Uranium–zirconium hydride fuel properties

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Nuclear Engineering and Design 239 (2009) 1406–1424

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Nuclear Engineering and Design

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ranium–zirconium hydride fuel properties

. Olandera,∗, Ehud Greenspana, Hans D. Garkischb, Bojan Petrovicc

Department of Nuclear Engineering, University of California at Berkeley, Berkeley, CA 94720, USAWestinghouse Electric Company LLC, Pittsburgh, PA 15236, USASchool of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

r t i c l e i n f o

rticle history:eceived 31 July 2007eceived in revised form 4 February 2008ccepted 2 November 2008

a b s t r a c t

Properties of the two-phase hydride U0.3ZrH1.6 pertinent to performance as a nuclear fuel for LWRs arereviewed. Much of the available data come from the Space Nuclear Auxiliary Power (SNAP) program of4 decades ago and from the more restricted data base prepared for the TRIGA research reactors some3 decades back. Transport, mechanical, thermal and chemical properties are summarized. A principaldifference between oxide and hydride fuels is the high thermal conductivity of the latter. This featuregreatly decreases the temperature drop over the fuel during operation, thereby reducing the release offission gases to the fraction due only to recoil. However, very unusual early swelling due to void formationaround the uranium particles has been observed in hydride fuels. Avoidance of this source of swellinglimits the maximum fuel temperature to ∼650 ◦C (the design limit recommended by the fuel developeris 750 ◦C). To satisfy this temperature limitation, the fuel-cladding gap needs to be bonded with a liquidmetal instead of helium. Because the former has a thermal conductivity ∼100 times larger than the latter,there is no restriction on gap thickness as there is in helium-bonded fuel rods. This opens the possibilityof initial gap sizes large enough to significantly delay the onset of pellet-cladding mechanical interaction(PCMI). The large fission-product swelling rate of hydride fuel (3× that of oxide fuel) requires an initialradial fuel-cladding gap of ∼300 m if PCMI is to be avoided. The liquid-metal bond permits operationof the fuel at current LWR linear-heat-generation rates without exceeding any design constraint. Thebehavior of hydrogen in the fuel is the source of phenomena during operation that are absent in oxidefuels. Because of the large heat of transport (thermal diffusivity) of H in ZrHx, redistribution of hydrogenin the temperature gradient in the fuel pellet changes the initial H/Zr ratio of 1.6 to ∼1.45 at the centerand ∼1.70 at the periphery. Because the density of the hydride decreases with increasing H/Zr ratio, theresult of H redistribution is to subject the interior of the pellet to a tensile stress while the outside of thepellet is placed in compression. The resulting stress at the pellet periphery is sufficient to overcome the
tensile stress due to thermal expansion in the temperature gradient and to prevent radial cracking thatis a characteristic of oxide fuel. Several mechanisms for reduction of the H/Zr ratio during irradiation areidentified. The first is transfer of impurity oxygen in the fuel from Zr to rare-earth oxide fission products.The second is the formation of metal hydrides by these same fission products. The third is by loss to theplenum as H2.
The review of the fabrication method for the hydride fuel suggests that its production, even on a largey high
scale, may be significantl
. Introduction

The history of uranium–zirconium hydride as a fuel or zir-onium hydride as a moderator for nuclear reactors goes nearly
s far back as that of oxide fuels. This fuel/moderator occu-ies a niche in reactor technology with a number of proposedesigns and fewer actual units. Among the former are the hydride-oderated boiling-water superheat reactor investigated by the
∗ Corresponding author. Fax: +1 510 526 0556.E-mail address: [email protected] (D. Olander).

029-5493/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2009.04.001

er than the cost of oxide fuel fabrication.© 2009 Elsevier B.V. All rights reserved.

National Aeronautics Administration as early as 1960 (Gylfe et al.,1960).

Despite the paucity and age of available data on U,Zr hydrides,such information is essential for determining whether anyfuel-related constraints are likely to limit performance as apower-reactor fuel. Potential limiting factors include maximumtemperature, internal rod pressure rise due to fission-gas release,
cladding strain from pellet-cladding mechanical interaction (PCMI)and waterside corrosion.
The purpose of this contribution is to review the history ofhydride-fueled reactors in order to extract information requiredfor the design of a power-reactor fuel using this material and to

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D. Olander et al. / Nuclear Engineering and Design 239 (2009) 1406–1424 1407

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Table 1Comparison of reactor fuel features.

Reactor type SNAP LWR-hydride LWR-oxide

Weight fraction uranium in fuel, wU 0.1 0.45 0.88Enrichment in 235U, e 0.93 0.125 <0.05U/Zr atom ratio in fuel, y 0.043 0.31 –H/Zr atom ratio, x 1.68–1.83 1.6 –Fuel density, �, g/cm3 6.1 8.3 10.5Uranium density, �U, g U/cm3 0.6 3.7 9.3235U density = e�U 0.56 0.46 0.46Fuel pellet (diameter × length, in cm) 1.4 × 35.6 1.2 × 1.5 1.2 × 1.5Gap filler He, 0.1 atm Liquid metal He, 20 atmCladding material Hastelloy Zircaloy (?) Zircaloy-2Peak fuel temperature, ◦C 850 550 1450Peak linear heat rate, kW/m ∼14 37.5 37.5Peak cladding temperature, ◦C ∼750 ∼350 ∼350

ig. 1. Photomicrograph of (U0.31Zr)H1.6. The black areas are (probably) uraniumetal; the gray region is ZrH1.6. The white dots are unidentified (from West et al.,

986).

ummarize what is known about the properties ofranium–zirconium hydride pertinent to its use as a fuel for LWRs.

This section reviews the work done on the early Space Nuclearuxiliary Power (SNAP) project starting in the 1960s, about theame time that the popular TRIGA research reactor was marketedo universities and nuclear laboratories. Section 2 presents most ofhat is known about the transport, thermal, mechanical and chem-

cal properties of ZrHx. Section 3 gives information extracted from0 to 40-year-old reports on the irradiation properties of hydrideuel. A summary of these properties up to 1981 is given by Simnad1981). Section 4 discusses the in-reactor chemical/materials per-ormance of this material. Section 5 presents a comparison of oxidend hydride fuels and Section 6 reviews batch production methodsf (U,Zr)Hx. Section 7 calculates the closure of the fuel-cladding gaps a function of burnup.

.1. Measures of composition

As shown in Fig. 1, the hydride fuel is a two-phase mixture con-isting of a continuous ZrH1.6 matrix in which small particles ofranium metal are embedded.

Hydride fuel contains three elements, and a variety of units haveeen used to denote its composition. One convenient designation

s (UyZr)Hx, where x is the H/Zr atom ratio and y is the U/Zr atomatio:

= NU

NZr(1)

here

Zr = 6.02 × 1023�(1 − wU)91.2

(2)

is the density of the fuel and wU is the weight fraction of uranium.eight fraction and atom ratio are related by

= 91.2MU

× wU

1 − wU(3)

here MU is the atomic weight of uranium:

U = 235e + 238(1 − e) (4)

nd e is the enrichment.The room-temperature density of the ura-ium phase is �o

U = 19.9 g/cm3, and that of the zirconium hydride
hase is (Simnad, 1981):
ZrHx = (0.154 + 0.0145x)−1 g/cm3 x < 1.6 (5a)

ZrHx = (0.171 + 0.0042x)−1 g/cm3 x > 1.6 (5b)

Average burnup 1.4 × 10−3 60FIMAa MWd/kgU

a Fissions per initial metal atoms; also called “metal atom fraction fissioned”.

The density of the two-phase mixture that constitutes the hydrideis

� =(

wU

�oU

+ 1 − wU

�ZrHx

)−1

(6)

The uranium density of the fuel, given by

�U = wU� (7)

is a key property as it dictates the enrichment of the uraniumrequired to achieve a desirable cycle length. The upper limit iswU = 0.45 (Chesworth and West, 1985).The molecular weight of thehydride is defined as the mass in grams per mole of zirconium,or:

M = yMU + 91.2 + x (8)

1.2. The SNAP reactors

A hydride-fueled reactor that received more than passing atten-tion was developed for the SNAP program at Atomics Internationalunder the auspices of the Atomic Energy Commission, the prede-cessor of the current Dept. of Energy (Lillie et al., 1973). Six reactorswith thermal outputs ranging from 50 kW to 1 MW were built andoperated, and one was placed in earth orbit. A substantial body ofexperimental irradiation tests was reported in this program, manyof which have a bearing on the hydride-fueled LWR that is the sub-ject of this issue. Table 1 compares the pertinent characteristicsof three reactor types: the SNAP reactor, the LWR-hydride reactor(Shuffler et al., this issue-a) and the LWR-oxide reactor (a standardBWR).

Noteworthy in Table 1 is the wide range of uranium contents ofthe fuels. Hydride fuels operate most reliably with low U concentra-tions, which is the reason for the choice of 10 wt% U, correspondingto a uranium density of 0.6 g U/cm3, in the SNAP reactors. To pro-duce acceptable amounts of nuclear energy with so little uraniumper unit volume, the enrichment is 93% 235U. In order to attainthe same 235U density of the fresh fuel as in an oxide-fueled core,the enrichment of the LWR-hydride fuel would have to be scaledaccording to the total uranium density, or:

e(LWR − hydride) = e(LWR − oxide) × (9.3/3.7).

To match a 5%-enriched oxide fuel in this regard, the hydride fuel
for LWR use would require 12.5% enriched uranium. This enrich-ment is higher than the current regulatory limit of 5%, but is belowthe LEU limit of 20%.
The power density of SNAP fuel was only ∼1/4 that of currentLWR oxide fuel. But then, the SNAP reactors were not designed

1 ring and Design 239 (2009) 1406–1424

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Fig. 2. Diffusivity of H in �-Zr.

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408 D. Olander et al. / Nuclear Enginee

or power production. They did, however, operate at very muchigher fuel and cladding temperatures than the proposed hydrideWR fuel. At 850 ◦C fuel centerline temperature and the H/Zr valuesisted in the table for the SNAP reactor, the equilibrium H2 pres-ure is ∼3 atm. While this pressure does not threaten the claddingechanically, it risks hydrogen loss by permeation through theetal. This phenomenon was the major performance constraint for

hese reactors, and is in part the reason for the choice of Hastelloyladding for SNAP reactor fuel.

LWRs cannot tolerate Hastelloy as cladding because of its highickel content and consequent negative effect on neutron economy.lso, LWR hydride fuel cannot operate for a long period at >800 ◦Cecause of the assured catastrophic reaction of the Zircaloy claddingith gaseous hydrogen inside the fuel element. Fortunately, the

ydride fuel peak temperature at the LWR power density is onlybout 550 ◦C (Shuffler et al., this issue-b).

