carbon atoms (1s2, 2s2, 2p2) allows several types of covalent-bonded structures. In graphite, we observe sp2 hybridization in a planar network in which the carbon atom is bound to three equidistant nearest neighbors 120° apart in a given plane to form the hexagonal graphene structure. Covalent double bonds of both а-type and p-type are present, causing a shorter bond length than that in the case of the tetrahedral bonding (а-type sp3 orbital hybridization only) observed in diamond. Thus, in its perfect form, the crystal struc­ture of graphite (Figure 1) consists of tightly bonded (covalent) sheets of carbon atoms in a hexagonal lattice network.1 The sheets are weakly bound with van der Waals type bonds in an ABAB stacking sequence with a separation of 0.335 nm.

The invention of an electric furnace2,3, capable of reaching temperatures approaching 3000 °C, by Acheson in 1895 facilitated the development of the process for the manufacture of artificial (synthetic) polygranular graphite. Excellent accounts of the properties and application of graphite may be found elsewhere.4-6

CVI SiC/SiC and CVI SiC/Si-B-C composites exhibit primary creep only, even during long tests (Figures 11 and 12).54

Creep of CMCs involves local stress transfers depending on the respective creep rates of the fiber and the matrix. Such stress transfers may lead to fiber failures or matrix cracking and debonding, and sliding at the interfaces. When the matrix is elastic and creep-resistant, fiber creep induces stress trans­fers from the fibers onto the matrix, which may cause matrix cracking. This creep-induced matrix damage has been observed on CVI SiC/SiC composites.55-57

In CVI SiC/SiC composites, the SiC matrix is far more creep-resistant than the SiC fibers, which creep at 1100 ° C.55,58,59

The creep behavior of CVI SiC/SiC composites with a multilayered matrix (SiC/Si-B-C) is caused by the creep of the Nicalon SiC fibers, whatever the extent of initial damage created upon loading (Figure 11). The Si-B-C matrix is less creep — resistant and stiffer than the SiC matrix.

Most of the physical properties of oxide fuel such as lattice parameter, diffusion coefficient, and thermal conductivity are affected by the O/M ratio.

The lattice parameter is needed for calculation of the theoretical density (TD) ratio in the fuel fabrica­tion process. The thermal expansion coefficient, which is defined as the temperature dependency of the lattice parameter, is also an important thermophysical property in fuel design when the variation in heat transport between the fuel and the cladding tube by thermal expansion of the fuel pellets and the stress to the cladding tube by fuel pellets under irradiation are evaluated.

The lattice parameters and thermal expansion coefficients of actinide dioxides are summarized in Table 2 in Section 9.1.З.1. As mentioned in Section 9.1.3.1.2, the dependency of the lattice parameter of stoichiometric mixed oxides on their chemical composition usually obeys Vegard’s law. The lattice parameter of MOX fuel decreases with an increase in the plutonium content. In the hypostoi — chiometric region, the lattice parameter of MOX fuel increases with a decrease in O/M ratio. In addition, Leyva et al.14 showed that the lattice parameter of (U, Gd)O2 decreases with an increase in Gd content.

As mentioned in Section 9.1.3.1.2, Vegard’s law is applied to the evaluation of lattice parameters as a function of composition and temperature in many cases (refer to Figure 13 in Section 9.1.3.1.2). It means that the thermal expansion coefficient of MOX fuel is independent of plutonium content. Martin15 showed that the thermal expansion coeffi­cient of MOX fuel tends to increase with an increase in deviation from stoichiometry in the hypostoichio — metric region.

The melting point of oxide fuel is one of the most important thermophysical properties for fuel design and performance analyses. As the chemi­cal composition and the O/M ratio of the oxide fuel change the melting point of the fuel itself, fuel design and performance analysis should be done in consid­eration of not only the chemical composition at the time of fuel fabrication but also its variation subsequent to nuclear transmutation during reactor operation. In addition, the melting point is also used in the estimation of sintering temperature, as men­tioned before.

Section 9.1.2 shows that the melting point of uranium oxide has its largest value near the stoichio­metric region and the melting point decreases with an increase in deviation from stoichiometry (refer to Figure 1 in Section 9.1.2.1). Further, the melting point of stoichiometric MOX decreases with an increase in plutonium content (refer to Figure 7 in Section 9.1.2.7). In the hypostoichiometric MOX, the melting point of MOX fuel increases with a decrease in O/M ratio.16 Beals et al.17 studied the UO2-GdO15 system at high temperatures and showed that the melting point of Gd bearing UO2 decreases with an increase in Gd content.

