Why

Ever since I read about Lord Vetinari’s clock I wanted to build one that is driven by radioactive decay. But I’ve been struggling with coming up with a mechanism that is both reasonably accurate and also sufficiently insensitive to background interference to call it a clock. As Dave also figured with his Gammaclock this is not trivial, however the "Atomic" Clock by alnwlsn has been using radioactive decay to track time for more than a year.

How

In order to have some immunity to background radiation I used a coincidence measurement of the most common two products from Am-241 decay: an alpha particle and a 59.5 keV gamma. When an Am-241 nucleus decays it emits an alpha particle (two protons and two neutrons) and turns into Np-237. Most of the time the Np-237 has some left-over energy that it quickly emits as a gamma ray. If we detect an alpha and a 59.5 keV gamma ray appearing at the same time we can be fairly sure this came from our Am-241 source, not some background radiation that we have no control over. Adjusting the geometry of the setup one can change the rate of these coincidences until an average of one event per second is detected. On a long timescale this can be used as a timebase, as Physics is very kind in that regard. But on a short timescale events have the characteristic randomness of radioactive decay. Perfect for Lord Vetinari's clock.

What

Two of the Pomelo detectors I'm working on are run in coincidence, such that they deliver a pulse output only when both fire. One of them detects gamma rays, whereas the other detects the alpha particles from an Am-241 source. The second detector is made sensitive to alphas by having the radioactive source fixed inside the scintillator housing with a clear path for the alphas to hit the scintillator.

Adjusting the distance between these two detectors changes the number of gamma rays detected and in turn the coincidence rate. With some careful tuning this was brought to an average of one coincidence per second, with the characteristic exponential distribution of time intervals of radioactive decay.

This "one becquerel" pulse is then fed into an Arduino that advances the seconds on a loud clock to produce the desired functionality of Lord Vetinari's clock.

Project Logs

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Clock timing accuracy
mihai.cuciuc • 08/07/2025 at 05:21 • 0 comments

One can make some measurements to determine the performances of the clock -- both to estimate the randomness as well as to evaluate the long-term accuracy.
The distribution of intervals between individual ticks shows a very different picture between a normal clock and our contraption.
Left: tick duration you want from a normal clock. Right: tick duration you get from Lord Vetinari's clock
The tick duration in our clock has the expected exponential distribution of time intervals, with short ticks being balanced out by long ones. The mean value of this distribution is very close to 1, providing the long-term accuracy of the timepiece.
Looking at the duration (in seconds) of an hour measured by our clock we are again greeted with a fair bit of randomness.
Left: Time series of the duration of an hour, as measured by Lord Vetinari's clock. Right: Histogram of the same values
While the duration of each individual hour, as counted by our clock, can be off by more than a minute, the histogram shows that the standard deviation is about 60 seconds. That is to be expected from counting statistics, with sigma being on the order of the square root of our measured counts -- here about 3600.
Detector design
mihai.cuciuc • 08/06/2025 at 05:03 • 0 comments

Pomelo detector pair configured in coincidence mode. Bottom one also houses the Am-241 source.
Two Pomelo detectors are configured in coincidence, in a fixed configuration with the Am-241 source. One of the detectors is sensitive just to the gamma rays that easily pass through the enclosures, whereas the other will see the alphas too.
Schematic representation of the two detectors and the physics process. A coincidence pulse is generated only when one gamma hits the top detector and one alpha hits the bottom one.
The bottom detector is made insensitive to gamma rays by setting its energy threshold above the gamma ray energy. Even slowed down by some air in between the source and detector, alphas still deposit more energy than the 59.5 keV gammas.
Changing the distance between the two detectors adjusts the coincidence rate by lowering the gamma count rate in the top detector. This distance has been adjusted to produce around one coincidence pulse per second.
Other timing options: cosmic muons
mihai.cuciuc • 08/04/2025 at 04:56 • 0 comments
One option for using radiation but not radioactivity for timekeeping would be to use cosmic rays that the Universe throws at Earth. A pair of scintillator detectors can be arranged to detect cosmic muons, but there are two aspects of this approach that don't make it a great option:
- The scintillators Pomelo uses are small for this purpose, only catching about 20 muons per hour.
- The 11 year solar cycle influences the cosmic ray flux on Earth, which means the clock would run fast for about 5 years and then slow for another 5.
This idea was thus promptly abandoned.
Other timing options: high energy gamma line
mihai.cuciuc • 08/01/2025 at 05:42 • 0 comments

Another option I considererd before settling on the coincidence setup was to use a higher enerrgy gamma line where there is lower background, as this was the main problem identified in the previous log entry.
The natural background quiets down at higher energies. Above the 1.46 MeV peak from K-40 there are not enough counts in the detector to interfere with a one count per second source, if we can find it.
Background gamma spectrum taken with Pomelo. The K-40 is visible at 1.46 MeV
The only source I have that gives such high energies are thorium welding rods. Unfortunately they are way too weak, the highlighted peak in the Th-232 spectrum below, around 1.6 MeV, only has ~0.5 counts per second including its background.
Th-232 gamma spectrum taken with Pomelo from thorium welding rods. Bump around 1.6 MeV is a collection of closely spaced gamma lines from thorium decay
Unfortunately for my setup this means this method is unavailable for the clock timebase.
Other timing options: gamma line from Am-241
mihai.cuciuc • 07/29/2025 at 05:13 • 0 comments

Before settling on the coincidence setup I considered using just the gamma line from Am-241 decay. As Pomelo can perform gamma spectroscopy we can look for the 59.5 keV gamma line and use that for our timebase. In the example gamma spectrum below we see we would have to look for counts in the energy range ~40 keV to ~80 keV, because of limited detector energy resolution.

Gamma spectrum of Am-241 with source pretty close to the detector

While we can increase the source distance to the detector to get on average 1 count per second in that region, natural radioactive background also has a significant contribution there. The background spectrum below is accumulated over a very long time without the Am-241 source close by.
Background gamma spectrum with no Am-241 source. Position of the Am-241 gamma energy is still indicated for reference.
This spectrum has ~2.6 counts per second in the energy region of interest. This means background alone gives more signal than we need for the timebase. One fix for this would be to shield the detector and source in lead to remove the background contribution, but I have not explored this option.