Given the high 235U content of SNAP reactor fuel, high bur-up was easily attainable. The maximum burnup of the oxide fuel60 MWd/kgU) is 1/5 that of the SNAP hydride fuel.

.3. TRIGA reactors

The most widely used of hydride-fueled reactors is the well-nown TRIGA developed by General Atomics (Simnad, 1981;hesworth and West, 1985). With a steady-state power of a fewW, this reactor is primarily for research purposes. Early TRIGA fuel

tilized 8 wt% of highly enriched uranium. With the restriction onnrichment to 20%, the proportion of uranium in the fuel increasedo 45 wt%, or 21 volume percent. Even at this loading, the uraniumensity in the hydride fuel is only 40% of that in UO2. Increasing the35U content is the only way of overcoming this deficiency. TRIGAores are cooled by natural convection with water at about 60 ◦C.ompared to current oxide power-reactor fuel, TRIGA fuel is very

arge: a single “pellet” is about 4 cm diameter and 35 cm long. Theladding is either aluminum or stainless steel. All proposed or con-tructed hydride-fueled reactors have adopted the basic TRIGA fuel.

The exception to the usual low power of these research reactorss the Romanian TRIGA, which utilizes standard-size LWR fuel pel-ets made of (U,Zr)H1.6 instead of UO2. This hydride fuel is reportedo have operated at a linear heat rate (LHR) of ∼80 kW/m at a fuelenterline temperature of 820 ◦C with a forced-convection coolantemperature of 60 ◦C (Iorgulis et al., 1998; Toma et al., 2002). Theesign limits set for the high-power TRIGA core are (Iorgulis et al.,998; Toma et al., 2002) fuel temperatures of 750 ◦C at steady-statend 1050 ◦C during transients. The proposed hydride-fueled LWR isess thermally- demanding than the high-power TRIGA.

. (U,Zr) hydride properties

.1. Hydrogen diffusion

Unlike oxide fuel, where diffusion of corrosion-product hydro-en in �-Zry is a key transport property, the other two majorhases (-Zry metal and in the ceramic -ZrHx) are important forydride fuels. Hydrogen diffusion in the metal controls the kineticsf hydriding during fabrication and in the hydride phase, hydro-

able 2iffusion coefficients in zirconium hydride.

uthors Year Methoda H

lbrecht and Goode (1960) 1960 Diff 1aetz and Lücke (1971) 1971 Diff 1ajer et al. (1994) 1994 NMR 1

a Diff: rate of absorption of hydrogen by solid; NMR: nuclear magnetic resonance.b For H/Zr = 1.58.

Fig. 3. Diffusivity of H in �-hydride.

gen mobility dictates the kinetics of hydrogen redistribution in thetemperature gradient during operation.

The hydrogen diffusivities in these two phases are shown inFigs. 2 and 3. While the agreement among the measured diffusivi-ties in �-Zr is fair (maximum of a factor of 10 discrepancy), the datain Fig. 3 exhibit differences of a factor of 50 between the lowest andhighest lines. Table 2 provides additional details on hydrogen diffu-sion in the �-hydride. The two early measurements were obtainedusing the classical method of absorption of hydrogen from H2 intoa disk or cylinder specimen of ZrHx. In this method, diffusivities aredetermined from curves of weight gain versus time or progressionof the delta phase into the metal. The latest measurement by Majeret al. (1994) utilized nuclear magnetic resonance, which detectsthe mean residence time (�) of a proton on an interstitial site in
the lattice. This measurement yields the activation energy for dif-fusion (Ed, last column in Table 2). Related techniques yield themean jump distance (L), which corresponds to the separation oftetrahedral interstitial sites in the fcc structure of the Zr atoms inthe crystal. The diagram of the structure of the �-hydride crystal in
/Zr range T range, ◦C Do, cm2/s ED/R, K

.56–1.86 500–750 6.0 × 102 17600

.50–1.70 650–800 2.5 × 10−1 8960

.58–1.86 330–700 1.5 × 10−3b 7100b


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ig. 4. Crystal structure of zirconium hydride. The zirconium atoms (large, gray)orm a face-centered-cubic crystal lattice. The H atoms (small sphere) occupy tetra-edral sites, one of which is outlined in the sketch.

ig. 4 shows that there are 8 tetrahedral interstitial sites in the unitell, which consists of 4 zirconium atoms (8 corner atoms shared bycontiguous unit cells and 6 face-centered atoms shared between

wo adjoining unit cells).The hydrogen diffusion coefficient the delta hydride is given by

H = fL2

6�

The factor f is a correlation factor; it accounts for the probabilityhat the jumping atom returns to the site whence it came. It is mod-rately less than unity. The mean residence time � depends upon theump frequency �[exp(−ED/RT)], where � is the vibration frequencyf the H atom in the interstitial site and ED is the potential-energyarrier height separating sites, the number of nearest-neighbor

nterstitial sites (6) and the probability that a site is occupied (x/2,here x represents the H/Zr ratio).

1�

= 6(

1 − x

2

)�[

exp(

− ED

RT

)]

The NMR method measures the diffusivity at a single concen-ration. Based on this feature, Majer et al. (1994) showed that the

easured concentration dependence of the pre-exponential factorlosely follows the theoretical expectation:

H =[

fL2(

1 − x

2

)�]

exp(

− ED

RT

)(9)

he quantity in the square brackets is the pre-exponential factoro. In the range of the experiments by Majer et al. (1994) shown

n Table 2, the activation energy for diffusion (divided by the gasonstant) is a weak function of H/Zr ratio, increasing from 7100 Kt H/Zr = 1.58 to 7800 K at H/Zr = 1.86. This feature may be due toncursions of the �-hydride in the sample.

.2. Thermal diffusivity

The other transport property of ZrHx that affects fuel perfor-ance is the thermal diffusivity (or heat of transport). This property

auses hydrogen in the Zr matrix to move towards cold regions,ven in the absence of a concentration gradient. The process reachesteady state when the gradient due to concentration diffusion just

Fig. 5. Hydrogen redistribution in ZrH1.6 with helium or liquid metal in the fuel-cladding gap; To and TS are the centerline and surface temperatures, respectively(Olander and Ng, 2005).

balances that due to thermal diffusion. In cylindrical coordinates,this condition of zero net flux is given by

dx

dr+ TQ

T2x

dT

dr= 0 (10)

where T is the temperature (in K), x is the H/Zr ratio, r is the radialposition in the fuel pellet and TQ is the heat of transport of H inZrHx divided by the gas constant. The only known measure of thisquantity is that due to Sommer and Dennison (1960), who reportTQ = 640 K.

The solution to Eq. (10) is (Huang et al., 2000; Olander and Ng,2005):

x = AeTQ/T (11)

The constant of integration A is determined from the specifiedaverage H/Zr ratio of the fuel:

xavg = 2R2

∫ R

0

rx(r) dr (12)

Fig. 5 shows the extent of hydrogen redistribution in ZrH1.6 in aparabolic temperature distribution. The solid curve is for a helium-bonded fuel element and the dashed curve is for a fuel element witha liquid metal in the fuel-cladding gap. Redistribution is extensive;the original H/Zr ratio of 1.6 has diminished to 1.46–1.49 at thecenter of the pellet and grown to 1.74–1.78 at the periphery. Thisredistribution has only a minor effect on the neutronic characteris-tics of hydride fuel.

2.3. Thermodynamic properties

The most important thermodynamic properties of the Zr–H sys-tem are the phase diagram and the equilibrium H2 pressure as afunction of H/Zr and temperature. These two properties are con-tained in Fig. 6, which shows isobars of the equilibrium hydrogenpressure superimposed on the binary phase diagram (Zuzek andAbriata, 1990; Wang and Olander, 1995). At temperature exceeding∼800 ◦C, the equilibrium H2 pressure over the hydride is sufficientlylarge that accumulation of this gas in the plenum or hydriding ofthe cladding would occur, accompanied by a reduction of the H/Zrratio of the fuel. If all released H2 migrated to the plenum, theneutron-moderating capability of the fuel would be reduced.

2.4. Thermal and mechanical

Table 3 summarizes the principal thermal and mechanical prop-erties of the delta hydride.

1410 D. Olander et al. / Nuclear Engineering and Design 239 (2009) 1406–1424

essures superimposed (Huang et al., 2000; Olander and Ng, 2005).

∼T

mfio

rrr(es(iti“nw

Ttsawat

TT

P

THYPFTH

Fig. 6. H-Zr phase diagram with isobars of equilibrium H2 pr

Since the uranium metal in the hydride has a conductivity of28 W/m-K, the two-phase thermal conductivity is ∼20 W/m-K.his is about 7 times that of UO2.

To reduce the fuel centerline temperature in hydride fuel, a low-elting, inert liquid metal (Pb–Bi–Sn) replaces helium as the gap

ller. This replacement lowers the centerline temperature by wellver 100 ◦C (Wongsawaeng and Olander, 2007).

The combination of the density variation with H/Zr ratio (2ndow of Table 3), thermal expansion (1st row of Table 3) and hydrogenedistribution due to the in-reactor temperature distribution (Fig. 5)esults in peculiar mechanical behavior of hydride fuel on startupOlander and Ng, 2005). In the parabolic temperature distributionngendered by fission, thermal expansion results in azimuthal ten-ile stresses at the pellet periphery that exceed the fracture stressbarely or quite a bit, depending on which value of the fracture stressn Table 3 is accurate). The combination of hydrogen redistributionowards the cool periphery of the pellet and expansion with increas-ng H/Zr ratio results in significant compressive stresses, calledhydrogen stresses” in the outer portion of the pellet. This phe-omenon was first noted (but not analyzed) by Gylfe et al. (1960),here it was termed “migration stress”.

The total stress is the sum of the thermal and hydrogen stresses.hese two axial components and their sum are shown in Fig. 7 forypical liquid-metal-bonded fuel-pellet operating conditions. Axial
tresses are shown because this component is larger than the totalzimuthal stress. According to Table 3, the fracture stress lies some-here between the dotted lines in the figure. The thermal stress
cting alone is capable of cracking the pellet at the surface. However,he hydrogen stress is highly compressive at large radii, and more

able 3hermal and mechanical properties of (U0.31,Zr)H1.6.

roperty Value

hermal expansion coeff., ◦C−1 ˛ = 7.4 × 10−6(1 + 2 × 10−3T)a

ydrogen expansion (�L/L)H/Zr = 0.027(H/Zr–1.6)oung’s modulus, GPa 130oisson’s ratio 0.32racture stress, MPa 200 (ten.), 55 (ten.), 100 (comp.),hermal Conductivity, W/m-K 18 ± 1eat capacity, J/mole-K (25 + 4.7x) + (0.31+2.01x)T/100 + (1.9+6.4x)/T2 ×a 300 < T (K) < 1000; x = H/Zr.