During reactor operation, the heat generated in the oxide fuel pellets flows from the central high temperature region to the low temperature periphery of the pellets, and consequently thermal equilibrium is achieved in the pellets. To evaluate the tem­perature distribution when thermal equilibrium is reached, thermal conductivity is one of the most important thermophysical properties. As thermal conductivity is a function of O/M ratio, density, chemical composition, and so on, the variation in chemical composition that occurs during reactor operation should be noted, along with the evaluation of the melting point, as mentioned before.

As mentioned in Section 9.1.6.2, thermal con­ductivities of oxide fuel decrease with an increase in temperature up to 1600-1800 K but increase with an increase in temperature beyond this range

(refer to Figures 33 and 34 in Section 9.1.6.2). The factors which heavily influence the thermal conduc­tivity are O/M ratio and fuel density. Thermal con­ductivity decreases significantly with an increase in deviation from stoichiometry and with a decrease in density. In addition, the thermal conductivity of a gadolinium-bearing uranium oxide decreases signifi­cantly with an increase in Gd content.18,19

2.15.2.1.3.1 Solubility in nitric acid solution

When the nuclear fuel cycle is considered, the disso­lution of oxide fuel is the essential first step in

100

E о

O)

E,

ф

й

c

о

Й

о

(Л

<л

b

1

Figure 3 Dissolution rate of mixed oxide of uranium and plutonium with various Pu contents as a function of the nitric acid concentration. Reproduced from Oak Ridge National Laboratory. Dissolution of high-density UO2, PuO2, and UO2-PuO2 pellets in inorganic acids, ORNL-3695; Oak Ridge National Laboratory: Oak Ridge, TN, 1965.

aqueous reprocessing. The solubility and dissolution rate of oxide fuel in nitric acid solution are important parameters related to the capabilities of the reproces­sing process. Generally, it has been supposed that the dissolution of MOX fuel decreases with an increase in the plutonium content. The maximum plutonium content of MOX driver fuel for fast reactors has been limited to about 30%, from the viewpoint of solubility in nitric acid solution.

There have been many studies on the solubility of oxide fuel in nitric acid solution.2 — From the results of these studies, it has been supposed that the factors affecting the dissolution rate of MOX are the fuel fabrication conditions (homogeneity of the admixture of UO2 and PuO2, sintering conditions and plutonium content, etc.) and the fuel dissolution conditions (nitric acid concentration, solution tem­perature, dissolution time, etc.) (see Figure 3).

D

A Thermal conductivity (W itT1 K-1) r density (kg itT3)

2.17.1 Introduction: Importance of Thermal Conductivity

Knowledge of the thermal conductivity of the fuel of a nuclear reactor is required for the prediction of fuel performance during irradiation, in particular for the determination of the temperature distribu­tion and of the fission gas release. The principal objectives of this chapter are to give elements useful to understand the phenomena causing the degradation of the thermal conductivity during irradiation and to provide guidance for the inter­pretation and comparison of in-pile or out-of-pile measurements, especially as a function of burnup and for samples having different irradiation tem­peratures, in-pile histories, and microstructures. The importance of such studies is more significant when the discharge burnup of the fuel is increased and with the formation of the high burnup struc­ture (HBS), because these two parameters have a significant impact on the thermal conductivity. More details on the performance of LWR UO2 fuel can be found in Chapter 2.19, Fuel Perfor­mance of Light Water Reactors (Uranium Oxide and MOX). The impact of the introduction of pluto­nium or additives (Gd, Cr, etc.) in standard UO2 also requires assessment (see also Chapter 2.16, Burnable Poison-Doped Fuel). Uranium-plutonium mixed oxide (MOX) fuel represents a significant fraction of the nuclear fuel used in commercial light water reac­tors (LWRs). The industrial processes used for the production of MOX fuel are based on the mixing of a few percent of plutonium oxide with UO2. The differ­ent microstructures that can be obtained are mainly characterized by the degree of homogeneity of the plutonium distribution. The impact ofthe introduction of plutonium in UO2 and the different microstructures therefore need to be considered because the presence of Pu in the UO2 lattice will reduce the thermal conductivity. UO2 fuel with increased grains size is produced by doping with chromium oxide, with the objectives of reducing the pellet-cladding interaction by an increased viscoplasticity and of reducing fission gas release.

