The Story of Gold

Jose Ribeiro

Het611A 1st Semester 2002

Gold is a rare metal that has always appealed men’s attention. Its colour, its chemical stability, and its physical properties turned this metal into the ideal support for the manufacture of jewels, as well as an element used in high technology. Its rarity allowed it to be the ruler element of currencies during centuries.

The purpose of this text is to explain how heavy elements were formed, amongst which is gold, and the reason why they are rare. In fact, even today hydrogen and helium are 99% (by atoms) of the whole baryonic matter in the Universe, and only the remaining 1% is distributed by the other elements [1].

After the Big Bang, about 10^-5 seconds, neutrons and protons were formed – the hydrogen nucleus was born. A second after the Big Bang, there was about 1 neutron for every 10 protons. Three minutes after the Big Bang media had already cooled enough for the primordial nucleosynthesis to happen. Neutrons and protons came together to form helium [9]

¹H₁+⁰n₁®¹H₂

¹H₂+⁰n₁®¹H₃

¹H₃+¹p₁®²He₄

At the end of this process, the abundance was of an atom of helium to 10-11 protons (or 27% of helium by mass). Some traces of deuterium and lithium were also to be found. Therefore, one can conclude that in the beginning the Universe was almost free of metals. And this went on for about a billion years until gravity acted over these light elements and gave origin to the formation of stars. A first generation of stars took place, which is today classified as Population III Stars, made of initial matter and of very low metallicity. Those stars were very massive of around 100-300 solar masses. Most of these stars probably collapsed into black holes, and others created the first metals [5].

A star creates heavier elements than its initial components through nuclear fusion in its core.

A star is formed through the accretion of the matter in a molecular cloud, due to the gravity that begins to act in an inward pressure. The gas inside it heats up. When the temperature reaches the minimum values for nuclear reactions to begin (8e6K for the fusion of hydrogen in helium), the star begins its life. For this to happen, the protostar must have over 0.08 solar masses.

The transformation of hydrogen into helium is made through the two following processes:

PPI chain for temperature lower than 1.3e7K,PPII chain for temperatures of about 2e7K and PPIII chain for temperatures beyond 3e7K; in massive stars (that are hotter) and of more metallicity, the conversion of hydrogen into helium is made through the CNO cycle, in which carbon 12 acts as a catalyst of the reaction.

When all the hydrogen is converted into helium the nuclear reactions in the core finish. Yet, a shell of fusing hydrogen can still be found around the helium core. This shell will then force the beginning of the nuclear fusion of helium into carbon, through the triple alpha process: 3x²He₄®⁶C₁₂+g. Another reaction taking place is the fusion of one atom of helium with one atom of carbon, thus resulting one atom of oxygen: ²He₄+⁶C₁₂®⁸O₁₆+g.

As heavier the nucleus to fuse are the higher the temperature must be, because heavier nuclei, with more protons, repel themselves more strongly. And so, in order for core reactions to continue it is necessary for the star to have enough mass for gravity to exert enough pressure in the core. This pressure will increase temperature in order to allow fusion of those heavier elements to continue.

Stars with mass between 8-10 solar masses can still slowly fuse carbon, but there is not enough pressure to fuse oxygen. In stars with mass between 10-15 solar masses it is possible the oxygen, which is in a degeneracy state, to fuse, giving origin to a supernova. In more massive stars it is still possible to burn oxygen into silicon and silicon, by photodisintegration, in a variety of nucleus between sulphur and iron. Iron is the most tightly bound atomic nucleus. Fusion of lighter elements than iron release energy. But fusion of iron in heavier elements will absorb energy [4]. And so fusion reactions in the core of the stars will cease. A star will exist while a balance between the outer pressure due to gravity and the inner pressure due to nuclear reactions will stand. With the end of nuclear reactions the star will collapse. Due to its high mass, the collapse will not be stopped by the shells in fusion neither by the core that is in a degeneracy state due to pressure. Then, a nuclear process will occur, in which protons and electrons will merge forming neutrons and releasing neutrinos. From hereon, the collapse will end suddenly when neutrons cannot be more compressed, giving origin to a shock wave which will give origin to a supernova.

For the above stated, one reaches the conclusion that in stars, by nuclear fusion and by photodisintegration, only elements up to the group of the iron (Co, Fe, Ni) are synthesised.

We are still far from the heavy elements: an atom of iron has 26 protons and 30 neutrons, while an atom of gold has 79 protons and 118 neutrons.

In 1957, Geoffrey Burbidge et al pointed the solution for the formation (nucleosynthesis) of the heavy elements: slow (s-process), or rapid (r-process) neutron capture by existing atoms followed by nuclear decay. There is also a nuclear process, the p-process, that explains the production of the rare proton-reach isotopes like tin that cannot be created by neutron capture.