Fig. 7. Axial stresses in a LM-bonded hydride fuel rod (Olander and Ng, 2005).

than overcomes the tensile thermal stress. The total axial stress istensile out to a fractional radius of 0.8 and exceeds the range of thefracture stresses over most of this interval.

However, the thermal and hydrogen stress components have dif-
ferent time responses. The thermal stress develops as soon as thesteady-state temperature distribution in the pellet is established.This occurs in a couple of days over which reactor startup takesplace. On the other hand, the kinetics of hydrogen redistribution,which is controlled by the diffusivity of hydrogen in the hydride
Reference

Simnad (1981), Beck and Mueller (1968), Yamanaka et al. (1999)Gylfe et al. (1960), Simnad (1981)Simnad (1981), Yamanaka et al. (1999)Simnad (1981)Merten et al. (1958), Gylfe et al. (1960), Beck and Mueller (1968)Yamanaka et al. (2001)

10−5a Yamanaka et al. (2001)

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wU

)(1 + y) × FIMA (15)

D. Olander et al. / Nuclear Enginee

olid are slower. The transient hydrogen redistribution calculationsy Huang et al. (2000) show a strong dependence upon the lin-ar heat rate: at 30 kW/m, steady state is achieved in ∼75 h, but at5 kW/m, ∼10 days are required. Interpretation of curves such ashose shown in Fig. 7 must take into account the possible differ-nces in the time constants of the thermal- and hydrogen-stressomponents.

.5. Chemical properties

Chemical interaction between zirconium hydride and Zircaloyladding is thermodynamically favored but the kinetics arenknown. Hence, designation of Zircaloy as the cladding metal forydride fuel rods must be approached with great caution. First,onsider the worst case.

The surface temperature of a helium-bonded hydride fuel pel-et operating at a linear heat rate of 37 kW/m with a 35-�m gaphickness is ∼500 ◦C (Table 5). Taking into account the redistribu-ion shown in Fig. 5 and the phase diagram of Fig. 6, the fuel surfaceenerates an equilibrium H2 pressure of 5 × 10−3 atm. This partialressure is not sufficiently large to move hydrogen along the gap tohe plenum, but it can drive hydrogen to the cladding inside surfacehere metallic zirconium essentially reduces p(H2) to zero. Means

f avoiding this possibility are discussed below.Replacing helium in the gap with a liquid metal prevents hydro-

en from reaching the cladding inner surface as long as the gap ispen. However, closure of the fuel-cladding gap generates pellet-ladding mechanical interaction (PCMI). Hard contact of the twoolids may provide a mechanism to overcome the sluggishness ofhe gas-surface reaction. The conservative design response to thisituation is to avoid PCMI entirely by making the initial gap largenough that the combination of fuel swelling and cladding creep-own does not close the gap in the lifetime of the fuel. An initial cold,adial gap of ∼150 �m (compared to ∼80 �m in conventional oxideuel elements) is sufficient to prevent PCMI in BWR hydride fuel toburnup of 60 MWd/kgU. With LM-bonding, no fuel-temperature

ncrease results from the larger gap size.Other methods have been suggested to separate the fuel and

ircaloy cladding. Most of them involve adding a hydrogen perme-tion barrier to the cladding’s inner surface. They include:

.5.1. Stainless steel linerThe transition metals do not form stable hydrides, and the sol-

bility of hydrogen in stainless steel (SS) is low (but not zero).o exploit this property, duplex cladding consisting of a Zircaloyuter tube and a SS inner liner has been considered as a means ofeducing hydrogen loss from the fuel. Analysis of the hydrogen per-eation process is given in Appendix A. Using the permeability of

ydrogen in stainless steel reported by LeClaire (1984), 17 years areequired to reduce the H/Zr ratio of the fuel from 1.6 to 1.55. Fromhydrogen-retention point of view, the SS liner is very effective.

The advantages of the liner over cladding entirely made of stain-ess steel are

(a) Reduced parasitic neutron capture by the elements in the alloy.b) Avoidance of waterside intergranular stress-corrosion cracking

(IGSCC) of the SS.

The primary disadvantages of this approach include:

a) In BWR cladding, the absence of the soft Zr liner for alleviating
cracking by pellet-cladding interaction (PCI).
b) The SS liner may also be susceptible to internal stress corrosioncracking by fission products.

c) Differential expansion between Zr and SS may cause debondingof the two.

nd Design 239 (2009) 1406–1424 1411

2.5.2. SiC internal coating or sleeveSilicon carbide is very resistant to chemical attack by or perme-

ation of hydrogen; neutronically, it is practically inert and is stableagainst radiation damage to very high neutron fluences. It is usedvery successfully in HTGR fuel as a hydrogen (tritium) permeationbarrier (Greenspan, 1998).

2.5.3. Glass-enamel coatingA glass-enamel coating metal cladding, about 0.08 mm thick,

has been successfully bonded to the inner surface of the Hastelloycladding in SNAP reactors and survived operation at temperaturesup to 700 ◦C (Hesketh and Stanbridge, 1993).

2.5.4. Zirconia coatingsThe solubility of H2 in ZrO2 is very low (several ppm atomic);

consequently the oxide should be very resistant to hydrogen per-meation. From the point of view of fabrication, oxidizing the innersurface of Zircaloy cladding is the simplest, and certainly theleast expensive, of all coating methods. However, its effectivenessdepends on its resistance to cracking, which afflicts the watersidecorrosion scale on the cladding outer surface.

Oxidizing the outer surface of the hydride fuel pellets has beendemonstrated (and patented, Eggers, 1978) and appears to providea satisfactory hydrogen permeation barrier up to 800 ◦C. In addi-tion, when the fuel-cladding gap closes, the oxide layer betweenthe hydride and Zircaloy prevents direct contact between the lattertwo solids.

3. Irradiation effects

In common with all nuclear fuels, the key irradiation propertiesare fuel swelling, fission gas release and fission-product chemistry.These are functions of temperature (or linear heat rate) and burnup.

3.1. Burnup units

The literature on hydride fuels expresses burnup either as F, thenumber of fissions per unit volume, or FIMA, “Fissions per InitialMetal Atom”1:

FIMA = F

(NU + NZr)(13)

NU and NZr are the atom densities of U and Zr in the as-fabricatedfuel, respectively. NZr is given by Eq. (2).

In power reactor literature, on the other hand, burnup isexpressed as MWd/kgU, where the mass of U refers to fresh fuel.However, this unit is not appropriate for comparing hydride andoxide fuels, as can be seen from the following. With the energy offission taken as 3.2 × 10−11 J/fission, the MWd/kgU unit of burnup isrelated to the number of fissions per cm3 and the uranium densityof the fresh fuel by

BU(

MWdkgU

)= 3.7 × 10−19 F

�U(14)

Conversion from FIMA to BU is accomplished with:

BU = 3.7 × 10−19× NZr(1 + y) × FIMA

1 %FIMA is equivalent to the burnup unit “metal atom %” that is commonly usedin the literature on hydride fuel.

1 ring and Design 239 (2009) 1406–1424

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det“swm

wtafttrmews

cthaen∼awfsuda∼s(


As shown in Table 1, the uranium densities of the hydride fuelsre substantially lower than that of oxide fuel. If oxide and hydrideuels are to be compared on the basis of energy output per unit fuelolume (which is proportional to F), the uranium density shoulde removed from Eq. (14). A more appropriate definition for thisurpose is the “equivalent oxide” burnup:

Uequiv.ox. = BU × �U

9.3= 4.0 × 10−20F (16)

here 9.3 is the density of uranium in UO2. Fuels with the samequivalent-oxide burnup have generated the same amount ofnergy per unit volume.

Because FIMA is commonly used for hydride fuels, conversion tohe equivalent-oxide burnup is required. This is accomplished withhe aid of Eq. (15):

Uequiv.ox. = 2.4 × 103(

�U

9.3

)(1 − wU

wU

)(1 + y) × FIMA (16)

or the 45 U wt% hydride considered here, Eq. (16) reduces to:

Uequiv. oxide = 1.5 × 103 × FIMA (16a)

Thus, 1% FIMA in this particular hydride fuel is equivalentin terms of energy production per unit volume) to a burnup of5 MWd/kgU in UO2.

.2. Fuel Swelling due to void formation

Very early in life, oxide fuel shrinks (densifies) because ofestruction of fabrication porosity by fission fragments. Thearly-time volume change of hydride fuel is either nonexis-ent (T < ∼700 ◦C) or exhibits large increases (T > 700 ◦C) termedoffset swelling”(Lillie et al., 1973). Following these initialwelling/densification stages, both fuels continue to swell linearlyith burnup as a result of introduction of fission products into theatrix.In the SNAP program (Lillie et al., 1973), swelling of hydride fuel

as measured both in-reactor and by quite sophisticated irradia-ion tests. In normal irradiation tests, the effects of temperaturend fission rate cannot be separated because the latter controls theormer. The SNAP program utilized a test rig in which cooling ofhe in-reactor specimens was accomplished by a gas flowing alonghe exterior of the specimen holder. Without changing the fissionate, the specimen temperature was controlled by using differentixtures of helium and xenon in the coolant gas, thereby enabling

xamination of the effect of each variable separately. Swellingas determined by density measurements of the irradiated

pecimens.Microscopic examination of swollen hydride fuel revealed large

avities adjacent to uranium particles. These cavities are believedo be true voids, not fission-gas bubbles. Voids are generated in theydride matrix close to the uranium particle by the radiation dam-ge created by escaping fission fragments. Fig. 8 is a transmissionlectron micrograph of these voids (Lillie et al., 1973). The ura-ium particles are not imaged in this TEM, but were reported as5 �m in diameter and ∼40 �m apart. The temperature of the fuelt the location of the TEM was estimated at 785 ◦C and the burnupas ∼2 × 10−3 FIMA, which is about twice the saturation burnup

or offset swelling. The void-size distribution was roughly bell-haped, ranging from the microscope’s resolution limit of 10 nmp to a maximum diameter of ∼120 nm. The average diameter (notefined) was about 60 nm. The number density of these voids, aver-ged over an area comprising numerous uranium particles, was
5 × 10−7 nm−3. From these figures, the overall volume swelling
hould be:

�V

V

)void

= �D3

6Nvoid = � × 603

6× 5 × 10−7 = 0.06

Fig. 8. Voids near a uranium particle following irradiation of hydride fuel in a SNAPreactor (Lillie et al., 1973).

