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This web page is concerned with choice of a fuel tube alloy that gives a long fuel tube working life in a fast neutron flux while also meeting other required performance constraints.
EFFECTS OF FAST NEUTRON IMPACTS ON FUEL TUBE ATOMS:
The effects of fast neutron impacts on fuel tube atoms are:
1) Addition of energy to the fuel tube material lattice which reduces the depth of its crystal lattice binding energy wells and hence reduces the material strength. This material strength reduction relates to the material's yield stress Sy;
2) Severe fuel tube alloy swelling occurs if there is a FCC to BCC phase transition;
3) Unacceptable fuel tube swelling also occurs on a BCC alpha to BCC (alpha + alpha prime) phase transition;
FUEL TUBE WEAR MITIGATION:
A key issue in prolonging fuel tube life is periodic fuel tube annealing. Fuel tube annealing is accomplished simply by removeing the thermal load from the reactor so that the primary liquid sodium temperature and hence the fuel tube temperature gradually rises to about 550 degrees C. After a suitable annealing period the thermal load is restored.
FUEL TUBE SWELLING:
A key issue in making a Fast Neutron Reactor (FNR) economic is to minimize fuel tube swelling. An increase in fuel tube outside diameter (OD) due to fuel tube material swelling reduces the fuel bundle cross sectional area available for liquid sodium coolant flow, which reduces reactor power output and hence limits the practical fuel tube working life. The fuel tube mounting arrangements should accommodate substantial fuel tube swelling late in the working life of a fuel bundle. The fuel tube swelling mitigation methodology contemplated herein is to use a swelling resistant fuel tube alloy and to use a square tube lattice. Fuel tube swelling in a FNR is challenging because one of the FNR design objectives is to burn the fuel as long as possible to minimize the frequency of fuel reprocessing.
Experimentally, with the fuel tube material HT-9, the fuel tube volume increase at 15% fuel burnup is acceptable. However, HT-9 has issues related to temperature and neutron irradiation embrittlement. Relieving the embrittlement requires periodic fuel tube annealing.
It is helpful to understand the fuel tube swelling problem both in terms of fuel tube centre-to-centre geometry and in terms of the underlying causes of fuel tube swelling.
The increase in fuel tube diameter is caused by a combination of phenomena including:
a) Swelling of the fuel tube material caused by lattice dislocation formation within the fuel tube material;
b) Swelling of the fuel tube material due to the high thermal flux and high temperature causing material creep;
c) Swelling of the fuel rod inside the fuel tube due to formation of fission product gas bubbles within the fuel rod;
d) Swelling of the fuel rod inside the fuel tube due to formation of two atoms in place of one during the fission process;
e) An increase in fuel tube internal pressure caused by differential thermal expansion of the contained liquid sodium as compared to the fuel tube material;
f) An increase in fuel tube internal pressure due to formation and trapping of of inert gas fission products;
g) A change in fuel tube material phase from FCC to BCC if the initial alloy is incorrect
These problems are aggravated by a decrease in fuel tube wall yield stress due to low nickel content, high operating temperature, fast neutron flux disruption of the fuel tube atomic constituants and spontaneous changes in the fuel tube crystal lattice.
The solutions to this fuel tube swelling problem include:
1) Use a square fuel tube lattice instead of a staggered fuel tube lattice so that the impact of fuel tube swelling on the external primary liquid sodium coolant flow is low;
2) Use of a fuel tube material that maintains a sufficient yield stress at 550 C under fast neutron irradiation that it resists diameter expansion due to thermal and internal gas pressure stress;
3) Use of a fuel tube material with a relatively small Youngs modulus (modulus of elasticity) to minimize thermal stress in the tube material;
4) Use of a fuel tube material with a relatively high thermal conductivity to minimize thermal stress in the fuel tube material due to the radial thermal flux;
5) Use of core fuel rod and blanket fuel rod ODs that are sufficiently small with respect to the fuel tube ID that mechanisms (c) and (d) have no effect on fuel tube hoop stress;
6) Use of a fuel tube steel wall that is sufficiently thick with respect to its ID that below the melting point of sodium the fuel tube can withstand the larger thermal expansion of sodium as compared to the fuel tube material;
7) Use of a large gas plenum at the top of the fuel tube to limit the inert gas pressure inside the fuel tube;
8) Provide sufficient additional plenum volume to allow for differential thermal expansion of liquid sodium;
9) Provide sufficient additonal plenum volume to allow for the extra sodium that is required as the fuel tube material swells in diameter;
10) Provide sufficient additonal plenum volume to allow for extra sodium that is required as the fuel rod material swells in length;
11) Provide sufficient sodium to chemically absorb the fission products bromine and iodine.