Neutrons are electrically neutral and are not subject to the Coulomb barrier, and so they can be more easily captured by an atomic nucleus, thus being kept by the strong nuclear force. When an atom captures a neutron, it remains the same element, increasing only its own mass. Atoms with the same number of protons and with different masses are isotopes. When the number of protons in the nucleus of an atom is changed, it turns into a different element. Depending on the number of neutrons in its nucleus an isotope can be stable or unstable. If unstable, the isotopes usually decay into another element through one of the following processes:

b(-)decay: (Z,A) ® (Z+1,A)+e(-)+antineutrino electron

b(+)decay: (Z,A) ® (Z-1,A)+e(+)+neutrino electron

e(-)capture: (Z,A)+e(-) ® (Z-1,A)+neutrino electron

a decay: (Z,A) ® (Z-2,A-4)+He (2,4)

fission: (Z,A) ® 2x(»Z/2, »A/2)

being Z the number of protons, A the number of mass (number of protons + number of neutrons)

Apart from fission, the decay processes can take variable times depending the isotope is more or less unstable. The decay is usually by b(-).

In the s-process, capture of neutrons will be taking place until the next unstable isotope is reached, which will then decay into the next element before capturing the next neutron. The reactions through the s-process can happen from helium burning in the cores of massive stars, M>15 solar masses, as well as in the core of carbon burning and in the shell of helium burning in massive stars. Yet, the most accepted place for the reactions of the s-process to occur, is the helium-burning shell of the low-mass AGB stars [6]. These stars ended helium fusion in their cores, having therefore an inactive carbon core and a burning helium shell around it. These star migrate from the Horizontal Branch to the Asymptotic Giant Branch of the Hertzprung-Russell diagram.

In the r-process, the capture of neutrons is sufficiently rapid so that there is no time for the unstable isotope to decay. Continuous neutron capture leads to nuclei with decreasing neutron binding energies [8]. When the process ends, these unstable elements decay through a cascade of electron emission until they reach stability [1]. Due to the great flux of neutrons required for the occurrence of the r-process, this must happen essentially during the supernovae. Yet, in practice, there is an incoherence between the mass fraction of r-nuclei in our Galaxy and the number of supernovae that took place. Observations point that about 10⁴ solar masses of matter synthesised by the r-process exist in our Galaxy. One estimates the existence of 10⁸ supernovae since the beginning of our Galaxy. This results that only 10^-4 solar masses is synthesised by r-process in a supernova, which is a small quantity regarding the total mass expelled by the explosion.

A possibility in exploration is that the r-process happens in the nascent neutron star winds in Type II and Type Ib supernovae star remnants.

P-process tries to explain the formation of proton-rich nuclei, as these cannot be formed through the neutron capture. Yet, it seems not very likely that the process takes place with the direct capture of protons. The process can be explained by disintegration reactions in high temperature environments, from “element-seeds” made in the s and r-processes. Should the temperature decrease quickly the process is interrupted leaving meanwhile a series of rich-protons nuclei.

These reactions occur more frequently in Type Ia supernovae and in Type II supernovae [6].

The production of the elements is ordered in the following way[3]:

Elements	#Protons	Production
H	1	Big Bang
He	2	Big Bang + Stars
C-O	6-8	Low and High-Mass Stars
Ne-Fe	10-26	High-Mass Stars
Co-Bi	27-83	S and/or R-Process; AGB and S.N.
Po-U	84-92	R-Process in S.N.

From a table of solar system abundances [2], it is indicated that the element gold, ⁷⁹Au₁₉₇, has an abundance of 0.187 atom per 10⁶ Si atoms. Silicon is used as a base because it allows the distribution of solar element abundances and the distribution of planetary element abundances to be compared [7]. Gold is considered to have been formed through the r-process [1,2] up to ⁷¹Lu₁₉₇ and then a cascade of electron emission up to ⁷⁹Au₁₉₇, the stable element in the path.

⁷¹Lu₁₉₇®⁷²Hf₁₉₇+e(-)+antineutrino electron

(...)

⁷⁸Pt₁₉₇®⁷⁹Au₁₉₇+e(-)+antineutrino electron

From observations of meteorites and from abundance in the Sun [2,6], one can infer that the mass fraction of r-nuclei in our Galaxy is 2^-7. Being gold formed by r-process, gold has to be very rare even among the heavier elements.

References

1. Golden Stardust

By James Gillies

http://www.slac.standford.edu/pubs/beamline/29/3/29-3gillies.pdf

2. Isotopic Abundances from Anders & Grevesse

http://ultraman.berkeley.edu/anders.txt

3. Synthesizing the Chemical Elements

http://www.ucolick.org/~bolte/AY4/notes12/node1.html

4. Thermonuclear Explosions and Element Synthesis

By Richard McCray

http://cosmos.colorado.edu/astr1120/16s3.htm

5. The Nucleosynthetic Signature of Population III