The (�V/V) values reported by Lillie et al. (1973) were ∼10% inthe immediate vicinity of the uranium particles and ∼4% averagedover a large cross-section of the fuel. The swelling calculated by theabove equation lies between these two observed values.

Fig. 9 shows that offset swelling can be quite large and highlytemperature-sensitive: at 760 ◦C, it is 5%, but it vanishes at ∼650 ◦C.In these plots, the offset swelling saturates at a burnup of 10−3

FIMA; however, no experimental evidence was offered to supportthis supposition.

The top graph in Fig. 9 shows unusual changes in offset swellingwith the fission rate, or the linear heat rate. The decrease in offsetswelling with this variable is attributed to behavior of voids as theprimary source of the volume change.

The data underlying the plots in Fig. 9 are shown in Fig. 10. Unfor-tunately, the burnup rates for each data point are not given by Lillieet al. (1973). The lines shown in the graph were estimated fromoffset swelling values taken from Fig. 9. They fit the equations:

log(

%�V

V

)void

= A − B

(103

T

)(17)

The coefficients A and B depend on the burnup rate accordingto:

A = 9.2 + 2.2 × 103(FIMA/year)

B = 8.7 + 2.4 × 103(FIMA/year) (18)

Comparison of the void production in irradiated hydride reac-tor fuel with the well-developed theories of void swelling in metalsprovides some insight into the behavior shown in Fig. 9. In par-ticular, the features for comparison are the dependence of voidsize/swelling on temperature and burnup rate and the conditions
that lead to saturation of void growth.
3.2.1. Temperature dependenceFig. 9 shows a sharply increasing offset swelling with increasing

temperature. The typical bell-shaped curves of void-growth rate

D. Olander et al. / Nuclear Engineering a

vsews

3

h

Fig. 9. Swelling behavior of (U,Zr)Hx SNAP fuel.

s temperature in metals (e.g., Fig. 19.15 of Olander, 1976) exhibitimilar behavior at the onset of swelling. However, the temperatureffect observed in hydride fuel is on the magnitude of offset swelling,hile the temperature effect seen in metals refers to the rate of void

welling.

.2.2. Burnup rateThe dramatic effect of the burnup rate on offset swelling in

ydride fuel (Fig. 9) does not have a direct counterpart in void

Fig. 10. SNAP fuel-offset void-swelling data (from Lillie et al., 1973).

nd Design 239 (2009) 1406–1424 1413

swelling of metals. The simple theory of the latter (e.g., Section19.5.11 of Olander, 1976) predicts a persistent, slow void-radiusgrowth rate of the form R ∝

√dpa/s, where dpa/s is the rate of

atomic displacements. If this behavior also implies an increase inthe saturation void size in metals with damage rate, the burnup-rateeffect in hydride fuel is diametrically opposite.

3.2.3. Saturation of swellingThe offset swelling values plotted as data or correlation lines

in Fig. 10 are (supposedly) independent of burnup. However, itis doubtful that the experiments reported by Lillie et al. (1973)accurately measured the burnup at which saturation occurred.It is unlikely that saturation occurred at 10−3 FIMA for all tem-peratures and burnup rates, as shown in Fig. 9. Nonetheless, itappears clear that saturation of offset swelling occurred, so acomparison with the analogous phenomenon in metals is appro-priate.

Two theories explaining saturation of void growth in metals aresummarized in Section 19.5.15 of Olander (1976), which containscitations of the original sources. However, there is no experimentalevidence for saturation of void swelling in metals.

The first model visualizes a stationary state with all voids con-nected by curved dislocations, with no free dislocations left toclimb. This situation just balances the preference of interstitials fordislocation lines, which is the root cause of void swelling in metals.Because all dislocation lines are pinned by the voids, they can nolonger climb by absorbing interstitials, even though the bias factordifference favoring interstitials remains. The quantitative develop-ment of this model yields a function giving the combinations of voidradius, void number density, and dislocation density at which voidgrowth ceases.

The second model examines the effect of dislocation loops nearvoids. The dislocation creates a stress field around itself. In orderto maintain a stress-free void surface, an induced, or image, stressfield is created in the void. The void in essence now behaves like adislocation, and acquires the same bias for interstitials as the actualdislocations. Because both sinks for point defects are equally biasedfor interstitials, all point defects generated by irradiation are eitherannihilated by recombination or flow in equal numbers to voidsand dislocations. As a result, void growth ceases.

It is conceivable that saturation of void growth in hydride fueloccurs because of one of the above metal-based models. However,all models for metals are founded on the creation of damage byfast neutrons whereas the principal atom-displacement agent inirradiated hydride fuel is the fission fragment. Fission fragmentscan destroy voids or intragranular bubbles in UO2 by a mecha-nism termed “re-solution”. A brief review of the literature on thissubject is given by Olander and Wongsawaeng (2006). A com-mon observation in irradiated UO2 is a population of intragranularbubbles whose size is independent of burnup. This observation isexplained by a balance between bubble growth by absorption ofgas atoms (and vacancies) generated by fission in the solid latticeand bubble destruction by fission-fragment re-solution. Althoughthis model is advanced for cavities containing fission gas, thereis no reason that it could not be applied to voids in hydridefuel.2

3.3. Fuel swelling due to fission products

For UO2, fuel dimensional changes during irradiation are dueprincipally to the ingrowth of solid fission products, with smaller

2 Lillie et al. (1973) assume that the cavities observed in irradiated hydride fuelwere true voids, but the possibility that the cavities contained fission gas was notinvestigated.

1 ring a

cos

bFpa

OtvHdnvgs

tm

3

tiusHrgtW1fb

fi

2

3

pf

undefined “diffusion” process.Two problems are immediately evident from Fig. 11.First, release fractions measured by post-irradiation anneal tests

are reported as a function of temperature only. However, the release


ontributions due to fission-gas bubbles and early-on, to removalf as-fabricated porosity (densification). The solid fission-productwelling rate is about 0.07% per MWd/kgU.

In hydride fuel, the fission-product-swelling rate is representedy the slope of the lines in Fig. 9 after cessation of offset swelling.ollowing this period, hydride fuel swells at a constant rate of ∼3%er %FIMA. Converting from FIMA to equivalent-oxide burnup givesswelling rate of 3/1.5 × 103 = 0.002, or

�V

V= 0.2% per BUequiv. ox

n this basis, the fission-product swelling of hydride fuel is ∼3imes larger than that of oxide fuel. It is also twice as large as thealue computed for the contribution of solid fission products byuang et al. (2001). A good part of the reason for this significantifference is the presence of Xe + Kr, Te and I in the fuel, which wereot taken into account by Huang et al. (2001). Below ∼750 ◦C theseolatile elements are retained in the fuel (see Section 3.4). The rareases may exist as nanobubbles that were not observed in the SNAPtudies.

Fission-product swelling has a significant effect on closure ofhe fuel-cladding gap and the concomitant onset of pellet-cladding

echanical interaction (PCMI) (see Section 7).

.4. Fission-gas release

A major difference between oxide and hydride fuels involveshe mechanisms responsible for the release of fission gas duringrradiation. This phenomenon has been exhaustively studied forranium dioxide fuel, and there is enough empirical evidence toupport the predictions of analytical and computational models.owever, the data on fission-gas release from hydride fuel lack

obustness and careful validation. What data are available sug-est that recoil is the only mechanism of fission-gas release upo temperatures in the neighborhood of 700 ◦C (Chesworth and

est, 1985). The release fraction due to recoil is of the order of0−4, supporting the assumption that fission gas is not releasedrom hydride fuel. The justification for this statement is presentedelow.

Many ways are available for quantitative measurement ofssion-gas release from irradiated fuel.

In-reactor tests include measurement of:

1. the buildup of pressure within an instrumented test fuel rodresulting from the release of the stable Xe isotopes (132Xe, 134Xeand 136Xe) and 85Kr. The released gas accumulates in the plenumand the fuel-cladding gap. The fraction released increases withtime.

. the rate of release of a short-half-life isotope (85mKr or 131Xe) bypassing a carrier gas through a test fuel rod or fuel specimen. Thereleased radioisotopes are trapped on refrigerated charcoal andthen measured by gamma spectroscopy. Steady-state release isachieved and the ratio of the release rate (R) to the birth rate (B)(i.e., the production rate in the fuel) is determined. This R/B ratiois often (erroneously) called the fraction released.

The post-irradiation test involves:. annealing the specimen in a furnace through which a carrier gas

flows. Typically, 133Xe gamma activity is used to measure thequantity released. For such an experiment the fraction releasedis the ratio of the amount of nuclide released in a certain timedivided by the quantity of the isotope contained in the specimen
following prior irradiation.
Interpretation of these experiments ranges from the very sim-lest Booth model to partially mechanistic models included in largeuel-behavior codes. The Booth model is based on diffusion from the

nd Design 239 (2009) 1406–1424

interior of the grains of the fuel to the grain boundaries, whencerelease occurs (see Section 15.4 of Olander, 1976). The basic proper-ties that govern the interpretation of all three of the tests describedabove are the diffusivity of the isotope in the grains (D) and theradius of the grains (a), which appear as the combination a2/D. Thisparameter is the only one needed in the Booth model and appears indifferent forms in the quantitative interpretation of the tests. What-ever model is used to analyze test data, the expectation is that thesame model and its parameters can be used to accurately predictrelease under power reactor conditions, an expectation that is rarelymet.

All fission-gas release theories, from the Booth model on, weredeveloped for application to UO2 fuel. Because the microstructure ofU–Zr hydride in no way resembles that of UO2, with one exception,the models are useless for understanding release from the formerfuel. The exception is the mechanism by which fission fragmentsborn within ∼10 �m of an exposed surface escape from the solid.This so-called recoil mechanism produces a release rate-to-birthrate ratio equal to 1/4�(S/V)�, where S/V is the surface-to-volumeratio of the fuel, � is the range of fission fragments in the fuel and� is the fraction of the escaping fission fragments that are not re-implanted in the opposite surface. Typical values of recoil R/B are10−4.

