text: Post-Irradiation Examination (PIE) is the study of used nuclear materials such as nuclear fuel. It has several purposes. It is known that by examination of used fuel that the failure modes which occur during normal use (and the manner in which the fuel will behave during an accident) can be studied. In addition information is gained which enables the users of fuel to assure themselves of its quality and it also assists in the development of new fuels. After major accidents the core (or what is left of it) is normally subject to PIE to find out what happened. One site where PIE is done is the ITU which is the EU centre for the study of highly radioactive materials.
  Materials in a high-radiation environment (such as a reactor) can undergo unique behaviors such as swelling and non-thermal creep. If there are nuclear reactions within the material (such as what happens in the fuel), the stoichiometry will also change slowly over time. These behaviors can lead to new material properties, cracking, and fission gas release.
  The thermal conductivity of uranium dioxide is low; it is affected by porosity and burn-up. The burn-up results in fission products being dissolved in the lattice (such as lanthanides), the precipitation of fission products such as palladium, the formation of fission gas bubbles due to fission products such as xenon and krypton and radiation damage of the lattice. The low thermal conductivity can lead to overheating of the center part of the pellets during use. The porosity results in a decrease in both the thermal conductivity of the fuel and the swelling which occurs during use.
  According to the International Nuclear Safety Center the thermal conductivity of uranium dioxide can be predicted under different conditions by a series of equations.
  The bulk density of the fuel can be related to the thermal conductivity.
  Where ρ is the bulk density of the fuel and ρ is the theoretical density of the uranium dioxide.
  Then the thermal conductivity of the porous phase (K) is related to the conductivity of the perfect phase (K, no porosity) by the following equation. Note that s is a term for the shape factor of the holes.
  :K = K(1 − p/1 + (s − 1)p)
  Rather than measuring the thermal conductivity using the traditional methods such as Lees disk, the Forbes method, or Searle's bar, it is common to use Laser Flash Analysis where a small disc of fuel is placed in a furnace. After being heated to the required temperature one side of the disc is illuminated with a laser pulse, the time required for the heat wave to flow through the disc, the density of the disc, and the thickness of the disk can then be used to calculate and determine the thermal conductivity.
  :λ = ρCα
  *λ thermal conductivity
  *ρ density
  *C heat capacity
  *α thermal diffusivity
  If t is defined as the time required for the non illuminated surface to experience half its final temperature rise then.
  :α = 0.1388 L/t
  *L is the thickness of the disc
  For details see K. Shinzato and T. Baba (2001).