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4.8: Questions

  • Page ID
    35387
  • The cross-section data needed to answer these questions have been supplied here. To find further cross-sections, consult the Evaluated Nuclear Data File (ENDF).

    Quick questions

    You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

    Check which elements are fissionable but not fissile:

    a U-233
    b U-235
    c U-238
    d Pu-239
    e Th-232
    Answer

    C, E

    Which of the following are NOT suitable moderating materials?

    a Deuterium (A=2)
    b Helium (A=4)
    c Beryllium-9 (A=9)
    d Boron (A=11)
    e Graphite (A=12)
    f Iron (A=56)
    Answer

    B, D, F

    Helium is unsuitable because it exists as a gas and so is not dense enough (the nuclear number density is too low).

    Boron is unsuitable because it absorbs neutrons.

    Iron is unsuitable because its atomic mass is too large.

    Which of the following would NOT be classified as "Sabsorption" cross-sections?

    a (n, n)
    b (n, n')
    c (n, γ)
    d (n, f)
    e (n, α)
    f (n, p)
    Answer

    A, B

    since the neutron emerges from the interaction unchanged.

    Which of the following discourages void formation?

    a More interstitial atoms.
    b Fewer interstitial atoms.
    c More vacancies.
    d Fewer vacancies.
    e More transmutation.
    f Less transmutation.
    Answer

    B, C, F

    Voids shrink when they absorb interstitial atoms, but grow when they absorb vacancies, and can be nucleated by the helium formed by (n,α) transmutations.

    Which of the following material properties have lower values after irradiation?

    a Yield strength
    b Thermal conductivity
    c Electrical conductivity
    d Tensile strength
    e Ductility
    f Density
    g Creep rate
    Answer

    B, C, E, F

    See Effects of Radiation Damage for reasons why.

    Deeper questions

    The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

    Zirconium minerals are often found with small amounts of hafnium present due to their chemically similar nature. Zirconium is also used as a primary component of Zircaloy, a cladding material designed to be almost transparent to neutrons.

    By comparing how the mean free path of a thermal neutron in pure zirconium differs from that of zirconium with 0.01% hafnium impurities, comment on the consequences of hafnium impurities in Zircaloy.

    (Zr: A = 91.22, ρ = 6.52 g cm−1, σc = 0.18 barns;
    Hf: A = 178.49, ρ = 13.31 g cm−1, σc = 105 barns)

    Answer

    Using the standard equations for calculating neutron cross section given here, the macroscopic cross section of pure zirconium is 0.0078 m−1 and so the mean free path of pure zirconium is about 129 m, i.e. many orders of magnitude larger than the thickness of the cladding material.
    For the impure metal, assume macroscopic cross section can be written as 0.99ΣZr + 0.01ΣHf. The macroscopic cross section of Hf is about 4.76 m−1, and so the overall cross section is 0.99 × 0.0078 m−1 + 0.01 × 4.76 m−1 = 0.055. This gives a mean free path of about 18 m, which is almost 7 times shorter than that of pure zirconium!
    This means that hafnium poisoning is a very significant factor in the efficiency of zircaloy as a cladding material, though it is important to realise that a 18 m mean free path still means that even the impure material only very weakly absorbs neutrons.

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