There are numerous reports of fission product release fromU–Zr hydride (TRIGA) fuel (Chesworth and West, 1985; Westet al., 1986; GA Technologies, unknown). Unfortunately none ofthem are the original sources of the data they report. A com-pendium of these second-hand reports is shown in Fig. 11. Thisplot appears in all reports of fission-gas release from hydridefuel, with the latest experimental results added to it. Most of theresults come from post-irradiation anneal experiments, with a fewexperiments of the in-reactor type 2 described above. No datahave been obtained from in-reactor fuel rods (method 1 above),the claim being that no fission gas isotopes could be detected inpost-irradiation examination. How seriously to take this claim isuncertain, since the temperature of the fuel was poorly known orunknown.

The dashed horizontal line in Fig. 11 is attributed (by the citedreferences) to recoil release, which, given the magnitude of the frac-tion release and its temperature independence up to 600–800 ◦C, isa reasonable interpretation. The curve through the remaining datapoints is not model-based. The only claim is that it is due to some

Fig. 11. Fission-gas release from U–Zr hydride fuel (Olander and Ng, 2005).


Table 4Probable chemical and physical states of fission products in oxide and hydride fuels.

Elementa Yield States in oxide States in hydride

Chemical Physical Chemical Physical

Zr (Nb) 0.3 ZrO2 Solutionb ZrH1.6-x �-hydrideREc (Y) 0.53 RE2O3 Solution REH2 In �-hydride?Ba (Sr) 0.15 BaZrO3 Oxide #1 (Ba,Sr)H2 In �-hydride?Cs (Rb) 0.2 Cs, Cs2UO4, CsI Gas, oxide #2 Cs, CsI Gas, solidMo 0.25 MoO2, Mo Solution, alloy ? ?NMd 0.25 Elements Alloy U(NM)3 IntermetallicI (Te) 0.01 CsI Compound CsI SolidXe (Kr) 0.25 Element Gas Element GasU (Pu) – UO2 Oxide U Element

a rst ele

ft

ter

nsdSpbib

3

atZtidbtnr

U(

4

4

ia

apat

The element in parentheses is closely related chemically and physically to the fib Dissolved in UO2.c RE = rare earths (La, Ce, Pr, Nd, Sm, Pm, Eu, Gd).d NM = noble metals (Pd, Ru, Rh, Tc, Pt).

raction from this type of test is a function of time as well asemperature.3

Second, the low-temperature data points in Fig. 11 were reportedo have been determined by the post-irradiation technique. How-ver, recoil release can only be detected while fission is occu-ring.

Despite the rudimentary state of understanding of the mecha-ism(s) of fission-gas release from hydride fuel, the available datatrongly suggest that if fuel temperatures are kept below ∼650 ◦Curing operation, fission-gas release is negligible. In the article byhuffler et al. (this issue-b), the design limit for the centerline tem-erature at steady-state is 750 ◦C. In view of the observed swellingehavior, this value may be somewhat aggressive. It is essential that

rradiation tests of hydride fuel be conducted in order to verify theehavior shown in Fig. 11.

.5. State of fission products

The chemical and physical states of the fission products in irradi-ted U/Zr hydride fuel has been studied by Huang et al. (2001) usinghe thermochemical code Thermo-Calc. Mixtures of the elements U,r, H, O, and a variety of fission products (FPs) were analyzed forhe equilibrium composition for element ratios simulating burnupn reactor. In addition to the chemical states, Thermo-Calc also pre-icts the phases present at equilibrium. Oxygen was assumed toe present as an impurity (in the form of ZrO2) at a concentra-ion of 1000 wt ppm. Unfortunately, the U/Zr and H/Zr ratios wereot specified, but they are taken here to be 0.31(45 wt%) and 1.6,espectively.

Table 4 summarizes the states of fission products in irradiatedO2 and (U0.31Zr)H1.6O0.01. The former are taken from Olander

1976) and the latter from Huang et al. (2001).

. In-reactor chemical behavior

.1. Impurity oxygen

The small quantity of impurity oxygen in the fresh hydride fuels present as ZrO2. The oxides of the rare-earth elements and of Band Sr are more stable than ZrO2, so as the fission products (FP)

3 Justification for this omission is based on the claim that the post-irradiationnneal data in Fig. 11 apply to fuel that has been irradiated long enough for all fission-roduct activity to achieve equilibrium, when (it is claimed), the release fraction ismaximum (Chesworth and West, 1985). This does not obviate the need to report

he length of time of the anneal.

ment.

grow in, the following reaction takes place:

2RE + 1.5ZrO2 + 1.5xH → RE2O3 + 1.5ZrHx (19a)

2(Ba, Sr) + ZrO2 + xH → 2(Ba, Sr)O + ZrHx (19b)

The “H” in these reactions is taken from the hydride in orderto combine with the “liberated” Zr, thus reducing the value of x.The details of this process are given in Appendix B. The end resultis reduction of the initial H/Zr ratio of 1.6 to 1.59 when all oxygenhas been transferred from ZrO2 to the fission-product oxides. Forfuel with a fission rate density of 2 × 1013 cm−3 s−1, this stage iscomplete after approximately 4 months of irradiation.

4.2. Oxygen potential in hydride fuel

The oxygen potential (�GO2 = RT ln pO2 ) in a fuel rod isimportant because it determines (thermodynamically) whether thecladding inner wall can be corroded, as it is in oxide fuel. The onlyoxygen present in hydride fuel is an impurity, and it becomes boundas rare-earth or alkali-earth oxides. Accordingly, the oxygen poten-tial is expected to be very low. Just how low can be determined fromthe thermochemistry of the following reaction4

(RE)2O3 + 2H2 = 2(RE)H2 + 32 O2 (20)

Although not technically a rare earth, yttrium is very similarin its chemistry to the true members of this group. Consequently,Y will be taken as a surrogate for RE. The above reaction can bebroken into component formation reactions and their associatedfree energy changes at 800 K:

RE + H2 = (RE)H2 �Gf(RE)H2

= −26 kcal/mole (21H)

2RE + 32 O2 = (RE)2O3 �Gf

(RE)2O3= −400 kcal/mole (21O)

Subtracting (21O) from twice (21H) gives reaction (20), so thestandard free energy change of the latter is

�Go(20) = 2�Gf

(RE)H2− �Gf

(RE)2O3= 348 kcal/mole

and the law of mass action gives the oxygen pressure:

p = [exp(−348 × 103/1.986 × 800) × p2 ]2/3 = 2 × 10−67 atm
O2 H2
or an oxygen potential of −245 kcal/mole. Zirconium does not oxi-dize at this oxygen pressure, so the cladding inner surface shouldnot become oxidized.

4 It is immaterial that the reaction as written does not actually occur; it is sufficientthat all species it contains are present in the system.

1 ring and Design 239 (2009) 1406–1424

4

qtr

�

ht

pHZ

gtntMcHoaot

4

gedchgfiT

Z

oaTamoaotsvstTs


.3. Reduction of the H/Zr ratio during irradiation

After conversion of impurity ZrO2 to the FP oxides, all subse-uent RE and Ba,Sr produced by fission extracts hydrogen from ZrHx

o form the hydrides (RE)H2 and (Ba,Sr)H2. The result is a continualeduction in the H/Zr ratio of the hydride.

NH = 2(YRE + YBa,Sr)1.5YRE + YBa,Sr

(2.6 × 10−6)(td − 190)

= 3.8 × 10−6(td − 190)

After 1 year of irradiation, the quantity of hydrogen bound in FPydrides is 6.7 × 10−4 moles/cm3. The initial hydrogen concentra-ion is (from the numbers in the previous paragraph).

9.4 × 10−3 moles H/g hydride × 8.3 g hydride/cm3

= 7.8 × 10−2 moles H/cm3

So, a fraction 6.7 × 10−4/7.8 × 10−2 = 8.5 × 10−3 of the hydrogenresent has been removed from the ZrH1.59, further reducing the/Zr ratio to 1.576. Every 6 months, ∼1% of the hydrogen in therHx matrix is transferred to fission products.

This process may not be as serious as it first appears. The hydro-en removed from the Zr remains in the fuel as FP hydrides, sohe total hydrogen concentration is unchanged. Since the fuel doesot lose hydrogen, the neutronics of the system are not affected byhe switch of the metal atoms to which the hydrogen is attached.

oreover, The fission-product hydrides are more stable thermo-hemically than ZrHx, so at a given temperature, the equilibrium2 pressure over a mixture of ZrHx and FPH2 is lower than thatver pure ZrHx − y, where y depends on the burnup, as indicatedbove. The lower H2 pressure reduces the risk of overpressurizationf the rod in the event of a transient that substantially increases fuelemperature.

.4. Hydrogen loss to the gas phase

During normal operation, loss of hydrogen from ZrH1.6 to theas phase in the fuel element is not significant, owing to the lowquilibrium H2 pressure at fuel temperature. However in acci-ent conditions accompanied by high temperature excursions andladding failure, rapid hydrogen release may constitute a uniqueazard. Release from the fuel occurs when the equilibrium hydro-en pressure of the fuel (from Fig. 6, modified by conversion tossion-product hydrides) exceeds that in the gap or plenum gas.he dehydriding reaction is:

rHx → ZrHy + 12 (x − y)H2 (22)

In order to determine the kinetics of this reaction, a specimenf ZrHx was suspended from a microbalance in a vacuum furnacend the mass loss recorded as a function of time (Gutkowski, 2005).he top graph in Fig. 12 shows a typical result. The most significantspect of this plot is its linearity. This is wholly unexpected from aechanistic point of view. One of two steps can control the kinetics

f this reaction. The first is diffusion of hydrogen (as interstitial Htoms) in the zirconium hydride matrix to the free surface. The sec-nd is recombination of H atoms at the surface to form H2, whichhen escapes to the gas phase. For either rate-limiting step, the ratehould have decreased with time, with a consequent upward cur-
ature of this plot. The constant dehydriding rate implied by thetraight line in the top graph implies zero order for the above reac-ion (i.e., the rate is independent of H concentration in the hydride).hese experiments need to be repeated in a typical in-reactor atmo-phere (∼20 atm He) in order to verify this strange behavior.
Fig. 12. Dehydriding kinetics of ZrHx; top: mass loss (converted to H/Zr ratio) as afunction of time at 692 ◦C; bottom: Arrhenius plot of rate data (Gutkowski, 2005).

The bottom graph in Fig. 12 is a conventional Arrhenius plot ofthe dehydriding rates. The line is represented by

rate = 8 × 1011 exp(

−34, 000T

)mmoles H

cm2-s

The number in the exponential term corresponds to an activa-tion energy of 280 ± 60 kJ/mole.