This section mainly deals with LWR fuel because the data available for fast reactor fuel are extremely inadequate. The specific heat of the fuel is also affected by irradiation. This parameter is required for the investigation of fuel performance during transients and also for the calculation of the thermal conductivity from thermal diffusivity measurements. The evolution of the thermal conductivity as a function of burnup is nonlinear, and numerous approaches and approxima­tions are used, leading to a large number of publica­tions on this subject. This is not the case for the specific heat which generally obeys the law of mixtures. The thermal expansion, melting temperature, and oxygen potential of the fuel are also important for fuel per­formance studies, but they are not addressed in this section.

The thermal conductivity distributions as a func­tion of the radial position in a pellet for two tem­perature profiles (central temperatures of 1000 and 1500 K) and for burnups of 0 (fresh fuel) and 40 MWd kg HM-1 calculated with the equation of Ronchi et a/.1 are shown in Figure 1. A large temperature gradient exists over the small distance between the pellet center and the pellet rim, inducing large varia­tions in the conductivity. It can be seen that the conductivity decreases with temperature and burnup.

Under steady-state irradiation conditions and assuming a purely radial heat transfer, the temper­ature distribution T(r) in a fuel pellet is given by eqn [1] and depends on the thermal conductivity 1(r T) and volumetric heat generation rate q(r).

7 dr (r1(r ’T )+ q(r ) = 0 [1]

The local thermal conductivity 1(r, T) depends on the radial position and local temperature. The local heat generation rate requires information on the fission cross sections and depends on the radial distribution of the thermal neutron flux and of the fissile isotopes. This distribution changes during irradiation as a result of the consumption of the initial fissile isotopes and the production of fissile Pu.

From the point of view of heat transfer, both fresh and irradiated fuels are heterogeneous materials (e. g., due to the presence of the porosity). However, fresh fuels can be considered as homogeneous, even the heterogeneous MOX, and an effective or equivalent thermal conductivity can be defined. This is because the size of the pores and the plutonium-rich

Figure 1 Thermal conductivity distribution1 as a function of the radial position in a pellet, for two temperature profiles and for burnups of 0 (fresh fuel) and 40 MWd kg HM-1.

agglomerates is small (compared with the dimensions of the pellet) and has a uniform distribution as required by fuel fabrication specification. (See also Chapter 2.15, Uranium Oxide and MOX Produc­tion for more information on the uranium oxide and MOX production). The heterogeneity is higher in irradiated fuel because irradiation induces the forma­tion of numerous elements and compounds, bubbles, pores, etc., with concentrations depending on the radial position. The definition of the effective thermal conductiv­ity of a heterogeneous material such as irradiated fuel is not straightforward. The different scales that may be considered for the heat transfer are shown in Figure 2, where m is the microscale corresponding to the size of the larger heterogeneities, L is the mesoscale corresponding to the elementary repre­sentative volume (ERV), and M is the macroscale corresponding to the pellet radius. The thermal con­ductivities of the matrix and of the inclusions are noted 1m and 1i, respectively. If the separation of scales is verified,2 M ^ L ^ m and the equivalent thermal conductivity 1eq is defined from the mean temperature gradient (V T) and the mean density of the heat flux (‘) within the ERV: 1eq =-(‘)/(V T). The equivalent thermal conductivity 1eq can be evaluated from the conductivity and the geometric distribution of the constituents on the basis of the following assumptions:

M Heterogeneous solid: pellet

Equivalent medium

Figure 2 Notion of separation of scales: an elementary representative volume exists for the heat transfer, with M > L > m.

1. If the equivalent conductivity is evaluated over a volume V, and there exists a value of V beyond which the value of the conductivity no longer varies as Vis increased, this volume is the ERV. 2. The medium is statistically homogeneous: the sta­tistical distribution of the phases does not depend on the position within the material, and the equiv­alent conductivity is the same irrespective of the position of the ERV. 3. The dimensions of the material are large com­pared with the dimensions of the ERV. 4. Steady-state heat transfer is assumed. For transient heat transfer, homogenization is inappropriate, and the real microstructure has to be considered. 5. The medium is opaque to thermal radiation.

6. Fourier’s law applies within the ERV and in the

entire medium.