12) Use a fuel tube alloy that has no phase transitions below 560 degrees C.
The aforementioned fuel tube design keeps the maximum fuel tube material stress safely below the fuel tube material yield stress at all projected operating temperatures.
CRYSTAL LATTICE ACRONYMS:
Common crystal lattice configurations are:
HCP = hexagonal close packed
FCC = face centered cubic
BCC = body centered cubic
The fuel tube alloy optimization strategy is to prevent fuel tube swelling by choosing a fuel tube alloy crystal structure which remains in the same BCC (alpha plus alpha prime) phase at all times and to choose fuel tube constituant elements that have relatively low fast neutron scattering cross sections to minimize the fast neutron impact rate.
If the fuel tube crystal lattice is initially FCC a fast neutron impacts on the crystal atoms will cause a transition to a BCC like atomic density lower by as much as a factor of two and which causes a linear swelling dimension increase by as much as a factor of 1.26. This material swelling can severely reduce the primary liquid sodium circulation. The solution to this problem is to fabricate the fuel tubes from a 85% Fe-12% Cr alloy known as HT9 that under fast neutron irradiation remains BCC over a wide temperature range and hence has an insignificant atomic density change.
FNR fuel tubes are a key part of FNR design. The fuel tubes must be replaced every fuel cycle so the cost of the fuel tubes, their working life and their irradiated material disposal are all significant issues. The fuel tube working life should be sufficiently long that it does not determine the frequency of FNR fuel reprocessing. One of the factors determining fuel tube working life is fuel tube alloy swelling.
Under sustained fast neutron bombardment FNR fuel tubes will eventually swell due to formation of metal crystal lattice dislocations.. However, tha amount and rate of swelling are dependent on the fuel tube element neutron scattering cross sections and on the fuel tube's initial crystal structure.
There are three common metal crystal structures: hexagonal close packed (HCP), face centered cubic (FCC) and body centered cubic (BCC). With HCP the number of atoms per unit volume is close to its theoretical maximum for a solid at atmospheric pressure. With FCC the number of atoms per unit volume is moderate. With BCC the number of atoms per unit volume is close to its theoretical minimum for a solid at atmospheric pressure.
The effect of fast neutron bombardment is to reduce the metal crystal structure atomic density. This reduction in atomic density increases the metal volume, causing swelling in three dimensions. Swelling due to fast neutron impacts can be minimized by choosing a fuel tube alloy that is initially BCC so that the primary mechanism for swelling is relatively ineffective. Hence the fuel tube alloy should be chosen so that it remains BCC throughout its working temperature range and working life.
CONSIDER THE NUMBER OF FISSION NEUTRONS EMITTED PER FUEL CYCLE:
From FNR Fuel Rods each core fuel rod has an initial mass of 0.362047 kg and is 0.45 m long. Hence in one fuel cycle the number of neutrons / m emitted by this fuel rod is:
0.362047 kg X 0.15 burnup X (6.023 X 10^23 atoms / 0.239 kg) X (3.1 neutrons / atom fission) / 0.45 m = 9.4280 X 10^23 neutrons / m
NUMBER OF CRYSTAL CUBES PER UNIT LENGTH IN A FUEL TUBE:
In a FCC crystal lattice each of 8 cube corner atoms is shared among 8 cubes for a net contribution of 1 atom / cube
In a FCC crystal lattice each of 6 cube face atoms is shared between 2 cubes for a net contribution of 3 atoms/ cube
Thus in an FCC crystal lattice there are 4 atoms per cube.
In a BCC crystal lattice each of 8 cube corner atoms is shared among 8 cubes for a net contribution of 1 Fe atom/ cube.
In BCC crystal lattice each cube center atom is associated only with that cube for a net contribution of 1 atom/Cube;
Thus in a BCC lattice there are 2 atoms per cube.