The significance of these results can be appreciated from thefollowing example in a fuel rod with breached cladding. Suppose a1-cm diameter, 1-cm long pellet of U0.31ZrH1.6 is at a uniform tem-perature of 700 ◦C. The ∼80 volume percent hydride in this fuelhas a density of 5.64 g/cm3. The pellet contains 0.0475 moles ofZr and 0.076 moles of H. From Fig. 12, the H flux at this temper-ature is ∼3 × 10−7 moles H/cm2-s, so the rate of H loss from thesides of the pellet exposed to the open gap is ∼10−6 moles H/s.In 1 h, the pellet loses 3.6 × 10−3 moles H, which corresponds toa reduction in the H/Zr ratio from 1.6 to 1.52. If continued, thisrate of H loss may lead to a significant buildup of H2 in the ex-core environment and to increased reactivity of the H-depleted fuelwith steam. In intact LWR fuel rods, on the other hand, the smallplenum volume allows the H2 pressure to build up to its equilib-rium value before significant H depletion of the fuel occurs (seeSection 5).

4.5. Stability of hydride fuel in water

The compatibility of hydride fuel with coolant water is a primeconsideration in the use of this material in LWRs. Although long-term tests of the fuel in high-pressure water at ∼300 ◦C have notbeen performed, quench tests of TRIGA fuel (identical in com-
position to the proposed power-reactor fuel) have been reported(Lindgren and Simnad, 1979). Specimens about the size of a BWRoxide fuel pellet were heated up to 1200 ◦C (atmosphere not spec-ified) for a matter of minutes and dropped into water. The authorsreport the retrieved specimens to have suffered “minor cracking”


Table 5Operating temperatures of PWR fuel rods with hydride or oxide fuel. The fuel ODis 12 mm and the LHR is 37.5 kW/m. The coolant temperature is 300 ◦C. He and LMgap-fillers are compared.

Temperature, ◦C U0.31ZrH1.6 (He) U0.31ZrH1.6 (LM) UO2 (He)

Fuel centerline 680 555 1450a

�Tfuel 170 170 665�Tgap 125b 1+ 125b

�Tclad 46 46 46T

bfc

5o

egca

fto(tfb(o�attolg

bfoZsobsdtm

ticifpe

riL

fluid 39 39 39

a UO2 thermal conductivity = (22.7 + 7 × 10−3T(K)]−1.b For a gap thickness of 35 �m.

ut otherwise were in excellent condition. The average weight lossor 8 tests was 2%. This was attributed to hydrogen loss, partiallyounterbalanced by surface oxidation.

. Comparison of liquid-metal-bonded hydride- andxide-fueled LWRs

Estimated temperatures are shown in Table 5 for three PWR fuellements: two hydride fuels, one with helium in the fuel-claddingap and the other with a liquid-metal bond. For comparison, theomparable temperatures in a conventional oxide-fueled systemre also given.

This table illustrates some of the favorable features of hydrideuel relative to oxide fuel. The first is the much lower fuel tempera-ures for the same LHR. This is due to the large thermal conductivityf the hydride fuel, which is approximately equal to that of ZircaloyZry). However, the important consideration is not the tempera-ures per se; it is how the lower temperatures in the hydride affectuel performance. At the maximum temperature of the helium-onded hydride fuel, fission product release is due to recoil onlysee Section 3.4), whereas the UO2 fuel is hot enough for releasef fission gases by diffusion to be significant. The ∼4-fold lowerTfuel in the hydride fuel compared to the oxide version consider-

bly reduces the thermal stresses in the former, probably enougho avoid pellet cracking entirely. For the conditions given in Table 5,he stored energy in the helium-bonded hydride fuel is one-quarterf that in the oxide fuel at the same LHR. The factor is evenarger if the hydride fuel has a liquid-metal in the fuel-claddingap.

The choice of the H/Zr atom ratio of 1.6 is a compromiseetween incorporating the largest possible hydrogen concentrationor neutron-moderation without generating too large a hydrogenverpressure. At 700 ◦C, for example, Fig. 6 gives p(H2) = 0.1 atm forrH1.6. Hydrogen gas filling a 15-cm3 plenum at this pressure con-titutes less than 0.1% of the hydrogen in a standard LWR-size pelletf (U0.31Zr)H1.6, so there is no risk of hydrogen depletion of the fuely this mechanism. The choice of an H/Zr ratio of 1.6 places the fuelquarely in the center of the �-Zr–H phase, which eliminates theanger that modest composition variations will result in precipita-ion of another phase. However, the H2 pressure does not limit the

aximum operating temperature during normal operation.Hydride fuel-element designs call for replacement of helium in

he fuel-cladding gap by a liquid metal (LM). The alloy of choices the ternary Pb–Sn–Bi eutectic, which melts at ∼100 ◦C and ishemically benign (Wongsawaeng and Olander, 2007). It serves twomportant purposes. The first is to protect the cladding inner wallrom noxious fission products. The second is to reduce the fuel tem-eratures by much 100 ◦C or more compared to helium-bonded fuel
lements.
Demonstration of the thermal benefits of LM-bonded fuelequires a test-reactor irradiation. Until this is done, the follow-ng simple transient test served the same purpose. Helium- andM-bonded, UO2-fueled, Zircaloy-clad rodlets were quenched from

Fig. 13. Transient responses of fuel centerline thermocouples in 3-pellet rodlets withhelium or a liquid metal in the fuel-cladding gap.

600 ◦C by immersion in a large body of water at 25 ◦C. Each rodlethad a thermocouple in a hole drilled into the centerline of themiddle pellet in order to measure the transient response of thefuel centerline temperature. The external heat-transfer coefficientwas determined by performing the same test on a solid copperrod of the same diameter as the miniature fuel elements. Fig. 13shows the experimental results along with the theoretical predic-tions obtained by solving the heat conduction equation in fuel withthe boundary condition accounting for the series resistances dueto the fuel-cladding bond material, the cladding, and the externalfluid film. The only difference between the two rodlets was the bondmaterial.

Two conclusions can be drawn from this test. The first is thatthe LM is a much more efficient heat transfer medium than helium,which is not surprising considering the difference in the thermalconductivities (kLM ∼ 100kHe). The second feature of Fig. 13 is thegood agreement between the calculated and experimental curvesfor the LM bond but the vast discrepancy for helium in the gap.The latter is due to the large radial gap thickness (estimated at250 �m cold) and the likelihood of off-center pellets. However,these geometrical details are unimportant for the LM-bonded ele-ment, because the gap thermal conductivity is so large that thereis no temperature drop across it irrespective of its size or align-ment.

6. Hydride fuel fabrication

A glance at the phase diagram in Fig. 6 suggests that fabri-cating massive, crack-free pieces of (U0.31Zr)H1.6 is likely to be acostly process. Following preparation by arc melting the pure met-als, the U–Zr alloy needs to be hydrided carefully. Adding hydrogenat constant temperature moves the system through three phases:first �-Zr, then the two-metal-phase region, then �-Zr, then themetal-hydride two phase region and finally into the � hydride singlephase. Volume changes in this process are significant. The zirco-nium atom density in �-Zr is 16% greater than that in the �-hydride,which implies a volume increase on hydriding of the same amount.In addition, the crystal structure changes.

Fig. 14 shows the flow chart for producing (U,Zr)Hx pellets readyfor insertion into cladding. Uranium hexafluoride received from theenrichment plant is reduced to the tetrafluoride with hydrogen gas,leaving a waste of corrosive HF to be disposed of. Fig. 15 shows the
apparatus in which this step is performed. The conditions are an H2pressure of 1 atm and a temperature of ∼500 ◦C. The UF4 powdercollected at the bottom of the reaction vessel is transferred to areduction furnace (called a bomb), in which Ca (or Mg) reduces the

1418 D. Olander et al. / Nuclear Engineering a

U

U

pmlua

asapmo

affii

2

34

Fig. 14. Overall hydride-fuel pellet production flow diagram.

F4 to a metal:

F4(s) + Ca → U(L) + CaF2(s)

This reaction is highly exothermic, so care must be taken torevent runaway temperatures. The final temperature is above theelting point of uranium (1132 ◦C). The CaF2 slag floats on top of the

iquid metal, so separation is relatively straightforward. The prod-ct of this step is an ingot of impure uranium (mainly bits of slagnd unreacted calcium).

The alloy is made by melting the uranium ingot along with theppropriate amount of zirconium metal in the induction furnacehown in Fig. 16. In this apparatus, the remaining calcium vaporizesnd the CaF2 separates as a slag. Once homogenized in the liquidhase, the U–Zr alloy is released from the crucible and flows into theolds (called moules in the figure) which are roughly the diameter

f the fuel pellet.After breaking the rough pellet-size ingots out of the molds, the

lloy surface is cleaned and the ingot transferred to the hydridingurnace shown in Fig. 17. Thorough removal of oxides and nitridesrom the surface is essential because hydrogen absorption is eas-ly impeded by this type of contamination. The cleaning procedurencludes:

1. degreasing in trichloroethylene;
. abrading (machining, filing, grit blasting, grinding, wire brush-
ing);. pickling with a solution of HNO3 and HF;. washing in distilled water, alcohol.

nd Design 239 (2009) 1406–1424

Addition of hydrogen to the alloy must be done very carefullyto avoid cracking the hydride because of the volume change men-tioned above. The preferred method is to heat the metal to ∼800 ◦Cand add hydrogen at ∼100 Torr above the equilibrium pressure ofthe �-Zr/� two-phase region, which is 130 Torr at this temperature.The objective is to bring the H/Zr ratio to about unity, which is theterminal solubility of hydrogen in �-Zr. As long as the hydride phaseis not formed, there is no risk of cracking the metal. The hydrogenpressure is then increased to 1 atm, and the gas is admitted in smallpulses to avoid too-rapid absorption in the metal, which would riskcracking of the hydride being formed. Additional details of the fab-rication process are provided by Huffine (1968) and in many of thepatents for TRIGA fuel elements (Eggers, 1978; Simnad et al., 1964).

7. Gap closure

The objective of this section is to determine the thickness of thefuel-cladding gap as a function of burnup. The fuel is U0.31ZrH1.6and the gap is filled with a liquid metal. Because of the low fueltemperature, there is no fission-product release (Fig. 11) and theonly fission-related swelling is due to solid and all volatile fissionproducts (Section 3.3).

7.1. Fuel swelling

The variables affecting this calculation are the initial fuel radiusRFo and the fuel centerline and surface temperatures, To and TS.These are taken from Table 5.

The increase in the fuel radius, �RF, is related to the azimuthalstrain at the fuel surface, εtot

� , by

�RF = εtot� × RFo (23)

where

εtot� = εth

� + εH� + εFP

� (24)

The three terms on the right are due to the following expansionmechanisms: temperature distribution; hydrogen redistributionand swelling due to solid fission products and probably xenon andkrypton as well. The first two terms are calculated using the methodby Olander and Ng (2005).