7. No mass transfer is involved.

8. No internal heat sources exist.

The first three criteria, relating to the microstruc­ture, are not perfectly met for irradiated fuel. A rigorous homogenization is therefore not possible because the thermal conductivity depends on the radial position in the pellet as a result of the radial distribution of burnup and the irradiation tempera­ture. However, a local homogenization is usually made by assuming that over a small radial position interval, the characteristics of the fuel are constant and allow the measurement or calculation of an effective thermal conductivity. For standard irra­diated fuels, the unit cell required for homogeniza­tion has dimensions of about 1 mm3, considering that the biggest heterogeneities are pores of size up to 100 pm. However, burnup and irradiation temperature are not constant over a radial interval of 1 mm, and therefore this unit cell is not rigor­ously suited for homogenization. Homogenization can be accomplished in a more rigorous way in the case of disc fuels obtained during test irradiations, if uniform burnup and irradiation temperature pro­files are obtained. This homogenization allows an average temperature field to be calculated. Local temperature variations exist, for instance, because of plutonium-rich zones or a particular local arrangement or shape of the pores.

The criteria 4-6 are met for irradiated fuel. The seventh criterion can be considered as met because the effect of mass transfer is negligible for LWR fuels: some elements migrate as a result of the gradients in the pellet, but the heat transferred by this mechanism is small when compared to conduction. The eighth criterion is not met when the effective thermal con­ductivity is deduced from in-pile temperature mea­surements. The internal heat sources should not be considered when the effective thermal conductivity of heterogeneous fuels is evaluated, for instance from finite-element temperature calculations.

The thermal properties of irradiated fuels are investigated in pile by temperature measurements and out of pile by thermal diffusivity measurements. Theoretical studies exist for the effect of some single parameters. Direct out-of-pile measurements on irradiated fuel samples appear more reliable because of the well-defined and optimized measurement parameters, although the in-pile conditions cannot be completely reproduced (temperature gradient, fission rate, etc.). Therefore, in-pile determinations are indispensable, even though the deduction of the thermal conductivity from eqn [1] is less accurate. The published correlations range from empirical for­mulae to more sophisticated models integrating explic­itly and semiempirically the effect ofsome parameters. A new correlation is often a combination of different existing approaches, for instance, fresh fuels results, out-of-pile experiments on simulated or real irradiated samples, and correlations obtained from in-pile tem­perature measurements.

No consensus exists on the most reliable correla­tion and usually, fuel performance codes incorporate a number of correlations, leaving it to the user to select which is the most appropriate for a specific case. For instance, the FEMAXI-6 code3 includes about 10 thermal conductivity correlations for irra­diated UO2. Before presenting the most representa­tive results, the different burnup effects that have an impact on the thermal conductivity are discussed individually.

The crystal structure of Be is closed-packed hexago­nal with a c/a ratio of 1.5671 and lattice parameters a = 0.22866nm and c = 0.35833 nm.3 Table 1 shows the basic properties of Be.4,5 It weighs only about
two-thirds as much as aluminum (Al), and both its melting point and its specific heat capacity are quite high for a light metal. It is widely known for its high Young’s modulus and other elastic coefficients. Its nucleus is small in neutron absorption cross-section and relatively large in scattering cross-section, both of which are advantageous for use as a moderator or reflector. Its superior high-temperature dynamical

Table 1 Basic properties of Be

properties are also advantageous for use in nuclear reactors. It emits neutrons under g-ray irradiation and can thus be used as a neutron source. Its soft X-ray absorption is less than one-tenth that of Al, making it highly effective as a material for X-ray tube windows.

Figure 1 shows the temperature dependence of the specific heat capacities of various Be samples.3 The following equations describing the specific heat capacity of Be are reported.3

CP = 11.8 + 9.12 x 10-3T

(JK-1g-1 atom, from 600 to 1560 K)

CP = 25.4 + 2.15 x 10-3T

(JK-У1 atom, from 1560 to 2200K)

Temperature dependences of the thermal expansion coefficient and the electrical resistivity of Be3 are given in Figures 2 and 3, respectively. Figure 4 shows the temperature dependence of the thermal conductivities of various Be samples.3,6 Be exhibits relatively high thermal conductivity values around 200 W m-1 K-1 at room temperature, and the values decrease with temperature. The effect of high-dose neutron irradiation on the thermal conductibility of Be has been investigated.7,8 It is reported by Chakin et al.7 that neutron irradiation at 303 K to a neutron fluence of 2 x 1022 cm-2 (E > 0.1 MeV) leads to sharp decrease of thermal conductivity, in particular at 303 K, the thermal conductivity decreases by a factor

of five, but short-term high-temperature annealing (773 K for 3 h) leads to partial recovery of the thermal conductivity.

