Chain Evolution

One obvious way to examine the output data is by decay chain.  The mix of fission fragments changes over time, and the exponential view of this evolution makes nice charts.  Several principles of decay become apparent.

A Simple Case

The decay along the main chain of atomic weight 67 is well behaved.  The chart below follows the entire run.  English time units at the bottom lend perspective.  The relevant isotope names are on the top, but it is their Rung number that charts best.  Here, the most popular initial product sits on rung 2.  It gets a small contribution from two hotter isotopes, 67-Co (red) and 67-Fe (dark blue).  The Rung 2 isotope has a half-life of 21 seconds, so after a minute, its daughter dominates the mix.  The Rung 1 isotope decays in a few days to the Sink.  By the end of the first year of reactor operation 99.9% of the population of isotopes of atomic weight 67 is 67-Zn.

Normalized yield for Decay Chain 67

Note the Y-axis!

These charts show the relative contribution of each isotope over time.  The cumulative yield is normalized by dividing it by the exponential (2^Timestep).  The total number of normalized atom at each TimeStep is 2.00.  This is different from the chart of 135-Xe population in the sidebar.  There, the y-axis is total yield, measured in atoms.  After a few days, the creation and decay (and capture!) of 135-Xe atoms come to equilibrium at a constant yield of about 1600 atoms.  The flat lines on the right of that sidebar chart indicate a constant population.

In the chart above, the line after a year is flat, but 67-Zn has not come to equilibrium.  A flat line here means the isotope represents a constant proportion of the entire waste stream.  The total waste stream is growing in mass (a term we need to use carefully) at a rate of two atoms per second.  Therefore, the population of 67-Zn keeps growing. As the 67 chain is near the tail of the distribution, the 67-Zn population (relative or absolute) is tiny – 3.5 parts per billion.  That’s seven atoms out of the 2 billion fission fragments in the waste stream at TimeStep 30.

Chain 171 is another very symmetric chart.  The near equal spacing of the transfers from one rung to the next is striking.  (Most other chains are not so neat.)

Normalized yield for Decay Chain 171

Most of the nuclei “born” at atomic weight 171 are on Rung 3.  The decays from 3 to 2, 2 to 1 and 1 to 0 are also shown here with red arrows.  Rung 1 has a half-life long enough that the Sink takes years to dominate the mix.  Even after 34 years, there is still some 171-Tm.

A Significant Neutron Poison

The two chains above have Sinks that do nothing but collect mass from higher rungs.  The last parts of the curves of the Sinks are rising or flat.  The population curve for a strong neutron poison’s curve will fall.  149-Sm is the second-most important poison.  As the Sink for the main chain at atomic weight 149, it takes everything with it as it goes.

Chain 149 yield flows to Chain 150, due to 149-Sm neutron capture

A minor point is that the population stops dropping at the very end, and even rises a bit.  147-Pm and 148-Pm both capture neutrons readily, but 148-Pm most often decays before it plumps to 149.  148-Nd, the Main Sink for chain 148, has a small capture cross section, but the last time frame is long enough for it to contribute a bit to decay chain 149.

A Plumper Recipient

The main Sink for chain 114 inherits more from chain 113 than from its own parents.  This comes from the plumping of 113-Cd, which has the fifth highest capture barns.  Calling it a Major poison is a bit inflated, though.  Chain 113 is in the Sparse Valley, so 133-Cd doesn’t capture all that many neutrons.

Chain 114 population swells due to 113-Cd neutron capture

Short-lived Daughter

In general, the lower the rung, the longer the half-life.  There are a few dozen exceptions.  When the parent lives a lot longer than the daughter, it is noticeable on these charts as a small bump to the right of the parent.

Chain 97: A daughter outlives its parent

For Chain 144 the bump can only be seen in the numerical data.

Chain 144: A very, very short-lived daughter

Chain 135 shows the small bump of 135-Xe to the right of its parent, 135-I.  The half-life of 135-Xe is longer, but the HLE is shorter!  The presence of 135-I complicates the 135-Xe problems, as it keeps feeding the 135-Xe population.

Chain 135: Parent outlives daughter – if capture is included!

Long-Lived Fission Products (LLFP)

Chain 135 (above) does not end at 135-Ce (Rung 1).  There are seven fission products with half-lives in the “million-year” range.  These are the main long-term radioactive hazard after failed fuel.  Fortunately, 90% of the radioactivity is due to one isotope. 99-Tc, and this has a decent capture cross-section.  Keep it in the reactor!

Chain 126 has another LLFP, 126-Sn.  This is, at Rung 2, the most popular of the initial fission fragments at atomic weight 126.  Therefore, one can assume a non-zero initial yield for “nearby” isotopes.  In this case, that includes isomers at rungs 1.2 and 1.1.  These are lower on the energy ladder than 126-Sn, so avoid getting hung up there.  Instead, they reach stability fairly quickly, supplying the slight rise in 126-Te at Rung 0 at the right.

LLFP delays the evolution to the real Sink

Quick to stability

Most of Chain 126 settles to stability very quickly.  The flatness of the Rung 2 curve starts early.  Only a few chains become stable as quickly.  Chain 100 is the fastest, with the longest half-life of an unstable isotope being 7.1 seconds.  100-Mo flattens out faster than any other Sink.

Stable within minutes