Thus for the same size cubes a BCC lattice has only half the atomoc density of a FCC lattice. Viewed another way if a material transitions from a FCC phase to a BCC phase while maintaining the same crystal cube size along any one dimension it linearly expands by a factor of:
in addition to normal thermal expansion. Transition from a HCP crystal structure to a BCC crystal structure also causes unacceptable fuel tube material swelling.
For our fuel tube design the number of fuel tube atoms per meter is given by:
[Pi / 4][(0.5 inch)^2 - (0.37 inch)^2](.0254 m / inch)^2 (7.874 gm / cm^3)(1 kg / 1000 gm)(10^6 cm^3 / m^3) X (6.023 X 10^23 atoms / 0.056 kg)
= 0.0485333384 X 10^26 atoms / m
= 48.5333384 X 10^23 atoms / m
That is a sufficient number of atoms to form:
(48.5333384 / 2) X 10^23 = 24.26667 X 10^23 BCC cubes / m
(48.5333384 / 4) X 10^23 = 12.13333 X 10^23 FCC cubes / m.
Recall that during the fuel tube working life to 15% burnup the number of energtic fission neutrons emitted per m was:
9.4280 X 10^23 neutrons / m
Thus on average each fission neutron causes conversion of one fuel tube metal FCC cube to two fuel tube metal BCC cubes.
To prevent serious swelling occurring the fuel tube alloy must be chosen so that it is initially BCC.
The room temperature crystal structures, densities and melting points of pure Ni, Fe, Mn, Cr, V and Ti are as follows:
Ni: FCC, 8.90 g / cm^3, 1455 C
Co: BCC for Co < 70% in Fe, T < 910 C; 8.90 gm / cm^3, 1495 C
Fe: BCC for T < 720 deg C, 7.874 g / cm^3, 1538 C
Mn: BCC for Mn < 1.5% in Fe, 7.21 g / cm^3, 1246 C
Cr: BCC at 0 to 20% in Fe for T < 512 C (problems for T > 460 C, 7.19 g /cm^3, 1907 C
V: BCC, 6.0 g / cm^3, 1910 C
Ti: HCP, 4.506 g / cm^3, 1668 C
Note the very low density of pure Ti as compared to pure Cr, which potentially leads to rapid fuel tube material swelling if the Ti fraction in Fe becomes too large.
ISSUES RELEVANT TO FUEL TUBE ALLOY CHOICE:
Zirconium is not a good fuel tube component because it is expensive and because Zr-93 with a half life of 1.5 X 10^6 years will eventually become a waste disposal problem. Zirconium also has a HCP crystal structure which swells a lot in a sustained fast neutron flux.
Nickel is not a suitable fuel tube component because it is expensive, its fast neutron scattering cross section is much higher than iron, on neutron absorption it forms the long lived isotope Ni-59 with a half life of 10^5 years which is a nuclear waste disposal problem and when the ratio of Ni to Fe exceeds about 5% there is a BCC to FCC phase change in the fuel tube alloy.
The cobalt concentration in the fuel tube must be kept under 70% to maintain a BCC lattice through the fuel tube operating temperature range.
The manganese (Mn) concentration in a fuel tube must also be kept under 3.0% to maintain a BCC crystal structure through the fuel tube's operating temperature range.
Titanium (Ti) is an unsuitable fuel tube material due to both a HCP lattice and fabrication difficulties.
An important consideration in the choice of fuel tube alloy is that neutron interactions with the fuel tube material should not produce long lived low atomic weight isotopes that create long term waste disposal problems. This issue leads to rejection of Be, C and Ni as initial fuel tube components, in spite of the favorable physical characteristics that these elements can potentially provide to a fuel tube alloy.
The amounts of carbon, oxygen, beryillium and nickel initially present in the fuel tube alloy should be minimized to avoid formation of long lived C-14, Be-10 and Ni-59.
At temperatures below 720 deg C pure Fe, pure Cr, pure Mn and pure V have a BCC crystal structures but pure Ti has a HCP crystal lattice. Ti is held in a BCC lattice via the compound Fe2Ti. Hence during a fuel tube's working life the number of Fe atoms present must always be more than twice the number of Ti atoms.
THE Fe - Cr SYSTEM:
P>One of the most suitable FNR initial fuel tube components is iron. At temperatures below 460 degrees C the Fe-Cr system has a stable BCC crystal lattice configuration at all Fe/Cr ratios.
