Fuel Densification and Swelling — Pellets That Shrink Early and Swell with Burnup

Principle and mechanism

Densification — irradiation resinters the pellet

• Sintered pellets are made at about 95 % of theoretical density (TD); the remaining 5 % or so is porosity.
• During irradiation, fission-fragment tracks (fission spikes) pass by fine pores (around 1 μm) and dissolve the vacancies around them back into the lattice, so the pores disappear. This is also called in-reactor resintering; in hot regions thermal sintering adds to it.
• Large pores (several μm or more) do not disappear easily, so controlling the pore-size distribution in manufacturing suppresses densification.
• NRC RG 1.126 Rev. 2 takes the maximum in-reactor density increase to be equal to the density increase in an out-of-reactor resintering test (1,700 °C, 24 hours), Δρ_sntr. The maximum is generally reached below 10,000 MWd/t; in the model kinetics for Δρ_sntr < 4 %TD, the change is zero up to 20 MWd/t, rises in proportion to log(BU) from 20 to 2,000 MWd/t, and is saturated beyond 2,000 MWd/t.
• Dimensions are converted with ΔD/D = Δρ/3ρ for diameter (isotropic) and ΔL/L = Δρ/2ρ for length (conservative anisotropic).

Swelling — one U atom becomes two FP atoms

• Solid FP swelling: Zr, Mo, rare earths, Cs and others dissolve in the lattice or precipitate, increasing the volume. It is independent of temperature and nearly proportional to burnup.
• Gaseous FP swelling: Xe and Kr grow and coalesce into intragranular and grain-boundary bubbles. It matters at high temperature, above about 1,200 °C, and can jump during power-increase transients.
• Post-irradiation examination of PWR fuel (17 rods, 49 samples) measured a swelling rate of 0.091 %/(GWd/tU), almost the same as the theoretical value of 0.088 %/(GWd/tU) for solid FPs alone. This means pellet swelling in normally operating PWRs is mainly the solid-FP share; it is often remembered as "about 0.7–1 %ΔV per 10 GWd/tU".
• The same examination reported that the burnup at which cumulative densification and cumulative swelling cancel (the pellet regains its initial volume) was 5–20 GWd/tU, depending on the powder manufacturing characteristics.

Net volume change — the sum of two curves

Assuming an initial density of 95 %TD and Δρ_sntr = 1 %TD, and adding the swelling rate of 0.091 %/(GWd/tU) as a constant slope extrapolated onto the RG 1.126 kinetics, gives the following (example calculation; gaseous swelling and rim porosity not included).

The maximum volume decrease from densification is −Δρ/(ρ₀+Δρ) = −1/96 ≈ −1.04 %, or about −0.35 % in diameter. For an 8.19 mm pellet that is about 0.03 mm, enough to widen the initial diametral gap (about 0.17 mm, standard 17×17 example) by about 17 % in cold geometry. The volume minimum is not, however, the point of maximum hot gap: the actual gap is set together by thermal expansion, crack relocation and cladding creep-down.

What it means in a plant

Densification — thermal and mechanical issues early in life

RG 1.126 sums up the effects of densification in three points:

1. The smaller diameter widens the gap, so the gap conductance h_gap drops and fuel temperature and stored energy rise. This is why 10 CFR 50 Appendix K requires densification to be included in the pre-LOCA stored-energy calculation.
2. The shorter pellets raise the linear power at the same power.
3. If axial gaps form in the fuel column, local power spikes appear at those locations and the cladding can collapse into the gaps.

Point 3 actually happened. During the 1972 refueling inspection at R.E. Ginna, short flattened sections of fuel rods were found; the cause was creep collapse of the cladding under coolant pressure into axial gaps created by densification. All the collapsed rods were unpressurized rods, and neutron flux measurements at Point Beach 1 and Robinson confirmed local peaks at the gap locations. In November of the same year the AEC issued a technical report on densification and required it to be reflected in licensing analyses. Since then, helium prepressurization, stable pellets (large grains, controlled pore distribution), plenum springs and resintering-test quality control have become standard.

Swelling — closing the gap and pushing the cladding

• The gap narrows through pellet crack relocation, thermal expansion and swelling (on the pellet side) and cladding creep-down (coolant pressure of 15.5 MPa exceeds the internal pressure), so depending on the design the hot gap closes at roughly several tens of GWd/tU.
• After closure, swelling and thermal expansion push directly on the cladding, causing pellet–cladding mechanical interaction (PCMI), which during power-increase transients can lead to iodine stress corrosion cracking (PCI-SCC).
• After closure, contact conduction raises h_gap again and fuel temperature falls — one reason why the fuel temperature coefficient changes with burnup.

High burnup — the rim structure (HBS)

At the pellet periphery, Pu-239 builds up from U-238 resonance capture, so the local burnup is higher than the average. Above a local burnup of about 60–80 GWd/t and below about 1,000–1,200 °C, the grains subdivide to about 0.1–0.3 μm and μm-sized pores increase (the high-burnup structure, HBS). It appears in an outer layer 100–200 μm thick once the pellet average exceeds about 40–45 GWd/t. The rim traps gas in its pores, increasing local swelling and lowering thermal conductivity, and it is a source of fine fragmentation and rapid gas release in an RIA or LOCA.

Since 1 %FIMA ≈ 9.4 GWd/tHM, the swelling rate of 0.091 %/(GWd/tU) is about 0.86 % per %FIMA.

Regulatory and design criteria

The criteria below are US NRC requirements and guidance, given as examples.

The densification model moved from the 1970s first edition of RG 1.126 to Rev. 2 in 2010, but its resintering-test framework is the same. Attention has since extended to the high-burnup rim structure and to burnup-dependent RIA and LOCA criteria.

Easily confused pairs

Key points at a glance

1. Densification, definition: early in irradiation, fine pores (about 1 μm) in UO₂ pellets are removed by fission fragments → higher density, smaller diameter and length (in-reactor resintering).
2. Densification, characteristics: saturates within a few GWd/tU; magnitude = Δρ of the resintering test (1,700 °C, 24 h) (RG 1.126).
3. Densification, effects: wider gap → lower h_gap, higher fuel temperature and stored energy; higher linear power; axial gaps → power spikes and cladding collapse (1972 Ginna, unpressurized rods).
4. Densification, countermeasures: He prepressurization, control of pore distribution and grain size, plenum springs, inclusion in design analyses.
5. Swelling, definition: volume increase from FP production (one U atom → two FP atoms).
6. Swelling, types: solid FP (independent of temperature, about 0.9 %ΔV per 10 GWd/tU), gaseous FP (above about 1,200 °C, bubble growth and coalescence).
7. Swelling, effects: gap closure → PCMI and PCI; linked to internal pressure and FGR; high-burnup rim (HBS) porosity and grain refinement.
8. Net behaviour: early decrease (densification dominates) → cumulative cancellation at 5–20 GWd/tU (initial volume regained) → linear increase afterwards (swelling dominates).
9. Regulation: GDC 10 (SAFDLs), App. K (stored energy), RG 1.126, SRP 4.2.