7.1.1. Thermal expansionThe conventional method for calculating εth

� consists of sum-ming the unrestrained expansion of differential rings in the pellet:

εth� = 2

R2o

∫ Ro

0

˛(T) × (T − Tref)r dr (25)

If the thermal expansion coefficient ˛ is independent of temper-ature and the temperature distribution is parabolic, Eq. (25) givesthe well-known result: εth

� = ˛[1/2(To + TS) − Tref]where Tref is thecold temperature (25 ◦C). In the case of a temperature-dependentlinear thermal expansion coefficient, however, this method givesincorrect results; thermoelasticity theory must be used.

Following the procedure used in Appendix A of Olander and Ng(2005), stresses are expressed in dimensionless form:

Sthi = th

i

∗th

(26)

where i = r, � or z and:

∗th = ˛oE(To − TS)

1 − �(27)

The physical properties of the fuel are given in Table 3:Young’s modulus is E = 130 GPa and Poisson’s ratio is � = 0.32.


g UF6

Td

˛

w

r

ε

Fig. 15. Apparatus for reducin

he thermal expansion coefficient of ZrHx is temperature-ependent:

= ˛o(1 + aT) (28)

here ˛o = 7.4 × 10−6 ◦C−1 and a = 2 × 10−3 ◦C−1.From Table 6, To − TS = 170 ◦C. With these parameter values, the

∗
eference thermal stress of Eq. (27) is: th = 241 MPa.The radial strain due to thermal expansion is
th� = �∗

thE

[Sth� − �(Sth

r + Sthz )] + ˛(T − Tref) (29)

(g) to UF4(s) (Sauteron, 1965).

The dimensionless stresses at the fuel surface are (Olander andNg, 2005):

Sthr = 0

Sth�

= Sthz = (1/2)(1 + aTS) + (1/3)a(To − TS)

(30)

Substituting Eq. (28) (at the surface) and Eq. (30) into Eq. (29)
yields:
1˛o

εth� = (To − TS)[(1/2) + (1/3)a(To + 1/2TS)] + (1 + aTS)(TS − Tref)

(31)

1420 D. Olander et al. / Nuclear Engineering and Design 239 (2009) 1406–1424

produ

wn

t

c

I

E˛

ε

7

t

ε

wh

Wlst

S

is especially severe in PWRs because of the thinner cladding andhigher operating temperature compared to those in BWRs. The

Fig. 16. Induction-melting furnace for

here Eq. (26) has been used to dimensionlize the stress compo-ents.

In terms of to = To − Tref and tS = TS − Tref, Eq. (31) is

1˛o

εth� = (to − tS)[(1/2) + (1/3)a(to + (1/2)tS + (3/2)Tref)]

+tS + a × tS(tS + Tref) (32)

The “1/2” in the brackets and “tS” following it combine to givehe constant-� result. The coefficient of “a” is

oef. of a = (1/2)Tref(to + tS) + (1/3)(t2o − (1/2)totS + (5/2)t2

S ) (33)

The conditions given in Table 5 are used: To = 555 ◦C, TS = 385 ◦C.n addition, Tref = 25 ◦C, ˛o = 7.4 × 10−6 ◦C−1, a = 2 × 10−3 ◦C−1.

The thermal strain corresponding to �o alone is 3.3 × 10−3. Usingq. (33), the contribution from the temperature-dependent part ofis 2.7 × 10−3. The total thermal strain at the pellet surface is

th� = 6.0 × 10−3 (34)

.1.2. Hydrogen expansionThe strain arising from volume changes due to hydrogen redis-

ribution is given by

H� = ∗

HE

[SH� − �(SH

r + SHz )] + ˇ(x − 1.6) (35)

here x is the H/Zr ratio and ˇ = 0.027 (Table 3). The referenceydrogen stress is

∗H = ˇE

1 − �(36)

ith the given parameter values, ∗H = 5200 MPa. From the formu-

as given in Section 6 of Olander and Ng (2005), the dimensionlesstress components at the surface of the fuel due to hydrogen redis-ribution are

Hr = 0 SH

� = SHz = −0.174 (37)

ction of U–Zr ingots (Sauteron, 1965).

The negative sign indicates that the surface stress components arecompressive.Substituting these values, along with H/Zr = 1.78 at thefuel surface (from Fig. 5), into Eq. (35) yields the following azimuthalstrain due to this mechanism:

εH� = −4.72 × 10−3 + 4.86 × 10−3 = 1.4 × 10−4 (38)

The magnitude of the hydrogen stress contribution (first term inEq. (38)) is practically equal in magnitude to the component due tounrestrained hydrogen expansion (second term in Eq. (38)). How-ever, the two terms are of opposite sign, which renders this straincomponent very small.

7.1.3. Solid fission-product swellingAs shown in Section 3.3, hydride fuel swelling due to solid fission

products is proportional to burnup:

εFP� = 1

3

(�V

V

)FP

= 13

× 2 × 10−3 × BUequiv. ox (39)

7.1.4. Total fuel-surface strainSubstituting Eqs. (34), (38) and (39) into Eq. (24) gives the total

azimuthal strain at the pellet surface:

εtotF = 6.0 × 10−3 + 1.4 × 10−4 + 6.7 × 10−4 BUequiv. ox (40)

7.2. Cladding creepdown

Because of the pressure difference across the cladding, creepcauses a slow reduction in the cladding radius. This phenomenon

model used for analyzing this process is that proposed by Limbackand Andersson (1996), which is also used in the FALCON fuel-performance code (Lyon et al., 2004). In the following equations ofthe model, numerical values of the parameters for stress-relieved-annealed (SRA) Zry-4 are used.

D. Olander et al. / Nuclear Engineering a

7

ε

Tc

rp

a

Ti

7

ε

wp

ε

pi

ıC = 0.78ıo

g = 0.08 and 0.15

Thermomechanical state:

Fig. 17. Hydriding furnace (Van Houten, 1974).

.2.1. Secondary thermal creepThe steady-state secondary strain rate is

˙ ss = 1.08 × 109 E

T

(sinh

ai�

E

)2exp

(−24, 200

T

)(41)

is the temperature in K and � is the azimuthal stress in MPa. Thereep strain rate is in h−1.

ai accounts for irradiation hardening of thermal creep, whichesults from the accumulation of immobile dislocation loops andoint defects:

i = 650[1 − 0.56{1 − exp(−1.4 × 10−27˚1.3)}] (42)

he hardening effect depends on the fast fluence, ˚, in n/cm2. �ss

s thus a known function of time.

.2.2. Primary thermal creepThe strain due to primary thermal creep is given by:

p = εsatp [1 − exp(−52

√�sst)] (43)

here t is the time in hours and εsatp is the saturation value of

rimary creep:

satp = 0.0216 × �0.109

ss [2 − tanh(35, 500 × �ss)]−2.05 (44)

The time variation of �ss is taken into account in calculatingrimary creep in the following approximate manner. Over a time

nterval �t, �ss in Eqs. (43) and (44) is assumed to be constant at

nd Design 239 (2009) 1406–1424 1421

the average value in the interval. Only the explicit time dependencein Eq. (43) is retained. The result is:

εp(t + �t) = εp(t) + εsatp (e−52

√�ss

√t − e−52

√�ss

√t+�t) (45)

In this equation, �ss and �satp are evaluated at t + 1/2�t.

7.2.3. Irradiation creepThe irradiation creep strain depends on both stress and the fast

flux �(n/m2-s), but time t is in hours5:

εirr = 3.56 × 10−24�0.85� × t (46)

7.2.4. Total cladding creep strainThe total cladding creep strain as a function of time (in hours) is

given by

εtotC = εp + εss + εirr (47)

The creep strains in this equation are considered to be positivequantities even though they apply to creepdown of the claddingtube. This is taken into account in Eq. (49).

7.3. Gap closure

7.3.1. Dimension changesThe total creep strain of Eq. (47) is applied to the mean radius of

the cladding, the initial value of which is

RoC = 1

2(DO − ıC) (48)

DO is the cladding outer diameter and ıC is the cladding thickness.At time t, the mean cladding radius is

RC = RoC(1 − εtot

C ) (49)

with the strain taken from Eq. (47). The inside wall radius is

RCi = RC − 12

ıC (50)

The initial fuel radius (cold) is

RoF = 1

2DO − ıC − ıo

g (51)

where ıog is the thickness of the initial cold gap.The radius of the

fuel pellet is

RF = RoF (1 + εtot

F ) (52)

where εtotF is given by Eq. (40).

7.3.2. Parameters of typical hydride fuel elementThe following parameter values are utilized to apply the model

to a typical hydride fuel element in a BWR:Geometry (in mm):

DO = 12

5 The creep model of Limback and Andersson (1996) unfortunately mixes units.The fast flux in Eq. (46) is in n/m2-s, while the fast fluence in Eq. (42) is in n/cm2.The two are related by ˚ = �t. Strain rates are expressed in h−1 but the flux utilizesseconds.

1 ring and Design 239 (2009) 1406–1424

b

�

t

B

t

B

7

dcb

ac


�p = pressure difference between coolant and rod interior = 3 MPa.The hoop stress (compressive) in the cladding is:

� = �p1/2DO

ıC= 3 × 6

0.78= 23 MPa

T = mean cladding temperature. For the thermal conditions in Table6, T = 635 K.E = Young’s modulus for SRA-Zry-4. At 635 K it is 7.7 × 104 MPa(Limback and Andersson, 1996).

Irradiation conditions:

� = 1018 n/m2-sThe fast fluence is:

˚ = (� × 10−4)(t × 3600) n/cm2

F = 3 × 1013 fissions/cm3-st = time, h

Steady-state creep rate:For the conditions listed above, the steady-state creep rate given

y Eqs. (41) and (42) is fitted to the following formula:

˙ ss = (0.242 + 1.22e−0.001×t) × 10−7, h−1

ime and burnup are related by

Uequiv.ox = 3.2 × 10−11 Jfiss

× 3600 Ftfisscm3

× 10−6 MWW

× 103

�U

cm3

kgU

× 13600 × 24

d

s× �U

9.3

The last ratio converts burnup to equivalent-oxide burnup. Withhe fission density given above, the conversion is:

Uequiv. ox = 7.2 × 10−3t

.3.3. ResultsFig. 18 shows that the three components of the cladding creep-

own strain are of comparable magnitude, although irradiation
reep starts to dominate after ∼25 MWd/kgU equivalent-oxideurnup.
Fig. 19 shows the variations of the fuel and cladding ID radiis functions of burnup. Gap closure occurs when the fuel andladding lines intersect. The fuel radii at time zero include the

Fig. 18. Components of cladding creepdown.

