How many atoms does a relativistic ion dislodge?

Given a large chunk of some hard, refractory material e.g. graphite, diamond, tungsten, at low temperature surrounded by vacuum, and an impacting relativistic ion – to be specific, say an alpha particle at 99% of lightspeed,

On average, to an order of magnitude, how many atoms will be dislodged? I'm not talking about breaking/rearranging chemical bonds within the material, but only about how many atoms will fly off into space and be lost. Put another way, I'm not asking about internal damage, but only about shrinkage. Assuming the material is the best possible for the purpose (whatever element or compound will most strongly resist losing atoms this way), and the object is large enough that the ion comes to rest somewhere within its bulk. Though at .99c, it might have enough energy to fission normally stable nuclei, which would have its own kind of detrimental effect on the material.

(My reason for asking the question is that I'm trying to estimate ultimate maximum space travel speed, assuming a spacecraft must have radiation shielding made of matter, no unobtainium force fields or suchlike. However, it seems to me this should be answerable based on experience with particle accelerators, experimental fusion reactors etc.)

• Commented Jan 31, 2021 at 6:37
• to get answers consistent with your aim in the question the title should be "what is the radiation damage by relativistic ions". A relativistic particle hitting a lattice of atoms will not dislodge atoms in general, it will lose energy penetratin the first levels and destroying the lattice and interacts with the nuclei of the atoms. see Commented Jan 31, 2021 at 7:07
• google.com/… Commented Jan 31, 2021 at 7:07
• Neutrons ( E>10 Mev ) can displace atoms in metals . For instance , this appears in PWR reactors vessel and could be a difficult problem to solve for the first wall in a real fusion reactor running for a long time . Commented Jan 31, 2021 at 7:41

You are asking about the sputter yield. From Andrew H. Simon, "Handbook of Thin Film Deposition" (2012):

Above an ion threshold energy of ~1 keV, collision-cascade (nonlinear cascade) sputtering behavior is observed, in which the incident ions have enough energy to dislodge multiple cathode atoms. Sputter yields in this regime will be in the range of ~5 to 50 and higher. Due to the high energies required and the high ejected energies of the sputtered atoms, this regime is usually not of industrial interest. Incident ion energies above 50 keV result in deep-ion implantation into the cathode and a reduction in net sputter yield.

So yields are highest around 10 keV (around two or three atoms per ion for ions lighter than silicon). At higher energies, the ions get implanted.

• Note the question is about "relativistic" ions keV and even MeV , depending on mass of the ion are not relativistic velocities Commented Jan 31, 2021 at 10:45
• @annav It does not matter. At higher energies, the ions just get implanted at greater depth in the material. See for example en.wikipedia.org/wiki/Ion_implantation
– user137289
Commented Jan 31, 2021 at 11:05
• it is a different story see link.springer.com/article/10.1557/JMR.2010.0180 The destruction is a track in the material, not sputter Commented Jan 31, 2021 at 13:06
• @annav I am well aware of tracks, for example in mica for radiometric dating. But OP was explicitly not asking about internal damage. The faster the atom, the sooner it passes the surface layer. That is why the sputter yield has a maximum at some energy (about 10 keV as it turns out experimentally).
– user137289
Commented Jan 31, 2021 at 23:33

I will turn my comments to an answer, though it is still a comment.

"I'm trying to estimate ultimate maximum space travel speed, assuming a spacecraft must have radiation shielding made of matter, no unobtainium force fields or suchlike."

In this link one can see that at relativistic energies the ions penetrate deep leaving a track of destruction in the material.

The dynamics of track development due to the passage of relativistic heavy ions through solids is a long-standing issue relevant to nuclear materials, age dating of minerals, space exploration, and nanoscale fabrication of novel devices.

....

Track size and internal structure depend on energy density deposition, irradiation temperature, and material composition.

Random ions in the interstellar space at rest with the cosmic microwave background, if the velocity of the spacecraft becomes relativistic , would get radiation tracks through the shielding, in addition with any sputter at the surface. This could damage electronics, people etc. depending on the density of ions the spaceship would meet. Off hand I would say that the velocity of the space ship should be kept below relativistic to avoid this extra danger.