If the fuel tube crystal lattice is initially FCC there will soon be a transition to BCC which reduces the fuel tube material density by a factor of two and which causes a linear swelling dimension increase factor of 1.26. This material swelling will obstruct the primary liquid sodium circulation. To minimize the fuel tube swelling the fuel tube alloy lattice must always be BCC because a BCC lattice is less dense than a FCC lattice. The solution to this problem is to fabricate the fuel tubes from (Fe + Cr) that are initially BCC and have no lattice phase change in the temperature range of interest.
The optimum Fe - Cr fuel tube life maximization strategy is to start with nearly pure Fe and add enough Cr to stabilize the material in the (alpha + alpha prime) zone. Hence at the start of fast neutron exposure the fuel tubes consist of:
85% Fe + 12% Cr + 3% other.
Ensure that the Fe - Cr fuel tube alloy is free of nickel, which has a relatively large fast neutron scattering cross section. Minimizing nickel concentration avoids formation of long half life Ni-59 which is a waste disposal problem.
The amounts of Be, and C present must also be minimized because they lead to formation of long lived isotopes Be-10 and C-14.
The normal low temperature crystal structure of pure iron is BCC with one side of a cube unit cell
= 286.65 pm.
However, from 912 deg C to 1394 deg C the crystal structure of iron becomes FCC with one side of a cube unit cell
= 286.65 pm
The Fe - Cr system has two BCC phases designated alpha and (alpha + alpha prime). The initial chromium (Cr) concentration in a fuel tube must be set at 12% to keep the fuel tubes in the alpha phase throughout most of their length and throughout their working life.
Successful FNR fuel tubes have been made with an initial component ratio of 85% Fe, 12%Cr, 3% other alloy known as HT-9.
The HT-9 alloy has a BCC crystal structure throughout its contemplated working temperature and component ratio range.
During its working life the fuel tube alloy operating temperature should be kept above its 460 C phase transition temperature for a Fe-Cr alloy with a Cr fraction ~ 0.12 . Typically the FNR primary liquid sodium operating temperature is set at about 490 deg C. The theoretical maximum liquid sodium operating temperature is 560 deg C above which there is a threat of Pu melting on the fuel rod center line.
Below is the Fe-Cr alloy phase diagram with a red line showing the position of HT9 on that diagram. Note that over the temperature range from about 460 deg C up to the alloy melting point at about 1500 deg C HT9 remains in the alpha phase with a BCC crystal lattice. The bottom of the fuel tubes will frequently be as cool as 340 deg C and hence requires periodic annealing.
Accumulation of lattice dislocations causes HT9 fuel tube embrittlement at lower operating temperatures (330 degrees K to 425 degrees K). However, there is experimental evidence that the lattice dislocations anneal out at 650 degrees C.
NEUTRON ACTIVATION OF Fe AND Cr:
Stable Fe-54 + n becomes unstable Fe-55 which positron decays to stable Mn-55;
Stable Fe-56 + n becomes stable Fe-57;
Stable Fe-57 + n becomes stable Fe-58;
Stable Fe-58 + n becomes unstable Fe-59 which decays by electron emission into stable Co-59.
Stable Mn-55 + n becomes unstable Mn-56 which decays by electron emission into stable Fe-56 .
Stable Cr-52 +n becomes stable Cr-53;
Stable Cr-50 + n becomes unstable Cr-51 which decays by electron emission into Mn-51 which then decays by positron emission into stable V-51;
Stable Cr-53 + n becomes stable Cr-54;
Stable Cr-54 + n becomes unstable Cr-55 which decays by electron emission into stable Mn-55.
Thus a fuel tube initially composed of a Fe + Cr alloy appears from a neutron activation perspective to be very good.
Fast Neutron Reactor (FNR) tube wear can be expressed in terms of number of fast neutron scattering impacts per fuel tube atom (fnipa).
The number of fast neutron impacts per fuel tube atom (fnipa) can be calculated by starting from the reactor power level, finding the rate of neutron impacts on fissionable atoms, and using relative fast neutron scattering cross sections of fuel tube atoms to find the rate of fast neutron impacts on FNR fuel tube atoms.
