Why do we want to normalize the solar abundance of elements to Si?

Question

When discussing nucleosynthesis, there is typically a line graph of atomic number vs. relative abundance, like the ones shown in this Wikipedia article . The relative abundance is normalized to a certain element, such as H or Si. I have seen many such graphs where the Si abundance is set to $10^6$ . Is there any advantage or convenience to this choice?

For example, the vertical axis label of the "elemental abundance" plot in the figure from the linked Wikipedia article is

Abundance, atoms of element per 10 ^six atoms of Si

source: Elemental abundances.svg

Answer 1

The abundances for many elements are judged or estimated from rocky material. i.e. Material that often contains silicon, but not that much hydrogen, or the hydrogen has been heavily modified. For example, meteorites contain very little hydrogen or helium. The graph you show is for abundances in the upper Earth's crust.

Elemental abundances in materials from the Solar System or indeed the Sun, have to be given in terms of abundance ratios (or possibly a mass fraction). In the Sun we can often assume that the abundance relative to hydrogen will be unmodified from its primitive state. In meteoritic or terrestrial material, we can't assume that for hydrogen, but possibly can for silicon.

As for the $10^6$ that's an arbitrary choice, I suppose to avoid very small numbers for the rare elements, or so that abundances could be expressed in "parts per million". When expressed as a ratio to hydrogen, abundances are often given in numbers per $10^{12}$ hydrogen atoms (nuclei actually). Again, this is an arbitrary choice.

A review article by Lodders (2019) , though has this additional historical detail:

Goldschmidt (1937) introduced the normalization to silicon, the most abundant cation in the crust (oxygen is typically the most abundant element by number in the crust and rocks, but is difficult to measure routinely). Cations are a better choice to normalize the rock-based abundance scale. Originally, this scale was set to N(Si) = 100 (Goldschmidt 1938), then N(Si) = 10,000 (Brown 1949). With more refined analyses, smaller quantities of many elements could be measured, and it became more practical to increase the normalization. In their seminal paper, Suess & Urey (1956) changed the scale to N(Si) = $10^6$ explaining, “We use $10^6$ in order to get values for the rarer elements which can be written without negative exponentials or awkward decimal fractions.”

In a similar vein, it is claimed that the hydrogen scale being based on numbers per $10^{12}$ hydrogen atoms/nuclei is to avoid negative exponential values for the rarer elements (though that fails for at least uranium).