Fig. 19. Gap closure—fuel and cladding inner radii as functions of burnup.

strains due to thermal and hydrogen stresses. The difference inthe initial fuel radii for the two cold gap thicknesses is due tothe requirement that the cladding geometry remain constant. Theincrease thereafter is due solely to fission-product swelling. Withan 80 �m initial cold gap, PCMI occurs at an equivalent-oxideburnup of ∼10 MWd/kgU. With a 150-�m initial gap, closure isdelayed until ∼27 MWd/kgU equivalent-oxide burnup. The goalof avoiding gap closure until 60 MWd/kgU cannot be achievedusing the liquid-metal in the gap unless the initial gap is ∼300 �m.According to Eq. (51), a gap of this size contains fuel of 4.92 mmradius, compared to 5.17 mm for the 80-�m cold radial gap. For afixed linear heat rate, the enrichment varies as the square of thefuel pellet diameter. In order to maintain the same LHR for the twofuel pellet dimensions, the enrichment of the small pellet must be9% larger than for the large pellet. If fuel the in the rod with the80-�m gap is has an enrichment of 12%, this figure needs to beincreased to 13% if the gap thickness is increased to 300 �m.

The reason for the necessity of a large initial gap to avoid PCMIat ∼60 MWd/kgU is the sizeable fission-product swelling rate of thehydride fuel. According to the only data available, this quantity isthree times larger in hydride fuel than in oxide fuel.

8. Conclusions

Building on the early work on hydride reactor fuel in the SNAPand TRIGA programs, an assessment of the potential for its useas LWR fuel is presented. The principal properties of (U,Zr)Hx,notably its high thermal conductivity, provide this material withseveral attractive features as a nuclear fuel. The low fuel temper-ature reduces fission-product release to negligible amounts anddecreases stored energy in the fuel. With a low-melting liquid metalin the fuel-cladding gap, PCMI can be delayed or avoided by increas-ing the thickness of the cold gap. Initial fuel cracking due to thermalstress may be avoided because of the countervailing effect of hydro-gen redistribution.

A cautionary note is the appearance of voids produced byfission-fragment damage the hydride lattice adjacent to the ura-nium particles. The swelling (�V/V) due to the voids appears earlyin irradiation (burnup ∼10−3 FIMA) and is highly temperature-

◦ ◦ ◦
sensitive: it is absent at 650 C, reaches 1% at 700 C and 5% at 750 C.Liquid-metal bonding of the fuel-cladding gap is necessary to avoidtemperatures where severe initial swelling occurs.
Although many of the essential radiation properties of hydridefuel have been determined, a well-instrumented irradiation test

ring and Design 239 (2009) 1406–1424 1423

uae(chaco

hmf

msofr

As

t

H

i

C

wiTHZ

J

Ts

D

ditgc

wm(

A

otriF

D. Olander et al. / Nuclear Enginee

nder power-reactor conditions is needed, particularly in order tossess (i) the effect of released fission gas (if any) on the thermalffectiveness of the liquid metal bond in the fuel-cladding gap;ii) whether the initial void swelling occurs during power-reactoronditions. Additional laboratory tests include measurement ofydrogen loss as a function of temperature in∼20 atm of helium andssessing the long-term compatibility of the hydride fuel with PWRoolant water at 300 ◦C and with steam at T > 1000 ◦C representativef accident conditions.

A significant unknown is the cost of large-scale fabrication ofydride fuel elements, which, when added to the increased enrich-ent cost, may compromise its competitiveness vis-à-vis oxide

uel.Avoiding closure of the fuel-cladding gap during irradiation

ay be problematic because of the possibly large fission-productwelling rate of hydride fuel compared to oxide fuel. In order tovercome this feature (if it is true), the thickness of the LM-filleduel-cladding gap must be made very large (∼300 �m radial), whichequires a ∼1% enrichment increase to maintain the design LHR.

ppendix A. Permeation of hydrogen through stainlessteel

Dissolution is accompanied by dissociation of H2 into atoms, sohe equilibrium between gaseous hydrogen and the metal:

2(g) = 2H(dissolved) (A1)

s given by Sieverts’ law:

H = KH√

pH2 (A2)

here CH is the concentration of H in the metal in moles/m3, pH2s the hydrogen pressure in Pa and KH is the Sieverts’ law constant.he flux of H atoms through stainless steel of thickness ıSS with2 pressure pH2 in the fuel-cladding gap and zero pressure at thery/SS interface is:

H = DHCH

ıSS= (DHKH)

√pH2

ıSS(A3)

he product DHKH is the permeability of hydrogen in the metal. Fortainless steel, LeClaire gives the equation (LeClaire, 1984):

HKH = 3.3 × 10−7 exp(

−7900T

)moles/m-s-Pa0.5 (A4)

To assess the utility of this protection scheme in the presentesign, consider a 0.4-mm-thick SS liner at 340 ◦C exposed at its

nner surface to the equilibrium hydrogen pressure generated byhe hydride fuel (∼5 × 10−3 atm, Fig. 5). The above two equationsive a permeation rate JH = 5 × 10−12 moles H/cm2-s. The fractionalhange rate of the H/Zr ratio (x) of the fuel is

d(x/x0)dt

= − JHNH0d

(A5)

here x0 is the initial H/Zr ratio (1.6), NH0 = 0.08 moles H/cm3 is theolar density of hydrogen in ZrH1.6 and d is the ID of the cladding

∼1 cm).

ppendix B. Effect of fission products on H/Zr ratio of fuel

Reaction of impurity oxygenDuring the early stage of irradiation, zirconium attached to

xygen impurity as ZrO2 is released as the oxygen is transferredo fission products by reactions (19a) and (19b). The zirconiumeleased by these reactions, along with fission-product, Zr join thatn the original ZrH1.6. Hydrogen is not affected by this conversion.ig. B(a) depicts this process using a basis of 1 mole of ZrH1.6 and NO

Fig. B1. Changes in H/Zr ratio during irradiation. (a) Change of H/Zr ratio duringtransfer of oxygen from Zr to Re and Ba,Sr and (b) Reduction in H/Zr ratio withburnup.

moles of oxygen. In order to move this quantity of oxygen from Zr tothe reactive fission products, n moles of U are fissioned per mole ofinitial Zr. During this period, nYZr moles of Zr are produced, whereYZr is the fission yield of zirconium. The H/Zr ratio at this point is:

HZr

= 1.61 + nYZr + 1/2NO

(B1)

The moles fissioned required to consume the NO moles of impu-rity oxygen as the oxides in reactions (19a) and (19b) is obtainedfrom:

NO = 3/2NRE + NBa,Sr = (3/2YRE + YBa,Sr) × n

or, solving for n:

n = NO

3/2YRE + YBa,Sr(B2)

The amount of oxygen corresponding to ∼1000 ppm wt in thefuel is NO ∼0.011 moles O per mole Zr. Using this value, along withthe yields from Table 4, Eq. (B2) gives n = 0.012 moles fissioned permole of initial Zr. Substituting these values of NO and n into Eq. (B1)gives H/Zr = 1.586 at the point of complete reaction of ZrO2.

Using the information in Table 1, the molar density of zirconiumin (U0.31Zr)H1.6 is:

�Zr = 8.0g fuelcm3

× 0.55g Zr

g cm3× 1 mole

91.2 g Zr= 0.050

moles Zrcm3

(B3)

The fission density required for this process is:

F∗ = n × �Zr × NAv = 1.2 × 10−2 × 0.050 × 6.02 × 1023

= 3.6 × 1020 fissions/cm3

where NAv is Avogadro’s number. Assuming a fission rate of2 × 1013 fissions/cm3-s, the time to achieve the above fission densityis 1.8 × 107 s, or about 7 months.

Using Eq. (13), F* can be converted to burnup:

F ∗ /NAv = �Zr(1 + y) × FIMA ∗ moles fissioned/cm3

Substituting the above values of F* and �Zr along with y = 0.31yields FIMA* = 9.2 × 10−3.

Subsequent change in H/Zr with burnup

1 ring a

ttSh

n

w

a

f

y

fi

F

9E

t

R

A

B

C

EG

G

GG

Yamanaka, S., et al., 1999. Thermal and mechanical properties of zirconium hydride.


This step, shown in Fig. B(b), is based on one mole of ZrH1.59 athe burnup FIMA* of oxygen removal from ZrO2. Following n′ addi-ional fissions per mole of initial Zr, 1 + n′YZr moles of Zr are present.ince the active fission products form dihydrides, the quantity ofydrogen is reduced to 1.59 − 2n′(YRE + YBa,Sr). The H/Zr ratio is:

HZr

= 1.59 − 2n′(YRE + YBa,Sr)1 + n′YZr

(B4)

The number of moles of fissions is given by Eq. (13):

′ = (F − F∗)/NAv = �Zr(1 + y)(FIMA − FIMA∗)

= 0.066(FIMA − FIMA∗) (B5)

ith �Zr given by Eq. (B3) and y = 0.31.The function obtained by substitution of Eq. (B5) into (B4) is

dequately represented by a line with a slope:

(H/Zr) (FIMA)

∼= 0.1 (B6)

The relation between U-235 consumption and FIMA is obtainedrom Eq. (13):

N235

N0235

= (N0235 + N0

Zr) × FIMA

e × N0235

= 1 + y−1

e× FIMA = 33.8 × FIMA

(B7)

The numerical coefficient in the above equation corresponds to= 0.31 and e = 0.125.

Time is related to FIMA according to Eq. (13), which, for constantssion rate, yields:

˙ t = N0U(1 + y−1) × FIMA (B8)

For the uranium density given in Table 1 (3.7 g U/cm3), N0U =

.3 × 1021 atoms U/cm3. With a fission rate of 2 × 1013 cm−3 s−1,q. (B8) becomes:

= 774 × FIMA mos (B9)

eferences

lbrecht, W., Goode, W., 1960. Diffusion of hydrogen in zirconium hydride. USAECRept. BMI-1426.

eck, R., Mueller, W., 1968. Zirconium and Hafnium Hydrides. In: Mueller, W., Black-ledge, J., Libowitz, G. (Eds.), Metal Hydrides, Section 7.3. Academic Press.

hesworth, R., West, G., 1985, October. Final results of qualification testing ofTRIGA fuel. Presented at the International Meeting On Reduced Enrichment forResearch & Test Reactors, Petten, The Netherlands, October.

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