Brookhaven elastic and inelastic neutron scattering data for Fe-56 and average fission neutron energy data indicates that Nk > 7. In doing this calculation we can assume that within a particular fuel tube bundle the various atomic types are uniformly distributed within the critical portion of the fuel bundle volume.
N = number of fast neutrons randomly moving through the fuel bundle
Np = number of Pu atoms in the fuel bundle;
Vol = volume of fuel bundle;
Sigmaf = 1.7 b = plutonium fission core neutron cross section;
Ef = energy release per Pu atom fission
P = thermal power of fuel bundle;
Ni = number of iron atoms in the fuel bundle;
Nn = nimber of nickel atoms in the fuel bundle;
Nc = number of chromium atoms in the fuel bundle;
Sigmais = 3.8 b = iron atom core neutron scattering cross section;
Sigmaia = 0.0086 b = iron atom core neutron absorption cross section;
Sigmacs = 4.2 b = chromium atom fast neutron scattering cross section;
Sigmaca = 0.014 b = chromium atom fast neutron absorption cross section;
Vn = neutron velocity;
Mp = 0.072409 kg = mass of plutonium;
Mi = mass of iron
= [Pi / 4][(0.5 inch)^2 - (0.37 inch)^2](.0254 m / inch)^2 [0.45 m](7.874 gm / cm^3)(1 kg / 1000 gm)(10^6 cm^3 / m^3) X 0.88 = 0.1787 kg;
Mc = mass of chromium
= [Pi / 4][(0.5 inch)^2 - (0.37 inch)^2](.0254 m / inch)^2 [0.45 m](7.874 gm / cm^3)(1 kg / 1000 gm)(10^6 cm^3 / m^3) X 0.12 = 0.02436 kg;
Wp = 239 = atomic weight of plutonium;
Wi = 56 = atomic weight of iron;
Wc = 52 = atomic weight of chromium.
Consider a single fast neutron passing through the fuel bundle. The number of fissions per unit time due to this single neutron is:
[(Sigmaf Np Vn) / Vol]
The number of fast neutron scatters per unit time off iron atoms due to a single neutron is:
[(Sigmais Ni Vn) / Vol]
The number of fast neutron scatters per unit time off chromium atoms due to a single neutron is:
[(Sigmacs Nc Vn) / Vol]
Np = [(mass of plutonium) / (atomic weight of plutonium)] X 6.023 X 10^23
= Mp / Wp
Ni = [(mass of iron) / (atomic weight of iron)] X 6.023 X 10^23
= Mi / Wi
Nc = [(mass of chromium) / (atomic weight of chromium)] X 6.023 X 10^23
= Mc / Wc
Hence the number of fast neutron scatters off fuel tube atoms per fission is:
[(Sigmais Ni) + (Sigmacs Nc)] / (Sigmaf Np)
= [(Sigmais Mi / Wi) + (Sigmacs Mc / Wc)] / (Sigmaf Mp / Wp)
= [(3.8 b (0.1787 kg) / 56) + (4.2 B (0.02436 kg) / 52)] / (1.7 b (0.072409 kg) / 239)
= [0.012126 + 0.0019675385] / (5.15043 X 10^-4)
However, since only (3 / 4) of the original Pu fissions the average number of fast neutron impacts per fuel tube atom in the reactor core region is:
(3 / 4) X 27.2638 = 20.52
On a per neutron basis that is 7 fuel tube atom strikes / neutron.???????????????
Brookhaven fast neutron elestic and inelastic scattering data for Fe-56 indicates that Nk ~ 7.
Hence the fuel tubes can withstand about:
7 (0.37) fnipa = 2.59 fnipa
before fuel tube swelling becomes a concern.
Judging by the storage margin the fuel tubes are probably good to past 3.0 fnipa.
The fuel tube rating places an upper limit on the fuel burn-up fraction per FNR fuel cycle.
Thus the fast neutron damage that fuel tubes initially consisting of (85% Fe + 12% Cr) can absorb without significant swelling is Nk (0.37) fast neutron impacts per fuel tube atom (fnipa).
Thus the fuel tube will not accommodate wear above Nk (0.37) fnipa.
Hence for HT-9 fuel tubes fuel tube swelling is not a life limiting factor. The fuel tube working life will instead be limited by Pu depletion and fission product accumulation.
This web page last updated March 21, 2020.
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