In addition to the data listed in Table 1, the thermodynamic properties of Be have been reported recently,9 in which the temperatures of transforma­tion Ttr and melting Tm, and the enthalpies of trans­formation AtrH and melting DmH are measured
by difference thermal analysis and by anisothermal calorimetry. It is reported by Kleykamp9 that the results for hcp-bcc transformation of Be are Ttr = 1542 ± 1K and DtrH = 6.1 ± 0.5 kJ mol-1 and those for the melting process are Tm = 1556 ± 2K and DmH = 7.2 ± 0.5 kJ mol-1.

A fine, transparent BeO film of about 10-6cm thickness forms on Be in air, and it therefore retains

its metallic gloss when left standing. This results in its passivation in dry oxygen at up to 923 K, but the oxidized film breaks down at temperatures above about 1023 K and it thus becomes subject to progres­sive oxidation.10 It reacts with nitrogen at 1173 K or higher, forming Be2N3, and with NH3 at lower tem — peratures.10 Be undergoes passivation in dry CO2 at up to 973 K, but only up to 873 K in moist CO2.11,12 Its resistance to corrosion by water varies with tem­perature, dissolved ion content, pH, and other factors; it is reportedly poor in water containing CP (1-10ppm), SO2~ (5—15ppm), Cu2+ (0.1-5ppm), Fe2+ (1-10 ppm), or other such ions.10

Among the various compounds formed by Be, BeO and Be2C may be taken as typical. The basic properties of BeO are shown in Table 2.4 Its melting point and thermal conductivity are both high,13 its heat shock resistance is excellent, its thermal neutron absorption cross-section is small, and its corrosion resistance to CO2 at high temperatures is also excellent. Be2C is formed by reaction of Be or BeO with C. Its basic properties are density, 2.44 gcm ; specific heat capac­ity, 41.47J K-1 moP1 (303-373 K); thermal expansion coefficient, 10.5 x 10-6K-1 (298-873 K); and electric resistivity, 0.063 O m (303 K). It is reportedly unstable in moist air.10

Intrinsically, BeO is an excellent moderator and reflector material in nuclear reactors. Various utiliza­tions of BeO in reactors14 and behavior of BeO under neutron irradiation have been reported.15 Especially,

the effect of neutron irradiation on the thermal conduc­tivity of BeO has been widely studied.16,17 Figure 5 shows the temperature dependence of the thermal con­ductivity of unirradiated and irradiated BeO.17 It is observed that irradiation of BeO with neutrons consid­erably reduces the thermal conductivity. It has also been reported that the irradiation-induced change in thermal conductivity can be removed by thermal annealing, but complete recovery is not achieved until an annealing temperature of 1473 K is reached.

One further important property of Be that must be noted is its high toxicity. The effect of Be dust, vapor, and soluble solutes varies among individuals,

0

260 280 300 320 340 360

Temperature, T (K)

Figure 5 Temperature dependence of the thermal conductivity of unirradiated and irradiated BeO. Reproduced from Pryor, A. W.; et al. J. Nucl. Mater. 1964, 14, 208.

but exposure may cause dermatitis and contact or absorption by mucous membrane or respiratory tract may result in chronic beryllium disease, or ‘berylliosis.’ Maximum permissible concentrations in air were established in 1948 and include an 8-h average concen­tration of 2 pgm~3, a peak concentration of 25 pgm~3 in plants, and a peak concentration of 0.01 pgm~3 in plant vicinities.18 In relation to workplace health and safety, particular care is necessary in the control of fine powder generated during molding and mechan­ical processing. Dust collectors must be installed at the points of generation, and dust-proof masks, dust — proofgoggles, and other protective gear must be worn during work. InJapan, Be is subject to the Ordinance on Prevention of Hazards due to Specified Chemical Substances.

Two relevant thermomechanical processes in high — temperature structural applications are creep and stress relaxation. Steady-state creep deformation, or time-dependent strain under an elevated — temperature stress, has been observed for ZrC. In general, creep rate is dependent on applied stress (s) and temperature (T) according to

є = Aan exp —§ [12]

where є is strain rate, A is a constant dependent on the material and creep mechanism, n is an exponent dependent on the creep mechanism, R is the gas constant, and Qis the activation energy of the creep mechanism. Activation energies for creep under various conditions are summarized in Table 4. Zubarev and Kuraev13 proposed a creep mechanism map of stress normalized to shear modulus versus homologous temperature, based on compressive creep in He atmosphere of ZrC10 with 14 pm grain size. The authors distinguished between different temperature-stress regimes governed by creep pro­cesses having low or high activation energies. Indeed,

aKumashiro et a/.,124 Vickers indentation in {100} surface, for

(100)(001), (110)(001), and (111)(110) slip systems, respectively.

bDarolia and Archbold,117 compression in vacuum.

cLee and Haggerty,116 compression in vacuum along (111) crystal

axis.

dLeipold and Nielsen,72 1-5% porosity, 1.6-2.5 wt% free carbon. eMiloserdin et a/.,125 tension, 3.4-9.8MPa, 7% porosity. fSpivak et a/.,126 creep in He atmosphere, 4-6% porosity. 9Zubarev and Dement’ev,127 in tension, bending, and compression, respectively, 0.96-19.6 MPa, inert atmosphere, 15-17% porosity.

hZubarev and Shmelev,128,129 in tension, 0.96-73.5 MPa, Ar atmosphere, 3-5% porosity, 0.38-1.1 wt% free carbon.

‘Single crystal.

the two activation energies provided by Leipold and Nielsen72 are attributed to a change in creep mecha­nism above 2423 K.

At low or intermediate temperatures (below about 1623-2473 K for ZrC, or <0.5Tm) and high stress relative to shear modulus, creep has a low activation energy and is controlled by the movement of disloca­tions. Zubarev and Kuraev130 proposed more specific mechanisms for various regions ofthis overall regime, such as dislocation multiplication, cross-slip, disloca­tion climb, work-hardening, and gross plastic yield. The TEM analysis of Britun et a/.119 supports these hypotheses, revealing intragranular dislocations and slip bands after compression of ZrC098 between 1420 and 2100 K.

At high temperatures (generally >2073 K for ZrC) and intermediate or low stress, creep has a higher activation energy and is controlled by diffusion. The activation energy for creep in this regime is close to that of bulk self-diffusion in ZrC, which is ^500 kJ moP1 for C and ^700 kJ moP1 for Zr, as detailed in Table 4. The diffusion rate of the lower-mobility species should be rate-limiting, so creep in this regime is usually attributed to self-diffusion of Zr. However, diffusion along grain boundaries may reduce the activation energy for creep relative to that of bulk diffusion. Diffusional mass transfer (Nabarro-Herring creep) and grain boundary sliding are suggested mechanisms,130 with the latter con­firmed by scanning electron microscopy (SEM) cer — amography and not applicable to single crystals.13 Britun eta/.119 also confirmed grain boundary shear and rotation by TEM ceramography of ZrC098 com­pressed at 2100-2500 K.

The dependence of creep mechanism on grain size has been studied by Zubarev eta/.131 Analysis of creep mechanisms among polycrystalline (14-1000 pm grain size) and single-crystal ZrC10 revealed that with increasing grain size and with the single crystal, dislo­cation creep mechanisms occurred at lower threshold stresses, and the Nabarro-Herring and grain boundary sliding processes diminished in importance or disap­peared. Free carbon has been reported to facilitate grain boundary creep.131

Creep has been studied as a function of C/Zr ratio. Creep in compression of ZrC0.89-096 at 2773­2973 K132 showed a monotonically decreasing creep rate with decreasing C/Zr ratio. In the same work, a v-shaped trend of creep rate with C/Zr ratio was found for creep in bending of NbC0 82-0.98 at 2273­2473 K, decreasing to a minimum creep rate at a composition of approximately NbC0 85. They specu­lated that such a trend may exist for ZrC*, but that the associated minimum existed below the composi­tional range they investigated. Based on creep of ZrC075-098 between 2400 and 3030 K, Spivak et a/.126 found activation energy increased with increasing C/Zr ratio. This would be consistent with expectations of enhanced diffusion with an increase in C vacancies. However, their earlier work83 reported activation energy for self-diffusion of Zr in ZrC as being composition-independent between ZrC0 84_0 97, and that of C decreasing with increasing C/Zr ratio. Some hypotheses have been put forth (see Section 2.13.4.4), but further study of Zr diffusion in ZrC* is required to explain this conclusively.

Stress relaxation, or an evolution in stress with time for a component at fixed strain, has been inves­tigated to a lesser degree than creep. Repeated four — point bend loading of ZrC095-1 (6-35 pm grains) at 1873-2273 K, with unloading at intervals, resulted in increased resistance to relaxation, via work hard­ening, upon subsequent loading cycles.9 , The authors concluded that under these conditions slip occurs by diffusion along grain boundaries. At higher temperatures, up to 2473 K, no beneficial effects were imparted by repeated loading, and the authors con­cluded that no work hardening occurred. They judged stress relaxation and creep in ZrC to be con­trolled by different mechanisms.